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3 years ago

What is the distance between -34 and -11 on a number line?

Mathematics

2 answers:

const2013 [10]3 years ago

7 0

im fairly sure the answer is 23

Kaylis [27]3 years ago

4 0

Answer:

The distance between -34 and -11 is 23

Step-by-step explanation:

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Find the value of k such that x-2 is a factor of 3x³-kx²+5x+k

Nuetrik [128]

Answer:

$\displaystyle k = \frac{34}{3}$

Step-by-step explanation:

We are given the polynomial:

$\displaystyle P(x) = 3x^3 - kx^2 + 5x + k$

And we want to determine the value of k such that (x - 2) is a factor of the polynomial.

Recall that the Factor Theorem states that a binomial (x - a) is a factor of a polynomial P(x) if and only if P(a) = 0.

Our binomial factor is (x - 2). Thus, a = 2.

Hence, by the Factor Theorem, P(2) must equal zero.

Find P(2):

$\displaystyle \begin{aligned} P(2) &= 3(2)^3 - k(2)^2 + 5(2) + k \\ \\ &= 3(8) - 4k + 10 + k \\ \\ &= 34 - 3k \end{aligned}$

This must equal zero. Hence:

$\displaystyle \begin{aligned} 34 - 3k &= 0 \\ \\ -3k &= -34 \\ \\ k = \frac{34}{3} \end{aligned}$

In conclusion, k = 34/3.

6 0

2 years ago

Over the last three evenings, Ashley received a total of 106 phone calls at the call center. The third evening, she received 2 t

V125BC [204]

Change X and Z. X is first evening
Y is second
Z is third evening

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3 years ago

A line passes through the point (3,2) and (6,2) a write an equation for the line in point-slope form rewrite the equation in sta

NeTakaya

(3, –2) and (6, 2)First, we must establish slope...m=(y-y1)/(x-x1)m=(-2-2)/(3-6)m=-4/-3m=4/3Point slope formula is...y-y1=m(x-x1)Let's select either coordinate. I randomly select the first (3, –2)...y--2=4/3(x-3)Subtracting a negative number is the same as adding a positive number...y+2=4/3(x-3)This corresponds to the first answer.Standard form...Ax+By=Cy+2=(4/3)x-4y=(4/3)x-6-(4/3)x+y=-6Multiply both sides by 3...-4x+3y=-18This also corresponds to the first answer. How about the second coordinate, (6, 2)...y-y1=m(x-x1)y-2=(4/3)(x-6)Let's convert it into standard form..y-2=(4/3)x-8y=(4/3)x-6-(4/3)x+y=-6Multiply both sides by 3...-4x+3y=-18

8 0

3 years ago

What is the picture equal to? Help please

amm1812

$25(3n - 2) \\ \\ 1. \: 25 \times 3n + 25 \times - 2 \\ 2. \: 75n + 25 \times - 2 \\ 3. \: 75n - 50$

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2 years ago

A consulting firm had predicted that 35% of the employees at a large firm would take advantage of a new company Credit Union, bu

m_a_m_a [10]

Answer:

a) 0.4770

b) 3.9945

c) z-statistics seem a large value

Step-by-step explanation:

a. Find the standard deviation of the sample proportion based on the null hypothesis

Based on the null hypothesis:

$p_{0}$ : 0.35

and the standard deviation σ = $\sqrt{p_{0} *(1-p_{0}) }$ = $\sqrt{0.35 *0.65 }$ ≈0.4770

b. Find the z statistic

z-statistic is calculated as follows:

z= $\frac{X-p_{o} }{\frac{s}{\sqrt{N} } }$ where

X is the proportion of employees in the survey who take advantage of the Credit Union ( $\frac{138}{300}=0.46$ )
$p_{0}$ is the proportion in null hypothesis (0.35)
s is the standard deviation (0.4770)
N is the sample size (300)

putting the numbers in the formula:

z= $\frac{0.46-0.35} }{\frac{0.4770}{\sqrt{300} } }$ = 3.9945

c. Does the z statistic seem like a particularly large or small value?

z-statistics seem a large value, which will cause us to reject the null hypothesis.

4 0

3 years ago