Please help thank you

Please Help Thank You

Answers

Answer 1

The values of sine, cosine, and tangent of the angle 'θ' are: sinθ = [tex]\frac{1}{2}[/tex],

cosθ = [tex]\frac{\sqrt{3}}{2}[/tex]  and tanθ = [tex]\frac{1}{\sqrt{3} }[/tex] .

How to find trignometric ratios far an angle?

To begin, determine the angle for which you wish to compute trigonometric ratios. Let's call the angle "θ".

Find the lengths of the sides of the right triangle that correspond to the angle "θ". Choose the trigonometric ratio you wish to calculate: sine (sin), cosine (cos), or tangent (tan).

Now, using the proper trigonometric formula, determine the needed ratio:

            sin θ [tex]= \frac{Opposite side}{Hypotenuse }[/tex]

            cos θ [tex]= \frac{Adjacent side }{Hypotenuse}[/tex]

            tan θ [tex]= \frac{Opposite side }{Adjacent side}[/tex]

In the given problem, values for angle θ are-:

opposite side = 4 and Adjacent side = 4[tex]\sqrt{3}[/tex]

Using Pythagorean theorem to find the value of hypotenuse:

[tex]hypotenuse = \sqrt{(opposite^2 + adjacent^2)}[/tex]

[tex]hypotenuse=\sqrt{4^{2}+(4\sqrt{3})^2 } =\sqrt{16+48} =\sqrt{64} =8[/tex]

Now, putting values to find required trignometric ratios-:

sin θ[tex]= \frac{Opposite side}{Hypotenuse }=\frac{4}{8 }=\frac{1}{2}[/tex]

cos θ[tex]= \frac{Adjacent side }{Hypotenuse} =\frac{4\sqrt{3}}{8}=\frac{\sqrt{3}}{2}[/tex]

tan θ [tex]= \frac{Opposite side }{Adjacent side}=\frac{4}{4\sqrt{3}}=\frac{1}{\sqrt{3} }[/tex]

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Related Questions

in order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. company a company b sample size 80 60 sample mean $6.75 $6.25 population standard deviation $1.00 $0.95 refer to exhibit 10-8. the value of the test statistic is . a. 3.01 b. 1.645 c. 2.75 d. .098

Answers

The value of the test statistic is approximately 2.84. Its significance can't be determined.

To determine whether or not there is a significant difference between the hourly wages of two companies, we need to conduct a hypothesis test.

The null hypothesis states that there is no significant difference between the hourly wages of the two companies, while the alternative hypothesis states that there is a significant difference.

The test statistic for this hypothesis test is calculated using the formula:

[tex]t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)[/tex]

where x1, x2 are the sample means for companies A and B, s1 and s2 are the sample standard deviations for companies A and B, and n1 and n2 are the sample sizes for companies A and B.

Plugging in given values, we get:

[tex]t = (6.75 - 6.25) / [(1^2/80) + (0.95^2/60)]^(1/2)[/tex]

t = 0.5 / 0.1759

t = 2.8437

Without knowing the significance level or the degrees of freedom, we cannot determine whether or not the test statistic is statistically significant.

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The value of the test statistic is 2.75.

To determine the test statistic for comparing the hourly wages of two companies, the researcher would need to conduct a two-sample t-test with equal variances.

The formula for the test statistic is:

[tex]t = (\bar x1 - \barx2) / [s_p \times \sqrt(1/n1 + 1/n2)][/tex]

where:

[tex]\bar x1[/tex] and[tex]\bar x2[/tex] are the sample means for Company A and Company B, respectively

[tex]s_p[/tex] is the pooled standard deviation of the two samples, calculated as:

[tex]s_p = sqrt [((n1 - 1) \times s1^2 + (n2 - 1) \times s2^2) / (n1 + n2 - 2)][/tex]

n1 and n2 are the sample sizes for Company A and Company B, respectively

s1 and s2 are the sample standard deviations for Company A and Company B, respectively.

