what is meant by the statement that two variables are related? choose the correct answer. two variables are related when a scatterplot can be made of points using the two variables as values. two variables are related when a change in one can be shown to cause a change in the other. two variables are related when a discernible pattern exists between them. two variables are related when the value of one can be derived mathematically from the value of the other.

1) For this question, all we need to do is to plug it in the value for x.

So,

2/3x -8 =0 Plugging into x the value x=12

2/3(12) -8 =0

8 -8 =0

0

So when x=12, then the equation is equal to zero. This leads us to conclude that 12 is the root or the solution of this equation.

Answer:

The value of P(3,3) is 6

Step-by-step explanation:

We have to evaluate P(3,3)

As permutation can be calculated by the formula

Hence, the value of P(3,3) is 6

The probability that Victor selects a code that has four even digits is approximately 0.0238 or 1/42.

To solve this problem, we can use the permutation formula to determine the total number of possible codes that Victor can choose. Since he can only use each digit once, the number of permutations of 10 digits taken 4 at a time is:

P(10,4) = 10! / (10-4)! = 10 x 9 x 8 x 7 = 5,040

Next, we need to determine how many codes have four even digits. There are five even digits (0, 2, 4, 6, and 8), so we need to choose four of them and arrange them in all possible ways. The number of permutations of 5 even digits taken 4 at a time is:

P(5,4) = 5! / (5-4)! = 5 x 4 x 3 x 2 = 120

Therefore, the probability that Victor selects a code with four even digits is:

P = (number of codes with four even digits) / (total number of possible codes)

= P(5,4) / P(10,4)

= 120 / 5,040

= 1 / 42

≈ 0.0238

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Answer:

Debt. Federal debt held by the public is projected to dip from 100 percent of GDP at the end of 2021 to 96 percent in 2023.

Step-by-step explanation:

The simplified expression in terms of fractional exponents and in the form 10 to the power of a times x to the power of b is 10^((4/3)x).

To simplify the given expression, we can use the properties of exponents and fractional exponents. Let's break down the expression step by step.

The given expression is the cube root of 10 to the power of (4x). We can rewrite this as:

(10^(4x))^(1/3)

Using the property (a^m)^n = a^(m*n), we can simplify further:

10^((4x)*(1/3))

Multiplying 4x and 1/3 gives us:

10^(4x/3)

Now, let's write this in the form 10 to the power of a times x to the power of b. To do this, we need to express 4x/3 as a sum of two terms, one involving a and the other involving b.

We can rewrite 4x/3 as (4/3)x. Therefore, our expression becomes:

10^((4/3)x)

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Step-by-step explanation:

100% = $2000

1% = 100%/100 = 2000/100 = $20

how many % are $300 ?

well, as many % as 1% fits into these $300 :

300 / 1% = 300 / 20 = 15%

15% of last semester's costs were spent on books.

Answer:

total= 2000

spent = 300

300/2000x100

= 15 %

PLsss mark as Brainliest

Answer: A

Step-by-step explanation:

So we know that to find the area of a triangle you have to multiply the base times the height and divide it by two or multiply it by 1/2.Looking the information given it say that theta is equal to 26 degrees  and the length of a or the hypotenuse is 25 and b which in this case is the base is 32. So the information gives us the base but now we need to find the height.

To find  H we need to apply trigonometry solve for h the height.

As we could see theta which is 26 degrees is opposite the height and we know the hypotenuse length. So using soh cah toh we have to know that the length of h is  going to be using the sin formula opposite over hypotenuse.

\(sin(26)=\frac{h}{25}\)    solve for h by multiplying both sides by 25.

h= 25 sin(26)

h= 10.96   is being rounded to the nearest hundredth because that is essential

Now we know H is equal to 10.96  which is the Height so now we have all the information we need the height and the base.

Multiply 10.96 by 32 and divide it by 2.

10.96 * 32 =  350.72

350.72 /2 = 176.36  

The best answer is A  because that is the only best approximation to 175.35.

