The table shows the hours, h. Gianna worked, and the amount of money, m, she earned.
Hours (h) Money (m)
4
$44
8
$88
12
$132
Write an equation to represent the relationship between the number of hours worked and the amount of money earned.
m
h

Answer:

37.5

Step-by-step explanation:

150/4 divide it hope this helps

Answer:

-4d

Step-by-step explanation:

Answer:

n = 13

Step-by-step explanation:

Given

n - 26 = - 13 ( add 26 to both sides )

n = 13

Final Answer: \(n = 13\)

Steps/Reasons:

Question: Solve for n. n - 26 = -13. n = ?

Step 1: Add 26 to both sides.

\(n = -13 + 26\)

Step 2: Simplify -13 + 26 to 13.

\(n = 13\)

~I hope I helped you :)~

Answer:

6g + 6h

Step-by-step explanation:

6(g+h) = 6×g + 6×h

The 340 liters of leaves did Adam rake.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Let X = the liters of leaves that Adam raked.

We have to find How many liters of leaves did Adam rake.

According to given question we have

Convert 5.0% into a decimal by moving the decimal point two spaces to the left we get

Then Tapiwa raked X + .05X liters of leaves is equal to 1.05X liters of leaves  is equal to 357.

Divide both sides by 1.05

X = 340 liters

Therefore, the 340 liters of leaves did Adam rake.

Learn more details about arithmetic here:

https://brainly.com/question/11559160

#SPJ1

By composite compostion f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions

A function is a relationship between inputs where each input is related to exactly one output.

Given: f(x) = 5x-6 and f⁻¹(x) = (x+6)/5

To show the inverse relationship exists using composite composition, f(f⁻¹(x)) must be equal to f⁻¹(f(x))

Let's check:

f(f⁻¹(x)) = f((x+6)/5)

Substitute x = (x+6)/5  into  f(x) = 5x-6:

f(f⁻¹(x)) = 5((x+6)/5) - 6

f(f⁻¹(x)) = (x+6)- 6

f(f⁻¹(x)) = x

Also,

f⁻¹(f(x)) = f⁻¹(5x-6)

Substitute x = 5x-6 into f⁻¹(x) = (x+6)/5:

f⁻¹(f(x)) =  ((5x-6)+6)/5

f⁻¹(f(x)) =  5x/5

f⁻¹(f(x)) =  x

Since f(f⁻¹(x)) = f⁻¹(f(x)). Therefore, f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions

Learn more about composite composition of inverse function on:

brainly.com/question/29363352

#SPJ1

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

The proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places.

To find the proportion of Arts majors who have not found a job, we first need to calculate the total number of students who have not found a job.

The total number of students who have not found a job would be 1500 - 1380 = 120.

To calculate the proportion of students who have not found a job, we can divide the number of students who have not found a job by the total sample size:

The proportion of students who have not found a job = 120 / 1500 = 0.08 or 8%.

Therefore, the proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places. This suggests that a majority of the graduating Arts majors from the University of Western Cape have found employment before their graduation.

To learn more about Proportion :

https://brainly.com/question/1496357

#SPJ11

Answer:

8 3 -2 -7

Step-by-step explanation:

becoz the y values are the ranges of the function

Answer:

{y: y = –7, –2, 3, 8}

Step-by-step explanation:

To check out how efficient or accurate a model is, we use the akaike information criterion or the Bayesian. If the AIC or BIC are lower, then this model would be better. They are also used to control for model complexity

Akaike information criterion = 2k-2ln where k is the number of parameter. A higher k gives a higher AIC.

In the real world complex models are discouraged and avoided since

1. They cause data to be over fitted and can capture noise and information from this data.

2. They are complex and therefore difficult to interpret

3. They consume a lot of time and computing them has several inefficiencies.

Using these two as measure of performance, we can select optimal choice of independent variable.

With forward/backward regression, we are able to put new variables in the model or remove from it. The best is the one with lowest AIC.

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

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

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

Read more about trigonometry functions at

https://brainly.com/question/24349828

#SPJ1

Answer:

-110601

Step-by-step explanation:

All you have to do is replace the variables with their value. So the equation would look like this,

6(-8)³ - 9

Always solve the parenthesis first ending up with

-48³ - 9

Now the exponents,

-110592 -9

Here we just subtracting getting the answer of...

-110601

Hope that helps and have a great day!

We know that two vertical angles are equal.

\(108° \: = \: (12x \: + \: 24)°\)

\( - 12x \: = \: 24 \: - \: 108\)

\( - 12x \: = \: -84\)

\( \boxed{ \bold{x \: = \: 7°}}\)

We know that a complete angle measures 360°.

\(108° \: + \: 108° \: + \: z \: + \: z \: = \: 360°\)

\(216 \: + \: 2z \: = \: 360\)

\(2z \: = \: 360 \: - \: 216\)

\(2z \: = \: 144\)

\( \boxed{ \bold{z \: = \: 72°}}\)

Answer:

x=−4 or x=6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: We can use both formulas to calculate the interest on an investment of $3500 at 2.75% for 3 years.

Using the formula A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years, we have:

A = 3500(1+0.0275/1)^(1*3) ≈ $3843.84

Therefore, the interest earned is:

Interest = A - P = $3843.84 - $3500 = $343.84

Using the formula A = Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.71828, we have:

A = 3500e^(0.0275*3) ≈ $3843.84

Therefore, the interest earned is:

Interest = A - P = $3843.84 - $3500 = $343.84

The interest earned is $343.84 in both cases.

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

For such more questions on differential equation

https://brainly.com/question/18760518

#SPJ8

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Answer:

99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].

Step-by-step explanation:

We are given that a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans.

Firstly, the Pivotal quantity for 99% confidence interval for the population proportion is given by;

                           P.Q. =  \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\)  ~ N(0,1)

where, \(\hat p\) = sample proportion of customers who purchased boot-cut jeans = \(\frac{56}{178}\) = 0.315

           n = sample of customers = 178

           p = population proportion of customers who prefer boot-cut jeans

Here for constructing 99% confidence interval we have used One-sample z test for proportions.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                 of significance are -2.58 & 2.58}  

P(-2.58 < \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < 2.58) = 0.99

P( \(-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < \({\hat p-p}\) < \(2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ) = 0.99

P( \(\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < p < \(\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ) = 0.99

99% confidence interval for p = [ \(\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\), \(\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\)]

    = [ \(0.315-2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }\) , \(0.315+2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }\) ]

    = [0.225 , 0.405]

Therefore, 99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].

The interpretation of the above confidence interval is that we are 99% confident that the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans will lie between 0.225 and 0.405.

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:

See below.

Step-by-step explanation:

Gertrude is correct. Any angle can have one line of symmetry going directly down the center of the angle, intercepting at the angles point. Emmet is incorrect because not only polygons can have lines of symmetry. A circle, square, rhombus, etc. can have lines of symmetry.

Answer: X axis , Y axis , y=-2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angles are supplementary, so they add to 180.

x + (6x -2 ) = 180

7x = 182

x = 182/7 = 26 = m∠2

6(26) - 2 = 154 = m∠1

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

Learn more about circles at:

https://brainly.com/question/1559324

#SPJ1