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2 years ago

Write the polynomial of least degree with roots -2, 5, and 7.

1 answer:

fomenos2 years ago

3 0

For roots of -2, 5, and 7.

x = -2, x = 5, and x = 7

x = -2 x = 5    x = 7

(x + 2) = 0 (x - 5) = 0    (x - 7) = 0

The polynomial of least degree would be:
(x -2)(x - 5)(x - 7) = 0

(x -2)(x -5) = x(x - 5) - 2(x -5)

   = x² - 5x - 2x + 10

   = x² - 7x + 10

(x² - 7x + 10)(x -7)

x(x² - 7x + 10) - 7(x² - 7x + 10)

x³ - 7x² + 10x - 7x² + 49x - 70

x³ - 7x² - 7x² + 10x + 49x - 70

x³ - 14x² + 59x - 70

The least is   x³ - 14x² + 59x - 70

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Body armor provides critical protection for law enforcement personnel, but it does affect balance and mobility. The article "Imp

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Answer:

No, there is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that true average task time with armor is less than 2 seconds.

Then, the null and alternative hypothesis are:

$H_0: \mu=2\\\\H_a:\mu< 2$

The significance level is 0.01.

The sample has a size n=52.

The sample mean is M=1.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.2.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.2}{\sqrt{52}}=0.028$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1.95-2}{0.028}=\dfrac{-0.05}{0.028}=-1.803$

The degrees of freedom for this sample size are:

$df=n-1=52-1=51$

This test is a left-tailed test, with 51 degrees of freedom and t=-1.803, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.039) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

3 0

2 years ago

Which number line models the expression 1/8-(-3/4)

RideAnS [48]

Answer:

$\frac{7}{8}$

Step-by-step explanation:

Given: $\frac{1}{8}-(\frac{-3}{4} )$

To find: number which represents the expression

Solution:

Integers refers to natural numbers, 0 together with negative of rational numbers.

A rational number is the number of the form $\frac{p}{q}$ where p and q are integers and $q\neq 0$ .

$\frac{1}{8}-(\frac{-3}{4} )=\frac{1}{8}+\frac{3}{4}\\ =\frac{1+6}{8}\\ =\frac{7}{8}$

So, $\frac{7}{8}$ represents $\frac{1}{8}-(\frac{-3}{4} )$

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2 years ago

A researcher wants to estimate the mean weekly family expenditure on clothing purchases and maintenance. First, she needs to det

Blizzard [7]

Answer: C. 461

Step-by-step explanation:

We know that the formula to find the sample size is given by :-

$n=(\dfrac{z^*\cdot \sigma}{E})^2$

, where $\sigma$ = Population standard deviation from prior study.

E = margin of error.

z* = Critical value.

As per given , we have

$\sigma=125$

E= 15

Significance level : $\alpha=0.01$

Critical value (Two tailed)= $z^*=z_{\alpha/2}=z_{0.005}=2.576$

Now , Required sample size = $n=(\dfrac{(2.576)\cdot 125}{15})^2$

$n=(21.4666666667)^2\\\\ n=460.817777779\approx461$ [Round to next integer]

Hence, the required sample size to be taken is 461.

Correct answer = C. 461

3 0

2 years ago

6 tractors take 10days to collect the harvest. How long would it take 18 tractors to do the same amount of work?

Nutka1998 [239]

This is a question of proportionality. However, it is not direct proportionality as it is expected that as the number of tractors increases, the work is finished faster as opposed to fewer number of tractors. This is referred to as inverse proportionality.

Therefore;
6 tractors ----- 10 days
18 tractors --- x days

Then,
x = (6*10)/18 = 10/3 days = 3 days, and 8 hours.

This means that 18 tractors will take 3 days and 8 hours to collect the same harvest.

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2 years ago

How to factor polynomial 48a2b2-12ab

Verdich [7]

Answer - 12ab (4ab-1) :)

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2 years ago

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