Which graph shows a proportional relationship between the number of hours of renting a pair of roller skates and the total amount spent to
rent the roller skates?

To answer this question, we need to remember that a ratio is a comparison of two or more units. We can also need to have into account that these units must be in the same units.

We have one of the quantities is 6ft, the other is equal to 78 inches. We can convert 6ft to its equivalent in inches, or 78 inches into its equivalent in feet. Then, we have:

Then, we can conclude that the ratio of 6feet (72 inches) to 78 inches is equivalent to:

The amount of wall surface in square feet is there to paint is: 364 square ft. While the floor area is 169.58sq ft. See the calculations below:

The square foot is an imperial measure of area and a customary unit of area in most countries. It is defined as the area of a square with one-foot sides.

The calculation for the above solution is given as:

Step I - Recall the Given Stats:

Dimensions of the room are:

12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.

Let Lenght (l) = 13'9" = 13(9/12) ft = 13(3/4) = 55/4 ft.

Let Width(w) = 12'4" = 12(4/12) ft = 12(1/3)ft = 37/3 ft

Let Height h = 8'0" = 8ft.

Recall that we have a door with dimensions 3' x 7' and two windows 4'x4'

Step II - A) Surface area of the wall to be painted is:

Area of 4 walls less (area of door plus area of window)

Surface Area = 2LH + 2WH - ((3 x7) + 2(4x4))

= 2(l +w)h - (21 + 32)
= 2 ((55/4) + (37/3))8 -53

= 220 + 592/3 - 53
= 167 + 592

= (501+ 592)/3
= 1093/3

Hence,

The Surface Area to be painted is = 364.33 Sq ft.

Step III - B) The Area of the Floor = Lx W

= (55/4) x (37/3)

= 2035/12

= 169.583333333

Hence,

Area of the Floor is approximately = 169.58

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Full Question:

A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.

Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.

A. How much wall surface in square feet is there to paint?

B. What is the floor area?

Answer:

4.number 1

5.number 2

Step-by-step explanation:

4.Because the the expression tan can be written as sin divided by cos it will be beneficial to write the square of cos as cos multiplied by cos so that after canceling out we are left with cos multiplied by sin of the left hand side.

5.because transforming cos squared to 1-sin squared will allow us to to have a fraction where both the numerator and denominator are the same which equals one.

Yes, because the ladder will reach 16 feet high

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

Given:

Hypotenuse= 20 feet

base= 12 feet

Using Pythagoras theorem

H²= P² + B²

20² =12² +P²

P²= 400-144

P²= 256

P= 16 FEET.

Hence, Yes, because the ladder will reach 16 feet high

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Answer:

Slope formula is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.

Slope = (-7-(-6)) ÷ (0-(-8))

= (-7+6) ÷ (0+8)

= -1/8

No, a function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree is not a one-to-one function.

A one-to-one function is also referred to as an injective function and it can be defined as special type of function in which every element of the range is mapped to exactly a single element of its domain. This ultimately implies that, the output values (y-values) of a one-to-one function never repeat themselves.

Additionally, a one-to-one function maps distinct elements of its domain (y-values) to distinct elements of the range (x-values) and as such, it connotes the mapping of two (2) sets.

In this context, we can reasonably and logically deduce that this function is not a one-to-one function because it fails the horizontal line test as there could be the same temperature at different times of the day.

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SOLUTION

This is a probability question that has to do with the "without replacement" scenario, because every chocolate eaten leaves the box and never returns

The probability that both pieces are milk chocolate is calculated thus:

Number of milk chocolates = 5

NUmber of dark chocolates = 5

Total number of chocolates in the box = 5+5 =10

The probability that both pieces are milk chocolate is:

The probability that both pieces are milk chocolate is:

Answer:

See below

Step-by-step explanation:

Answer:

The value of the given expression is;

Explanation:

Given the logarithmic expression;

To solve, Recall the rules of logarithm;

Apply the above rules;

Aplplying rule 2;

Therefore, the value of the given expression is;

Answer

7 years

Explanation

Given:

Principal, P = $10,000

Rate, R = 6.75%

Amount, A = $15,000

What to find:

The years will it take the investment to reach $15,000 in value.

