Homework 18.1.-trigonometric ratios

Find the 3 trigonometric ratios. If needed, reduce fractions.

Solving the equations we get the average cost of movie tickets for Japan is $17.42 and Switzerland is $13.07.

What is equation?

An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

Let, the cost for 1 movie ticket in Japan = $x

the cost for 1 movie ticket in Switzerland = $y

It would cost $78.40 to buy three tickets in Japan plus two tickets in Switzerland.

So the first equation will be,

3x+2y= 78.40 ------------(1)

Three tickets in Switzerland plus two tickets in Japan would cost $74.05

From this the 2nd equation will be,

2x+3y= 74.05 --------------(2)

Multiplying equation (1) by 2 and multiplying equation (2) by 3 we get,

6x+4y= 156.8 --------------(3)

6x+9y= 222.15 ------------(4)

equation (4)- (3) gives,

5y= 65.35

y= 13.07

putting this value in equation (1) we get,

x= (78.40- 2× 13.07)/ 3

 = 17.42

Hence, the average cost of movie tickets for Japan is $17.42 and Switzerland is $13.07.

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Answer:

BC=4

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

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

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 probability that at most a fifth of the buyers would prefer green is approximately 0.0198

This problem can be solved by using the binomial distribution. Let X be the number of buyers out of 15 who prefer green. Then X follows a binomial distribution with parameters n = 15 and p = 0.6.

We want to find the probability that at most a fifth of the buyers would prefer green. This means we want to find P(X ≤ 3), since a fifth of 15 is 3.

Using the binomial probability formula, we have

P(X ≤ 3) = Σ P(X = k) for k = 0 to 3

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (15 choose 0) (0.6)⁰ (0.4)¹⁵ + (15 choose 1) (0.6)¹(0.4)¹⁴ + (15 choose 2) (0.6)² (0.4)¹³ + (15 choose 3) (0.6)³ (0.4)¹²

= 0.0000265 + 0.000397 + 0.00312 + 0.0163

Add the number

= 0.0198

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Angle ACB = 180 degrees - angle ADC . AXB and angle ACB are supplementary

Supplementary angles are  angles whose sum is 180 degrees. For example, an angle of 130° and an angle of 50° are supplementary angles, because the sum of 130° and 50° is  180°. Similarly, complementary angles add up to 90 degrees.

 To show that angle AXB and angle ACB are supplementary, we must show that their sum is  180 degrees.  

First, we can use the fact that angle AXB is a circumscribed angle of circle C to say that XA and XB are the ears of the circle that intersect at  B. Let O be the center of  circle C. Then, by the inscribed angle theorem, we get:

angle AOB = 2 * angle AXB

Similarly, we can say that AC is a chord of a circle that intersects  XB at  D. Then, using the inscribed angle theorem again, we get:

angle AOC = 2 * angle ADC

Since the angles AOB and AOC are both subtended by the arc AC, they are equal. Therefore, we can equate the expressions  AOB and AOC:

2 * angle AXB = 2 * angle ADC

Simplifying this expression, we get:

angle AXB = angle ADC

Now we can use this fact to show that angle AXB and angle ACB are supplementary. Since the angles AXB and ADC are opposite angles of the cyclic quadrilateral AXDC, we know that they add up to 180 degrees:

angle AXB + angle ADC = 180 degrees

Replacing angle AXB with angle ACB (since they are equal), we get:

angle ACB + angle ADC = 180 degrees

In the reorganization, we have:

angle ACB = 180 degrees - angle ADC

So angle ACB and angle ADC are also supplementary. Therefore, we have shown that angle AXB and angle ACB are supplementary by necessity.

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

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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|z| = 0.669 < 1.96, we fail to reject the null hypothesis at any significance level up to α = 0.05.

In other words, we do not have enough evidence to conclude that the true proportion of executives who would agree with the statement is different from one-half.

The null hypothesis that the true proportion of all such executives.

Agree with this statement is one-half, we can use a two-sample z-test for proportions.

Let p be the true proportion of executives who would agree with the statement and let. [tex]\^p[/tex] be the sample proportion.

