In a physics class, the teacher proposes that the velocity of a car in miles per hour and the stopping distance in feet are represented by inverse functions. Assuming this is true, which graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses?

Answer:

Find every possible factors of 32, and pair them

Step-by-step explanation:

if the same value for width/length cant be repeated, 3 total possible values is possible

1 × 32 = 32

2 × 16 = 32

4 × 8 = 32

if the value of width/length can be repeated, 6 total different values.

1 × 32 = 32

2 × 16 = 32

4 × 8 = 32

32 × 1 = 32

16 × 2= 32

8 × 4= 32

you can easily find all factors using online factor calculator

Answer:

x = -9

Step-by-step explanation:

To solve these types of questions,

a). If both the sides of the equation are different,

    2x + 3 = 3x - 6

   There will be exactly one solution.

b). If the coefficient of variable 'x' is same in both the sides of the equation,

    x - 3 = x - 6

    Solution set will be 'none'.

c). If both the sides of the equation are exactly same then equation will have infinite solutions.

   2x + 3 = x + x + 3

In the given equation,

6x - (5x + 5) = -8 - 2(x + 12)

Further simplify the equation,

(6x - 5x) - 5 = - 8 - 2x - 24

x - 5 = -2x - 32

x + 2x = 5 - 32

3x = -27

x = -9

Answer:

[tex]mean = \frac{9 + 4 + 4 + 1 + 0 + 6 + 4}{7} = \frac{28}{7} = 4[/tex]

[tex]mean \: deviation = \frac{ |9 - 4| + |4 - 4| + |4 - 4| + |1 - 4| + |0 - 4| + |6 - 4| + |4 - 4| }{7} = \frac{5 + 0 + 0 + 3 + 4 + 2 + 0}{7} = \frac{14}{2} = 7[/tex]

Answer:

$1,540.70

Step-by-step explanation:

1675/335 = 5

3.65 * 335 = 1222.75

Cost of $8.65 per plant, or $2,897.75 for every plant.

12.99 - 8.65 = 4.34

Profit of $4.34 per plant, or $1,540.70 total.

Answer:

m<VRU = 80°

m<URW = 15°

Step-by-step explanation:

<SRW and <VRT are vertical opposite angles. Vertical opposite angles are equal. Therefore:

[tex] 2x + 15 = 85 [/tex]

Use this expression to solve for the value of x

[tex] 2x + 15 - 15 = 85 - 15 [/tex]

[tex] 2x = 70 [/tex]

[tex] \frac{2x}{2} = \frac{70}{2} [/tex]

[tex] x = 35 [/tex]

Find m<VRU by plugging in the value of x in the expression for its angle given.

m<VRU = [tex] 2x + 10 [tex]

[tex] 2(35) + 10 = 70 + 10 = 80 [tex]

m<VRU = 80°

FIND m<URW.

m<URW = 180° - (m<VRU + m<SRW) (angles on a straight line is 180°)

m<URW = 180 - (80 + 85)

= 180 - 165

m<URW = 15°

Answer/Step-by-step explanation:

∆ABC is similar to ∆CDE. Therefore, the ratio of their corresponding sides are proportional.

This,

[tex] \frac{DE}{AB} = \frac{DC}{AC} [/tex]

[tex] \frac{4}{3} = \frac{x + 3}{x + 1} [/tex]

Solve for x

[tex] 4(x + 1) = 3(x + 3) [/tex]

[tex] 4x + 4 = 3x + 9 [/tex]

[tex] 4x + 4 - 4 = 3x + 9 - 4[/tex]

[tex] 4x = 3x + 5 [/tex]

[tex] 4x - 3x = 3x + 5 - 3x [/tex]

[tex] x = 5 [/tex]

Use the value of x to find AC and DC

[tex] AC = x + 1 = 5 + 1 = 6 [/tex]

[tex] DC = x + 3 = 5 + 3 = 8 [/tex]

Answer:

A length of a ray cannot be measured therefore it's refferd to as infinite. same

Answer:

Step-by-step explanation:

step one:

let us re-write the expression in mathematical terms for clarity

we have the expression stated  below

[tex]64a^3-27b^3-144b^2+108ab^2[/tex]    

step two:

