use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the y-axis.
y = 5/x,y = 0, x1 = 2, x2 = 7
v = ____
Sketch the region and a typical shell. (Do this on paper. Your instructor may ask you to turn in this sketch.)

a. The null hypothesis (H0) would state that the mean recall of ad information for children who receive an audiovisual presentation is equal to the mean recall.

a.The alternative hypothesis (Ha) would state that the mean recall of ad information differs between the two groups.

b. To find the test statistic, we can use the two-sample t-test formula:

t = (x1_bar - x2_bar) / sqrt((s1^2/n1) + (s2^2/n2))

Substituting the given values:

t = (3.70 - 3.30) / sqrt((1.98^2/20) + (2.13^2/20))

c. The rejection region for a significance level of α = 0.10 in a two-tailed test can be determined using a t-table or a t-distribution calculator. Since the alternative hypothesis is two-tailed, we need to split α equally between the two tails. In this case, the rejection region would be t < -1.734 or t > 1.734.

d. Based on the test statistic value calculated in part (b), we can compare it to the rejection region. If the test statistic falls within the rejection region, we reject the null hypothesis. If it falls outside the rejection region, we fail to reject the null hypothesis. In this case, we would fail to reject the null hypothesis since the test statistic does not fall within the rejection region. Therefore, we cannot conclude that the mean recall of ad information differs between the two groups, supporting the researchers' theory.

e. The p-value is a measure of the strength of evidence against the null hypothesis. In this case, the researchers reported a p-value of 0.62. Since this p-value is greater than the significance level of α = 0.10, it indicates that the observed data is likely to occur by chance alone assuming the null hypothesis is true. Therefore, we fail to reject the null hypothesis and cannot conclude that there is a significant difference in the mean recall of ad information between the two groups.

f. For the inference to be valid, certain conditions must be met. These conditions include random sampling, independence between observations, approximately normal distributions of the populations or large sample sizes, and equal variances between the groups. Without information about the sampling method and data characteristics, we cannot determine if these conditions were met. It is important to note that if the conditions for inference are not met, the validity and reliability of the test results may be compromised.

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Answer:

F(x)=h(x)-8

I think

Step-by-step explanation:

On the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.

The function f(x) = sin(x) is a periodic function with a period of 2π. Within one period, the function oscillates between the values of -1 and 1. The maximum value of sin(x) is 1, and it occurs when the angle x is π/2.

In the given interval [0, 2π), the function f(x) = sin(x) completes one full period. Starting from x = 0, the function increases and reaches its maximum value of 1 at x = π/2. After that, it starts decreasing and goes through one complete cycle by the time it reaches x = 2π.

Therefore, on the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.

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Answer:

81

Step-by-step explanation:

81

Answer:

6+3=9x9=81 final answer 81.

Step-by-step explanation:

Answer:

I believe its 10 but forgive me if I'm wrong

Answer:

45 degree

Step-by-step explanation:

The value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]

From the given diagram, we have the following

The required angle is x

Using the SOH CAH TOA identity

[tex]cos \theta =\frac{adj}{hyp}\\ cos \theta =\frac{14}{13}\\ \theta = arccos(\frac{14}{13} )[/tex]

Hence the value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]

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Answer:

I got 1.75 too

Step-by-step explanation:

20/3.5 is 5.7

10/5.7 is 1.75

The rectangular billboard is 1.75 inches tall in the scale model.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the ratio between the dimensions of the new and old shapes.

Given that, a rectangular billboard for a high school is 10 feet high and 20 feet long.

In a scale model of the school, the billboard is 3.5 inches long.

So, the scale factor = 3.5/20

= 0.175 inches

Thus, the height is 10×0.175

= 1.75 inches

Therefore, the rectangular billboard is 1.75 inches tall in the scale model.

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Answer: 98

Step-by-step explanation: According to the corresponding angles theorem m<1=82. Then according to the linear supplements theorem m<2=98. Hope this helps!

Answer:

98°

Step-by-step explanation:

Angle 1 also measures 82° because it is a corresponding angle to the given angle. Angles 1 and 2 are supplementary and therefore must add up to 180°.

Answer:

-3.5

all u have to do is get the 2 and the 7 and just subtract and the 8 and 10

Answer:

it is wrong

Step-by-step explanation:

the reason it is wrong is because I said so

Answer:

I am going to say no BECAUSE there are two y values, on the same point. For it to be linear it should only have one point per value. I think... good luck.

