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sertanlavr [38]
3 years ago
13

The average of two numbers is 25 and their difference is 8. What are the numbers?

Mathematics
1 answer:
nika2105 [10]3 years ago
8 0
x;y-the\ numbers\\\\  \left\{\begin{array}{ccc}\frac{x+y}{2}=25&|multiply\ both\ sides\ by\ 2\\x-y=8\end{array}\right\\+\left\{\begin{array}{ccc}x+y=50\\x-y=8\end{array}\right\ \ \ |add\ sides\ of\ the\ equations\\---------\\.\ \ \ \ \ \ \ \ 2x=58\ \ \ \ \ \ \ |divide\ both\ sides\ by\ 2\\.\ \ \ \ \ \ \ \ \ \ x=29\\\\29+y=50\\y=50-29\\y=21\\\\Answer:29\ and\ 21.
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Complete the table of values
Agata [3.3K]
Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify! 

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, 3^{-2} =
\frac{1}{3^{2} }.
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, (\frac{3}{4}) ^{3}  =  \frac{ 3^{3} }{4^{3} }.
3) The zero exponent rule<span> says that any number raised to zero is 1. For example, 3^{0} = 1.
</span>

Back to the Problem:
Problem 1 
The x-values are in the left column. The title of the right column tells you that the function is y =  4^{-x}. The x-values are:
<span>1) x = 0
</span>Plug this into y = 4^{-x} to find letter a:
y = 4^{-x}\\&#10;y = 4^{-0}\\&#10;y = 4^{0}\\&#10;y = 1
<span>
2) x = 2
</span>Plug this into y = 4^{-x} to find letter b:
y = 4^{-x}\\ &#10;y = 4^{-2}\\ &#10;y =  \frac{1}{4^{2}} \\  &#10;y= \frac{1}{16}
<span>
3) x = 4
</span>Plug this into y = 4^{-x} to find letter c:
y = 4^{-x}\\ &#10;y = 4^{-4}\\ &#10;y =  \frac{1}{4^{4}} \\  &#10;y= \frac{1}{256}
<span>

Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is y =  (\frac{2}{3})^x. The x-values are:
<span>1) x = 0
</span>Plug this into y = (\frac{2}{3})^x to find letter d:
y = (\frac{2}{3})^x\\&#10;y = (\frac{2}{3})^0\\&#10;y = 1
<span>
2) x = 2
</span>Plug this into y = (\frac{2}{3})^x to find letter e:
y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\&#10;y =  \frac{4}{9}
<span>
3) x = 4
</span>Plug this into y = (\frac{2}{3})^x to find letter f:
y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}
<span>
-------

Answers: 
a = 1
b = </span>\frac{1}{16}<span>
c = </span>\frac{1}{256}
d = 1
e = \frac{4}{9}
f = \frac{16}{81}
5 0
3 years ago
Name and describe the methods for determining a marketing budget.
Mekhanik [1.2K]

Answer: There are several ways in which we can determine our marketing budget. Some of these are given below:

<u><em>1. Percentage of revenues:</em></u>

Under this method we usually  take a fixed percentage of our revenues and further allocating this amount for marketing. We will choose the percentage that works best for us.

<u><em>2. Percentage of net sales:</em></u>

This method determines our marketing budget as a fraction of our net sales. This method will take a lot of trial and error to find the percentage that works well for our company.

<u><em>3. Industry specific:</em></u>

Nowadays, industries have specific projections as to the amount they will need to spend on marketing . The best way to get these numbers is to find a firm that represents our industry and ask them to provide us with averages. We can then refine the actual costs.

<em><u>4. Objective/task oriented </u></em>

This is model that works by setting out goals, planning out the tasks and then estimating the cost for all of these tasks. It works greatly for firms who have a immense knowledge about measurements and information of their business processes.

4 0
3 years ago
0.5 is what type of number?
zepelin [54]
0.5 is a rational number.
4 0
2 years ago
Read 2 more answers
2x + 6 = x – 1<br> Real solutions
pogonyaev

Answer:

x = -7

Step-by-step explanation:

2x+6 = x-1

add -6 to both sides

2x = x-7

add -x to both sides

x = -7

6 0
3 years ago
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2135 miles, with a variance
stiv31 [10]

Answer:

0.36878

Step-by-step explanation:

Given that:

Mean number of miles (m) = 2135 miles

Variance = 145924

Sample size (n) = 40

Standard deviation (s) = √variance = √145924 = 382

probability that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles

P( 2135 - 29 < z < 2135 + 29)

Z = (x - m) / s /√n

Z = [(2106 - 2135) / 382 / √40] < z < [(2164 - 2135) / 382 / √40]

Z = (- 29 / 60.399503) < z < (29 / 60.399503)

Z = - 0.4801364 < z < 0.4801364

P(Z < - 0.48) = 0.31561

P(Z < - 0.48) = 0.68439

P(- 0.480 < z < 0.480) = 0.68439 - 0.31561 = 0.36878

= 0.36878

3 0
2 years ago
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