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3 years ago

Write a piecewise function

Mathematics

1 answer:

Hoochie [10]3 years ago

7 0

Answer:

The answer to your question is:

f(x) = - x - 4 if (-∞, -3)

2x + 6 if [-3, ∞)

Step-by-step explanation:

Find the equations of the two lines

Blue line

A (-4, 1)

B (-6, 3)

m = (3 - 1) / (-6 + 4)

m = 2 / -2

m = -1

(y - 1) = -1(x + 4)

y - 1 = -x - 4

y = - x - 4 + 1

y = - x - 4 Interval (-∞, -3)

Red line

C(-2, 2)

D(0, 6)

m = (6 - 2) / 0 + 2)

m = 4 / 2

m = 2

(y - 2) = 2(x + 2)

y - 2 = 2x + 4

y = 2x + 4 + 2

y = 2x + 6 Interval [-3, ∞)

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An employee earns $200 for 14 hours work. Assuming he is paid by the hour, how much will this employee earn in 35 hours?

bezimeni [28]

If an employee earns 200 dollars for 14 hours work, that means this person gets approximately 14 dollars and 29 cents per every hour.

Thus, in 35 hours, you can multiply 14.29 by 35 to get about 500 dollars.

In 35 hours, the employee will earn 500 dollars.

3 0

3 years ago

in a random sample of 200 people, 154 said that they watched educational television. fine the 90% confidence interval of the tru

melisa1 [442]

Answer:

[0.7210,0.8189] = [72.10%, 81.89%]

Step-by-step explanation:

The sample size is

n = 200

the proportion is

p = 154/200 = 0.77

Since both np ≥ 10 and n(1-p) ≥ 10

We can approximate this discrete binomial distribution with the continuous Normal distribution. As the sample size is large enough, not applying the continuity correction factor makes no significant difference.

The approximation would be to a Normal curve with this parameters:

Mean

p = 0.77

Standard deviation

$\bf s=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.77*0.23}{200}}=0.0298$

The 90% confidence interval for the proportion would be then

$\bf [0.77-z^*0.0298, 0.77+z^*0.0298]$

where $\bf z^*$ is the 10% critical value for the Normal N(0,1) distribution , this is a value such that the area under the N(0,1) curve outside the interval $\bf [-z^*,z^*]$ is 10%=0.1

We can either use a table, a calculator or a spreadsheet to get this value.

In Excel or OpenOffice Calc we use the function

NORMSINV(0.95) and we get a value of 1.645

The 90% confidence interval for the proportion is then

$\bf [0.77-1.645^*0.0298, 0.77+1.645^*0.0298]=[0.7210,0.8189]$

This means there is a 90% probability that the proportion of people who watch educational television is between 72.10% and 81.89%

If the television company wanted to publicize the proportion of viewers, do you think it should use the 90% confidence interval?

Yes, I do.

5 0

3 years ago

caitlin got a haircut that cost 42.30 she tipped the stylist 8.46. What percent did she tip the stylist?

Julli [10]

Answer:

ok so we need to find the percent so

8.46 divided by 42.3=0.2

she she tipped 20%

Hope This Helps!!!

5 0

2 years ago

In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches.

Vladimir79 [104]

Answer:

A. 16%

Step-by-step explanation:

Problems of normally distributed samples can be 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:

$\mu = 64, \sigma = 4$