In a certain video game, there is a mini-game where the main character can choose from a selection of twenty
presents. The presents are wrapped, so the character does not know what is in them. If 7 presents contain money, 3
presents contain gems, 6 presents contain ore, and 4 presents contain fish, what is the probability that the main
character does not choose a present that contains a gem?
Your answer should be an exact decimal value.
The probability of randomly selecting a present that does not contain a gem is

The 90% confidence interval for the true proportion of all adults in the town who have health insurance is approximately 0.7294 to 0.8804.

Using the formula for calculating a confidence interval for a proportion.

The formula for the confidence interval is:

Confidence Interval = Sample proportion ± Margin of error

where:

Sample proportion = Number of adults with health insurance / Total sample size

Margin of error = Critical value * Standard error

The critical value depends on the desired confidence level. For a 90% confidence level, the critical value can be obtained from the standard normal distribution table, which corresponds to a Z-value of 1.645.

The standard error can be calculated using the formula:

Standard error =[tex]\sqrt{} ((p * (1 - p)) / n)[/tex]

Given:

Number of adults with health insurance (sample proportion) = 66

Total sample size = 82

Confidence level = 90%

Now, let's calculate the confidence interval:

Sample proportion = 66 / 82 ≈ 0.8049

Standard error = [tex]\sqrt{}[/tex]((0.8049 * (1 - 0.8049)) / 82) ≈ 0.0459

Margin of error = 1.645 * 0.0459 ≈ 0.0755

Lower bound of the confidence interval = Sample proportion - Margin of error ≈ 0.8049 - 0.0755 ≈ 0.7294

Upper bound of the confidence interval = Sample proportion + Margin of error ≈ 0.8049 + 0.0755 ≈ 0.8804

Therefore, the 90% confidence interval for the true proportion of all adults in the town who have health insurance is approximately 0.7294 to 0.8804.

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It based on this estimation, Sheri plans to give her groomer a tip of around $11.

To estimate the tip Sheri plans to give her dog groomer, we can use a benchmark fraction and the given table. Let's assume that Sheri plans to give a tip as a percentage of the cost of grooming her dog.

First, let's look at the table and round the cost to the nearest ten. For example, if the cost of grooming is $57, we round it to $60. Let's choose a benchmark fraction such as 1/5 (or 20%) to estimate the tip.

Next, we find the cost in the table that is closest to the rounded amount. Let's say the rounded cost is $60, and in the table, the closest cost is $55. Using the benchmark fraction of 1/5, we estimate the tip to be approximately 20% of $55, which is $11.

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Answer:

A) Yes, he is correct because substituting x = 4 into the equation yielded a true statement.

Step-by-step explanation:

He in total work in 48 weeks and still there 4 weeks for vacations but in another case , Labron didn't take any vac cause he don't want

The difference is: [tex]500 = (25 \times f) + (100 \times c)[/tex]

To write the inequality describing the total calorie count, we need to consider the calorie count of the french fries and chicken wings and ensure that it is less than 500 calories.

Let's start by defining the variables:

Let f be the number of french fries.

Let c be the number of chicken wings.

Next, we can determine the total calorie count for the french fries and chicken wings:

The number of calories per french fry is 25.

The number of calories per chicken wing is 100.

To calculate the total calorie count, we multiply the number of french fries by the calorie count per french fry and the number of chicken wings by the calorie count per chicken wing. Then, we sum the two values:

Total calorie count = [tex](25 \times f) + (100 \times c)[/tex]

We want this total to be less than 500 calories, so we can write the inequality as:

[tex](25 \times f) + (100 \times c) < 500[/tex]

This inequality ensures that the sum of the calories from the french fries and chicken wings is less than 500.

By varying the values of f and c within the constraints of the inequality, Ashley can ensure that the total calorie count for the lunch remains within her desired limit.

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Answer:

  C. 1•3

Step-by-step explanation:

You want to know which number could not be the average of 5 integers:

The total number of children in the village will be an integer. The average per family will be found by dividing that total by the number of families: 5.

