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vladimir1956 [14]
3 years ago
9

74 students choose to attend one of three after school activities: football, tennis or running. There are 49 boys. 16 students c

hoose football, of which 6 are girls. 28 students choose tennis. 8 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
7 0

Answer:

The probability that student chose running is \frac{30}{74}.

Step-by-step explanation:

Consider the provided information.

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

16 students choose football,  28 students choose tennis.

The students choose running = 74 - 16 - 28

The students choose running = 30

It means out of 74 students 30 choose running.

\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}

\text{Probability of Running}=\frac{30}{74}

Hence, the probability that student chose running is \frac{30}{74}.

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Savannah is 9 years older thanDevante. The sum of their ages is 53. How old are Savannah and Devante?
pickupchik [31]

Answer:

Devante is 23 and Savannah is 32.

Step-by-step explanation:

We can set up a system of equations.

s - savannah's age

d - devante's age

s = d + 9

s + d = 53

Now we can substitute (d + 9) for s in the second equation.

(d + 9) + d = 53

2d + 9 = 53

2d = 46

<u>d = 23</u>

To find Savannah's age, we just add 9 to Devante's age. (plugging in 23 for d)

23 + 9 = 32

<u>s = 32</u>

6 0
3 years ago
What is the percent of decrease from 200 to 110? A. 45% B. 55% C. 82% D. 90%
strojnjashka [21]
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8 0
4 years ago
Divide f(x) by d(x), and write a summary statement in the form indicated.
Mandarinka [93]

Answer:

The correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

Step-by-step explanation:

Consider the provided function.

f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5 and d(x) = x^2+1

We need to divide f(x) by d(x)

As we know: Dividend = Divisor × Quotient + Remainder

In the above function f(x) is dividend and divisor is d(x)

Divide the leading term of the dividend by the leading term of the divisor:\frac{x^4}{x^2}=x^2

Write the calculated result in upper part of the table.

Multiply it by the divisor: x^2(x^2+1)=x^4+x^2

Now Subtract the dividend from the obtained result:

(x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5

Again divide the leading term of the obtained remainder by the leading term of the divisor: \frac{4x^3}{x^2}=4x

Write the calculated result in upper part of the table.

Multiply it by the divisor: 4x(x^2+1)=4x^3+4x

Subtract the dividend:

(4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5

Divide the leading term of the obtained remainder by the leading term of the divisor: \frac{5x^2}{x^2}=5

Multiply it by the divisor: 5(x^2+1)=5x^2+5

Subtract the dividend:

(5x^2+5)-(5x^2+5)=0

Therefore,

Dividend = x^4 + 4x^3 + 6x^2 + 4x + 5

Divisor = x^2+1

Quotient = x^2+4x+5

Remainder = 0

Dividend = Divisor × Quotient + Remainder

f(x) = (x^2+1)(x^2+4x+5)

Hence, the correct option is B)  f(x) =(x^2+1)(x^2+4x+5)

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