please help with all three !!!!

Answer:

Triangle XYZ is shifted 9 units to the right, then 4 units down.

P(X > 60) = P(Z > 1.7321) = 0.0418

When answering questions on Brainly, it is important to be factually accurate, professional, and friendly. Additionally, answers should be concise and relevant to the question being asked. When possible, provide a step-by-step explanation using the following terms: sample, observation, and probability. In this particular question, the following information is provided:Part a) A sample of n=25 observations is drawn from a normal population with μ=100 and σ=2. Find the following: i) P(X < 96) ii) P(96 < X < 105)Part b) The amount of time university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. Find the probability that a professor works for more than 60 hours per week. Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours.Part a) Calculate the value of the test statistic, set up the rejection region, undertake the hypothesis test, and interpret the result.

i) P(X < 96)First, we calculate the z-score as follows:z = (X - μ) / σ = (96 - 100) / 2 = -2P(X < 96) = P(Z < -2) = 0.0228ii) P(96 < X < 105)We first calculate the z-scores for both X values as follows:z1 = (X1 - μ) / σ = (96 - 100) / 2 = -2z2 = (X2 - μ) / σ = (105 - 100) / 2 = 2.5Next, we look up the area between these two z-scores using a standard normal distribution table. We have: P(96 < X < 105) = P(-2 < Z < 2.5) = 0.9944 - 0.0228 = 0.9716b) i) Probability that a professor works for more than 60 hours per weekWe first calculate the z-score as follows:z = (X - μ) / σ = (60 - 52) / 6 = 1.3333Using a standard normal distribution table, we find the area to the right of the z-score as follows:P(X > 60) = P(Z > 1.3333) = 0.0912ii) Probability that the mean amount of work per week for three randomly selected professors is more than 60 hoursLet X be the random variable representing the mean amount of work per week for three randomly selected professors. We know that X ~ N(μ, σ / sqrt(n)), where μ = 52, σ = 6, and n = 3. We calculate the z-score as follows:z = (X - μ) / (σ / sqrt(n)) = (60 - 52) / (6 / sqrt(3)) = 1.7321Using a standard normal distribution table, we find the area to the right of the z-score as follows:P(X > 60) = P(Z > 1.7321) = 0.0418Part a) Calculate the value of the test statistic, set up the rejection region, undertake the hypothesis test, and interpret the result.No information is provided about the hypothesis test in Part a of the question, so it is not possible to provide an answer to this part. Please provide more information or clarify the question if possible.

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Answer: True

Step-by-step explanation:

It is generally recommended that adults drink at least 8 cups or 2 liters of water per day to maintain proper hydration.

Therefore, based on the data provided, Oldtown is more popular than Newburg.

To determine which city is more popular, we need to compare their populations for each year.

In 2015, Oldtown had a population of 1518, which is significantly larger than Newburg's population of 100. Therefore, Oldtown was more popular in 2015.

In 2016, Oldtown's population increased to 1643, while Newburg's population increased to 110. Again, Oldtown had a larger population and was more popular.

In 2017, Oldtown's population increased to 1768, while Newburg's population increased to 121. Once again, Oldtown had a larger population and was more popular.

In 2018, Oldtown's population increased to 1893, while Newburg's population increased to 133. Yet again, Oldtown had a larger population and was more popular.

Therefore, based on the data provided, Oldtown is more popular than Newburg.

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The mayors of old town and newborn were having a disagreement about which city was more popular. They made the table below to show the population of their cities for the past several years.

2015 Newburg Population 100. Oldtown Population 1518

2016 Newburg Population 110. Oldtown Population 1643

2017 Newburg Population 121. Oldtown Population 1768

2018 Newburg Population 133. Oldtown Population 1893

Which city is more popular?

Answer:

[tex]y = \frac{3}{2} x + 2[/tex]

Step-by-step explanation:

[tex]2y - 3x = 4[/tex]

[tex]y - \frac{3}{2} x = 2[/tex]

[tex]y = \frac{3}{2} x + 2[/tex]

Answer:

True answers:

f(x) is an increasing exponential function.

f(x) has a greater y-intercept

Step-by-step explanation:

Option 1:

Both functions have the same y-intercept is FALSE

The y-intercept of f(x) is found by plugging in 0 for x

[tex]f(0) = 5^0 - 3 = 1 - 3 = -2[/tex]

The intercepts are different, so option 1 is FALSE.

Option 2:

f(x) is an increasing exponential function is TRUE

the largest term is positive and exponential.

