The graph represents the piecewise function

The given Commutative Property is 8y - 0.2y + 0.5y + 2.2 + 1.3 - 0.4 by solving this property we get the answer as (8.3y + 3.1).

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped. According to the question,

Steps involved are:-

So,

8y - 0.2y + 0.5y + 2.2 + 1.3 - 0.4

= (8 - 0.2 + 0.5) y + (2.2 + 1.3 - 0.4)

= (8 + 0.5 - 0.2) y + (2.2 + 1.3 - 0.4)    

= (8.5 - 0.2) y + (3.5 - 0.4)    

= (8.3) y + 3.1    

= (8.3y + 3.1)

Thus , by following all the steps and properties we get the obtained result.

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The given geometric series [tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex] is convergent in nature.

[tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex]

Since it is geometric series. (As it is given in the question)

A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.

Here the value of a=8, while the value of the common ratio [tex](r)=\frac{a_2}{a_1}=\frac{7}{8}=\frac{7}{8}[/tex]

since [tex]$|r|=\frac{7}{8} < 1$[/tex]

So the given series is convergent.

The sum of geometric series with infinite terms is equal to [tex]$\frac{a}{1-r}$$$[/tex]

Sum[tex]=\frac{8}{1-\frac{7}{8}}=\frac{8}{\frac{1}{8}}=64[/tex]

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To find the loan amount after five years, we need to calculate the compound interest on the loan. The compound interest is calculated by multiplying the principal (the initial amount borrowed) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 5.75%/12 = 0.475% per month, and there are 12*5 = 60 compounding periods (12 months per year for 5 years).

The compound interest is therefore calculated as follows:

Compound interest = $1,500 * (1 + 0.475%)^60 - $1,500

= $1,725 - $1,500

= $225

So the loan amount after five years is $1,725. Therefore, the correct answer is [D] $1,725.

Answer:

Step-by-step explanation:c because I’m in college and Ik trust me

Answer:b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It is calculated using a formula that takes into account the values of the two variables and their relationship to each other. This formula is not affected by changes in the units of measurement of either variable. Therefore, changing the units of time from minutes to seconds in this scenario would not affect the value of the correlation coefficient, so it would remain the same.

Option A, "The correlation and time measurement would change proportionally to one another," is incorrect because the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option C, "The correlation would increase because changing the units for time would result in an increase in time values," is also incorrect because the correlation coefficient is not affected by changes in the actual values of the variables, only by the strength and direction of the relationship between them.

Option D, "It is impossible to determine the amount of change experienced by the correlation," is incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.

Option E, "The correlation would decrease because only the units for one of the variables changed," is also incorrect because, as explained above, the correlation coefficient is not affected by changes in the units of measurement of either variable.

The probability that all three will be in box 1 will be  [tex]\frac{1}{8}[/tex] or 0.125.

As per the given data the three balls which are labeled as A, B, C are placed into two different boxes of box 1 and box 2.

Box 1 has 10 balls and box two has 5, if all the arrangements are equally likely we have to determine the probability that all the three will be in box 1.

Formula for finding the probability:

Probability = The total number of outcomes ÷ The favorable number of outcomes.

The total number of outcomes:

= [tex]$${ }^3 C_3+{ }^3 C_2+{ }^3 C_1+{ }^3 C_0$$[/tex]

= 1+3+3+1

=8

The favorable number of outcomes:

= [tex]{ }^3 C_3[/tex]

=1

The probability that all the three will be in box 1:

= [tex]\frac{1}{8}[/tex]

= 0.125

Therefore the probability is  [tex]\frac{1}{8}[/tex] or 0.125.

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Area of a square:

We have s = 6⁴, then the area is:

Or, apply the power of the power rule (xᵃ)ᵇ=xᵃᵇ to get:

Answer:

∠M ≅ ∠G

Step-by-step explanation:

Given:

This means that triangle MTD is congruent to triangle GLS.

Two triangles are said to be congruent if:

Therefore:

Similarly:

Therefore, the true statement is ∠M ≅ ∠G.

Answer: 0 = 2

Step-by-step explanation:

First you need to multiply the numbers:

2x + 2(-x) = 2

2x - 2x = 2

Combine the like terms:

2x-2x = 2

So, 0 = 2

Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

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The linear equation for their total combined age in 5 years is 2x + 17 = 31.

Let the age of Alex be x years old.

Let the age of June be 'y'.

June is exactly 7 years older than Alex.

y = x+7

In next 5 years, combined  total age will be of 31 years.

