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Korolek [52]
3 years ago
13

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

Mathematics
1 answer:
tatiyna3 years ago
7 0
F(x) = 4 - x²    g(x) = 6x

(g - f)(x) = g(x) - f(x)

(g - f)(3) = g(3) - f(3)

g(x) = 6x

g(3) = 6*3 = 18

f(x) = 4 - x²

f(3) = 4 - 3² = 4 - 9 = -5

(g - f)(3) = g(3) - f(3) = 18 - (-5) = 18 + 5 = 23

 (g - f)(3) = 23
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Line p has a slope of 6/7. Line q is perpendicular to p . What is the slope of line q
Serjik [45]

Answer:

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Step-by-step explanation:

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3 years ago
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
3 years ago
What is the equation of the line that passes through the point (–2,7) and has a slope of zero?
scZoUnD [109]

Answer:

y = 7

Step-by-step explanation:

Given:

x1 = -2

y1 = 7

slope (m) = 0

y - y1 = m ( x - x1 )

y - 7 = 0 ( x - (-2) )

y - 7 = 0 ( x + 2 )

y - 7 = 0

y = 7

4 0
2 years ago
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