We are going to collect like terms before factorization we have

    [tex]64a^3+108ab^2-27b^3-144b^2[/tex]

We can now factorize the expression we have  

[tex]4a(16a^2+27b^2)-3b(9b^2+48b)[/tex]

Answer:

I got 2 as an answer

Step-by-step explanation:

[tex]( {3x}^{4} ) - 5 = 43 \\ ( {3x}^{4} ) = 43 + 5 \\ ( {3x}^{4} ) = 48 \\ \frac{ {3x}^{4} }{3} = \frac{48}{3} [/tex]

[tex] {x}^{4} = 16 \\ \sqrt[4]{ {x}^{4} } = \sqrt[4]{16} \\ x = 2[/tex]

Answer:

[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

cross simplify

[tex]\frac{1}{8}[/tex] • [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex]

multiply

[tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{10}[/tex]

Answer:

A. 9

Step-by-step explanation:

54/6 = 9

Answer:

9

Step-by-step explanation:

The scaling factor for this image is 9.

Notice that 54/6 = 9 and 108/12 = 9.

Cheers.

Answer: 7+0.7+0.05

Since 7 is in the ones place it goes in front of the decimal. .7 is in the tenth place because it's behind the decimal. .05 is also behind the decimal so it's in the hundredths place.

Answer:

Options (C), Option (D), Option (E), Option (F).

Step-by-step explanation:

It's given in the question,

ΔTUV ≅ ΔWXY

Therefore, corresponding sides and angles will be congruent.

∠T ≅ ∠W

∠U ≅ ∠X

∠V ≅ ∠Y

TV ≅ WY

UV ≅ XY

TU ≅ WX

By these properties, following options will be the correct options.

Option (C). ∠V ≅ ∠Y

Option (D). TV ≅ WY

Option (E). UV ≅ XY

Option (F). ∠X ≅ ∠U

Answer:

C,D,E, and F are correct

Step-by-step explanation:

In order to solve problems like this, you need to see which angles and segment correspond. Also, you would need to make sure that the order is the same on both sides of the equal side. For example, the first angle on one side of the equal sign will be congruent to the FIRST angle on the other side of the equal side.

Answer:

210

Step-by-step explanation:

10x9x8x7x6x5x4x3x2x1 divided by 6x5x4x3x2x1x4x3x2x1=

(Take out 1 through 6 on both sides)

10x9x8x7 divided by 4x3x2x1=

5040 divided by 24=

210

Dance instructor can chose 4 students out of 10 if order doesn't matter in 210 ways

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.

For example, suppose we have a set of three letters: A, B, and C. We might ask how many ways we can select 2 letters from that set. Each possible selection would be an example of a combination.

Formula of combination:

[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]

Where

nCr is   the selection of objects from a group of objects where order of objects does not matter.

n is the total number of objects

r is the number of selected objects.

According to the question

A dance instructor chose four of his 10 students to be on stage for a performance and order does not matter .

i.e,

if we have to chose and order does not matter that means we have to use combination .

[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]

Total number of students (n)= 10

Number of selected students (r) = 4

[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]

[tex]C_{n} ^{r} = \frac{10!}{4! (6)!}[/tex]

[tex]C_{n} ^{r} = \frac{10*9*8*7}{4*3*2*1 }[/tex]

[tex]C_{n} ^{r} = \frac{5040}{24 }\\[/tex]

[tex]C_{n} ^{r} = 210[/tex]

Hence, Dance instructor can chose 4 students out of 10 in 210 ways

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Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

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

From the question the points are

(9, -3) and (2, 4)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

the answer would be 9.9

Step-by-step explanation

You must use the distance formula which is [tex]\sqrt{(2-9)^2 +(4-(-3))^2}[/tex]

Simplify - [tex]\sqrt{(-7)^2 +(7)^2}[/tex]

simplify again - [tex]\sqrt{49+49}[/tex]

once more simplify - [tex]\sqrt{98}[/tex]

and you can get your answer by [tex]\sqrt{98\\}[/tex]=9.899 or rounded to the nearest 10th 9.9. I hope this helps!

