Barbara drew a scale drawing of a game room. The scale she used was 2 inches : 1 foot. If the actual length of the pool table is 6 feet, how long is the pool table in the drawing?​

Applying the centroid theorem, the missing measures are:

FM = 22

A.F = 66

CM = 36

ME = 18

MB = 46

DB = 69

The centroid theorem states that the distance from the centroid of the triangle to the opposite vertex is equal to one-third of the length of the segment that connects the midpoint of a side of a triangle to the opposite vertex.

Given:

AM = 44, CE = 54, and DM = 23, where M is the centroid of the triangle, thus:

FM = 1/3(FA) = 1/3(AM + FM)

Substitute

FM = 1/3(44 + FM)

3FM = 44 + FM

3FM - FM = 44

2FM = 44

FM = 44/2

FM = 22

A.F = AM + FM = 44 + 22

A.F = 66

CM = 2/3(CE)

CM = 2/3(54)

CM = 36

ME = CE - CM = 54 - 36

ME = 18

MB = 2/3(DB) = 2/3(DM + MB)

MB = 2/3(23 + MB)

3MB = 2(23 + MB)

3MB = 46 + 2MB

3MB - 2MB = 46

MB = 46

DB = DM + MB = 23 + 46

DB = 69

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Answer:

Step-by-step explanation:

(4-3)/(2-1= 1/1 = slope = 1

y =(1)x + b,  plug in either point to solve for b

3 = 1 +b

b = 2

Yes this an example of simple random sampling.

What is simple random sampling?

Every person in the population has an equal probability of getting chosen in a simple random sampling. The entire population should be included in your sampling frame.

You might utilize instruments like random number generators or other methods that just rely on chance to carry out this kind of sampling.

Main Body:

It is uncommonly attainable to collect knowledge from each member of a gaggle of people once conducting analysis on them. In its place, you choose a sample. The population that may really participate within the study is that the sample.

As in this case we select 100 random people out of 1000 , so it is an example of simple random sampling.

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The graph is in the image uploaded.

Given function:

y = -2x - 3

Table:

x          y

-2        0

0        -2

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z >1 for the given inequality for x.

To solve the following inequality for x.

-26 + 13z + 2 > 2 132

Since there is no x in this I'm assuming we are looking for z

Step 1: Simplify both sides

15r - 26 > -13z + 2

Step 2: Add 13z to both sides

15r - 26 + 13z > -13z + 2 + 13z

28 - 26 > 2

Step 3: Add 26 on both sides

28 - 26 + 26 > 2 + 26

28z > 28

Step 4: Divide both sides by 28z / 28 > 28 / 28

z > 1

Hence the answer is z >1 for the given inequality for x.

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After finding the ratio for each person, Ben will get $72

A ratio  shows the relative sizes of two or more values. Ratios can be shown in different ways:

It was given that Alice, Ben and Charlie are to share $213.

Ratio of Alice's share to Ben = 4 : 3

Ratio of Ben's share to Charlie = 8 : 5

Combining these ratios, their shared item (Ben's share) must be the same in each ratio.

Taking Alice's share to Ben, 4 : 3 and multiplying both parts by 8 to get an equivalent ratio, we have:

Alice : Ben = 4(8) : 3(8) = 32 : 24

Likewise, taking Ben's share to Charlie, 8 : 5 and multiplying both parts by 3, we have:

Ben : Charlie = 8(3) : 5(3) = 24 : 15

Combining these ratios, we have:

Alice : Ben : Charlie = 32 : 24 : 15

Adding the ratios together, we have: 32 + 24 + 15 = 71

If the money to be shared is $213, Ben's share will be:

[tex]\frac{24}{71}[/tex] × [tex]$213[/tex] = 72

Therefore, Ben will get $72 from the total amount of $213

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Answer: x∈(-3,-1)

Step-by-step explanation:

13<-5x+8<23

13-8<-5x+8-8<23-8

5<-5x<15

Divide the double inequality by 5:

1<-x<3

Multiply the double inequality by -1:

-1>x>-3

Thus, x∈(-3,-1)

Answer: x= 1

Step-by-step explanation:

Ren will have to wait for approximately 31 years for the money compounded annually and a rate of 2.3% to double it's original investment.

