Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.

Answer:

[tex]\frac{10\pi}{3}[/tex]

Step-by-step explanation:

According to the information of the problem we have to compute the following integral.

[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA[/tex]

Where the region of integration is

[tex]R = \Big\{ (r,\theta) : 0 \leq r \leq 2 , \,\,\,\, \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \Big\}[/tex]

If you plot, that is just a circle between [tex]\pi/2[/tex]  and  [tex]3\pi/2[/tex], which is just half of the circle on the negative part of the plane.

When you switch coordinates

[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA = {\displaystyle \int\limits_{0}^{2} \int\limits_{\pi/2}^{3\pi/2}} \bigg(\frac{1}{3} + r \bigg)r \, d\theta\, dr = \frac{10\pi}{3}[/tex]

Answer:  the minute hand travel 39.6 cm

Step-by-step explanation:

Length of minute hand of a clock = 9 cm

Central angle made by the minute hand = 252°

To find: how far the minute hand travel

Therefore

Length of minute hand is equal to the radius of circle

As we know the circumference of a circle is given by

[tex]C= 2\pi r \dfrac{\theta}{360^\circ}[/tex] where C is circumference , r is radius and ∅ is the central angle  

So we have

[tex]C= 2 \times \dfrac{22}{7} \times 9 \times \dfrac{252^\circ}{360^\circ} \\\\\Rightarrow C= 2 \times \dfrac{22}{7} \times \dfrac{252^\circ}{40^\circ} \\\\\Rightarrow C= \dfrac{11}{7} \times \dfrac{252^\circ}{10^\circ} = 39.6[/tex]

Hence, the minute hand travel 39.6 cm in 42 minute period

Final answer:

The minute hand of the clock, which measures 9 centimeters in radius, travels approximately 39.3 centimeters along the arc when it moves through a 252-degree central angle in a 42-minute period.

Explanation:

To determine how far the minute hand of a clock travels in a 42-minute period, we need to calculate the arc length, which is a portion of the circumference of the circle traced by the minute hand's tip. We are given that the minute hand is 9 centimeters long, meaning it is the radius of the circle, and it travels through an arc of 252° during a period of 42 minutes.

The formula to calculate the arc length is:

ℓ = θ/360 × 2πr

Where:

ℓ is the arc length

θ is the central angle in degrees

r is the radius of the circle

In this case:

θ = 252°

r = 9 cm

Now, let's substitute these values into the formula:

ℓ = 252/360 × 2 × π × 9

ℓ ≈ 0.7 × 2 × 3.14159 × 9

ℓ ≈ 39.27 cm

So, to the nearest tenth of a centimeter, the minute hand travels approximately 39.3 cm during a 42-minute period.

Answer:

x=-3(y-5)

Step-by-step explanation:

The expressions that are solutions to the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C

as  [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution and  [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.

Let's solve the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] and then check each expression to see if it is a solution:

1. Solve the equation:

[tex]\[ x = \frac{15}{\frac{3}{4}} \][/tex]

  To divide by a fraction, we can multiply by its reciprocal:

[tex]\[ x = 15 \times \frac{4}{3} = 20 \][/tex]

Now, let's check each expression:

A. [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution.

B. [tex]\( \frac{15}{\frac{4}{3}} \)[/tex] - This expression is equivalent to [tex]\( \frac{15 \times 3}{4} = \frac{45}{4} \)[/tex], not equal to 20.

C. [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.

D. [tex]\( \frac{3}{4} \times 15 = 11.25 \)[/tex] - This is not equal to 20.

E. [tex]\( \frac{15}{\frac{3}{4}} \)[/tex] - This is equivalent to expression A, which is a solution.

Therefore, the expressions that are solutions to the equation[tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C.

Complete Question: Which expressions are solutions to the equation 3/4 x=15 ? Select all that apply.

A. frac 15 3/4

B. frac 15 4/3

C. 4/3 · 15

D. 3/4 · 15

E. 15/ 3/4

Answer:

the fourth one

Step-by-step explanation:

Answer:

Answer: f(x) = 500(2)^x

Step-by-step explanation:

Just took the test .

Here is your answer! uwu

Answer:D

Step-by-step explanation:

(5x9)^12

5^12 x 9^12

Answer:

Kelly walks 4/5 of a mile each day.

After 3 days, Kelly walks a distance: D = 3 x 4/5 = 12/5 = 2.4 miles

Hope this helps!

:)

Kelly walks 4/5 of a mile each day, and after three days, she would have walked 2 and 2/5 miles.

Kelly walks 4/5 of a mile each day. To find out how many miles Kelly walks after three days, we simply multiply the daily distance by three.

