right and can solve and find the answer to the following rate problems a gardener store sell 6 plant per hour how many plants they will sell in 5 hours

Answer:

(48, 3), (80, 5), (160, 10)

Answer:

\(g^-^1(x)=-8\)

\(h^-^1(x)=\frac{x-4}{3}\)

\((h^-^1 \ o\ h)(-3)=-3\)

Step-by-step explanation:

When given the following functions,

\(g=[(-2,-7),(4,6),(6,-8),(7,4)]\)

\(h(x)=3x+4\)

One is asked to find the following,

1. Question 1

\(g^-^1(4)\)

When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;

\(g^-^1(4)\)

\(g(4)=6\\g(6)=-8\\g^-^1(4)=-8\)

2. Question 2

\(h^-^1(x)\)

Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,

\(h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)\)

\(h^-^1(x)=\frac{x-4}{3}\)

3. Question 3

\((h^-^1 \ o\ h)(-3)\)

This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function (\(h^-^1\)) and simplify. Then substitute (-3) into the result.

\(h^-^1\ o\ h\)

\(\frac{(3x+4)-4}{3}\\\\=\frac{3x+4-4}{3}\\\\=\frac{3x}{3}\\\\=x\)

Now substitute (-3) in place of (x),

\(=-3\)

Answer:

I believe it is 4

Step-by-step explanation:

Answer:

9/2

Step-by-step explanation:

m=∆y/∆x

m= (5+4)/(2—0)

m=9/2

Answer:

$437.74

Step-by-step explanation:

16 x 44 = 704 -150=554 x 0.08= 554-44.32= 509.68 x 0.07= 509.68 - 35.6776 = 474 x 0.0765 = 474 - 36.261 = 437.74

Answer:

$ 394.54

Step-by-step explanation:

Sarah makes $16 and hour. She works 44 hours this week.

Optional deductions are

- $50 for health insurance and

- $100 for child care.

- Federal  taxes are 8%

- State taxes are 7% and

- FICA is 7.65%.

What is Sarah's NET  pay?

salary for a week: $16 x 44 =                   $704

deductions:

- health insurance and                             - $50

- child care.                                               - $100

- Federal  taxes are 8%  = 0.08 (704) =   - $53.32

- State taxes are 7% 0.07 (704)          =   - $49.28

- FICA is 7.65% = 0.0765 (704)          =    -$53.86

                                                                ---------------

                                                  total = $ 394.54  (net pay)

A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.

In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.

Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).

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Answer:

it’s D dotted line with shading below

Step-by-step explanation:

i got it on my quiz

Answer:

x = 9 , y = 12

Step-by-step explanation:

Solve the following system:

{4 y - 5 x = 3

x = 2 y - 15

Hint: | Perform a substitution.

Substitute x = 2 y - 15 into the first equation:

{4 y - 5 (2 y - 15) = 3

x = 2 y - 15

Hint: | Expand the left-hand side of the equation 4 y - 5 (2 y - 15) = 3.

4 y - 5 (2 y - 15) = 4 y + (75 - 10 y) = 75 - 6 y:

{75 - 6 y = 3

x = 2 y - 15

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{75 - 6 y = 3

x = 2 y - 15

Hint: | Isolate terms with y to the left-hand side.

Subtract 75 from both sides:

{-6 y = -72

x = 2 y - 15

Hint: | Solve for y.

Divide both sides by -6:

{y = 12

x = 2 y - 15

Hint: | Perform a back substitution.

Substitute y = 12 into the second equation:

{y = 12

x = 9

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 9 , y = 12

When you know the area and one side of a rectangle, divide the area by the known side to find the length of the other side.

Length = 63/6

Length = 10.5 inches

Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

Answer:

25%

Step-by-step explanation:

Take the new price and subtract the original price

15-12 = 3

Divide by the original price

3/12 = .25

Multiply by 100%

25%

The percent increase is 25%

Answer:

6 or -1.5

Step-by-step explanation:

We can let this integer be x.

Therefore, according to the question we have:

\(2x^2-18=9x\)

Subtracting 9x, we have a quadratic:

\(2x^2-9x-18=0\)

Plugging into the quadratic equation:

\(\frac{9+\sqrt{81+144}}{4}, \frac{9-\sqrt{81+144}}{4},\)

the square root of 81+144 is 15, so the answer is either 6 or -1.5

Answer:

median: 6

Range: 9

Mode: 7

Step-by-step explanation:

Answer:

a) 6

b) 0

c) 7

Step-by-step explanation:

a) the middle number in a sorted ascending or descending order.

b) the difference between the highest number and the lowest

c) The most frequent number

Answer:

Below.

Step-by-step explanation:

So 4-6 to 8-12.

4 can be devised by 12, and so can 6.

4:8 6:12

If we flip them over we can find the dilation.

so?

8:4 12:6

Each can be divided by 2.

