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3 years ago

Help me with these math questions.

Mathematics

1 answer:

Olegator [25]3 years ago

6 0

graph A

no x-intercept

no y-intercept

H.A is y = 5

V. A. is x = 0

*****************************************

Answer: $\frac{150}{31}$

<u>Step by step explanation:</u>

log₆(5x + 6) - log₆(x - 4) = 2

log₆ $(\frac{5x+6}{x-4})$ = 2

$(\frac{5x+6}{x-4})$ = 6²

$(\frac{5x+6}{x-4})$ = 36

5x + 6 = 36(x - 4)

5x + 6 = 36x - 144

6 = 31x - 144

150 = 31x

$\frac{150}{31}$ = x

**********************************************************

Answers:

a. (-1, -5)
b. up
c. x = -1
d. $\frac{-2+\sqrt{15}}{3} and\frac{-2-\sqrt{15}}{3}$
e. -2
f. see attachment
g. domain (-∞, ∞) range [-5, ∞)

<u>Explanation:</u>

f(x) = 3x² + 6x - 2

a=3 b=6 c=-2

x = $\frac{-b}{2a} =\frac{-6}{2(3)} = \frac{-6}{6} = -1$

Axis Of Symmetry: x = -1

f(-1) = 3(-1)² + 6(-1) - 2

= 3 - 6 - 2

= -5

Vertex: (-1, -5)

x = $\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}$

= $\frac{-6+/-\sqrt{6^{2}-4(3)(-2)}}{2(3)}$

= $\frac{-6+/-\sqrt{36+24}}{6}$

= $\frac{-6+/-\sqrt{60}}{6}$

= $\frac{-6+/-2\sqrt{15}}{6}$

= $\frac{-2+/-\sqrt{15}}{3}$

x-intercepts: $\frac{-2+/-\sqrt{15}}{3}$

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B) The proportion of men that sometimes do not drive safely while talking or texting on cell phone is 32%, and the proportion of women that sometimes do not drive safely while talking or texting on cell phone is 25%.

C) There is enough evidence to support the claim that the proportion of men and women who used their cell phone in an emergency differ significantly (P-value=0.014).

Step-by-step explanation:

A. We have two populations: American men and American women. This are the populations from which we want to infere the difference of means.

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These are unbiased estimators of the populations proportions.

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The claim is that the proportion of men and women who used their cell phone in an emergency differ significantly.

Then, the null and alternative hypothesis are:

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The significance level is 0.05.

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The sample 2 (women), of size n2=643 has a proportion of p2=0.77.

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The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.7403*0.2597}{643}+\dfrac{0.7403*0.2597}{643}}\\\\\\s_{p1-p2}=\sqrt{0.0003+0.0003}=\sqrt{0.0006}=0.0245$

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$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.06-0}{0.0245}=\dfrac{-0.06}{0.0245}=-2.45$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z$

As the P-value (0.014) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of men and women who used their cell phone in an emergency differ significantly.

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