Step-by-step explanation:

f(a):

   So for this you simply plug in "a" as x, and this doesn't really do anything beside replace all values with x, so you just have the equation:

  \(f(a) = 5a+4\)

2 f(a):

   So for this one, you want to represent f(a) using the equation it's equal to (5a + 4), and substitute it in for f(a). In doing so, you get the expression:

   2*f(a) -> 2(5a + 4) -> 10a + 8

f(2a):

   So this is very similar to the first question, although you will have to do some multiplication. So just plug in 2a as "x" to get the equation:

   \(f(2a) = 5(2a) + 4 = 10a+4\)

f(a+2):

   Basically the same process, you plug in (a+2) as "x" and simplify:

   \(f(a+2) = 5(a+2) + 4\\f(a+2) = 10a+10+4\\f(a+2) = 10a+14\)

f(a) + f(2):

  This is similar to the second question, and you simply want to replace the f(a) with the equation that represents it (5a + 4) and same thing for f(2) = 5(2) + 4

   \(f(a) + f(2) = (5a+4)+(5(2)+4) \\f(a) + f(2) = (5a+4)+(10+4)\\f(a)+f(2) = (5a+4) + (14)\\f(a) + f(2) = 5a+18\)

Explanation:

(i)Total number of copies are at Pradnya = 5 dozen

We know that 1 dozen = 12

⇛5×12 = 60

Given copies to Anushka = half of 60

⇛60/2 = 30 copies

Given copies to Prajwala = 1/5 the copies

⇛ (1/5)×60

⇛60/5

⇛12 copies

Total number of given copies = 30+12 = 42

Remaining copies = 60-42 = 18

Answer: Remaining copies = 18

(ii)Let the number of Rs. 10 notes be X

So given that

all are equal in number

So, Number of Rs 20 notes = Number of Rs. 50 notes = Number of Rs. 100 = X

Total number of notes

= X+X+X+X = 4X

Value of Rs. 10 = 10X

Value of Rs. 20 = 20X

Value of Rs. 50 = 50X

Value of Rs. 100 = 100X

Total amount = Rs. 900

⇛10X +20X +50X+100X = 900

⇛180X = 900

⇛X = 900/180

⇛X = 5

Number of Rs. 10 notes = Number of Rs. 20 notes = Answer: number of Rs. 50 notes = Number of Rs. 100 = 5

(iii) Let the number of rows be X

Number of saplings per each row = 47

Total number of saplings of X rows = 47X

According to the given problem,

Total number of saplings purchased by Mangalakaku = 6016

⇛47X = 6016

⇛X = 6016/47

⇛X = 128

Answer: Total number of rows = 128

Answer:

Andrew must run 1 5/12 Laps to complete the race.

Step-by-step explanation:

Total lap run by Michael, Nate, Ben, and Andrew = 4 laps

laps run by Michael = 1 1/3 laps =(3+1)/3 =  4/3 laps

laps run by Nate =1/2 laps

laps run by ben =3/4 laps

Let laps run by Andrew = x

therefore

laps run by Michael + laps run by Nate + laps run by ben + laps run by Andrew = 4 laps

4/3 + 1/2 + 3/4 + x = 4

LCM of 3,2 and 4 is 12

=> (4*4 + 6*1 + 3*3+12x)/12 = 4

=> (16+6+9+12x)/12 = 4

=> 31+12x = 12*4 = 48

=> 12x = 48-31= 17

=> x = 17/12 = 1 5/12

Thus, Andrew must run 1 5/12 Laps to complete the race.

The main answer is that the volume of the solid is 1024π/3 cubic units and it can be computed using the method of disks or washers via an integral V= - S.C pi((y^2/16)-y) with limits of integration a=0 b = 16 and dy.

The given problem can be solved using the Washer Method. In the problem, the region enclosed by y=x², y=4x is revolved around the line x=4.

Then we have to find the volume of the solid thus obtained.To use the Washer Method, we have to follow the following steps:

Draw the region enclosed by y=x², y=4x.

Draw the line x=4 which is the axis of rotation

Draw an arbitrary line x=h which is parallel to the axis of rotation. Thus the washer is formed.

Find the outer radius and the inner radius of the washer.Step 5: The area of the washer is given by π(outer radius)² - π(inner radius)².Step 6: Now we need to add all such washers to obtain the total volume.Let's follow these steps to solve the problem:

We are given that the limits of integration are a=0, b=16 and we have to integrate with respect to dy.So, the height of the washer is given by ∆y.

