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Amanda [17]
3 years ago
10

Carl’s square swimming pool has a volume of 1000 cubed feet. What are dimensions of his pool?

Mathematics
1 answer:
RUDIKE [14]3 years ago
5 0

Answer: the answer is down bellow

Step-by-step explanation:

x3-10oo Dimensions ft each S.

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one end of a tent is a triangle. the height of the triangle is 1.5 m and the base is 2.5 m. what is the area of the triangle?​
Anarel [89]

Answer:

1.5×2.5/2=1.875.

Step-by-step explanation:

We all know that area of triangle is base into hight upon 2.

3 0
1 year ago
An urn contains n white balls andm black balls. (m and n are both positive numbers.) (a) If two balls are drawn without replacem
Genrish500 [490]

DISCLAIMER: Please let me rename b and w the number of black and white balls, for the sake of readability. You can switch the variable names at any time and the ideas won't change a bit!

<h2>(a)</h2>

Case 1: both balls are white.

At the beginning we have b+w balls. We want to pick a white one, so we have a probability of \frac{w}{b+w} of picking a white one.

If this happens, we're left with w-1 white balls and still b black balls, for a total of b+w-1 balls. So, now, the probability of picking a white ball is

\dfrac{w-1}{b+w-1}

The probability of the two events happening one after the other is the product of the probabilities, so you pick two whites with probability

\dfrac{w}{b+w}\cdot \dfrac{w-1}{b+w-1}=\dfrac{w(w-1)}{(b+w)(b+w-1)}

Case 2: both balls are black

The exact same logic leads to a probability of

\dfrac{b}{b+w}\cdot \dfrac{b-1}{b+w-1}=\dfrac{b(b-1)}{(b+w)(b+w-1)}

These two events are mutually exclusive (we either pick two whites or two blacks!), so the total probability of picking two balls of the same colour is

\dfrac{w(w-1)}{(b+w)(b+w-1)}+\dfrac{b(b-1)}{(b+w)(b+w-1)}=\dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

<h2>(b)</h2>

Case 1: both balls are white.

In this case, nothing changes between the two picks. So, you have a probability of \frac{w}{b+w} of picking a white ball with the first pick, and the same probability of picking a white ball with the second pick. Similarly, you have a probability \frac{b}{b+w} of picking a black ball with both picks.

This leads to an overall probability of

\left(\dfrac{w}{b+w}\right)^2+\left(\dfrac{b}{b+w}\right)^2 = \dfrac{w^2+b^2}{(b+w)^2}

Of picking two balls of the same colour.

<h2>(c)</h2>

We want to prove that

\dfrac{w^2+b^2}{(b+w)^2}\geq \dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

Expading all squares and products, this translates to

\dfrac{w^2+b^2}{b^2+2bw+w^2}\geq \dfrac{w^2+b^2-b-w}{b^2+2bw+w^2-b-w}

As you can see, this inequality comes in the form

\dfrac{x}{y}\geq \dfrac{x-k}{y-k}

With x and y greater than k. This inequality is true whenever the numerator is smaller than the denominator:

\dfrac{x}{y}\geq \dfrac{x-k}{y-k} \iff xy-kx \geq xy-ky \iff -kx\geq -ky \iff x\leq y

And this is our case, because in our case we have

  1. x=b^2+w^2
  2. y=b^2+w^2+2bw so, y has an extra piece and it is larger
  3. k=b+w which ensures that k<x (and thus k<y), because b and w are integers, and so b<b^2 and w<w^2

4 0
3 years ago
26. (02.08)
Mama L [17]

Answer:

X^2 -5x -36

Step-by-step explanation:

formula of an area of a rectangle: ab

a-length

b-width

(x+4)*(x-9) = x^2 -5x -36

7 0
2 years ago
A bookstore bought a case of 10 books for a wholesale price of $74. The bookstore will sell the books at a 20% markup. How much
Darya [45]

Answer:

8.88 dollars so D

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Linear regression is often used to find fair prices of homes for sale. What
ivanzaharov [21]

Answer:

B. Graphing a scatterplot of the comps data in a table and finding the

equation of the line that best matches the coordinates

Explanation:

apex

8 0
3 years ago
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