10 POINTS!
What is the constant of proportionality in this proportional relationship?

x 2 4 6 8
y 5/6 1 2/3 2 1/2 3 1/3

A. 12
B. 5
C. 12/5
D. 5/12

Answers to ratios are first one is option B, second one is option A and third one is option C.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

1. Ratio of smoothie size to mangos used for Kim = 8 : 1

Ratio of smoothie size to mangos used for Bri = 24 : 3

                                                                             = 8 × 3 : 1 × 3

                                                                             = 8 : 1

Ratio of smoothie size to mangos used for Angela = 32 : 4

                                                                                    = 8 × 4 : 1 × 4

                                                                                    = 8 : 1

So the ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

So the answer is option B.

2. Ratio of width to length of larger canvas = 4 : 6 = 2 : 3

Ratio of width to length of smaller canvas = 2 : 3

So the painting's width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

So the answer is option A.

3. Ratio of students who prefer free time at the beginning of the class to students who prefer free time at the end of the class is 12/19

Total students = 12 + 19 = 31

Out of 31 students, 12 students prefer free time at the beginning of the class and 19 students prefer free time at the end of the class.

So the answer is option C.

Hence the answers on ratios are done.

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Answer: To find the expected amount of money the radio caller should win, you can multiply the prize amount by the probability of winning that prize, and add those products for each prize. The expected value is also known as the mean value.

$500 * 1/8 = $62.50

$750 * 1/8 = $93.75

$1,250 * 1/8 = $156.25

$2,500 * 1/8 = $312.50

$5,000 * 1/8 = $625.00

$10,000 * 1/8 = $1250.00

$25,000 * 1/8 = $3,125.00

Total expected value = $62.50 + $93.75 + $156.25 + $312.50 + $625.00 + $1250.00 + $3,125.00 = $5,050.00

So, the expected amount of money the radio caller should win if the caller gets to spin the wheel once is $5,050.

It's worth to mention that the probability for each prize is the same, but the prizes are not the same so each prize win will be different according to the prize amount.

The expected value doesn't assure that the prize will be won, but it's a good approximation of the prize the caller could win.

Step-by-step explanation:

Answer:

[tex] \sf \: d) \: 82[/tex]

Step-by-step explanation:

Given information,

→ d = 10

→ u = 7

→ e = 3.2

The expression is,

→ d(e + 5)

Let's evaluate the expression,

→ d(e + 5)

→ 10(3.2 + 5)

→ 10 × 8.2

→ 82

Hence, option (d) is correct.

Answer:

Option D) 82

Step-by-step explanation:

Given ,

d = 10

u  = 7

e = 3.2

To Find  : [tex]d(e+5)[/tex]

Applying the values in the equations we get

[tex]10(3.2+5)\\[/tex] Applying Distributive property

[tex]32+50 = 82[/tex]

Hence , Option D) is the answer

[tex]9x-5=3x+7[/tex]

Subtract 3x from both sides:

[tex]9x-5-3x=3x+7-3x[/tex]

[tex]6x-5=7[/tex]

Add 5 to both sides:

[tex]6x-5+5=7+5[/tex]

[tex]6x=12[/tex]

Divide both sides by 6:

[tex]\dfrac{6x}{6} =\dfrac{12}{6}[/tex]

[tex]\fbox{x = 2}[/tex]

Answer:

[tex] \sf \: x = 2[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

[tex] \sf \rightarrow \: 9x - 5 = 3x + 7[/tex]

Then the value of x will be,

[tex] \sf \rightarrow \: 9x - 5 = 3x + 7[/tex]

[tex] \sf \rightarrow \: 9x - 3x = 7 + 5[/tex]

[tex] \sf \rightarrow \: 6x = 12[/tex]

[tex] \sf \rightarrow \: x = \frac{12}{6} [/tex]

[tex] \sf \rightarrow \: x = 2[/tex]

Hence, the value of x is 2.

Answer:

Step-by-step explanation:

C.) 15 upgraded phones

Answer:

Q1. Answer: According to the guidelines, the ratio of the rise (height) to the run (length) of a wheelchair ramp should be no greater than 1:12.

Option A: A ramp with a length of 30 feet and a height of 3 feet. The ratio of the rise to the run is 3/30 = 1/10, which is less than 1:12, so this ramp follows the guidelines.

Option B: A ramp with a length of 20 meters and a height of 0.5 meters. The ratio of the rise to the run is 0.5/20 = 1/40, which is less than 1:12, so this ramp follows the guidelines.

Option C: A ramp with a length of 384 inches and a height of 32 inches. The ratio of the rise to the run is 32/384 = 8/96 = 2/24, which is less than 1:12, so this ramp follows the guidelines.

Option D: A ramp with a length of 1 feet and a height of 12 feet. The ratio of the rise to the run is 12/1 = 12, which is not less than 1:12, so this ramp does not follow the guidelines.

Therefore, the ramps that follow the guidelines are options A, B, and C.

Q2. Answer: The guidelines for a wheelchair ramp suggest that the ratio of the rise (height) to the run (length) of the ramp should be no greater than 1:12. In this case, the rise is 2.5 feet and the run is the length of the ramp (x feet). The ratio of the rise to the run is 2.5/x.

