The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches. To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years.
Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches.
Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches.
To compute for the z-score, we have
z-score = (x – μ) / (σ / √n)
where x is the computed/measured value, μ is the expected mean, σ is the standard deviation, and n is the number of samples.
Using the information we have,
z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68
In order to reject the null hyptohesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05.
Therefore, the answer is B.
Answer:
(2, -2)
Step-by-step explanation:
Multiply the first equation by -3,and multiply the second equation by 1.
−3(5x+6y=−2)
1(15x+4y=22)
Becomes:
−15x−18y=6
15x+4y=22
Add these equations to eliminate x:
−14y=28
Then solve−14y=28for y:
−14y=28
−14y
−14
=
28
−14
(Divide both sides by -14)
y=−2
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
5x+6y=−2
Substitute−2foryin5x+6y=−2:
5x+(6)(−2)=−2
5x−12=−2(Simplify both sides of the equation)
5x−12+12=−2+12(Add 12 to both sides)
5x=10
5x
5
=
10
5
(Divide both sides by 5)
x=2
Answer:
x=2 and y=−2
First let's find the GCF of 27, 36, and 72:
-->Find the factors of each number:
27: 1, 3, 9, 27
36: 1, 2, 3, 4, 9, 12, 18, 36
72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
-->Now look for the factors they have in common.
1, 3, and 9
-->Now see which one is the biggest number in value
9
--> So therefore, 9 is the GCF
Now let's find the LCM of 7, 4, 10, and 12
-->Start listing all the multiples of of each number
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40... 420
7: 7, 14, 21, 28, 35, 42, 49, 56, 64, 70... 420
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120... 420
12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120... 420
(sorry got bored of typing so I fast forwarded at the '...'s)
--> The least number in value that they have in common is the LCM of those numbers
The LCM is 420
*Just saying that took forever to do that LCM part but not way too long thank goodness :p