Date
9. Mike bought a set of golf clubs that cost k dollars. He signed an installment agreement requiring
a 5% down payment and monthly payments of g dollars for 1 1/2 years.
a. Express his down payment algebraically.
b. How many monthly payments must Mike make?
c. Write expressions for the total amount of the monthly payments and the finance charge.

The mapping diagram above does not represent a function since for each number in Set A (the input) where there are multiple mappings from Set B (the output).

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).

Based on the mapping diagram shown above, we can reasonably infer and logically deduce that the inputs (4, 3), (-2, 3), (8, 6), and (4, 7) are ordered pairs which does not represent a function because they indicate multiple mappings in Set B (the output).

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Concept: Proportion, to find the km/h return journer

3 hours to 84 km/hr = 3.5 hours to x km/hr

(since its inverse proportion, multiply the 1st to 2nd and 3rd to 4th)

Inverse proportion: as the other quantities increase, the other one decreases

3 : 84 = 3.5 : x

3(84) = 3.5x

252 = 3.5x                (divide 3.5 both sides)

x = 72

Step-by-step explanation:

The probability that a driver chosen at random from the community will be in the low-risk category for the next year is 0.8

Probability:

In math,  the ratio of the times an event is likely to occur divided by the total possible events is known as probability.

Given,

Here we need to find if 80% of the drivers in the community are in the low-risk category this year, then the probability that a driver chosen at random from the community will be in the low-risk category for the next year.

Here we know that, 80% of the drivers in the community are in the low-risk category this year.

Then as per the definition of probability, the the community will be in the low-risk category for the next year is calculated as,

=> 80/100

=> 0.8

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The measure of angle 1 is given as follows:

m < 1 = 150º.

From the image given at the end of the answer, we have that two Railroad tracks are transversal to the Olive Street.

Considering that Olive Street is transversal to the parallel lines, we have that the angle 2 forms a linear pair with the angle of 30º.

Linear pairs are supplementary angles, meaning that the sum of their measures is of 180º, hence the measure of angle 2 is given as follows:

m < 2 + 30º = 180º

m < 2 = 180º - 30º

m < 2 = 150º.

Now we have that angles 1 and 2 are alternate interior angles, as they are between the two parallel lines, on the opposite side of the transversal.

Alternate interior angles are congruent, meaning that the measure of angle 1 is given as follows:

m < 1 = 150º.

The diagram is given by the image shown at the end of the answer.

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This indicates that the probability is 0.4402% without replacement.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

n = 5

x = 1

p = 5/20 = 0.25

15C4 = 15! / 4! * 11! = 1365

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Hence, This indicates that the probability is 0.4402% without replacement.

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When a store is offering a 30% discount on all jeans. If the regular price of a pair of jeans is $49.99, then the sale price of the jeans after discount will be $34.99 per pair.

The computation of the discounted price or the actual sales price of the jeans after applying the given discount can be calculated using the generalized formula, and putting the values of the provided information, as below,

Sale Price = Regular Price – Discount Rate

Sale Price = 49.99 – 30%

Sale Price = 49.99–14.97

Sale Price = $34.99

Therefore, the actual sales price of the pair of jeans will be $34.99.

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The possible variable terms for the given expression are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression is (2a+4b)⁸.

The expansion is

(2a+4b)⁸=256a⁸+4096a⁷b+2867a⁶b²+114688a⁵b³+286720a⁴b⁴+458752a³b⁵+458752a²b⁶+262144ab⁷+65536b⁸

Hence, in the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

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Answer:

Step-by-step explanation:

The answer as I believe is H.

I just used the rise/run method, so you’ll go six up and 5 to the left ( the answer is negative because you’re moving to the left).

Hope this helps

If the bookstore sells 15 pencils, the ratios of pens to pencil written as fraction is 2 / 3.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

Therefore, proportional relationship can be represented as follows:

y ∝x

y = kx

where

Therefore,

4 = 6k

k = 4 / 6

k = 2 / 3

Therefore, let's find the number of pen sold when the bookstore sells 15 pencils.

y = 15 × 2 / 3

y = 30 / 3

y = 10

Therefore, if the bookstore sell 15 pencils the ratio of pen to pencil is 10 / 15 = 2 / 3

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The statement "considered multiple regression which is a sample at 36 observations for a given eggs and fitted why the 95% approximate prediction interval for individual why is wider than the corresponding approximate 95% confidence interval for the conditional mean" is false.

