The expression, 20(4x) + 500, represents the cost in dollars of the materials and labor needed to build a square fence with side length x feet around a playground. What is the meaning of the coefficient 20?

Answer:

C

Step-by-step explanation:

Let's go through each of the answer choices:

I) All real numbers are rational numbers.

This is immediately proven false by irrational numbers: real numbers that are not rational. Examples include π or √2.

II) Zero is an integer number.

This is true. Integers include the set of whole numbers, which includes 0.

III) All counting numbers are whole numbers.

This is true. Whole numbers (0,1,2,3...) is basically the counting numbers (1,2,3,...) but with 0.

IV) Irrational Numbers are not real numbers.

This is false. Real numbers can be divided into two subsets: irrational and rational.

So, our answer is C :)

Answer:

x = -3

Step-by-step explanation:

-5x + 32 = 47

-5x + 32 - 32 = 47 - 32

-5x = 15

-5x / -5 = 15 / -5

x = -3

Answer:

[tex]\Huge \boxed{x=-3}[/tex]

Step-by-step explanation:

[tex]\sf -5x + 32 = 47[/tex]

Subtract 32 from both sides.

[tex]\sf -5x + 32-32 = 47-32[/tex]

[tex]\sf -5x=15[/tex]

Divide both sides by -5.

[tex]\sf \displaystyle \frac{-5x}{-5} =\frac{15}{-5}[/tex]

[tex]\sf x=-3[/tex]

Answer: B) The mean will increase and the median will stay the same.

======================================================

Explanation:

Let's look at a small example of why this works.

Suppose that we had the set of 5 items {1,2,3,4,5}. The value 3 is right in the middle so this is the median. The mean is also 3 because adding all the values gets us 15 and then we divide over 5 (the number of items in the set) to get 15/5 = 3.

For any symmetric set of data like this, the mean and median are the same value.

Now let's change that last item 5 to something larger. Let's bump it up to 10

The new data set is {1,2,3,4,10}. The median is still 3 as it's still in the middle. But now the mean is (1+2+3+4+10)/5 = 20/5 = 4. The old mean was 3, and the new mean is 4. So we have the mean increased thanks to that 5 increasing to 10.

We could increase 10 to 20 getting {1,2,3,4,20}. The median is still the same. The mean is now (1+2+3+4+20)/5 = 30/5 = 6. So we've increased the mean again. This process can be continued on for as long as you like.

The outliers to the right hand side effectively pull on the mean in a similar analogy to how gravity pulls on an object. So this is one way to remember that the mean is effected by outliers. The median only cares about being in the middle so that's why it doesn't change. If we changed the number of items in the data set, then it's a different story. However, Kay is only changing her salary rather than bring on a new hire (or two).

So that small example can be applied to Kay's situation even though the numbers are much larger. The median stays the same, but Kay's (much) higher salary pulls on the mean to make it larger than it should be. This is often why a trimmed mean is used when looking at centers of data sets. For data sets that have very large outliers, the median is the more reliable measure of center.

Answer:

66%

Step-by-step explanation:

To find the percentage, we can use this formula:

Part/Whole

In this case, the Part=Seniors and Whole=All of the students in the class

Part/Whole

23/(23+12)

=23/35

=0.65714

=0.66

=66%

Answer:

C) 12.2 cm

Step-by-step explanation:

To find the area of a square, you multiply length and width, which for a square, are the same. So to find the length of one of its sides, you have to take the square root of the area.

[tex]L^{2} = 150\\\\L=\sqrt{150} \\L= 12.2\\[/tex]

Answer:

14

Step-by-step explanation:

Follow DMAS formula:

DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction.

=50+6*3 -82

=50+18-82

=68-82

=14

Answer:

64

Step-by-step explanation:

PEMDAS

6(12+4) distribute the 6 to the numbers inside

96

50+96-82

50+96= 146

146-82 = 64

The domain of a function is the input value.

