Mike has 4 times as many stamps as Andrew
Let Mike = M and Andrew = A, eq.1 will be M = 4A
However, if Mike gives Andrew 8 stamps, then the number of stamps Mike has is now twice the number of stamps Andrew has. This will give us another equation.
eq. 2 will be M-8 = 2 (A+8)
The expression on the left tells us that Mike gave away eight stamps, while the expression on the right tells us that whatever this new number is is equal to twice the total number of Andrew's stamps after receiving eight from Mike.
Simplifying this further gives us:
M-8 = 2A + 16
M = 2A + 16 + 8 = 2A + 24
Use 2A + 24 and substitute this for M in eq. 1. This gives us:
2A + 24 = 4A
24 = 4A - 2A
24 = 2A
12 = A, and therefore M = 48 (because M=4A)
To begin with, Andrew had 12 stamps and Mike had 48 stamps.
If only M-8 = 2A is used, this will only meet the condition given in situation 1 (M=4A) but not situation 2, wherein after giving away 8 stamps, Mike's stamps is twice as many as Andrew's. You can check it. :)
Answer:
Option D
Step-by-step explanation:
Complete question
A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A random sample of 18 sophomores is surveyed and asked whether they support the school adopting uniforms, and three students said yes. The student wants to construct a 95% confidence interval for the proportion of sophomores who favor the adoption of uniforms. Are the conditions for inference met?
- Yes, the conditions for inference are met.
- No, the 10% condition is not met.
- No, the randomness condition is not met.
- No, the Large Counts Condition is not met.
Solution
10 % of population size of 200 is 20. The sample of 18 is smaller than the 10 % of sample size of 200. As per the 10% rule, the size of sample must be less than 10% of the total size of population. This indicate that the sample is random but its size is less that 30. However, it should be greater that 30. Hence, the large count condition is not met.
Hence, option D is the correct choice of answer
Answer:
i)
0.79m
ii)
1.21m
iii)
7/5m
iv)
3/5m
Step-by-step explanation:
i)
The price of a USB memory stick selling at a 21% discount off its marked price (m)
The marked price m represents 100% of the value of the USB memory stick. Offering a 21% discount off the marked price will mean that the USB will be selling at;
(100 - 21)% of the marked price m
=79% of m
= (79/100)*m
= 0.79m
ii)
The price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD.
The amount (m) needed to manufacture the CD would represent 100% of the value of the CD. Selling the CD for 21% more than the amount (m) needed to manufacture the CD will imply that the selling price is;
(100+21)% of m
= 121% of m
= (121/100)*m
= 1.21m
iii)
The final value of a painting after its initial value, m, increases by 2/5.
The initial value of the painting is given as m. The value of the painting is said to increase by 2/5 which means that the increase in its value would be;
2/5 of m
=2/5 * m
=2/5m
The final value of the painting will thus be;
initial value + increase in value
=m + 2/5m
= m(1+2/5)
=7/5m
iv)
The total number of markers that Nancy has if she gives away 2/5 of her m markers to Amy.
Initially, Nancy had a total of m markers. By giving away 2/5 of her markers to Amy, her markers reduced by;
2/5 of m
=2/5*m
=2/5m
The new number of her markers will be given by;
initial numbers - total given to Amy
= m - (2/5m)
= m(1 - 2/5)
=m(3/5)
=3/5m
The answer is 6. 49 you welcome :)