Under the null hypothesis, the test statistic z is given by:

[tex]z = (\^p - 0.5) / \sqrt(0.5 \times 0.5 / n),[/tex]

n is the sample size (104 in this case).

This test statistic follows a standard normal distribution under the null hypothesis.

To reject the null hypothesis at a significance level α, we need to find the critical values.[tex]z\alpha/2[/tex] and [tex]-z\alpha/2[/tex] such that [tex]P(Z > z\alpha/2) = \alpha/2[/tex] and[tex]P(Z < -z\alpha/2) = \alpha/2[/tex], where Z is a standard normal random variable.

The lowest level of significance at which the null hypothesis can be rejected against a two-sided alternative.

The smallest α such that [tex]|z| > z\alpha/2.[/tex]

The two-sided alternative implies that we are interested in deviations from the null value of 0.5 in either direction.

Using the given information, we have:

[tex]\^p = 50/104 = 0.4808,[/tex]

n = 104.

Substituting these values into the formula for z, we get:

[tex]z = (0.4808 - 0.5) / \sqrt(0.5 \times 0.5 / 104) = -0.669.[/tex]

The critical value [tex]z\alpha/2[/tex], we look up the corresponding value in the standard normal distribution table.

[tex]z\alpha/2[/tex] such that [tex]P(Z > z\alpha/2) = \alpha/2[/tex], or equivalently, [tex]P(Z < -z\alpha/2) = \alpha/2[/tex]. Since the standard normal distribution is symmetric, we can look up the value of zα/2 that satisfies. [tex]P(Z > z\alpha/2) = \alpha/2[/tex], and then take its absolute value to find. [tex]-z\alpha/2.[/tex]

Using a standard normal distribution table, we find that z0.025 = 1.96 (rounded to two decimal places).

The critical values for rejecting the null hypothesis at a significance level α are:

[tex]z\alpha/2[/tex] = ±1.96.

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The ratio of their surface areas is x^2

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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The value of x is -6.5.

First, substitute the value of y into the equation:

2x - 3(-7) = 8

Now, solve for x:

2x + 21 = 8

Subtract 21 from both sides:

2x = -13

Divide by 2:

x = -13/2 or -6.5

So, the value of x is -6.5.

We started with the given equation and information:

Equation: 2x - 3y = 8

Given: y = -7

Our task is to find the value of 'x' using the given information which was solved above and of which we substituted the value of y into the equation, simplified, subtracted and divided and got the answer to the equation which is -6.5.

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Given the equation 2x - 3y = 8 and y = -7, find the value of x.

The upper and lower values of the range of the dataset are: Option E: -12 and 104

The range of a dataset is defined as the difference between the highest and lowest values of that dataset when arranged in ascending or descending order.

The dataset is given by:

36, 45, 40, 36, 84, 72, 20, 53, 32, 45, 64, 76

The lowest value = 20

Highest value = 84

Thus:

Upper value of range will be: 80 + 24 = 104

Lower value of range will be: 20 - 32 = -12

There is no outlier

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The graph is a positive association

The graphs shows a linear relationship

There is outliers in coordinate (3, 105) and clusters from domain value of 8

Variable association refers to the relationship between two variables, and it can be either positive or negative. A positive association means that as one variable increases, the other variable tends to increase as well, while a negative association means that as one variable increases, the other variable tends to decrease.

Linear association specifically refers to the relationship between two variables that can be best represented by a straight line. This means that as one variable increases or decreases, the other variable changes proportionally.

Specialty in statistics can refer to two different concepts: outliers and clusters.

Outliers are data points that are significantly different from the other data points in a dataset. These points can have a large effect on statistical analysis and can distort results, so they are often removed or treated separately.

Clusters refer to groups of data points that are close together in a dataset. These clusters can indicate that there are subpopulations within the dataset or that there is a relationship between the variables being studied. Clusters can also be used to identify patterns or trends in the data.

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From the given information , the brand which is a "better-buy" is (c) Brand C .

To determine which brand is the better buy, we calculate the "price-per-ounce" for each brand.

