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Marat540 [252]
3 years ago
10

Cole gets paid $5,000 plus 16% of all his popcorn sales,x, while Michael gets A fixed salary of $55,000.Write an inequality that

represents the dollar amount of sales that Cole must generate each in order to make more than Michael
Mathematics
1 answer:
Hitman42 [59]3 years ago
4 0

Answer:

5000 + (0.16)x > 55,000

Step-by-step explanation:

<u><em>DATA:</em></u>

Michael's salary = $55,000

Cole's basic salary = $5,000

--> Commission = 16% of sales

--> Sales = x

<u><em>Cole's total salary</em></u>

<em>--> Basic salary + Commission x sales</em>

--> 5000 + 16% of x

--> 5000 + (0.16)x  as 16 percent is equal to 16/100 = 0.16

<u><em>Cole's total salary should be more than Michael's total salary</em></u>

5000 + (0.16)x > 55000

<em>--> Make x the subject</em>

0.16x > 55000-5000

0.16x > 50,000

x > 50,000/0.16

x > 312500

The inequality that represents the dollar amount of sales is 5000 + (0.16)x > 55000.

The dollar amount of sales that Cole must generate should be more than $312500.

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10 L of 30 % saline solution can be formed by mixing 4 L of 60 % saline solution and 6 L of  10 % saline solution.

Step-by-step explanation:

Let x be the number of liters of 60% saline solution

Now we require 10 L of 30% saline solution.

Liter soln %  liters  saline %  

30 %                 10        0.3  

60 %                   x        0.6

10 %                  10-x      0.1

Now forming the algebraic equation,

0.6x + 0.1 (10-x) = 10 (0.3)

0.6x + 1 - 0.1 x  = 3

0.5 x = 2

x = 4 ( 4 l of 60 % solution is required. So 10 % saline solution required is 10 - 4 = 6 L).

Hence, 10 L of 30 % saline solution can be formed by mixing 4 L of 60 % saline solution and 6 L of  10 % saline solution.

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3 years ago
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Use three different values of n to demonstrate that 2n + 3n is equivalent to 5n.
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Using ten would have them all equal 50, using 6 would have them all equal 30 and using 7 would have them all equal 35.

Hope this helps!
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You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provid
ohaa [14]

Answer:

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

274 shelters will be needed.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 250, \sigma = 75

If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?

What is the percentile of 350?

This is the pvalue of Z when X = 350.

Z = \frac{X - \mu}{\sigma}

Z = \frac{250 - 150}{75}

Z = 1.33

Z = 1.33 has a pvalue of 0.9082.

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

If not, what number of shelter openings will be needed?

The 95th percentile, which is X when Z = 1.645. So

Z = \frac{X - \mu}{\sigma}

1.645 = \frac{X - 150}{75}

X - 150 = 1.645*75

X = 274

274 shelters will be needed.

5 0
2 years ago
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