Natalie can bike 10 kilometers per hour faster than Aaron. By the time
Natalie travels 60 kilometers, Aaron has gone 40 kilometers. Find the speed
of Natalie and Aaron.

36 minutes

Going through the question in bits:

i. Two people together can do a certain job in 20 minutes.

This implies that the time taken to finish the job is 20 minutes.

This also means that in 1 minute, they will do [tex]\frac{1}{20}[/tex] of the job i.e the rate at which the job is done by the two of them is [tex]\frac{1}{20}[/tex]

ii. If one of them can do the job in 45 minutes.

This implies that the time taken by one of them to finish the job is 45 minutes.

This also means that in 1 minute, he will do [tex]\frac{1}{45}[/tex]  of the job. i.e the rate at which the job is done by one of them is [tex]\frac{1}{45}[/tex]

iii. let the other person do the job in x minutes.

This implies that the time take by the other person to finish the job is x minutes.

This also means that in 1 minute, he will do [tex]\frac{1}{x}[/tex] of the job. i.e the rate at which the job is done by the other person is [tex]\frac{1}{x}[/tex]

Now,

The rate by which the job will be done by the two of them combined is the sum of the individual rates.

i.e

[tex]\frac{1}{20}[/tex] = [tex]\frac{1}{45}[/tex] + [tex]\frac{1}{x}[/tex]

Multiply through by 90x and solve

(90x * [tex]\frac{1}{20}[/tex]) = (90x *  [tex]\frac{1}{45}[/tex]) + (90x *  [tex]\frac{1}{x}[/tex])

4.5x  = 2x + 90

4.5x - 2x = 90

2.5x = 90

x = [tex]\frac{90}{2.5}[/tex]

x = 36

Therefore it will take the other person 36 minutes to finish the job.

Answer:

b

Step-by-step explanation:

expense is usually done everywhere.

Answer:

A

Step-by-step explanation:

Cash

Answer:

There are 8 legs for every 4 ears.

There are 2 legs for every 1 ear.

Step-by-step explanation:

The pig and the mouse have a total of 4 ears.

We can count to see that there are 8 legs for every 4 ears.

We want to find a ratio of legs to ears that is equivalent to 8:4

Answer:

Hello! answer: 105

Step-by-step explanation:

When doing these for squares you have to do base × height and for triangles you do base × height ÷ 2 So Lets do the triangles sense there more complex so we can get them out of the way. The base for the triangles our 5 and the height is 8 so we will do 5 × 8 = 40 now we will just divide that by 2 so 40 ÷ 2 = 20 now sense we have four identical triangles we will just multiply 20 by 4 so 20 × 4 = 80 now for the 1 in the middle its nice and simple just 5 × 5 so 5 × 5 = 25 now we just add 80 + 25 and 80 + 25 = 105 So 105 is the area! Hope that helps!

Answer:

The mode is 75

Step-by-step explanation: It is the one that appears most often

Answer:

Step-by-step explanation:

taylor is building doghouses to sell. each doghouse requires 3 full sheets of plywood which taylor cuts into new shapes. the plywood is shipped in bundles of 14 full sheets. how many doghouses can taylor make from 12 bundles of plywood?

Answer:

3 more cents per mile

Step-by-step explanation:

Answer:9

Step-by-step explanation:

You have to add it together

Answer:

Yes

Step-by-step explanation:

-1 < 6 + 2  True

-1 > 3 - 2(6)  

-1 > 3 - 12

-1 > -9   True

Answer:

(3, -3)

Step-by-step explanation:

To solve for a system of equations, use substitution.

First, solve for one variable in an equation.

2x - 3y = 15

Add 3y to both sides.

2x = 3y + 15

Divide both sides by 2 to get x by itself.

x = 1.5y + 7.5

Put this in the other equation.

5x + 2y = 9

Substitute the variable.

5(1.5y + 7.5) + 2y = 9

Distribute the 5 inside the 1.5y + 7.5.

7.5y + 37.5 + 2y = 9

Combine like terms.

9.5y + 37.5 = 9

Subtract 37.5 from both sides.

9.5y = -28.5

Divide both sides by 9.5.

y = -3.

Now take this value and put it in the other equation to get your x.

2x - 3y = 15

Substitute variable.

2x - 3(-3) = 15

Multiply.

2x + 9 = 15

Subtract 9 from both sides.

2x = 6

Divide both sides by 2.

x = 3.

Your pair is (3, -3).