Here we have given the statement and we need to identify whether this one is true or not.

As we all know that then Confidence interval is narrower than the prediction interval because Prediction intervals must account for both the uncertainty in estimating the population mean, plus the random variation of the individual values.

Therefore the prediction interval is always wider than a confidence interval.

And also here the prediction interval will not converge to a single value as the sample size increases.

Therefore, the statement is incorrect.

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Answer:

240 = 150 + 120 + x

240 = 270 + x

x = 30

150 - 30 = 120 learned math only

120 - 30 = 90 english

30 = both subject

Step-by-step explanation:

The number of students who learn math only is 120 and those who learn both subjects are 30.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that in a class of 240 students 150 learn math and 120 learn English.

The number of students learning both subjects will be,

240 = 150 + 120 + x

240 = 270 + x

x = 30

The number of students learning math only,

150 - 30 = 120 learned math only

120 - 30 = 90 English

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The number line of the set C ={x : x ≤ -3} is attached

From the question, we have the following parameters that can be used in our computation:

Set C ={x:x<=-3}

Rewrite properly

So, we have

Set C ={x : x ≤ -3}

Remove the curly braces from the set notation

So, we have the following representation

x ≤ -3

There are no multiples and factors to divide or multiply

Also, there are no terms to subtract or add

This means that the inequality to represent on the number line is x ≤ -3

See attachment for the number line

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Answer:

I'm sorry I don't know

Step-by-step explanation:

........

The expression representing the perimeter of the triangle is (5x+3)

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given that, The length of the bottom of the triangle is x. Another side is 1 more than three times the length of the bottom of the triangle. The last side is 2 more than the bottom of the triangle.

Let the bottom length of the triangle be x, then, according to question, other two sides will be, (3x+1) and (x+2)

Perimeter = sum of all the side

Perimeter = x+x+2+3x+1

= 5x+3

Hence, The expression for the perimeter of the triangle is (5x+3)

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There are 20 numbers in the set.

Given,

Set of numbers is 120

one number is increased by 300

and, mean increases to 135.

To find the how many numbers are in the set?

Now, According to the question:

Let the number of numbers be 'n'

Then, (sum of numbers)/n = 120

or, old sum = 120n

if one number is increased by 300, the new sum = (old sum + 300)

Then, (new sum)/ n= 135

or new sum = 135n = old sum + 300 = 120n + 300

The equation will  be:

135n = 120n + 300

15n = 300

n = 20

Hence, There are 20 numbers in the set.

In the question:

The mean of a set of numbers is 120. if one number is increased by 300, the mean increases to 135.

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Answer:

A

Step-by-step explanation:

y=-2 when x=-4 y=-4 when x=-8

what's given: 4. what's given:2

-4k=-2. -8k=-4

-4/4. -2/4. -8/8. -4/8

k=0.5. k =0.5

0.5(2) =1. 0.5(2)=1

Answer:

Step-by-step explanation:

You want to identify the proportional relations in the given tables and equations, and you want to find and use the constant of variation given that y=35 when x=7.

A proportional relation is one that has an equation of the form ...

  y = kx

One variable is a constant multiple of the other. If the relation cannot be put in this form, it is not a proportional relation.

The value of k in the above equation can be found as ...

  k = y/x . . . . . . . divide both sides by x

This is a constant if the relation is proportional.

  y/x = -8/-4 = -4/-2 ≠ 18/6 . . . . . not a proportional relation

  y/x = -4/-5 ≠ 10/2 . . . . . not a proportional relation

  y/x = -12/-3 = 24/6 = 32/8 = 4 . . . . . a proportional relation

You are looking for equations of the form y = kx. The only ones having that form are ...

The others represent inverse proportions and a linear (not proportional) relation.

