4. Separate 77 into two parts so that one part is 4 less than twice as much as the other. Find each part.​

Answer:

The dimensions of the frame are 8 inches by 10 inches.

Step-by-step explanation:

Let's use "w" to represent the width of the frame. Then the length would be "w+2".

The perimeter of the frame is 36, so we can write an equation:

2(w + w+2) = 36

Simplifying the equation, we get:

4w + 4 = 36

4w = 32

w = 8

So the width of the frame is 8 inches, and the length would be 10 inches (8 + 2).

Therefore, the dimensions of the frame are 8 inches by 10 inches.

Answer:

\(7x+21\)

Step-by-step explanation:

Let the number be \(x\).

\(x+3\)

\(7(x+3)\)

Expand the brackets.

\(7x+21\)

The least squares regression quadratic polynomial for the given data points is y = 0.7x^2 + 1.1x + 1.8.

To find the least squares regression quadratic polynomial, we first need to set up a system of equations using the normal equations.

Let xi and yi denote the x and y values of the ith data point. We want to find the coefficients a, b, and c of the quadratic polynomial y = ax^2 + bx + c that minimizes the sum of the squared residuals.

The normal equations are:

nΣxi^4 + Σxi^2Σxj^2 + nΣx^2yi^2 - 2Σxi^3yi - 2ΣxiyiΣxj^2 - 2Σx^2yiΣxj + 2Σxi^2y + 2ΣxiyiΣxj - 2ΣxiyΣxj = 0

Σxi^2Σyi + nΣxiyi^2 - Σxi^3yi - Σxi^2Σxjyi + Σxi^2y + ΣxiΣxjyi - ΣxiyiΣxj - nΣyi = 0

nΣxi^2 + Σxj^2 + nΣxi^2yi^2 - 2Σxiyi - 2Σxi^2y + 2Σxiyi - 2Σxiyi + 2nΣyi^2 - 2nΣyi = 0

Solving these equations yields the coefficients a = 0.7, b = 1.1, and c = 1.8. Therefore, the least squares regression quadratic polynomial is y = 0.7x^2 + 1.1x + 1.8.

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Each banana Split costs $6 and each hot fudge sundae costs $2.

Let b be the cost of one banana split and h be the cost of one hot fudge sundae. We can set up a system of two equations with two variables based on the given information:

6b + 5h = 46    (equation 1)

2b + 5h = 22    (equation 2)

We can solve for one variable in terms of the other in one of the equations and substitute that expression into the other equation to solve for the remaining variable. For example, we can solve equation 2 for b in terms of h:

2b + 5h = 22

2b = 22 - 5h

b = (22 - 5h)/2

We can substitute this expression for b into equation 1 and solve for h:

6b + 5h = 46

6[(22 - 5h)/2] + 5h = 46

66 - 15h + 5h = 46

-10h = -20

h = 2

Now that we know the cost of one hot fudge sundae is $2, we can substitute this value into either equation to solve for the cost of one banana split:

6b + 5(2) = 46

6b + 10 = 46

6b = 36

b = 6

Therefore, each banana split costs $6 and each hot fudge sundae costs $2.

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Answer:

9 sides

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

To find the number of sides n divide the sum by 40°

n = 360° ÷ 40° = 9

Answer:

B

Step-by-step explanation:

We use the distance formula

Origin(0,0)

P(2,-5)

and get that it's root of 29

Answer:

it's B

Step-by-step explanation:

i just took the test and made sure that was the correct answer :-PPPPPPPPPPPPPPPPP

Answer:

choice b

Step-by-step explanation:

Answer: After the 10th day choice A will be ahead. Choice A will be at 51.2, and choice B will be at 50

Step-by-step explanation:

Day 1: $.10 / $5

Day 2:$.20 / $10

Day 3:$.40 / $15

Day 4:$.80 / $20

Day 5:$1.6 / $25

Day 6:$3.2 / $30

Day 7:$6.4 / $35

Day 8:$12.8 / $40

Day 9:$25.6 / $45

Day 10:$51.2 / $50

The Expected Value of a Discrete Probability Distribution

Given a number of events:

x = {x1, x2, x3,..., xn}

And their respective probabilities:

P = {p1, p2, p3,..., pn}

The expected value is calculated as follows:

We are given:

x = {-1.25, -0.25, 0, 1.25}

P = {0.1, 0.4, 0.2, 0.3}

Substituting:

Calculating:

The expected value is $0.15

Answer:

Hello...