(x+5) + (y+5) = 31

Now, the linear equation that models total combined age in 5 years

Replace y with (x+7)

x + 5 + (x+7) + 5 = 31

2x + 17 = 31

Thus, linear equation for their total combined age in 5 years is 2x + 17 = 31.

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Step-by-step explanation:

45° is an alternate angle with 5y+10. All alternate angles are equal. opposite sides of a parallelogram are equal, we equate to find x.

source: A tutor on another math app. (Brainly doesn't recognize the name)

IQ is normally distributed with a mean and Standards deviations .

a) The probability that this person has an iq greater than 95 is 0.6306 or 63.1%

b) The probability that this person has an IQ less than 125 is 0.9522 or 95.2 %.

c) In a sample of 700 people, the number of people would have an IQ less than 110 is 598 people.

d)In a sample of 700 people, how many people would have an IQ greater than 140 is three in count.

We have normal distribution here with

Mean , u = 100

Standard deviations, s = 15

let X be random variable, X~ N(15, 100)

a) P(X > 95)

From Z- statistic, Z = (X - u) /s

Converting to standard normal variable,

P( X- u/sd <( 95 - u)/s)

P(Z > (95 - 100) / 15)

= P(Z > -0.3333)

Using standard normal tables, value of P(Z > -0.3333) = 0.6306

Therefore 63.1% is the required percentage here.

b) P(X < 125)

= P(Z < (125 - 100) / 15)

= P(Z < 1.6667)

Using standard normal tables,

= 0.9522

Therefore 95.2% is the required percentage here.

c) The probability here is computed as:

P(X < 110)

= P(Z < (110 - 100) / 15)

= P(Z < 0.6667 )

Using the standard normal tables,P(Z < 0.6667 ) = 0.7475

Therefore expected number of people:

= 800×0.7475

= 598

Therefore 598 is the required expected number of people here.

d) P(X > 140)

= P(Z > (140 - 100) / 15)

= P(Z > 2.6667)

Getting from standard normal tables,

= 0.0038

Therefore expected number of people here:

= 800×0.0038

= 3.04

Therefore 3 is the expected number of people here. Hence, we get the required probability for each case

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Complete question:

IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ less than 125) = % c) In a sample of 700 people, how many people would have an IQ less than 110? people d) In a sample of 700 people, how many people would have an IQ greater than 140? people

The right response is C. Only X-values inside the original data's range give meaning to the prediction values.

A statistical model that depicts the relationship between two variables is a regression line. It is utilized to forecast the value of a dependent variable depending on the value of an independent variable (independent variable).

The degree to which the regression line matches the data determines how accurate these forecasts are. For values of the independent variable that are similar to the values used to fit the model, the regression line will typically offer the most precise predictions. Prediction values therefore typically only have significance for X-values that fall within or very near the range of the original data set.

The predictions might not be correct if you use the regression line to construct them for independent variable values that are far outside the original data range. This is because, outside of the range of the data that was used to construct the model, the model may not effectively represent the connection between the two variables.

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Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

Many straightforward inequalities can be resolved by adding, taking away, multiplying, or dividing both sides until the variable is all that remains. However, these factors will shift the direction of inequality: Using a negative number to multiply or divide both sides. switching the left and right sides. When resolving an inequality, you can do one of the following:

• Add the same amount to each side;

• Subtract the same amount from each side;

• Multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

5 x (23-18) x (8-4)=100

So we can subtract 23 from 18 where we will get 5 and by subtracting 4 from 8 you will get 4. By multiplying the numbers using × operator you will get the final answer.

Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.

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The probability that exactly two people out of a group of five have responded to a telephone poll is approximately 26%.

The probability that exactly two people out of a group of five have responded to a telephone poll can be calculated using the binomial distribution. The probability of a single person responding to a call in a poll is 15%, and the probability of a single person not responding to a call in a poll is 85%.

The probability of two people out of a group of five responding to a call in a poll can be calculated using the formula for the binomial probability mass function:

[tex]P(X=2) = (5 choose 2) * (0.15)^2 * (0.85)^3[/tex]

where (5 choose 2) is the binomial coefficient, which represents the number of ways to choose 2 people out of a group of 5.

Plugging in the values, we get:

[tex]P(X=2) = (10) * (0.15)^2 * (0.85)^3 = 0.2574[/tex]

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Answer: $28 per week

Step-by-step explanation:

1 month = 4 weeks

18 times 4 = 72 weeks

So you know you want to save 2000 to buy a car 72 weeks from now.

