Find the factorization of the polynomial below.
81x2 - 18x + 1

Answer:

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

Step-by-step explanation:

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.

In this problem, we have that:

Mean = 185

Standard deviation = 26

The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.

What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?

133 = 185 - 2*26

So 133 is two standard deviations below the mean.

By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133

p = 0.05*0.5 = 0.025

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

The complete question is;

The height of water in a bathtub,h, is a function of time,t. Let P represent this function. Height is measured in inches and time in minutes.

Match each statement in function notation with a description.

A: P(0) = 0

B: P(4) = 10

C: P(10) = 4

D: P(20) = 0

1:After 20 minutes, the bathtub is empty.

2:The bathtub starts out with no water.

3:After 10 minutes, the height of the water is 4 inches.

4:The height of the water is 10 inches after 4 minutes.

Answer:

-option D is the correct answer for sentence 1.

-option A is the correct answer for sentence 2.

-option C is the correct answer for sentence 3.

-option B is the correct answer for sentence 4

Step-by-step explanation:

The height of water in a bathtub h is a function of time t.

-If t = 20 minutes, then height of water represented by P is empty so, P(20) = 0. Thus, option D is the correct option for sentence 1.

-The bath tub starts out with no water. Thus, P(0) = 0. So option A is the correct option for sentence 2.

-After 10 minutes, the height of the water is 4 inches. Thus, P(10) = 4. So, option C is the correct option for sentence 3.

- The height of the water is 10 inches after 4 minutes. Thus, P(4) = 10. So option B is the correct answer for sentence 4

Answer:

3,325,140 Joules

Step-by-step explanation:

Work done by the pump = Force applied to pump * distance covered by the water.

Since Force = mass * acceleration due to gravity

Force = (density of water * volume of the tank) * acceleration due to gravity

F =ρVg

Workdone = (ρVg )* d

Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m

[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]

Workdone by the pump = 1000 * 113.10 * 9.8 * 3

Workdone by the pump  = 3,325,140Joules

Answer:

a) C. The population must be normally distributed.

b) P(x < 65.8) = 0.8159

c) P(x > 64.2) = 0.3015

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me

n < 30, so the distribution of the population must be normal.

The correct answer is:

C. The population must be normally distributed.

(b) Assuming the normal model can be used, determine P(x < 65.8).

This is the pvalue of Z when X = 65.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{65.8 - 62}{4.22}[/tex]

[tex]Z = 0.9[/tex]

[tex]Z = 0.9[/tex] has a pvalue of 0.8159.

So

P(x < 65.8) = 0.8159

(c) Assuming the normal model can be used, determine P(x > 64.2).

This is 1 subtracted by the pvalue of Z when X = 64.2. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{64.2 - 62}{4.22}[/tex]

[tex]Z = 0.52[/tex]

[tex]Z = 0.52[/tex] has a pvalue of 0.6985.

1 - 0.6985 = 0.3015

So

P(x > 64.2) = 0.3015

Answer:

[tex]\pi =\frac{C}{d}[/tex]

Step-by-step explanation:

[tex]C=\pi d[/tex]

[tex]\pi =\frac{C}{d}[/tex]

Answer:

I'm not 100%sure but i'm think that it is c

Step-by-step explanation:

Hope this helps! May have gotten it wrong really sorry if I did

Corrected Question

A cylinder with a base diameter of x units has a volume of  [tex]\pi x^3[/tex] cubic units

Which statements about the cylinder are true? Check all that apply.

Answer:

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]

Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]

Volume =Base Area X Height

[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]

Therefore:

Answer:

  $18,862.91

Step-by-step explanation:

The appropriate formula is ...

 A = P(1 +r/n)^(nt)

where P is the amount invested (14,000), r is the APR (.05), n is the number of times per year interest is compounded (4), and t is the number of years (6).

Filling in the numbers and doing the arithmetic, we get ...

  A = 14,000(1 +.05/4)^(4·6) = 14,000·1.0125^24 ≈ 18,862.91

The balance after 6 years will be $18,862.91.

