Caroline bought 3 pairs of pants for $68.25. Each pair of pants costs the same amount. How much will she pay for 5 pairs of pants at the same price per pair?

The solution of the questions is given as

a)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments. (This is a two-tailed case)

c)

Test Statistic is given by:

z= 2.00

d)

Critical values of Z come from the table and equal \(\pm\)1.96.

e)

, p-value = 0.0455

f)

CI= (3.006, 3.594)

g)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

a)

The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments.

c)

Test Statistic is given by:

\(z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100\)

z= 2.00

d)

\(\alpha = 0.05\)

Critical values of Z come from the table and equal \(\pm\)1.96.

e)

Z Score = 2.00

reading from table, p-value = 0.0455

f)

Confidence Interval:

\(CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}\)

\(CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}\)

CI= (3.006, 3.594)

g)

The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i)

The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.

Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

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Answer:

I think is: odd

Step-by-step explanation:

Answer:So the radius of the cylinder is 2.65 cm.

A cylinder can be defined as a solid figure that is bound by a curved surface and two flat surfaces. The surface area of a cylinder can be found by breaking it down into 2 parts:

1.  The two circles that make up the caps of the cylinder.

2.  The side of the cylinder, which when "unrolled" is a rectangle.

The area of each end cap can be found from the radius r of the circle, which is given by:

A = πr2

Thus the total area of the caps is 2πr2.

The area of a rectangle is given by:

A = height × width

The width is the height h of the cylinder, and the length is the distance around the end circles, or in other words the perimeter/circumference of the base/top circle and is given by:

P = 2πr

Thus the rectangle's area is rewritten as:

A = 2πr × h

Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

A = 2πr2 + 2πrh

where:

π  is Pi, approximately 3.142

r  is the radius of the cylinder

h  height of the cylinder

By factoring 2πr from each term we can simplify the formula to:

A = 2πr(r + h)

The lateral surface area of a cylinder is simply given by: LSA = 2πr × h.

Example 1: Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm.

Solution:

SA = 2 × π × r2 + 2 × π × r × h

SA = 2 × 3.14 × 42 +  2 × 3.14 × 4 × 3

SA = 6.28 × 16 + 6.28 × 12

SA = 100.48 + 75.36

SA = 175.84

Surface area = 175.84 cm2

Example 2: Find the surface area of the cylinder with a radius of 5.5cm and height of 10cm.

Solution:

The radius of cylinder = 5.5 cm.

The height of cylinder = 10 cm.

The total surface area of the cylinder is therefore:

TSA = 2πr(r+h)

TSA = 11π (5.5+10)

TSA = 170.5 π

TSA = 535.6 cm2

Example 3: Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

Solution:

Again as in the previous example:

TSA = 2πr(r+h)

TSA = 2π× 17(17+3)

TSA = 2π×17×20

TSA = 2136.56 cm2

Example 4: Find the surface area of the cylinder with radius of 6 cm and height of 9 cm.

Solution:

The radius of cylinder: r = 6 cm

The height of cylinder: h = 9 cm

Total surface area of cylinder is therefore:

TSA = 2πr(r + h)

TSA = 12π (6+9)

TSA = 180 π

TSA = 565.56 cm2

Example 5: Find the radius of cylinder whose lateral surface area is 150 cm2 and its height is 9 cm.

Solution:

Lateral surface area of cylinder is given by:

LSA = 2πrh

Given that:

LSA = 150cm2

h = 9cm

π is the constant and its value = 3.14

Substitute the values in the formula and find the value of r by isolating it from the equation:

LSA = 2πrh

150 = 2× π × r × 9

r = 150 / (2×9× π)

r = 2.65cm

So the radius of the cylinder is 2.65 cm.

The lateral surface area of cylinder is 62.8 square units, total surface area is 87.92 square units and 62.8 cubic units is the volume.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let us consider the radius of the cylinder is 2 and height of cylinder is 5.

Lateral surface area = 2πrh

Plug in the values of radius and height

=2×3.14×2×5

=62.8 square units.

Total surface area TSA= 2πr(h+r)

=2×3.14×2(5+2)

=2×3.14×2×7

=87.92 square units

Volume of cylinder= πr²h

=3.14×4×5

=62.8 cubic units

Hence, the lateral surface area of cylinder is 62.8 square units, total surface area is 87.92 square units and 62.8 cubic units is the volume.