As we saw above, the constant of variation is ...

  k = y/x = 35/7

  k = 5

Then the value of x can be found from ...

  49 = 5x

  49/5 = x = 9.8

Translation is one of the four types of mathematical transformations that may be applied to a function graph.

(x, y) = (x + a, y + b)

In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered. There is no change in the form because it is just being moved from one location to another.

When the shape is moved towards the left by k units, then replace x with x - k.

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

When the shape is moved down by k units, then replace y with y - k.

Example: What are the new coordinates when the translation (x, y) → (x - 2, y + 3) is applied to the point (2, 5).

Solution:

The coordinates of old point (preimage) are (x, y) = (2, 5). Now, applying the given translation to this point,

x - 2 = 2 - 2 = 0

y + 3 = 5 + 3 = 8

Thus, the coordinates of the translated point (image) are (0, 8).

This was the example of translation.

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The answer of the given scientific multiplication is,  8.84 x 10^-1.

What is scientific multiplication?

Multiply the decimal numbers to multiply the numbers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.

Given:

(6.8 x 10^2) x (1.3 x 10^-3)

We have to solve this using scientific multiplication.

First to multiply the decimals,

6.8 x 1.3 = 8.84

Now to solve

10^2 x 10^-3 = 10^(2-3) = 10^-1

⇒  (6.8 x 10^2) x (1.3 x 10^-3) = 8.84 x 10^-1

Hence, the answer of the given scientific multiplication is,  8.84 x 10^-1.

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When two numbers have the same sign, the result will be the number with the larger absolute value. 25 + (-15) - (-10) = 30

To calculate 25 + (-15) - (-10), we must first look at the order of operations. We start with the parentheses, so we need to calculate -15 and -10 first. When two numbers have the same sign, the result will be the number with the larger absolute value. In this case, -15 and -10 both have negative signs, so the result will be -15.

Next, we move on to the addition and subtraction signs. We add 25 and -15 to get 10. Then we subtract -10 from 10, and the result is 30. So, 25 + (-15) - (-10) = 30.

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The ratios of calories Robyn burned on Thursday to the number of calories she burned for the week is 3 : 20.  

Ratio, in math, is a term that is used to compare two or more numbers. In other words, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

Therefore, the ratios of calories Robyn burned on Thursday to the number of calories she burned for the week can be calculated as follows:

Let's represent it in fractions,

calories burn on Thursday / calories burn for the week

calories burn on Thursday = 360

calories burn for the week = 488 + 551 + 610 + 360 + 391 = 2400

Hence,

360 / 2400 = 36 / 240 = 12 / 80 = 3 / 20

Therefore, the ratio is 3:20

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Answer:

There is no solution

Step-by-step explanation:

x - 4y = 15

3x -12y = 12

Times the first equation by -3

-3x +12y = -45

3x - 12y = 12

0 = -33

This is untrue; 0 is not equal to -33

So, there is no solution for this system.

If you can please give me a Brainliest, thank you, and have a good day!

g(x) = x^2 - 3

f(x) = x^3+7x^2-x

Start with the g(x) function. Replace every x with f(x)

g(x) = x^2 - 3

g(f(x)) = ( f(x) )^2 - 3

Then replace the f(x) on the right side with x^3+7x^2-x

g(f(x)) = (x^3+7x^2-x)^2 - 3

The highest term inside the parenthesis is x^3. Squaring this leads to (x^3)^2 = x^(3*2) = x^6

So the highest exponent found in g(f(x)) is 6, meaning the degree of is 6

- [(2x - cos x) / (2y - cos y)] of the following expressions represents sin x + sin y = x² + y², using the concept of differentiation.

One method is to determine a function's derivative by differentiation. Finding the instantaneous rate of change of a function depending on one of its variables is a technique known as differentiation in mathematics.

