A 25ftX20ft room has an 8ft
diameter circular rug in it.
How much of the floor is not
covered
by the rug?

Answer:Top right answer (You had extra money at the end of the month

Step-by-step explanation:

Answer:

to subtract fractions, find the LCD and then combined

The answer is 1/12.

Answer: y=3x2

Step-by-step explanation:

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of cubic feet.

The dimensions of the most economical shed are height = 10 ft and side 5 ft

Taken data

volume = 250 cubic feet

base costs = $4 per square​ foot

material for the roof costs =  ​$6 per square​ foot

material for the sides costs = ​$2.50 per square foot

to find out the dimensions of the most economical shed solution

let us consider length of side x and height is h

so we can say x²h = 250

and h = 250 / x²

now cost of material  = cost of base + cost top + cost 4 side

cost  = x²(4) + x²(6)  + 4xh (2.5)

cost = 10  x² + 10xh

put here h = 250 / x²

cost = 10  x² + 10x (250/ x² )

cost = 10  x² +  (2500/ x )

if we differentiate and we get

c' = 20 x - 2500 / x²

put c' = 0 solve x

20 x - 2500 / x²  = 0

x = 5

so we say one side is 5 ft  base

and height is  h = 250 / x²

h = 250 / 5²

height = 10 ft

Hence the answer is, the dimensions of the most economical shed are height = 10 ft and side 5 ft

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Answer:

∴ x = 32

Step-by-step explanation:

For J to be parallel to K,

(2x)° + (4x-12)° = 180°

   2x + 4x - 12 = 180

                  6x = 192

                 ∴ x = 32

Answer:

z=53 y=37 and x=90

Step-by-step explanation:

Since there's a transversal, x is 90 because of alternate angles. Also alternate exterior angles are z so z=53 degrees. 180-(90+53)=37 degrees is y.

Answer:16

Step-by-step explanation:

The rate of calories burned by bike riding is 4 calories per minute

First we have to choose points from the graph

The coordinates of the first point = (10, 40)

The coordinates of the second point = (20, 80)

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line = (80-40) / (20-10)

= 40/10

= 4 calories per minute

Hence, the rate of calories burned by bike riding is 4 calories per minute

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James is 24 years old.

Let John's age now is J.

Let james's age now is A.

From the question, we have

John is 3/4 the age of  james.

J=3/4*A

J=3A/4

Three years ago, John was 5/7 the age of james.

J-3=5/7*(A-3)

J-3=(5A-15)/7

J=(5A-15)/7+3

3A/4=(5A-15)/7+3

21A=4(5A-15)+84

21A=20A-60+84

A=24

James is 24 years old.

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Jada could say to her cousin that we get a negative value which we is needed to make solution complete.

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

Given,

Jada was helping her cousin with his math homework.

He was supposed to solve the equation 8 + x = 5.

He said, "If I subtract 8 from both sides, I get x = 5-8.

5 grapes, I can't eat 8 of them!" Jada said.

Actually we can subtract 8 from five but we get a negative value.

5-8=-3

It means we should three more apples to eat.

Hence we can subtract 8 from five which makes sense.

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15 additional kcalories is she likely to burn in the post-exercise period .

What do food calories mean?

jules burns 100 kcalories during her morning walk.

15 additional kcalories is she likely to burn in the post-exercise period .

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Answer:

1.  x = 2

2.  x = 360

3.  x = -41 and x = 49

4.  All real numbers.

5.  x = 1

Step-by-step explanation:

[tex]\begin{aligned}&\textsf{Given}: & \dfrac{x+16}{3}&=3x\\&\textsf{Multiply both sides by 3}: & x+16&=9x\\&\textsf{Subtract $x$ from both sides}: & 16&=8x\\&\textsf{Divide both sides by 8}: & x&=2\end{aligned}[/tex]

Therefore, the solution is x = 2.

[tex]\begin{aligned}&\textsf{Given}: & x &= 0.8x + 72\\&\textsf{Subtract $0.8x$ from both sides}: & 0.2x&=72\\&\textsf{Divide both sides by 0.2}: & x&=360\end{aligned}[/tex]

Therefore, the solution is x = 360.

[tex]\begin{aligned}&\textsf{Given}: & \dfrac{1}{5}|x-4|-3&=6\\&\textsf{Add 3 to both sides}: & \dfrac{1}{5}|x-4|&=9\\&\textsf{Multiply both sides by 5}: &|x-4|&=45 \\\end{aligned}[/tex]

Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, and solve both equations.

[tex]\begin{aligned}\underline{\sf Equation\; 1}&&\underline{\sf Equation\; 2}\\x-4&=45 & x-4&=-45\\x-4+4&=45+4 & \quad \quad \quad x-4+4&=-45+4\\x&=49 & x&=-41\\\end{aligned}[/tex]

Therefore, the solutions are x = -41 and x = 49.

[tex]\begin{aligned}&\textsf{Given}: & -2(x + 3) &= -2x-6\\&\textsf{Distribute}: &-2x-6&=-2x-6\\&\textsf{Add 6 to both sides}: & -2x&=-2x\\&\textsf{Divide both sides by -2}: & x&=x\end{aligned}[/tex]

Therefore, the solution is all real numbers.