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.

The formula of compound interest is given as

A = P(1 + r/n)^nt

Substituting the values into the equation;

It will take approximately 31 years to double the investment.

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The perimeter "P" is equal to the length of the base of one triangle multiplied by the "n" number of triangles in the figure plus two times the length of another side. The equation for the perimeter is P = 5n + 14.

We are given triangles. The triangles are arranged in a certain pattern. The length of the base of each triangle is equal to 5 units. The length of the other two sides is 7 units each. We conclude that all the triangles are isosceles. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P".

P(1) = 14 + 5(1)

P(2) = 14 + 5(2)

P(3) = 14 + 5(3)

We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.

P(n) = 14 + 5n

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Answer:

Step-by-step explanation:

14

Answer:

I believe it's 18x2(14x + 7)

Step-by-step explanation:

I took the test :)

18x² + 14x + 7 ( may be expressed in any order )

= 14x +18x² + 7

Answer: 7

Explain: 2x + 4 = 18 which is required an equation, so the sum of thrice a number and 7 is 25. So 3x + 7 = 25

Answer:

7

Step-by-step explanation:

As per given data of living children under 18 years of age , percent of children whose age is under 18 years lived with their mother only is equal to 39.3%.

As given in the question,

Let us consider 100% be the total percent representing the living status of children under 18 years of age

Given:

Percent of children living with both the parents = 49.2%

Percent of children living with only father = 8%

Percent of children living with neither of the parents = 3.5%

Let us consider percent of children living with only mother = x%

Required equation is:

( x + 49.2 + 8 + 3.5 )% = 100%

⇒ x + 60.7% = 100%

⇒ x = 100 - 60.7

⇒ x = 39.3%

Therefore, for the given data of living children under 18 years of age , percent of children whose age is under 18 years lived with their mother only is equal to 39.3%.

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Answer:

5/8, 3/4, 1/2

Step-by-step explanation:

divide each and find out which one is the smallest to biggest :)

Answer:

The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b

Answer:

Domain: {-1,0,1,4}

Range: {3,5,35}

Step-by-step explanation:

The domain is the set of x values while range is the set of y values

Here, the set of x values would be -1 , 0 , 1 and 4

And the y values would be 5, 3, 5, and 35

When writing the domain and range, you put the values into brackets "{}" and put them in order from least to greatest. Also if there are repeated values you do not repeat them, you only put them once.

This means that the domain would be {-1,0,1,4}

And the range would be {3,5,35}

The third degree polynomial function with zeros of −3, −1, and 4, and a y-intercept of −13 is y = -13/12 (x³ - 13x + 12)

Polynomial function:

polynomial function refers a functions of single independent variables, in which variables can occur more than once, raised to an integer power.

Given,

Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.

Here we need to construct  a polynomial function with the stated properties and reduce all fractions to lowest terms.

The standard form for the third degree polynomial function is written as,

y = K (x + zero1) (x + zero2) (x + zero3)

Here we know the values of zeros as -3, -1 and -4.

Apply it on the general form,

y = K (x -3) (x - 1) (x + 4) ----------------------(1)

And the value of y intercept is -13 then the value of x is 0.

So, it can be written as,

-13 = K(0 - 3) (0 - 1) (0 + 4)

-13 = K (-3)(-1)(4)

-13 = K (12)

K = -13/12

Now, we have to apply these value on the equation (1), then we get,

y = -13/12 (x -3) (x - 1) (x + 4)

When we expand these, then we get the polynomial function as,

y = -13/12 (x³ - 13x + 12)

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264 naira tax doe he pays in a year.

