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mario62 [17]
3 years ago
14

The quotient of a number and -7 decreased by 2, is 10.

Mathematics
1 answer:
klasskru [66]3 years ago
3 0
Hello!

This expression can be broken down into 3 separate parts:

1. "the quotient of a number and (-7)"
2. "decreased by 2"
3. "is 10"

We'll begin with the first part. The word "quotient" implies the result of a division problem. Therefore, this part can be represented by the following expression (let "x" represent the unknown number):

\frac{x}{(-7)}

Now we'll move on to the second part. If something is decreased by a value of 2, we know that 2 is being subtracted. Therefore, this part can be represented by the following expression:

– 2

Now we'll move on to the third and final part. The phrase "is 10" implies that the operations preceding this part are equal to 10. Therefore, this part can be represented by the following expression:

= 10

Finally, put the three parts together to create the following equation:

\frac{x}{(-7)} – 2 = 10

The equation has now been fully translated. If, however, you are required to find the unknown value (x), begin by adding 2 to both sides of the equation:

\frac{x}{(-7)} = 12

Now multiply both sides by (-7):

x = (-84)

We have now proven that the unknown number is equal to (-84).

I hope this helps!
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Answer:

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We need to check the conditions in order to use the normal approximation.

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Since both conditions are satisfied we can use the normal approximation and the distribution for the proportion is given by:

p \sim N (p, \sqrt{\frac{p(1-p)}{n}})

With the following parameters:

\mu_ p = 0.78

\sigma_p = \sqrt{\frac{0.78*(1-0.78)}{50}}= 0.0586

Step-by-step explanation:

Previous concepts

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Solution to the problem

We know that n = 50 and p =0.78.

We need to check the conditions in order to use the normal approximation.

np=50*0.78=39  \geq 10

n(1-p)=50*(1-0.78)=11 \geq 10

Since both conditions are satisfied we can use the normal approximation and the distribution for the proportion is given by:

p \sim N (p, \sqrt{\frac{p(1-p)}{n}})

With the following parameters:

\mu_ p = 0.78

\sigma_p = \sqrt{\frac{0.78*(1-0.78)}{50}}= 0.0586

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