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kkurt [141]
3 years ago
7

A box contains 5 plain pencils and 7 pens. A second box contains 3 color pencils and 3 crayons. One item from each box is chosen

at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
Mathematics
1 answer:
Andru [333]3 years ago
8 0
Multiply the two desired probabilities to find the answer.

5/12 is the probability for the plain pencil since there are 5 pencils out of 12 total items.

1/2 is the probability for the colored pencil since there are 3 colored pencils out of 6 total items. 3/6 simplifies to 1/2.

5/12*1/2= 5/24

Final answer: 5/24
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What is x if n≠m? Please help!
lorasvet [3.4K]

Answer: x = \frac{mn(q - p)}{n-m}\\\\

================================================

Work Shown:

Part 1

\frac{x-m}{m} + p = \frac{x-n}{n} + q\\\\\frac{x-m}{m} - \frac{x-n}{n} = q - p\\\\\frac{n(x-m)}{mn} - \frac{m(x-n)}{mn} = q - p\\\\\frac{xn-mn}{mn} - \frac{xm-mn}{mn} = q - p\\\\\frac{xn-mn-(xm-mn)}{mn} = q - p\\\\

Part 2

\frac{xn-mn-xm+mn}{mn} = q - p\\\\\frac{xn-xm}{mn} = q - p\\\\\frac{x(n-m)}{mn} = q - p\\\\x(n-m) = mn(q - p)\\\\x = \frac{mn(q - p)}{n-m}  \\\\

-------------------------------

Explanations:

  • There are quite a bit of steps. I decided to break things into two parts.
  • The goal is to get x all by itself on its own side, which is why I subtracted (x-n)/n from both sides in part 1, step 2. I also subtracted p from both sides.
  • Afterward, I gave each fraction the LCD mn. I multiplied top and bottom of the first fraction by n/n. I did a similar operation to the second fraction, but with m instead.
  • From there, we distribute and simplify. The mn terms cancel on the left side numerator (second step of part 2).
  • The n≠m is there to prevent the denominator (n-m) from being zero. We cannot divide by zero.
  • If the formulas don't properly display, then you might have to refresh the page.
7 0
3 years ago
Translate: Six more than the product of two numbers.
RoseWind [281]

Answer:

You write it like this:  

6  +  8 n.

Step-by-step explanation:

You can translate the sentence in English into math. "The product of" means multiplying two numbers, and "6 more than" means adding 6:

hope this helps :)

6 0
3 years ago
Read 2 more answers
The work of a student to solve the equation 2(6y − 3) = 20 + 6y is shown below:
Gnom [1K]
Step 2: 8y-5=10+3y is wrong
And the second step is right
7 0
3 years ago
Solve this equation -129=6(7+7x)-3
leva [86]

Answer:

-4

Step-by-step explanation:

-129 = 6(7 + 7x) - 3

Distribute the 6 into the parentheses.

-129 = 42 + 42x - 3

Add like terms.

-129 = 39 +42x

Subtract 39 from both sides.

-168 = 42x

Divide 42 from both sides.

-4 = x

7 0
4 years ago
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Unit rate of 14.25 for 3 pounds of deli meat
Neko [114]
To find the unit rate, you have to find how much each pound costs

so 14.25/3 is the expression that will get you the answer

14.25/3= 4.75

4.75 per pound is your answer

hope this helps
6 0
3 years ago
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