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3 years ago

12

Type the correct answer in each box. Consider the sum of cubes identity: a3 + b3 = (a + b)(a2 − ab + b2). For the polynomial 8x3

+ 27, a = and b = .

1 answer:

zhuklara [117]3 years ago

4 0

Answer:

a = 2x, b = 3.

Step-by-step explanation:

8x^3+27 = (2x)^3 + 3^3

a = 2x and b = 3.

We can cube root 8x^3 getting 2x and cube root 27 getting 3.

You might be interested in

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

Luden [163]

Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

6 0

2 years ago

Alicia, Quentin, and Rosalyn are siblings. Alicia is the oldest sibling. Quentin is four years younger than Alicia. Rosalyn is t

tatiyna

Answer:

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

Step-by-step explanation:

Let the age of Alicia be x

Let the age of Quentin be y

Let the age of Rosalyn be z

If the sum of the siblings’ ages, in years, is 48 then;

x+y+z = 48.... 1

If Rosalyn is two years older than Quentin then;

z =y+2 ..... 2

Also if Quentin is four years younger than Alicia then;

y = x-4 ... 3

From 3:

x = y+4 ... 4

Substitute 2 and 4 into 1 to have:

y+4+y+y+2 = 48

3y + 6= 48

3y = 48-6

3y= 42

y = 14

Since x= y+4

x = 14+4

x = 18

Since z = y+2

z = 14+2

z = 16year

This means that;

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

6 0

2 years ago

A rectangle measures 15 2 inches by 4 3 inches. What is its area?

IRINA_888 [86]

Answer:

65.36

Step-by-step explanation:

15.2 x 4.3 = 65.36

4 0

2 years ago

HELP PLEASE ILL BE GIVING OUT 13 POINTS TO WHOEVER ANSWERS EARLY! PLEASE QUICKLY HELP

jok3333 [9.3K]

<em>Answer:</em>

D)(6(-3)/9)

<em>Step-by-step explanation:</em>

<em> -1</em>

<em>Simplify ——</em>

<em> 3 </em>

<em> -1</em>

<em>6 • ——</em>

<em> 3 </em>

<em>-2</em>

<em>If this was helpful, please mark brainliest. Have a beautiful day!</em>

<em />

7 0

3 years ago

Using faucet P, you can fill a sink in 10 minutes. Faucet Q takes only 8 minutes to fill the same sink. How long will it take to

nevsk [136]

It would take 4.44 minutes to fill the sink using both faucets P and faucet Q together

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Let t represent the time it takes to fill the sink using both faucets together, hence:

(1/10 + 1/8)t = 1

t = 4.44 minutes

It would take 4.44 minutes to fill the sink using both faucets P and faucet Q together

Find out more on equation at: brainly.com/question/2972832

#SPJ1

4 0

1 year ago