How do i solve 5x-9y=-17 and 5x+3y=19 in elimation
1 answer:
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Answer:
The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.
Step-by-step explanation:
We are given;
Number of males selected; n₁ = 150
Number of females selected; n₂ = 190
Proportion of the males; p₁ = 0.6
Proportion of females; p₂ = 0.5
Let's define the hypotheses;
Null hypothesis; H0: p₁ ≥ p₂
Alternative hypothesis; Ha: p₁ < p₂
Now, the z score formula for this is;
z = (p₁ - p₂)/√(p^(1 - p^))(1/n₁ + 1/n₂))
Where;
p^ = (p₁ + p₂)/2
p^ = (0.6 + 0.5)/2
p^ = 0.55
Thus;
z = (0.6 - 0.5)/√(0.55(1 - 0.55))((1/150) + (1/190))
z = 0.1/0.0543
z = 1.84
From online p-value from z-score calculator attached, using z = 1.84, significance level = 0.05, one tailed hypothesis, we have;
P-value = 0.033
The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.
Although if we check at 0.01 significance level, we will not have the same answer as the p-value will be greater.
Answer:
a.
Clear Prints =
Sue =
b. 10 posters
c. See Below
d. Clear Prints
e. See Below
Step-by-step explanation:
<u>Complete Question:</u>
<em>Ms. Chang’s class decides to order posters that advertise a walkathon to raise money for a local charity. Ichiro obtains quotes from two different companies.Clear Prints charges $2 per poster. Posters by Sue charges $15 plus $.50 per poster.</em>
<em>a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.</em>
<em>b. For what number of posters is the cost the same for both companies? Explain.</em>
<em>c. Which company do you think the class should buy posters from? Explain your reasoning.</em>
<em>d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from? </em>
<em>e. If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made? What factors influenced your decision?</em>
<em />
<u>Solution:</u>
a.
Let the number of posters be "p" so
Clear Print would take 2 * p or "2p"
Sue would take a fixed cost of $15 and 0.5p, so "15 + 0.5p"
b.
We want cost of both to be same. So we can equate:
Now, using algebra, we can solve for "p", the number at which both of the printers will cost same. Lets do this:
So, for 10 posters, the cost of both will be same
c.
It depends.
If the number of posters they order is LESS THAN 10, they should order from Clear Prints. If the number of posters they print is "10", then they can choose any one of the printers since cost would be same. If they print more than 10 posters, then they should choose to go with Sue, as it will cost less.
d.
If the budget is $18, they can get:
Clear Prints = 18/2 = 9 posters made
Sue = 15 already gone as fixed cost, so remaining is 18 - 15 = 3
At 0.5 per poster, 3/0.5 = 6 posters
So, taking Clear Prints would be better.
e.
The budget of 18 is increase by 10, so the budget is:
18 + 10 = $28
From clear prints, you can get:
28/2 = 14 posters
From Sue, you can get:
28 - 15(fixed cost) = 13 left for posters
13/0.5 = 26 posters
Definitely, Sue gives more, so decision made at $18 budget to get Clear Prints would be impacted because they should now go with Sue since it will give them better deal and more posters.