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3 years ago

Lf a+b=10 ,ab=21 then a^3+b^3=

Mathematics

2 answers:

Goshia [24]3 years ago

8 0

Answer:

370

Step-by-step explanation:

a=3 or 7

b=7 or 3

3³+7³=370

maksim [4K]3 years ago

6 0

Equations
a + b = 10 ... (1)
ab = 21 ...(2)

Answer: a³ + b³ = 370

• Form a new equation out of either eq. 1 or 2
b = 10 - a ... (3)

• Substitute b in second equation

-> a(10 - a) = 21

• Solve

-> 10a - a² = 21
-> 10a - a² - 21 = 0

• Simplify the quadratic expression

-> (a - 5)² - 4 = 0 (using completing the square method.
-> a - 5 = √4 or a - 5 = -√4
-> a - 5 = 2 or a - 5 = -2
-> a = 7 or a = 3

• Substitute values of a in second equation

When a = 7,

-> (7)b = 21
-> 7b = 21
-> b = 21/7
-> b = 3

When a = 3,

-> (3)b = 21
-> 3b = 21
-> b = 21/3
-> b = 7

(a, b) = (7, 3) or (3, 7)

• Substitute values for a and b into new equation

-> (7)³ + (3)³
-> 343 + 27
-> 370

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Answer:

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Step-by-step explanation:

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3 years ago

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. t

zhuklara [117]

Answer:

a) By the Central Limit Theorem, the mean is $142 and the standard deviation is $0.7488.

b) By the Central Limit Theorem, approximately normal.

c) 0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

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.

The mean monthly fee is $142 and the standard deviation is $29.

This means that $\mu = 142, \sigma = 29$

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Sample of 1500(larger than 30).

By the Central Limit Theorem

The mean is $142

The standard deviation is $s = \frac{29}{\sqrt{1500}} = 0.7488$

Part b: what is the shape of the sampling distribution of x hat justify your answer.

By the Central Limit Theorem, approximately normal.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $143?

This is 1 subtracted by the pvalue of Z when X = 143. So

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

By the Central Limit Theorem

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

$Z = \frac{143 - 142}{0.7488}$

$Z = 1.34$

$Z = 1.34$ has a pvalue of 0.9099

1 - 0.9099 = 0.0901

0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143

4 0

3 years ago

Your class is having a pizza party. You buy 5 pizzas Each pizz has 4 slices. How many slices is that altogether?

bixtya [17]

Answer:

Step-by-step explanation:

5 x 4 = 20

3 0

2 years ago

Read 2 more answers

HURRY LIMITED TIME

lakkis [162]

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The max miles depends on the max gallons of gas, so the miles possible with 20 gallons is M(20) = 17(20) = 340.

So, g ranges from 0 to 20 and M(g) ranges from 0 to 340.
Therefore your answer is the last option.

8 0

3 years ago

Write a real-world problem that could be represented by the following inequality. 70 + 5x < 30 + 15x

kondaur [170]

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3 years ago

Lf a+b=10 ,ab=21 then a^3+b^3=​

Lf a+b=10 ,ab=21 then a^3+b^3=