Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean
The total weight of candies is unknown. Let x = the total weight of candies.
"One student ate 3/20 of all candies and another 1.2 lb":
The first student ate (3/20)x plus 1.2 lb which is 0.15x + 1.2.
"The second student ate 3/5 of the candies and the remaining 0.3 lb."
The second student ate (3/5)x and 0.3 lb which is 0.6x + 0.3.
Altogether the 2 students ate 0.15x + 1.2 + 0.6x + 0.3.
That was all the amount of candies, so that sum equals x.
0.15x + 1.2 + 0.6x + 0.3 = x
Now we solve the equation for x to find what the total amount of candies was.
0.75x + 1.5 = x
-0.25x = -1.5
x = 6
The total amount of candies was 6 lb.
The first student ate 0.15x + 1.2 = 0.15(6) + 1.2 = 0.9 + 1.2 = 2.1, or 2.1 lb of candies.
The second student ate 0.6x + 0.3 = 0.6(6) + 0.3 = 3.6 + 0.3 = 3.9, or 3.9 lb of candies.
Answer: The first student ate 2.1 lb of candies, and the second student ate 3.9 lb of candies.
Answer:
x = -8
Step-by-step explanation:
Solve for x by getting rid of the fraction.
414/(x-10) = -23
414 = -23(x-10)
414 = -23x + 230
184 = -23x
-8 = x
Answer:
(-7,-3)
Step-by-step explanation:
From A to M, the x value went down 2. If it goes down another 2, it will be at -7.
From A to M, the y value went down 3. If it goes down another 3, it will be at -3.
(-7,-3)
