Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1.

Records at an insurance company showed that the first 30 customers made an average of 5 claims each through their lifetime. Afte

umka2103 [35]

The average of the 75 customers will be 6.4.

<h3>How to calculate the value?</h3>

The first 30 customers made an average of 5 claims each. The total claims will be:

= (5 × 30) = 150

When 75 more people were assessed, the average was 6. Therefore, the total claims will be:

= (75 + 30) × 6

= 105 × 6

= 630

Therefore, the average of the 75 customers will be:

= (630 - 150)/75

= 480/75

= 6.4

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8 0

1 year ago

Peter is at a lumber yard. He gets 2 free boxes of nails for every 10 boards he buys. Write an expression for the number of boxe

Sati [7]

A. The number of 10-boards Peter bought is equal to n divided by 10. Then, each of the 10-boxes will get two boxes of nails. The number of boxes of nails that Peter will have after buying n boards will be,

N = (2)(n/10)

Simplifying,

<em> N = n/5</em>

b. If the number of boards are 90 then,

N2 = (90/10)(2)(100 nails/box)
N2 = 1800

Answer: 1800

7 0

3 years ago

Read 2 more answers

what is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube

Dmitrij [34]

Let the least possible value of the smallest of 99 cosecutive integers be x and let the number whose cube is the sum be p, then

$\frac{99}{2} (2x+98)=p^3 \\ \\ 99x+4,851=p^3\\ \\ \Rightarrow x=\frac{p^3-4,851}{99}$

By substitution, we have that $p=33$ and $x=314$ .

Therefore, <span>the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube is 314.</span>

3 0

3 years ago

How do you solve 3 1/4 - 1 5/6

rjkz [21]

Answer:

to solve $3\frac{1}{4} -1\frac{5}{6}$ you would first need to convert them from mixed numbers to improper fractions. You can do this by multiplying the denominator with the whole number and then adding the numerator. Then you should make sure that the denominators are the same. You can do this by first finding a number that they will both multiply into. In this example it is 12. And when changing the denominator you must apply it to the numerator. So if you multiplied the denominator by 3 then you must multiply the numerator by 3. After you can just minus the numerators. However remember to keep the denominator the same. Then you can change it back into a mixed number by dividing the numerator by the denominator and having that whole number on the side of the fraction . lets say it is $\frac{13}{6}$ then you would divide 13 by 6 which is 2 and a decimal and then minus the number that is multiplied by the numerator and it will give a number that is smaller than the denominator and then it would become $2\frac{1}{6}$ .