A random sample of high school students is used to estimate the mean time all high school students study for Geometry tests. A 95% confidence interval based on this sample is: 0.9 hours to 2.7 hours.
What is the sample mean ( )?

Answer:

x < 6.5

Step-by-step explanation:

3(2x - 7) < 4x - 8

6x - 21 < 4x - 8

6x - 4x < -8 + 21

2x < 13

x < 6.5

TheThe general solution to the wave equation utt = 4 (uxx + Uyy) is given by the D’Alembert’s formula. Therefore, the solution to the given problem is obtained by finding the specific form of the initial conditions u (x, y, 0) = f (x, y) and ut (x, y, 0) = g (x, y) and then use these values to find u (x, y, t) using the D’Alembert’s formula.

Let us find the form of the wave u(x,y,t) that satisfies the wave equation utt = 4 (uxx + Uyy) given the initial displacement f(x,y) = -3sin(5x)sin(6y) + 11sin(6x)sin(9y) and g(x,y) = 0.

Solution:
The D’Alembert’s formula for the wave equation is given by:

`u(x,y,t) = (1/2) [f(x+ct,y) + f(x-ct,y)] + (1/(2c)) ∫_((x-ct))^(x+ct)∫_((y-c(t-s)))^(y+c(t-s)) g(s,r) dr ds`

where c is the speed of the wave. Comparing with the wave equation `utt = c^2(uxx + uyy)` we have `c = 2`

Therefore, the solution to the wave equation is given by:

`u(x,y,t) = (1/2) [-3sin(5(x+2t))sin(6y) -3sin(5(x-2t))sin(6y) +11sin(6(x+2t))sin(9y) +11sin(6(x-2t))sin(9y)]`

Hence, the solution is:

`u(x,y,t) = (1/2) [-3sin(5(x+2t))sin(6y) -3sin(5(x-2t))sin(6y) +11sin(6(x+2t))sin(9y) +11sin(6(x-2t))sin(9y)]`

So, this is the required solution.

71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

We need to find out the sample size of citizens that should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

The formula for the Margin of error is

E: E = Zc/2 * (σ/√n)

Where E is the margin of error Zc/2 is the Z-value for the level of confidence cσ is the population standard deviation is the sample size.

So the formula for the sample size n is: n = (Zc/2 / E)² * σ²

We have Zc/2 = Z0.02/2 = Z0.01 = 2.33 (using z-table) σ = 22 years

E = 3 years

n = (2.33 / 3)² * 22²

n ≈ 70.36 ≈ 71 (rounded up)

Therefore, 71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

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If the ship is travelling at a constant rate of 17 mph, the distance between the ship and San Francisco is changing at a rate of approximately 1 mile per hour. So, the rate of change is 1mph.

What is the concept of related rates?

The concept of related rates is a fundamental topic in calculus that deals with how the rates of change of different variables are related to each other. It involves analyzing how the rates of change of two or more related quantities are connected through their derivatives.

To solve this problem, we can use the concept of related rates. Let's assume that the cruise ship starts at point A, the port 3 miles directly south of San Francisco, and moves towards the west.

Let's denote the position of the cruise ship at a given time as point B. We are interested in finding the rate at which the distance between point B and San Francisco (let's call it point C) is changing.

We can create a right triangle with points A, B, and C, where the distance between A and C is the constant 3 miles. Let's call the distance between B and C as "x" (in miles).

We are given that the ship is traveling at a constant rate of 17 mph, which means its speed is 17 miles per hour.

To find how fast the distance between the ship and San Francisco is changing, we need to find dx/dt (the rate at which "x" is changing) when 1 hour has passed.

Using the Pythagorean theorem, we have:

[tex]x^2 + 3^2 = (distance\ traveled \ by\ the\ ship)^2[/tex]

Taking the derivative of both sides with respect to time (t):

2x(dx/dt) = 2(distance traveled by the ship)(speed of the ship)

Plugging in the given values:

2x(dx/dt) = 2(17 mph)

Simplifying:

x(dx/dt) = 17 mph

Now, we need to find x when 1 hour has passed. The ship is traveling at a constant speed of 17 mph for 1 hour, so the distance it travels is 17 miles.