To follow the guidelines, the ratio of the rise to the run should be no greater than 1:12, or 1/12. Therefore, the length of the ramp (x) should be greater than or equal to 2.5/1/12 = 30 feet.

Therefore, the correct answer is C: X ≥ 30.

Step-by-step explanation:

Therefore , the solution of the given problem of expression comes out to be  22[tex]z^{8}[/tex].

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Here,

Given : -20[tex]z^{8}[/tex]+ (-2[tex]z^{8}[/tex])

=> -22[tex]z^{8}[/tex]

So ,

In order to find the solution we add them

Thus ,

simplification of given expression is:

=> - 22[tex]z^{8}[/tex]

Therefore , the solution of the given problem of expression comes out to be  22[tex]z^{8}[/tex].

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Answer:

3

Step-by-step explanation:

Step-by-step explanation:

3 1/7 × [3 1/3 × (2/3 + 1/6) - 1 5/18] ÷ 2 3/7

well, first we have to bring everything to true fractions.

then we need to bring all fractions we need to add or subtract to the same denominators.

and then we simply calculate.

3 1/7 = (3×7 + 1)/7 = 22/7

3 1/3 = (3×3 + 1)/3 = 10/3

1 5/18 = (1×18 + 5)/18 = 23/18

2 3/7 = (2×7 + 3)/7 = 17/7

22/7 × [10/3 × (2/3 + 1/6) - 23/18] ÷ 17/7

to be able to add 2/3 and 1/6 we need to bring the to the same denominator, with its simply 6.

2/3 + 1/6 = 2/2 × 2/3 + 1/6 = 4/6 + 1/6 = 5/6

22/7 × [10/3 × 5/6 - 23/18] ÷ 17/7

22/7 × [50/18 - 23/18] ÷ 17/7

22/7 × 27/18 ÷ 17/7

22/7 × 27/18 × 7/17

22/17 × 27/18 = 22/17 × 3/2 = 66/34 = 33/17

so, the result is 33/17 = 1 16/17

Answer:the third one

Step-by-step explanation:

The fraction of the entire bulletin board decorated by each classmate is N/20.

Fraction is a mathematical expression which is made up of denominator and a numerator. So that fractions may generally be categorized into 3 types. These are: proper fraction, improper fraction, and mixed fraction.

Considering the given question, let the size of the bulletin board be represented by N.

The section of the bulletin board to be decorated = 1/5 * N

                                                                       = N/ 5

There are 4 classmates that has been selected to divide the section to be decorated equally among themselves. So.

Fraction of the board to be decorated by each student = (N/ 5)/ 4

                                                                             = 1/20 N

The fraction of the board to be decorated by each student is N/20.

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Considering the definition of a line, the correct answer is option A: the equation of the line in point-slope form is y + 7= 3/8(x- 15.2)

A linear equation o line can be expressed in the form y = mx + b

where

The point-slope form of an equation of a line is written as y-y₁=m(x-x₁)

where:

In this case, you know:

The point-slope form of the line is written as:

y- (-7)= 3/8(x- 15.2)

y + 7= 3/8(x- 15.2)

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Rising action and climax are best used to describe the narrative element of Plot.

The rising action of the novel encompasses all the developments of the characters and the dramatic events that build to the eventual climax. The most thrilling section of the story is the climax, which also marks a turning point in the plot or the objectives of the main character.

Rising action in literature refers to all the incidents that take place in a narrative leading up to the climax. The tale moves along thanks to the mounting action, which also heightens the tension and keeps us interested in what happens next. It comes after the first step of exposition in the plot.

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Answer: just be positive

Step-by-step explanation:

the width of a rectangle is measured at 6 cm, its length at 10 cm, and its area at 60 cm2.

An example of a quadrilateral is a rectangle, which has four vertices that are all 90 degrees apart and parallel sides that are equal to one another. As a result, it is sometimes referred to as an equiangular quadrilateral. The rectangle is a 2D shape with 4 sides, 4 corners, and 4 right angles. The length of each pair of the diagonal sides of a rectangle is equal, with one pair being longer than the other. If all the sides of a rectangle were the same size, the shape would be referred to as a square.

given

Consequently, the rectangle has a length of 10 cm and an area of 60 cm2.

Since,

Area of a rectangle equals length times width

=60=10*breadth

width is 60/10.

= 6 cm in breadth.

the width of a rectangle is measured at 6 cm, its length at 10 cm, and its area at 60 cm2.

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We can conclude that, if --

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that the cost (y) of red grapefruit can be represented by the equation y = 2x, where {x} is the number of pounds of red grapefruit. Also the graph shows the cost of pink grapefruit.

The cost (y) of red grapefruit can be represented by the equation y = 2x. So, we can write that the cost per unit pound of red grape is $2. The graph of the pink grapefruit is not given, but its slope {m} will tell us its costs per pound.

Now, if -

Therefore, we can conclude that, if -

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As seen in the illustration, the polygon's surface area is 12 + 4√5 square units.

