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kondor19780726 [428]
3 years ago
12

Lana finished the race in 13.2 seconds . If 84 other girls ran in the event, approximately how many runners did she beat?

Mathematics
1 answer:
BabaBlast [244]3 years ago
6 0

Complete question :

The 100m dah times in the girl's track meet were normally distributed with a mean of 13 seconds and a standard deviation of 0.3 seconds.

Lana finished the race in 13.2 seconds . If 84 other girls ran in the event, approximately how many runners did she beat?

Answer:

21 runners

Step-by-step explanation:

Mean, μ = 13 seconds

Standard deviation, σ = 0.3

Lana's race time = 13.2

We find the proportion of runners who had race time above 13.2 ;

Proportion of who had race tune above 13.2

P(x > 13.2)

Obtain the Zscore

Zscore = (x - μ) / σ

Z = (13.2 - 13) / 0.3

Zscore = 0.2 / 0.3 = 0.6667

P(Z > 0.6667) = 0.25239 (Z probability calculator)

This is about 0.25239 * 100 = 25.24% = 25% (nearest percent)

Hence, Number of runners Lana beat = 25% of total runners ;

0.25 * 84 = 21

Hence, Lana beat about 21 runners

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Answer:

1. Steve's age is 18 and Anne's age is 8.

2. Max's age is 17 and Bert's age is 11.

3. Sury's age is 19 and Billy's age is 9.

4. The man's age is 30 and his son's age is 10.

Step-by-step explanation:

1. Let us assume that:

S = Steve's age now

A = Anne's age now

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S + 4 = (A + 4)2 - 2

S + 4 = 2A + 8 - 2

S + 4 = 2A + 6 .................. (1)

Three years ago, we have:

S - 3 = (A - 3)3

S - 3 = 3A - 9 ................................ (2)

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S = 3A - 9 + 3

S = 3A – 6 …………. (3)

Substitute S from equation (3) into equation (1) and solve for A, we have:

3A – 6 + 4 = 2A + 6

3A – 2A = 6 + 6 – 4

A = 8

Substitute A = 8 into equation (3), we have:

S = (3 * 8) – 6

S = 24 – 6

S = 18

Therefore, Steve's age is 18 while Anne's age is 8.

2. Let us assume that:

M = Max's age now

B = Bert's age now

Therefore, five years ago, we have:

M - 5 = (B - 5)2

M - 5 = 2B - 10 .......................... (4)

A year from now, we have:

(M + 1) + (B + 1) = 30

M + 1 + B + 1 = 30

M + B + 2 = 30 .......................... (5)

From equation (5), we have:

M = 30 – 2 – B

M = 28 – B …………………… (6)

Substitute M from equation (6) into equation (4) and solve for B, we have:

28 – B – 5 = 2B – 10

28 – 5 + 10 = 2B + B

33 = 3B

B = 33 / 3

B = 11

Substituting B = 11 into equation (6), we have:

M = 28 – 11

M = 17

Therefore, Max's age is 17 while Bert's age is 11.

3. Let us assume that:

S = Sury's age now

B = Billy's age now

Therefore, now, we have:

S = B + 10 ................................ (7)

Next year, we have:

S + 1 = (B + 1)2

S + 1 = 2B + 2 .......................... (8)

Substituting S from equation (7) into equation (8) and solve for B, we have:

B + 10 + 1 = 2B + 2

10 + 1 – 2 = 2B – B

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Substituting B = 9 into equation (7), we have:

S = 9 + 10

S = 19

Therefore, Sury's age is 19 while Billy's age is 9.

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S = His son's age now

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M = 3S ................................... (9)

Five years ago, we have:

M - 5 = (S - 5)5

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-2S = - 20

S = -20 / -2

S = 10

Substituting S = 10 into equation (9), we have:

M = 3 * 10

M = 30

Therefore, the man's age is 30 and his son's age is 10.

5 0
3 years ago
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