Plugging in the given values, we get:

[tex]t = (6.75 - 6.25) / [\sqrt(((80-1)\times 1^2 + (60-1)\times 0.95^2)/(80+60-2)) \times \sqrt(1/80 + 1/60)][/tex]

[tex]t = 2.75[/tex]

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What is the first step to solve this equation? (4)/(x)+(1)/(2)=(5)/(x) The first step in solving the equation is to multiply both sides by

Answers

The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of the denominators.

To solve the equation (4)/(x) + (1)/(2) = (5)/(x):

Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 2x.

Multiply the left side of the equation by 2/2 to get:

(8)/(2x) + (1)/(2) = (5)/(x)

Combine the two fractions on the left side of the equation:

(8+1)/(2x) = (9)/(2x)

Set the left side of the equation equal to the right side:

(9)/(2x) = (5)/(x)

Cross-multiply:

9x = 10x

Simplify:

x = 0

Therefore, the solution to the equation is x = 0.

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The ratio of the lengths of the edges of two cubes is #. What is the ratio of their
surtace areas?

Answers

The ratio of their surface areas is x^2

What is the ratio of their surface areas?

Let's assume that the lengths of the edges of the first cube are a, and the lengths of the edges of the second cube are bx, where b is a constant.

The surface area of a cube is given by the formula A = 6a^2, where a is the length of an edge.

Therefore, the surface area of the first cube is 6a^2 and the surface area of the second cube is 6(bx)^2 = 6b^2x^2.

The ratio of their surface areas is:

(6b^2x^2) / (6a^2) = b^2x^2 / a^2

Since the ratio of the lengths of the edges of the two cubes is x, we have:

a / bx = 1 / x

Solving for a, we get:

a = bx^2

Substituting this value into the ratio of their surface areas, we get:

(b^2x^2) / (bx^2)^2 = (b^2x^2) / b^2x^4 = x^2

Therefore, the ratio of the surface areas of the two cubes is x^2.

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To help determine what types of clubs to offer at harding middle school the principal surveyed fifty 8th grades. Does the sampl fairly represent the population ? explain

Answers

To determine if the sample fairly represents the population, we need to consider whether the sample is representative and whether there is any bias present in the sampling process.

If the principal surveyed fifty 8th graders in a way that ensures that each 8th grader in the population has an equal chance of being selected, then the sample can be considered representative. This means that the sample accurately reflects the characteristics of the population, and any conclusions drawn from the sample can be applied to the population.

However, if the sampling process was biased in some way, the sample may not be representative of the population. For example, if the principal only surveyed 8th graders in one class or in one particular group, the sample may not be representative of the entire 8th-grade population at Harding Middle School. In this case, any conclusions drawn from the sample may not accurately reflect the entire population.

Therefore, the key factor in determining whether the sample fairly represents the population is the sampling method used. If the sampling method is random and unbiased, then the sample can be considered representative of the population.

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Find the missing measures in each diagram.

Answers

Answer:

X = 65°

Y = 75°

Z = 65°

Step-by-step explanation:

Hello!

Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.

There is also another set of corresponding angles, and those are Angle Z and Angle X.

Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.

Angle Z:180° - 40° - 75°180°-115°65°

The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.

Find the length of the rectangular prism.

Answers

The length of the rectangular prism given the volume, width and height is 19 yd.

What is the length of the rectangular prism?

