Solving Exponential Equations (lacking a common base) 4^x-5=8
2 answers:
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Answer:
The answer is below
Step-by-step explanation:
a) Cost of hiring the bicycle for 14 days is:
Cost = 65 * 14 days + 44 = 954 riyals
b) The number of days the bicycle is hired is to be the same as the number of days the bicycle is to be hired. Let us assume that the bicycle and helmet is to be hired for x days, hence:
Cost of bicycle = 65 * x + 14 = 65x + 44
Cost of helmet = 12.5 * x = 12.5x
Total cost = 65x + 44 + 12.5x = 77.5x + 44
Since 750 riyals is available, hence:
750 = 77.5x + 44
77.5x = 706
x = 9.11
Therefore the maximum number of days is 11. The total cost for 11 days is:
Total cost = 77.5(9) + 44 = 741.5 riyals
Money not spent = 750 riyals - 741.5 riyals = 8.5 riyals
Answer:
1) No, there is not enough evidence to support the claim that the vaccine was effective (P-value=0.104) .
The null and alternative hypothesis are:
being the subindex 1 for the experimental group and subindex 2 for the control group.
2) Test statistic z=-1.26
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the vaccine was effective.
Then, the null and alternative hypothesis are:
The significance level is 0.01.
The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.
The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.
The difference between proportions is (p1-p2)=-0.0001.
The pooled proportion, needed to calculate the standard error, is:
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the z-statistic as:
This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):
As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the vaccine was effective.