scores on a recent national statistics exam were normally distributed with a mean of 78 and a standard deviation of 9. (you may need to use the appropriate appendix table or technology to answer this question.) (a) what is the probability that a randomly selected exam will have a score of at least 71? (round your answer to four decimal places.) (b) what percentage of exams will have scores between 89 and 92? (round your answer to two decimal places.) % (c) if the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award? (round your answer to two decimal places.)

Answer:

0.857

Rounded: 0.86

Step-by-step explanation:

6/7 = 0.857

Answer:

See attached image!!

Step-by-step explanation:

a) We would expect it to land on green (1/5) x 300 = 60 times.

b) The probability of landing on purple is 24%.

c) We can expect it to land on blue (1/5) x 1000 = 200 times out of 1000 spins.

If the spinner is fair, we can expect it to land on each color with equal probability. Since there are 5 colors, we can expect it to land on green approximately 1/5 of the time. Therefore, we would expect it to land on green (1/5) x 300 = 60 times.

The probability of landing on purple can be estimated by dividing the number of times the arrow stops on purple by the total number of spins. From the given table, the arrow stopped on purple 72 times out of 300 spins. Therefore, the estimated probability of landing on purple is 72/300 = 0.24 or 24%.

Since the spinner is fair, we can expect it to land on each color with equal probability. From the given table, the arrow stopped on blue 45 times out of 300 spins. Therefore, we can expect it to land on blue (1/5) x 1000 = 200 times out of 1000 spins.

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--The complete question is, The spinner shown is spun 300 times.

a) How many times would you expect the arrow

to stop on green if the spinner is fair?

The table below shows the number of times

the arrow stops on each colour.

Blue 45

Red 37

Pink 52

Green 94

Purple 72

b) The spinner is spun once more.

Estimate the probability of landing on purple.

c) If the spinner is spun another 1000 times,

about how many times would you expect it to land on blue?--

Answer:

( x + 2 )² + ( y - 6 )² = 49

Step-by-step explanation:

→ Write the form of an equation of a circle

( x - a )² + ( y - b )² = r²

→ Substitute in the centre remembering to switch the signs

( x + 2 )² + ( y - 6 )² = r²

→ Substitute in radius

( x + 2 )² + ( y - 6 )² = 49

The percentage decrease is 19.4%

In contrast to being expressed as a fraction, a percentage is a portion of a total expressed as a number between 0 and 100. The percentages are as follows: 100% of everything, 0% of nothing, 50% of something, and 0% of nothing. Divide the component by the total, then multiply the result by 100 to get the percentage.

(Original Cost - New Cost) / Original Cost x 100 equals the percentage decrease.

In this case, the original cost is $36 and the new cost is $29, so we plug these values into the formula:

Percentage decrease = ($36 - $29) / $36 x 100 = $7 / $36 x 100 = 0.1944 x 100 = 19.44%

We can round the answer to the nearest tenth of a percent:

19.44% rounded to the nearest tenth is 19.4%

So the percentage decrease is 19.4%

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OC (x+1)(x-8)(4)=56 indicates that the volume of the box is 56 in³ because it takes into account the length of the sides after the four corners were cut off, and the height of the box which is 4 in. The equation can be written as (length of sides)(width of sides)(height) = volume.

A volume is a three-dimensional space that contains a specific amount of material, which is commonly measured in liters, cubic meters, or gallons. It is frequently used to calculate the capacity of containers like tanks, bottles, and barrels. Volume may also refer to the quantity of space occupied by an item, such as the volume of a room or the volume of a sphere.

In the given question, OC is the correct answer: (x+1)(x-8)(4)=56. This equation reveals that the volume of the box is 56 \(in^{3}\) because it considers the length of the sides after the four corners were taken off, which are (x+1) and (x-8), as well as the height of the box, which is 4 in. The formula is (length of sides)(width of sides)(height) Equals volume. As a result, the equation (x+1)(x-8)(4) = 56 reveals that the box's volume is 56 \(in^{3}\).

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m is 1/4

b is 2

As for Y I think its wants you to write out the problem so it would be Y=1/4x+2

It’s a personal challenge

Answer:

Step-by-step explanation:

A scientist is working with 12 meters of gold wire. How long is the wire in millimeters?

12 meters = 12000 mm

(1m = 1000 mm)

12 * 1000 = 12000

Answer:

the purchase price is $2.05

Step-by-step explanation:

The computation of the purchase price is shown below:

The purchase price is

= Cost of the sandwich - coupon amount

= $2.55 - $0.50

= $2.05

Hence, the purchase price is $2.05

Answer: 36,960 ft

Step-by-step explanation:

Each lap around the track was a mile in distance.

Petrov therefore ran a total of 7 miles.

A mile is 5,280 feet.

