A company is producing picture frames as well as the glass for the front of the frames. The amount of wood required for the frame is represented by the function W(x), and the amount of glass is represented by the function G(x). The frames have lengths represented by the function f(x) and widths represented by g(x). Which statement describes the combined functions W(x) and G(x)? The amount of glass required has a constant rate of change, but the amount of wood does not. The amount of wood required has a constant rate of change, but the amount of glass does not. Both the amount of wood required and the amount of glass required have a constant rate of change. Neither the amount of wood required nor the amount of glass required has a constant rate of change.

Answer:

37+82+x=180

119+x=180

x=180-119

x=61

Answer:

3

Step-by-step explanation:

if you look at the graph, you can see that the line intercepts where the points are

Paul earns more interest than Monica does.

Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time.

Given that,

Money deposited by Monica is $200 at simple interest of 3.7%.

Money deposited by Paul is $300 at simple interest of 2.9%.

The expression to calculate simple interest is given as,

(P × r × t)/100

Substitute the corresponding values to obtain the simple interest for both cases as follows,

Interest gained by Monica is (200 × 3.7 × 1)/100 = $7.4.

Interest gained by Paul is (300 × 2.9 × 1)/100 = $8.7.

Hence, monica is not correct as the interest earned by Paul is greater than that of monica.

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Answer:

[tex]\huge\boxed{\sf s = 320}[/tex]

Step-by-step explanation:

Given that,

[tex]s \propto t^2[/tex]

Converting proportionality into equality and adding a constant.

s = kt² ----------------(1)

Given that, s = 80 when t = 4

Put in Eq. (1)

80 = k(4)²

80 = k(16)

Divide 16 to both sides

80/16 = k

5 = k

Now,

Put t = 8 in Eq. (1)

s = (5)(8)²

s = (5)(64)

[tex]\rule[225]{225}{2}[/tex]

Answer: last one should be it

Step-by-step explanation:

Answer:

3rd one is correct.

Step-by-step explanation:

The required value of y is -20, when x is -5.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given that,

y varies directly with x,

implies that,

y = k x     (1)

Substitute the values x = 2 and y = 8,

8 = k x 2

k = 4

Substitute x = -5 and k = 4, to find the values of y,

y = -5 x 4

y = -20

The value of y is -20, when x is -5.

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Answer:

A), C)

Step-by-step explanation:

Let's round all numbers below to the nearest 10.

A) 34,590

B) 34,650

C) 34,590

D) 34,600

E) 35,010

The area of the Rhombus ABCD is 1.2 square meter.

What is Rhombus?

A quadrilateral with four equal-length sides is known as a Rhombus in plane Euclidean geometry. Another name for this shape is an equilateral quadrilateral because all of its sides are equal in length.

Let ABCD be the given Rhombus of Perimeter = 52 cm.

Since all the sides are equal to each other.

Therefore, each side of Rhombus measures = 13 cm

So,

AD = CD = 13 cm and AC = 24 cm.

Area of the triangle ACD = √[ s (s - a) (s - c) (s - d) ] ….. Heron’s Formula.

where s = semi-perimeter,

a, c, and d are side measures.

s = (1/2) [ 13 + 13 + 24 ] = 25

Area (A) = √[ 25 (25 – 13) (25 – 13) (25 - 24) ] = 60

Hence Area of the entire Rhombus = 2 * 60 = 120 cm²

Convert 120 cm^2 into meter square

⇒ 120 cm^2 = 1.2 m^2

Hence, the area of the Rhombus ABCD is 1.2 square meter.

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Answer: The possible outcomes are — 1, 2, 3, 4, 5, and 6. The probability of getting any of the outcomes is 1/6

Step-by-step explanation:

Given that there are six blue marbles in the bag out of a total of 16, there is a 3/8 chance that the marble selected will be blue.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

Total number of marbles in bag,

=3+6+5+2

=16 marbles

Number of blue marbles=6

Probability of selecting blue marbles,

=6/16

=3/8

The probability that the marble chosen is blue will be 3/8 as the bag contains 6 blue marbles when total number of marbles is 16.

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Answer:

$63.90

Step-by-step explanation:

cost = $639

markup = 10%

cost * markup = $63.90

Answer:

Step-by-step explanation:

Answer:

-2.875

Step-by-step explanation:

-12x-9-20x-4=79

-32x-13=79

-32x=92

92/-32= -2.875

Answer:

Step-by-step explanation:

The steps are given in option B and option C are used in paper folding.