Step-by-step explanation:

A)It is similar but not congruent.

B)segment AB.

C)angle A.

HOPE IT HELPS YOU DEAR.....

The answers to all parts are given below.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle PQR and line segment AB, which is parallel to QR.

[A] -

ΔPQR is similar to ΔPAB as -

∠P = ∠P (Common)

∠PAB = ∠PQR (Corresponding angles)

∠PBA = ∠PRQ (Corresponding angles)

Using AAA similarity rule, ΔPQR is similar to ΔPAB.

[B] -

Line segment AB corresponds to line segment QR

[C] -

∠A in ΔPAB corresponds to ∠Q.

Therefore, the answers to all parts are given above.

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Answer:

5.25

Step-by-step explanation:

4.20 ÷ 12 = 0.35

0.35 x 15 = 5.25

Answer:

\(f^{-1}(x)=-\frac{2}{5}x+2}\)

Step-by-step explanation:

Find the inverse of the function.

\(f(x)=\frac{5}{2}x+5\)

(1) - Switch f(x) and x

\(f(x)=-\frac{5}{2}x+5\\\\\Longrightarrow x=-\frac{5}{2}f(x)+5\)

(2) - Solve for f(x)

\(x=-\frac{5}{2}f(x)+5\\\\\Longrightarrow \frac{5}{2}f(x)=5-x\\\\\Longrightarrow f(x)=\frac{2}{5}(5-x)\\\\\Longrightarrow f(x)=\frac{10}{5}-\frac{2}{5}x \\\\\Longrightarrow f(x)=-\frac{2}{5}x+2\)

(3) - Replace f(x) with f^-1(x)

\(\therefore \boxed{f^{-1}(x)=-\frac{2}{5}x+2}\)

Thus, the inverse is found.

The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.

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To find the markup price you need to multiply the 83% by the cost:

83%=0.83

16*0.83=13.28

and the selling price is the cost plus the markup price so

16+13.28=29.28

So the answer is:

The mark up is $ 13.28 and the final selling price is $ 29.28

The quotient of the rational expression, x²- 49 / x + 2 ÷ x²- 14x + 49 / 3x + 6  is 3(x + 7) / (x - 7). The answer is C.

The number we obtain when we divide one number by another is the quotient.

Therefore, let's find the quotient of the rational expression as follows:

x²- 49 / x + 2 ÷ x²- 14x + 49 / 3x + 6

Hence, lets factorise individually,

x² - 49 = (x + 7)(x - 7)

x²- 14x + 49  = (x - 7)² = (x - 7)(x - 7)

3x + 6  = 3(x + 2)

Therefore,

(x + 7)(x - 7) /  (x + 2) × 3(x + 2) /  (x - 7)(x - 7)

(x + 7)  × 3 / (x - 7)

Therefore,

x²- 49 / x + 2 ÷ x²- 14x + 49 / 3x + 6 = 3(x + 7) / (x - 7)

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Answer:

Mean:15 Median:15 Mode:15

Step-by-step explanation:

Mean: 14+14+15+15+16+15+15+16= 120

120/8=15

Median: 14,14,15,15,15,15,16,16

Median is sorted from least to greatest and then it is the number that is in the middle

Mode is 15 because 15 appears the most often

Answer:

It would be B.

Step-by-step explanation:

divide Y by X.

The factored form of the given quadratic equation y = x^2 - 5x - 36 is y = (x - 9) (x + 4) and the x-intercepts of the given quadratic equation y = (x - 9) (x + 4) is (9, 0) and (-4, 0).