Volume of a rectangular prism = length × width × height

Volume of the prism = 2,280 yd³

Width of the prism = 20 yd

Height of the prism = 6 yd

Length of the prism = x

So,

Volume of a rectangular prism = length × width × height

2,280 = x × 20 × 6

2,280 = 120x

divide both sides by 120

x = 2,280 / 120

x = 19 yd

Therefore, the length is 19 yd

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Discuss the similarities and the differences between the Empirical Rule and Chebychev's Theorem What is a similarity between the Empirical Rule and Chebychev's Theorem? 0 A. O B. ° C. Both apply only to symmetric and bell-shaped distributions. Both do not require the data to have a sample standard deviation. Both calculate the variance and standard deviation of a sample. D. Both estimate proportions of the data contained within k standard deviations of the mean What is a difference between the Empirical Rule and Chebychev's Theorem? A. The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions O B. Chebychev's Theorem estimates proportions of data contained within infinite standard deviations and the Empirical Rule has a limit of 5 standard deviations ° C. The Empirical Rule assumes a small data set (less than 50 values) where Chebychev's Theorem has no limit on data size. O D. Chebychev's Theorem applies only to distributions which are approximately symmetric or bell-shaped and the Empirical Theorem has no restrictions

Answers

A. The correct option for similarity is option D -  Both estimate proportions of the data contained within k standard deviations of the mean.

Both the Empirical Rule and Chebyshev's Theorem are used to estimate the proportion of data contained within a certain number of standard deviations from the mean.

Therefore, option 'D' is the correct answer: Both estimate proportions of the data contained within k standard deviations of the mean.

B. The correct option for difference is option A - The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

The Empirical Rule assumes that the distribution is approximately symmetric and bell-shaped, while Chebyshev's Theorem makes no assumptions about the shape of the distribution.

Another difference is that the Empirical Rule is only applicable for normal distributions, while Chebyshev's Theorem can be applied to any distribution.

Therefore, option 'A' is the correct answer: The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.

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marvin company sells pens ($6) and flashlights ($10). if total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold?

Answers

If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.

Let's start by assigning variables to represent the unknown quantities.

Let x be the number of flashlights sold.

Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.

The total sales can be expressed as the sum of the sales of each item:

10x (sales from flashlights) + 6(7x) (sales from pens) = 624

Simplifying this equation

10x + 42x = 624

52x = 624

x = 12

So, the number of flashlights sold is 12.

And the number of pens sold would be 7x = 7(12) = 84.

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If you have a 19 out of 30 what would be the percentage?

Answers

Answer:

63.3%

Step-by-step explanation:

30 divided by 100 and then multiplied by 19 gives u the answer

The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.

Which drive-thru typically has more wait time, and why?

Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean

Answers

The correct answer is option b. Burger Quick, because it has a larger mean.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.

Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.

Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.

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The area of a semicircle is 1. 2717 square meters. What is the semicircles diameter

Answers

The diameter of the semicircle for the given area of the semicircle 1. 2717 square meters is equal to 1.8 meters.

Area of a semicircle = 1. 2717 square meters

The area of a semicircle is given by the formula,

A = πr^2 / 2

where A is the area

And r is the radius of the semicircle.

Rearrange the formula to solve for r,

r = √(2A/π)

Substituting the given value of A = 1.2717 square meters into this formula, we get,

⇒ r = √(2 × 1.2717 / π)

⇒ r = 0.9 meters

Since the diameter of a semicircle is twice the radius,

The diameter of this semicircle is equal to,

d = 2r

  = 2 × 0.9

   = 1.8 meters

Therefore, the diameter of the semicircle is equal to 1.8meters.

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at my office, $16$ people own cats, $8$ people own dogs, and $5$ people own both cats and dogs. how many people own a cat or a dog?

Answers

There are 19 people who own a cat or a dog.

What is number refers to?

A number is a mathematical object used to represent quantity, measurement, or a count of something. It can be an integer (whole number), a rational number (fraction), an irrational number (such as pi), or a real number (which includes all rational and irrational numbers).

To find the number of people who own a cat or a dog, we need to add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs.

Let's start by finding the number of people who own only cats. We know that 16 people own cats, and 5 people own both cats and dogs. Therefore, the number of people who own only cats is:

16 - 5 = 11

Next, let's find the number of people who own only dogs. We know that 8 people own dogs, and 5 people own both cats and dogs. Therefore, the number of people who own only dogs is:

8 - 5 = 3

Finally, we can add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs:

11 + 3 + 5 = 19

So, there are 19 people who own a cat or a dog.

