Which of the following is a proportional relationship?
y = 2x
y = 2x2
y = x3
y = 2x2 + 3x + 4

Answer:

Step-by-step explanation:

To find g(4), we substitute x = 4 into the expression for g(x):

g(4) = -3(4) - 4 = -12 - 4 = -16

To find g(4) + 8, we add 8 to the value we just found for g(4):

g(4) + 8 = -16 + 8 = -8

Therefore, g(4) + 8 = -8.

The value of tSTAT is 4.08. The slope of the regression line tells us the rate at which Y changes for each unit increase in X.

tSTAT stands for "t statistic". t statistic is a parameter that estimates how far a sample mean is likely to be from the population mean. A t-test is used to determine whether a difference between two groups is significant. The formula for calculating the t-statistic is:tSTAT = (b1 - 0) / Sb1Where b1 is the slope of the regression line, Sb1 is the standard error of the slope, and 0 is the hypothesized value of the slope (which is zero when testing for no linear relationship between two variables, X and Y).In this case, b1 = 5.3, Sb1 = 1.3, and 0 = 0. Therefore:tSTAT = (5.3 - 0) / 1.3 = 4.08Thus, the value of tSTAT is 4.08.

In statistics, the t statistic is a ratio between the difference between the sample mean and the null hypothesis and the standard error of the mean. The null hypothesis in this case is that there is no linear relationship between two variables, X and Y. The t-test is used to determine whether this null hypothesis is true or not.In order to calculate the t statistic, we need to know the slope of the regression line (b1) and the standard error of the slope (Sb1).  The standard error of the slope tells us how much variation there is in the slope estimate from sample to sample.The formula for calculating the t statistic is:tSTAT = (b1 - 0) / Sb1Where b1 is the slope of the regression line, Sb1 is the standard error of the slope, and 0 is the hypothesized value of the slope (which is zero when testing for no linear relationship between two variables, X and Y).In this case, b1 = 5.3, Sb1 = 1.3, and 0 = 0. Therefore:tSTAT = (5.3 - 0) / 1.3 = 4.08.Thus, the value of tSTAT is 4.08.

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It Equals 5.875 Hope this helps

The speed of the cyclist in still air is 13 mph

Let the speed of the cyclist in still air be x mph

when she rides with the wind her speed = (x + 3) mph

when she rides against the wind her speed = (x - 3) mph.

Mathematically we can represent the problem as:

16 / (x + 3) = 10 / (x - 3)

cross multiplying and simplifying

16 (x - 3) = 10 (x + 3)

16x - 48 = 10x + 30

6x = 78

x = 13

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Answer:

7t - 4

Step-by-step explanation:

f(t) + g(t)

= 3t + 4t - 4 ( collect like terms )

= 7t - 4

Find f(t) t g(t)

Replace values

3t + 4t - 4

Solve for t

3t + 4t = 7t

Organize values

7t - 4

Answer = 7t - 4

The probability of this occurring is 4C2/5C2 = 3/5

What is the meaning of probability in math?

Three Types of Probability-

Let's assume we don't stop picking until all of the chips are picked.

To satisfy this condition, we have to arrange the letters: W, W, R, R, R such that both W's appear in the first 4.

We find the number of ways to arrange the white chips in the first 4 and divide that by the total ways to choose all the chips.

Therefore, the probability of this occurring is 4C2/5C2 = 3/5

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The amount that Whitney actually made selling wrapping paper is given as follows:

$125.

The profit made is obtained solving the proportions in the context of the problem.

Her prediction of the profit of $160 is 28% higher of the actual profit x, hence the equation relating these two amounts is given as follows:

1.28x = 160.

(as 28% higher than 100% is 128% = 1.28).

Then the value of x, representing the actual profit, is obtained as follows:

x = 160/1.28

x = $125.

