The confidence interval formula is computed by:
Xbar ± Z s/ sqrt (n)
Where:
Xbar is the mean
Z is the z value
S is the standard deviation
N is the number of samples
So our given are:
90% confidence interval with a z value of 1.645
Sample size 40, 45
Mean 180, 179
Standard deviation 2, 4
So plugging that information in the data will give us a
confidence interval:
For 1:
Xbar ± Z s/ sqrt (n)
= 180 ± 1.645 (2 / sqrt (40))
= 180 ± 1.645 (0.316227766)
= 180 ± 0.520194675
= 179.48, 180.52
For 2:
Xbar ± Z s/ sqrt (n)
= 179 ± 1.645 (4 / sqrt (45))
<span>= 179 ± 1.645 (0.596284794)</span>
therefore, the answer is letter b
Answers:
(a) p + m = 5
0.8m = 2
(b) 2.5 lb peanuts and 2.5 lb mixture
Explanations:
(a) Note that we just need to mix the following to get the desired mixture:
- peanut (p) - peanuts whose amount is p
- mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as
By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.
Hence,
p + m = 5
Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).
Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.
Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m).
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.
In terms mathematical equation,
0.8m = 2
Hence, the system of equations that models the situation is
p + m = 5
0.8m = 2
(b) To solve the system obtained in (a), we first label the equations for easy reference,
(1) p + m = 5
(2) 0.8m = 2
Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have
m = 2.5
Then, we substitute the value of m to equation (1) to solve for p:
p + m = 5
p + 2.5 = 5 (3)
To solve for p, we subtract both sides of equation (3) by 2.5. Thus,
p = 2.5
Hence,
m = 2.5, p = 2.5
Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.
Answer:
2(2x-5)(2x+5)
Step-by-step explanation:
I think you meant to say 8x^2-50. If so then factoring this down should be easy. Since there is no x value in the middle the equation will have a positive and a negative number. This is also a perfect square therefore, this factors down to: 2(2x-5)(2x+5).
Answer:
8377
Step-by-step explanation:
Growth rate is exponential, so it is determined by the formula (1+growth rate)^n where n is years
1.035^15 = 1.675...
multiply by 5000, you get 8376.744....