Answer:

216in

Step-by-step explanation:

6 + 8 + 10 = 24

24 * 9 = 216

Answer:

[tex]Pr = \frac{9}{49}[/tex]

Step-by-step explanation:

Given

[tex]d = 28[/tex] --- big circle

[tex]A_2 = 36 \pi[/tex] --- area of small circle

Required

Probability that a point selected lands on the small circle

Calculate the area of the big circle using;

[tex]A_1 = \pi r^2[/tex]

Where

[tex]r = d/2[/tex]

So, we have:

[tex]r = 28/2 = 14[/tex]

This gives:

[tex]A_1 = \pi * 14^2[/tex]

[tex]A_1 = \pi * 196[/tex]

[tex]A_1 = 196\pi[/tex]

The probability that a point selected lands on the small circle is calculated by dividing the area of the small cicle by the big circle

This gives:

[tex]Pr = \frac{36\pi}{196\pi}[/tex]

[tex]Pr = \frac{36}{196}[/tex]

Simplify

[tex]Pr = \frac{9}{49}[/tex]

Answer:

15%

Step-by-step explanation:

You kind of have two ways to do this:

Way 1:

Find how many 60 cents fit into $4. To do that, divide $4 by $0.60 or 400 by 60. You get 6.66666667.

You can divide 100 by 6.66666667, and get 15%,

Way 2:

Knowing that 400 cents is 100%, you can divide 60 by the same number that you divide 400 by to get to 100. To get from 400 to 100, you divide by 4, so divide 60 by 4 and get the same answer, 15%

Hope that helps :)

Answer:

The equation of a line in point-slope form is.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣aay−y1=m(x−x1)aa∣∣−−−−−−−−−−−−−−−−−−−−−−

where m represents the slope and (x1,y1) a point on the line.

To calculate the slope use the gradient formula

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣∣aam=y2−y1x2−x1aa∣∣∣−−−−−−−−−−−−−−−−−

where (x1,y1) and (x2,y2) are 2 coordinate points.

here the 2 points are (-3 ,4) and (0 ,3)

let (x1,y1)=(−3,4) and (x2,y2)=(0,3)

⇒m=3−40+3

Step-by-step explanation:

this is guid to answer that hope it help to you mahar

Answer:

D.

Step-by-step explanation:

Based on the attached picture we can say that function representing these values would be exponential because the Y values for successive Integer values of X have a common ratio of 16. This can be proven by multiplying each one of the y values by 16, which would give us the next y value in the successive set. For example,

2.5 * 16 = 40

40 * 16 = 640

640 * 16 = 10,240

Meaning that the values have a common ratio of 16, and are increasing exponentially.

Answer:

[tex]B' = (-2,-3)[/tex]

Step-by-step explanation:

Given

[tex]A = (1,-4)[/tex]

[tex]B = (4,-6)[/tex]

[tex]C = (2,-1)[/tex]

reflection across y

[tex]d = \frac{1}{2}[/tex]

Required

New coordinate of B

When reflected across the y-axis.

The rule is:

[tex](x,y) \to (-x,y)[/tex]

So:

[tex](4,-6) \to (-4,-6)[/tex]

Next is a dilation by 1/2

To do this, we multiply the new point by 1/2

So:

[tex]B' = (-4,-6) * \frac{1}{2}[/tex]

[tex]B' = (-4* \frac{1}{2},-6* \frac{1}{2})[/tex]

[tex]B' = (-2,-3)[/tex]

Answer:

e) 20

Step-by-step explanation:

Segment lengths:

|(2, 7) -> (8, 7)| = |(8-2, 7-7)| = |(6, 0)| = 6

|(8, 7) -? (8, 11)| = |(8-8, 11-7)| = |(0, 4)| = 4

because we know it's a rectangle, we can infer that the other two sides also have lengths 4 and 6, so the perimeter is 4+4+6+6=20

Answer:

6.2

Step-by-step explanation:

15+16=31

31/5=6.2

Step-by-step explanation:

[tex]15 + 16 \div 5 \\ calculate \: the \: sum \: of \: 15 \: and \: 16 \\ 31 \div 5 = 6 \frac{1}{5} \\ or \: 6.2[/tex]

Answer:

3 and -(-2)

Step-by-step explanation:

Answer:

2.85125 is the answer.

Step-by-step explanation:

according to the calculator

Answer:

2.75124851367

Step-by-step explanation:

8/8.41=951248513674+1.8=2.75124851367 so its 2.75124851367

Answer: h _<_ 46

there’s the line underneath the sign

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

Answer:

1/8 and 2/1 or 1:8 and 2:1

Step-by-step explanation:

Answer:pi

Step-by-step explanation:

pi

Answer:that eqauls pie

Step-by-step explanation:

Answer:

EASSYYY

Step-by-step explanation:

1364

The series using sigma notation is [tex]^5\sum_{n=1}=4(4)^{n-1}[/tex]. Therefore, option A is the correct answer.

The general formula for finding the sum of an infinite geometric series is S=a/r-1, where s is the sum, a1 is the first term of the series, and r is the common ratio.

Given that, sum = 4 + 16 + 64 + 256 + 1024

Using sigma notation, this can be expressed as:

[tex]^5\sum_{n=1}=4(4)^{n-1}[/tex]

Therefore, option A is the correct answer.

Learn more about the sum of the infinite series here:

brainly.com/question/11752555.

#SPJ2

Answer:

top left

Step-by-step explanation:

a function is if there is only one number that isnt the same as the other x