I need help. A building with a height of 48 m casts a shadow that is 30 m long. A person standing next to the building casts a shadow that is 0.8 m long. How tall is the person?

Answer:

y = 6

Step-by-step explanation:

when they work together, you square the 3 and get 6

Step-by-step explanation:

I have attached the answer above

Answer:

560 students

Step-by-step explanation:

1400*.40=560 students in 6th grade

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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We will have the following:

We can see that the function follows a path of exponential decay, so the expression that models it is:

Answer:

The desired divisor is n = 21

Step-by-step explanation:

Let that number be n.  Then:

-15/56        -5

---------- = ---------

     n            6

Through cross-multiplication we get:

(-15/56)*6 = -5n, which reduces to:

(-15)(7) = -5n, or 3(7) = n

The desired divisor is n = 21

To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

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Answer:

x>2

Step-by-step explanation:

Answer:

5+1<6x-3x

6<3x

3. 3

x= 2

Answer: He needs 80 cups.

Step-by-step explanation:$12/$.15=80 cups

There is no graph provided for reference, but if the graph shows a probability distribution, then the probabilities that are equal to 0.3 would depend on the specific shape and values displayed on the graph.

Without this information, it is impossible to determine which probabilities are equal to 0.3. Based on the given information, the graph represents a probability distribution. To determine which probabilities are equal to 0.3, you would need to analyze the graph (which is not provided). However, I can explain each term:
1. p(5≤x≤8): This represents the probability that x falls between 5 and 8, inclusive.
2. p(x≤3): This denotes the probability that x is less than or equal to 3.
3. p(x≥3): This signifies the probability that x is greater than or equal to 3.
4. p(3≤x≤5): This indicates the probability that x falls between 3 and 5, inclusive.

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Answer:

a. 0.85

b. \(f(t) =1000(0.85)^t\)

c. $272.49

Step-by-step explanation:

Given that:

Initial investment made, 8 years ago = $1000

Depreciation value each year = 15%

To find:

a. Multiplier

b. Function \(f(t)\) to describe the situation.

c. Worth of stock now.

Solution:

a. Depreciation of 15% means the value becomes (100 - 15) % = 85% or 0.85 of the actual value.

Therefore, the multiplier is 0.85.

b.

Every year the value becomes 0.85 times of the actual value.

If it continues for \(t\) years, then the values will be:

\(f(t) =1000(0.85)^t\)

c. Let us put \(t=8 \ years\) to find the worth of stock now.

\(\Rightarrow f(8) =1000(0.85)^8\\\Rightarrow \bold{\$272.49}\)

So, the answers are:

a. 0.85

b. \(f(t) =1000(0.85)^t\)

c. $272.49

Answer: C

Step-by-step explanation:

Perpendicular lines are irrelevant. A is to create a triangle and to show 2 angles in the triangles are congruent. B is to prove the 2 triangles are congruen. D is to prove that AC and BD are congruen. no where is perpendicular lines involved.

Answer:

What's the question it awnsers itself?

Step-by-step explanation:

The dimensions of the box that maximize the volume are x = √700 and h = 100 / √700.

To find the largest possible volume of the box, we need to optimize the dimensions of the box. Let's denote the length of each side of the square base as x and the height of the box as h.

The surface area of the box consists of the area of the square base (x^2) and the four sides of the box (4xh). Since the box has an open top, we do not consider the top surface. The total surface area is given as 2100 square centimeters, so we have:

x^2 + 4xh = 2100

To maximize the volume, we need to express the volume of the box (V) in terms of a single variable. The volume of a rectangular prism is given by V = x^2h.

We can rewrite the equation for the surface area to solve for h:

h = (2100 - x^2) / (4x)

Now we can substitute this expression for h in the volume equation:

V = x^2 * [(2100 - x^2) / (4x)]

Simplifying, we have:

V = (1/4) * (2100x - x^3)

To find the maximum volume, we need to find the critical points of this function. We take the derivative of V with respect to x and set it equal to zero:

dV/dx = 2100/4 - (3/4)x^2 = 0

Solving this equation, we find:

2100/4 = (3/4)x^2

x^2 = 700

x = √700

Substituting this value back into the equation for h, we find:

h = (2100 - 700) / (4 * √700) = 1400 / (4 * √700) = 100 / √700

Therefore, the largest possible volume of the box is:

V = (1/4) * (2100 * √700 - 700 * √700) = 350√700 cubic centimeters.

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Answer: A. 125h + 10 B. $385

Step-by-step explanation:

let h = the number of hours Mathew rents the jet ski

a. 125h + 10

B. Plug in 3 for h

125(3) + 10

375 + 10

⇒ $385

Answer:

F(h)= 125h+10

F(3)=125(3)+10

F(3)=375+10

F(3)=385

Step-by-step explanation:

So sorry if this is incorrect. I hope I could help!