Answer:

1,512

Step-by-step explanation:

36x42

Answer:

72

Step-by-step explanation:

Answer:

72 units

Step-by-step explanation:

The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex] in a right triangle when a and b are the two legs and c is the hypotenuse (the longest side).

[tex]a^2+b^2=c^2[/tex]

In the diagram, 30 measures one of the legs and 78 measures the hypotenuse. Plug these in as a and c.

[tex]30^2+b^2=78^2\\900+b^2=6084[/tex]

Subtract 900 from both sides

[tex]900+b^2-900=6084-900\\b^2=5184[/tex]

Take the square root of both sides

[tex]900+b^2-900=6084-900\\\sqrt{b^2} =\sqrt{5184}\\b=72[/tex]

Therefore, the length of the missing side is 72 units.

I hope this helps!

Answer:

45

Step-by-step explanation:

3 out of 12 is 1/4, or 0.25, so if you divide 180 by 4, then using the same logic, you can expect 45 kids to have played last year.

3 = 1/4 OR .25 of 12, 12 divided by 4 = 3

180 divided by 4 = 45

Answer:

yes its 45 i did the test and i got an 100

Step-by-step explanation:

heres proof

Step-by-step explanation:

From the table, let's extract a set of data.

let's take x = 3, y = -9.

Let's substitute x into each of the equation to check.

A.

[tex]y = \frac{x}{ - 3} \\ y = \frac{3}{ - 3} \\ = - 1[/tex]

From here we can see the calculated y is not equal to the y in the table, therefore this cannot be the answer.

B.

[tex]y = x \\ y = - 3[/tex]

From here we also can see the calculated y is not equal to the y in the table, therefore this also cannot be the answer.

C.

[tex]y = 3x \\ = 3( - 3) \\ = - 9[/tex]

From here we can see the calculated y is equal to the y in the table , therefore this is the answer.

D.

[tex]y = - 3x \\ = - 3( - 3) \\ = 9[/tex]

From here we can see the calculated y is not equal to the y in the table, therefore this is not the answer.

Answer:

5a - 3

Step-by-step explanation:

3a + 2a = 5a

1 - 4 = -3

5a + (-3) or 5a - 3

Answer:

(x1, y1) = (1, 3)

(x2, y2) = (4, 12)

Step-by-step explanation:

y= x^2 - 4

y= 5x - 8

(substitute the value for y)

x^2 - 4 = 5x - 8

(solve the equation)

x = 1

x = 4

(substitute the values)

y = 5 × 1 - 8

y = 5 × 4 - 8

(solve the equations)

y = -3

y = 12

( the possible solutions are)

x1, y1 = 1, -3

x2, y2 = 4, 12

(check the solutions)

-3 = 1^2 - 4

-3 = 5 × 1 - 8

12 = 4^2 - 4

12 = 5 × 4 - 8

(simplify)

-3 = -3

-3 = -3

12 = 12

12 = 12

(the ordered pairs are the solutions)

The profit function if the cost and revenue is given  P(x) = -0.01x² + 3.2x - 150.

To find the profit function P(x), we subtract the cost function C(x) from the revenue function R(x). This gives us the expression for P(x) as P(x) = R(x) - C(x).

The profit function P(x) represents the difference between the revenue R(x) and the cost C(x). To find P(x), we subtract C(x) from R(x):

P(x) = R(x) - C(x)

Substituting the given expressions for R(x) and C(x), we have:

P(x) = (9x - 0.01x²) - (150 + 5.8x)

Simplifying this expression, we get:

P(x) = 9x - 0.01x² - 150 - 5.8x

Combining like terms, we have:

P(x) = -0.01x² + 3.2x - 150

Thus, the profit function is given by P(x) = -0.01x² + 3.2x - 150. This function represents the profit made as a function of the quantity of goods sold, x. It allows us to analyze the relationship between revenue, cost, and profit for different values of x.

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Answer:

5

Step-by-step explanation:

Answer:

50°

Step-by-step explanation:

We are to find m ∠2

And lines A and B are parallel

m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°

Hence,

m ∠2 = 50°

Therefore, m ∠2 = 50°

Answer:

546

Step-by-step explanation:

3 1/2 times 3 equals 10 1/2. 10 1/2 times 52 equals 546.

