USING YOUR MATH
4. A semi-truck is being loaded with boxes of varying weights. The total weight of boxes loaded is shown below as a function of the number of boxes loaded into the truck.
(a) For each interval below, find the average rate of change. Do not round. Include units with your answers.
5 to 11 boxes:
11 to 20 boxes:
20 to 25 boxes:
(b) Over which interval was the average weight per box the greatest?
5. A hot liquid was placed in a freezer and its temperature was recorded. The data for the first 8 minutes is shown below.
At what average rate is the temperature changing from 2 to 8 minutes? Use proper units.

By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given system of equations,

2x + 7y = 32 and 2x + y = 8

Subtract both equations from each other,

(2x + 7y) - (2x + y) = 32 - 8

2x + 7y - 2x - y = 24

2x - 2x + 7y - y = 24

6y = 24

y = 4

Hence "By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations".

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The average rate of change of g(x) = 3x² - 8x from x= 1 to x = 6 is 13.

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

g(x) = 3x² - 8x

The intervals, x = 1 to x = 6

Calculate the values of g(6) and g(1) as shown below,

g(6) = 3 × 6² - 8 × 6

g(6) = 3 × 36 - 48

g(6) = 108 - 48

g(6) = 60

And, g(1) = 3 × 1² - 8 × 1

g(1) = 3 - 8

g(1) = -5

Calculate the average rate of change as shown below,

The average rate of change = [g(6) - g(1)] / x₂ - x₁

The average rate of change = [60 - (-5)] / 6 - 1

The average rate of change = 65 / 5

The average rate of change = 13

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At the local bunny-hop, the sum of geometric sequences showing the jumps performed by Mr. Meyering is 40

The Sequences of the jump include

20, 10, ...

The common ratio, r is calculated from

first term, a * common ratio, r = second term

20 * r = 10

20r = 10

r = 10/20

r = 1/2

hence r < 1

The sum of gp to infinity for r < 1 is

Sum = a/ (1 - r)

Sum = 20 / (1 - 1/2)

Sum = 20 / 1/2

Sum = 20 * 2

Sum = 40

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Therefore ,the radius of the given cylinder is 10 inches

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

Here,

The volume of the cylinder is 1570 cubic inches

Volume of the cylinder = 1570 cubic inches

Volume of cylinder = π[tex]r^{2}[/tex]h

Where r is the radius of cylinder

h is the height of cylinder

So,

Volume of the cylinder = 1570 cubic inches

=> 1570 = π[tex]r^{2}[/tex]h

=> 1570 = 3.14*[tex]r^{2}[/tex]*5

=> 1570/3.14 = [tex]r^{2}[/tex]*5

=> 500=[tex]r^{2}[/tex]  *5

=> 500/5 =[tex]r^{2}[/tex]

=>100 =[tex]r^{2}[/tex]

=>r=10 inches

Therefore the radius of the given cylinder is 10 inches.

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Answer:

The total amount of the sales tax: $3.00

The total amount paid: $47.25

Step-by-step explanation:

Tip (In $): 6.75

Sales tax: 3.00

The total amount of food (before additional fees): 37. 50

So, to find the amount (in dollars) of the sales tax and tip, we must use this formula:

Amount = whole number * part percent/100

So, plugging in the numbers to the formula, it would look like this:

37.50 * 18 / 100
That is how to find the tip, you would do the same to find the sales tax. Then, when you get both amounts, you add them to 37.50 (the total before the fees) and get $47.25.

The sampling types in this problem are given as follows:

The sampling types used in this problem are defined as follows:

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Answer:

Step-by-step explanation: the amswer is B trust me

Answer:

1st darw

[tex] p(purple)= \frac{5}{20} \\ = \frac{1}{4} [/tex]

[tex]p(green) = \frac{1}{20} [/tex]

2nd draw

[tex]p(purple) = \frac{4}{18} \\ = \frac{2}{9} [/tex]

[tex]p(green) = 0[/tex]

The rectangle has the consecutive integers of 21 inches and 22 inches for its width and length respectively.

Consecutive integers are numbers that follow in a particular order, usually just one after the for example, 1, 2, 3,... and so on.

