Which of the following could be used as a statement in a two-column proof?

Answer:

Measures of center generally tell us about the middle , or center of a distribution. They are the mean , the Mexican , and the mode. Each plays a useful role in statistics. The mean or arithmetic average , is calculated by adding all the data values and dividing by the number of values.

The factors are mentioned in the table given below.

Number    Number of factors        prime or composite

12                    6                                      composite

20                   6                                      composite

21                    4                                       composite

31                    2                                      prime

43                   2                                        prime

Factors are those numbers which when divide the given number leaves zero as a remainder.

Factor of 12 = 1, 2 ,3, 4, 6 , 12

Factor of 20 = 1, 2 , 4,5,10 , 20

Factor of 21 = 1 ,3, 7, 21

Factor of 31 = 1, 31

Factor of 43 = 1, 43.

Prime number is a number which has only 2 factors that is number one(1) and the number itself.

Composite numbers which has more than 2 factors.

Therefore, the number of factors are mentioned in the table.

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The materials travel faster on Belt One, considering the constants of the proportional relationships.

A proportional relationship is a linear function with intercept zero in which the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, according to the equation presented as follows:

y = kx

For each belt in this problem, the constant gives the velocity that the materials travel.

For Belt One, the relation is:

y = 157.1x.

Hence the velocity is of 157.1 inches per minute.

For Belt Two, the velocity is obtained as follows:

k = 125.6/2 = 62.8 inches per minute.

157.1 > 62.8, hence it travels faster on Belt One.

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The z-score for this amount of advertising time is z = -4.17 so option B is correct.

Given:

Average = 13 minutes

Standard deviation = 1.2 minutes.

Advertising time x = 8 minutes.

z = x - mean / standard deviation.

= 8 - 13/1.2

= -5/1.2

= -5/12/10

= -50/12

= -4.17.

Therefore the z-score for this amount of advertising time is z = -4.17 so option B is correct.

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Answer:

Step-by-step explanation:

we cant see the problem or there answers

For each goody bag we need 3.4 cookies

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

We are given that there are 17 cookies that will be divided equally among 5 goody bags.

17 cookies = 5 goody bags.

For each goody bag.

Thus,

17/5 = 3.4 cookies.

Therefore, 3.4 cookies needed.

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[tex]4(x)+4(-b)=x\\4x-4b=x\\4x-x=4b\\3x=4b\\\frac{3x}{3} =\frac{4b}{3} \\x=\frac{4b}{3}[/tex]

⇒They simply wanted you to simplify and make x the subject of the equation.

The y-intercept is y = 3, and this is the initial height of the ball, and the maximum height is y = 19

The y-intercept is what we get when we evaluate in x = 0, then:

y = -0.25*x² + 4x + 3

replacing x by zero we get:

y = -0.25*0² + 4*0 + 3 = 3

The y-intercept is y = 3.

The maximum height is at the vertex, we know this because the leading coefficient is negative, which means that the parabola opens down.

The vertex is at:

x = -4/(2*-0.25) = 8

Evaluating there:

y = -0.25*8² + 4*8 + 3 = 19

that is the maximum height.

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Answer: _______________________________

72

Answer:

81 degrees

This is an acute angle since it’s less then 90 degrees

Step-by-step explanation:

All three angles of a triangle always equal 180 degrees

180-(78+31)

180-109

81 degrees

Hopes this helps please mark brainliest

Answer: 15 cm

Step-by-step explanation:

just divide 60 by 4 and because a squar has 4 sides and that is it

Answer:

27/256

Step-by-step explanation:

=(27)(1/4)(1)/(64)

=27/256

Answer:

[tex] \huge{ \bold{ \orange{ - \frac{4}{3} }}}[/tex]

Step-by-step explanation:

The slope of a line passing through two points can be found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} \\ [/tex]

where

(x1, y1) and (x2, y2) are the points

From the question

The points are (4, 8) and (7, 4)

We have

[tex]m = \frac{4 - 8}{7 - 4} = - \frac{4}{3} \\ [/tex]

