Answer:
x = 3 ±
or
x = 3 + , x = 3 -
Step-by-step explanation:
given f(x) = 2(x - 3)^2 - 8, find when f(x) = 40
So, we plug in 40 for f(x) in the 1st equation and solve for x. (Aim to got x on its own)
40 = 2 (x - 3)^2 - 8
+ 8 + 8
-----------------------------
48 = 2 (x - 3)^2
/2 /2
-----------------------------
24 = (x - 3)^2
square root both sides
--------------------
= x - 3
x = 3 ±
Answer:
The probability of the sample mean foot length less than 23 cm is 0.120
Step-by-step explanation:
* Lets explain the information in the problem
- The eighth-graders asked to measure the length of their right foot at
the beginning of the school year, as part of a science project
- The foot length is approximately Normally distributed, with a mean of
23.4 cm
∴ μ = 23.4 cm
- The standard deviation of 1.7
∴ σ = 1.7 cm
- 25 eighth-graders from this population are randomly selected
∴ n = 25
- To find the probability of the sample mean foot length less than 23
∴ The sample mean x = 23, find the standard deviation σx
- The rule to find σx is σx = σ/√n
∵ σ = 1.7 and n = 25
∴ σx = 1.7/√25 = 1.7/5 = 0.34
- Now lets find the z-score using the rule z-score = (x - μ)/σx
∵ x = 23 , μ = 23.4 , σx = 0.34
∴ z-score = (23 - 23.4)/0.34 = -1.17647 ≅ -1.18
- Use the table of the normal distribution to find P(x < 23)
- We will search in the raw of -1.1 and look to the column of 0.08
∴ P(X < 23) = 0.119 ≅ 0.120
* The probability of the sample mean foot length less than 23 cm is 0.120