In the above formula the domain would be the value of p, which is the number of people at the game.

The capacity of the stadium is 650 people, so they can have anywhere from 0 people to 650 people at the game.

The domain would be [0,650]

Answer:6.00

Step-by-step explanation:

yes

Answer:

The answer is 6!

Step-by-step explanation:

The best estimate of Start Fraction 90 over 7 End Fraction divided by 1 and three-fourths is 6 so, option B is correct.

It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

Start Fraction 90 over 7 End Fraction divided by 1 and three-fourths,

Write the  above phrase in mathematical form as shown below,

90 / 7 ÷ 1 3 / 4

convert the mixed fraction into improper fraction as shown below,

90 / 7 ÷ 4 + 3 / 4

90 / 7 ÷ 7 / 4

90 / 7 × 4 / 7

360 / 49

7.346

The nearest value in the option is 6.

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Answer:

Troy ran 228 miles.

Step-by-step explanation:

Ashlynn (a) ran 19 miles. Troy (t) ran 3 times as many miles as Edwin, and Edwin (e) ran 4 times as many miles as Ashlynn.

So,

a=19

E=a•4

t=e•3

Knowing a=19, we can solve the first equation. e=19•4, 19•4=76 so e=76

Knowing e=76 we can solve the second equation t=76•3, 76•3=228 so t=228

Answer:

Ashlynn is my name!

Step-by-step explanation:

The product of sin 30 and sin 60 is same as the product of cos 60 degrees tan 30 degrees and cos 30 degrees tan 60 degrees .

The product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.

From the complementary angle theorem, we have that

sinθ = cos (90° - θ)

and

cosθ = sin (90° - θ)

By applying the theorem,

sin 30° = cos (90° - 30°)

∴ sin 30° = cos 60°

Also,

sin 60° = cos (90° - 60°)

∴ sin 60° = cos 30°

Thus, sin 30° = cos 60° and sin 60° = cos 30°

Hence, the product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.

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Answer:

number of tiles needed = 2500 pieces

Step-by-step explanation:

Floor area = 5m x 20m = 100 m²

area of 1 square tile = 20cm x 20cm = 400 cm² ---- convert to m²

400 cm² x [tex]\frac{1 m^{2} }{100^2 cm^2}[/tex] = 0.04 m²

To get the number of tiles required to cover the floor area 5x20 = 100 m²

just divide it by the area of tile.

so Number of tile req'd = 100 / 0.04 = 2500

therefore,

the number of tiles needed = 2500 pieces

Answer:

the full solution is in the picture

d= -3

n= -2

x= -32

Answer:

Step-by-step explanation:

The formula for finding the distance between two points is expressed as shown

D = √(x₂-x₁)²+(y₂-y₁)²

Given the coordinate (17,3) and (17,−5), from the coordinates x₁ = 17, y₁ = 3, x₂ = 17 and y₂ = -5.Substituting the values given into the formula;

D = √(17-17)²+(-5-3)²

D = √0²+(-8)²

D = √64

D = 8

According to the result gotten, it can concluded that Marcia is correct although she didn't use the right expression to calculate her distance. She should have taken the square root of the sum of the square of difference in the coordinates axis according to the formula used.

Answer:

20%

Step-by-step explanation:

200 mocha flavored cupcakes of the 500 cupcakes were sold. (200/500).

Reduce to 2/5. Then multiply 20/20 to 2/5 and get 20/100.

20% cupcakes were mocha flavored.

The logic behind me rewriting the fraction to 20/100 was because 200/500 could easily be divided be 100 and 5.

Answer:40%

Step-by-step explanation: 200/500=?/100

2/5 x 20/20= 40/100

40%

[tex]\huge{\underline{\mathfrak{Question:-}}}[/tex]

» [tex]\dfrac{3}{20}[/tex] convert it to decimal and percentage 62.5% convert it to decimal and fraction.