Step-by-step solution:

You need to first calculate the total interest on the investment using;

Interest, I = Amount, A - Principal, P

Interest, I = $15,000 - $10,000

Interest, I = $5,000

The final step is to find the years it takes the investment to reach $15,000 in value using simple interest formula.

Putting the values of the parameters into the formula, we have;

Therefore, it will take 7 years for the investment to reach $15,000 in value.

Given:

a.) f(x) = x²

b.) g(x) = f(x) + d

c.) d = 2

To be able to complete the equation of function g(x), let's substitute the function of f(x) and d.

We get,

g(x) = f(x) + d

g(x) = x² + 2

Therefore, g(x) = x² + 2.

1

Step

Multiple both numerator and both denominator

2

3

4

Answer:

See below

Step-by-step explanation:

If I did the math numbers correctly :  ( a = 51° too)

As calculated by the given ratios, 36 more skiers were there than snowboarders at the local resort on Saturday.

What is ratio?

A ratio illustrates how two or more values differ in terms of size.

Ratios can be displayed in a variety of ways, including as decimals (after dividing one value by the whole), percentages (after dividing one value by the entire), and using the ":" or "/" to separate values.

As given in the question,

Ratio of Snowboarders to Skiers

On Friday: ratio is 6:2

On Saturday: 5:3

Population = 144

Now, lets calculate the number of snowboarders and skiers at Saturday:

Given ratio: 5:3

total = 5+3

total = 8

No. of skiers is:

= (3/8)(144)

= 54

No. of snowboarders is:

= (5/8)(144)

= 90

Now lets calculate the difference between no. of snowboarders and skiers:

= 90-54

= 36

Hence, there are 36 more snowboarders than skiers.

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The no. of students who usually bring their own lunch is 15.

The ratio is a comparison between two or more quantities in simplest form.

Given there are 36 students in an s2a class some of them bring their own lunch and the others buy their lunch.

Assuming x students bring their own lunch hence (36 - x) students buy their lunch.

(1/5)th of the student who brings their own lunch is (1/5)×x = (x/5).

∴ x - (x/5) : (36 - x) + (x/5) = 1 : 2.  (The reduced students are added to the      

                                                                              other category).

4x/5 : 36 - 4x/5 = 1 : 2.

4x/5 : (180 - 4x)/5 = 1 : 2.

(4x/5)÷(180 - 4x)/5 = 1/2.

(4x/5)×5/(180 - 4x) = 1/2.

4x/(180 - 4x) = 1/2.

4x = (180 - 4x)/2.

8x = 180 - 4x.

12x = 180.

x = 15.

∴ 15 students usually bring their own lunch.

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Answer: x=-3, x=3

Step-by-step explanation:

Answer:

4-[x]=1

-4.    -4

-[x]=-3

x=3

The luckiest person is Clinton because it is more likely.

Answer: Clinton

Explanation:

To determine if the table is proportional or not, we need to find the ratio between x and y for each of the data. if it is constant, then it is proportional

Proportional relationship:

y = kx

k = constant of proportionality

k = y/x

for the x = 7, y = 8.4

k = 8.4/7 = 1.2

for x = 11, y = 13.2

k = 13.2/11 = 1.2

for x = 20, y = 24

k = 24/20 = 1.2

for x = 25, y = 30

k = 30/25

k = 1.2

when x = 100, y = 120

k = 120/100

k = 1.2

Since the ratio between y and x is the same for all, the table is proportional

The correct option:

The

well, keeping in mind that a year has 12 months, that means 6 months is 6/12 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1498\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases} \\\\\\ I = (1498)(0.06)(\frac{1}{2}) \implies I = 44.94[/tex]

The length of the support when Maria is to weld a support for a 23-m conveyor is 7.87 m.

From the information, Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle.

