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Sav [38]
2 years ago
6

Jack and Jim went biking. Jack biked for 5 1/3 hours with average speed 12 1/2 miles per hour. Jim traveled exactly 1 1/5 as far

as Jack did. How long was Jim’s trip?

Mathematics
2 answers:
GuDViN [60]2 years ago
5 0
The relation between distance, velocity and time can be expressed using the following equation:
Distance = velocity * time

We are given that:
Jack biked 5 1/3 hours (time = 5 1/3 hours) with average speed of 12 1/2 miles per hour (velocity = 12 1/2 miles/hour)
Substitute in the above equation to get the distance traveled by Jack as follows:
Distance traveled by Jack = 12 1/2 * 5 1/3 = 66.6667 miles

Now, we know that:
Jim traveled 1 1/5 as far as Jack, this means that:
Distance traveled by Jim = 66.6667 * 1 1/5 = 80 miles
JulijaS [17]2 years ago
5 0
I don't know if you are allowed to use a calculator for these problems, but I did. I am able to multiply the mixed fractions without a calculator if you need help with that please comment below.  Please let me know if you are still confused on how to get the answer! Hope this helped!

My Final Answer: Jim's trip was 146 2/3 miles long.

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Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?
Trava [24]

f (n + 1) = f(n) – 5  is the recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1

<h3><u>Solution:</u></h3>

Given that,

f(1) = 6 and n ≥ 1

Given sequence is 6, 1, -4, -9, -14

<em><u>Let us first analyse the logic used in this sequence</u></em>

6 - 5 = 1

1 - 5 = -4

-4 - 5 = -9

-9 - 5 = -14

Thus the next terms in sequence are obtained by subtracting 5 from previous term

Thus a recursive formula can be formed as:

f (n + 1) = f(n) – 5

Where "n" is the nth term

Let us check our recursive formula:

f(1+ 1) = f(1) - 5

f(2) = f(1) - 5

f(2) = 6 - 5 = 1

Thus we have got f(2) = 1 which is correct as per given sequence

4 0
2 years ago
Read 2 more answers
The side length, s, of a cube is 4x2 3. if v = s3, what is the volume of the cube?
Veseljchak [2.6K]

Answer:

The Volume of the cube is

(64x^{6}+144x^{4}+108x^{2}+27)

Step-by-step explanation:

we know that

The volume of a cube is equal to

V=s^{3}

where

s is the length side of the cube

In this problem we have

s=(4x^{2} +3)

Substitute

V=(4x^{2} +3)^{3}

Remember that

(4x^{2} +3)^{3}=(4x^{2} +3)^{2}(4x^{2} +3)

(4x^{2} +3)^{2}(4x^{2} +3)=[16x^{4}+24x^{2} +9]( 4x^{2} +3)

=64x^{6}+48x^{4}+96x^{4}+72x^{2}+36x^{2}+27

Combine like terms

=64x^{6}+144x^{4}+108x^{2}+27


4 0
2 years ago
Read 2 more answers
A circular rug has a radius of 3 ft. What is the circumference of the rug? Use 3.14 for mc014-1.jpg.
Pavel [41]
Hello!

We must use a certain formula to find the circumference of anything circular.

The formula is:

C = 2 × pi × r

We know that pi = 3.14 approximately and the radius is 3 feet.

Substitute:

C = 2 × 3.14 × 3

C = 6.28 × 3

C = 18.84 ft

ANSWER:

The circumference of the circular rug is 18.84 ft. (Last option)
3 0
2 years ago
Read 2 more answers
Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.
bonufazy [111]

Answer:

The ratio of Tan B is

\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}

OR

\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}

Step-by-step explanation:

In Right Angle Triangle ABC

angle C = 90°

AB = Ramp = 17 feet

BC =Horizontal distance = 15 feet

AC = Height from floor = 8 feet

To Find:

Ratio of Tan B = ?

Solution:

In Right Angle Triangle ABC By Tangent Identity we have

\tan B= \dfrac{\textrm{side opposite to angle B}}{\textrm{side adjacent to angle B}}

Substituting the given values we get

\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}

OR

\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}

5 0
2 years ago
To make a profit, a clothing store sells jeans at 115% the amount they paid for them. How much did the store pay for the jeans s
Svetllana [295]

Answer:

The store paid 6.67 times the profit made on the jeans

Step-by-step explanation:

Let the amount the clothing store pay for Jean be X

Let the amount the clothing store sells Jean be Y = X ×1.15

The profit (P) made is the difference between amount the clothing store sells Jean and the amount paid for Jean = Y - X = 1.15X - X

Profit (P)  = 0.15X

X =  P/0.15 = 6.67P

Therefore, the store paid 6.67 times the profit made on the jeans

8 0
1 year ago
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