Answer:

7m and 49 m^2

Step-by-step explanation:

i am not sure on the second answer

Answer:

48

Step-by-step explanation:

Number of comedy = 6

Number of action = 4

Number of drama = 2

Selecting one of each ; total Number of possible combinations ;

nCr

Comedy = 6C1

Action = 4C1

Drama = 2C1

6C1 * 4C1 * 2C1 = 6 * 4 * 2 = 48

Answer:

[see below]

Step-by-step explanation:

[tex]5(2)=7\\\\10\neq 7[/tex]

No, (2, 7) is not the answer to the equation 5x = y.

[tex]5x=y\\\\5(2)=y\\\\\boxed{10=y}[/tex]

The value of y should be 10.

Hope this helps.

a. The mean of the data set is 6.3333, the median is 4.5, and there is no mode. b. The range of the data set is 9, and the variance is 11.8667.

a. To compute the mean, we sum up all the values in the data set and divide it by the number of data points. In this case, the sum is 4 + 9 + 10 + 4 + 3 + 12 = 42. Dividing this by 6 (the number of data points), we get a mean of 42/6 = 6.3333.

To compute the median, we arrange the data set in ascending order: 3, 4, 4, 9, 10, 12. Since the number of data points is even, we take the average of the middle two values, which are 4 and 9. The median is (4 + 9) / 2 = 4.5.

The mode is the value(s) that appear most frequently in the data set. In this case, none of the values are repeated, so there is no mode.

b. The range is the difference between the largest and smallest values in the data set. In this case, the largest value is 12 and the smallest value is 3, so the range is 12 - 3 = 9.

The variance measures the variability of the data set. It is calculated by taking the average of the squared differences between each data point and the mean. Using the formula for sample variance, the calculations are as follows:

[tex](4 - 6.3333)^2 + (9 - 6.3333)^2 + (10 - 6.3333)^2 + (4 - 6.3333)^2 + (3 - 6.3333)^2 + (12 - 6.3333)^2 = 71.2[/tex]

Dividing this sum by n-1 (where n is the number of data points) gives us the sample variance: 71.2 / 5 = 14.24.

Therefore, the variance is 14.24.

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Answer:

[tex] m\angle SXW =113\degree [/tex]

Step-by-step explanation:

In circle with center X, VS is diameter.

So [tex] \widehat {SWV} [/tex] is a semicircular arc.

[tex] \therefore m\widehat{SWV} = 180\degree [/tex]

[tex] \therefore (12x+7)\degree + (21x +8)\degree = 180\degree [/tex]

[tex] \therefore (33x+15)\degree = 180\degree [/tex]

[tex] \therefore 33x+15 = 180 [/tex]

[tex] \therefore 33x = 180-15 [/tex]

[tex] \therefore 33x = 165 [/tex]

[tex] \therefore x =\frac{165}{33} [/tex]

[tex] \therefore x =5 [/tex]

[tex] m\angle SXW =m\widehat{SW} [/tex]

(Measure of central angle is equal to the measure of its corresponding minor arc)

[tex] m\angle SXW =(21x + 8)\degree [/tex]

[tex] m\angle SXW =(21\times 5+ 8)\degree [/tex]

[tex] m\angle SXW =(105+ 8)\degree [/tex]

[tex] m\angle SXW =113\degree [/tex]

Answer:

104.8

Step-by-step explanation:

16 x 6.55 = 104.8

Answer:

104.8 millimeters

Step-by-step explanation:

16 x 6.55 = 104.8

Answer:

36%

Step-by-step explanation:

30/2500 x 30/2500=

900/2500=0.36

0.36*100=36%

Answer: 9π≈28.26 squared units

Step-by-step explanation: The distance between the two points, 3 units, is the radius. And then we use that to find the area by squaring and multiplying by pi.

The forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).

To find the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero, we need to find a vector [tex]F_3[/tex] that satisfies the equation

[tex]F_1 + F_2 + F_3 = 0.[/tex]

Given the forces:

[tex]F_1[/tex] = (10, 6, 3)

[tex]F_2[/tex] = (0, 4, 9)

We can rearrange the equation to solve for [tex]F_3[/tex]:

[tex]F_3 = -F_1 - F_2[/tex]

Now, let's calculate [tex]F_3[/tex]:

[tex]F_3[/tex] = -(10, 6, 3) - (0, 4, 9)

  = (-10, -6, -3) - (0, 4, 9)

  = (-10-0, -6-4, -3-9)

  = (-10, -10, -12)

Therefore, the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).

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