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Answer:

1. 9

2. increase

3. 1

4. 1

5. 7

Answer:

-4

Step-by-step explanation:

g(x)= -x+4

g(x)=8

x=?

we know,

g(x)= -x+4

8= -x+4

4= -x

x= -4#

Meters and seconds are the two units of measurement required to describe speed.

A ball freely falling at 20 m/s will in the next second have a speed of 30 m/s.This is because the speed of a freely falling item rises by 9.8 m/s per second owing to gravity's acceleration. The ball begins at a speed of 20 m/s and adds 9.8 m/s to its initial speed after one second, ending in a final speed of 20 + 9.8 = 29.8 m/s (approx. 30 m/s).

Meters and seconds are the two units of measurement required to describe speed. These units are used to calculate the distance travelled by an item as well as the time it takes to traverse that distance. In this scenario, the ball's speed is measured in metres per second (m/s), which is the distance the ball travels in one second.

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Main Answer:

(a)The natural coefficient of variation is approximately 75%.

(b)The coefficient of variation of the job of 60 panels is approximately 83.33%.

(c)The effective mean of the process time for a job of 60.

Supporting Question and Answer:

How do you calculate the mean and variance of a job with multiple panels when the times remain independent?

The mean of a job with multiple panels is obtained by multiplying the mean of a single panel by the number of panels. The variance of a job with multiple panels is equal to the variance of a single panel multiplied by the number of panels, assuming independence.

Body of the Solution:

(a) The natural coefficient of variation (CV) can be calculated by dividing the standard deviation by the mean and multiplying by 100 to express it as a percentage.

Given:

Mean = 2 minutes

Standard Deviation = 1.5 minutes

CV = (Standard Deviation / Mean) * 100

CV = (1.5 / 2) * 100

CV ≈ 75%

Therefore, the natural coefficient of variation is approximately 75%.

(b) If the times remain independent, the mean of a job of 60 panels can be calculated by multiplying the mean time for a single panel by the number of panels in the job.

Mean of a job of 60 panels = Mean of a single panel * Number of panels Mean of a job of 60 panels = 2 minutes * 60 Mean of a job of 60 panels = 120 minutes

The variance of a job of 60 panels is equal to the variance of a single panel multiplied by the number of panels, assuming independence.

Variance of a job of 60 panels = Variance of a single panel * Number of panels

Variance of a job of 60 panels = (Standard Deviation of a single panel)^2 * Number of panels

Variance of a job of 60 panels = (1.5 minutes)^2 * 60

Variance of a job of 60 panels = 2.25 minutes^2 * 60

Variance of a job of 60 panels = 135 minutes^2

The coefficient of variation (CV) of a job of 60 panels can be calculated by dividing the standard deviation of the job by the mean of the job and multiplying by 100.

CV = (Standard Deviation of the job / Mean of the job) * 100 CV = (sqrt(Variance of the job) / Mean of the job) * 100 CV = (sqrt(135 minutes^2) / 120 minutes) * 100 CV ≈ 83.33%

Therefore, the coefficient of variation of the job of 60 panels is approximately 83.33%.

(c) Given that the times to failure on the expose machine are exponentially distributed with a mean of 60 hours and the repair time is also exponentially distributed with a mean of 2 hours, we need to consider the effective mean and coefficient of variation (CV) for the process time of a job of 60 panels.

For exponential distributions, the mean (μ) is equal to the reciprocal of the rate parameter (λ), and the variance (σ^2) is equal to the reciprocal of the squared rate parameter (λ^2).

Mean time for a job of 60 panels = Mean of a single panel * Number of panels Mean time for a job of 60 panels = 2 minutes * 60 Mean time for a job of 60 panels = 120minutes.

Mean time for a job of 60 panels with exponential distributions = Mean time for a job of 60 panels / 60 (to convert minutes to hours) Mean time for a job of 60 panels with exponential distributions = 120 minutes / 60 Mean time for a job of 60 panels with exponential distributions = 2 hours

To calculate the effective mean, we add the mean time for the job (process time) and the mean repair time:

Effective Mean = Mean time for a job of 60 panels with exponential distributions + Mean repair time

Effective Mean = 2 hours + 2 hours

Effective Mean = 4 hours

To calculate the effective coefficient of variation (CV) for exponential distributions, it remains the same as the natural coefficient of variation.

Therefore, the effective mean of the process time for a job of 60.