Therefore the correct option is C) 12 + 4√5 square unit

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The key features of the graph of the given equation -8x + 20y = 240 include the following:

D. As x → -∞, y → ∞.

E. The y-intercept is (0, 12).

H. The x-intercept is (-30, 0).

Making y the subject of formula in order to determine the slope, we have:

20y = 8x + 240

Dividing both sides of the equation, we have:

y = 8x/20 + 240/20

y = 8x/20 + 12

Therefore, the slope is equal to 8/20.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

When x = 0, the y-intercept is given by;

20y = 8(0) + 240

y = 240/20

y = 12.

Therefore, the y-intercept is equal to (0, 12).

When y = 0, the x-intercept is given by;

-8x + 20(0) = 240

x = -240/8

x = -30

Answer:

27

Step-by-step explanation:

To find 45% of 60, you can multiply 60 by 0.45

60 x 0.45 = 27
45% of 60 is 27.

Answer: The sum of the digits of 99 × n is 27 - 10 = 17.

Step-by-step explanation:

To find the sum of the digits of 99 × n, we can use the fact that 99 × n = 100 × n - n. The sum of the digits of 100 × n is simply n, since the hundreds digit is zero. Therefore, the sum of the digits of 99 × n is equal to the sum of the digits of n - n, which is simply zero.

For example, if n = 37, then 99 × n = 99 × 37 = 3,699. The sum of the digits of 3,699 is 3 + 6 + 9 + 9 = 27. The sum of the digits of 37 is 3 + 7 = 10. Therefore, the sum of the digits of 99 × n is 27 - 10 = 17.

By analyzing the inequality and solving, the range of values of x for which the inequality is true is x € (-4/3, 4)

Domain is the input to the function.

Range is the output of the function.

First, we'll consider the case where |2x+1|-x-3<0.

|2x+1|-x-3<0

|2x+1|<x+3

Now we need to take the absolute value of 2x+1, we have two cases to consider:

Case 1:

2x + 1 > 0

2x + 1 < x + 3

2x - x < 3 + 1

x < 4

Case 2:

2x + 1 < 0

-2x - 1 < x + 3

-2x - 1 -x - 3 < 0

-3x - 4 < 0

x > -4/3

Now we must find the intersection between the two cases:

x € (-4/3, 4)

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Ellie spend of $37.8 for  2 packs of hot dogs , 3 lbs of hamburger, and 2 lbs. of potato salad

Two or more expressions with an Equal sign is called as Equation.

The amount is not given for each hot dog, hamburger and potatos.

But Ellie brought 2 packs of hot dogs ,

3 lbs of hamburger, and

2 lbs. of potato salad

Let us consider each hot dog is $6

Hamburger is $5.6 and potatoes is $4.5

Total amount is 2(6)+3(5.6)+2(4.5)

12+16.8+9

$37.8

Hence, Ellie spend of $37.8 for  2 packs of hot dogs , 3 lbs of hamburger, and 2 lbs. of potato salad

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Roller coaster B has greater top speed than roller coaster A.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.

Given,

speed of roller coaster A = 110ft./s

speed of roller coaster B = 85mph

1 mile = 5280 feet

⇒ 85 mile = 5280 × 85 = 448800 feet

1 hour = 3600 seconds

speed of roller coaster  B = 448800/3600 ft/s = 124.67 ft/s

comparing speed of both

Speed of roller coaster B > speed of roller coaster A

Hence, Top speed of roller coaster B is greater than roller coaster A.

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Answer:

Given,eqn is -6x-18y=20

or,-18y=6x+20

or,y=6x+20/-18

or,y=6x/-18 +20/-18

or,y= - X/3 -10/9

Comparing above eqn with y=mx +c,we get

m= -1/3 and y-intercept (c)=-10/9

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Answer:

slope: -1/3  y-int: -10/9

Step-by-step explanation:

first step is to turn the equation into slope intercept form (y=mx+b)

-6x-18y=20

+6x        +6x

-18y=6x+20

divide -18 on both sides

y=-1/3x-10/9

the m is the slope, and the b is the y-intercept

Answer: 121%

Step-by-step explanation:

move the decimal place two to the right

Answer:

To find the range of flight times, you need to find the difference between the shortest and longest flight times. The shortest flight time was on Monday at 314 minutes, and the longest flight time was on Friday at 407 minutes. The range is 407 - 314 = 93 minutes. The correct answer is therefore (b) 93 min.

Step-by-step explanation:

Answer: An equilateral triangle is a three-sided polygon with three equal sides and three equal angles of 60 degrees each. If you know the length of one of the sides of an equilateral triangle, you can use the formula for the area of an equilateral triangle to determine the values of n and m. The formula for the area of an equilateral triangle is:

Area = (sqrt(3)/4) * s^2

where s is the length of one of the sides of the triangle.

To determine the values of n and m, you can rearrange the formula to solve for s. For example, if you know that the area of the triangle is n and the value of m is the length of one of the sides of the triangle, you can rearrange the formula to solve for s:

s = sqrt(4n/sqrt(3))

Then, you can use the value of s to determine the value of m.

Step-by-step explanation: