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andrew-mc [135]
3 years ago
10

Which is an equation? a. 17 + x b. 45 / x c. 20x = 200 d. 90 - x

Mathematics
1 answer:
eimsori [14]3 years ago
6 0
C. 20x = 200 because an equation always has an equal sign and other three are expressions because it doesn't have any signs, hoped this helped:)
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Sales increased by only 12% last month. If the sales from the previous month were $152,850, what were last months sales
Tamiku [17]

Answer:

\$171,192

Step-by-step explanation:

Remember that

100\%+12\%=112\%=112/100=1.12

we know that

The sales from the previous month were $152,850

This amount represent the 100%

so

Find out what were last months sales, multiply the sales from the previous month by the factor 1.12

\$152,850(1.12)=\$171,192

3 0
3 years ago
Is 3/8 Greater than, less than or equal 7/12
Alborosie

Answer:

3/8 is less then 7/12

Step-by-step explanation:

7 0
3 years ago
one morning it was- 9°F in Columbus, Ohio and -7°F in Pittsburgh,Pennsylvania. was it warmer in Columbus or Pittsburgh
Klio2033 [76]
Pittsburgh because -9°F is colder than -7<span>°F</span>
7 0
3 years ago
Read 2 more answers
5 b.) Bill swims 2/3 of a lap in 7 minute.<br> What is his speed in laps per minute?
Arlecino [84]

Answer:

.095 laps per minute (if you need this answer as well 10.5 minutes per lap)

Step-by-step explanation:

(2/3)/7 =.095238 this is laps per min

7/(2/3)= 10.5 this is minutes per lap

I hope this is what you were looking for.

8 0
2 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
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