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5. 45°

6. 61°

7. 33°

8. 108°

9. 98°

10. 82°

11. 52°

12. 142°

13. 36°

14. 64°

The equation required to modelled sound waves is given by y₁ + y₂ = 40 sin 3x cos θ.

Equations used to modelled sound waves are,

y₁= 20 sin (3x + θ)

A waves travelling in the opposite direction are,

y₂ = 20 sin (3x - θ)

To show that y₁ + y₂ = 40 sin 3x cos θ,

Simply substitute the given expressions for y₁ and y₂ and simplify using trigonometric identities.

sin A + sinB = 2 sin  [(A + B)/2] cos [(A - B)/2].

y₁ + y₂ = 20 sin (3x + θ) + 20 sin (3x - θ)

⇒y₁ + y₂ = 20 ( sin (3x + θ) + sin (3x - θ) )

Using the identity for the sum of two sines, simplify this expression,

⇒y₁ + y₂ = 2 ×20 × sin (3x + θ + 3x -  θ)/2 cos (3x + θ - 3x + θ)/2

⇒ y₁ + y₂ = 2 ×20 × sin (3x) cos (θ)

⇒ y₁ + y₂ = 40 sin (3x) cos (θ)

Therefore, for the sound waves y₁ + y₂ = 40 sin 3x cos θ, as required.

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The above question is incomplete, the complete question is:

Sound waves can be modeled by the equations of the form y₁= 20 sin (3x + θ). a wave traveling in the opposite direction can be modeled by y₂ = 20 sin (3x - θ). show that y₁ + y₂ = 40 sin 3x cos θ.

Answer:

.17 i think

Step-by-step explanation:

i honeslty dont know

Answer:

Step-by-step explanation:

Answer:

The tax is 0.82

Step-by-step explanation:

If you take 11.75 and add 0.7 you'll get 12.57. Then you do 12.57-11.75 which is 0.82.

Answer:

The tax is $0.82

Step-by-step explanation:

11.75x.07=.82

Answer:

In D=(−∞,−3]∪[3,+∞), the range of x→x2−9 is [0,+∞).

Step-by-step explanation:

The probability that 2 out of 10 call center representatives will be rated as unsatisfactory is approximately 0.002853, or 0.2853%.

To find the probability that 2 out of 10 call center representatives will be rated as unsatisfactory, we can use the binomial probability formula.

The formula is:
P(X=k) = (n C k) * p^k * (1-p)^(n-k)

Where:
P(X=k) is the probability of getting exactly k successes in n trials
n is the number of trials (sample size), which is 10 in this case
k is the number of successes (call center representatives rated as unsatisfactory), which is 2 in this case
p is the probability of success (call center representatives rated as unsatisfactory), which is 5% or 0.05

Using this information, we can calculate the probability as follows:

P(X=2) = (10 C 2) * 0.05^2 * (1-0.05)^(10-2)

Calculating this equation gives us:

P(X=2) = (10 C 2) * 0.05^2 * 0.95^8

The combination formula (10 C 2) can be calculated as:

(10 C 2) = 10! / (2! * (10-2)!)

Simplifying further:

(10 C 2) = 10! / (2! * 8!)

Calculating 10! and 8! gives us:

(10 C 2) = 10 * 9 / (2 * 1)

Simplifying:

(10 C 2) = 45

Substituting the values back into the equation:

P(X=2) = 45 * 0.05^2 * 0.95^8

Calculating this equation gives us:

P(X=2) = 0.002853

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The perimeter when x=41mm is equal to 284mm.

What is meant by perimeter?

The perimeter of a form is the space surrounding its edge. The perimeter of various shapes can be calculated by adding the side lengths.

Given that area of the square is

Dimension of the square is in the form ax-b

Which means that the side length of the square is ax-b.

Therefore square of the side length is equal to the Area of the square.

\((ax-b)^{2} =4x^{2} -44x+121\\a^{2} x^{2} -2abx+b^{2} = 4x^{2} -44x+121\\\)

Compare the similar terms on both sides.

\(a^{2}=4\\b^{2} =121\)

Therefore a= 2, b= 11.

Now, the dimension of the square is 2x-11.

When x=41, dimension is 2*41-11= 71.

Therefore perimeter of the square is equal to 4*71= 284mm.

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The perimeter when x=41mm is equal to 284mm.

What is meant by perimeter?

The perimeter of a form is the space surrounding its edge. The perimeter of various shapes can be calculated by adding the side lengths.