When we simply fold the paper in such a manner that we can achieve our objectives, the method is called Paper Folding.

Now, WE get;

Option A can not be accomplished as we need the proper equipment to construct the circle.

Option B can be done by folding the paper along the point.

Option C can be done by folding the paper in the exact half measure.

Option D can not be done.

Hence, the steps are given in option B and option C are used in paper folding.

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Answer: i think either 256/6561 or -256/6561

Step-by-step explanation:

The physics student predicted that a force of 377.28N would be needed to stretch the spring by 15 cm using the regression model.

The relevant points from the regression model are

B. He predicted something that was outside the range of forces seen.

C. He predicted something that was outside the range of stretched distances that were observed.

D. His data contained outliers or significant points.

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There are 360 different skirt-blouse-shoe outfits can she wear.

What is outfits?

A group of clothes that have been specifically chosen or designed to be worn together is known as an outfit. The term "outfit" can also refer to a business, an association, or a team of people who collaborate frequently. It can be used as a verb to mean "provide with the necessary gear."

A dress is different from a blouse and a skirt!  So I'll rephrase this as how many ways can she dress, to wear one blouse, one skirt and one pair of matching shoes.

You just multiply the number of blouses, the number of skirts, and the number of pairs of shoes;

= 5*9*8 = 360

Hence, there are 360 different skirt-blouse-shoe outfits can she wear.

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Answer: 40

Step-by-step explanation: the answer is 40

Answer:

40

Step-by-step explanation:

12=[tex]\frac{30}{100}[/tex]*x

12=[tex]\frac{3}{10}[/tex]x

multiply both sides by 10/3

x=40

Zane's velocity climbing the volcano is given as follows:

B. 5/7 meters per second.

The linear function in the context of this problem is defined as follows:

y = 5/7x - 25.

Hence the coefficients of the linear function are given as follows:

The meaning of each of these coefficients is given as follows:

Thus the correct option of Zane's velocity climbing the volcano is of option B.

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The measure of both the angles will be x = 80° and y = 100°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Two lines are said to be parallel if they have same slope. These lines never intersect each other and have no common point of intersection.

Given is the same side interior angles of two parallel lines is 20° less than the other same side interior angles.

Same side interior angles are supplementary, we can write -

x + x + 20 = 180

2x = 160

x = 80°

Other angle will be -

y = x + 20 = 100°

y = 100°

Therefore, the measure of both the angles will be x = 80° and y = 100°.

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The given statement that Diagonal WY bisects angles ZWX and ZYX has been proven below to be true.

Bisection of an angle is simply defined as dividing an angle into two equal parts.

We are given that Diagonal WY bisects angles ZWX and ZYX.

Now, from the image attached, we can see that side XY is congruent to side ZY and so; XY ≅ ZY.

Similarly, XW is congruent to ZW and as such; XW ≅ ZW

Since XY is congruent to ZY and XW is congruent to ZW, then the statement that  diagonal WY bisects angles ZWX and ZYX is true

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Answer:

below

Step-by-step explanation:

density  *   volume = mass

7.92 g / cm^3    *   60 cm^3 = 475.2 g

By using t distribution, it can be calculated that

b) Degree of freedom is 65

c) P value of 2.115 at 65 degrees of freedom = 0.0383

What is t-distribution?

t - distribution is used to find the distance between two sample means if the population standard deviation is unknown and it is assumed that the observation comes from a normally distributed population.

b) Here,

Degree of freedom =

[tex]=\frac{(\frac{s_1^2}{n_1} + \frac{s_1^2}{n_2})^2}{\frac{s_1^4}{n_1^2(n_1 -1)} + {\frac{s_2^4}{n_2^2(n_2 -1)}}}\\\\=\frac{(\frac{5.3^2}{35} + \frac{8.8^2}{40})^2}{\frac{5.5^4}{35^2(35 -1)} + {\frac{8.8^4}{40^2(40 -1)}}}[/tex]

=  65

c) The value of test statistic obtained is 2.115

P value of 2.115 at 65 degree of freedom = 0.0383

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Complete Question

The complete question has been attached

Differentiation reverses the parity of a function, means if f(x), is an even function, then its derivative f'( x ) is odd which is true i.e f(x) is even function implies f'(x) is odd and if f(x) is odd function implies f'(x) is even .

First, let's we start with the definition of even and odd functions.

f is even if and only if f(x) = f(-x) --(1)

f is odd iff f(x) = -f(-x) ---(2)

If f is even and differentiating equation (1) we get,

f'(x) = f'(-x)× (-1) = -f'(-x).

f'(x) = - f'(-x).

Since, f'(x) is some function, then let

g(x) = f'(x) So, we see g(x) = -g(-x) which shows that the derivative of an even function is an odd function.

If f is odd then: f(x) = -f(-x)

differentiating above function with respect to x we get ,

f'(x) = -f'(-x)× (-1 ) = f'(-x).

Let g(x) = f'(x), then g(x) = g(-x) which shows that the derivative of an odd function is an even function.

Hence, Differentiation reverses the parity is hold.

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The equation which is equivalent to 60% of 25 is x = 0.6 * 25

1. Equivalent equations: Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.

2. How to find equivalent equation : Steps to find weather the equations are equivalent are:

An equation is used to show the relationship between variables, numbers.

Let x represent the value of 60% of 25. Hence:

x = 60% of 25

x = 0.6 * 25

Hence the equation which is equivalent to 60% of 25 is x = 0.6 * 25

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a)The linear equation is C=25n + 2500 to produce n 3000 toys, b) The total cost to produce 3000 toys is $77,500, c) With $32500, a total of 1200 toys can be produced in Pinwheel Industries.

An equation is a mathematical statement with an equal symbol (=) between the algebraic expression. Equations with a degree of one are called linear equations. It is the straight line's equation. Whenever values are substituted for the unknown values in linear equations, the solutions produce values that make the equation true. Since there is only one variable, there is only one solution. For instance, the equation x + 2 = 0 has just one solution, which is x = -2. In the case of the two-variable linear equation, however, the solutions are determined as the Cartesian coordinates of a point on the Euclidean plane.

The three different types of linear equations are: 1) Standard Form

2) The slope intercept form

3)Point Slope Form

How to solve?

A) Linear equation y=mx+b,

C (total cost) = y and n (number of toys) =x.

C=25n + 2500

B) Put n=1750

C= 25(3000) + 2500

C= $77,500

C)

32500= 25n +2500

30000=25n

n = 1200

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4 square units will be the area of the largest rectangle.

Given,

First, let's build a rectangle ABCD, where A is the point at the bottom right corner and B,C, and D are the points designated in accordance with A.

Now,

Let A = (p, 0)

B = (-p, 0)

C = (-p, 3 - p²)

D = (p, 3 - p²)

Then the area of rectangle is given as: BA×AD

= 2p × 3 - p²

A = 6p - 2p³

Taking the derivative with respect to p, we have

A' = 6 - 6p²

Now,

A' =0

⇒ 6 - 6p² = 0

⇒ 6p² = 6

⇒ p² = 1

Since, we have to find the greater area, therefore we will take p = 1.

Now, substituting the value of p in (A), we have

Greater area = A= 6 - 2 x 1 = 4 square units

Therefore,

The  area of the largest rectangle should be 4 square units.

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Question is incomplete. Completed question is given below;

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x2?

Relative dimensions which will make the surface area a maximum is

x=y = \sqrt{area/3 }

z = 1/2(  \sqrt{area/3 })

Volume = 2xh

Let the box have dimensions x,y,z>0.

The surface area is A=xy+2xz+2yz

The volume is V=xyz

The Lagrangian is L=V−λ(A−constant)=xyz−λ(xy+2xz+2yz−constant).

∂L∂x=yz−λ(y+2z)=0

∂L∂y=xz−λ(x+2z)=0

∂L∂z=xy−λ(2x+2y)=0

Hence, λ=yzy+2z=xzx+2z=xy2x+2y

On cross multiplication,

xyz+2yz2=xyz+2xz2which implies x=y.

Cross-multiplying the middle and the right expressions ,2x2z+2xyz=x2y+2xyzwhich implies z=12y.

So, optimal volume with fixed surface area is to have the width and the depth equal and the height to be half the width and depth.

To find x,y,z given a fixed surface area Area one would use x=y=2z in the equation

Area=xy+2xz+2yz=x2+x2+x2 so

x=y = \sqrt{area/3 }

z = 1/2(  \sqrt{area/3 })

Volume is a measurement of three-dimensional space that is occupied. Numerous imperial units or SI-derived units, such as the cubic metre and litre, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.

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