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3 years ago

X^3+13x^2+32x+20 please help me factorizing above equation

1 answer:

7 0

$x^3+13x^2+32x+20=x^3+x^2+12x^2+ 12x+20x+20 =\\\\=x^2(x+1)+12x(x + 1 )+20(x+1 )=(x+1)(x^2+12x+20)=\\\\=(x+1)[(x^2+10x+2x+20)]=(x+1)[x(x +10)+2(x+10))]=\\\\=(x+1) (x +2) (x+10)$

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An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample

valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

3 0

3 years ago

Bella is making button barrettes. She allows each of her friends to reach into er bag of buttons and randomly pick a color.

slava [35]

Answer:

Total no. of buttons = 300 + 700 + 1000

+ 500 = 2500

Possibility for a person to pick a pink button = 300/2500 = (3/25)%

Amount of pink buttons she can expect her friends to pick = 50(3/25) = 6

She can expect to make 6 pink barrettes

Step-by-step explanation:

4 0

3 years ago

A bank says you can double your money in 10 years if you put $1,000 in a simple interest account. What annual interest rate does

katrin2010 [14]

The simple interest formula allows us to calculate I, which is the interest earned or charged on a loan. According to this formula, the amount of interest is given by I = Prt, where P is the principal, r is the annual interest rate in decimal form, and t is the loan period expressed in years. The rate r must be converted from a percentage into decimal form.

Then, 2,000 = 1,000 * r * 10 ;

Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.2

hope this helps you

8 0

3 years ago

7/8 = ?/48<br> A.13<br> B. 1<br> C. 42<br> D. 6

Ugo [173]

Hi Brainiac

7/8 =?/48

Let's replace the unknown place by x

7/8 = x/48

Cross multiply

(7)(48)= (X)(8)

336 = 8x

Flip it

8x = 336

Divide both sides by 8

8x/8 = 336/8

x= 42

The answer is C

Now if you wanna see if the answer is good just replace 42 in blank space

7/8 = 42/48

Now didivde 7 by 8 and divide 42 by 48

7/8= 0.875

42/48= 0.875

The answer C is correct

I hope that's help:)

If you have questions please let me know :)

4 0

3 years ago

Write the equation of the line that has an x-intercept of -3 and passes through the point (-3, 7).

Marina86 [1]

Answer:

$x=-3$

Step-by-step explanation:

'x = -3', when graphed, passes through the point (-3,7) and (-3,0).

Since the line passes (-3,0), the x-intercept is -3.

(-3, 7) lies on the equation.

I have attached a picture of the graphed equation.

'x = -3' should be the correct answer.

3 0

3 years ago

Read 2 more answers