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Please help me with this homework

Answers

Answer:

14

Step-by-step explanation:

c = 2[tex]\pi r[/tex]

c = 2[tex]\pi[/tex]7

x = 14[tex]\pi[/tex]

Helping in the name of Jesus.

Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4

Answers

We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,

To determine between which two integers 7/3 lies, we can use division and rounding.

Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:

7/3 = 2 + 1/3

Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.

This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.

Answer C, 2 and 3, is the correct answer.

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highway accidents: dui the u.s. department of transportation, national highway traffic safety administration, reported that 77% of all fatally injured automobile drivers were intoxicated. a random sample of 27 records of automobile driver fatalities in kit carson county, colorado, showed that section 8.3 testing a proportion p 479 15 involved an intoxicated driver. do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in kit carson county? use a 5 0.01.

Answers

The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.

No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.

The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.

The p value for this test is 0.788, which is greater than the alpha level of 0.01.

The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.

This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.

The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.

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can yall help me with this question this would rlly help me out!

Answers

Answer:

59.5[tex]cm^{2}[/tex]

Step-by-step explanation:

You have two shape: a square and a triangle

Square:

The area of a square is the sides squared

a = [tex]s^{2}[/tex]  The side length is 7 (7 x 7 = 49)

a = [tex]7^{2}[/tex]

a = 49

Triangle:

a [tex]\frac{bh}{2}[/tex]  The base times the height divided by 2

The base is 7 and the height is 3.

a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5

Add the two areas together: 49 + 10.5 = 59.5

Helping in the name of Jesus.

# 15) A boat is heading towards a lighthouse, where Jeriel is watching from a vertical distance of
113 feet above the water. Jeriel measures an angle of depression to the boat at point A to be
8°. At some later time, Jeriel takes another measurement and finds the angle of depression to
the boat (now at point B) to be 52°. Find the distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.

Answers

the distance between point A and point B is approximately 777.9 feet.

what is  distance ?

Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.

In the given question,

Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.

From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:

tan(8) = 113/x

x = 113/tan(8)

x =802.5

From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:

tan(52) = 113/y

y = 113/tan(52)

y =72.4

Now we can use the Law of Cosines to find d:

d² = x² + y² - 2xy cos(130)

where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:

d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)

d =777.9

Therefore, the distance between point A and point B is approximately 777.9 feet.

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3. In raising a 7000 N motorcycle with a pulley system, the workers note that for every 3 m of rope pulled down- ward, the piano rises 0. 3 m. Show that 700 N is required to lift the motorcycle

Answers

If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.

The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.

In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.

We use the formula for mechanical advantage in a pulley system, which is given by:

⇒ MA = (distance moved by the effort) / (distance moved by the load),

In this case, the distance moved by the effort is 3 m, and

The distance moved by the load is 0.3 m,

Substituting the values,

We get,

⇒ MA = 3/0.3,

⇒ MA = 10,

So, mechanical advantage of "pulley-system" is 10.

Now, we use mechanical advantage to calculate the required force to lift the motorcycle.

Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:

⇒ Input force = (Output force)/(Mechanical advantage),

Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,

We get,

⇒ Input force = 7000/10,

⇒ 700 N,

Therefore, the required force to lift motorcycle is 700 N.

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Which table represents a function?

Answers

Answer:

Table 4 represents a function because each x-value corresponds to exactly one y-value.

Find the measures of angle and B. Round to the nearest degree.

Answers

The measure of angle A and angle B are 30° and 60° respectively.

What is the measure of angle A and angle B?

The figure in the image is a right-triangle.

To find the measure of angle A and angle B, we use the trigonometric ratio.

