Simplify (4x − 6) + (3x + 6). 7x 7x − 12 x 7x + 12

A boat travels 105 km downstream in 5 hours. The return trip upstream takes 7 hours. Find the speed of the boat in still water a

notsponge [240]

Speed of the boat = u
speed of the current = v

in downstream,
u - v = 105/5
u - v = 21

in upstream
u + v = 105/7
u + v = 15

add both equations
2u = 36
u = 18

v = -3

so
speed of the boat = 18 km/h
speed of the current = 3 km/h

4 0

3 years ago

In a study of red/green color blindness, 700 men and 2850 women are randomly selected and tested. Among the men, 66 have red/gre

olga55 [171]

Answer:

$z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197$

$p_v =P(Z>15.197) \approx 0$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

Step-by-step explanation:

Data given and notation

$X_{M}=66$ represent the number of men with red/green color blindness.

$X_{W}=8$ represent the number of women with red/green color blindness.

$n_{M}=700$ sample of male slected

$n_{W}=2850$ sample of female selected

$p_{M}=\frac{66}{700}=0.0943$ represent the proportion of male with red/green color blindness.

$p_{W}=\frac{8}{2850}=0.00281$ represent the proportion of female with red/green color blindness.

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion of men with red/green color blindness. is higher than the proportionof women with red/green color blindness. , the system of hypothesis would be:

Null hypothesis: $p_{M} \leq p_{W}$

Alternative hypothesis: $p_{M} > p_{W}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

Where $\hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{66+8}{700+2850}=0.0208$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =P(Z>15.197) \approx 0$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

8 0

3 years ago

Hellppppp me its so confusing ????!!!!

melomori [17]

I'm not sure but
A) 3 out of 20
B) 11 out of 100

3 0

3 years ago

Complete the paragraph proof.

lions [1.4K]

Answer:

wea did tha r come from??

Step-by-step explanation:

it is supposed to be d

3 0

3 years ago

Please help! I dont understand! Thank you

Digiron [165]

QUESTION A

The given inequality is

$x-1\:>\:5$

Add 1 to both sides of the inequality to obtain;

$x\:>\:5+1$

$x\:>\:6$

Answer: 2. $x\:>\:6$ , open dot at 6 and shaded to the right.(A)

QUESTION B.

The given inequality is $2x \le 6$ .

Divide both sides by 2;

$x \le \frac{6}{2}$ .

$x \le 3$ .

Answer: 5. $x \le 3$ , closed dot at 3 and shaded to the left(B).

QUESTION C

The given inequality is $x-7\:>\:-4$

Add 7 to both sides to get;

$x\:>\:-4+7$

$\Rightarrow x\:>\:3$

Answer: 7. $x\:>\:3$ , open dot at 3 and shaded to the right.(C)

QUESTION D

We want to solve;

$-2x \:$

Divide through by -2 and reverse the inequality sign;

$x \:>\:\frac{6}{-2}$

$x \:>\:-3$

Answer; 3. $x \:>\:-3$ Open dot at -3 and shaded to the right. (D)

QUESTION E

We have

$4\:$

Divide through by -4 and reverse the sign.

$\frac{4}{-4}\:>\:x$

$-1\:>\:x$

or

$x\:$

Answer: 6. $x\:$ open dot at -1, and shaded to the left(E)

QUESTION F

The given inequality is $-2x+3\:$

Add -3 to both sides to get;

$-2x\:$

Divide both sides of the inequality by -2 and reverse the sign;

$x\:>\:5$

Answer:9. $x\:>\:5$ , open dot at 5 and shaded to the right(F)

QUESTION G

The given inequality is

$5x+1\ge11$

$5x\ge11-1$

$5x\ge10$

Divide by 5

$x\ge2$

Answer ; 10. $x\ge2$ , closed dot at 2 and shaded to the right(G)

QUESTION H

We have $3(x+4)\:>\:8x-6$

Expand the bracket to get;

$3x+12\:>\:8x-6$

Group similar terms to get;

$3x-8x\:>\:-6-12$

Simplify

$-5x\:>\:-18$

Divide through by -5 and reverse the sign;

$x\:$

Answer: 1. $x\:$ Open dot at 18/5 and shaded to the left(H)

QUESTION I

We have $-3x+4\:$ .

$-3x+x\:$

$-2x\:$

Divide by -2 and reverse the sign;

$x\:>\:1$

Answer: 8. $x\:>\:1$ , open dot at 1 and shaded to the right(I)

J. The given inequality $-2(x-4)\:>\:5-(x+2)$

Expand the bracket to get;

$-2x+8\:>\:5-x-2$

Group like terms to get;

$-2x+x\:>\:5-2-8$

$-x\:>\:-5$

Divide by -1 and reverse the sign to get;

$x\:$

Answer; 4. $x\:$ , open dot at 5 and shaded to the left.(J)

6 0

4 years ago