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Answer:

6

Step-by-step explanation:

The Official Answer is C. 6

In this case, since the eigenvalue λ2 = 4 is positive, the solution decays exponentially towards the origin along the line defined by the eigenvector [1; 1].

To solve the system dx/dt = [6, -2; 20, -6]x with x(0) = [-2; 2], we can find the eigenvalues and eigenvectors of the coefficient matrix [6, -2; 20, -6]. Let's denote the coefficient matrix as A.

The characteristic equation of A is given by det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix. So we have:

|6 - λ, -2|

|20, -6 - λ| = 0

Expanding the determinant, we get:

(6 - λ)(-6 - λ) - (-2)(20) = 0

(λ - 2)(λ - 4) = 0

Solving for λ, we find two eigenvalues: λ1 = 2 and λ2 = 4.

To find the corresponding eigenvectors, we substitute each eigenvalue back into the equation (A - λI)v = 0 and solve for v. Let's find the eigenvectors for each eigenvalue.

For λ1 = 2:

(A - 2I)v1 = 0

|4, -2|v1 = 0

|20, -8|v1 = 0

Simplifying, we get the equation 4v1 - 2v2 = 0, which gives us v1 = v2.

For λ2 = 4:

(A - 4I)v2 = 0

|2, -2|v2 = 0

|20, -10|v2 = 0

Simplifying, we get the equation 2v1 - 2v2 = 0, which gives us v1 = v2.

So, the eigenvectors for both eigenvalues are v = [1; 1].

Now we can express the general solution of the system as:

x(t) = c1 * e^(λ1 * t) * v1 + c2 * e^(λ2 * t) * v2

Substituting the values, we have:

x(t) = c1 * e^(2t) * [1; 1] + c2 * e^(4t) * [1; 1]

Since x(0) = [-2; 2], we can solve for the constants c1 and c2. Plugging t = 0 into the equation, we get:

[-2; 2] = c1 * e^0 * [1; 1] + c2 * e^0 * [1; 1]

[-2; 2] = c1 * [1; 1] + c2 * [1; 1]

[-2; 2] = [c1 + c2; c1 + c2]

From the first component of the vector equation, we have -2 = c1 + c2.

From the second component of the vector equation, we have 2 = c1 + c2.

Solving these equations, we find c1 = 0 and c2 = -2.

Therefore, the particular solution to the system dx/dt = [6, -2; 20, -6]x with x(0) = [-2; 2] is:

x(t) = -2 * e^(4t) * [1; 1]

The trajectory of the solution represents a line in the direction of the eigenvector [1; 1], with exponential growth/decay based on the eigenvalues.

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Answer:

{ Sunday , Saturday }

{Tuesday , Thursday}

Answer:

17.6%

Step-by-step explanation:

50×8%=4

75×24%=18

4+18=22

50+75=125

22÷125=17.6%

Answer:

14.4 percent increase

Step-by-step explanation:

Givens.

• a = 5 ft.

• b = 12 ft.

Use Pythagorean's Theorem to find c.

\(\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }\)=\(5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }\)

\(\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }\)

Therefore,

125 = 5³

27 = 3³

Hence,

\(5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} }\)

Hence,

Both cube root are the same now,

Therefore, we have to add them together.

\(5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }\)

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Answer:

-44

Step-by-step explanation:

You multiply 11 times 2 to the second power then multiply negative 1

Answer:

\(9a^3b^3\)

Step-by-step explanation:

Answer:

distributive property

Step-by-step explanation:

Answer:

Yes. It works.

Step-by-step explanation:

3 x (4 + 5) = First you have to add 4 + 5 since it's in parentheses, and whatever is in parentheses, you have to do it first. so 4+ 5 = 9. Then you multiply 9 by 3 which gives you 27.

(3 x 4) + (3 x 5) is equivalent to 3 x (4 + 5).

First you do whatever is in parentheses, since they're both in parentheses, I don't think it matters which you do first, but I would do the first problem. 3 x 4 is equal to 12, then 3 x 5 is equal to 15, so you add your answers. 12 + 15 = 27.

