Answer:
The margin of error for the 90% confidence interval is of 0.038.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
The margin of error is of:
To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene.
This means that 
90% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
Margin of error:
The margin of error for the 90% confidence interval is of 0.038.
Let x be the amount that Jeff spent for the food and medication of his dog. With this representation, the cost of food and medication for each cat is 2x/3 - 5. The equation that best represent the given situation is
x + 6(2x/3 - 5) = 195
The value of x from the equation is 45. Jeff spent $45
Answer:
x = tan⁻¹(⅘)
Step-by-step explanation:
We can solve for x by using trigonometric ratios (sin, cos, and tan)
We need to apply the appropriate ratio that uses the two sides 8 and 10 from the perspective of x. See attached image for information about ratios. (Source: Math is Fun)
The tangent ratio is opposite divided by adjacent. It will relate x to the two sides. So we would write
tan(x) = ⁸⁄₁₀
Then we simplify and move the tan to the other side by multiplying both sides by the inverse of tan (since you cannot divide by tan)
tan(x) = ⅘
x = tan⁻¹(⅘)
Then we can use a calculator to evaluate x
If you want to find y, now that you have two angles of the triangle, you can find the sum of 90 + x and subtract that from 180 (since all angles of a triangle add up to 180) to find y.
The sign at the end changes because both sides of the equation are being divided by a negative number.