[tex]\huge{\underline{\mathfrak{Solution:-}}}[/tex]

= [tex]\dfrac{3}{20}[/tex]

= 3 ÷ 20

= 0.15

Now,

We know that,

= 62.5%

= [tex]\dfrac{625}{100}[/tex]

= 6.25

Here, now for the fraction one,

= [tex]\dfrac{625}{100}[/tex]

= [tex]\dfrac{625÷5}{100÷5}[/tex]

= [tex]\dfrac{125÷5}{20÷5}[/tex]

= [tex]\dfrac{25}{4}[/tex]

And, the answer in fraction comes [tex]\dfrac{25}{4}[/tex]

Answer:1. 0.15

1. 15

2. 0.625

2. 5/8

Step-by-step explanation:

Answer: $ 2800

Step-by-step explanation:

2400 is 96% of the initial price of camera which is 2400/0.96 =$2500

Now to gain 12% profit the camera should be sold at 2500+ .12*2500=$2800

The estimated distance between the park and your school is 5 miles.

Here,

To estimate the distance between the park and your school, we can use the Pythagorean theorem, as the distance forms a right-angled triangle with the school, apartment, and park as its vertices.

Let's label the points as follows:

S = School

A = Apartment

P = Park

Given:

School (S) is 4 miles east and 1 mile south of the apartment (A).

Park (P) is 3 miles east and 4 miles south of the apartment (A).

Now, we have two right-angled triangles:

The triangle formed by S, A, and P. This is the triangle for which we want to estimate the distance between the school and the park.

The triangle formed by A, S, and P.

Since both triangles share the side AS (4 miles east), we can use the Pythagorean theorem for the triangle ASP to find the distance between the school and the park.

The Pythagorean theorem states that for a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, let's represent the distance between the school and the park as d (the hypotenuse), and the other two sides as 3 miles (east) and 4 miles (south).

Using the Pythagorean theorem:

[tex]d^2 = 3^2 + 4^2\\d^2 = 9 + 16\\d^2 = 25\\[/tex]

Now, take the square root of both sides to find d:

d = √25

d = 5

So, the estimated distance between the park and your school is 5 miles.

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Step-by-step explanation:

Mohammed used 3 1/2 ink cartridges = [tex]\dfrac{7}{2}[/tex]

Luigi used 1 3/4 ink cartridges = [tex]\dfrac{7}{3}[/tex]

It means that Mohammed used more ink cartridges than Luigi. The more amount is calculated as follows :

[tex]\dfrac{7}{2}-\dfrac{7}{3}=\dfrac{7\times3-7\times 2}{6}\\\\=\dfrac{21-14}{6}\\\\=\dfrac{7}{6}[/tex]

So, [tex]\dfrac{7}{6}[/tex] more ink cartridges Mohammed used than Luigi.

Answer: Switch steps 2 and 3.

explanation: Have a good day stay safe

Answer:

No

Step-by-step explanation:

The rock has more mass and will therefore always have greater density than a piece of cork. This is also due to the atomic structure of the elements, molecules, and compounds that make it up.

Answer:

3.009

Step-by-step explanation:

1 Kg is 1000 grams therefore

3 kg 9 g is

3.009

hope this helps you

Answer:

Step-by-step explanation:

Given two coordinates (x₁,x₂) and (y₁,y₂), their midpoint (w,y) is expressed as:

M(X,Y) = [tex](\dfrac{x_1+w}{2}, \dfrac{y_1+y}{2})[/tex]

From the question, we are given the midpoint (X,Y) to be (2,2) and one endpoint as (1, -2) and we are to find the other end point expressed as (w,y). From the coordinates given, i can be seen that X = 2, Y =2, x₁ = 1 and y₁ = -2

Substituting the given end points into the given formula to get the other end points, we will have;

[tex]X = \dfrac{x_1+w}{2} \\2 = \dfrac{1+w}{2} \\cross\ multiply\\4 = 1+w\\w = 4-1\\w = 3[/tex]

Similarly;