So take 2000 divided by 72 = $27.77 per week

So you need to save about $28 per week.

The simplest expression is x³ - x² - 17x + 20.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(x - 4) (x² + 3x - 5)

x³ + 3x² - 5x - 4x² - 12x + 20

x³ - x² - 17x + 20

Thus,

The final expression is

x³ - x² - 17x + 20

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Answer: x = 9

Step-by-step explanation:

Let's start with what we know. We know that the sum of all angles is 180 so:

13x + 2 + 3x - 4+ 5x - 7 = 180

21x - 9 = 180

21x = 189

Divide by 21 on both sides:

x = 9

The new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5).

What is the Dilation of the rectangle?

Dilation occurs when a polygon grows or shrinks while maintaining its overall shape. It's similar to zooming in or out on a camera. The polygon in the figure above is a rectangle JKLM. As you move the slider on the right, the transformed rectangle J'K'L'M' grows and shrinks but retains its shape.

We have,

Rectangle JKLM with vertices:

J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2

New dilation vertices of the rectangle are:

J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5)

Hence, the new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0), and M'(-5, -5).

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The lines q and t are, perpendicular to each other.

If two lines are perpendicular to each other, then their slopes are negative reciprocal of each other. That means, if one line's slope is 'a', then its perpendicular line's slope would be -1/a

Noted that Parallel lines have the same slope, the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Given that Lines q, r, s, and t are distinct lines in the same plane.

IF the lines are;

q is perpendicular to r,

r is perpendicular to s

s is perpendicular to t

Then we can conclude that q is perpendicular to t

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The expression when expressed in its exponent is a²+c²

In mathematics, we should understand that exponent tell the power to which a number is raise.

 It shows the number of times a number multiplies itself to get the certain member.

The given expression is a*a*c*.

Using the law of multiplication that says when two or more numbers in the same base are multiplied, we add their powers.

Here a appeared twice a*a=a²

And c appeared twice that is c*c=c²

Combining the two exponents together we have that

a²+c²

In conclusion, the exponent of a*a*a*a is a²+c²

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Answer:

The ball travels (exactly) 75 feet.

Step-by-step explanation:

Assuming the balls comes to rest:

S = a1 / (1 - r)

Now a1 is the first bounce, 20 ft (10 feet up, 10 feet down.

r is 2/3

S = 20 (1 / (1 - 2/3)

S = 20 / (1/3)

S = 60

Yet that is only the bounce. The drop of 15 feet must be added.

Answer:

all of them are true except the last one ( no. e)

The z-score for that condition is 0.38. To be exact, the z-score is 0.38461538461.

First we have to extract mean and standard deviation from x~n(145, 13) where mean (μ) = 145 and standard deviation(б) = 13. As per given corresponding to an observation(x) is directly given = 150 we can start to find the z-score with formula z-score = (x - μ) :  б. So

z = (x - μ) :  б.

z = [tex]\frac{150-145}{13}[/tex]

z = [tex]\frac{5}{13}[/tex]

z = 0.38461538461

Normally z written in 2 to 4 digit after decimal, so z-score = 0.38

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When they buy 125 identical stuffed animals for $312.50 and sell them for $7 a piece, the percent markup is 64.2%.

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The sign "%" represents it. To compute a percentage, divide the value by the entire amount and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.

Here,

Total cost=$312.50

Total sell price=7*125

=$875

Markup Price=(875-312.5)/875*100

=0.642*100

=64.2%

The percent markup is 64.2% when they purchase 125 identical stuffed animal for total cost of 312. 50 and sell them for $7 each.

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Answer:

2

Step-by-step explanation:

2x - y = -1

-y = -2x - 1

y = 2x + 1

parallel line = same slope

The price of the microwave before sales is 350 dollars.

Javier bought a microwave for $105. The cost was 30% off the original price.  Therefore, the price of the microwave before sales can be calculated as follows:

let

x = price before sales(original price)

Therefore,

105 = 30% of x

105 = 30 / 100 × x

105 = 30x / 100

cross multiply

10500 = 30x

divide both sides by 30

10500 / 30 = 30x / 30

x = 350 dollars

Therefore, the original price is 350 dollars.

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Answer:

[tex] \sf \: t = 19[/tex]

Step-by-step explanation:

Given equation,

→ t - 6 = 13

Now the value of t will be,

→ t - 6 = 13

→ t = 13 + 6

→ [ t = 19 ]

Hence, the value of t is 19.