What is the surface area of the right rectangular prism?
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The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

17

Step-by-step explanation:

because the mode is the number the appeared the most

x= 60.34 is the solution to In x = 4.1 , rounded to the nearest two decimal places.

The value of x from the give equation is 60.3402. Therefore, option D is the correct answer.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given equation is ln x=4.1.

Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.

Exact Form:

\(x=e^{4.1\)

Decimal Form: x=60.3402

Therefore, option D is the correct answer.

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The square of a binomial, when the binomials are subtracted, is defined as follows:

(a - b)² = a² - 2ab + b².

When the two binomials are added, the square is given as follows:

(a + b)².

Expanding the square, we have that:

(a + b)² = (a + b) x (a + b).

(a + b)² = a² + ab + ab + b².

(a + b)² = a² + 2ab + b².

Which is the result presented in this problem.

Now, when the binomial has a minus sign, involving a subtraction, the pattern is obtained as follows:

(a - b)² = (a - b) x (a - b).

(a - b)² = a² - ab - ab + b².

(a - b)² = a² - 2ab + b².

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Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. The true statements are A, D, and E.

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.

The following points about the scatter plot are true,

A. The graph shows a linear association

As there can be drawn a line between the two axes of the graph, and this line will give the approximate values, therefore, the graph shows a linear association. Thus, the statement is true.

B. The graph has no outliers

The graph has an outlier lying at the bottom right of the graph. Thus, the statement is False.

C. The graph shows a nonlinear association

As the graph has a linear association, it can not have a non-linear association. Thus, the statement is False.

D. The graph shows a positive association.

As the slope of the imaginary line is positive, the graph shows a positive association. Thus, the statement is true.

E. The graph could be used to show an association between the hours worked and the amount earned.

The above situation can be depicted by the given graph. Thus, the statement is true.

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Answer:

4/9 = 2/ x = 4.5

Step-by-step explanation:

Hope this would help.

Answer: The answer is 2/4.5

Step-by-step explanation: I found this because 4 is half of two so i just found half of nine and got my answer.

Hope this helps.

Missy will need a minimum of 570 square inches of wrapping paper to completely cover the box.

To calculate the minimum amount of wrapping paper needed to cover the box, we need to find the surface area of the box.

A rectangular box has six sides: a top, a bottom, two sides, and two ends.

The top and bottom sides have the same dimensions, which are 17.5 inches by 10 inches. So each of these sides has an area of 17.5 in × 10 in = 175 square inches.

The two side surfaces also have the same dimensions, which are 17.5 inches by 4 inches.

Each of these sides has an area of 17.5 in × 4 in = 70 square inches.

The two end surfaces have the same dimensions, which are 10 inches by 4 inches. Each of these sides has an area of 10 in × 4 in = 40 square inches.

To find the total surface area of the box, we add up the areas of all six sides:

175 in² (top) + 175 in² (bottom) + 70 in² (side 1) + 70 in² (side 2) + 40 in² (end 1) + 40 in² (end 2)

Total surface area = 570 in².

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Answer:

y>-2

Step-by-step explanation:

Answer on E2020

Answer:

The correct answer is D)  y>-2

Step-by-step explanation:

Edge 2021.

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Answer: 2 patches of fabric needed

Step-by-step explanation:

Given

Quilt: 6 ft × 8 ft

Fabric: 4 ft × 4 ft

Solve

Area of quilt=4×8=32 ft²

Area of fabric=4×4=16 ft²

To find the number of fabric needed, we need to divide the area of fabric from the total area of the quilt.

32/16=2

Hope this helps!! :)

Please let me know if you have any questions

Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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Answer:

C. 101 3/4; $1017.50

Step-by-step explanation:

Correct on E2020!

Answer:

  (3x +1)(x -7)

Step-by-step explanation:

Identify the first and last coefficients, and form their product.

  (3)(-7) = -21

Find factor pairs of this number that have a sum equal to the middle coefficient.

  -21 = (1)(-21) = (3)(-7) . . . . . sums are -20, -4

Rewrite the middle term as the sum of these factors.