Solving for the measure of angle A:

sinθ = opposite / hypotenuse

opposite of angle A = 8

hypotenuse = 16

Plug in the values

sinθ = 8/16

sinθ = 1/2

θ = sin⁻¹( 1/2 )

θ = 30°

Solving for angle B

cosB = adjacent / Hypotenuse

adjeacent of angle B = 8

Hypotenuse = 16

Plug in the given values

cosB = 8/16

cosB = 1/2

B = cos⁻¹( 1/2 )

B = 60°

Therefore angle A is 30 degrees and angle B is 60 degree.

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I NEED HELP ASAP IT'S DUE IN 20MIN
Question 2
The box plot represents the number of tickets sold for a school dance.

A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.

Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.


Question 5

A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?

Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7

A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sports Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44

Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8

A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27

Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.

Answers

2. The appropriate measure of center for the given data is the median, and it equals 19.

5.  We can predict that there were about 169 principals in attendance at the conference.

6. The best graphical representation for the teacher's data would be a bar graph.

7.  A histogram is used to display continuous data, while a bar graph is used to display categorical data.

8. The correct circle graph to represent the data is titled "New York City Visitor's Transportation"

9. We can predict that the college will need about 1440 scoops of ice cream.

Median, bar chart, histogram

Answer 2:

The appropriate measure of center for the given data is the median, and it equals 19. We can determine this from the box plot since the line inside the box represents the median of the data, and the box itself represents the middle 50% of the data. Since the box extends from 17 to 21, we know that half of the data falls below 19 and half above, making it the median. The mean is not a good measure of center for this data because it can be influenced by outliers, which are present in this dataset.

Answer 5:

Since we know that 15 out of 80 people in the exhibit room were principals, we can assume that about 15/80 (or about 0.1875) of the attendees were principals. To estimate the number of principals in attendance, we can multiply this fraction by the total number of attendees:

0.1875 x 900 ≈ 169

Therefore, we can predict that there were about 169 principals in attendance at the conference.

Answer 6:

The best graphical representation for the teacher's data would be a bar graph. A bar graph is a useful way to display categorical data, such as the subject preferences of the students. Each subject can be represented by a bar, with the height of the bar representing the frequency or percentage of students who prefer that subject.

Answer 7:

The correct graph to display the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The bars should be labeled "Basketball" with a value of 17, "Baseball" with a value of 12, "Soccer" with a value of 27, and "Tennis" with a value of 44. A histogram is used to display continuous data, while a bar graph is used to display categorical data.

Answer 8:

The correct circle graph to represent the data is titled "New York City Visitor's Transportation" and has five sections labeled "Walk" at 30%, "Bicycle" at 6%, "Car Service" at 11.25%, "Bus" at 7.5%, and "Subway" at 20.25%. To calculate the percentages, we can divide the number of visitors for each mode of transportation by the total number of visitors (i.e., 300), then multiply by 100% to get the percentage.

Answer 9:

To estimate the number of students who prefer ice cream, we can add up the number of students who chose ice cream, which is 81. Then, we can set up a proportion:

81/225 = x/4000

where x represents the number of students who prefer ice cream out of the total population of 4000. Solving for x, we get:

x = 81 x 4000 / 225 = 1440

Therefore, we can predict that the college will need about 1440 scoops of ice cream.

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Find the closing cost, to the nearest cent: house value of $89,548, two points, attorney's fees $324, title fees $105.

a 4,439. 92

b 2,219. 96

c 2,114. 96

d 1324. 48

Answers

If the house value of $89,548 and two points, attorney's fees $324, title fees $105, then closing cost is option (b) $2,219.96

Closing costs are fees associated with the purchase or refinance of a property that are paid at the closing of the transaction.

To calculate the closing cost, we need to add up all the fees associated with the purchase of the house.

First, we need to calculate the cost of the points. Two points on a house value of $89,548 would be

2 x $89,548 x 0.01 = $1,790.96

Next, we need to add the attorney's fees and title fees

$1,790.96 + $324 + $105 = $2,219.96

Therefore, the correct option is (b) $2,219.96

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It is possible to bisect any given angle using only a straightedge and a compass.