Thus the arbitrary line x=h is given by x=√y.Now, the distance between the axis of rotation and the line x=√y is given by 4-√y.

The outer radius of the washer is given by 4-√y.The inner radius of the washer is given by 4-2√y.Thus the area of the washer is given by π[(4-√y)² - (4-2√y)²].

Simplifying this expression, we get, π(8√y - 4y) dy.The volume of the solid is given by integrating this expression from y=0 to y=16.So, we have,V = ∫[0,16] π(8√y - 4y) dy.Now, we have to evaluate this integral to find the volume.

We have used the Washer Method to find the volume of the solid obtained by rotating the region enclosed by y=x², y=4x about the line x=4.Using the method, we have obtained the expression π(8√y - 4y) dy and after integrating it from y=0 to y=16, we obtain the volume of the solid. The main answer is that the volume of the solid is 1024π/3 cubic units and it can be computed using the method of disks or washers via an integral V= - S.C pi((y^2/16)-y) with limits of integration a=0 b = 16 and dy.

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Answer:

CORRECT ANSWER IS B " Y - 1/2 x - 2 "

Answer:

z=80°(corresponding angles)

\(x+z=180°(linear \: pair \: ) \\ 80° + x = 180° \\ x= 100° \)

y=100 ° (alternate angles)

His account balance will be $6.5 greater in August than in June.

Assuming that the balance in June is equal to the balance in July, we can use the given information to find the difference between the August and June balances.

Let's say the balance in July (and June) was x. Then, according to the problem, the balance in August was:

     x + $6.50.

To find the difference between the August and June balances, we can subtract the June balance from the August balance:

August balance - June balance = (x + $6.50) - x = $6.50

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Answer:

G (-2,8)

Step-by-step explanation:

(-8+x)/2 = -5

-8 + x = -10

x = -10 + 8

x = -2

(0+y)/2 = 4

y = 4 · 2

y = 8

Answer:

y = =4x+9

4x+y=9

y+7=-4(x-4)

Step-by-step explanation:

The graphs of equations a, d, and e contain the points (4, -7) and (1, 5). To check which equation's graph contains the points (4, -7) and (1, 5), we can substitute the x and y coordinates of each point into the equation and see if the equation holds true for both points. Correct options are a, d and e.

Given points:

Point A: (4, -7)

Point B: (1, 5)

Let's check each equation:

a. y = -4x + 9

For Point A: -7 = -4(4) + 9 = -7 (holds true)

For Point B: 5 = -4(1) + 9 = 5 (holds true)

b. y = -4x - 23

For Point A: -7 = -4(4) - 23 = -39 (does not hold true)

For Point B: 5 = -4(1) - 23 = -27 (does not hold true)

c. y - 1 = -4(x - 5)

For Point A: -7 - 1 = -4(4 - 5) => -8 = 4 (does not hold true)

For Point B: 5 - 1 = -4(1 - 5) => 4 = 16 (does not hold true)

d. y + 7 = -4(x - 4)

For Point A: -7 + 7 = -4(4 - 4) => 0 = 0 (holds true)

For Point B: 5 + 7 = -4(1 - 4) => 12 = 12 (holds true)

e. 4x + y = 9

For Point A: 4(4) - 7 = 9 => 9 = 9 (holds true)

For Point B: 4(1) + 5 = 9 => 9 = 9 (holds true)

Equations that hold true for both points are:

a. y = -4x + 9

d. y + 7 = -4(x - 4)

e. 4x + y = 9

So, the graphs of equations a, d, and e contain the points (4, -7) and (1, 5).

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Complete question is:

Check each equation whose graph is the line that contains the points (4, –7) and (1, 5).

a. y = –4x + 9

b. y = –4x – 23

c. y – 1 = –4(x – 5)

d. y + 7 = –4(x – 4)

e. 4x + y = 9

Answer:

1: B

2: C

(I need 20 characters so bla bla bla bla bla bla bla)

According to the model, a car with a 4-liter engine would have a gas mileage of approximately 20.54 miles per gallon (CombinedMPG).we can use the given regression model to estimate the gas mileage for a car with a 4-liter engine.