The quotient from that division must be an integer multiple of 1/5 = 0.2. The number 1.3 is not an integer multiple of 0.2.

The number Marie could not get is 1.3.

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Answer:

[tex]\frac{5}{6}[/tex] of the shelves of prescriptions have been picked up.

Step-by-step explanation:

First, let's write out the problem they want us to solve.

[tex]\frac{3}{6} +\frac{2}{6}[/tex]

Since the denominators are the same, we know our answer will have the same denominator, 6, and a numerator of whatever the two numerators, 3 and 2, totals.'

[tex]\frac{3}{6} +\frac{2}{6}=\frac{3+2}{6} =\frac{5}{6}[/tex]

Since 5 can't go into 6, we know the fraction can't be simplified. So, [tex]\frac{5}{6}[/tex] of the shelves of prescriptions have been picked up.

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The scatter plot shows (c) negative correlation

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values decreases

This represents a negative linear association.

Hence, the correlation is negative

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It will take approximately 6.8 hours for the population to reach 250,000.

To solve this problem, we can use the concept of exponential growth. Let's denote the population size at time t as P(t).

Given that the culture grows at a rate proportional to its size, we can write the following differential equation:

dP(t)/dt = k * P(t),

where k is the proportionality constant.

We also know that after 1.5 hours, the population has increased to 875. Therefore, we have the following information:

P(0) = 50 (initial population size),

P(1.5) = 875.

To find the value of k, we can substitute the values into the differential equation:

875 = 50 * e^(1.5k).

Simplifying the equation, we get:

e^(1.5k) = 17.5.

Taking the natural logarithm of both sides, we have:

1.5k = ln(17.5).

Solving for k, we find:

k ≈ 0.6733.

Now, to find the time it takes for the population to reach 250,000, we can substitute the values into the exponential growth equation:

250,000 = 50 * e^(0.6733t).

Dividing both sides by 50 and taking the natural logarithm, we get:

ln(5,000) = 0.6733t.

Solving for t, we find:

t ≈ 6.84 hours.

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Answer:

Step-by-step explanation:

Use the Law of Sines since this isn't a right triangle and you can't use right triangle trig. The equation will look like this:

[tex]\frac{sin103}{11.89} =\frac{sin?}{9}[/tex]

Cross multiply to get

[tex]sin?=\frac{9sin103}{11.89}[/tex] which gives us the decimal .7375383165

Take the inverse sin of this on your calculator to find the missing angle (the 2nd key and then the sin key) to be 47.52°

In this case,the weighted average cost of capital (WACC)   for the firm is approximately 16.305%.

First, let's calculate the   cost of equity (Ke) using the Capital  Asset Pricing Model(CAPM) -  

Ke = Rf + β x   (Rm - Rf)

Where -  

Rf = Risk-free rate = 5%

β = Beta of equity = 1.4

Rm = Expected market return = 15%

Ke = 0.05 + 1.4 x  (0.15 - 0.05) = 0.05 + 1.4 x  0.1 = 0.05 + 0.14 = 0.19 = 19%

Next let's calculate the   cost of debt (Kd) using the yield to maturity(YTM) of the bonds -  

Kd = YTM = 8.5%

Since the interest payments on debt are   tax-deductible,we need to calculate the after-tax cost of debt (Kd(1 - Tax Rate)) -  

Kd(1 - Tax Rate) = 0.085 x   (1 - 0.35)

= 0.05525

= 5.525%

Now, let's calculate   the weights of equity (We) and debt (Wd)in the firm's capital structure -  

We = Market value of equity / Total market value

Market value of equity = Number of shares x   Market price per share

= 6,000,000 x $12

= $72,000,000

Total market value = Market value of equity +   Market value of debt

Total market value= $72,000,000 + (20,000 x $900)

= $72,000,000+  $18,000,000

= $90,000,000

We = $72,000,000/   $90,000,000

= 0.8

= 80%

Wd = Market value of debt/ Total market value

= $18,000,000   /$90,000,000

= 0.2

= 20%

Finally, let's calculate the WACC -  

WACC =(We   x Ke) + (Wd x Kd(1 - Tax   Rate))

WACC = (0.8 x   0.19) + (0.2 x 0.05525) = 0.152 +0.01105

= 0.16305

= 16.305%

Therefore, the corrected weighted average cost of capital (WACC) for the firm is approximately 16.305%.