Calculation:
4/5 mile/day * 3 days = 12/5 miles

To convert 12/5 miles into a mixed number, we divide 12 by 5. The quotient is 2 with a remainder of 2, so Kelly walks 2 and 2/5 miles after three days.

Answer:

C. (3, 7)

Step-by-step explanation:

plug all the numbers into all of the coordinates and (3, 7) is the lowest number :) pls rate 5 stars and thank me

The option of buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business, based on the objective function C = 5x + 3y and the given constraints of at least 10 boxes in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.

To minimize the cost of buying office supplies, particularly red and black pens, we need to use the given objective function C = 5x + 3y where x represents the number of boxes of red pens and y represents the number of boxes of black pens. We have the following constraints: at least 10 boxes of pens in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.

By applying these constraints, we can determine the combinations of x and y that meet the criteria:

Looking at the choices provided, (6, 4) meets all our constraints, and when plugged into the objective function:

C = 5(6) + 3(4) = 30 + 12 = $42

This results in the lowest cost when compared to the other presented options. Therefore, buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business.

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A score of 120 is one standard deviation below the mean of 150 on a test with a standard deviation of 30.

The score that is 1 standard deviation below the mean is found by subtracting the standard deviation from the mean. In the context of this normal distribution of test scores, with a mean of 150 and a standard deviation of 30, we calculate the score one standard deviation below the mean as follows:

Score = Mean – Standard Deviation = 150 – 30 = 120

This calculation indicates that a score of 120 is one standard deviation below the mean on this test.

The total surface area that she paints will be 96 square feet. Thus, the correct option is C.

Let W be the rectangle's width and L its length. The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be given as,

Area of the rectangle = L × W square units

Given that:

Length, L = 12 ft

Width, W = 8 ft

The area of the rectangle is given as,

A = 12 x 8

A = 96 square feet

Thus, the correct option is C.

More about the area of the rectangle link is given below.

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The missing diagram is given below.

Answer:

A

Step-by-step explanation:

Plate X will result in the lightest place since it's density and thickness both are less.

Answer:

a) 471.5 kilo-watt hours.

b) 31.76 kilo-watt hours

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the population:

Mean 471.5 kilo-watt hours.

Standard deviation of 187.9 kilowatt-hours.

For the sample:

Sample size of 35, by the Central Limit Theorem:

a) Mean

471.5 kilo-watt hours.

b) Standard deviation

[tex]s = \frac{187.9}{\sqrt{35}} = 31.76[/tex]

31.76 kilo-watt hours

Final answer:

The mean of the sampling distribution of sample means is 471.5 kilo-watt hours, and the standard deviation (or standard error) of the sampling distribution, rounded to the third decimal place, is 31.749 kilo-watt hours.

Explanation:

The question concerns the concept of sampling distribution and its parameters, namely the mean and standard deviation, within the field of statistics. Given that the per capita electric power consumption level in Ecuador is normally distributed with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilo-watt hours, and considering samples of size 35, we are to find the mean and standard deviation of the sampling distribution of sample means.

(a) The mean of the sampling distribution of sample means is equal to the population mean. Therefore, the mean is:

471.5 kilo-watt hours

(b) The standard deviation of the sampling distribution of sample means, also known as the standard error (SE), is calculated using the following formula:

SE = σ / √n

where σ is the population standard deviation and n is the sample size. In this case:

SE = 187.9 / √35 ≈ 31.749 kilo-watt hours (rounded to the third decimal place)

The value of x makes the equation true is -16. Therefore, option A is the correct answer.

The given equation is x+7=-9.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solved as follows:

x+7=-9

Transpose 7 to RHS of the equation, we get

x=-9-7

=-16

The value of x makes the equation true is -16. Therefore, option A is the correct answer.

To learn more about an equation visit:

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Answer:

This is an example of placebo testing.

Step-by-step explanation:

This is an example of placebo testing in which, the two groups are given two substances that are said to have an effect on the condition that is being treated but one of them is the actual medicine that is being tested while the other one has no real effect over the medical condition. But the volunteers are not given information on which of the medicines is real and which is not, so that this does not affect the outcome of the experiment.

I hope this answer helps.

Answer:

lateral surface area = 48 inches²

Step-by-step explanation:

The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.

area of a triangle = 1/2 × b × h

The slant height of the triangle is gotten using Pythagoras theorem

lateral surface area = 4 × (1/2 ×  3 × 8)

lateral surface area = 4 × 24/2

lateral surface area = 4 × 12

lateral surface area = 48 inches²

Answer:

48 in

Step-by-step explanation:

<3 hoped this helped <3

Answer:

The probability that she will not pull lipstick is 71%.