So the factor if dilation is 2.

The statistical analysis is created using the chi-squared test. The significance level used is 5% because of the probability to reject the null hypothesis. The given data indicate that there are significant preferences among the four flavors of ice cream.

When the sample sizes are big, the statistical hypothesis test known as the chi-squared test is utilized in the study of contingency tables. This test is primarily used to determine whether two categorical factors have independent effects on the test statistic. We shall use a significance level of α=0.05 in this case.

First, determine the null and alternative hypotheses.

Null hypothesis H₀: There is no preference in choosing ice cream flavors.

Alternate hypothesis H₁: There is a preference in choosing ice cream flavors.

The probability of choosing a particular flavor of ice cream is 1/4. Then, the Ei= (1/4)×80= 20.

Now construct the chi-square table. And find the chi-square value,

\(\begin{aligned}\chi^2&=\sum\frac{(O_i-E_i)^2}{E_i}\\&=3.2+0.2+3.2+0.2\\&=6.8\end{aligned}\)

Find the degree of freedom (df).

df = n-1 = 4-1 = 3.

From the chi-square table, using the chi-square value and df, we get the p-value,

P(χ²＞6.8)= 0.0786

Here, the p-value is greater than 0.05. As a result, the alternative hypothesis is accepted and the null hypothesis is rejected. From this, we can tell that there is a significant preference in choosing the flavors.

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The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

Null hypothesis: The proportion of homes in Oregon heated by natural gas is the same as the reported national average of 45%.

Alternative hypothesis: The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

We can use a two-tailed z-test to test this hypothesis.

The test statistic is calculated as:

z = (p - P) / √[P(1-P)/n]

where p is the sample proportion, P is the hypothesized population proportion (0.45), and n is the sample size.

Using the values given in the problem, we have:

p = 175/314 = 0.557

P = 0.45

n = 314

Plugging these values into the formula, we get:

z = (0.557 - 0.45) / √[0.45(1-0.45)/314] = 3.039

Using a standard normal distribution table, we find that the probability of getting a z-value of 3.039 or higher (in absolute value) is less than 0.005.

Since the significance level is 0.05, which is greater than the p-value, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Therefore, the proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

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(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

56x - 7 =

56x = 7

x = 7/56

x = ⅛

the answer is 1/8

there's no formula but u only have to shift to the other side and change the sign

Answer:

-2

Step-by-step explanation:

because Multiply 2 and 5 to get 10.

10−4×3

Multiply 4 and 3 to get 12.

10−12

Subtract 12 from 10 to get −2.

−2

Answer:

A.

Step-by-step explanation:

Just means for every 4 cans of soup, you need 3 pb jars

Cans of soup : jars of peanut butter

4:3

8:6

16:12

20:15

Answer: 139/7

Step-by-step explanation:

Answer:

139/7

Step-by-step explanation:

182/10 = 18.2 < 18 7/11

219/12 = 18 + 3/12 = 18 1/4  < 18 7/11

139/7 = 19 + 4/7 > 18 7/11

179/10 = 17.9 < 18 7/11

Answer:

x = 1/2 or .5

Step-by-step explanation:

JK = 7x + 2, KL = 5x + 4 and JL = 12

JK + KL = JL

Plug in the equations for the Lines

7x + 2 + 5x + 4 = 12

Combine like-terms

12x + 2 + 4 = 12

12x + 6 = 12

Subtract 6 from either side

12x + 6 = 12

      -6      -6

12x = 6

Divide either side by 12

12x / 12 = 6/ 12

x= 1/2 or .5

Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Answer:

x = 23/5 and y = 7/20

Step-by-step explanation:

2x + 8y = 12 and 3x - 8y = 11 are two given equations

Now,

Step 1:

2x + 8y = 12 ...(1)

3x - 8y = 11 ...(2)

Step 2:

From equation (2) we get the value of x

i.e.,

3x - 8y = 11

3x = 8y + 11

x = 8y + 11/3

Step 3:

Now,

Put the value of x = 8y + 11/3 in equation (1) we get,

i.e.,

2x + 8y = 12

2(8y + 11/3) + 8y = 12

16y + 22/3 + 8y = 12

16y + 22 + 8y(3)/3 = 12

16y + 22 + 24y/3 = 12

16y + 24y + 22 = 12 * 3

40y = 36 - 22

40y = 14

y = 14/40

y = 7/20

Step 4:

Now,

Substitute the value of y = 7/20 in equation (2) we get,

i.e.,

3x - 8y = 11

3x - 8(7/20) = 11

3x - 56/20 = 11

3x - 14/5 = 11

3x = 11 + 14/5

3x = 11 * 5 + 14/5

3x = 55 + 14/5

3x = 69/5

x = 69/3 * 5

x = 23/5

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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Answer:

B and D

Step-by-step explanation: I got it right