Answer:
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
x = number of nickels in the student's pocket
y = number of dimes in the student's pocket
Each nickel has a value of $0.05, so x nickels have a value of 0.05x
Each dime has a value of $0.10, so y dimes have a value of 0.10y
The student has a total of 10 coins, thus:
The total value of the coins is $0.85, thus
The system of linear equations that represents this scenario is:
Answer:
The 98% confidence interval of the proportion = (0.312, 0.374)
Step-by-step explanation:
(Give answers accurate to 3 decimal places.)
The formula for Confidence Interval of Proportion is given as:
p ± z × √p(1 - p)/n
Where p = Proportion = x/n
x = 440
n = 1282
p = 440/1282 = 0.34321372854
Approximately = 0.343
z = z-score of 98 % confidence interval
= 2.326
Confidence Interval =
= 0.343 ± 2.326 × √0.343(1 - 0.343)/1282
= 0.343 ± 2.326 × √0.225351/1282
= 0.343 ± 2.326 × √0.00017578081
= 0.343 ± 2.326 × 0.01325823555
= 0.343 ± 0.03083865589
0.343 - 0.03083865589
= 0.31216134411
Approximately = 0.312
0.343 + 0.03083865589
= 0.37383865589
Approximately to = 0.374
Therefore, the 98% confidence interval of the proportion = (0.312, 0.374)
Answer:
D
Step-by-step explanation:
Angle 5 is equal to angle 8 because the two angles are an alternate interior angle. We already know that angle 7 and 8 are supplementary because it's adjacent to each other on a straight line. So, since angle 5 and 8 is equal to each other, angle 5 is also supplementary to angle 7.
