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Drupady [299]
3 years ago
5

Use the given facts about the functions to find the indicated limit

Mathematics
1 answer:
Alika [10]3 years ago
3 0

Answer:

B. -12

Step-by-step explanation:

The given limit are;

\lim_{x \to -11} f(x)=-3 and \lim_{x \to -11} g(x)=4

We want to find;

\lim_{x \to -11} (fg)(x)=\lim_{x \to -11} f(x)\times \lim_{x \to -11} g(x)

We substitute the given limits to obtain;

\lim_{x \to -11} (fg)(x)=-3\times 4

\lim_{x \to -11} (fg)(x)=-12

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Solve the equation, justify<br> each step with an algebraic<br> property<br> -(x - 6) = 4
lesantik [10]

Answer:

x=2

Step-by-step explanation:

Step 1_  −(x−6)=4

              −x+6=4(Distribute)

               −x+6=4

Step 2_       −x+6−6=4−6

                   −x=−2

Step 3_       −x    equals   -2

                    −1                   -1

x=2

Hope this helps :)

3 0
3 years ago
What sequence of rigid transformations takes figure C to figure D?
Nutka1998 [239]

Answer:

D

Step-by-step explanation:

Hope this helps :)

8 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
Determine the density in g/cm3 of a mineral that has a volume of 3.8 cm3 and a mass of 22.4 g.
kherson [118]

Answer:

5.89 g/cm³

Step-by-step explanation:

givens,

Mass = 22.4 g

volume = 3.8 cm³

Density = mass / volume

= 22.4 / 3.8

= 5.89 g/cm³

4 0
3 years ago
Which polynomial is represented by the algebra tiles?
kogti [31]

A. 2x2 – 4x – 6

Looking at the diagram, there two positive x's to the power of 2, and there are four negative x and six minus signs. Inspecting it and adding all the same terms, you will get the quadratic expression 2x^2 - 4x - 6.

8 0
3 years ago
Read 2 more answers
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