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steposvetlana [31]
3 years ago
15

Identify the zeros of the polynomial function N(x)=1/2 (x-1)(x+3).

Mathematics
1 answer:
zhannawk [14.2K]3 years ago
6 0

Answer:

a:x=-3

c:x=1

Step-by-step explanation:

The zeros of a function are the values of x for which the value of the function f(x) becomes zero.

In this problem, we have the following function:

f(x)=\frac{1}{2}(x-1)(x+3)

Here we want to find the zeros of the function, i.e. the values of x for which

f(x)=0

In order to make f(x) equal to zero, either one of the factors (x-1) or (x+3) must be equal to zero.

Therefore, the two zeros can be found by requiring that:

1)

x-1=0\\\rightarrow x=+1

2)

x+3=0\\\rightarrow x=-3

So the correct options are

a:x=-3

c:x=1

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The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation
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Answer:

0.7780

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population:

We have that \mu = 7.19, \sigma = 0.86

Sample of 12:

n = 12, s = \frac{0.86}{\sqrt{12}} = 0.2483

What is the probability that the mean cost will be more than $7.00?

This is 1 subtracted by the pvalue of Z when X = 7. So

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

By the Central Limit Theorem

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

Z = \frac{7 - 7.19}{0.2483}

Z = -0.765

Z = -0.765 has a pvalue of 0.222

1 - 0.222 = 0.778

So the answer is 0.7780

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3 years ago
A landscaper makes a $2,000 profit in a week when he services 25 lawns. He makes a $600 profit in a week when he services 11 law
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2000 - 600 = 1400
-------------- 
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100 dollars per 1 lawn. 

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He will earn $3,600.
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Read 2 more answers
For which intervals is the function decreasing?
lilavasa [31]

Answer:

The function is decreasing in the following intervals

A. (0, 1)

C. (2, pi)

Step-by-step explanation:

To answer this question, imagine that you draw lines of slope m parallel to the function shown at each point.

-If the slope of this line parallel to the function is negative for those points then the function is decreasing.

-If the slope of this line parallel to the function is positive for those points then the function is increasing.

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(0, 1) U (2, pi)

Therefore the correct option is:

A. (0, 1)

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5 0
4 years ago
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