One lap around the school track is 5/8 of a mile Carin ran 3 1/2 laps how far did she run
1 answer:
Given length of a lap = 5/8 mile.
Number of laps Carin ran = 3 1/2 laps.
3 1/2 can be read as 3 and a half. In improper fractions, it can be written as
(3*2+1)/2 = 7/2 laps.
In order to find the total distance covered in 3 1/2 or 7/2 laps, we need to multiply length of a lap by total number of laps ran.
Therefore, total distance covered = 7/2 × 5/8.
=
Multiplying across, we get
=
=
Let us convert 35/16 into mixed fractions.
On dividing 35 by 16, we get 2 quotient and 3 remainder.
So, the mixed fraction would be 2 3/16.
Therefore, she ran 2 3/16 miles in 3 1/2 laps.
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Question:
Below are 36 sorted ages of an acting award winner. find the percentile corresponding to age 38 using the method presented in the textbook. 18 19 20 20 21 23 25 31 33 34 35 37 38 47 50 51 55 55 58 59 62 62 64 66 69 70 70 70 71 71 72 74 74 75 77 80 percentile of value 38 = ______ (round to the nearest integer as needed.)
Answer:
33 percentile
Step-by-step explanation:
Given the ages:
18, 19, 20, 20, 21, 23, 25, 31, 33, 34, 35, 37, 38, 47, 50, 51, 55, 55, 58, 59, 62, 62, 64, 66, 69, 70, 70, 70, 71, 71, 72, 74, 74, 75, 77, 80.
We are told to find the percentile corresponding to age 38.
To find the percentile corresponding to age 38 simply means to find the percentage of ages that are less than 38.
From the given values, the number of ages less than 38 are 12. Therefore, the percentile corresponding to age 38 would be:
(Ages less than 38/ total number of ages) * 100
33.333 ≈ 33
The percentile corresponding to age 38 = 33 percentile
Part (a)
Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer
For example, if x = 7, then x+2 = 9 is right after.
<h3>Answer: x+2</h3>========================================================
Part (b)
The consecutive odd integers we're dealing with are x and x+2.
Their squares are x^2 and (x+2)^2, and these squares add to 394.
<h3>Answer: x^2 + (x+2)^2 = 394</h3>========================================================
Part (c)
We'll solve the equation we just set up.
x^2 + (x+2)^2 = 394
x^2 + x^2 + 4x + 4 = 394
2x^2+4x+4-394 = 0
2x^2+4x-390 = 0
2(x^2 + 2x - 195) = 0
x^2 + 2x - 195 = 0
You could factor this, but the quadratic formula avoids trial and error.
Use a = 1, b = 2, c = -195 in the quadratic formula.
If x = 13, then x+2 = 13+2 = 15
Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394
Or we could have x = -15 which leads to x+2 = -15+2 = -13
So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394
We get the same thing either way.
<h3>Answer: Either 13, 15 or -15, -13</h3>The given angles 3 and 4 shares a common arm, therefore the angles are known as Adjacant Angles