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3 years ago

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Anu and Eby went on a hiking trip that was 36 km. Amy's backpack weighed 7kg and Eby's backpack 8kg. They hiked 9km the 1st day

and 6km the 2nd day. If they hiked equal number of km the next 3 days, how many km a day did they hike on these days?

1 answer:

luda_lava [24]3 years ago

4 0

Answer: 7km

Step-by-step explanation:

Hi, to answer this question, first we have to add the kilometers hiked in the first 2 days.

9km+6km= 15km

Since the trip was 36km, we have to subtract 15 to 36:

36-15= 21 km left

Since they hiked an equal number of km the next 3 days, we have to divide the remaining km by 3:

21/3 = 7km

Feel free to ask for more if needed or if you did not understand something.

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At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical popul

vampirchik [111]

Answer:

a) Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b) The 95% confidence interval would be given by (910.05;959.95)

c) Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d) $z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

Step-by-step explanation:

a. State the hypotheses.

On this case we want to check the following system of hypothesis:

Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x¯¯¯= 935?

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".

$\bar X=935$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=180$ represent the population standard deviation

n=200 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=3278.222$

The sample deviation calculated $s=97.054$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$935-1.96\frac{180}{\sqrt{200}}=910.05$

$935+1.96\frac{180}{\sqrt{200}}=959.95$

So on this case the 95% confidence interval would be given by (910.05;959.95)

c. Use the confidence interval to conduct a hypothesis test. Using α= .05, what is your conclusion?

Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d. What is the p-value?

The statistic is given by:

$z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

If we replace we got:

$z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

So then since the p value is less than the significance we can reject the null hypothesis at 5% of significance.

8 0

3 years ago

Andre45 [30]

A. Yes B. Yes C. No.

4 0

3 years ago

The sum of three numbers is 10. Two times the second number minus the first number is equal to 12.

eimsori [14]

<u>Answer:</u>

-10,1,19

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

<u></u>

x+y+z = 10 (Equation 1)

2y-x= 12 (Equation 2)

x-y+2z = 7 (Equation 3)

(Equation 2): -x = -2y+12

x = 2y-12 (Equation 4)

(Equation 1) - (Equation 3): 2y-z = 3

-z = -2y+3

z = 2y-3 (Equation 5)

Substitute (4) and (5) into (1)

x+y+z = 10

(2y-12)+y+(2y-3) = 10

5y-15 = 10

5y = 5

y=1

Substitute y=1 into (2)

2y-x= 12

2(1)-x= 12

2-x= 12

-x= 12-2

-x= 10

x= -10

Substitute y=1 and x=-10 into (1)

x+y+z = 10

-10+1+z = 10

z-9 = 10

z = 10+9

z = 19

Order: x = -10, y = 1, and z = 19

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3 years ago

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X + y = 0<br> x - y = 4 <br> Then what does x =

mylen [45]

X - (-x) = 4
2x = 4

x=2

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3 years ago

Can you solve this? ;)

katovenus [111]

Hi there!

The answer is C.
$25x + 12y + 4 \leqslant 130$

The question has already revealed the following data:
x = number of tickets.
y = number of t-shirts.

We can now find the total cost function.
The cost of 1 ticket is $ 25
and therefore the total cost for all of the tickets is $25 ×
the amount of tickets, mathematically $25 × x, hence 25x.

The cost of 1 shirt is $ 12
and therefore the total cost for all of the tickets is $12 ×
the amount of shirts, mathematically $12 × y, hence 12y.

When making the total cost function, don't forget to include the service fee of $4.

Now we can conclude that the total cost function is the following:
$25x + 12y + 4$

Maya only has $130 and therefore the total cost must be smaller than or equal to this amount of money. The answer is C.
$25x + 12y + 4 \leqslant 130$

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3 years ago