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Answer: -1

Step-by-step explanation: It's asking for x when it is f(x) = -3, so you simply scan/look down the column to find -3 and then look to the left to see your answer, -1. You look to the left because it is the x column and the question is asking for x.

In the  word problem above, 0 small pizzas, 1 medium pizza, and 5 large pizzas were delivered to the college.

Let  S = number of small pizzas delivered

Let M = number of medium pizzas delivered

Let L = number of large pizzas delivered

We'll start by solving equation 1 for one variable and substituting it into the other equations.

S + M + L = 12

We can rewrite this equation as -

S = 12 - M - L

Now, substitute this value of S in equations 2 and 3 -

4S + 10M + 15L = 109

4(12 - M - L) + 10M + 15L = 109

48 - 4M - 4L + 10M + 15L = 109

6M + 11L = 61

2S + 4M + 13L = 81

2(12 - M - L) + 4M + 13L = 81

24 - 2M - 2L + 4M + 13L = 81

2M + 11L = 57

Now we have a system of two equations with two variables -

6M + 11L = 61 ...(4)

2M + 11L = 57 ...(5)

Subtract  equation   (5)from equation (4) -

(6M +   11L) - (2M +11L) = 61 - 57

4M = 4

M = 1

Substitute the value of M into equation (5) -

2(1) + 11L = 57

2 + 11L = 57

11L = 55

L = 5

Now substitute the values of M and L into equation (1) -

S + 1 + 5 = 12

S + 6 = 12

S = 6 - 6

S = 0

Therefore, the solution is -

S = 0 (no small pizzas)

M = 1 (1 medium pizza)

L = 5 (5 large pizzas)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

a pizza shop delivered 12 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $109. a small pizza costs $4 and contains 2 ounces of pepperoni. a medium pizza costs $10 and contains 4 ounces of pepperoni. a large pizza cost $15 and contains 13 ounces of pepperoni. the owner of the pizza shop used 5 pounds 1 ounces of pepperoni in making the 12 pizzas. how many pizzas of each size were delivered to the college?

The solution to the equation cos(6x) = sin(3x - 9) from the given options is x = -10. Option C.

To solve the equation cos(6x) = sin(3x - 9) according to the given options, we can substitute each option into the equation and check if it satisfies the equation.

A. x = 10:

cos(6 * 10) = sin(3 * 10 - 9)

cos(60) = sin(21)

However, cos(60) does not equal sin(21), so x = 10 is not a solution.

B. x = 11:

cos(6 * 11) = sin(3 * 11 - 9)

cos(66) = sin(24)

Again, cos(66) does not equal sin(24), so x = 11 is not a solution.

C. x = -10:

cos(6 * -10) = sin(3 * -10 - 9)

cos(-60) = sin(-39)

Interestingly, cos(-60) does equal sin(-39). Therefore, x = -10 satisfies the equation cos(6x) = sin(3x - 9). Thus, C. x = -10 is a solution.

D. x = 12:

cos(6 * 12) = sin(3 * 12 - 9)

cos(72) = sin(27)

Once again, cos(72) does not equal sin(27), so x = 12 is not a solution.

In summary, the solution to the equation cos(6x) = sin(3x - 9) from the given options is x = -10, which corresponds to option C.

