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2 years ago

B) 2x² - 4x + 3 = 0 a) x² + 3x – 10 = 0

Mathematics

1 answer:

kozerog [31]2 years ago

3 0

Answer:

a. x = 2 , x = -5

b. no real roots

Step-by-step explanation:

a. x² + 3x – 10

= x² - 2x + 5x - 10

= x (x²/x - 2x/x) + 5 (5x/5 - 2*5/5)

= (x - 2) (x + 5)

x - 2 = 0 x + 5 = 0

+ 2 +2 -5 -5

-------------- ---------------

x = 2 x = -5

x = 2 , x = -5

b. 2x² - 4x + 3

This can't be solved because the equation has no real roots, and also the discriminant is negative.

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3 years ago

three sets of the sum of a number and four are added to the sum of seven times the same number and thirteen

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The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)

Solution:

Given the statement:

Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen

Let us first understand the given statement,

Let the number be "x"

" sum of a number and four" means x + 4

"Three sets of a sum of a number and four" translated to 3(x + 4)

"sum of seven times the same number and thirteen" means 7x + 13

Thus the algebraic expression for given statement is:

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Using distributive property in above expression

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Therefore,

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2 years ago

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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

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By the Central Limit Theorem

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

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

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

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