Step-by-step explanation:

The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.

[tex]P(E)=\frac{n(E)}{N}[/tex]

Here,

n (E) = favorable number of outcomes

N = total number of outcomes

The contents in Mrs. Braddock's bag are:

Number of lipsticks = n (L) = 6

Number of eye shadows = n (S) = 4

Number of eye liners = n (E) = 6

Number of mascaras = n (M) = 5

Total number of items in the bag = N = 21

Consider that the probability of an event occurring is P. Then the probability of the given event not taking place is known as the complement of that event.

Complement of the given event is, 1 – P.

Compute the probability of selecting a lipstick as follows:

[tex]P(L)=\frac{n(L)}{N}\\\\=\frac{6}{21}\\\\=\frac{2}{7}[/tex]

Compute the  probability of not selecting a lipstick as follows:

[tex]P(L^{c})=1-P(L)[/tex]

          [tex]=1-\frac{2}{7}\\\\=\frac{7-2}{7}\\\\=\frac{5}{7}[/tex]

Convert this probability into percentage as follows:

[tex]\frac{5}{7}\times 100 = 71.4286\approx 71\%[/tex]

Thus, the probability that she will not pull lipstick is 71%.

Answer:

We have two relations

2*x*y = 6 (2 times x times y is equal to six)

x - y = 3  ( the difference between x and y is trhe)

Where whe have two variables, x and y.

To solve this system, the first step is isolation one of the variables in one of the equations, let's isolate x in the second equation.

x - y = 3

x = 3 + y

now we can replace this in the other equation and then solve it for y.

2*x*y = 6

2*(3 + y)*y = 6

6y + 2y^2 = 6

now we have the quadratic equation:

2y^2 + 6y - 6 = 0

the solutions are:

[tex]y = \frac{-6 + -\sqrt{6^2 - 4*2*(-6)} }{2*2} = \frac{-6 +- 9.2}{4}[/tex]

the solutions are:

y = (-6 + 9,2)/4 = 0.8

y = (-6 - 9.2)/4 = -3.8

if y = 0.8, then:

x = 3 + y = 3.8

if y = -3.8

x = 3 + y = 3 - 3.8 = -0.8

so we have two possible solutions:

(-0.8, -3.8) and (3.8, 0.8)

Answer:

t ≤ 33

Step-by-step explanation:

The answer can be 33 or below.

Answer:

30 PS4 in the shipment are likely to be defective

Step-by-step explanation:

We take the estimate from the sample and estimate to all the PS4 in store. This means that we can solve this question using a rule of 3.

From the sample of 50 PS4, 3 are defective. How many are expected to be defective out of 500?

50PS4 - 3 defective

500 PS4 - x defective

[tex]50x = 3*500[/tex]

[tex]x = \frac{1500}{50}[/tex]

[tex]x = 30[/tex]

30 PS4 in the shipment are likely to be defective

Answer:

don't take my word but I think 150

Step-by-step explanation:

Answer:

The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.

Step-by-step explanation:

For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The probability that an independent restaurant will fail in the first year is 32%.

This means that [tex]p = 0.32[/tex]

72 independent restaurants

This means that [tex]n = 72[/tex]

Mean:

[tex]E(X) = np = 72*0.32 = 23.04[/tex]

Standard deviation:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{72*0.32*0.68} = 3.96[/tex]

The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.

Final answer:

The mean number of independent restaurants in the sample expected to fail within the first year is 23.04, and the standard deviation is approximately 4.28.

Explanation:

To find the mean and standard deviation of the number of restaurants that failed within a year in Kristen's research, we can use the properties of the binomial distribution. The probability of a single restaurant failing (success in this context) is 0.32 (32%). Given a sample size of 72 restaurants, the mean number of restaurants that fail within a year is the product of the sample size and the probability of failure.

The formula for the mean (μ) of a binomial distribution is μ = n * p, where n is the sample size and p is the probability of success. Therefore, the mean number of failed restaurants is 72 * 0.32 = 23.04.

The formula for the standard deviation (σ) of a binomial distribution is σ = √(n * p * (1 - p)). Thus, the standard deviation of failed restaurants is √(72 * 0.32 * (1 - 0.32)) = √(72 * 0.32 * 0.68) ≈ 4.28.

Therefore, the mean number of restaurants that failed within a year is 23.04, and the standard deviation is approximately 4.28.

Answer:

a. .92

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error of the interval is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The lower bound is the point estimate [tex]\pi[/tex] subtracted by the margin of error.

The upper bound is the point estimate [tex]\pi[/tex] added to the margin of error.