So, you can write 3 x (4 + 5) as (3 x 4) + (3 x 5) = 27. They both equal to 27. Hope this clarifies your question.

Also the property is called the distrubitive property.

Answer:

8

Step-by-step explanation:

1+2+3=6

4+5+6=15

15-6=9-1=8

Answer:

You spent $14.5

Step-by-step explanation:

You just add tgem ad yeah

Answer:

Step-by-step explanation:

barrier = parameter, so we add all the sides:

8+3+3+5+5 = 24

24*1.75 = $42.

THEN, we need the area to solve for the mulch.

I would split it up into two parts so the rectangle and then the triangle.

First, 8*3 is 24

now we divide this by four because one bag covers four square feet

so, 6 bags (24/4=6) which is $36 (6*$6).

_______________

Now, the triangle, which a = (hb*b)/2

12 divided by four again so 3

3 * 6 = $18.

Now we add ALL costs up to get

42+36+18 = $96 total for the entire project.

Answer:

Step-by-step explanation:

1.50x + 10[x/30] >= 450

x >= 246.3

check:

1.50*246 + 10*8 = 449

$450

Answer:

7, 10, 13, 16

Step-by-step explanation:

Given,

Frist term=7

term-to-term rule is add 3

Therefore first three terms will be

7, 7+3=10, 10+3= 13, 13+3=16

Answer: Length = 90 meters

Width = 20 meters

Step-by-step explanation: Step 1: The formula for the area of a rectangle is A = length x width, so we can solve for the length of the field:

A = 2000

length x width = 2000

length = 2000 / width

Step 2: The formula for the perimeter of a rectangle is P = 2(length + width), so we can solve for the width of the field:

P = 180

2(length + width) = 180

2length + 2width = 180

2width = 180 - 2length

width = (180 - 2length) / 2

Step 3: Substitute the equation for width into the equation for length to solve for length:

A = 2000

length x (180 - 2length) / 2 = 2000

2length2 - 180length + 2000 = 0

length2 - 90length + 1000 = 0

(length - 90)(length - 10) = 0

length = 90

Step 4: Substitute the value of length into the equation for width to solve for width:

width = (180 - 2length) / 2

width = (180 - 2(90))

A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Answer: (m-3)(5m-2)

Step-by-step explanation:

5m^2-17m+6 factored is (m-3)(5m-2).

The central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

To find the central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

If you want the central angle in degrees, you can convert it using the fact that there are 2π radians in a full circle (360 degrees):

Central angle (in degrees) = (Arc length / Radius) * (180 / π)

Make sure to use consistent units for the arc length and radius, such as meters or centimeters, to obtain accurate results.

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Step-by-step explanation:

f(x) = 2x² + 5√(x - 2)

Domain

√(x - 2) ≥ 0

x - 2 ≥ 0

x ≥ 2

x is greater than or equal to 2

Answer: Greater than

Step-by-step explanation:

Answer: 50% I think

Step-by-step explanation: blue and orange are both good colors so I think it would be a 50/50 chance. blue isn't better then orange and orange isn't better then blue.

The answer is True. Finding a parametric description of the solution set of a linear system is the same as solving the system.

Finding a parametric description of the solution set of a linear system is equivalent to solving the system. A parametric description of the solution set of a linear system is a way of representing all solutions to the system in terms of a set of parameters. Solving a linear system involves finding the specific values of the variables that satisfy the constraints specified by the system. By finding a parametric description of the solution set, we are effectively solving the system and finding all possible solutions. In this sense, finding a parametric description of the solution set and solving the system are equivalent.

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Answer: Greatest common factor (GCF) of 12 and 28 is 4. We will now calculate the prime factors of 12 and 28 then find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12 and 28.

Step-by-step explanation: BRAINLESS PLEASE