We have the final answer as

[tex] \bold{ - \frac{4}{3} }[/tex]

Hope this helps you

Answer:  Tommys dispacement 17 miles

Step-by-step explanation:

pyhagorean theorem

he went 15 up (leg 1)

and then right 8 (leg 2)

and Tommy's displacement is the hypotenuse

15^2+8^2=c^2

c^2 = 289

c = 17

Answer: -1.631

Step-by-step explanation:

[tex]\log_{3} \frac{a}{3}=\log_{3} a-\log_{3} 3=-0.631-1=-1.631[/tex]

The Z-score for a GPA of 2.98 is 1.60345

A Z-score is a numerical value or measurement that explains the relationship between a value of data and the mean of a group of values. It will be calculated in terms of standard deviations from the mean.

The formula to calculate the Z -score is given by

                     Z - score =  [tex]\frac{( \bar{x} -\mu) }{\sigma}[/tex]    

Where  [tex]\bar {x}[/tex]  = test value

μ = mean and σ = standard deviation

Here we have

GPAS at CCCOnline are normally distributed with a mean of 2.05 and a standard deviation of 0.58

⇒ mean μ = 2.05

⇒ Standard deviation σ = 0.58  

And we need to find the z-score for a GPA of 2.98

⇒  [tex]\bar {x}[/tex] = 2.98

From above observations

Z - score =  [tex]\frac{( 2.98 -2.05) }{0.58}[/tex]  

= [tex]\frac{( 0.93) }{0.58}[/tex]

= 1.60345  

Therefore,

The Z-score for a GPA of 2.98 is 1.60345

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The measure of <FEG= 61 and <HEG = 119.

The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.

when two lines in a plane intersect, one of the angles that are directly across from one another.

Given:

m< DEF= 119

Now, <DEF + <FEG= 180 (Linear Pair)

119+ <FEG = 180

<FEG = 180- 119

<FEG = 61

and, <DEF= <HEG = 119  (Vertical opposite angle)

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The equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

According to the question,

We have the following information:

y = 3x-1 and the point through which line is passing is (3,2)

We know that the slope of the given line (denoted by m) is 3.

Now, the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

In this case, we have x' = 3 and y' = 2.

y-2 = 3(x-3)

y-2 = 3x-9

Moving 2 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

y = 3x-9+2

y = 3x-7

Hence, the equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

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The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43°

In the given figure the angle ∠ABD is intersected by the straight line BC such that two new angles are formed ,∠ABC and ∠ADC  .

Now from the properties of angles on a 2-dimensional plane we can see that :

m ∠ABC + m ∠ADC  = m ∠ABD

The values of the angles given are:

m ∠ABC = 5x - 5

m ∠ADC = 5x + 3

m ∠ABD = 78°

now we put these above values in the equation:

(5x - 5) + (5x + 3) = 78

or, 10 x - 2 = 78

or, 10 x = 80

or , x = 8

m ∠ABC = 5×8 - 5 = 35°

m ∠ADC = 5×8 + 3 = 43°

The value of the angles that are intersected by BC are m/ABC is 35° and m/DBC is 43° .

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There are 15 crates and 35 boxes in the van when it is completely full.

Given,

Total number of crates and boxes=50

For every 7 crates the van can hold, there is room of 3 boxes.

let,

Number of crates =x

Number of boxes =y

As given,

Equation for total number of crates and boxes can be written as

[tex]x+y=50....i[/tex]

Space for 7 crates is equal to space for 3 boxes in van, it's equation can be written as

[tex]7x=3y\\\\x=\frac{3y}{7}[/tex].

Substituting 'x' in eq.[tex]i[/tex]

[tex]\frac{3y}{7}+y=50\\\\ \frac{3y+7y}{7}=50 \\\\10y=7*50\\\\10y=350\\\\y=\frac{350}{10}\\ \\y=35[/tex]

Substituting 'y' in eq.[tex]i[/tex]

[tex]x+35=50\\\\x=50-35\\\\x=15[/tex]

Thus, there are 15 crates and 35 boxes in the van when it is completely full.

