Answer:
the answers are true, false, true.
Step-by-step explanation:
Answer:
The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.
Step-by-step explanation:
What is Confidence Interval?
The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.
The confidence interval is given by
Where is the mean weight is the standard deviation is the critical value from t-table and n is the sample size.
The term is known as margin of error.
As the sample size is decreased the corresponding margin of error increases which results in wider confidence interval which means smaller precision.
The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.
We can say with 95% confidence that the true mean weight of the rock is within the interval of (25.2, 29.1).
Answer:
75
Step-by-step explanation:
Step 1
Matt is ordering basketball jerseys For his country's league. Last year he ordered 512 jerseys. 64 those jerseys were orange.
The ratio of all Jerseys to Jerseys that are Orange =
512 : 64
8 : 1
Step 2
If he ordered 600 jerseys this year, how many of them will be Orange if the ratio of orange jerseys to all the jerseys remain the same?
Since we are maintaining the ratio in step 1
Let the number of orange jerseys = x
600 : x = 8 : 1
Hence
600/x = 8/1
Cross Multiply
8 × x = 600 × 1
8x = 600
x = 600/8
x = 75
Therefore, this year, the number of orange jerseys = 75
It's not compounded interest, you just get $3.20 every year.
$100 * 0.032 = $3.20
$3.20 * 3 years = $9.60
Assume that the amount needed from the 5% solution is x and that the amount needed from the 65% solution is y.
We are given that, the final solution should be 42 ml, this means that:
x + y = 42 ...........> equation I
This can also be written as:
x = 42-y .......> equation II
We are also given that the final concentration should be 45%, this means that:
5% x + 65% y = 45% (x+y)
0.05x + 0.65y = 0.45(x+y)
We have x+y = 42 from equation I, therefore:
0.05x + 0.65y = 0.45(42)
0.05x + 0.65y = 18.9 .........> equation III
Substitute with equation II in equation III as follows:
0.05x + 0.65y = 18.9
0.05(42-y) + 0.65y = 18.9
2.1 - 0.05y + 0.65y = 18.9
0.6y = 18.9 - 2.1
0.6y = 16.8
y = 28 ml
Substitute with y in equation II to get x as follows:
x = 42-y
x = 42 - 28
x = 14 ml
Based on the above calculations:
amount of 5% solution = x = 14 ml
amount of 65% solution = y = 28 ml
The correct choice is:
The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.