If Petrov ran 7 miles in total, this distance in feet is:

= 7 * 5,280

= 36,960 ft

Answer:

0.429

Step-by-step explanation:

3/7 is of course a fraction. But to do this calculation we will divide. 3/7 also means 3 ÷ 7

3 ÷ 7 is 0.42857142

Rounded to the nearest thousandth (three decimal places) it is .429

3/7 ~= 0.429

We are given the differential equation below:y"-2y' + y = cos 4t- sin 4t, y(0) = 4, y'(0) = 4 We have to find the Laplace transform of the solution y(t) of the above differential equation. We know that the Laplace transform is linear. Therefore we can take Laplace transform of each term of the differential equation separately.

We have:  L{y"} - 2L{y'} + L{y} = L{cos 4t} - L{sin 4t}Taking the Laplace transform of each term: (s²Y(s) - s*y(0) - y'(0)) - 2[sY(s) - y(0)] + Y(s) = (s/(s²+16)) - (4/(s²+16)) + (s/(s²+16)) + (4/(s²+16))Simplifying the above equation, we get: s²Y(s) - 4s + 4 - 2sY(s) + 2Y(s) = (2s/(s²+16))Y(s) + (8/(s²+16))Y(s) = (2s/(s²+16)) - (4/(s²+16)) + (4/(s²+16)) + (2s/(s²+16)).

Thus, we get: Y(s) = [(2s/(s²+16)) - (4/(s²+16)) + (4/(s²+16)) + (2s/(s²+16))] / [(s²-2s+1) + (2s/(s²+16))]Y(s) = [(4s/(s²+16))] / [(s-1)² + 4²] + 2/(s-1)This is the required solution to the given problem.In conclusion, we have obtained the Laplace transform of the solution to the initial value problem.

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A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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The problem involves finding the distance from a given point (12, 14, 1) to the y-z plane. The distance can be determined by finding the perpendicular distance from the point to the plane.

The equation of the y-z plane is x = 0, as it does not depend on the x-coordinate. We need to calculate the perpendicular distance between the point and the plane.

To find the distance from the point (12, 14, 1) to the y-z plane, we can use the formula for the distance between a point and a plane. The formula states that the distance d from a point (x₀, y₀, z₀) to a plane Ax + By + Cz + D = 0 is given by the formula:

d = |Ax₀ + By₀ + Cz₀ + D| / √(A² + B² + C²)

In this case, since the equation of the y-z plane is x = 0, the values of A, B, C, and D are 1, 0, 0, and 0 respectively. Substituting these values into the formula, we can calculate the distance from the point to the y-z plane.

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Answer:

25%

Step-by-step explanation:

Let's set up a percent proportion:

12/x = 48/100

To solve for x, we would do:

x = (12*100)/48 = 1200/48 = 25

x = 25%

In my opinion, the easiest way to do this would be to look at this and notice that 12 * 4 =48 so that means 12 is 1/4 of 48 and 1/4 = 25%.

Let me know if you have any questions.

Answer:

164 degrees

Step-by-step explanation:

The measure of the individual internal angle in a polygon is;

(n-2)180/n

n = 22

So we have;

(22-2)180/22

= (20 * 180)/22

= 163.64 degrees

To the nearest whole number, this is 164

Answer:

0.0625

Step-by-step explanation:

b. convergent Since the limit approaches infinity, the integral diverges. Therefore, the answer is convergent .

To determine the convergence of the integral [infinity] 39 ln(x) x dx, we can use the integral test. This test states that if f(x) is a continuous, positive, and decreasing function on [a, infinity), then the improper integral [a, infinity) f(x) dx converges if and only if the series sum from n=a to infinity of f(n) converges.

In this case, we have f(x) = 39 ln(x)/x, which is a continuous, positive, and decreasing function on [1, infinity). Thus, we can apply the integral test.

Let's evaluate the integral using integration by parts:

∫ 39 ln(x)/x dx = 39 ∫ ln(x) d(ln(x))
= 39 (ln(x))^2/2 + C

Now, we need to check whether the integral converges or diverges.

As x approaches infinity, ln(x) grows without bound, so (ln(x))^2 grows even faster. Thus, the integral is improper at infinity.

We can evaluate the limit as x approaches infinity of (ln(x))^2/2 to determine whether the integral converges or diverges:

lim (x → infinity) (ln(x))^2/2 = infinity

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Answer:

\(154cm^{2} \)

Step-by-step explanation:

The area of the triangle =

\(a = \frac{1}{2} \times base \times haight\)

The researcher will need 25 participants to obtain 20 measurements within each of the 25 conditions in this within-subject design.

To determine the number of participants needed for a within-subject design with 25 conditions and 20 measurements within each condition, we need to consider the concept of counterbalancing. Counterbalancing involves systematically varying the order of conditions across participants to account for potential order effects.