Answer:

Induction

Step-by-step explanation:

Induction reasoning refers to conjectures which is what you will need for this

The Inductive reasoning allows to use observation to find the next three

values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

For given example,

We have been given the number pattern 1, 4, 7, 10, . . .

Here, 4 - 1 = 3                             ..................(i)

7 - 4 = 3                                       ..................(ii)

10 - 7 = 3                                      ..................(iii)

From (i), (ii) and (iii),

the common difference between consecutive terms is 3.

The next three values would be,

10 + 3 = 13

13 + 3 = 16

16 + 3 = 19

So, the number pattern would be 1, 4, 7, 10, 13, 16, 19, . . .

Therefore, an Inductive reasoning allows to use observation to find the next three values in the number pattern 1, 4, 7, 10, . . .

The correct answer is option (B)

Learn more about the inductive reasoning here:

https://brainly.com/question/8419798

#SPJ2

Answer:

The perimeter is 26 yards

Step-by-step explanation:

Area of rectangle = A= l x w

1st rectangle = 6 x 5 = 30 yards squared

2nd rectangle= 10 x 3 = 30 yards squared

perimeter of rectangle = 2l+2w= 10 + 10 + 3 + 3= 26

Answer:

Option C is correct.

The 437 county residents were a random sample of all county residents.

a) If p is the proportion of Hispanics in the county,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.35

b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.

c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

Test statistic = -4.09

p-value = 0.000043

d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.

Step-by-step explanation:

According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.

a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).

Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).

The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).

Mathematically,

The null hypothesis is represented as

H₀: p = 0.16

The alternative hypothesis is represented as

Hₐ: p ≠ 0.16

b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.

Hence, the model of this test is two-tailled, one-proportion test.

And the major conditions for an hypothesis test is that

- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.

- The sample must be a normal distribution sample or approximate a normal distribution.

The conditions to check this is that

np ≥ 10

and

np(1-p) ≥ 10

p = sample proportion = (44/437) = 0.101

np = 437×0.101 = 44 ≥ 10

np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10

The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.

c) So, we compute the t-test statistic

z = (x - μ)/σₓ

x = sample proportion = 0.101

μ = p₀ = The proportion we are comparing against = 0.16

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 437

σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144

z = (0.101 - 0.16) ÷ 0.0144

z = -4.093 = -4.09

checking the tables for the p-value of this z-statistic

Degree of freedom = df = n - 1 = 437 - 1 = 436

Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)

The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).

p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043

The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).

d) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.000043

0.000043 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.

Hope this Helps!!!

Answer:

16

Step-by-step explanation:

[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]

Hope this helps!

x = -3

[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]

Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]

Answer: -13.37

Explanation: I did it in decimals because I didn’t know if your assignment required fraction or decimal. 5 4/7= 5x7=35+4=39/7 so this means 5 4/7 is equal to 39/7. -2 2/5= -2x5=-10+2=-8/5. So it comes out to 39/7x-8/5.

Answer:

r = 4.2805cm

Step-by-step explanation:

ok first the shape its made of two slant height and and an arc of degree 70°

The total perimeter = 28cm

The formula for the total perimeter= 2l + 2πl(70/360)

Where l is the radius of the shape.

But l = 2r

So

= 2l + 1.2217l

= 3.2217l

28 = 3.2217l

l = 28/3.2217

l = 8.691

Recall that l = 2r

8.691= 2r

r = 8.691/2

r = 4.2805cm

Answer:

Step-by-step explanation:

a) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 451

x = 1.5/100 × 451 = 7

p = 7/451 = 0.02

q = 1 - 0.02 = 0.98

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.97 = 0.1

α/2 = 0.01/2 = 0.03

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.03 = 0.97

The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17

Therefore, the 97% confidence interval is

0.02 ± 2.17√(0.02)(0.98)/451

= 0.02 ± 0.014

b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

The distribution that should be used is the normal distribution

Answer:

StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction

Solve the proportion for x.

After using cross products, the proportion becomes the equation

✔ 4x = 10

.

Isolate the variable by dividing both sides of the equation by

✔ 4

.

x = ✔ 2.5

.

