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Otrada [13]
3 years ago
12

© A boy has N800. He spends N160. What

Mathematics
2 answers:
Gre4nikov [31]3 years ago
6 0
Answer: 4/5

Explanation:

800 - 160 = 640

640/800= 8/10 = 4/5
Anni [7]3 years ago
5 0

Answer:

4/5

Step-by-step explanation:

800 - 160 = 640  \\   \frac{640}{800}  =  \frac{4}{5}

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The freight is traveling at a constant speed the table below shows how far the train travels after different amounts of time com
Artist 52 [7]
Using  the 2nd row it traveled 120 miles in 3 hours
 so 120/3 = 40 miles per hour

so distance (d) = 40h
5 0
3 years ago
A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury levels. To confirm that
suter [353]

Answer:

a. The 95% confidence interval for the difference between means is (0.071, 0.389).

b. There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.

c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.

In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.

In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.

Step-by-step explanation:

The table with the data is:

Sample 1 Sample 2

0.580    0.382

0.711      0.276

0.571     0.570

0.666    0.366

0.598

The mean and standard deviation for sample 1 are:

M=\dfrac{1}{5}\sum_{i=1}^{5}(0.58+0.711+0.571+0.666+0.598)\\\\\\ M=\dfrac{3.126}{5}=0.63

s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.58-(0.63))^2+...+(0.598-(0.63))^2]}\\\\\\            s=\sqrt{\dfrac{1}{4}\cdot [(0.002)+(0.007)+(0.003)+(0.002)+(0.001)]}\\\\\\            s=\sqrt{\dfrac{0.015}{4}}=\sqrt{0.0037}\\\\\\s=0.061

The mean and standard deviation for sample 2 are:

M=\dfrac{1}{4}\sum_{i=1}^{4}(0.382+0.276+0.57+0.366)\\\\\\ M=\dfrac{1.594}{4}=0.4

s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(0.382-(0.4))^2+(0.276-(0.4))^2+(0.57-(0.4))^2+(0.366-(0.4))^2]}\\\\\\            s=\sqrt{\dfrac{1}{3}\cdot [(0)+(0.015)+(0.029)+(0.001)]}\\\\\\            s=\sqrt{\dfrac{0.046}{3}}=\sqrt{0.015}\\\\\\s=0.123

<u>Confidence interval</u>

We have to calculate a 95% confidence interval for the difference between means.

The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.

The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.

The difference between sample means is Md=0.23.

M_d=M_1-M_2=0.63-0.4=0.23

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

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07

The critical t-value for a 95% confidence interval is t=2.365.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_{M_d}=2.365 \cdot 0.07=0.159

Then, the lower and upper bounds of the confidence interval are:

LL=M_d-t \cdot s_{M_d} = 0.23-0.159=0.071\\\\UL=M_d+t \cdot s_{M_d} = 0.23+0.159=0.389

The 95% confidence interval for the difference between means is (0.071, 0.389).

<u>Hypothesis test</u>

This is a hypothesis test for the difference between populations means.

The claim is that the fish in this particular polluted lake have signficantly elevated mercury levels.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0

The significance level is 0.05.

The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.

The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.

The difference between sample means is Md=0.23.

M_d=M_1-M_2=0.63-0.4=0.23

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

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07

Then, we can calculate the t-statistic as:

t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.23-0}{0.07}=\dfrac{0.23}{0.07}=3.42

The degrees of freedom for this test are:

df=n_1+n_2-1=5+4-2=7

This test is a right-tailed test, with 7 degrees of freedom and t=3.42, so the P-value for this test is calculated as (using a t-table):

\text{P-value}=P(t>3.42)=0.006

As the P-value (0.006) 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 fish in this particular polluted lake have signficantly elevated mercury levels.

<u> </u>

c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.

In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.

In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.

7 0
3 years ago
HELP PLEASE!! Victoria and Jennifer walk at a different averagr speed. Victoris walks at an average speed of 1 1/5 miles in 1/2
Zanzabum

Answer:

Jennifer

4/15 mph

Step-by-step explanation:

First, we find the two speeds in miles per hour.

Victoria:

1 1/5 mile per 1/2 hour = (1 1/5 mile)/(1/2 hour) = 2 2/5 mph = 2.4 mph

Jennifer:

2/3 mile per 1/4 hour = (2/3 mile)/(1/4 hour) = 8/3 mph = 2 2/3 mph

2 2/3 mph > 2 2/5 mph, so Jennifer's speed is greater.

The difference in speeds in mph is:

2 2/3 - 2 2/5 = 2 10/15 - 2 6/15 = 4/15

5 0
2 years ago
Read 2 more answers
Write an equation that is not a linear function explain why it is not linear​
Gre4nikov [31]

Answer:

x=y^2

Step-by-step explanation:

cause the definition of equation is one x correspond to one y,but one y can correspond to 2 x,

the picture I give to you a x correspond to 2 y

3 0
3 years ago
Two angles are supplementary. One angle measures 16 degrees less than 3 times the other. Find the measure of each angle.
Arisa [49]
Y = 1st angle
X = 2nd angle

Y = 3X - 16

90 = X + Y

90 = X + (3X -16)

Do some algebra and X=26.5

So substitute x back in to find y, and Y=63.5
5 0
3 years ago
Read 2 more answers
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