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2 years ago

Use the intersect method to solve the equation x^2-1=-x^2+7

Mathematics

1 answer:

olga55 [171]2 years ago

4 0

Answer:

The solutions of the equation x^2-1=-x^2+7 are (-2,3) and (2,3)

Step-by-step explanation:

Please, see the attached file.

Thanks.

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The cost of petrol rises by 2 cents a liter. Last week a man bought 20 liters at the old price. This week he bought 10 liters at

In-s [12.5K]

Answer: the old price for 1 liter is $0.3

Step-by-step explanation:

Let x represent the old price for 1 liter of petrol.

Last week a man bought 20 liters at the old price. This means that the total amount that the man paid for 20 liters is 20x.

The cost of petrol rises by 2 cents a liter. This means that the new price per liter is x + 2/100 = x + 0.02

This week he bought 10 liters at the new price. This means that the total amount that the man paid for 10 liters is

10(x + 0.02)

= 10x + 0.2

Altogether, the petrol costs $9.20. This means that

20x + 10x + 0.2 = 9.2

30x + 0.2 = 9.2

30x = 9.2 - 0.2

30x = 9

x = 9/30

x = 0.3

3 0

3 years ago

) The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday

Vsevolod [243]

Answer:

a) The standard deviation of this sampling distribution is 2.07.

b) The missing number is 4.14.

c) The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

Step-by-step explanation:

To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

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 question:

$\mu = 272, n = 840, \sigma = 60$

(a) If we take many samples, the sample mean x⎯⎯⎯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?

Using the Central Limit Theorem:

$s = \frac{\sigma}{\sqrt{n}} = \frac{60}{\sqrt{840}} = 2.07$

The standard deviation of this sampling distribution is 2.07.

(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x⎯⎯⎯ fall within _______ on either side of the unknown mean μ. What is the missing number?

Within 2 standard deviations of the mean.

So, 2*2.07 = 4.14

The missing number is 4.14.

(c) What is the 95% confidence interval for the population mean score μ based on this one sample?

Within 4.14 of the mean

272 - 4.14 = 267.86

272 + 4.14 = 276.14

The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

6 0

3 years ago

Which is better: having a stock that goes up 30% on Wednesday than drops 20% on Thursday, or a stock

finlep [7]