[tex]Y = \dfrac{y_1+y}{2} \\2 = \dfrac{-2+y}{2} \\cross\ multiply\\4 = -2+y\\y = 4+2\\y = 6[/tex]

Hence the other endpoint (w, y) is (3,6)

Answer:

x = -5

Step-by-step explanation:

− 6 x − 15 = 4 x + 35

Add 6x to each side

− 6 x+6x  − 15 = 4 x+6x + 35

-15 = 10x+35

Subtract 35 from each side

-15-35 = 10x+35-35

-50 = 10x

Divide each side by 10

-50/10 = 10x/10

-5 =x

Answer: x = -5

Step-by-step explanation:

In order to solve this problem, you need to isolate the variable.

In this problem, you need to isolate the x.

-6x -15 = 4x +35

10x = -50

x = -5

Answer:

Hey there!

-3.4x-5.7x+4

-9.1x+4

Let me know if this helps :)

Answer:

c x 3 = ?

Step-by-step explanation:

you would get how many boxes you have solded then multiply it by 3

we are using c for boxes of candy.

The notation will be 3 × c = R .

A candy is being sold at $3 for school fundraiser.

If c is no. of boxes of candy then we have to find Revenue R.

What will be the value of 10 pens if one pen costs $3 ?

The cost of 10 pens will be 10 × 3 = $ 30 .

As per the question ;

Price at which candy is being sold is $3 per box.

So ,

price of 1 box = $3

price of c boxes = 3 × c

This is equal to total revenue from school fundraiser.

i.e., 3 × c = R

Thus , the notation will be 3 × c = R .

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Is the ratio 5:6 equivalent to 3:4

We can write the given expression as -

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

Factors of a number are numbers that divide evenly into another number. Factorization writes a number as the product of smaller numbers

Given is the expression -

{(x² + y²) - z²}² - 4x²y²

(x² + y²)² + z² - 2(x² + y²)z² - 4x²y²

(x² + y²) {(x² + y²) - 2z²} + z² - 4x²y²

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

Therefore, we can write the given expression as -

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

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Answer:

L = 22 cm

Step-by-step explanation:

Area of a triangle = L x W

where W = 13 cm

Area = 286 cm²

A = L x W

286 = L x 13

L = 286 / 13

L = 22 cm

proof:

286 = 22 x 13

286 = 286 --- ok

Answer: d. 4, 4.53%

Step-by-step explanation:

Given table :

Number of Children                 Frequency

0                                                      325  

1                                                       212

2                                                       660

3                                                       151

4                                                       68  ← Least frequency

5 or more                                         84

Total                                 =            1500

or Sample size of couples = 1500

The number of children occurred the least frequently = 4 [Minimum frequency is 68 at number of children=4]

Percentage =[tex]\dfrac{least\ frequency}{Total}\times100[/tex]

[tex]\dfrac{68}{1500}\times100=4.53\%[/tex]

Hence, the correct answer is d. 4, 4.53%

Answer:

It is 15

Step-by-step explanation:

A. on edge

Total number of animals for which (p ∪ q) ∩ r is true is 15.

What is meant by union of sets?

The set that contains all the elements present in both sets is the union of the two supplied sets.

Here,

It is given that,

Set p is {2, 5, 8, 9}

Set q is {2, 4, 7, 5}

Set r is {2, 4, 6, 9}

The union of p and q, which includes all creatures that are in p, in q, or in both p and q, is known as p ∪ q.

p ∪ q = {2, 4, 5, 7, 8, 9}

The creatures that must be present in both (p and q) and r are contained in (p ∪ q) ∩ r.

So, (p ∪ q) ∩ r = {2, 4, 9}

Therefore,

2 + 4 + 9 = 15

Hence,

Total number of animals for which (p ∪ q) ∩ r is true is 15.

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Attaching the image file here.

Answer:

0 it went minus 2 minus 3 minus and so forth

Answer:

-3,-2

Step-by-step explanation: