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Sonbull [250]
4 years ago
10

The following are the ages (years) of 5 people in a room: 23, 13, 17, 12, 15 A person enters the room. The mean age of the 6 peo

ple is now 22. What is the age of the person who entered the room?
Mathematics
1 answer:
Korolek [52]4 years ago
4 0

Answer: 52 years

Step-by-step explanation:

The formula for calculating mean = sum of each data / total number

Let the age of the sixth person be x , then

mean = 23 + 13 + 17 + 12 + 15 + x / 6

That is :

22 = 23 + 13 + 17 + 12 + 15 + x / 6

22 = \frac{80+x}{6}

80+ x = 22 x 6

80 + x = 132

x = 132 - 80

x = 52

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Step-by-step explanation:dom

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3 years ago
In the figure, a line was constructed through point R perpendicular to line L. If EF = 20, then what is the length of ES?
valkas [14]
ES is half of EF since a chord is bisected by the radius. ES = 10
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4 years ago
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A triangle has sides with lengths of 8 inches, 15 inches, and 17 inches. Is it a right triangle?
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Yes

Step-by-step explanation:

A square plus b square equal c square

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1.3 lesson help please
Airida [17]

Answer:

1. 125

2. 25

3. 40

4. 39

First question:

(15-10)^2 + (15-5)^2

parentheses first to get 5^2 + (15-5)^2

exponents next to get 25 + (15-5)^2

parentheses again 25 + 10^2

exponents again 25 + 100 = 125

Second question:

simplify the exponents (3 *3) + (4 * 4) + (2 * 2) to get 9 + 16 + 4 = 29

Third question:

simplify in the parentheses 6 1/7 - 1/7 = 6

divide 60 by 6 to get 10

multiply 10 by 4 to get 40!

Fourth question:

simplify the fractions to get 1/3 + 8/3 = 3

multiply the 3 by 13 to get 39

7 0
3 years ago
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Given the function f(x)=3x+5a / x^2-a^2 find the value of a for which f'(12) = 0
maria [59]
The function, as presented here, is ambiguous in terms of what's being deivded by what.  For the sake of example, I will assume that you meant

           3x+5a
<span> f(x)= ------------
</span>          x^2-a^2

You are saying that the derivative of this function is 0 when x=12.  Let's differentiate f(x) with respect to x and then let x = 12:

             (x^2-a^2)(3) -(3x+5a)(2x)
f '(x) = ------------------------------------- = 0 when x = 12
                [x^2-a^2]^2

(144-a^2)(3) - (36+5a)(24)
------------------------------------  =  0
               [   ]^2

Simplifying,

(144-a^2) - 8(36+5a) = 0

144 - a^2 - 288 - 40a = 0

This can be rewritten as a quadratic in standard form:

-a^2 - 40a - 144 = 0, or a^2 + 40a + 144 = 0.

Solve for a by completing the square:

a^2 + 40a + 20^2 - 20^2 + 144 = 0
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        Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)

         Finally, a = -20 plus or minus 2sqrt(39)

You must check both answers by subst. into the original equation.  Only if the result(s) is(are) true is your solution (value of a) correct.
6 0
3 years ago
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