Let the width of the rectangle be represented by x so that the length will be x + 1 as they consecutive integers

The perimeter of the rectangle will have the equation;

x + x + x + 1 + x + 1 = 86 inches

4x + 2 = 86 inches {collect like terms}

4x = (86 - 2) inches {subtract 2 from both sides of the equation}

4x = 84 inches

x = (84/4) inches {divide through by the coefficient of x}

x = 21 inches

Therefore, the rectangle has width of 21 inches and length of 21 + 1 = 22inches.

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Step-by-step explanation:

A)20+10x=y

B)20+10(3)=y

20+30=y

y=50

The question is incomplete , I am answering it with my general knowledge,

Zero exponent

Simplifying an expression with a 0 as the exponent does not need consideration of the base value.

Any non-zero number multiplied by 0 has the value 1.

x0 = 1, where x = 0 and x = 1, 2, 3, and so forth.

Negative exponent

For any positive integer m and non-zero number a,

a⁻ⁿ=1/a⁻ⁿ

This rule states that if the exponent is negative, it can be made positive by writing the same number in the denominator and writing one for the numerator.

When a number is positive, the exponent shows how many times it has been multiplied by itself.

On the other hand, the negative exponent indicates how many times we must divide the base number. The negative exponent, then, tells us how many times to multiply the reciprocal of the base, to put it another way.

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Answer:

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

Find the combination of 4 of 12 and 5 of 12:

The volume of a cone is given by the formula:

V = (1/3) * π * r^2 * h

Where V is the volume, r is the radius of the base, and h is the height of the cone.

In this case, the base diameter and the height of the cone are both equal to x units, so the radius of the base is x/2 units. Therefore, the volume of the cone is:

V = (1/3) * π * (x/2)^2 * x

= (1/3) * π * x^3 / 4

= (π/4) * x^3

The correct expression for the volume of the cone is therefore O πx^3.

The expression that represents the volume of the cone in cubic units is:

V = (1/12) π x³

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h

We have,

The volume of a cone can be calculated using the formula:

V = (1/3) πr²h

where r is the radius of the base and h is the height.

Since the diameter of the base is equal to x, the radius is equal to half the diameter, which is x/2.

Also, we know that the height of the cone is also equal to x.

Substituting these values into the formula, we get:

V = (1/3)π (x/2)² x

Simplifying this expression, we get:

V = (1/3)π(x²/4)x

V = (1/12)πx³

Therefore,

The expression that represents the volume of the cone in cubic units is:

V = (1/12) π x³

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The total area of the space will be equal to 175 square meters.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Elizaveta painted 35 square meters of wall space. This represents 20% of the total area.

The total area will be calculated as,

20% of area = 35 square meters

100% of the area = ( 35 x 100) / 20

100% of the area = 175 square meters

Therefore, the total area of the space will be equal to 175 square meters.

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Elizaveta painted 35 m2 of wall space. This represents 20% of the total area.

What is the total area of the walls to be painted?f ^(4) 2

The net signed area of f(x) = 2x - 6 on the interval [-8, 5] is - 21 units.

The definite integral can be used to calculate the net signed area, which is the area above the x-axis less the area below the x-axis.

Given, f(x) = 2x - 6 and the x-axis over the interval [-8 , 5].

∴ The net signed area is,[tex]\[ \int_{-8}^{5} 2x -6 \,dx \][/tex].

[tex]= \[ \int_{-8}^{5} 2x \,dx \ - \ \int_{-8}^{5} 6 \,dx \][/tex].

= (5)² - (-8)² - {(5×6) - (-8×6)}.

= 25 - 64 - 30 + 48.

= - 21 units.

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Retained profits for the upcoming year: 5551.

The amount of profit a business keeps after paying all of its direct and indirect expenses, income taxes, and dividends to shareholders is known as retained profits. This is the percentage of the company's equity that may be utilized, for example, to fund the purchase of new machinery, research and development, and marketing.

RE=[tex]RE_{0}[/tex]-NI-D

Reserved Earnings

RE stands for initial retained income.

Net income is referred to as NI.

the dividend D

Graham Auto Parts now has $42,700 in sales, $9,700 in EBIT, $6,600 in net income, $1,360 in interest expenditure, and $1,925 in dividends paid. and a $8,000 rise in revenue is anticipated for the following year.

