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yawa3891 [41]
3 years ago
9

99 students choose to attend one of three after school activities: football, tennis or running.

Mathematics
1 answer:
nordsb [41]3 years ago
3 0

Answer:   \dfrac{49}{99}

<u>Step-by-step explanation:</u>

There are 61 boys --> 38 girls

A) 19 chose football: 5 are girls --> 14 are boys

B) 38 girls: 28 chose running, 5 chose football --> 5 girls chose tennis

C) 31 students chose tennis: 5 are girls --> 26 are boys.

D) 61 boys: 14 chose football, 26 chose tennis --> 21 boys chose running.

\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&14&5&19\\Tennis&26&5&31\\\underline{Running}&\underline{\quad 21\quad}&\underline{\quad 28\quad}&\underline{\quad 29\quad}\\Total&61&38&99\end{array}}

Total running = 21 boys + 28 girls = 49

Total students = 99

\dfrac{\text{Total running}}{\text{Total students}}=\large\boxed{\dfrac{49}{99}}

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Step-by-step explanation:

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3 years ago
The mean number of hours per day spent on the phone, according to a national survey, is four hours, with a standard deviation of
Reika [66]

Answer:

The new mean is 5.

The new standard deviation is also 2.

Step-by-step explanation:

Let the sample space of hours be as follows, S = {x₁, x₂, x₃...xₙ}

The mean of this sample is 4. That is,\bar x=\frac{x_{1}+x_{2}+x_{3}+...+x_{n}}{n}=4

The standard deviation of this sample is 2. That is, s=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}=2.

Now it is stated that each of the sample values was increased by 1 hour.

The new sample is: S = {x₁ + 1, x₂ + 1, x₃ + 1...xₙ + 1}

Compute the mean of this sample as follows:

\bar x_{N}=\frac{x_{1}+1+x_{2}+1+x_{3}+1+...+x_{n}+1}{n}\\=\frac{(x_{1}+x_{2}+x_{3}+...+x_{n})}{n}+\frac{(1+1+1+...n\ times)}{n}\\=\bar x+1\\=4+1\\=5

The new mean is 5.

Compute the standard deviation of this sample as follows:

s_{N}=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=\frac{1}{n-1}\sum ((x_{i}+1)-(\bar x+1))^{2}\\=\frac{1}{n-1}\sum (x_{i}+1-\bar x-1)^{2}\\=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=s

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5 0
4 years ago
Factor completely. a 2 + 28a + 27 (a + 1)(a + 27) (a + 3)(a + 9) (a - 1)(a - 27)
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Answer:

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Step-by-step explanation:

Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial Ax^2+Bx+C multiply A*C then find two numbers which multiply to this number and add to B. When you find those numbers, write them as (x-/+ number)(x-/+number).

a^2+28a+27

A=1, C=27

A*C=27 and add to B=28 which 1 and 27 satisfy

The factors are (a+1)(a+27)


7 0
3 years ago
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Answer:

Step-by-step explanation:

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Step-by-step explanation:

8 0
3 years ago
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