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Answer: Its B (11)

Step-by-step explanation:

I did the test

Answer:

r=✓-m+p+k/T

to start you take m to the other side it turns to -m

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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The sum that Mahesh borrowed was Rs. 22,800, the interest that Mahesh has to pay was Rs. 6,492, the interest that Rakesh has to pay was Rs. 7,550, and the percentage by which Rakesh pays more interest than Mahesh was 16.3%.

a) Sum borrowed by Mahesh

Let us suppose that the principal sum borrowed by Mahesh from the bank at 9% per annum is Rs. x.

Hence, we can write that

Simple Interest = (P × R × T )/ 100

= (x × 9 × 3)/100

= 27x/100

Therefore, the amount that Mahesh has to pay after 3 years, including the interest, is

A = P + SI

= x + 27x/100

= 127x/100

Again, Mahesh invests the same amount of Rs. x to Rakesh at 10% per annum, which is compounded annually, for three years.

Hence, the total amount after three years that Rakesh has to pay Mahesh is:

Amount after 3 years = x (1 + R/100)³

= x (1 + 10/100)³ = 1.331 x

Therefore, Mahesh made a profit of Rs. 7,550 by investing Rs. x at 10% per annum, compounded annually, for three years.

Hence, we can write that

Compound Interest = Amount - Principal

CI = 1.331x - x = 0.331x

Therefore, 0.331x = Rs. 7,550=>

x = Rs. 22,800

Thus, Mahesh borrowed Rs. 22,800 from the bank.

b) Interest that Mahesh has to pay

Interest = P × R × T/100

= Rs. 22,800 × 9 × 3/100 = Rs. 6,492

Therefore, Mahesh has to pay Rs. 6,492 as interest.

c) Interest that Rakesh has to pay

The total amount that Rakesh has to pay to Mahesh is Rs. 30,350 [= (22,800 + 7,550)].

Therefore, interest that Rakesh has to pay = Total Amount - Principal

= Rs. 30,350 - Rs. 22,800 = Rs. 7,550

Therefore, Rakesh has to pay Rs. 7,550 as interest.

d) Percentage by which Rakesh pays more interest than Mahesh

Let us calculate the percentage difference between the interest paid by Rakesh and the interest paid by Mahesh.

Thus, the percentage difference can be calculated as

% Difference = (|Interest paid by Rakesh - Interest paid by Mahesh|/ Interest paid by Mahesh) × 100

% Difference = (|7,550 - 6,492|/6,492) × 100

% Difference = 16.3%

Therefore, Rakesh pays more interest than Mahesh by 16.3%.

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The inverse function would represent the time in hours in terms of the number of miles completed by the marathon runner.

The situation of the number of miles a marathon runner has completed in terms of the time in hours could be represented by a one-to-one function. Each unique value of time corresponds to a unique value of miles completed, and there are no two different times that would result in the same number of miles. The inverse function would represent the time in hours in terms of the number of miles completed by the marathon runner.

The situation of the depth of the tide at a beach in terms of the time over a 24-hour period may not be represented by a one-to-one function. It is possible for the tide to have the same depth at multiple different times within the 24-hour period, or for the depth to change and then return to the same value later on. Since the situation may not have a one-to-one function, the concept of an inverse function may not be applicable in this case.

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Answer:

Step-by-step explanation:

To solve the given equation, let's expand and simplify both sides:

Expanding the left side:

(2x + 1)(2x + 1) = 4(x^2 + x)

(4x^2 + 2x + 2x + 1) = 4x^2 + 4x

Simplifying:

4x^2 + 4x + 1 = 4x^2 + 4x

Now, we can eliminate the common terms on both sides of the equation:

4x^2 - 4x^2 + 4x - 4x + 1 = 0

Simplifying further:

0 + 0 + 1 = 0

1 = 0

Since we have arrived at an equation that is not true (1 = 0), there is no solution to the given equation.

Therefore, the equation (2x + 1)(2x + 1) = 4(x^2 + x) has no solution.

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Answer:

1 = 0, or no solution.

Step-by-step explanation:

There are three types of solutions to equations: no solutions, one solution, or infinitely many solutions.