The value of x is 2.5 for the given proportion.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

The proportion is given in the question, as follows:

4/2 = 5/x

Using cross-product, the proportion becomes the equation as:

4x = 2 × 5

4x = 10

Divide by 4 into both sides of the above equation,

x = 10/4

x = 2.5

Thus, the value of x is 2.5 for the given proportion.

Learn more about the proportion here:

brainly.com/question/1504221

#SPJ3

Answer:

Step-by-step explanation:

The answer is 54.5 on edg

For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.

[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]

Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.

The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.

Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,

[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]

Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.

For the second part, we need to find the value of x. Thus solve the above equation further as,

[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]

Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

Learn more about the right angle triangle property here;

https://brainly.com/question/22790996

Answer:

8x10^13

Step-by-step explanation:

Answer

A. 18(3/4)π

Explanation

In the attached file

Answer:

[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]

Step-by-step explanation:

[tex]6(1)-2=4[/tex]

[tex]6(2)-2=10[/tex]

[tex]5 \times 3^{(3)-1}=45[/tex]

[tex]5 \times 3^{(4)-1}=135[/tex]

[tex]5(-1^{(5)}+3)=10[/tex]

[tex]5(-1^{(6)}+3)=20[/tex]

a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)

b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹

c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is  an = 10 + 10 * ((n + 1) % 2)

(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.

(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.

To learn more about sequence click on,

https://brainly.com/question/30525908

#SPJ2

Answer:

10/18

=5/9

pls mark as brainliest

Answer:

5/9

Step-by-step explanation:

6 red cards, 8 green cards and 4 blue cards =  18 total cards

not green cards = 6 red+ 4 blue = 10 cards

P( not green) = number not green / total

                      = 10/18

                      =5/9

Answer:

X

Step-by-step explanation:

X and Y make up a graph

Answer:

A. Yes. Each subject is randomly assigned to a treatment

Step-by-step explanation:

In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.

In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.

Answer:

-4 · [tex]4^{7}[/tex]

Step-by-step explanation:

Answer;

1) The t-distribution is most suitable for this problem.

2) Test statistic = 2.356

3) p-value = 0.0214

4) Alpha = 5% = 0.05

5) The p-value is greater than the significance level at which the test was performed, meaning that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.

Step-by-step Explanation:

Wife's score 2 2 3 3 4 2 1 1 2 4

Husband's score 2 1 2 3 2 1 1 1 2 4

To conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife, we first take the difference in the respomses of wives and husbands

x = (wife's score) - (husband's score)

Wife's score 2 2 3 3 4 2 1 1 2 4

Husband's score 2 1 2 3 2 1 1 1 2 4

Difference | 0 | 1 | 1 | 0 | 2 | 1 | 0 | 0 | 0 | 0

To use the hypothesis test method, we have to make sure that the distribution is a random sample of the population and it is normally distributed.

The question already cleared these two for us that this sample size is randomly selected from the population and each variable is independent from the other.

The question also already explained that the distribution is assumed to be normally distributed.

1) The distribution to use for this test is the t-distribution. This is because the sample size isn't very large and we have no information about the population mean and standard deviation.

For any hypothesis testing, we must first define the null and alternative hypothesis

Since we want to investigate whether the husbands are happier, that the mean difference is negative, that is less than 0,

The null hypothesis, which normally counters the claim to be investigated, would be that there isnt evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness isn't less than 0, that it is equal to or greater than 0.

And the alternative hypothesis, which usually confirms the claim to be tested, is that there is significant evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness is less than 0.

Mathematically, if μ is the mean difference in happiness of wives and husbands,

The null hypothesis is represented as

H₀: μ ≥ 0

The alternative hypothesis is represented as

Hₐ: μ < 0

2) To obtain the test statistic, we need the mean and standard deviation first.

