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3 years ago

Solve f(x)=x²+7x+12/-x²-3x+4

1 answer:

8 0

$x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{The domain:} x\neq-4\ and\ x\neq1\\\\canceled\ (x+4)\\\\f(x)=\dfrac{x+3}{-(x-1)}=-\dfrac{x+3}{x-1}\ for\ x\neq-4\ and\ x=1$

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Cody wants to attend the fall festival at school. The price of admission to the festival is $5.50 and each game cost an addition

My name is Ann [436]

75 divided by 15.00 is 20 because of you put 75 into 150 you can put it in 2 times evenly then you take down the 0 and 00 - 0 = 0 so answer is 20 games.

5 0

3 years ago

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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 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.

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.

In this problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

3 years ago

Arrange these numbers from least to greatest:

zmey [24]

First let's put them all over 100.
- $\frac{5}{8}$ would change to - $\frac{62.5}{100}$

- $\frac{7}{9}$ to - $\frac{77.7}{100}$

- $\frac{4}{5}$ to - $\frac{80}{100}$

- $\frac{3}{7}$ to - $\frac{42.8}{100}$

Then if we put them from least to greatest it would be from highest to lowest (since they are negatives)

- $\frac{4}{5}$ , - $\frac{7}{9}$ , - $\frac{5}{8}$ , - $\frac{3}{7}$

The answer would be B

8 0

3 years ago

A cd that is originally priced at $15.85 red-tagged for the sale. what is the sale price of the cd

Svetradugi [14.3K]

Answer:

$6.34

Step-by-step explanation:

15.85 - 60% = $6.34

4 0

3 years ago

PLEASE ASAP !!! do 4-5

Sergeeva-Olga [200]

Answer:

number 5 is x+8 , y-4 i don't know about number 4 though :(

so down four units and right 8 units

5 0

3 years ago