  3x^2 +x -21x -7

Factor pairs of terms.

 x(3x +1) -7(3x +1) = (x -7)(3x +1) . . . . your factorization

The value of covariance cov(y1, y2) is -0.222

                      y1      

y2         0         1         2          Total

0          1/9      2/9     1/9          4/9

1          2/9      2/9      0            4/9

2          1/9        0       0            1/9

Total   4/9       4/9     1/9          1      

  marginal distribution of y2:

y2      P(y2)      y2P(y2)      y2^2P(y2)

0         4/9        0.0000        0.0000

1          4/9         0.4444        0.4444

2          1/9         0.2222        0.4444

total      1          0.66667       0.88889

E(y2) = 0.6667

E(y2^2) = 0.8889

Var(y2) = E(y2^2)-(E(y2))^2=0.4444

marginal distribution of y1  

y1       P(y1)       y1P(y1)      y1^2P(y1)

0         4/9       0.0000      0.0000

1          4/9        0.4444       0.4444

2          1/9         0.2222      0.4444

total  1.00          0.6667      0.8889

E(y1) = 0.6667

E(y1^2) = 0.8889

Var(y1)= σy = E(y1^2)-(E(y1))^2 = 0.4444

E(XY) =∑xyP(x,y)=0.2222

Cov(y1,y2) = -0.222

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Using sine rule, the value of B in the triangle is 53.13°

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other. The other names of the law of sines are sine law, sine rule and sine formula

The law of sine is explained in detail as follow:

In a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.

Mathematically, this can be represented as;

a / sin A = b / sin B = c / sin C

In this question given;

a = 400, b = 300, A = 2θ, B = θ

Using sine law;

a / sin A = b / sin B

400 / sin (2θ) = 300 / sin θ

400 / sinθcosθ = 300 / sinθ

400 / tanθ = 300

tan θ = 4/3

θ = tan⁻¹(4/3)

θ = 53.13°

The value of B is 53.13°

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Answer:

336

Step-by-step explanation:

7x48=

7(8)= 56

7(4)+5= 33

7(48) = 336

Answer:

336

Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

The new balance is a credit of $ 48.78.

Since Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%, and during the monthly billing cycle, Ben charged $ 238.75, made a payment of $ 300.00, and had a finance charge of $ 7.99, to find his new balance, the following calculations must be performed:

Therefore, the new balance is a credit of $ 48.78.

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Answer:

the constant of proportionality is 16

Step-by-step explanation:

To find the constant you have to find what 1 equals so when dividing 48 by 3 you get 16.

Sunn Comp sells a product for $120 per unit, with a variable cost of $84 per unit, according to the information provided.

As a result, the company generates a contribution margin of $36 per unit ($120 - $84).

What is unit?

A unit is a recognized quantity that is used in measuring.

For instance, when you say, "I traveled 50 meters," you are expressing the distance in numbers, i.e., 50, and the unit is meter.

5 kg of veggies; the unit used here is kg (kilogram).

Sunn Comp is a business that focuses on producing just one kind of goods.

The variable cost of this good is $84 per unit, but it sells for $120.

So, the company's units each have a contribution margin of $36.

In order for the business to turn a profit and pay its fixed annual costs of $529200, it must sell a particular number of units.

Divide the fixed costs by the contribution margin per unit to find the break-even threshold.

To break even and pay its fixed costs, Sunn Comp needs to sell at least units of its product.

For Sunn Comp, being aware of the break-even point is crucial.

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The complete question is:

Sunn Company manufactures a single product that sells for $120 per unit and whose variable costs are $84 per unit. The company's annual fixed costs are $529,200. (1) Prepare a contribution margin income statement at the break-even point. (2) If the company's fixed costs increase by $132,000, what amount of sales (in dollars) is needed to break even? Complete this question by entering your answers in the tabs below. Required 1 Required 2 Prepare a contribution margin income statement at the break-even point. SUNN COMPANY Contribution Margin Income Statement (at Break-Even) Percentage Amount of sales Required 1 Required 2 Prepare a contribution margin income statement at the break-even point. SUNN COMPANY Contribution Margin Income Statement (at Break-Even) Percentage Amount of sales Contribution margin Fixed costs Income Sales < Required 1 Required 2 > Variable costs Complete this question by entering your answers in the tabs below. Required 1 Required 2 If the company's fixed costs increase by $132,000, what amount of sales (in dollars) is needed to break even? Break-Even Point in Dollars Numerator: 1 Denominator: = Break-Even Point in Dollars / Break-even point in dollars S < Required 1 Required 2