Mean = (sum of variables)/(number of variables) = (5/10) = 0.5

Standard deviation = σ = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = 6(0 - 0.5)² + 3(1 - 0.5)² + (2 - 0.5)² = 1.5 + 0.75 + 2.25 = 4.5

σ = √(4.5/10) = 0.671

we compute the t-test statistic

t = (x - μ)/σₓ

x = sample mean difference = 0.50

μ = 0

σₓ = standard error of the sample mean = (σ/√n)

where n = Sample size = 10,

σ = Sample standard deviation = 0.671

σₓ = (0.671/√10) = 0.2122

t = (0.50 - 0) ÷ 0.2122

t = 2.356

3) checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 10 - 1 = 9

Significance level = 5% = 0.05

The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for t = 2.356, at 0.05 significance level, df = 9, with a one tailed condition) = 0.021441 = 0.0214

4) Alpha = significance level = 5% = 0.05

5) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.0214

0.0214 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.

Hope this Helps!!

Answer:

what's the question?

it's not showing

Answer:

C.

Step-by-step explanation:

To find the perimeter, we'll use the distance formula

Distance Formula = √(x₂-x₁)²+(y₂-y₁)²

Finding Distance of AB

|AB| = √(-2+5)²+(3+1)²

|AB| = √25

|AB| = 5

Now For BC

|BC| = √(6+2)²+(-3-3)²

|BC| = √(8)²+(-6)²

|BC| = √100

|BC| = 10

FOR CA:

|CA| = √(-5-6)²+(-3+1)²

|CA| = √125

Perimeter of Triangle = 10 + 5 + √125

= 15 + √125

Answer:

Step-by-step explanation:

The monthly interest rate is ...

  [tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]

a) The monthly payment is given by the amortization formula:

  A = Pr/(1 -(1+r)^-n)

where r is the monthly interest rate on a loan of amount P for n months.

  A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95

The monthly payment is $1214.95.

__

b) The amount to interest is the product of the remaining principal and the monthly interest rate.

 first month's interest = $140,000·0.0070833 = $991.67

__

c) The balance after the first payment is ...

  new balance = $140,000 +991.67 -1214.95 = $139,776.72

__

d) The amount to interest for the second payment is computed the same way:

  second month's interest = $139,776.72·0.00708333 = $990.09

__

e) The balance after the second payment is computed the same way:

  new balance = $139,776.72 +990.09 -1214.95 = $139,551.86

Answer:

That can be factored as

(x -1  (1/3) ) * ( x +3) * (x -4/5)

and the zeroes are located at:

x = 1.33333333...   x = -3    and x = .8

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ f(x)=(x+3)(5x-4)(3x-4) \ \ \ }[/tex]

Step-by-step explanation:

We need to factorise the following function

[tex]f(x)=15 x^3+13 x^2-80 x+48[/tex]

-3 is a trivial solution, we can notice that f(-3)=0

so we can factorise by (x+3)

let s note a, b and c real and let s write

[tex]f(x)=15 x^3+13 x^2-80 x+48=(x+3)(ax^2+bx+c)[/tex]

[tex](x+3)(ax^2+bx+c) = ax^3+bx^2+cx+3ax^2+3bx+3c=ax^3+(b+3a)x^2+(3b+c)x+3c[/tex]

let s identify...

the terms in [tex]x^3[/tex]

   15 = a

the terms in [tex]x^2[/tex]

   13 = b + 3a

the terms in x

   -80 = 3b+c

the constant terms

   48 = 3c

so it comes, c=48/3=16, a = 15, b = 13-3*15=13-45=-32

so [tex]f(x)=(x+3)(15x^2-32x+16)[/tex]

[tex]\Delta=32^2-4*15*16=64[/tex]

so the roots of [tex](15x^2-32x+16)[/tex] are

[tex]\dfrac{32-8}{15*2}=\dfrac{24}{30}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]

and

[tex]\dfrac{32+8}{15*2}=\dfrac{40}{30}=\dfrac{20}{15}=\dfrac{4}{3}[/tex]

so [tex]f(x)=(x+3)(5x-4)(3x-4)[/tex]

the zeros are -3, 4/5, 4/3

Answer:

So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.

70+N/4 = 120

480 = 70+N

So then we subtract 70 from both sides.  Then we get 410 = N.

The answer is

Answer:

Yes

Step-by-step explanation:

1 book = $4

2 books = 2*$4

3 books = 3*$4

4 books = 4*$4

5 books = 5*$4

This can be shown as:  y=4x

y=ax+b is linear function, Irena is right