Here are some examples:

Given equation: (2x + 1)(2x + 1) = 4(x² + x)

Step 1: Expand the left side of the equation.

(2x + 1)(2x + 1) = 4(x² + x)

2x (2x + 1) + 1(2x + 1) = 4(x² + x)

4x² + 2x + 2x + 1 = 4(x² + x) [Combine like terms.]

4x² +4x + 1 = 4(x² + x)

Step 2: Distribute 4 throught the parentheses on the right side.

4x² +4x + 1 = 4(x² + x)

4x² +4x + 1 = 4(x²) + 4(x)

4x² +4x + 1 = 4x² + 4x

Step 3: Subtract 4x² from both sides.

4x² +4x + 1 = 4x² + 4x

4x² - 4x² +4x + 1 = 4x² - 4x² + 4x

4x + 1 = 4x

Step 4: Subtract 4x from both sides

4x + 1 = 4x

4x - 4x + 1 = 4x - 4x

1 = 0

As the final answer is not a solution, the given equation has no solution.

Answer:

a) To find the total number of people in Congo Town, we can add up the number of ANC members, CDA members, neutral people, and those who are both ANC and CDA:

Total = ANC + CDA + Neutral + (ANC and CDA)

Total = 80 + 60 + 20 + 30

Total = 190

Therefore, there are 190 people in Congo Town.

b) To find the number of people who are only CDA members, we need to subtract the number of people who are both ANC and CDA from the total number of CDA members:

CDA only = CDA - (ANC and CDA)

CDA only = 60 - 30

CDA only = 30

Therefore, there are 30 people who are only CDA members.

c) To find the number of people who are only ANC members, we need to subtract the number of people who are both ANC and CDA from the total number of ANC members:

ANC only = ANC - (ANC and CDA)

ANC only = 80 - 30

ANC only = 50

Therefore, there are 50 people who are only ANC members.

The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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The area of the composite figure is

Area of the semi circle + Area of the rectangle.

Formula for the area of a circle is

π x r²

= 3.14 x (2)²

= 3.14 x 4

≈ 12.57

Formula for the area of the rectangle is

L x B

= 4 x 11

= 44m²

Since the area of the semi circle = Area of circle /2

⇒ (πr²)/2

= 12.57/2

= 6.29

Hence are of the composite shape is

6.29 + 44

≈  50.29m²

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Full Question:

See attached image.

Step-by-step explanation:

To calculate the correlation coefficient (r) given SSxx, SSxy, and other information, we need to use the following formula:

r = √(SSxy / SSxx)

Given SSxx = 950 and SSxy = 205.2, we can substitute these values into the formula:

r = √(205.2 / 950)

Calculating the value:

r = √(0.216)

r ≈ 0.465

The correlation coefficient (r) is approximately 0.465.

Interpretation: The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the value of r = 0.465 indicates a positive linear relationship between the variables, but it's not a strong relationship. The closer the value of r is to 1 or -1, the stronger the relationship. Since r = 0.465 is relatively close to zero, it suggests a weak positive linear association between the variables being an analyzed.

hope it help you

The Pearson's correlation coefficient (r) based on given data is approximately 0.44, implying a moderate positive correlation.

The formula for calculating Pearson's correlation coefficient (r) in this case is given as: r = SSxy / sqrt(SSxx * SSyy). However, we don't have the value for SSyy directly, but we can calculate it. We know that SSyy = Σy² -(Σy)² / n. Given that Σy² is 2028 and Σy is 120 and number of samples n is 12, we can calculate SSyy as: SSyy = 2028 - (120)² / 12 = 52. Now, substitute SSxx = 950, SSxy = 205.2 and SSyy = 52 in the formula to find r: r = 205.2 / sqrt(950 * 52), giving us an r-value of approximately 0.44. This value of r suggests a moderate positive correlation between the variables in the dataset.

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To find the equation of a line passing through two points, (-1, -5) and (5, 4), we can use the point-slope form of a linear equation.

The formula for the point-slope form is: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.