Answer:

x = 16

Step-by-step explanation:

Answer: No

Step-by-step explanation: the dot on the screenshot shows where (5,7) is

Answer:

Yes

Step-by-step explanation:

If you graph y=-3x+22 then it is on the line. (x is 5, y is 7)

Since the 1st brand is 70% pure antifreeze

Since the 2nd brand is 95% pure antifreeze

Since we need to obtain 110 g of a mixture that contains 85% pure antifreeze

Let the quantity of the first is x and the second is y

Then

Now let us solve the two equations to find x and y

Multiply equation (2) by -0.7

Add equations (1) and (3)

Divide both sides by 0.25

Substitute the value of y in equation (2) to find x

Subtract 66 from both sides

First brand: 44 gallons

Second brand: 66 gallons

Step-by-step explanation:

These two angles are same side corresponding interior angles so they are equal to each other

\(5x + 20 = 120\)

\(5x = 100\)

\(x = 20\)

Answer:

pick the simplest of the 2 equations

Step-by-step explanation:

5y-2x=10

5y = 2x +10

y = 2/5x + 2

now substitute

8x + 5(2/5X +2)=60

8x + 2x + 10 = 60

10x = 50

x = 5

y = 4

The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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Decomposition is used to perform ANOVA and test the significance of the independent variable and its interaction effect on the dependent variable.

The expression SS stands for "sum of squares", which is a statistical concept used in analysis of variance (ANOVA) to quantify the variation in a dataset. The components of this expression, a, b, c, and d, represent different sources of variation in the dataset, and their meanings are as follows:

a. (df)(s^2): This component represents the sum of squares due to the effect of the independent variable, also known as the factor or treatment. It is calculated by multiplying the degrees of freedom (df), which is the number of levels of the factor minus one, by the variance of the data within each level (s^2). This component quantifies the amount of variation in the dependent variable that can be explained by the independent variable.

b. (df)(s): This component represents the sum of squares due to the interaction between the independent variable and other factors, also known as the interaction effect. It is calculated by multiplying the degrees of freedom (df) by the standard deviation (s) of the data. This component quantifies the amount of variation in the dependent variable that is due to the joint effect of the independent variable and other factors.

c. (n)(s^2): This component represents the sum of squares due to the variation within groups, also known as the error or residual sum of squares. It is calculated by multiplying the sample size (n) by the variance of the data within each group (s^2). This component quantifies the amount of variation in the dependent variable that is not explained by the independent variable or other factors.

d. (n)(s): This component represents the sum of squares due to the variation between the sample mean and the overall mean, also known as the total sum of squares. It is calculated by multiplying the sample size (n) by the standard deviation (s) of the data. This component quantifies the total amount of variation in the dependent variable.

In summary, the expression SS = a. (df)(s^2) + b. (df)(s) + c. (n)(s^2) + d. (n)(s) represents the decomposition of the total sum of squares into its components due to the independent variable, interaction effect, error, and total variation. This decomposition is used to perform ANOVA and test the significance of the independent variable and its interaction effect on the dependent variable.

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First we need to place the j on one side only

So we can move "j" from left to right, doing the opposite operation

We can do the same for -9

We can operate the terms that have j and do the sum to the both sides

Then, to leave

Answer:

need coordinates of each or side lengths of each to solve

The common difference of the arithmetic sequence is 3.

To find the common difference (d) of an arithmetic sequence, we can use the formula:

a_n = a_1 + (n - 1) * d

Where:

a_n is the nth term of the sequence,

a_1 is the first term of the sequence,

n is the position of the term in the sequence, and

d is the common difference.

Given that the 6th term is 19 and the 10th term is 31, we can write the following equations:

a_6 = a_1 + (6 - 1) * d = 19 --(1)

a_10 = a_1 + (10 - 1) * d = 31 --(2)

From equation (1), we have:

a_1 + 5d = 19

From equation (2), we have:

a_1 + 9d = 31

Now, we can subtract equation (1) from equation (2) to eliminate a_1:

(a_1 + 9d) - (a_1 + 5d) = 31 - 19

Simplifying, we get:

4d = 12

Dividing both sides by 4, we find:

d = 3

Therefore, the common difference of the arithmetic sequence is 3.

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Answer:

y = 7.5\(\sqrt{x}\)

Step-by-step explanation:

given y is directly proportional to \(\sqrt{x}\) then the equation relating them is

y = k\(\sqrt{x}\) ← k is the constant of proportion

to find k use the condition y = 75 , x = 100 , then

75 = k\(\sqrt{100}\) = 10k ( divide both sides by 10 )

7.5 = k

y = 7.5\(\sqrt{x}\) ← equation of proportion

We would reject the null hypothesis in favor of the alternative hypothesis.

The null hypothesis (H0) is that the average number of classes per quarter for students is 2 or less. The alternative hypothesis (Ha) is that the average number of classes per quarter for students is greater than 2. We can express this as:

H0: μ ≤ 2 (mean number of classes per quarter)

Ha: μ > 2

Where μ represents the population mean. This hypothesis is based on the instructor's belief that students take more than 2 classes on average.

The significance level (alpha) is given as 0.01, which means that if the p-value of the test is less than 0.01, we would reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

1 1/2 (1 + 1/2)

Step-by-step explanation:

3 2/3 * 3/4 is 2 3/4. 2 3/4 divided by 1 5/6 is 1 1/2.