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4 years ago

10

Four students have summer jobs. The table shows how much each student earns after working a certain number of hours. Which stude

nt earns the highest hourly wage.

1 answer:

Ivan4 years ago

5 0

Answer:

C Jacob

Step-by-step explanation:

Alfredo: 157.5/18 = 8.75

Helene: 198/24 = 8.25

Jacob: 142.5/15 = 9.53

Leonna: 111/12 = 9.25

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S12 for the series 1+2+4+8+

Maru [420]

$S_{12}=1+2+4+8+\cdots+2048$
$S_{12}=2^0+2^1+\cdots+2^{11}$
$2S_{12}=2^1+2^2+\cdots+2^{12}$

$\implies S_{12}-2S_{12}=2^0-2^{12}$
$-S_{12}=1-2^{12}$
$S_{12}=2^{12}-1$
$S_{12}=4096-1=4095$

8 0

3 years ago

A magazine reports that women trust recommendations from a particular social networking site more than recommendations from any

Misha Larkins [42]

Answer:

a) $p_A$ represent the real population proportion for women

$\hat p_A =\frac{123}{150}=0.82$ represent the estimated proportion for women

$n_A=150$ is the sample size selected for women

b) $p_B$ represent the real population proportion for male

$\hat p_B =\frac{102}{170}=0.6$ represent the estimated proportion for male

$n_B=170$ is the sample size selected for male

c) $(0.82-0.6) - 1.96 \sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.124$

$(0.82-0.6) + 1.96 \sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.316$

And the 95% confidence interval would be given (0.124;0.316).

We are confident at 95% that the difference between the two proportions is between $0.124 \leq p_A -p_B \leq 0.316$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

$p_A$ represent the real population proportion for women

$\hat p_A =\frac{123}{150}=0.82$ represent the estimated proportion for women

$n_A=150$ is the sample size selected for women

Part b

$p_B$ represent the real population proportion for male

$\hat p_B =\frac{102}{170}=0.6$ represent the estimated proportion for male

$n_B=170$ is the sample size elected for male

$z$ represent the critical value for the margin of error

Part c

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$(0.82-0.6) - 1.96 \sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.124$

$(0.82-0.6) + 1.96 \sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.316$

And the 95% confidence interval would be given (0.124;0.316).

We are confident at 95% that the difference between the two proportions is between $0.124 \leq p_A -p_B \leq 0.316$

8 0

3 years ago

Christine watched a video for 3/8 minutes and she watched another video for 1/8 minutes how long did she watch videos in l

pashok25 [27]

Answer:

4/8=1/2 minutes

Step-by-step explanation:

You just add 3/8+1/8 and you get 4/8 and you can simplify that down to 1/2 minutes (half of a minute or 30 seconds)

3 0

3 years ago

angle 1 and angle 2 are vertical angles. if the measure of angle 1 is (6x+11)° and measure of angle 2 is (10x-9)° find measure o

Svetradugi [14.3K]

Answer:

Angle 1 = 41°

Step-by-step explanation:

Since they are both vertical angles

(6x+11)° = (10x-9)°

6x - 10x = -9 - 11

-4x = -20

4x = 20

x= 5.

Therefore,

Angle 1 = 6(5) + 11

Angle 1 = 30 + 11

Angle 1 = 41°

5 0

3 years ago

Evaluate f(x) = 2x - 4 for x = 5

algol13

Plug in x = 5
f(5) = 2(5) - 4
f(5) = 10 - 4
Solution: f(5) = 6

8 0

3 years ago