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2 years ago

The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?

Mathematics

2 answers:

adell [148]2 years ago

7 0

Answer: its C

Step-by-step explanation: i just took the test

grandymaker [24]2 years ago

3 0

Answer:

g(x) = x+5

Step-by-step explanation:

Given that,

$f(x)=x^4+5x^3-3x-15$

$q(x) = (x^3-3)$

We need to find the polynomial. We know that, Euclid division lemma states that

$f(x)=q(x)\times g(x)+r(x)$

Where

f(x) is dividend

g(x) is the poynomial

q(x) is quotient

r(x) is remainder

So,

$x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5$

So, the polynomial is (x+5).

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An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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2 years ago

When you translate to the right, the x-coordinate of a point ________.

wolverine [178]

Answer:

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Step-by-step explanation:

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3 years ago

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James bought a plant that was 3 inches tall. Each week the plant

sattari [20]

Answer:

1.5 inches/ week

Step-by-step explanation

Given

Height of he plant = 3in

If the plant grows by 2in every week

The rate of change = Height of plant/weekly increase

The rate of change = 3/2 = 1.5 inches/ week

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Examine the following graph of y=−3x+7.

likoan [24]

Y=7
X=-3
The following graph

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hoa [83]

Answer:

Step-by-step explanation:

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