Answer:
3 steps
Step-by-step explanation:
FIrst of all, if you think about it, we can just say -3 as 3 ( even though they are not equal, were just counting steps.)
On a number line, negative numbers are on the left of 0 and positive on the right of 0.
So, lets say the middle number is 0 on our number line. -3 is 3 steps to the left. We take 1 step to negative 1, another step to -2, and then a 3rd and final step to -3.
The steps represent how far the number is from 0. FIr example, we have to add 3 to -3 to get to 0, like how we add 7 to 0 to get 7!
Hope this helps!
Answer:
P(10 ≤ x ≤ 12) = 0.4274
Step-by-step explanation:
Population mean = u = 10
Population Standard Deviation =
= 9
Sample size = n = 43
Sample mean(
) is equal to the population mean. So,
Sample mean =
= 10
Sample standard deviation(
) is equal to population standard deviation divided by square root of sample size. So,
Sample standard deviation =
= 
We have to find the probability that for a random sample of n = 43, the value lies between 10 and 12 i.e. P(10 ≤ x ≤ 12)
P(10 ≤ x ≤ 12) = P(x ≤ 12) - P( x ≤ 10)
We can find P(x ≤ 12 ) and P(x ≤ 10) by converting these values to z scores.
The formula for z score is:

For x =12, we get:

For x =10, we get:

So,
P(x ≤ 12) - P( x ≤ 10) = P(z ≤ 1.457) - P(z ≤ 0)
From the z table,
P(z ≤ 1.457) = 0.9274
P(z ≤ 0) = 0.5
So,
P(x ≤ 12) - P( x ≤ 10) = P(z ≤ 1.458) - P(z ≤ 0) = 0.9274 - 0.5 = 0.4274
So,
P(10 ≤ x ≤ 12) = P(x ≤ 12) - P( x ≤ 10) = 0.4274
Therefore,
The probability that for a random sample of size 43, the mean lies between 10 and 12 is 0.4274.
Answer:
T = 3.5 hours
Step-by-step explanation:
this is a rate problem.
an experienced surveyor takes 7 hours to survey a roadbed
an apprentice surveyor takes 9 hours to survey a roadbed
the rate of the experienced surveyor =
the rate of the apprentice surveyor = 
if the two work together , 
T = 
T = 3.5 hours