Plugging in x = 17 and solving for dx/dt:

17(dx/dt) = 17 mph

dx/dt = 1 mph

Therefore, 1 hour after leaving port, the distance between the ship and San Francisco is changing at a rate of approximately 1 mile per hour.

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The mean amount of coffee to be dispensed should be set at μ + 0.0525 ounce, where μ represents the original mean amount of coffee. This ensures that the cup overfills only 4% of the time.

To determine the mean amount of coffee to be dispensed, we need to find the value that corresponds to the 96th percentile of the normal distribution. This value represents the amount of coffee that should not be exceeded 96% of the time.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to the 96th percentile is approximately 1.75.

Since the standard deviation is given as 0.03 ounce, we can set up the equation:

1.75 = (x - μ) / 0.03

Solving for x, the mean amount of coffee to be dispensed, we get:

x - μ = 1.75 * 0.03

x - μ = 0.0525

x = μ + 0.0525

Therefore, the mean amount of coffee to be dispensed should be set at μ + 0.0525 ounce to ensure that the cup overfills only 4% of the time.

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Answer:

$ 45,600

Step-by-step explanation:

The degree form for 3π/4 radians is 135°.The degree form for 3π/4 radians is 135°. To convert radians to degrees, we multiply the radian measure by the conversion factor of 180°/π.

In this case, we have (3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°. Therefore, 3π/4 radians is equivalent to 135° in the degree form.

To convert an angle from radians to degrees, we use the conversion factor of 180°/π. This conversion factor represents the relationship between a full circle (360°) and 2π radians.

In this case, we want to convert the angle 3π/4 radians to degrees. We multiply the radian measure (3π/4) by the conversion factor (180°/π):

(3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°

By canceling out the common factor of π and simplifying the expression, we find that 3π/4 radians is equal to 135°.

Therefore, the degree form of the angle 3π/4 radians is 135°.

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Answer:

[tex] cos^{-1}(cos\frac{ 7π}{6})=cos^{-1}(cos\frac{7*180}{6})[/tex]

[tex] cos^{-1}(cos{210})[/tex]

[tex] cos^{-}(cos(180+30))[/tex]

[since in third quadrant cos 30=-[tex] \frac{\sqrt{3}}{2}][/tex]

[tex] cos^{-}(- \frac{\sqrt{3}}{2})[/tex]

:150°or [tex] \frac{5π}{6}[/tex]

150°or [tex] \frac{5π}{6}[/tex]is a required answer.

Answer: 1.2 blocks

Step-by-step explanation:

Timothy walks 12 blocks in 10 minutes so it can be written as

12 blocks = 10 minutes

divide both sides by 10

1.2 blocks per minute

Answer:

NO

Step-by-step explanation:

From the graph attached,

Equation of the line parallel to x-axis is y = 3.

Since, the line is dotted line, equation will be an inequality (having sign of < or >)

Now shaded region is below the line so equation of the inequality will be,

y < 3

Any point below the dotted line will be the solution of the given inequality.

Therefore, blue dot on the dotted line represented by y = 3 will not be the solution of the inequality.

Answer is NO.

Answer:

$33,040

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

$30520

Step-by-step explanation:

Answer:

i think the answer would be A

Answer:

cubes have 6 numbers

3 odd, 3 even

Step-by-step explanation:

probablity=desiredoutcome/totalpossibleoutcomes

there are 6 total desired outcomes (3 on each cube)

total possible, there are 6*6 or 36 total possible outcomes

so 6/36 or 1/6 chance

Answer:

8%

Step-by-step explanation:

Answer:

295

Step-by-step explanation:

Answer:

295!

Step-by-step explanation:

72 - 12 = 60

48 x 60 = 2880

2880 - 225 = 2655

2655 / 9 = 295

Have you ever heard of PEMDAS? It is the order in which to solve equations like this one. Here's what it stands for:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

I hope this is helpful for future math equations similar to this one.

Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.

To determine how many boys Janice needs to be willing to ask in order to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance, we can use the concept of probability and the binomial distribution.

The probability of a random boy saying yes is 45%, which means the probability of a boy saying no is 55%. Let's assume Janice asks "n" boys.

The probability of at least one boy saying yes can be calculated using the complement rule. The complement of the event "at least one boy saying yes" is the event "all boys saying no."

The probability of all "n" boys saying no is (0.55)^n, as the probability of each boy saying no is 55%.

To find the number of boys Janice needs to ask to have a 99.7% chance of going, we want the complement probability (all boys saying no) to be 0.003. Therefore:

(0.55)^n ≤ 0.003

Taking the logarithm of both sides:

n * log(0.55) ≤ log(0.003)

Solving for "n":

n ≥ log(0.003) / log(0.55)

Using a calculator:

n ≥ 15.154

Since Janice can't ask a fraction of a boy, we need to round up the value of "n" to the nearest whole number.

Therefore, Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.

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Answer:

x = 49.5°

Step-by-step explanation:

∠ABC = 90°

∠CBD = 45%∠ABC

∠CBD = 0.45(90)

∠CBD = 40.5°

x = ∠ABC - ∠CBD

x = 90 - 40.5

x = 49.5°

Answer:

√89

Step-by-step explanation:

√(4+4)2+(0-5)2

√(8)2+(-5)2

√64+25

√89

I had this one before. I'm pretty sure it is 1.61

Answer:

1.61

Step-by-step explanation:

It just makes since.

Answer:

42.78cm2

Step-by-step explanation:

Area =100°/360 * 22/7 * 7^2

=42.78cm2

The integration is ∫∫(q · dS) = ∫[0 to √6] ∫[0 to √6] (-45y - 45z) dy dz.

The rate of heat flow inward across the cylindrical surface y² + z² = 6, 0 ≤ x ≤ 3 can be determined by calculating the flux of the heat vector field through the surface.

To find the rate of heat flow, we need to calculate the surface integral of the heat flux vector across the given cylindrical surface. The heat flux vector is given by q = -K∇u, where K is the conductivity and ∇u is the gradient of the temperature function u(x, y, z).

First, we find the gradient of u:

∇u = (∂u/∂x)i + (∂u/∂y)j + (∂u/∂z)k

= 0i + (6y)j + (6z)k

Then, we calculate the heat flux vector:

q = -K(∇u)

= -7.5(0i + (6y)j + (6z)k)

= -45yj - 45zk

Next, we calculate the surface area element vector, dS, of the cylindrical surface. Since the surface is defined by y² + z² = 6, we can parameterize it as r(y,z) = yi + zk. Taking the cross product of the partial derivatives, we obtain dS = (∂r/∂y) x (∂r/∂z) dy dz = (-j -k) dy dz.

Finally, we can calculate the surface integral by integrating the dot product of q and dS over the given cylindrical surface:

∫∫(q · dS) = ∫∫(-45yj - 45zk) · (-j -k) dy dz

To find the limits of integration, we note that the surface extends from y² + z² = 6 to the origin, which corresponds to 0 ≤ y² + z² ≤ 6. Since the surface is symmetric, we can integrate over a quarter of the surface, from y = 0 to y = √6 and z = 0 to z = √6.

Performing the integration, we get:

∫∫(q · dS) = ∫[0 to √6] ∫[0 to √6] (-45y - 45z) dy dz

Evaluating this double integral will give us the rate of heat flow inward across the cylindrical surface.

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Answer: 16.28?

Step-by-step explanation:

Answer:

y = 4x + 40

Step-by-step explanation:

At sunrise, 0 hours have passed, meaning x = 0.

When x = 0, the temperature is 40, meaning that 40 is the y-intercept.

