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Mama L [17]
3 years ago
12

Find the zeros of g(x) = -x^2 + 6x - 8

Mathematics
1 answer:
lbvjy [14]3 years ago
3 0

(Remember to set g(x) to zero).

For this, I will be completing the square. Firstly, what two terms have a product of 8x^2 and a sum of 6x? That would be 4x and 2x. Replace 6x with 2x + 4x: 0=-x^2+2x+4x-8

Next, factor -x^2 + 2x and 4x - 8 separately. Make sure that they have the same quantity on the inside of the parentheses: 0=-x(x-2)+4(x-2)

Next, you can rewrite the equation as 0=(-x+4)(x-2)

Now apply the Zero Product Property:

-x+4=0\\-x=-4\\x=4\\\\x-2=0\\x=2

<u>The zeros of this equation are 4 and 2.</u>

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What's the best definition of the word "ratio?"
ololo11 [35]

Answer:

Compare

Step-by-step explanation:

Or relation I believe so...

7 0
3 years ago
Kyle received the following course grades for 10​ (three-credit) courses during his freshman​ year:
timofeeve [1]

Answer:

(a) The average grade point is 2.5.

(b) The relative frequency table is show below.

(c) The mean of the relative frequency distribution is 0.3333.

Step-by-step explanation:

The given data set is

4, 4, 4, 3, 3, 3, 1, 1, 1, 1

(a)

The average grade point is

Average=\frac{\sum x}{n}

Average=\frac{4+4+4+3+3+3+1+1+1+1}{10}

Average=2.5

Therefore the average grade point is 2.5.

(b)

\text{Relative frequency}=\frac{\text{Frequency of number}}{\text{Total frequency}}

The relative frequency table is show below:

x                 f                  Relative frequency

4                3                 \frac{3}{10}=0.3

3                3                 \frac{3}{10}=0.3

1                 4                 \frac{4}{10}=0.4

(c)

Mean of the relative frequency distribution is

Average=\frac{0.3+0.3+0.4}{3}

Average=0.3333

Therefore the mean of the relative frequency distribution is 0.3333.

4 0
3 years ago
The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 16 years; the
STatiana [176]

Using the Emperical rule:

68% lie with one one standard deviation:

16 + 1.7 , 16-1.7 = 17.7, 14.3

14.3 is part of the 68%.

The remaining 32% of the distribution is outside the range, with half being less than and half being greater than.

32/2 = 16

The probability of living loner than 14.3 Would be 16%

3 0
3 years ago
Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample
fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

37% of the company's orders come from first-time customers.

This means that p = 0.37

A random sample of 225 orders will be used to estimate the proportion of first-time-customers.

This means that n = 225

Mean and standard deviation:

\mu = p = 0.37

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{225}} = 0.0322

What is the probability that the sample proportion is between 0.26 and 0.38?

This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.

X = 0.38

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

By the Central Limit Theorem

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

Z = \frac{0.38 - 0.37}{0.0322}

Z = 0.31

Z = 0.31 has a pvalue of 0.6217

X = 0.26

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

Z = \frac{0.26 - 0.37}{0.0322}

Z = -3.42

Z = -3.42 has a pvalue of 0.0003

0.6217 - 0.0003 = 0.6214

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

5 0
3 years ago
4|n+8| = 56 <br><br>please help
Alchen [17]
To solve the absolute value equation you first need to get everything not in the absolute value bars to the other side of the equation.

Step 1) Divide by 4
|n+8| = 14

*Remember: when solving absolute value equations, you make what the expression (n+8) is equal to negative and positive. Not the other way around.

Step 2) Make two equations

n+8 = 14
n+8 = -14

Solve and you'll see that n= 6 and -22
3 0
3 years ago
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