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4 years ago

Factor 3x^3+3x^2+x+1

Mathematics

2 answers:

Nat2105 [25]4 years ago

6 0

We can solve it like:
3x^3+3x^2+x+1= (3x^3+3x^2)+(x+1)=
3x^2(x+1)+(x+1)=
= (x+1)(3x^2+1)

Have a good day

bixtya [17]4 years ago

5 0

(3x³ + 3x²) + (x + 1)
3x²(x + 1) + 1(x + 1)
(3x² + 1)(x + 1)

Factored form: (3x² + 1)(x + 1)

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Help me with this plz no links

Kisachek [45]

Answer:

29,344.87 feet

Step-by-step explanation:

Tall Mountain is 8606.37 feet higher than Mt. Might. Let's replace the missing number with x.

Let's set up an equattion:

x = 20,738.5 + 8,606.37

Now let's solve the equation.

20,738.5 + 8,606.37 = 29,344.87

Add feet after the answer.

29,344.87

6 0

2 years ago

Read 2 more answers

What is the area of the circumference 176 Centimeters

Tems11 [23]

So I don’t have a step by step answer but I’m pretty sure it’s Area- =2461.76cm2 r= 28 but idk I just looked it up

6 0

3 years ago

Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.6}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

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

$Z = \frac{11 - 11}{0.6}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

X = 10.5

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

$Z = \frac{10.5 - 11}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 100, s = \frac{3}{\sqrt{100}} = 0.3$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.3}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.3}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

5 0

3 years ago

8 2. PROVE: tane+cotes: sececsc? (Hint: Convert to sin's and cos's.

Luden [163]

$\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf tan(\theta )+cot(\theta )=sec(\theta )csc(\theta ) \\\\[-0.35em] ~\dotfill\\\\ tan(\theta )+cot(\theta )\implies \cfrac{sin(\theta )}{cos(\theta )}+\cfrac{cos(\theta )}{sin(\theta )}\implies \cfrac{sin(\theta ) sin(\theta )+cos(\theta )cos(\theta )}{cos(\theta )sin(\theta )} \\\\\\ \cfrac{sin^2(\theta )+cos^2(\theta )}{cos(\theta )sin(\theta )}\implies \cfrac{1}{cos(\theta )sin(\theta )}\implies \cfrac{1}{cos(\theta )}\cdot \cfrac{1}{sin(\theta )}\implies sec(\theta )csc(\theta )$

4 0

3 years ago

Need help asapppp!!,

kenny6666 [7]

Answer:

ion even know cuh lol

Step-by-step explanation:

4 0

3 years ago