We are given a quadratic equation:

y = x^2 - 5x - 36

Let us factorize using the middle-term split method.

y = x^2 - 5x - 36

y = x^2 - 9x + 4x - 36

y = x (x - 9) + 4 (x - 9)

y = (x - 9) (x + 4)

So, the factorized form is y = (x - 9) (x + 4).

For x-intercepts, y should be zero.

So,

0 = (x - 9) (x + 4)

(x - 9) = 0 or (x + 4) = 0

x = 9 os  x = -4

So, the x-intercept will be (9, 0) and (-4, 0).

Thus, the factored form of the given quadratic equation y = x^2 - 5x - 36 is y = (x - 9) (x + 4) and the x-intercepts of the given quadratic equation y = (x - 9) (x + 4) is (9, 0) and (-4, 0).

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Answer:

A, B, D, E

Step-by-step explanation:

\(\sqrt{81}\) = ± 9 → D and E

Since 9 × 9 = 81 and - 9 × - 9 = 81

\(81^{\frac{1}{2} }\) = \(\sqrt{81}\) = 9 → B

- \(81^{\frac{1}{2} }\) = - \(\sqrt{81}\) = - 9 → A

Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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Answer:

H

Step-by-step explanation:

-4000 is the slope

pick a point

y = -4000x + 20000

Answer:

4,950

Step-by-step explanation:

:)

1,650-25% 3,300-50% 4,950-75% 5,280-100%

Step-by-step explanation:

convert the percentage to a decimal then multiply by 6,600. To get the number of people of 100%, divide 1.25 (the percent of 6,600) by 6,600. That should be right,

Answer:

You can set up the ratio 12.4:18.6 because it says that the parallelograms are similar.

Now simplify as much as possible

12.4:18.6

6.2:9.3

2:3

Step-by-step explanation:

Hope this helps! If it's wrong let me know so i can re-check it.

To determine the probability that the coating thickness for this process is less than 0.17, we need to count the number of thickness measurements that are less than 0.17 and divide it by the total number of measurements.

In this case, we have 5 thickness measurements: 0.15, 0.16, 0.17, 0.18, and 0.19. Out of these 5 measurements, only 2 measurements (0.15 and 0.16) are less than 0.17.

Therefore, the probability that the coating thickness is less than 0.17 is 2/5.

So the correct answer is 2/5.

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The critical t-score for estimating the population mean using a 99% confidence interval and a random sample of 35 individuals is approximately 2.733.

To estimate a population mean using a 99% confidence interval and a random sample of 35 individuals, you need to find the critical t-score.

Step 1: Determine the degrees of freedom. For a sample of 35 individuals, the degrees of freedom (df) = sample size - 1 = 35 - 1 = 34.

Step 2: Find the critical t-score using a t-table or an online calculator. For a 99% confidence interval and 34 degrees of freedom, the critical t-score is approximately 2.733.

Your answer: The critical t-score for estimating the population mean using a 99% confidence interval and a random sample of 35 individuals is approximately 2.733.

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Answer:

six dollars

Step-by-step explanation:

because each is a multiple of 3

Answer:

6

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Answer: 38

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

A simple way to find the answer is to first find 10% of 40 by moving the decimal one place to the left.

Then you have 4, multiply that by 9. Because 4 is 10% so 4 times 9 would give you 90%

Now you have 36, to find the last 5% just half 10%, so 2, and add that on

Your answer is 38.

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

The horizontal shift for the absolute value function f(x)=3 |x 6| 9 is  Left shift, 6 units.

f(x)=3 |x+6| +9

The horizontal shift is shown by the " +6 " at the x. X will always inform us of any horizontal or right/left movements. Therefore, changing the x results in a horizontal change.

But aware! Contrary to what you would believe, it is not. A LEFT shift is a PLUS6. (A MINUS6 would normally constitute a right shift, but not in this instance.)

This is the parent function:

f(x) = |x|

Hence, our equation:

f(x)=3 |x+6| +9

has undergone two alterations. LEFT6 as a result of

The x says " +6 ". Additionally, the equation's last +9 indicates a vertical shift of 9, or UP9.

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