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jekas [21]
2 years ago
11

Opal makes $15 per hour working for a photographer. She also coaches a competitive soccer team for $10 per hour.

Mathematics
1 answer:
Jlenok [28]2 years ago
7 0

The system of inequalities that represents the given situation are x + y ≤ 20 and 15x + 10y ≥ 90.

The parameters needed to model the inequalities;

  • amount made by Opal working for a photographer = $15 per hour
  • amount made in the soccer team = $10 per hour
  • minimum amount Opal needs to make a week = $90
  • maximum number of hours Opal needs to work = 20 hours

Let the number of hours Opal works for a photographer = x

Let the number of hours Opal works in soccer team = y

The first system of inequality in the given situation is represented as;

x + y ≤ 20

The second system of inequality in the given situation is represented as;

15x + 10y ≥ 90

Thus, the system of inequalities that represents the given situation are x + y ≤ 20 and 15x + 10y ≥ 90.

learn more here: brainly.com/question/9774970

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gavmur [86]

Answer:

  • b = -10, c = -106

Step-by-step explanation:

<h3>Given</h3>

<u>Quadratic function </u>

  • g(x) = ax^2 + bx + c

with the roots:

  • (-5+9i) and (-5-9i)
<h3>To find </h3>
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<h3>Solution</h3>

<u>As we know the sum of the roots is -b/a and the product of the roots is c/a. Substituting values and solving for b and c:</u>

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  • -10 = b
  • b = -10

And

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4 0
3 years ago
Scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100. Find the value th
Alinara [238K]

Answer:

The value that represents the 90th percentile of scores is 678.

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 = 550, \sigma = 100

Find the value that represents the 90th percentile of scores.

This is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

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

1.28 = \frac{X - 550}{100}

X - 550 = 100*1.28

X = 678

The value that represents the 90th percentile of scores is 678.

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