We just need to substitute the value of Displacement in liters (which is 4 in this case) into the model and calculate the corresponding value of CombinedMPG. To calculate the gas mileage for a car with a 4-liter engine using the provided regression model CombinedMPG = 33.46 - 3.23 * Displacement, follow these steps:

Step 1: Identify the given displacement value, which is 4 liters

Step 2: Plug the displacement value into the regression model equation:

CombinedMPG = 33.46 - 3.23 * Displacement

Step 3: Calculate the CombinedMPG using the displacement value:

CombinedMPG = 33.46 - 3.23 * 4

Step 4: Perform the multiplication and subtraction:

CombinedMPG = 33.46 - 12.92

Step 5: Calculate the final CombinedMPG value:

CombinedMPG = 20.54

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Step-by-step explanation:

the answer options are not clear.

but the solution itself is. please pick the real answer option that best fits the solution :

s = current salary

S = salary after 10 years

S = 3s + 2000

Answer:

It is 3s + 2,000

Step-by-step explanation:

Hope this helps :)

When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are statistically significant.

In statistical analysis, we use hypothesis testing to determine whether the results of a sample are likely to be representative of the population as a whole. If the results are statistically significant, we can infer that there is a low probability that the observed differences between the sample and the population occurred by chance alone.

This allows us to generalize the findings from the sample to the larger population with a reasonable degree of confidence.

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Answer:

ok so jacob threw 1/5 of x

Step-by-step explanation:

if you say julien threw x and jacob threw 1/5 of that than jacob threw 1/5 of x

The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B

To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:

y = 200 + W + 2W^2

= 200 + 2 + 2(2^2)

= 200 + 2 + 2(4)

= 200 + 2 + 8

= 210

Therefore, the forecast value for time period 2 is 210.

To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:

Forecast error = Actual value - Forecast value

= 100 - 210

= -110

Hence, the forecast error is -110.

Therefore, the correct answer is:

Forecast value = 210; forecast error is -110. So Option B is correct.

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Given

Solving, step-by-step

The ratio of the height of shape A to the height of shape C is \(\frac{3}{10}\)

Recall that similar figures have the same scale factor squared due to the ratio of its surface area.

Hence,

We would make:

\(z^2 = x/y\\z= 2/5\)

Therefore, the ratio of the height of shape A to the height of shape B is = \(\frac{hA}{hB} = \frac{2}{5}\)

To find the ratio of the height of shape B to the height of shape C, we would perform a similar operation which is:

\(z^3 = 27/64\\z= 3/4\)

The ratio is:

\(\frac{hB}{hC} = \frac{3}{4}\)

To find the ratio of the height of shape A to the height of shape C would be:

\((\frac{hA}{hB}) (\frac{hB}{hC} )= \frac{hA}{hC}\)

= 6/20

= 3/10

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After using the conversion from inches to centimeters and using the division we have found that if the child measures 159.5 cm then expressed in inches is 62.8 inches.

To convert the boy's height from centimeters to inches, we can use the following conversion factor: 1 inch = 2.54 cm.

Here are the steps to convert the boy's height from centimeters to inches:

Therefore, the boy's height expressed in inches is 62.8 inches.

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Answer:

Step-by-step explanation:

x- intercept is the point (x, 0)

y-intercept is the point (0, y)

Answer:

I believe the answer is c

Step-by-step explanation:

You see, in a standard form the term with greater stays at the very right.

Answer:

Step-by-step explanation:

The vertex form of  the equation of the parabola with vertex (h, k)  is:

f(x) = a(x - h)² + k

So for vertex (3, 6) it will be:

f(x) = a(x - 3)² + 6

y intercept: 2 means  f(0) = 2

f(0) = a(0 - 3)² + 6

2 = a(-3)² + 6

2 -6 = 9a + 6 -6

-4 = 9a

a = ⁻⁴/₉

Therefore:

The vertex form of quardatic function with vertex: (3,6) and y intercept: 2 is

                             f(x) = - ⁴/₉(x - 3)² + 6

The vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

The vertex: (3,6) and y-intercept: 2

As we know,

The parabola equation:

f(x) = a(x - h)² + k

Here (h, k) is the vertex of the parabola and a is the leading coefficient.

f(x) = a(x - 3)² + 6

f(x) =  2 at x = 0

2 = a(0 - 3)² + 6

a = -4/9

f(x) = -4/9(x - 3)² + 6

Thus, the vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2

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