The given function is
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments
We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:
1. Set y = f(x)
y = 4x - 3/2
2. Exchange x and y
x = 4y - 3/2
3. Solve for y
4y = x + 3/2
y = (x +3/2)/4
4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4
5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)
Answer:
Pedro needs about 8 weeks to complete 30 assignments.
Answer:
4 nickels
12 dimes
Step-by-step explanation:
Dimes are worth .1 each while nickels are .05 each.
We have 8 more dimes than nickels. Let d represent number of dimes and n for number of nickels. This means we have d=8+n.
If all our nickels and dimes together are worth 1.4 then we have another equation .1d+.05n=1.4
Lets put our equations together:
d=8+n
.1d+.05n=1.4
‐-----------------Plug first equation into second.
.1(8+n)+.05n=1.4
Distribute
.8+.1n+.05n=1.4
Combine like terms
.8+.15n=1.4
Subtract .8 on both sides
.15n=.6
Divide both sides by .15
n=.6/.15=4
Remember there are 8 more dimes so d=8+4=12.
Answer:
Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:
B.t
Step-by-step explanation:
Notation
represent the mean for male king penguins
represent the mean for the female king penguins
represent the sample standard deviation for the sample male
represent the sample standard deviation for the sample female
sample size for the male penguins
sample size for the female penguins
t would represent the statistic
Hypothesis
We need to conduct a hypothesis in order to check if the male king penguins weigh more than female king penguins, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:
B.t
The fraction is 2/3
So, there should be 100 squares.
Next, the 100 squares is divided into 3 by vertical lines. The lines will not coincide with the sides of the squares. This is okay. Next, the 2 out of 3 will be shaded, this will be equivalent to 66 squares and one more square but it will not be filled up completely. In percent form, the fraction is 66.67%.
