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3 years ago

Please help solve with steps

Mathematics

1 answer:

serg [7]3 years ago

7 0

Answer:

6 6/11, 6.547, 131/20, 6.77.

Step-by-step explanation:

First convert to decimal values.

131/20 = 6.55

6.77

6 6/11 = 6.54545

6.547

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Help me with #4

Sladkaya [172]

Step-by-step explanation:

a. lim(x→2) [g(x) + h(x)]

Use additive property of limits.

= lim(x→2) g(x) + lim(x→2) h(x)

= 0 + 5

= 5

b. lim(x→2) [3 h(x)]

Use multiplication property of limits.

= [lim(x→2) 3] [lim(x→2) h(x)]

= 3 lim(x→2) h(x)

= 3 (5)

= 15

c. lim(x→2) [g(x) h(x)]

Use multiplication property of limits.

= [lim(x→2) g(x)] [lim(x→2) h(x)]

= (0) (5)

= 0

6 0

3 years ago

I need help with this problem.

sdas [7]

Answer:

$\text{4}\quad -3x^{-1}+x^{-2}$

Step-by-step explanation:

The answer choices suggest there is a common factor of (x+2) that can be removed from numerator and denominator.

The denominator factors as ...

$x^3+2x^2=x^2(x+2)$

The numerator obviously has no factors of x. We can try any of several means to determine if (x+2) is a factor. I tried synthetic division and found that the numerator can be written as ...

$-3x^2-5x+2=(-3x+1)(x+2)$

Then the expression simplifies to ...

$\dfrac{-3x^2-5x+2}{x^3+2x^2}=\dfrac{(-3x+1)(x+2)}{x^2(x+2)}\\\\=\dfrac{-3x+1}{x^2}=\dfrac{-3x}{x^2}+\dfrac{1}{x^2}=-3x^{-1}+x^{-2} \qquad\text{matches choice 4}$

4 0

3 years ago

State the number of possible real zeros and turning points of f(x) = x7 – 6x6 + 8x5. Then determine all of the real zeros by fac

Rudiy27

Answer:

steps below

Step-by-step explanation:

f(x) = x⁷ – 6x⁶ + 8x⁵

f'(x) = 7x⁶ - 36x⁵ + 40x⁴

= x⁴ (7x² - 36x + 40) ... (1)

Critical point (x,y): x = 0 , x = (36 ± √(-36)²-4*7*40) / (2*7) = (18±2√11) / 7

x = 0 or x = 3.5 or x = 1.6

plug into (1): y = 0 , y = -394.3 , y = 10.1

extreme : maximum (1.6 , 10.1) minimum (3.5 , -394.3) ... turning points

x⁷ – 6x⁶ + 8x⁵ = x⁵ (x² - 6x + 8) = x⁵ (x-2) (x-4) =0

real zeros: x = 0, x=2, x=4

3 0

3 years ago

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

irakobra [83]

Answer:

We need a sample size of at least 383.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

85% confidence level

So $\alpha = 0.15$ , z is the value of Z that has a pvalue of $1 - \frac{0.15}{2} = 0.925$ , so $Z = 1.44$ .

How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03

We need a sample size of at least n.

n is found with $M = 0.03, \pi = 0.21$