To find the "price-per-ounce" we divide "the cost" by "the number of ounces",

On dividing cost by ounces,

We get,

⇒ For Brand A: $2.16 for 18 ounces,

The "price-per-ounce" is = $2.16/18 = $0.12 per ounce.

⇒ For Brand B: $1.50 for 12 ounces,

The "price-per-ounce" is = $1.50/12 = $0.125 per ounce.

⇒ For Brand C: $2.26 for 20 ounces,

The "price-per-ounce" = $2.26/20 = $0.113 per ounce.

⇒ For Brand D: $1.95 for 16 ounces,

The "price-per-ounce" is = $1.95/16 = $0.122 per ounce.

On comparing the price per ounce, we see that "Brand C" has the lowest price per ounce at $0.113, which makes it the better buy among the options given.

Therefore, the correct answer is (c) Brand C.

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The given question is incomplete, the complete question is

Given the following information, choose the brand that is the better buy.

Brand A: $2.16 for 18 ounces

Brand B: $1.50 for 12 ounces

Brand C: $2.26 for 20 ounces

Brand D: $1.95 for 16 ounces

(a) Brand A

(b) Brand B

(c) Brand C

(d) Brand D

Answer:

Step-by-step explanation:

yeah she is... i think.. this is twisting my mind rn

Answer:

2x+7>-13

Step-by-step explanation:

Let the unknown number be x.

Since the problem starts off with "7 more than twice a number," we need to find twice the number first. Let's multiply x by 2:

we end up with 2x.

Let's return to "7 more than twice a number..."

This means that the value is 7 more than 2x, so let's add 7 to 2x:

we end up with 2x+7.

Now, let's take a look at "...is greater than negative 13."

Our new value, 2x+7, is greater than -13.

So, we can write:

2x+7>-13

A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from the origin at time

t  is given by either d = a sin ωt or d = a cos ωt.

Simple harmonic motion, or SHM for short, is a particular kind of periodic motion of a body that results from a dynamic

equilibrium between an inertial force that is proportional to the body's acceleration away from the static equilibrium

position and a restoring force on the moving object that is directly proportional to the size of the object's displacement

and acts towards the object's equilibrium position. If friction or any other energy dissipation is not present, it leads to an

oscillation that is represented by a sinusoid and that lasts indefinitely.

The oscillation of a mass on a spring when it is subject to the linear elastic restoring force specified by Hooke's law is a

good example of simple harmonic motion, which may be used as a mathematical model for many different motions.

The motion has a single resonant frequency and is sinusoidal in time. Simple harmonic motion can be used to simulate

a variety of other phenomena, such as the motion of a simple pendulum, though it is only a good approximation when

the angle of the swing is small; for more information, see small-angle approximation. In order for the model to be

accurate, the net force acting on the object at the end of the pendulum must be proportional to the displacement.

Molecular vibration can also be modelled using straightforward harmonic motion.

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The numbers from least to greatest are: -1 4/5, -1 1/2, 1 2/5, 1 7/10.

To compare these numbers, we need to convert them to a common format. One option is to convert them all to improper fractions, so we can compare them more easily.

An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). In other words, the fraction represents a value that is greater than or equal to one.

-1 1/2 = -3/2

1 7/10 = 17/10

1 2/5 = 7/5

-1 4/5 = -9/5

Now we can order them from least to greatest:

-3/2 < -9/5 < 7/5 < 17/10

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The given question is incomplete, the complete question is:

What is -1 1/2, 1 7/10, 1 2/5, -1 4/5 from least to greatest

The p-value is greater than 0.05, the researcher would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

It appears that some values are missing in your question, specifically the sample mean and the population standard deviation.

Without these values, I cannot provide a complete answer to your question.

A general idea of how to approach this type of hypothesis test.

To test whether the average number of sick days a worker takes per year is greater than 5, the researcher would need to set up the following hypotheses:

Null hypothesis (H0):

The average number of sick days taken per year by workers is equal to or less than 5.

Alternative hypothesis (Ha):

The average number of sick days taken per year by workers is greater than 5.

The next step would be to collect a random sample of workers and calculate their sample mean and sample standard deviation.