8000/42700 = 0.1873536 is the sales growth rate as a result. Its proportion is 18.73536%.

Now project net income = 6600 * 1.1873536

7837

dividends = 1925*1.1873536 = 2286

7837 - 2286 = 5551

retained earnings for next year 5551

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The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

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Answer:

Step-by-step explanation:

The risk of getting a cold is calculated by dividing the number of people who have a chance of getting a cold by the total number of people. In this case, the risk of getting a cold is 4 people / 20 people = 20%. Therefore, the risk of getting a cold is 20%.

All the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

What is rigid motion?

A geometric figure is moved by rigid motions, but its size and shape remain unchanged. It generates visuals that make sense.

Rigid transformation comes in four different varieties.

1. translate 2. reflect. 3. Rotation 4. Gliding reflection

Here,

We have a series of rigid motion maps ΔNEM  onto ΔCDE.

We have to find the correct statement, so we concluded that all the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

Hence, ΔNEM and ΔCDE are congruent.

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The volume of the can of campbell's chicken Noodles Soup in cubic millimeters is 89,725.5 cubic millimeters

Volume of a cylinder = πr²h

Convert inch to millimeters:

Height of the cylinder = 5 inches = 127 millimeters

Radius = diameter / 2

= 30 millimeters / 2

= 15 millimeters

Volume of a cylinder = πr²h

= 3.14 × 15² × 127

= 3.14 × 225 × 127

= 89,725.5 cubic millimeters

Consequently, the can of campbell's chicken Noodles Soup has a volume of 89,725.5 cubic millimeters

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The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The equation of the form y = A[tex]2^x[/tex] + K  from the graph above is

y = (-5/3) . [tex]2^x[/tex] - (2/3)

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = [tex]2^x[/tex]

From the graph, we see that,

x = 0, y = -1

x = 1, y = -4

Now,

The equation in the form of y = A.[tex]2^x[/tex]  + K can be written as,

Taking (0, -1) we get,

-1 = A x 1 + K

-1 = A + K ______(1)

Now,

Taking (1, -4) we get,

-4 = A x 2 + K

-4 = 2A + K _____(2)

From (1) and (2) we get,

A = K - 1 putting in (2) we get,

-4 = 2(K - 1) + K

-4 = 2K - 2 + K

-4 = 3K - 2

3K = -4 + 2

3K = -2

K = -2/3

Now,

A = K - 1

A = -2/3 - 1

A = (-2 - 3) / 3

A = -5/3

Now,

The equation is y = (-5/3) . [tex]2^x[/tex] - (2/3)

Thus,

The equation of the form y = A[tex]2^x[/tex] + K  from the graph above is

y = (-5/3) . [tex]2^x[/tex] - (2/3)

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There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

P(A) = n(A)/n(S)

Where P(A) is the likelihood that an event "A" will occur and n(A) is the number of positive outcomes. The total number of occurrences in the sample space is denoted by n(S).

We must have a similar probability for both events in order for them to be independent. Because of the table, we may test for independence by knowing the likelihood that e and d will occur. When we are told that occurrences d and e are mutually exclusive, the entire table of values becomes somewhat of a red herring. The chance of d given e and the probability of d given d are both equal to zero if two events are mutually incompatible. There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent. There is a chance for it.

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When boys and girls are equally likely, the likelihood that at least 50 of 125 infants born will be females is 0.40.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

total number of sample=125

number of girls=50

Probability that out of 125 babies born, at least 50 will be girls,

=50/125

=0.40

The probability that out of 125 babies born, at least 50 will be girls is 0.40 when boys and girls are equally probable.

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Answer:

Grandma=P

Wagon=TH

Library= PL

Step-by-step explanation:

its pretty simple

Answer:

a)  $153,850

b)  $779.54

c)  $873.54

Step-by-step explanation:

[tex]\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 \times 0.15)\\&=181000-27150\\&=153850\end{aligned}[/tex]

Therefore, the loan amount is $153,850.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}$\\\\where:\\\\ \phantom{ww}$\bullet$ $P =$ loan amount \\\phantom{ww}$\bullet$ $i =$ interest rate per month (in decimal form) \\\phantom{ww}$\bullet$ $n =$ term of the loan (in months) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the  Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.045}{12}\left(1+\frac{0.045}{12}\right)^{360}}{\left(1+\frac{0.045}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{153850 \cdot 0.00375\left(1.00375\right)^{360}}{\left(1.00375\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=779.5353492[/tex]

Therefore, the monthly payments would be $779.54.