In this case, each participant will need to complete all 25 conditions, with 20 measurements within each condition. Therefore, we can calculate the total number of measurements per participant:

Total measurements per participant = Number of conditions × Number of measurements per condition

Total measurements per participant = 25 × 20

Total measurements per participant = 500

To determine the number of participants needed, we divide the total number of measurements by the number of measurements per participant:

Number of participants = Total measurements / Measurements per participant

Number of participants = 500 / 20

Number of participants = 25

Therefore, the researcher will need 25 participants to obtain 20 measurements within each of the 25 conditions in this within-subject design.

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The graph that has a slope that best represents the cost of each pencil at this store has a slope of 5

From the question, we have the following parameters that can be used in our computation:

The cost of 6 pencils at a store is 30 cents

Given that the pencils cost the same

The unit rate is

Unit rate = 30/6

Evaluate

Unit rate = 5

This represents the slope

Hence, the graph has a slope of 5

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Hey there! :)

Answer:

m∠A = 72°.

m<B = 108°.

Step-by-step explanation:

In a parallelogram, the opposite angles are congruent.

Therefore, we can set the two expressions equal to each other:

5y - 3 = 3y + 27

Add 3 to both sides:

5y = 3y + 30

Subtract 3y from both sides:

2y = 30

Divide both sides by 2:

y = 15

Substitute this value of y into an expression to solve for the measure of ∠A:

5(15) - 3 = 72°. m∠A = 72°.

In parallelograms, the neighboring angles are supplementary. Therefore:

m∠A + m∠B = 180°

72° + m∠B = 180°

m<B = 108°.

Answer:

Equation of line perpendicular to given graph is:

\(y = -\frac{1}{2}x+4\)

Step-by-step explanation:

Given equation of line is:

14x-7y=8

First of all, we have to convert the given equation into slope-intercept form to find the slope of the line

The slope-intercept form is:

\(y = mx+b\)

Now

\(14x-7y=8\\14x-8 = 7y\\\frac{7y}{7} = \frac{14x-8}{7}\\y = \frac{14}{7}x - \frac{8}{7}\\y = 2x - \frac{8}{7}\)

The co-efficient of x is 2 so the slope of given line is 2

Let m1 be the slope of line perpendicular to given line

The product of slopes of two perpendicular lines is -1

\(m.m_1 = -1\\2.m_1 = -1\\m_1 = -\frac{1}{2}\)

The equation for line perpendicular line to given line will be:

\(y = m_1x+b\\y = -\frac{1}{2}x+b\)

To find the value of b, putting (-2,5) in the equation

\(5 = -\frac{1}{2}(-2) + b\\5 = 1+b\\b = 5-1\\b = 4\)

The final equation is:

\(y = -\frac{1}{2}x+4\)

Hence,

Equation of line perpendicular to given graph is:

\(y = -\frac{1}{2}x+4\)

Answer:

It will take at least 45 cars

Step-by-step explanation:

so to start subtract 240 from 600

you get 360 then divide 8

this leaves you with 45

For n = 3, x = 9, and x = 2i, we can say that one of the factors is (x - 9) as well as (x - 2i).

(x - 2i) is derived from x² = -4 which is equal to (x² + 4). Therefore, the two factors are (x - 9) and (x² + 4). To get the polynomial function, let's multiply the two factors using FOIL Method.

The polynomial function of the first bullet is f(x) = x³ - 9x² + 4x - 36.

For n = 3, x = -1, and x = 4 + i, we can say that the factors are:

(x + 1) , (x - (4 + i)), and (x - (4 - i))

Note: Always remember those complex zeros like x = 4 + i come in conjugate pairs.

To solve the polynomial function, let's multiply the three factors.

The polynomial function of the second bullet is f(x) = x³ - 7x² + 9x + 17.

The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³

Given,

The constant rate at which helium is pumped into the spherical balloon, r = 5 ft.³/s

We have to find the rate at which the radius of the balloon is increasing after 2 minutes.

Here,

dV/dt = (dV/dr) × (dr/dt)

Then,

dr/dt = (dV/dt) / (dV/dr)

The volume of balloon after 2 minutes (120 seconds) V₁₂₀ ;

V₁₂₀  = 120 s × 5 ft.³/s = 600 ft.³

The radius of balloon after 2 minutes ;

V = 4/3 π r³

dV/dr = 4 π r²

r = \(\sqrt[2]{\frac{2}{4.\pi } V}\)

Then,

r₁₂₀ = \(\sqrt[2]{\frac{2}{4.\pi } 600}\) ≈ 9.77

dr/dt = (dV/dt) / (dV/dr) = 5 / 4π r²

At t = 2 minutes (120 seconds), r ≈ 9.77 feet

dr/dt ≈  5 / 4π 9.77² ≈ 4.16 × 10⁻³

That is,

The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³

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Answer:

There are 114 red marbles

Step-by-step explanation:

The ratio of red to black marbles is 19:1

19+1+20

20 units+120

1 unit= 120/20=6

19 units=120-6=114

There for you have 114 red marbles.

the answer to this question is $250