Answer:

-4

Step-by-step explanation:

Given:

To Find:

Concept used:

For the given equation, we have

a = 3, b = -12 and c = 108

So, Slope of line perpendicular to given line = -12/3 = -4

So, the slope of required line is -4.

The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

3x - 12y = - 108

Convert the equation into a slope intercept, then we have

3x - 12y = - 108

12y = 3x + 108

y = (1/4)x + 9

The product of the slopes of the perpendicular line will be a negative one. Then we have

(1/4)m = -1

m = - 4

The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.

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Answer:

4

Step-by-step explanation:

its 4 duh

Answer:

Step-by-step explanation:

2 + 2 = 4

The Find any domain restrictions on the given rational equation is: C. x = 5  D. x = -7.

The given rational equation is:

x/(2x + 14) + (x - 4)/6 = 3/(x^2 + 2x - 35)

To find any domain restrictions on this equation, we need to look for any values of x that would make the denominator of any fraction equal to zero, since division by zero is undefined. Let's check each denominator:

The denominator 2x + 14 can be factored as 2(x + 7). This expression will be zero when x = -7/2. So, we have a domain restriction at x = -7/2.

The denominator 6 is a constant, so it does not impose any domain restrictions.

The denominator x^2 + 2x - 35 can be factored as (x + 7)(x - 5). This expression will be zero when x = -7 or x = 5. So, we have domain restrictions at x = -7 and x = 5.

Therefore, the domain restrictions for the given rational equation are:

C. x = 5  D. x = -7

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The correct question is:

Find any domain restrictions on the given rational equation:

x/2x +14 + x -4/6 = 3/x^2 +2x -35

Select all that apply.

A. x = 4

B. x = -7

C. x = 5

D. x = 0

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

9 pounds = $8.37

1 pound = $0.98

The amount saved per pound is $0.98

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Krystal bought 9 pounds of ground beef. She saved $8.37 by using a coupon.

This means,

9 pounds = $8.37

Divide both sides by 9.

1 pounds = 8.37/9

1 pounds = $0.93

Thus,

The amount saved per pound is $0.98

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An ellipse is defined as the set of all points such that the sum of the distances between the point and the two foci is constant. The equation of an ellipse can be represented in the standard form as:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to a vertex, and b is the distance from the center to the focus.

Given that the center of the ellipse is at (2, 1), one vertex is at (2, -4), and one focus is at (2, -2), we can use this information to find the values of a and b, and represent the equation of the ellipse:

a = distance from center to vertex = |1 - (-4)|/2 = 2.5

b = distance from center to focus = |1 - (-2)|/2 = 1.5

The equation of the ellipse is:

(x-2)^2/2.5^2 + (y-1)^2/1.5^2 = 1

which can also be written as:

(x-2)^2/6.25 + (y-1)^2/2.25 = 1

This equation represents the ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)

Answer:

x<-2

Step-by-step explanation:

Using mental maths to solve the problem of 8.02 - 5.98 gives a difference of 2.04.

Mental mathematics is the method of working out maths calculations and solving problems in one's head (mentally) without writing them down or using calculators.

Mental maths provides a quick way of arriving at arithmetical solutions without mathematical tools.

First value =       8.02

Second value = 5.98

Difference =      2.04

The mental method used to solve the problem is the removal of the decimal points, thus making the values look like these whole integers:

First value =       802

Second value = 598

Difference =      204

After obtaining the difference as 204, the two decimal places are replaced to arrive at the final answer.

Thus, using mental maths to solve the problem of 8.02 - 5.98 gives a difference of 2.04.

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