Let AB = 23m

Let x = 20°

We can then use the sine rule to find the length. This will be illustrated thus:

Sin x = AC / AB

Sin 20° = AC / 23

AC = 23 × sin 20°

AC = 7.87

The length is 7.87m

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To solve the question, we will be using a Venn Diagram. Let's list down what's given first:

855 drank alcohol

657 smoked cigarettes

192 used illegal drugs

418 both drank alcohol and smoked cigarettes

109 drank alcohol and used illegal drugs

116 smoked cigarettes and used illegal drugs

88 engaged in all three

and 251 engaged in none of these

We will draw a Venn Diagram with 3 circles, one for each vice. Then we will start with the intersection of all three and the area outside of the circles (for those who do not engage in vices).

Because we know how many engaged in all 3 vices, we can deduct that number from those who belong to the intersection of 2 vices since they have already been counted in that too.

418 - 88 = 330 drank and smoked, but not used drugs

109 - 88 = 21 drank and used drugs, but not smoked

116 - 88 = 28 smoked and used drugs but not drank

Then, we subtract the numbers in each circle from the total for each vice.

855 - (330 + 88 + 21) = 416 drank only

657 - (330 + 88 + 28) = 211 smoked only

192 - (88 + 21 + 28) = 55 used drugs only

To find the total number of surveyed students, we just need to add all the numbers in the Venn Diagram.

416 + 330 + 88 + 21 + 211 + 28 + 55 + 251 = 1,400

Therefore, there were 1,400 students who were surveyed.

Given:

Total number of books is, N = 20.

Number of books donated is, d = 2/5 of books.

The objective is to find the number of books donated.

Consider the number of books donated as x.

Hence, the number of books donated is 8.

where A is the first value, B the second value and x the percent

we can solve x

this is the equation

and this is the percent:

the percent is 20%

The probability that a family’s first child will be born with down syndrome is 1/5000

Number of first borne babies  = 30000

Number of first borne babies having Down syndrome = 6

Probability is defined as the ratio of number of favorable outcomes to the total outcome.

Probability =  (number of favorable outcomes)/(total outcome)

We have to find the probability that a family’s first child will be born with down syndrome. So, Number of first borne babies having Down syndrome is equal to the total number of favorable outcomes and  Number of first borne babies will also be equal to total outcome. Hence we can write,

Probability = (number of favorable outcomes)/(total outcome)

Probability = 6/30000

Probability = 1/5000

So, the required probability is 1/5000.

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A 220lb person on earth would weigh 23.81lb on moon

Given

Weight of an object on moon varies same as that on the planet earth

This means the weights are directly proportional

Weight of person on earth = 162.7lb

Weight of person on moon = 27.66lb

Also,

Weight of person on earth = 220lb

We need to find weight of this person on moon.

Let weight of person on moon be x

According to the data equation can be formed as

27.66 x 220 = 162.71x

3885.2 = 162.71x

x= 23.81

Hence the weight of the person on moon is 23.lb

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1) To determine which is the function from the table we need to attentively look for a constant factor in the y-column.

2) As we can see from this table, the factor we can tell that goes from 64 to 16 and then 4 is 1/4. Or in decimal form 0.25. So, we can tell the factor "b" is going to be 1/4 considering this model:

3) Let's pick one point (0,4) and plug it to find the other elements:

And finally, we can tell the function is:

1) [tex]VX=ZX, \angle XVY=\angle XZW[/tex] (given)

2) [tex]\angle X=\angle X[/tex] (reflexive property)

3) [tex]\triangle VXY \equiv \triangle ZXW[/tex] (ASA)

ANSWER

Hypotenuse: 16 ft

Leg: 4 ft

EXPLANATION

Given:

A right angle triangle with only one leg = sqrt(240) feet

Desired Outcomes:

Lengths of the leg and hypotenuse

Declaration of variables

Let x represent the length of leg

Hypotenuse = 4 times the length of leg = 4x

Apply Pythagorean theorem

Hypotenuse = 4x = 4 (4) = 16 ft

Hence, the Lengths of the leg and hypotenuse are 4 ft and 16 ft respectively.