Option 3:

g(x) has a greater y-intercept. is FALSE

The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3

Option 4:

f(x) has a greater y-intercept is TRUE

The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3

If all three of them together have a total of 520 kroner then bill would have 205 kroner

amounts of money that Alan, Bill, and Cassie have:

Let A be the amount of money that Alan has.

Let B be the amount of money that Bill has.

Let C be the amount of money that Cassie has.

From the problem, we know that:

A + B = 250 (equation 1)

B + C = 475 (equation 2)

A + B + C = 520 (equation 3)

We want to solve for B, the amount of money that Bill has.

One way to do this is to use equation 1 to solve for A in terms of B:

A = 250 - B

We can then substitute this expression for A into equations 2 and 3:

(250 - B) + B + C = 520

Simplifying this equation, we get:

C = 270

Substituting this value of C into equation 2, we get:

B + 270 = 475

Solving for B, we get:

B = 205

Therefore, Bill has 205 kroner.

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let's recall that the point of tangency for a tangent line to a radius in a circle is alway a right-angle, also let's notice that ∡AOD as well as ∡ABC are both intercepting the same arc.

Check the picture below.

A triangle with sides lengths 9, 15, and 3√35 would be classified as a scalene triangle.

In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;

In Mathematics and Geometry, a scalene triangle can be defined as a type of triangle that has all of its three (3) sides and interior angles different in length and size respectively.

Since the given side lengths 9, 15, and 3√35 units are all different, we can logically deduce that they would form a scalene triangle.

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The value of x is 10 and the trapezoid has two base angles with measure 40 degrees and two non-base angles with measure 140 degrees.

What is the congruent angle?

When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.

In an isosceles trapezoid, the base angles (the angles opposite the parallel sides) are congruent. Let's call each of these angles "a". Then, we have:

a = 3x + 10 (from one of the congruent angles)

a = 5x - 10 (from the other congruent angle)

Setting these two expressions equal to each other, we get:

3x + 10 = 5x - 10

Solving for x, we get:

2x = 20

x = 10

Now that we know the value of x, we can substitute it back into either of the expressions for "a" to find the measure of each base angle:

a = 3x + 10 = 3(10) + 10 = 40

Therefore, each base angle of the trapezoid has measure 40 degrees.

The other two angles of the trapezoid are the non-base angles (the angles adjacent to the parallel sides).

These angles are supplementary to the base angles, so each non-base angle has measure:

180 - 40 = 140

Therefore, the value of x is 10 and the trapezoid has two base angles with measure 40 degrees and two non-base angles with measure 140 degrees.

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Approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.

According to the given function, the percent of annual snowfall at an altitude of h feet is given by p(h) = 82 in (h) - 649. To approximate the amount of snow at the altitudes of 3000 feet and 6000 feet, we can simply plug these values into the function and solve for p(h).

At an altitude of 3000 feet, we have:

p(3000) = 82 in (3000) - 649

p(3000) = 246000 - 649

p(3000) = 245351

Therefore, approximately 245351% of the annual moisture at an altitude of 3000 feet falls as snow.

Similarly, at an altitude of 6000 feet, we have:

p(6000) = 82 in (6000) - 649

p(6000) = 492000 - 649

p(6000) = 491351

Therefore, approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.

It's important to note that these values represent percentages and not the actual amount of snowfall in inches. To convert these percentages to the actual amount of snowfall, we would need to know the total annual moisture at each altitude. Nonetheless, we can use the given function to approximate the percentage of snowfall at different altitudes in the mountain range of California.

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Answer:

67.5

Step-by-step explanation:

4 1/2x6= 27 27x2 1/2=67.5

Answer:

d

Step-by-step explanation:

Answer:

62/3

Step-by-step explanation:

As it's a rectangle do the area is equal A = L*W

SO

[tex](7 \times \frac{3}{4} ) \times( 2\times \frac{2}{3} )[/tex]

Step-by-step explanation:

2 2/3 × 7 3/4

turn these into improper fractions =8/3 × 31/3

times the numerator and denominator together= 248/9

248/9 simplified=27.5555555 or 27 5/9 as a fraction

Answer:

Step-by-step explanation:

[tex]\frac{42}{x+5} =7[/tex]

[tex]42=7(x+5)[/tex]

[tex]42=7x+35[/tex]

[tex]7x=-7[/tex]

[tex]x=-1[/tex]

Answer:

x=-2+-8

Step-by-step explanation:

If you mean (x+2)^2=64

take the sqrt of both sides and get x+2 = +-8

then subtract 2 to get -2+-8 = x

Therefore, the total area of Riley's backyard is. [tex]6x^2-19x+8[/tex].

Length is a measure of distance or extent, typically referring to the measurement of an object or distance in one dimension. It describes how long an object or distance is, usually in units such as meters, feet, or inches. Length is one of the fundamental physical quantities, and is used in various fields including mathematics, physics, engineering, and construction. It is often represented by the symbol "L" or lowercase "l".

To find the area of the backyard, we need to multiply the length and width of the rectangular shape.

Length of the backyard = 3x - 8

Width of the backyard = 2x - 1

Area of the backyard = Length x Width

[tex]\\= (3x - 8)(2x - 1)\\= 6x^2 - 19x + 8[/tex]

Therefore, the total area of Riley's backyard is [tex]6x^2-19x+8[/tex]

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This indicates that the mean of the sample (16.5 seconds) is statistically significantly lower than the mean of the population (18 seconds). Therefore, the researcher can conclude that the noise does cause the mice to complete the maze faster.

Using a two-tailed t-test with a significance level of 0.05, the researcher can conclude that the noise does cause the mice to complete the maze faster. The test statistic for this experiment is -2.097, which is less than the critical value of -1.68. This indicates that the mean of the sample (16.5 seconds) is statistically significantly lower than the mean of the population (18 seconds). Therefore, the researcher can conclude that the noise does cause the mice to complete the maze faster.

the complete question is :

​experiments on learning in animals sometimes measure how long it takes for mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 36 randomly selected lab mice takes with noise as stimulus. Her sample data yielded a mean of 16. 5 seconds and a standard deviation of 6. 4 seconds. what can you conclude from the sample data ?

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Answer:25 sticks

Step-by-step explanation:

1st=5 sticks

2nd=9 sticks

3rd=13 sticks

4th=17 sticks

5th=21 sticks

6th=25 sticks

The minimum number οf identical cοntainers Rene wοuld need tο make 2,000 cm³ οf ice is 4. Optiοn b is the cοrrect οptiοn.

A cylinder is a three-dimensiοnal sοlid in mathematics that maintains, at a fixed distance, twο parallel bases cοnnected by a curved surface. These bases typically have a circular shape (like a circle), and a line segment knοwn as the axis cοnnects the centers οf the twο bases.

The base οf a cοntainer is 8 centimeters. The height οf the cοntainer is 10 centimetres.

The radius οf a shape is half οf its diameter.

The radius οf  cοntainer is 8/2 = 4 cm.

The vοlume οf a cylinder is πr²h.

The vοlume οf a cοntainer is π×4²×10

= 160 × 3.14

= 502.4 cm³

Assume that Rene needs x number οf cοntainers.

The vοlume οf x number οf cοntainers is 502.4 x.

Accοrding tο the questiοn:

502.4 x = 2,000

Divide bοth sides by 502.4:

x = 2000/502.4

x = 3.98

x ≈ 4

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Answer:it’s 0

Step-by-step explanation:

x=12°

so:(2x+1°)°+(5x+5)°+90°=180°

7x=180°-1°-5°-90°

7x=84°

x=84°÷7

x=12°

i don't know if it is x that you wanted but the it is

Answer:

45 degrees

Step-by-step explanation:

The first angle of the triangle is 45 degrees. This can be determined by the given information that the second angle is 30 degrees larger than the first and the third angle is 3 times the second. Since the second angle is 30 degrees larger than the first, the first angle must be 15 degrees, and the third angle must be 3x15=45 degrees.

The correct answer is:

x + 12 ≤ 5 − y ≤ 2(x − 3)

Explanation:

From the given inequalities:

x + 12 ≤ 5 − y ... (1)

5 − y ≤ 2(x − 3) ... (2)

We can see that 5 - y is common in both inequalities. We can isolate this term by subtracting 5 from both sides of (1) and (2):

x + 7 ≤ -y ... (3)

-y ≤ 2(x - 8) ... (4)

Multiplying (3) by -1, we get:

y - 7 ≥ x ... (5)

Substituting this value of x in (4), we get:

y - 7 ≤ -2(7 - y)

y - 7 ≤ -14 + 2y

y ≤ 7

Substituting this value of y in (5), we get:

0 ≤ x + 7 ≤ 14

Subtracting 7 from all sides, we get:

-7 ≤ x ≤ 7

Therefore, the statement x + 12 ≤ 5 − y ≤ 2(x − 3) is not true, but the statement -7 ≤ x ≤ 7 is true.

Answer:

To find the slope of the line through point B and perpendicular to line k, we need to first find the slope of line k.