And every x hours the temperature rises by 4 degrees F

Answer:

m = 4.7

Step-by-step explanation:

If you plug in these values in the slope formula, this is what happens:)

Answer:

47/10x

**Do not leave your answer as a decimal, slope is usually in fraction form**

Step-by-step explanation:

Slope Formula: [tex]\frac{\text{rise}}{\text{run}} / \frac{y_2 - y_1}{x_2 - x_1}[/tex] In this formula, subtract the 1st coordinate from the second. So, the 2nd y coordinate goes first, place a "minus" sign, and then the 2nd y-coordinate. This is the same for the x coordinates.

Finding the Answer: To find the answer, we just plug the numbers correctly into the equation, just as I explained above. We would do 55-8 first, which is 47, and then 12-2 which is 10.

Combined, the answer is 47/10x. You always place an x after the slope, which can be used to plug in other numbers. The answer cannot be simplified anymore, so this is simplfied.  

There is a significant relationship between y and both x1 and x2.

MSR = 306.625, MSE = 30.844b. F = 9.939 and p-value = 0.007. At a = 0.05, the overall model is significant.

tB₁ = 7.301 and p-value = 0.0009. At a = 0.05, there is a significant relationship between y and x1. d. tB₂ = 4.771 and p-value = 0.0008. At a = 0.05, there is a significant relationship between y and x2.

In a regression model, the F-test is used to determine whether the regression coefficient as a whole is statistically significant or not.

The p-value of the F-test is compared to the significance level (α) to determine statistical significance.

If the p-value is less than α, the regression coefficient as a whole is considered statistically significant. If it is greater than α, then it is not statistically significant.

t-test is used to determine whether each individual regression coefficient is statistically significant or not.

The p-value of the t-test is compared to the significance level (α) to determine statistical significance.

If the p-value is less than α, the regression coefficient is considered statistically significant.

If it is greater than α, then it is not statistically significant.

In this question, the F-test is significant at a = 0.05, and the t-test for both x1 and x2 is significant at a = 0.05.

Therefore, there is a significant relationship between y and both x1 and x2.

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Answer:

B. x=6

Step-by-step explanation:

substitute -7 into 2y to get -14. your new equation should be 4x-14=10. add 14 to both sides to get 4x=24, divide both sides by 4 to get x=6.

Answer:

B. 6

Step-by-step explanation:

y = -7

4x + 2(-7) = 10

4x + (-14) = 10

4x = 10 - (-14)

4x = 24

x = 6

Complete question :

An online store sold a gift basket at five different prices and recorded the number of gift baskets that were sold at each price. The results are shown in the scatterplot.

Which statement is correct based on the scatterplot?

There is no relationship between price and gift baskets sold because the points do not form a straight line.

There is no relationship between price and gift baskets sold because there are multiple prices at which 80 gift baskets were sold.

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold increases.

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Answer:

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Step-by-step explanation:

From the scatterplot provided, it could be observed thatbthere is a linear trend in the plot created. This shows that there is a relationship between the price of gifts and the number if gift basket sold.

Furthermore, the slope of the linear trend line that could be drawn from the plotted data is negative, A negative slope Indicates a negative relationship, that is an increase in x leads to corresponding decrease in y. He ce, as price increases the number sold decreases

Answer:

d and/ or the other dude

Step-by-step explanation:

The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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Answer:

area = 18.81 m²

Step-by-step explanation:

solving for the 7 sided polygon first:

divide into 7 equal isosceles triangles, each having sides of 10 m and a peak angle of 360°/7 = 51.43°. Drop a line from the peak & perpendicular to the base makes a right triangle with a 25.71° peak angle and a 10 m hypotenuse.

sin 25.71° = x/10, x = 4.34, the base of the full triangle will be 2 x 4.34 = 8.68 m

cos 25.71° = x/10, x = 9.01, the rise of the triangle is 9.01 m

The area of each triangle will be 1/2(8.68)(9.01) = 39.10 m²

39.10 x 7 triangles = 273.72 m²

area of 7 sided polygon = 273.72 m²

Next solve for the inner circle:

The rise of the triangle (9.01) is the radius of the inner circle.

area of inner circle = πr² = 3.14(9.01²) = 254.91 m²

273.72 - 254.91 = 18.81 m²