[tex]\begin{aligned}&\textsf{Given}: & \dfrac{3}{2}+\dfrac{1}{2}x & = 2x\\&\textsf{Subtract $\dfrac{1}{2}x$ from both sides}: & \dfrac{3}{2}&=\dfrac{3}{2}x\\&\textsf{Multiply both sides by 2}: & 3&=3x\\&\textsf{Divide both sides by 3}: & 1&=x\end{aligned}[/tex]

Therefore, the solution is x = 1.

Answer:

Below

Step-by-step explanation:

70 - 69 = 1

   1/1.2 is  .83 S.D. below the mean   for a z-score = -.83

       from a z-score table this corresponds to .2033  or 20.33%

Answer:

36.5x-53=543

Step-by-step explanation:

Fiona's age will be 'x' years, age of the Thomas is 'x+3' years whereas Cara is '2x' years old.

What is a system of linear equations in three variables?

A three-variable system of three equations can be solved using a series of steps that force one variable to be eliminated. The steps include rearranging equations, multiplying both sides of an equation by a nonzero constant, and adding a nonzero multiple of one equation to another.

If age of Fiona is 'x', the age of Thomas is 'y' and the age of Cara is 'z' years old.

Then by the given conditions, we can write

                   y = x + 3

                   z = 2x

Hence, if Fiona's age will be 'x' years, age of the Thomas is 'x+3' years whereas Cara is '2x' years old.

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Answer:

70.4*

Step-by-step explanation:

Supplementary angles add up to 180*. This means that we must take 109.6 and try to find a number to add up to 180. We do the equation

180-109.6=70.4 therefore, the answer is 70.4*

Answer: 70.4

Step-by-step explanation: i took the test and got it right

Answer:

[tex]\textsf{Solution}: \quad 5 < x < 13[/tex]

[tex]\textsf{Interval Notation}: (5, 13)[/tex]

Step-by-step explanation:

Given inequality:

[tex]|x-9|-3 < 1[/tex]

To solve an inequality containing an absolute value, isolate the absolute value on one side of the inequality:

[tex]\implies |x-9|-3 +3 < 1+3[/tex]

[tex]\implies |x-9| < 4[/tex]

Apply the absolute rule:

[tex]\textsf{If $|u| < a$\; and\; $a > 0$, \;then \; $-a < u < a$}.[/tex]

[tex]\implies -4 < x-9 < 4[/tex]

[tex]\implies -4 < x-9 \;\; \textsf{and}\;\;x-9 < 4[/tex]

Solve case 1:

[tex]\implies -4 < x-9[/tex]

[tex]\implies x-9 > -4[/tex]

[tex]\implies x-9 +9 > -4+9[/tex]

[tex]\implies x > 5[/tex]

Solve case 2:

[tex]\implies x-9 < 4[/tex]

[tex]\implies x-9+9 < 4+9[/tex]

[tex]\implies x < 13[/tex]

Therefore, x is greater than 5 and smaller than 13.

Merge the overlapping intervals to obtain the solution:

[tex]\boxed{5 < x < 13}[/tex]

245.31 (dollars) is the cost (in dollars) of materials for the least expensive such container.

Calculus maxima and minima are found  using the concept of derivatives. Knowing that the derivative concept gives information about the slope/slope of a function, we find the point where the slope is zero. These points are called inflection points/stationary points. These are the points associated with the maximum or minimum (local) values ​​of the function.

Knowledge of maxima and minima is essential for our everyday problems. In addition, this article also explains how to find the absolute maximum and minimum values.

Solvable maximum and minimum arithmetic problems  are discussed in this article.

Suppose the width is x (m), length of the base is 2x (m), the base area is 2x^2 (m^2).

Since the volume is 10 (m^3), the height has to be 10/2x^2 (m) = 5/x^2.

The cost of making such container is

cost of base: 2x^2*15 = 30x^2

cost of sides: (2*2x*5/x^2 + 2*x*5/x^2)*9 = 270/x

The overall cost is hence the sum of the base and the sides: f(x) = 30x^2 + 270/x

The get the minimum,

df(x)/dx = 30*(2x - 9/x^2) = 0

so x = (9/2)^(1/3) = 1.651 (m)

f(x) = 245.31 (dollars)

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The random variable used in this situation is discrete random variable.

What is a random variable?

Suppose there is an event and the outcome of an event has to be represented by a variable. That variable is called random variable.

50 students were randomly sampled and asked questions about their exercise habits. one of the questions they were asked concerned the frequency of exercise, defined to be the number of times they exercised in a week

Since there is a notation about frequency in this question, it cannot be continuous. So it is a discrete random variable.

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Rewritten equation using a common factor is (B) [tex]x^{2} y^{2}(x^{2} -2xy)[/tex].

Given equation,

[tex]x^{4}y^{2}-2x^{3}y^{3}[/tex]

Taking  [tex]x^{2} y^{2}[/tex]  common,

[tex]x^{2} y^{2}(x^{2} -2xy)[/tex]

Hence, the equation.