Point estimate:

The confidence interval is symmetric, so it is the mean between the two bounds.

In this problem:

[tex]\pi = \frac{0.372 + 0.458}{2} = 0.415[/tex]

Sample of 400, which means that [tex]n = 400[/tex]

Margin of error is the estimate subtracted by the lower bound. So [tex]M = 0.415 - 0.372 = 0.043[/tex]

We have to find z.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.043 = z\sqrt{\frac{0.415*0.585}{400}}[/tex]

[tex]z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}[/tex]

[tex]z = 1.745[/tex]

[tex]z = 1.745[/tex] has a pvalue of 0.96.

This means that:

[tex]1 - \frac{\alpha}{2} = 0.96[/tex]

[tex]\frac{\alpha}{2} = 1 - 0.96[/tex]

[tex]\frac{\alpha}{2} = 0.04[/tex]

[tex]\alpha = 0.08[/tex]

Confidence level:

[tex]1 - \alpha = 1 - 0.08 = 0.92[/tex]

So the correct answer is:

a. .92

To determine the confidence coefficient for the proportion of MSU students who attended at least three football games, the margin of error is calculated from the given interval range and related to the Z-value of a standard normal distribution. The coefficient that matches the margin of error from the calculation is approximately 0.95, indicating a 95% confidence level.

The confidence interval for the proportion of Michigan State University (MSU) students who attended at least three football games is given as (0.372, 0.458). To determine the confidence coefficient used to calculate this interval, we need to look at the width of the interval and how it relates to the standard error of the proportion.

The width of the confidence interval is 0.458 - 0.372 = 0.086. Since we know that the total width of the interval spans the range of twice the margin of error, one margin of error is then 0.086 / 2 = 0.043.

Using the Z-table for the normal distribution, we can find which confidence coefficient corresponds to a Z-value that gives a margin of error of 0.043, considering that the formula for the margin of error in this case would be: Z * sqrt((p*(1-p))/n). For a sample size of 400, and approximating p by the midpoint of the confidence interval (0.372 + 0.458)/2 = 0.415, the computation would look roughly like this:

Z * sqrt((0.415*(1-0.415))/400) = 0.043

After solving this equation for Z, we can then locate the corresponding confidence level on the standard normal (Z) distribution table. This process would lead to finding that the closest confidence coefficient that would generate the margin of error of 0.043 with the given sample size and point estimate proportion is approximately 0.95, or 95%.

Therefore, the confidence coefficient is 0.95, which corresponds to option b. 0.95.

Answer:

1.5 hours

Step-by-step explanation:

make each half hour represent t

Cost C(t) = 24 + 14t

66 = 24 + 14t

42 = 14t

t = 3

3 half hours = 1.5 hours

Answer:

1 and a half hours of work

Step-by-step explanation:

You minus 66 and 24 to get 42. Then you divide 42 and 14

Answer:

64

Step-by-step explanation:

The spinner has 8 equal sections numbered from 1 to 8

Each time she spinns the spinner has 8 possible outcomes.

To know the number of possible results when  spinning two times, you must multiply the possible results for the first spin (8 possible outcomes) by the possible results for the second spin (also  8 possible outcomes).

And because each spin has the same number of outcomes:

[tex]8*8=64[/tex]

the answer is that there are 64 possible outcomes

Answer:

64

Step-by-step explanation:

Answer: 108 minutes

Step-by-step explanation:

This translates to:

Juan Pablo takes 7 minutes to do a full lap on a football field, Pedro needs 2 more minutes ruuning at the same speed thanJuan Pablo.

How much time does Pedro need to do 12 laps?

The fact that Pedro runs at the same speed than Juan Pablo, and needs more time, may mean that the radius of the laps of Pedro are a little bit bigger than the ones of Juan Pablo (which means that the total distance that pedro runs is bigger)

If Juan Pablo does a lap in 7 minutes, then Pedro does a lap in 7 minutes + 2 minutes = 9 minutes.

Then to do 12 laps, he needs 12 times that amount of time, this is:

12*9 min = 108 minutes

Step-by-step explanation:

One hundred minus five n

Answer:[tex]f(x)=\frac{3}{4}x^2+2x-5[/tex]

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

b

Answer:$7.50+$0.50xN or C+$0.50xN

Step-by-step explanation:

Because the pizza is 7.50 and the extra toppings are 0.50 cents so the number of toppings is n and the cost for the pizza is c so C+0.50xN.

Good Luck!!

Answer:

A) y = 2 x

Step-by-step explanation:

The equation for direct variation is

y = kx where the constant of proportionality is k

y = 2x