Given that area of the square is

Dimension of the square is in the form ax-b

Which means that the side length of the square is ax-b.

Therefore square of the side length is equal to the Area of the square.

\((ax-b)^{2} =4x^{2} -44x+121\\a^{2} x^{2} -2abx+b^{2} = 4x^{2} -44x+121\\\)

Compare the similar terms on both sides.

\(a^{2}=4\\b^{2} =121\)

Therefore a= 2, b= 11.

Now, the dimension of the square is 2x-11.

When x=41, dimension is 2*41-11= 71.

Therefore perimeter of the square is equal to 4*71= 284mm.

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wait nvm

one candy bar costs 0.60 cents

multiply this number by 2 and get $1.20

Answer:

x=-5

Step-by-step explanation:

-4x+26≥6

-4x+26-6≥6-6

-4x+20≥0

-4x+20-20≥0-20

-4x≥20

-4x\4≤20/_4

x≤-5

The height of each bar in a histogram represents the frequency (or relative frequency) of the data within that interval.

in a histogram, the data is divided into intervals or bins, which are marked off along the horizontal axis. The height of each bar represents the number of data points (or the percentage of data points, if relative frequency is used) that fall within that interval. The area of each bar is proportional to the frequency of the data within that interval. The histogram is used to display the distribution of a continuous variable and to show the distribution of the data over a certain range. It is useful for identifying patterns and outliers in the data and comparing different sets of data.

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The standard normal distribution  becomes smaller.

What is standard deviation?

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

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Answer:

Angle 8

Step-by-step explanation:

Angles 7 and 8 are supplementary because they are both on a straight line.
A straight line is 180*, and the line that forms the angles 7 and 8 splits 180* into those degrees in the angles, so both of those angles add to 180* which makes them supplementary.

Answer: The answer is A, y-intercept.

Step-by-step explanation:

Virtual reality has had the most significant impact on de la Pena's journalism career due to its ability to provide a more immersive and engaging news experience and its potential to reach a wider audience.

The question is about the future of news and the impact of virtual reality on de la Pena's journalism career.

In terms of the most significant impact on de la Pena's career, it can be argued that virtual reality has had the most significant impact. This is because virtual reality has revolutionized the way news is presented and consumed.

Virtual reality allows journalists like de la Pena to immerse their audience in a story by providing a more immersive and engaging experience. By using virtual reality, de la Pena has been able to create powerful and impactful stories that allow the audience to experience events and situations firsthand. This has the potential to create a deeper understanding and empathy among viewers.

Furthermore, virtual reality has also expanded the reach of journalism by allowing audiences from different parts of the world to experience stories that they wouldn't have been able to otherwise. This has the potential to foster a more global perspective and increase awareness of important issues.

Overall, virtual reality has had the most significant impact on de la Pena's journalism career due to its ability to provide a more immersive and engaging news experience and its potential to reach a wider audience.

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Answer:

32.4

Step-by-step explanation:

8% of 30 is 2.4. So, 2.4 + 30 is 32.4.

Answer:

Fourty.

Step-by-step explanation:

8+4x8

Answer:

40

Step-by-step explanation:

If you do 8*4 that equals 32 then just add 8 your welcome :)

Social scientists gather data from samples instead of populations because c. populations are often too large to test.

Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.

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Answer:

Carl Friedrich Gauss hope this helps.

The first name of the mathematician who developed Gauss's law is Carl Friedrich. Gauss's law is just one of the many examples of his genius, and it remains an essential tool for physicists and engineers to this day.

Carl Friedrich Gauss was a German mathematician and physicist who lived from 1777 to 1855. He is best known for his work in mathematics, particularly in the field of number theory, but he also made significant contributions to physics. Gauss's law, named after him, is a fundamental law of electromagnetism that relates electric charge to the electric field it creates.

Carl Friedrich Gauss was one of the most influential mathematicians of all time. He made significant contributions to many areas of mathematics, including number theory, geometry, and statistics. Gauss's law is one of his most important contributions to physics. It states that the total electric flux through any closed surface is proportional to the total electric charge enclosed within that surface. Gauss's law is a fundamental principle of electromagnetism, and it is used to calculate the electric field due to a distribution of charges. The law was first published by Gauss in 1835, and it has been a cornerstone of physics ever since.

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Answer:

EL/EF

OS/OJ

Step-by-step explanation:

Tangent is equal to opposite/adjacent