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3 years ago

What is the quotient (6x4 + 15x3 − 2x2 + 10x − 4) ÷ (3x2 + 2)?

Mathematics

2 answers:

Kay [80]3 years ago

4 0

Answer:

$2x^2+5x-2$

Step-by-step explanation:

$(6x^4 + 15x^3 - 2x^2 + 10x -4)$ ÷ (3x2 + 2)

To divide it we use long division

$2x^2+5x-2$

------------------------------------------

$3x^2+0x + 2$ $6x^4 + 15x^3 - 2x^2 + 10x -4$

$6x^4 +0x^3+4x^2$

---------------------------------------------------(subtract)

$15x^3-6x^2+10x$

$15x^3+0x^2+10x$

-----------------------------------------------(subtract)

$-6x^2+0x-4$

-------------------------------------------------------

VMariaS [17]3 years ago

3 0

The given problem is :

(6x^4 + 15x^3 − 2x^2 + 10x − 4) ÷ (3x^2 + 2)?

now we can write expression (6x^4 + 15x^3 − 2x^2 + 10x − 4) as

(6x^4 + 4x^2 + 15x^3 + 10x - 6x^2 -4)

we have somehow arrange the expression in a way that 3x^2 + 2 is common

now the expression comes out to be

2x^2(3x^2 + 2) + 5x(3x^2+2) -2(3x + 2) / (3x^2+2)

After dividing final result comes out to be (2x^2 + 5x -2)

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gizmo_the_mogwai [7]

Answer:

$t=\frac{9.1-8}{\sqrt{\frac{(1.9)^2}{40}+\frac{(2.1)^2}{50}}}}=2.604$

$p_v =2*P(t_{(88)}>2.604)=0.0108$

So the p value is a very low value and using any significance level for given $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that the two means are significantly different at 5%

Step-by-step explanation:

Data given and notation

$\bar X_{1}=9.1$ represent the mean for the sample 1

$\bar X_{2}=8$ represent the mean for the sample 2

$s_{1}=1.9$ represent the sample standard deviation for the sample 1

$s_{2}=2.1$ represent the sample standard deviation for the sample 2

$n_{1}=40$ sample size for the group 1

$n_{2}=50$ sample size for the group 2

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean are different , the system of hypothesis would be:

Null hypothesis: $\mu_{1} = \mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

If we analyze the size for the samples both are higher than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) the results obtained like this:

$t=\frac{9.1-8}{\sqrt{\frac{(1.9)^2}{40}+\frac{(2.1)^2}{50}}}}=2.604$

Statistical decision

The first step is calculate the degrees of freedom, on this case:

$df=n_{1}+n_{2}-2=40+50-2=88$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{(88)}>2.604)=0.0108$

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3 years ago

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Alex17521 [72]

Answer:

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3 years ago

A box of cereal costs $3.49. How much do a dozen boxes of cereal cost?

antiseptic1488 [7]

Answer:

41.88

Step-by-step explanation:

3.49*12=41.88

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2 years ago

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HELP!!Part B What is the approximate volume of each slice that Hattie's grandma cut? (arc length of each slice is 3 in, vol. of

GalinKa [24]

The approximate volume of each slice will be 63.5 inch². The total cake is divided into the four cylindrical slice.

<h3>What is volume?</h3>

It is defined as a three-dimensional space enclosed by an object or thing.

The volume of the slice is;

$\rm V = \pi r^2 h\\\\\ \rm 81 \pi = \pi \times (r)^2 \times 4 \\\\ r= 4.5 \ inch$

If the grandma cut four pieces, is the approximate volume of each slice that Hattie's grandma cut will be;

The approximate volume of each slice will be;

$\rm V = \PI r^2 h \\\\ \rm V = 3.14 \times (4.5)^2 \times 1 \\\\ V=63.5 \ inch^2$

Hence, the approximate volume of each slice will be 63.5 inch².

Learn more about the volume here:

brainly.com/question/16788902

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2 years ago

Rebecca needs 10 ½ yards of fabric to make a quilt. She has one piece of fabric that is 2 ½ yards and another piece of fabric th

muminat

Answer:

3 $\frac{3}{4}$ yards of fabric

Step-by-step explanation:

In order to solve this problem, we should first make all of the fractions have common denominators. To do so we can turn the 1/2s into 2/4 which both equal 0.5 or 50%. Now we simply need to add together the pieces of quilt that she has and subtract that value from the total that she needs in order to calculate the amount of quilt that she is missing.

10 $\frac{2}{4}$ - (2 $\frac{2}{4}$ + 4 $\frac{1}{4}$ ) = x

10 $\frac{2}{4}$ - 6 $\frac{3}{4}$ = x

3 $\frac{3}{4}$ = x

Finally, we can see that Rebecca needs a total of 3 $\frac{3}{4}$ yards of fabric to finish her quilt.

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