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Answer:

Step-by-step explanation:

6.57

Option a is correct.

$2 more is Addison’s holiday hourly rate than her regular hourly rate

What are Time and Work?

According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.

The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.

W is the amount of work done.

N is the number of people.

D is the number of days or hours needed.

Let r be the regular rate and h the holiday rate.

Then you can write these two equations:

From the first statement:

188.50 = 5h + 16r

From the second statement:

254.00 = 8h + 20r.

There you have a system of two independent equations with two variables, which you can solve by several methods.

If you multiply the first by 8 and the second by 5, you get:

40h + 128r = 1508

40h + 100r = 1270

Subtract the second equation from the first one:

28r = 238

Divide by 28

r = 238/28 = 8.5

You can use now any of the two original statements to find h

254.00 = 8h + 20r

8h = 254 -20(8.5) = 84

h = 84/8 = 10.5

h - r = 10.50 - 8.50 = 2.00

The holiday hourly rate is $2.00 more than the regular hourly rate.

Hence,

$2 more is Addison’s holiday hourly rate than her regular hourly rate

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Answer:

16:48 or 16 to 48 or 16 / 48

Step-by-step explanation:

Answer:

16:48

Step-by-step explanation:

16 is the total amount of students who want lemonade.
You add 16 with 32 to get 48 students in total.
So the ratio is 16:48.

Answer:

For A, the confidence interval formula above cannot be applied because n is less than 30, so we use the t-score confidence interval value

C.I = Mean ± t score × Standard deviation/√n

Mean = 80

Standard deviation = 5

n = 25

Degree of freedom = 25 - 1 = 24

Hence, 95% confidence interval degree of freedom t score = 2.064

Hence, Confidence Interval =

80 ± 2.064 × 5/√25

80 ± 2.064 × 1

80 ± 2.064

Confidence Interval =

80 - 2.064

= 77.936

80 + 2.064

= 82.064

Confidence Interval: (77.936, 82.064)

[tex]\cfrac{tan(\theta )+1}{sec(\theta )}~~ = ~~sin(\theta )+cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{tan(\theta )+1}{sec(\theta )}\implies \cfrac{~~ \frac{ sin(\theta )}{cos(\theta ) } +1~~}{\frac{1}{cos(\theta )}}\implies \cfrac{~~ \frac{ sin(\theta )+cos(\theta )}{cos(\theta ) } ~~}{\frac{1}{cos(\theta )}}[/tex]

[tex]\cfrac{ sin(\theta )+cos(\theta )}{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \cdot \cfrac{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\implies sin(\theta )+cos(\theta )[/tex]

a. In 2001, it has been calculated that the number of enrolled students that the school would have is given as 150.

b. In the academic year 2018, 468 thousand students are anticipated to enroll at the institution abroad.

The equation that would be used to get the value of the population has been given to us as follows,

y = 123.1(1.069)^x

We are to find x and use it to solve the equation.

X would be used to tell us the number of years that have passed or what lies as the difference.

in which x is the number of years that have changed.

x = 2001 - 1998 = 3

We have to input the value of x to get the value of y

y = 123.1(1.069)³

This gives us y = 150.4

Hence 150 students  would be enrolled.

b. We have to solve for the year 2018

Similarly, the difference between these years is given as:

x = 2018 - 1998 = 20

Put the value in the equation

y = 123.1 * (1.069)²⁰

Y is therefore  467.5

y ~ 468 thousand

Hence 468 are enrolled in this year.

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The pair of polygons in the diagram are not similar.

What are polygons?

A closed polygonal chain made up of a finite number of straight-line segments is what defines a polygon in geometry. A polygon can be defined as a region that is circumscribed by a bounding circuit, a plane, or both. The edges or sides of a polygon circuit are its segments.

Solution Explained:

Similar polygons have proportional matching sides and all corresponding angles that are congruent.

Since the polygons' side lengths ensure that they are parallelograms, the congruence of just one pair of related angles is sufficient to guarantee the congruence of all the others.

The ratio of side lengths in the left polygon is 13/8, whereas in the right polygon it is 5.2/2.4, which equals 13/6. The matching sides are NOT proportionate since their ratios are different from one another.

Hence, the pair of polygons are not similar.

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A recipe says it produces the best summer drink. The recipe calls for 12 cup of lemonade for every 112 cups of iced tea. If 16 cups of the summer drink are made

then 8 cups of lemonade are needed.

What is unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams.

5 ice-creams cost is $125.

Step 1: Let's find the cost of 1 ice cream.

In order to do that, divide the total cost of ice-creams by the total number of ice-creams.

The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-

creams = 125/5 = 25.

Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams.

The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75.

Finally, we have the cost of 3 ice-creams i.e. $75.

lemonade: tea : total

1                 1    1+1=2

We need a total of 16 and divide it

= 16/2 = 8

Then the composition will be

lemonade:    tea:        total

1*8 = 8      1*8 = 8      2*8 = 16

Hence, 8 cups of lemonade are needed.

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