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2 years ago

What is the quotient of (x3 3x2 5x 3) Ă· (x 1)? x2 4x 9 x2 2x x2 2x 3 x2 3x 8.

Mathematics

1 answer:

Rina8888 [55]2 years ago

4 0

The quotient of expression is $\rm x^2+2x+3$ .

Given that,

Expression; $\rm\dfrac{ (x^3 + 3x^2 + 5x + 3) }{ (x + 1)}$

We have to determine,

The quotient of expression?

According to the question,

To determine the quotient of expression following all the steps given below.

Simplify the expression,

$\rm =\dfrac{ (x^3 + 3x^2 + 5x + 3) }{ (x + 1)}\\\\= \dfrac{ (x^3 + 2x^2 + 3x + x^2+2x+ 3) }{ (x + 1)}\\\\ = \dfrac{ x(x^2+ 2x+ 3) + 1(x^2+2x+ 3) }{ (x + 1)}\\= \dfrac{ (x^2+ 2x+ 3) (x+1) }{ (x + 1)}\\\\= x^2+2x+3$

Hence, The required quotient of expression is $\rm x^2+2x+3$ .

For more details refer to the link given below.

brainly.com/question/12895249

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Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale

nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) $Z = 1.05$

e) $Z = -1.10$

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

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.

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.

In this problem, we have that:

$\mu = 515, \sigma = 100$

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 620. So

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

$Z = \frac{620 - 515}{100}$

$Z = 1.05$

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 405. So

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

$Z = \frac{405 - 515}{100}$

$Z = -1.10$

3 0

4 years ago

What is three different ways to write 5^11 power as the product of two different powers please help.

Veronika [31]

Answer:

Three ways to write 5^11

In product:48828125

In powers:

$5^{11}$

5 to the power of 11

Step-by-step explanation:

I learned this before in class like few years ago

4 0

3 years ago

Read 2 more answers

Will mark brainlist for anyone who answers these parts correctly and properly showed their work.

dalvyx [7]

Answer:

The rise is -5 the run is 4

Step-by-step explanation:

Slope (m) =

ΔY

ΔX

-5

-1.25

θ =

arctan(

ΔY

) + 360°

ΔX

308.65980825409°

ΔX = 2 – -2 = 4

ΔY = -1 – 4 = -5

Distance (d) = √ΔX2 + ΔY2 = √41 = 6.4031242374328

Equation of the line:

y = -1.25x + 1.5

y =

When x=0, y = 1.5

When y=0, x = 1.2

Please give brainliest PLZPLZ

I really hope this helps have a beautiful day

3 0

3 years ago

Please help me with this problem! If anybody answers first in this, i will give brainliest to you! Be the first one to answer th

MA_775_DIABLO [31]

Answer:

32 remainder 2

Step-by-step explanation:

To divide 162 by 5, we simply do the following:

5 goes into 16 => 3

Multiply 5 by 3 => 3 × 5 = 15

Subtract 15 from 16 => 16 – 15 = 1

Put the 1 before 2 => 12

5 goes into 12 => 2

Multiply 5 by 2 => 5 × 2 = 10

Subtract 10 from 12 => 12 – 10 => 2

In summary,

162 divided by 5 => 32 remainder 2

Please see attached photo for further details.

4 0

3 years ago

What is fractions on a lineplot question 5

Ghella [55]

So, we know that

4/5n = 2/3

n = 2/3 x 5/4 . . . . .. if fraction is moved to other side of the equation the numerator and denominator will be swithced

n = 10/12 ......................... divide numerator and denominator by 2

n = 5/6

The answer is Fraction 5 over 6 hopes this help

7 0

3 years ago