Using the t-distribution, it is found that:
a) Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that significantly more electricity is used at the student center, on average, on weekdays than weekend days.
b) The 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days is (3.56, 33.18).
Item a:
At the null hypothesis, it is tested if there is no difference, that is, the subtraction is at most 0, hence:
[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]
At the alternative hypothesis, it is tested if there is difference, that is, the subtraction is positive, hence:
[tex]H_1: \mu_1 - \mu_2 > 0[/tex]
The standard errors are given by:
[tex]s_1 = \frac{32.07}{\sqrt{60}} = 4.14[/tex]
[tex]s_2 = \frac{43.29}{\sqrt{30}} = 7.9[/tex]
The distribution of the difference has mean and standard deviation given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 112.63 - 94.26 = 18.37[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{4.14^2 + 7.9^2} = 8.92[/tex]
The standard deviation are given for the samples, hence, the t-distribution is used.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{18.37 - 0}{8.92}[/tex]
[tex]t = 2.06[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 30 + 60 - 2 = 88 df is [tex]t^{\ast} = 1.66[/tex]
Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that significantly more electricity is used at the student center, on average, on weekdays than weekend days.
Item b:
The interval is:
[tex]\overline{x} \pm t^{\ast}s[/tex]
Hence:
[tex]\overline{x} - t^{\ast}s = 18.37 - 1.66(8.92) = 3.56[/tex]
[tex]\overline{x} + t^{\ast}s = 18.37 + 1.66(8.92) = 33.18[/tex]
The 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days is (3.56, 33.18).
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Supply the missing reasons to complete the proof.
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Answer: 60%
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Caleb decreases a number by 6 and then multiplies it by 2. He gets the same answer as
when he subtracts 8 from the original number. What is the number?
please answer!!
Answer: 4
Step-by-step explanation: If Caleb starts with 4 and subtracts 6, he'll get -2. -2 times 2, equals -4. If he starts with 4 and subtracts 8, he'll again end up with -4, meaning the original number is 4!
4-6= (-2)
-2*2= (-4)
4-8= (-4)
309 g to 299 g increase or decrease
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Rewrite this equation below into Slope-intercept form
y-10=2/3(x-3)
Answer:
y= 2/3x+8
Step-by-step explanation:
you add 10 to both sides then combine -2 with 10 to get 8
then 1x times 2/3 is 2/3x and -3 times 2/3 is -2
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A system of two equations is shown below:
Equation C: a = 2b + 7
Equation D: a = 5b − 3
What value of a can be substituted into equation D to solve the system of equations?
2b
5b
5b − 3
2b + 7
Answer:
25452664637378381234
Answer:
2b+7
Step-by-step explanation:
sorry for the dimwit who typed random numbers
Quadrilateral Properties
Match the properties to the shape. Properties may be used more than once and shapes may have more than one property.
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Answer:
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Answer:
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7
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If i watch a movie at 7:00 pm and the movie lasts 1h 49m what time will it be when it finishes?
Answer:
it would finish at 8:49
Step-by-step explanation:
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Answer:
it's really simple seriously, but it will end at 8:49m
Step-by-step explanation:
5/6+3/4+2/3 answer please
Answer:
2.25
Explanation
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find the distance between find the distance between following points: a) M(5,4) and N(2, 3)
Answer:
sqrt(10)
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Answer:
no its not a function
Step-by-step explanation:
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Step-by-step explanation:
Distributive property
2x - y = 1
3x + y = 9
Answer:s
Step-by-step explanation:
Answer:
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Step-by-step explanation:
Are the equations m+3=-5 and m-4=-12$ equivalent?
Answer:
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Step-by-step explanation:
I checked by multiplying them.
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Step-by-step explanation:
m= -5 -3
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m= - 8
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Answer:
X= -1/3 or 4
Step-by-step explanation:
Answer:
x =-1/3 and x=4
Step-by-step explanation:
solve by factoring:
separate into two equations:
3x+1=0
8-2x=0
(when the products of factors equals zero, at least one factor is zero)
3x=-1
x=-1/3
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x=4
im in school rn and i dont understand this!
Answer:
[tex]33\%, ~\dfrac 3{10},~0.32,~ \dfrac 13[/tex]
Step-by-step explanation:
[tex]33\% <\dfrac 3{10}<0.32<\dfrac 13[/tex]
Billy has 201 packages of postcards. Each package has 18 cards. Use rounding to estimate. About
how many cards does Billy have?
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Answer:
6 rainy days
Step-by-step explanation:
What is the contrapositive of the statement below?
If you are in Reykjavik, then you are in Iceland.
Answer:
If you are not in Iceland, then you are not in Reykjavik.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The contrapositive of a statement is as follows:
"Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."
So, for this one, we need to switch as well!
If you are in Reykjavik, then you are in Iceland.
If you are NOT in Iceland, then you are not in Reykjavik.
The answer would be D
Please answer number 1 and 2.
I have to do 2 pages of homework I need this done I have school tomorrow..
Have no idea how to do this. Please help I beg you.
1, a.) The two specific conjectures are in the first image.
1, b.) The two general conjectures are in the second image.
2, a.) Two specific conjectures for this pattern are:
The common difference between two consecutive terms is 3.And the given difference is A.P.2, b.) From our observation two general conjecture is that the given sequence is an arithmetic sequence and the common difference is 3.
For finding its nth term we can use the formula: a(n) = a + (n-1) x d.
2, c.) A formula for the given pattern is 5 + (n-1)3, where n is the number of the term.
Mr. Jones bought a piece of land for 60 000. The land increased in value by 20% in a year. The new value of the land is
Answer:
$72,000
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If we take 60,000 and then take 20 percent of it, we get 12,000. Then we add 12,000 to 60,000 and it gives us 72,000.
$20, $15,$10,$5. What is the range of allowance amounts?
Answer:
$15
Step-by-step explanation:
20-5= 15
Answer: The range is 15 because 20 is the highest and 5 is the lowest and when you subtract them you get 15.
Hope this helps :)
Please solve the equation below.
2x+4=3(x-4)
Answer:
x=16Step-by-step explanation:
[tex]\sf 2x+4=3(x-4)[/tex]
[tex]\sf 2x+4=3x-12[/tex]
[tex]\sf 2x+4-4=3x-12-4[/tex]
[tex]\sf 2x=3x-16[/tex]
[tex]\sf 2x-3x=3x-16-3x[/tex]
[tex]\sf -x=-16[/tex]
[tex]\sf \cfrac{-x}{-1}=\cfrac{-16}{-1}[/tex]
[tex]\sf x=16[/tex]
solve the equation below :-
2x+4=3(x-4)
Answer:-x = 16
Explanation:-=> 2x+4 = 3(x-4)
=> 2x+4 = 3x-12
=> 2x+4 - 4 = 3x-12 - 4 (Subtract 4 on both the sides)
=> 2x = 3x-16
=> 2x-3x = -16
=> -x = -16
=> -x/-1 = -16/-1
=> x = 16
can anyone answer this question please
6[y-2]/7-12=2[y-7]/3
Answer:
y =47.5.
Step-by-step explanation:
First eliminate the fractions by multiplying through by the LCM of 7 and 3 which is 21:
21* 6[y-2]/7-21*12 = 21*2[y-7]/3
18(y - 2) - 252 = 14(y - 7)
18y -36 - 252 = 14y - 98
18y - 14y = -98 + 36 + 252
4y = 190
y = 190/4
y = 47.5.
HELP ME WITH THIS TWO PROBLEMS
1. When I add 6 to five times my number I get 36. My mystery number is ....
2. When I add 7 to three times my number I get 43. My mystery number is....
Answer:
1) 6 & 2)12
Step-by-step explanation:
Solve the equations backwards-
1) Subtract 6 from 36, and then divide by 5.
36 = 6 + 5x
(36 - 6)/5 = x
x = 6
2) Subtract 7 from 43, and then divide by 3.
43 = 7 + 3y
(43 - 7)/3 = y
y = 12
What is the equation of the line that passes through the point (-6,1) and has a
slope of 1?
Answer:
y = x + 7
Step-by-step explanation:
If the slope is 1, the original equation is y = mx + b, with m being 1.
Now substitute -6 and 1 for x and y and solve for b
1 = 1(-6) + b
1 = -6 + b
7 = b
Put it all together:
y = x + 7