Based on these values, the researcher would then calculate the t-value using the formula:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

The hypothesized population mean in this case is 5, the sample size is 28, and the sample mean and sample standard deviation would be substituted in.

Once the t-value is calculated, the researcher would then use a t-distribution table to find the corresponding p-value based on the degrees of freedom (sample size minus 1) and the level of significance (0.05).

If the p-value is less than 0.05, the researcher would reject the null hypothesis and conclude that there is enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

The specific critical t-value would be based on the degrees of freedom and level of significance.

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Answer:

63.3%

Step-by-step explanation:

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

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.

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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Answer:

x = 16

Step-by-step explanation:

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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Based on the table, a relationship which best predicts the end behavior of the graph of f(x) include the following: C. as, x → ∞, f(x) → –∞, And as x → –∞, f(x) → ∞.

In Mathematics and Geometry, a function f(x) is generally considered as an odd function if the following condition holds for all x-values (both positive x-values and negative x-values) in the domain of function f(x):

-f(x) = f(-x) - f (x) = f(-x)

This ultimately implies that, the larger the x-values or independent values (domain) is, the smaller would be the y-values or output values (range). On the other hand (conversely), the smaller the x-values or independent values (domain) is, the larger would be the y-values or output values (range);

x → ∞, f(x) → –∞, And as x → –∞, f(x) → ∞.

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Answer:

3 1/5

Step-by-step explanation:

The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).

The volume of such a three-dimensional object is the amount of space it takes up in algebra and geometry. It is a description of an object's capacity and, depending on the situation, may be stated in terms of cubic metres, cubic centimetres, litres, or gallons. A cube's volume, for instance, can be determined by adding up its length, width, and height. An equation for calculating a cube's volume is: V = l × w × h where V indicates for volume, l for length, w for width, and h for height.

given

The following equation determines a sphere's volume:

[tex]V = (4/3)\pi r^3[/tex]

where r denotes the sphere's radius.

If we substitute r = 7 feet, we obtain:

[tex]V = (4/3)\pi (7 feet)^3[/tex]

Using V, 1436.76 cubic feet (3.14159)

To the nearest tenth, we round and obtain:

1436.8 cubic feet equals V.

The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).

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Answer:

(-7, 2)

Step-by-step explanation: (see attachment for work)

Multiply the second equation by -4 to eliminate the y. Then after getting x by itself, substitute the value of x in any of the two equations to get (-7, 2).

Answer:

four less than three times a number

Answer: 4.5

The interquartile range IQR is the range in values from the first quartile Q1 to the third quartile Q3. Find the IQR by subtracting Q1 from Q3.

To determine the creation date of system volumes on an older Apple computer, and the most effective methods for obtaining this information, such as checking file metadata or using file recovery tools.

The best way for Melissa to approach discovering the creation date of the system volumes on an older Apple computer would be to check the file metadata.

File metadata includes information about when a file was created, modified, or accessed, and can be accessed by;

right-clicking on the file and selecting "Get Info" or by using the Terminal command "ls -l" in the directory where the system volumes are located.

Alternatively, Melissa could use a file recovery tool such as Disk Drill or EaseUS Data Recovery to scan the hard drive for deleted files that may contain information about the creation date of the system volumes.

It is important to note that using file recovery tools can potentially overwrite or corrupt existing data, so caution should be exercised when using these tools.

If Melissa is unable to find the creation date of the system volumes through these methods, she could also try contacting Apple support or consulting online forums for assistance

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The volume of the cone is (100)π cubic centimeters.

Given that the slant height (l) of the cone is 13 cm, and the height from the vertex to the center of the base (h) is 12 cm, we need to find the volume (V) of the cone.

To do this, we'll first need to find the radius (r) of the cone's base.
We can use the Pythagorean theorem to find the radius, since the slant height, height, and radius form a right triangle:
l² = h² + r²
Plugging in the given values:
13² = 12² + r²
169 = 144 + r²
r² = 25
r = 5 cm
Now that we have the radius, we can find the volume of the cone using the following formula:
V = (1/3)πr²h
Substitute the known values:
V = (1/3)π(5²)(12)
V = (1/3)π(25)(12)
V = (1/3)π(300).

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