Differentiation refers to the process of calculating a function's derivative. The derivative, when applied to two variables x and y, is the rate at which x changes in relation to y. To calculate the immediate rate of change of quantities, differentiation is used.

sin x + sin y = x² + y²

Differentiating w.r.t x

d/dx (sin x + sin y) = d/dx (x² + y²)

or, cos x + cos y dy/dx = 2x + 2y dy/dx

or, cos y dy/dx - 2y dy/dx = 2x - cos x

or, dy/dx (cos y - 2y) = 2x - cos x

or, dy/dx = (2x - cos x) / (cos y - 2y)

or, dy/dx = - [(2x - cos x) / (2y - cos y)]

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After 7 years  the laptop computer will be worth $200 or less.

Given:

A laptop computer is purchased for $1400 .

Each year, its value is 75%  of its value the year before.

After how many years will the laptop computer be worth $200  or less = ?

1400(0.75)t≤ 200

0.75t  ≤ 1/7

ln(0.75t) ≤ ln(1/7)

tln(0.75) ≤ ln(1/7)

t ≥ ln(1/7)/ln(0.75)

t ≥ 6.76

The natural log of a number between 0 and 1 is negative, and dividing by a negative switches the sign.

So, after 7 years, the laptop computer will be worth $200 or less.

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Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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The slope and a point of a line are given then the equation of a line can be found. So the answer is true.

The equation of a line:

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The most popular form in algebra is the "slope-intercept" form. y = mx + b. This in effect uses x as a parameter and writes y as a function of x: y = f(x) = mx+b.

Here we have to get to know if the slope and a point on a line are given then we can find the equation of a line or not.

Let us assume m is the slope of a line and (x1, y1) is the point on a line.

By this, we get the equation:

y- y1 = m( x - x1)

Therefore from the slope and a point on a line, we can find the equation of a line.

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The radius reduced to 57.3% of its normal value.

The expression of Poiseuille's law for flow in a tube is:

Q = Δpπr⁴/8ηl

where:

Q = is the flow rate

P₁ = is the pressure at first end of vain

P₂ = is the pressure at the other end

η = is the viscosity of the concrete

r - radius of pipe

l = is the length

Re arrange the expression for the radius of the pipe,

r = (8Qηl/πΔP)¹/⁴

the flow rate in an artery has been reduced to 10.0%and the difference in blood pressure is increased by 20%.

so,

Q' = 0.100Q and

ΔP' = 1.20ΔP

SUbstitute the above points.

r' = (8( 0.100Qηl/π(1.20ΔP))¹/⁴

= 0.537(8Qηl/πΔP)¹/⁴

Combine the expression of radius before the flow and pressure changes and the expression derived or the new radius,

r' = 0.537r

Hence the radius reduced to 57.3% of its normal value.

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Answer: (-11,0) (Please make sure this answer is correct, as I am not a master...)

Step-by-step explanation:

We can solve this a super simple way.

The midpoint is (-6,-3/2) and the coordinate B is (-1,3)

We notice that we change y by positive 5 and we change our x by negative 3/2, from M to B. So to get to A from M, we change y by -5 and change our x by positive 3/2...

So we have:

(-6-5,-3/2+3/2)

(-11,0)

So the coordinate of A is:

(-11,0) (Please make sure this answer is correct, as I am not a master...)

Answer:

5

Step-by-step explanation:

1.24 × 4 = 5

or it can be 1.24 ÷2 =0.265

The probability that the person selected will be someone whose response is never and who is a woman is 0.0636 = 6.36%.

A probability of an occurrence in the context of a problem is calculated by dividing the desired outcomes in the problem by the entire number of outcomes in the problem.

In the context of this problem, these outcomes are given as follows:

Desired outcomes: people whose response is never and who are women.

Total outcomes: all participants.

Hence, as all participants represent the desired outcomes, the probability that the person selected will be someone whose response is never and who is a woman is the relative frequency of people who are women and who respond never, which is: 0.0636 = 6.36%.

Missing question:

(Refer to the image for the complete question)

One person surveyed will be selected at random:

What is the probability that the person selected will be someone whose response is never and who is a woman?

What is the probability that the person selected will be someone whose response is never 0r who is a woman?

What is the probability that the person selected will be someone whose response is never given and that the person is a woman?

For the people surveyed are the events of being a person whose response is never and being woman independent?

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