Amount earned per year = 2460

Rate of interest paid: 10k per naira earned

Tax paid by messenger per year :

100k = 1 naira

10k = (100/10) = 0.1 naira

Hence 0.1 naira is paid as tax on every naira earned

The total amount paid off is 2640 Naira :

Amount paid per naira * total amount earned

(0.1 * 2640) = 264 nairas.

A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.

Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.

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Answer:

1. Congruent, SAS

2. Congruent, SSS

3. Not congruent

4. Congruent, SAS

5. Congruent, SSS

6. Not congruent

7. Congruent, SAS

8. Not congruent

Answer: 4,5,6,7,8

Step-by-step explanation:

Let the first integer be A; then the five consecutive integers are A, A+1, A+2, A+3, and A+4.

If the sum of the first three equals the sum of the last two, then A + (A+1) + (A+2) = (A+3) + (A+4)

Combining, 3A + 3 = 2A + 7 … A =4

The five Integers are thus 4, 5, 6, 7, and 8

Answer:

God is good, satanist are L

Answer:

0 and -6

Step-by-step explanation:

Either x=0

Or, x+6=0 i.e, x= -6

The zeros of the function are-

The given expression is-

f(x)=(x-10)^2-49

To find the zero put f(x) = 0.

(x-10)^2-49 = 0

Including both sides of an equation, add 49.

(x-10)^2 - 49 + 49 = 49

(x-10)^2  = 49

To remove the exponent upon that left side of the equation, take the appropriate root of both sides.

x - 10 = ±√49

x - 10 = ±7

Solve each case;

a:  x - 10 = + 7

x = 7 + 10

x = 17 (greatest number)

b: x - 10 = - 7

x = -7 + 10

x = 3 (lesser value)

Thus, the zeros of the function are 3 and 17.

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Answer:

Step-by-step explanation:

Hi Strawberry  :D   so three ways to spend $120

T= tshirts

S=socks

20T +5S= 120

20(5)+5(4) =120      one

20(4) +5(8) =120     two

20(3) +5(12) = 120  three

20x +5y =120

When a fair die with faces numbered 1 to 6, the probability that the number landing face up is less than 3 is 1/3.

The probability measures how likely an event to occur. The probability of an event A is defined as:

P(A) = number of ways that event A can occur / all possible outcomes

In the given problem, let x be any number of die's face, then

number of ways x will show up = 1

all possible outcomes = 6

Hence,

P(x) = 1/6

Numbers that are less than 3 is 1 and 3. Therefore,

P (x<3) = P(1) + P(2)

P (x<3) = 1/6 + 1/6 = 2/6 = 1/3

Therefore, we can conclude that the probability that the number landing face up is less than 3 is 1/3

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Given that Phil takes 3 times as long as Meredith to complete the work . Let us take Meredith takes x hrs to complete the work, the Phil will do that work in 3x hrs . Now it is given that they together complete the work in 12hrs . So ,

[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{3x}=\dfrac{1}{12}\\ [/tex]

[tex]\longrightarrow \dfrac{3+1}{3x}=\dfrac{1}{12} \\[/tex]

[tex]\longrightarrow \dfrac{4}{3x}=\dfrac{1}{12}\\[/tex]

[tex]\longrightarrow x =\dfrac{(4)(12)}{3}\\[/tex]

[tex]\longrightarrow x = 16\ hrs [/tex]

Hence,

And we are done!

The length of the right triangle, y is 8.94 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right angle triangle can be found using trigonometric ratios or Pythagoras's theorem.

c² = a² + b²

where

Therefore,

12² - 8² = y²

144 - 64 = y²

y = √80

y = 8.94427191

y = 8.94 units

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Answer:

$35.10

Step-by-step explanation:

45 x 0.22= 9.9

45-9.90= 35.10

A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.

A function assigns the value of each element of one set to the other specific element of another set.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph.

Now, According t the question:

Given that, f(x) = (x - 1)(x + 2)(x − 3)

Therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.

Hence, the zeroes of the functions are -2, 1, and 3.

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Answer:

A

Step-by-step explanation: