Answer:
see below
Step-by-step explanation:
We need to find the diameter of the square
We can find this using the Pythagorean theorem
a^2+b^2 = c^2 where the legs are 7 and 7 and the diameter is c
7^2 +7^2 = c^2
49+49 = c^2
98 = c^2
Taking the square root of each side
sqrt(98) = sqrt(c^2)
9.899494937 = c
Since 9.9 is less than 11 which is the diameter of the circle it will never touch the circle.
Since the longest part of the square is less than the diameter of the circle, the square will fit inside the circle without touching
Answer:
B. Oliver can watch TV for 1.5 hours more this week.
Step-by-step explanation:
Oliver is not allowed to watch more than 4 hours of television a week. He watched his favorite show on Monday which was 1 hour long and his favorite Tuesday show which was 1.5 hours long.
So he has already finished 2.5 hours of watching . He can watch only for 4 hours for the total week.
Let x be the number of more hours for which he can watch television.
Then ,
x + 1 + 1.5 = 4
x + 2.5 = 4
x = 4 - 2.5
x = 1.5 hours.
So Oliver can watch television for at most 1.5 hours for the rest of the week.
Then the correct option is B.
Answer:
Step-by-step explanation:
230.86/23.8= and you'll have your answer (I don't have a calculator on me sorry)
Answer:
standard error = 2.11
Step-by-step explanation:
First we stablish the data that we have for each sample:
<u>Population 1</u> <u>Population </u>2
n₁ = 100 n₂ = 90
x¯1= 95 x¯2 = 75
σ₁ = 14 σ₂ = 15
To calculate the standard error of each sample we would use the formulas:
σ = σ₁/√n₁
σx¯2 = σ₂/√n₂
Now, in order to obtain the standard error of the differences between the two sample means we combine those two formulas to obtain this:
σx¯1 - σ x¯2 = √(σ₁²/n₁ + σ₂²/n₂ )
So as you can see, we used the square root to simplify and now we require the variance of each sample (σ²):
σ₁² = (14)² = 196
σ₂² = (15)² = 225
Now we can proceed to calculate the standard error of the distribution of differences in sample means:
σx¯1 - σx¯2 = √(196/100 + 225/90) = 2.11
This gives an estimate about how far is the difference between the sample means from the actual difference between the populations means.
volume of a sphere = 4/3 *pi * r^3
3/4 * pi = 4/3 *pi * r^3
divide each side by pi
3/4 = 4/3 * r^3
multiply each side by 3/4
3/4 * 3/4 = r^3
9/16 = r^3
take the cube root of each side
r = (9/16) ^ (1/3)