Equation to represent amount of money Jerry has after working x hours is

y = $7x + $20

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Jerry makes $7 per hour

He has $20.

Jerry works for x hours

Amount Jerry made working x hours = $7x

Then, equation for total amount y Jerry has after working x hours

y = $7x + $20

Hence, y = $7x + $20 is equation that represents the total amount of money Jerry has after working x hours.

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Answer:

It should be noted that the p.f of X and Y when they are independent can be obtained by multiplying together their marginal probability function.

Step-by-step explanation:

Two discrete random variables X and Y are said to be statistically independent if and only if , for all possible values ( xi, yi) the joint probability function f(x,y) can be expressed as the product of two marginal functions. That is X and y are independent if

f(x,y) = P(x=xi  and Y =yi)

          =  P(x=xi) P(Y =yi)         for all i and j

            = g(x)h(y)

It should be noted that the p.f of X and Y when they are independent can be obtained by multiplying together their marginal probability function.

The values of marginal probabilities are often written in the margins of the joint table as there are rows and columns totals in the table. The probabilities in each marginal probability function add to 1.

The statement which is true about the slope of the given graphed line is that the slope is positive.

Slope is the proportion of decrease or increase in variable y due to increase and decrease in variable x. The formula of calculating slope is as under:

Slope=[tex](y_{2} -y_{1}) /(x_{2} -x_{1})[/tex]

We have to find the slope of the graphed line and for that we have to first take two points which lie on the line whose slope we have to find.

Take the points (0,4) and (-5,2) and calculating slope we get:

slope=(2-4)/(-5-0)

=-2/-5

=2/5

Hence the statement which is true is that the slope is positive.

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Answer:

c)

The distribution is skewed down the middle,

Therefore it is symmetric.

Answer:

Difference = 3x² + 3x + 1

See Explanation

Step-by-step explanation:

Required: How changes in sides of a cube affects its volume.

Take for instance the side of the cube is x.

The initial volume would be:

Volume = x * x * x

Volume = x³

When then dimension is increased by 1 unit, the new volume would be

Volume = (x + 1) * (x + 1) * (x + 1)

Expand the brackets

New Volume = (x² + 2x + 1)(x + 1)

New Volume = x³ + 3x² + 3x + 1

[Calculate the difference between both volumes]

Difference = New Volume - Initial Volume

Difference = x³ + 3x² + 3x + 1 - x³

[Collect like terms]

Difference = x³ - x³ + 3x² + 3x + 1

Difference = 3x² + 3x + 1

So, there will be a difference of 3x² + 3x + 1 when the dimension is increased from x to x + 1

Take for instance: a dimension of 2 units is increased to 3 units

Initial Volume = 2³ = 8

New Volume = 3³ = 27

Difference = 27 - 8

Difference = 19

Using the derived formula (x = 2)

Difference = 3x² + 3x + 1

Substitute 2 for x

Difference = 3 * 2² + 3 * 2 + 1

Difference = 3 * 4 + 6 + 1

Difference = 12 + 6 + 1

Difference = 19

Answer:

gross income is $400

The net is $329.40

Deductions are $$70.6

Step-by-step explanation:

Based on the gross amount earned and the various deductions, the net income is $329.40

Net income is the amount that will be earned after all the taxes have been subtracted from the paystub amount.

The net income is therefore:

= 400 - 5.80 - 24.80 - 40

= $329.40

In conclusion, the net income is $329.40.

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h= number of hours

m= number of miles

Formula: 4h=12m

(4 hours equals 12 miles)

Divide 4 on each side.

h= 3m

3 miles per hour.

Then, convert miles to feet. And hours to minute.

To do this simultaneously,

Convert miles to feet and hours to minutes.

There should be 3 "fractions" to multiply.

The first should be the original problem:

3miles/1 hour. (3 miles per hour).

The second should be 1 hour/60min. (1 hour per 60 min).

The third should be 5280 ft/1 mile. (5280 feet per mile).

The second and the third fractions are to convert miles to feet and the hours to minutes.

