Answer:
2401
Step-by-step explanation:
Given that we want to estimate average income in a population.
The standard deviation of income in the population is $1,000
We want confidence interval around our estimate to be +/- $40
i.e Margin of error = 40
We know that margin of error = Std error * Z critical for 95%
i.e. 
Std error = 
Together we get
To solve this polynomial equation, we first factor the left side.
To factor x² + 8x + 12 = 0, look for factors of 12 that add to 8.
These factors are 6 and 2 so we have (x + 6)(x + 2) = 0.
So either x + 6 = 0 or x + 2 = 0 and solving for
x in each equation, our answer is {-6, -2}.
Answer:
Step-by-step explanation:
Let x represent the number of batches of soap that Lilth makes.
Let y represent the number of batches of lotion that Lilth makes.
It takes her 20 minutes(20/60 = 1/3 hours) to make a batch of soap and 35 minutes(35/60 = 7/12 hours) to make a batch of lotion. Lilth has 20 hours available to make soap and lotion. This means that
x/3 + 7y/12 = 20
4x + 7y = 240- - - - - - - - - - -1
The cost of producing each batch are $5 for the soap and $15 for the lotion. The materials to make the soap and lotion must cost at most $325. This means that
5x + 15y ≤ 325 - - - - - - - - -2
4x = 240 - 7y
x = (240 - 7y)/4
Substituting
5(240 - 7y)/4 + 15y ≤ 325
(1200 - 35y)/4 + 15y ≤ 325
1200 - 35y + 60y ≤ 1300
25y ≤ 1300 - 1200
25y ≤ 100
y ≤ 100/25
y ≤ 4
4x + 7 × 4 = 240
4x + 28 = 240
4x = 212
x = 212/4 = 53
Therefore, the solution (53, 4) means that she would make at most 53 batches of soap and at most 4 batches of lotion
Answer:
root 30
Step-by-step explanation:
10/x=x/3
x^2=30
x= root 30