Answers

The process of bisecting an angle with a straightedge and compass is an important process in geometry. It is used to prove theorems, construct regular polygons, and much more. With enough practice, anyone can perfect this process and use it to their advantage.

What is angle?

Angle is a mathematical concept that describes the relationship between two lines (or edges) that share a common point (or vertex). It is measured in degrees, with a full circle being equal to 360 degrees. Angles can be either acute (less than 90 degrees), right (equal to 90 degrees), obtuse (greater than 90 but less than 180 degrees), or straight (equal to 180 degrees). Angles can also be classified as complementary (two angles whose sum equals 90 degrees) or supplementary (two angles whose sum equals 180 degrees).

1. Draw two rays from the vertex of the angle, and label them A and B.

2. Place the compass at A and draw an arc that intersects both rays.

3. Place the compass at B and draw an arc that intersects both rays.

4. The two arcs intersect at the bisector of the angle.

Bisecting an angle with a straightedge and compass is a simple process, but requires some practice to perfect. The process of bisecting an angle can be used to prove theorems in geometry, such as the Angle Bisector Theorem, which states that the bisector of an angle divides it into two congruent angles. This theorem can be used to prove the equality of two angles, or to construct an angle with a given measure.

Bisecting an angle can also be used to construct regular polygons, such as a hexagon. To construct a regular hexagon, one can use the process of bisecting an angle to construct six congruent angles. These angles can then be connected to form the sides of the hexagon.

The process of bisecting an angle with a straightedge and compass is an important process in geometry. It is used to prove theorems, construct regular polygons, and much more. With enough practice, anyone can perfect this process and use it to their advantage.

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What is the value of the expression 8w−4j2 when w=0. 25 and j=0. 5?

Answers

The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.

The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.

First, we substitute w = 0.25 and j = 0.5 in the expression:

8(0.25) - 4(0.5)²

Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:

= 2 - 1

= 1

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The given question is incomplete, the complete question is:

What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?

In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.

Answers

The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.

What is angle?

Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.

The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.

In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.

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11. three players on a baseball team are only permitted to pitch. the remaining 12 players are multitalented and can play any of the 8 remaining positions. how many baseball teams of nine can be formed?

Answers

There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.

Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.

For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.

Therefore, the total number of baseball teams of nine that can be formed is:

C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7

which simplifies to:

(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)

= 455 x 665,280

= 302,702,400

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Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number

Answers

The value of the expression as a single rational number is -8.

Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:

= -9.5 - (-8) - 6.5

= -9.5 + 8 - 6.5      (replacing -(-8) with its positive equivalent 8)

= (-9.5 - 6.5) + 8    (grouping like terms)

= -16 + 8                (simplifying)

= -8

Therefore, the value of the expression is -8, which is a single rational number.

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Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table:

Color of Tile Purple Pink Orange
Number of times the tile is drawn 6 18 26
What is the experimental probability that Jenny will pull out an orange tile? (5 points)

a
fraction 18 over 26

b
fraction 24 over 26

c
fraction 24 over 50

d
fraction 26 over 50

Answers

The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].

What is an Experimental Probability?

Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).

Given:

[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]

Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.

We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:

The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50

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the town mouse and the country mouse

Answers

1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.

2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.

What is The Town Mouse and The Country Mouse?

"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.

3. The sequence of events in the story is as follows:

The country mouse invites the town mouse to visit him in the countryside.The town mouse accepts the invitation and visits the country mouse.The country mouse serves the town mouse simple food, which the town mouse finds unappetizing.The town mouse invites the country mouse to visit him in the town.The country mouse accepts the invitation and visits the town.The town mouse serves the country mouse luxurious food, but they both get scared and run away when the cat appears.The country mouse returns to his simple life, realizing that it's better to be safe and content than to live in luxury but in constant danger.

4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.

5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.

6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.

7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.

8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.

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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.

Calculate the lengths of the 2 unlabeled sides.
Leave your answer in exact form.

Answers

Answer:

BC=4

AC=[tex]4\sqrt{2}[/tex]

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