Answer:

2x

Step-by-step explanation:

Factor both terms given to simplest terms:

8x = 2 * 2 * 2 * x

22xy = 2 * 11 * x * y

Note that in each case, there is the factor of 2 & x that is shared by both. These are what is used to find the Greatest Common Factor. Multiply both terms together:

2 * x = 2x

2x is your GCF.

~

First find the greatest common factor of 8 and 22.

To find the greatest common factor of 8,

begin by dividing 8 by all the numbers you can.

8 ÷ 1 = 8

8 ÷ 2 = 4

Notice that I stopped here because if I continued

dividing, I would be dividing 8 by 4 which is 2.

Make sure to stop dividing when you see numbers repeat.

So the factors of 8 are 1, 2, 4, and 8.

Now do the same thing for 22.

22 ÷ 1 = 22

22 ÷ 11 = 2

So the factors of 22 are 1, 2, 11, and 22.

Now look for the largest number shared by the two lists.

In this case, the largest number is 2.

Now let's move to the variables.

To qualify for the Greatest Common Factor,

the variable must appear in every monomial.

Since the y doesn't appear in every monomial, it doesn't qualify.

However, notice that the x does appear in every monomial.

If the variable does appear in every monomial, the Greatest

Common Factor will use the smallest power on that variable.

Since the smallest power for x in both monomials is x, we use x.

So our greatest common factor is 2x.

Answer:

Discount = Original Price x Discount %/100

Discount = 2.88 × 1/100

Discount = 2.88 x 0.01

You save = $0.03

Final Price = Original Price - Discount

Final Price = 2.88 - 0.0288

Final Price = $2.85

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

So we have the equation:

[tex]3(x+1)=9+2x[/tex]

Distribute the left side:

[tex]3x+3=9+2x[/tex]

Subtract 2x from both sides. The right side cancels:

[tex](3x+3)-2x=(9+2x)-2x\\x+3=9[/tex]

Subtract 3 from both sides:

[tex](x+3)-3=(9)-3\\x=6[/tex]

So, x is 6.

Answer:

Step-by-step explanation:

Represent the equation as follows:

[tex]a * b = c[/tex]

Where a,b and c are decimal numbers

To solve further, we make use of trial by error method

Let

[tex]a = 2.52[/tex]

[tex]b = 0.6[/tex]

Such that

[tex]2.5 * 0.6 = c[/tex]

[tex]1.512 = c[/tex]

[tex]c = 1.512[/tex]

This set of digits do not follow the rule in the question

Let

[tex]a = 2.55[/tex]

[tex]b = 1.6[/tex]

[tex]2.55 * 1.6 = c[/tex]

[tex]4.08 = c[/tex]

[tex]c = 4.08[/tex]

The result has only 2 non zeros (4 and 8)

Hence

[tex]2.55 * 1.6 = 4.08[/tex] answers the question.

However, there are other set of numbers that can be used too

One of the equation which illustrates and meets the conditions given is :

First number, x = 1.25

First number, x = 1.25 Second number, y = 0.2

Result = first Number × second number

Result = 1.25 × 0.2

Result = 1.25 × 0.2 Result = 0.25

Evaluating the result : 0.25

Number of digits = 3

Non - zero digits = 2

There are several values of x and y which will satisfy the 3 conditions given.

Therefore, the product of the values 1.25 and 0.2 gives the required output.

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Answer:

Total Earnings = 18,160

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

2) principal1 + principal2 = 17,000

We'll multiply equation 2) by -1.06

2) -1.06*principal1 -1.06*principal2 = -18,020 then adding equation 1)

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

.01*principal1 = 140

principal 1 = 14,000

and therefore principal 2 = 3,000

Step-by-step explanation:

Answer:

In a standard normal distribution;

The mean of the population is going to be zero and the population standard deviation is automatically one.

In a nonstandard normal distribution;

The mean of the population is not equal to zero and the population standard deviation is not equal to one.

Step-by-step explanation:

When looking at a  normal distribution: There are three major keys we need  to understand:

The major difference between a standard normal distribution and a nonstandard normal distribution is that:

In a standard normal distribution, there are two additional things attached.

The mean of the population is going to be zero and the population standard deviation is automatically one.

In a nonstandard normal distribution;

The mean of the population is not equal to zero and the population standard deviation is not equal to one.