First, let's calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-1, -5) and (x2, y2) = (5, 4).

m = (4 - (-5)) / (5 - (-1))

m = 9 / 6

m = 3/2

Now, we can choose one of the points, let's use (-1, -5), and substitute the values into the point-slope form:

y - y1 = m(x - x1)

y - (-5) = (3/2)(x - (-1))

y + 5 = (3/2)(x + 1)

To convert this equation to the standard form (Ax + By = C), we can multiply through by 2 to eliminate the fraction:

2(y + 5) = 3(x + 1)

2y + 10 = 3x + 3

3x - 2y = 7

So, the equation of the line passing through the points (-1, -5) and (5, 4) is 3x - 2y = 7.

The coordinates of the vertices after the rotation are given as follows:

U'(1, -1), V'(0, 4) and W'(4,1).

The five more known rotation rules are given as follows:

The original coordinates of the triangle are given as follows:

U(−1, 1), V(0, −4), W(−4, −1).

For the 180º rotation, we just change the sign of each of the coordinates, hence:

U'(1, -1), V'(0, 4) and W'(4,1).

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The following food-cost problems:

FC ÷ FC % = SP: 2.75 ÷ 25% = 11.

FC ÷ SP = FC %: 3.80 ÷ $15.00 = 25.33%.

SP x FC % = FC: 24.00 x 21% = 5.04.

To complete the food-cost problems, we will apply the given formulas and solve for the missing values.

FC ÷ FC % = SP

Given: FC = 2.75, FC % = 25%

Substituting the values into the formula, we have:

2.75 ÷ 25% = SP

To divide by a percentage, we convert the percentage to a decimal by dividing it by 100:

2.75 ÷ 0.25 = SP

Simplifying the division, we get:

11 = SP

Therefore, the selling price (SP) is 11.

FC ÷ SP = FC %.

Given: FC = 3.80, SP = $15.00

Substituting the values into the formula, we have:

3.80 ÷ $15.00 = FC %

To divide by a dollar amount, we can simply perform the division:

0.2533... = FC %

Therefore, the food cost percentage (FC %) is approximately 25.33%.

SP x FC % = FC

Given: SP = 24.00, FC % = 21%

Substituting the values into the formula, we have:

24.00 x 21% = FC

To multiply by a percentage, we convert the percentage to a decimal by dividing it by 100:

24.00 x 0.21 = FC

Simplifying the multiplication, we get:

5.04 = FC

Therefore, the food cost (FC) is 5.04.

In summary:

2.75 ÷ 25% = 11

3.80 ÷ $15.00 = 25.33%

24.00 x 21% = 5.04

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1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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The students washed one car in each session, and the charge per car was $1.

To determine the charge per car, we need to find the total number of cars washed in each session and divide the total earnings by that number.

In the first session, the students earned $78. Since the charge per car is a whole dollar amount, the total number of cars washed must be a divisor of 78.

Let's calculate the divisors of 78: 1, 2, 3, 6, 13, 26, 39, and 78. However, we're looking for a whole number, so we can eliminate the decimal divisors. Therefore, the possible numbers of cars washed in the first session are 1, 2, 3, 6, 13, 26, 39, and 78.

Similarly, in the afternoon session, the students earned $54, and the divisors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The possible numbers of cars washed in the afternoon session are 1, 2, 3, 6, 9, 18, 27, and 54.

In the evening session, the students earned $81. The divisors of 81 are 1, 3, 9, 27, and 81. The possible numbers of cars washed in the evening session are 1, 3, 9, 27, and 81.

By comparing the possible divisors from each session, we find that the only common divisor is 1.

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Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

Answer:

Step-by-step explanation:

7, 24 and 25 is a Pythagorean triple

therefor a = 7 and c = 25

Using Pythagorean theorem to find b

b in small triangle is the hypotenuse

b^2 = a^2 + 6^2

b^2 = 7^2 + 6^2

b^2 = 49 + 36

b^2 = 85

b = 9.22