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The value of the function f(x) at x = -2 is ,  f(-2) = 1 , the correct option is (c) .

Function is defined as an expression that defines a relationship between one variable and another variable .

In the question ,

it is given that ,

the value of the function f(x) at different values of x is given ,

we have to find the value of the f(-2) , that is the value of the function f(x) at x = -2 .

from the table , we see that when x [tex]=[/tex] -2 , the value of f(x) is [tex]=[/tex] 1 ,

that means f(-2) [tex]=[/tex] 1 .

Therefore , The value of the function f(x) at x = -2 is ,  f(-2) = 1 , the correct option is (c) .

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If  each week it grow by 4% more than it did the previous week by  it grow in 9 week is  17.67cm.

Now let find the growth in 9 week

Growth in 9 week = 1.67cm × [( 1+ 0.04)^9 -1] ÷ [(1+0.04)-1]

Growth in 9 week = 1.67cm × [( 1.04)^9 -1] ÷ (1.04)-1]

Growth in 9 week = 1.67cm ×  [( 1.4233 -1) ÷ 0.04

Growth in 9 week = 1.67cm ×  [0.4233 ÷  0.04

Growth in 9 week = 1.67cm × 10.5825

Growth in 9 week = 17.67cm

Therefore 17.67cm is the 9 week growth.

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The earnings per hour be after working for 15 years is $11.4.

From the given table (2, 6.85), (4, 7.55), (6, 8.25).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)

1) Now, put (x1, y1)=(2, 6.85) and (x2, y2)=(4, 7.55) in slope formula, we get

m=(7.55-6.85)/(4-2)

= 0.7/2

= 0.35

Substitute m=0.35 and (x, y)=(2, 6.85) in y=mx+c, we get

6.85=0.35(2)+c

⇒ 6.85=0.7+c

⇒ c=6.85-0.7

⇒ c=6.15

Now, equation is y=0.35x+6.15

2). Put x=15 in the obtained equation, we get

y=0.35×15+6.15

⇒y=$11.4

3). Put y=9.65 in the obtained equation, we get

9.65=0.35x+6.15

⇒0.35x=9.65-6.15

⇒0.35x=3.5

⇒x=3.5/0.35

⇒x=10 years

Therefore, the earnings per hour be after working for 15 years is $11.4.

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Answer: x>-1

Step-by-step explanation:i just did that question

Answer:

Step-by-step explanation:

add 4 to -15 then divide that  by 11x the answer should be x=-1.

The graph of the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.

Function

Basically, function is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given,

Here we need to find how the graph of g(x)=(x-3)³ related to the graph of f(x) = x³.

Here we have the two equations of the function that are,

f(x) = x³

g(x) = (x - 3)³

By looking at the given functions, we have identified that f(x) be the parent function:

And it can be written as,

=> f(x) = x³

And the first transformation is applied as,

f(x) → f(x) - 3

Now, the function f(x)  will shift right side by 3 units

Therefore, the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.

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Answer:

Red paint  = 12.5 gallons

Blue paint = 7.5 gallons

Step-by-step explanation:

The given ratio of red paint to blue paint is:

Let x be the number of gallons of purple paint.

Therefore, the expression for each color of paint needed per x gallons of purple paint is:

[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8}x$}[/tex]

[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}x$}[/tex]

To calculate the number of gallons of red and blue paint needed to make 20 gallons of purple paint, substitute x = 20 into the found expressions:

[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8} \times 20=\dfrac{100}{8}=12.5$}[/tex]

[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}\times 20=\dfrac{60}{8}=7.5$}[/tex]

Therefore, the number of gallons of paint that should be used are:

The pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is  58.08 kPa.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

The atmospheric pressure, P = 101 kPa,

For every 1000 meters, the pressure decreases by 11.5%,

So at the height of 5000 meter, the % decrease will be 5 × 11.5 = 57.5%,

Now let the 57.5% of 101 kPa be x then,

x = 57.5/100 × 101  kPa,

x = 58.08 kPa,

Therefore, the pressure at an altitude of 5000 m if The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases by about 11.5% is  58.08 kPa.

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