Given:

Substitute the given values into the Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.055}{12}\left(1+\frac{0.055}{12}\right)^{360}}{\left(1+\frac{0.055}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=873.5433786[/tex]

Therefore, the monthly payments would be $873.54.

New coordinates become (-2,8) (-2,-4) and (4,-4)

What do you mean by scale factor?

Magnification is defined as the scale ratio of a given original object and a new object that is a representation of it but of a different size (larger or smaller).

The new figure obtained is similar to the original figure

The expansion description should state how much the shape was expanded.

Suppose a triangle with the vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2.

As we know, if (x,y) point dilated by scale factor a then new coordinates become (ax, ay)

So, if triangle having vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2 then new coordinates become (-2,8) (-2,-4) and (4,-4)

Therefore, new coordinates become (-2,8) (-2,-4) and (4,-4)

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The volume of the smaller wedge cut from a sphere of radius 4 by two planes that intersect along a diameter at an angle of π/6 is 1/6.

What is volume ?

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Consider that the tetrahedron is bounded by the coordinate planes and the plane 8 x+y+z=2

Evaluate the triple integral [tex]\iiint_E d V$.[/tex]

The lower boundary of tetrahedron is the plane z=0 and the upper boundary of tetrahedron is the plane z=2-8 x-y.

And the projection is y=2-8 x.

The x-limits are obtained by taking y=0 and z=0 in 8 x+y+z=2.

[tex]$$\begin{array}{r}8 x=2 \\x=\frac{2}{8} \\x=\frac{1}{4}\end{array}$$[/tex]

Therefore, the region becomes [tex]$R=\left\{(x, y, z) / 0 \leq x \leq \frac{1}{4}, 0 \leq y \leq 2-8 x, 0 \leq z \leq 2-8 x-y\right\}$[/tex].

Therefore, the integral becomes

[tex]$ \iiint_E d V=\int_0^{\frac{1}{4}} \int_0^{2-8 x} \int_0^{2-8 x-y} d z d y d x $[/tex]

[tex]$=\int_0^{\frac{1}{4}} \int_0^{2-8 x}[z]_0^{2-8 x-y} d y d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}} \int_0^{2-8 x}[2-8 x-y] d y d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[2 y-8 x y-\frac{y^2}{2}\right]_0^{2-8 x} d x . $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[2(2-8 x)-8 x(2-8 x)-\frac{(2-8 x)^2}{2}\right] d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[32 x^2-16 x+2\right] d x $[/tex]

[tex]$ =\left[32\left(\frac{x^3}{3}\right)-16\left(\frac{x^2}{2}\right)+2 x\right]_0 $[/tex]

[tex]$ =32\left(\frac{\left(\frac{1}{4}\right)^3}{3}\right)-16\left(\frac{\left(\frac{1}{4}\right)^2}{2}\right)+2\left(\frac{1}{4}\right)-0 $[/tex]

[tex]$ =\frac{1}{6} $[/tex]

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The rate of change is not constant.

What is rate of change ?

A rate of change is a measurement of how one quantity alters in proportion to another. The dependent variable y must be present if independent variable x is. rate of change = y-to-x conversion of change. Change rates may be positive or negative.

We know that the rate of change in a function is given by :-

(change in dependent variable) / (change in independent variable)

Let x denotes the Number of hours and y denotes the Cost of parking .

Here , x- independent variable

y- dependent variable

Now, rate of change = ( change in y) / ( change in x)

                                  = (14-10)/(3-1) = 2

Here , the rate of change = $ 2 per hour.

Again rate of change =  ( change in y) / ( change in x)

                                    = (16-14)/(5-3) = 1

Here , the rate of change = $ 1 per hour.

Since both rate of changes are not equal , it means the rate of change is not constant.

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Answer:

x = 8

Step-by-step explanation:

a rhombus has all equal sides so this means that you must set them equal to each other

8x - 5 = 5x + 19

now subtract 5x to both sides

3x = 24

x = 8

that is your answer