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Alexeev081 [22]
3 years ago
7

Shakira went bowling with her friends. She paid $3 to rent shoes and then $4.75 for each game. If she spent a total of $36.25, t

hen how many games did she play?
Mathematics
2 answers:
Ulleksa [173]3 years ago
5 0

4.75x + 3 = 21                                   x = 4 games

alexira [117]3 years ago
4 0

Answer:

7 games

Step-by-step explanation:

36.25-3=33.25

33.25÷4.75=7

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Need help plz Compare using <, >, or =.
jek_recluse [69]
Meanings of inequalities :

< less than
> more than
= equal

convert both fractions to their common denominators , which is 40.

7/2/5 = 7/16/40
7/3/8 = 7/15/40

as you can see, 7/2/5 is bigger. thus the answer is > .
3 0
3 years ago
Simplify the following expression:
Morgarella [4.7K]

Answer:

2nd option

Step-by-step explanation:

Given

2x - 8y + 3x² + 7y - 12x ← collect like terms

= 3x² + (2x - 12x) + (- 8y + 7y)

= 3x² + (- 10x) + (- y)

= 3x² - 10x - y

8 0
2 years ago
Issac put $5 in a shoe box every day for the months of april, may, and june. He then spent 75% of the money on baseball cards. H
igor_vitrenko [27]
As of 2021:
April-$150
May-$155
June-$150
Total-$455
Spent 75%=455/100x75
=341.25
455-341.25=$113.75
Round off to 3sf: $114
Have a good day
3 0
3 years 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
A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?
Aneli [31]
There are 10 deciliters in 1 liter (deci means 10).

Divide 5.25 by 10 to find how many liters are needed.

5.25/10 = 0.525

0.525 liters of milk are needed for the cake.
3 0
3 years ago
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