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3 years ago

51) Rewrite the formula for the circumference of a circle C=2 /pi "r" in terms of its diameter "d". Please show your working :)

1 answer:

3 0

The circumference of a circle=2 $\pi$ r
We know that diameter is double the radius, and therefore can be written as d=2r
Circumference of a circle in terms of diameter is C= $\pi$ d
The 2r cancels out

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Sam rented a bike one day in the summer. He paid $68 an hour and a rental fee of $85.00 If Sam paid $ 357.00 for the day, how ma

Sliva [168]

Answer:

Step-by-step explanation:

First of all, subtract the rental fee. 357 - 85 = 272. Now, simply divide 272 by 68 to find the number of hours. 272 / 68 = 4.

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1 year ago

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A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

topjm [15]

Answer:

a) The expected value is $\frac{-1}{15}$

b) The variance is $\frac{49}{45}$

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is $\binom{10}{2}$ .

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is $\binom{5}{2}$ . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is $\binom{5}{1}\cdot \binom{5}{1}$ . So, we define the following probabilities.

Probability of winning: $\frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}$

Probability of losing $\frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}$

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing = $1.10\cdot \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}$

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing = $1.10^2\cdot \frac{4}{9}+\frac{5}{9}=\frac{82}{75}$

We will use the following formula

$Var(X) = E(X^2)-E(X)^2$

Thus

Var(X) = $\frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}$

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3 years ago

Anita invested $6000, some at 5% and the rest at 6%. If the yearly income is $337.50, what is the amount invested at each rate?'

allochka39001 [22]

Is this rsm? lol okay.

x is the amount of money invested at 5%
y is the amount of money invested at 6%
the total amount of money invested is $6000, or x+y
when it says the yearly income is $337.50, it means that the 5% of x plus the 6% of y equals $337.50.

now write the two equations:

x+y =6000

0.05x + 0.06y = 337.50

now, find y for the first equations, which is y= 6000 - x. use this equation to substitute for the second equation.

0.05x + 0.06(6000 -x) = 337.50

blah, blah, blah, solve for x... you should get x = 2250, and y = 3750.

I hate money problems like this, hope it helps.

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2 years ago

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If you multiply by 3 negatives does it equal a negative?

qwelly [4]

Yes it does because when u multiply 2 negative you get a positive but since your adding another negative it goes back to a negative

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3 years ago

How much is 1 over 6 times negative 6

notsponge [240]

It’s -1

1/6 x -6 is -1

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2 years ago

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