If we have the equation of line k in slope-intercept form, y = mx + b, then the slope of line k is simply the coefficient of x, which is m.

Assuming we don't have the equation of line k, we can find its slope by using the slope formula, which is:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are two points on line k.

Let's say line k passes through points P and Q. Then we can write the slope of line k as:

m = (yQ - yP)/(xQ - xP)

Now, we want to find the slope of the line through point B and perpendicular to line k. We know that the product of the slopes of two perpendicular lines is -1. That is:

m1 * m2 = -1

where m1 is the slope of line k, and m2 is the slope of the line through point B and perpendicular to line k.

Therefore, we can write:

m2 = -1/m1

So we just need to find the slope of line k, and then we can use this formula to find the slope of the line through point B and perpendicular to line k.

Once we have the slope of the line through point B, we can write its equation in point-slope form:

y - yB = m2(x - xB)

where (xB, yB) is the point B.

Hope this helps with you with your question (it's not a direct answer, I think?) I'm sorry if it doesn't! If you need more help, ask me! :]

Answer:

63.25

Step-by-step explanation:

You need to calculate each figure separately.

The diameter of the circle = 4 + 3 + 3 = 10

=> radius = 5

area of 1/2 circle = 1/2πr^2 = 1/2π(5)^2 = 1/2(3.14)(25) = 39.25

area of the top rectangle = 3 x 6 = 18

area of the bottom rectangle = 2 x 3 = 6

total area = 39.25 + 18 + 6 = 63.25

Answer:Hi

Step-by-step explanation:

Applying the distance formula, the distance between points N and C in the coordinate plane is calculated as: 5 units.

To calculate the distance between two points on a coordinate plane, the distance formula can be applied which is given as:

d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the two points lie on the coordinate plane as the following coordinates:

N = (-8, 9)

C = (-4, 6)

Therefore, we will have:

d = √[(−4 − (−8))² + (6−9)²]

d = √[(4)² + (−3)²]

d = √(16 + 9)

d = √25

d = 5 units

Thus, the distance between points N and C is calculated as: 5 units.

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The expression for the nth term of the sequence is,  Tn = 3n^2 - 7n - 1

To find an expression for the nth term of a quadratic sequence, we need to find a quadratic function that describes the sequence.

Let the nth term of the sequence be denoted by Tn. We can use the method of finite differences to determine the degree of the quadratic function that describes the sequence.

The first differences between the terms are 6, 10, 14, 18, 22. The second differences between these first differences are all equal to 4. This tells us that the sequence is quadratic, since the second differences are constant.

To find the quadratic function that describes the sequence, we can use the formula for the nth term of a quadratic sequence,

Tn = an^2 + bn + c

where a, b, and c are constants to be determined.

We can use the first three terms of the sequence to form a system of three equations,

T1 = a + b + c = -5

T2 = 4a + 2b + c = 1

T3 = 9a + 3b + c = 11

Solving this system of equations, we get:

a = 3

b = -7

c = -1

Therefore, the expression for the nth term of the sequence is

Tn = 3n^2 - 7n - 1

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Answer:

Complex or Imaginary solutions

Step-by-step explanation:

In the Quadratic Formula, the discriminant is the part that is inside of the radical (square root symbol).

So there are three cases, the discriminant can be:

-positive, OR

-zero, OR

-negative

If its positive, there are two real solutions.

If its zero, there is one real solution.

If its negative, there are two complex (imaginary) solutions.



Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.

what is  Median?

The median is a statistical measure that represents the central value of a dataset.

To calculate the upper limit for outliers, we can use the interquartile range (IQR) and the formula:

Upper Limit = Q3 + 1.5 * IQR

where Q3 is the third quartile, and IQR is the interquartile range.

First, we need to find the values for Q1, Q2 (median), and Q3:

1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17

Arranging the data in order:

1, 6, 6, 6, 7, 7, 8, 9, 10, 13, 17

The median is the middle value. Since there are 11 values, the median is the average of the 6th and 7th values:

Median = (7 + 8) / 2 = 7.5

To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively:

Lower half: 1, 6, 6, 6, 7

Upper half: 8, 9, 10, 13, 17

Q1 is the median of the lower half, which is 6.

Q3 is the median of the upper half, which is 10.

Next, we can calculate the interquartile range:

IQR = Q3 - Q1 = 10 - 6 = 4

Finally, we can calculate the upper limit for outliers:

Upper Limit = Q3 + 1.5 * IQR = 10 + 1.5 * 4 = 16

Any value above 16 can be considered a potential outlier on the high end of the data.

Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.

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