Answer:
The critical value for the 95% confidence interval is z = 1.96.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of
So it is z with a pvalue of , so z = 1.96.
The critical value for the 95% confidence interval is z = 1.96.
Answer:
56√93 ≈ 540 ft²
Step-by-step explanation:
The roof is made up of 4 congruent isosceles triangles. Since the roof extends 2 ft over the edge of the cottage on each side, then the base of each triangle is 26 + 2 = 28 ft.
Let's calculate the area of one of the triangles and then just multiply by 4. See attachment. Drop a perpendicular from the vertex of a triangle to its base. We now have the triangle broken up into two right triangles. The hypotenuse is 17 ft and one of the legs of the right triangle is 28 / 2 = 14 ft. Then the height / other leg is:
We now have the dimensions of each triangle: the height is √93 and the base is 28. The area of a triangle is: A = (1/2) * b * h, so we have the following.
A = (1/2) * b * h
A = (1/2) * 28 * √93 = 14√93
Multiply this by 4:
14√93 * 4 = 56√93
The total surface area is 56√93 ≈ 540 ft².
Matt earns $4 and $3 for 1 load of laundry and 1 load of dishes respectively
<u>Solution:</u>
Given, Matt gets paid at home for doing extra chores.
We have to find How much does Matt earn for completing each type of chore?
Let the amount for 1 load of laundry be m and amount for 1 load of dish be n.
Now, last week, he did 6 loads of laundry and 1 load of dishes, and his parents paid him $27.
Then, 6 amount for 1 load of laundry + 1
amount for 1 load of dish = 27
The week before, he finished 1 load of laundry and 9 loads of dishes, earning a total of $31
Then, 1 amount for 1 load of laundry + 9
amount for 1 load of laundry = 31 ⇒m + 9n = 31 ⇒ (2)
Now let us solve equations (1) and (2)
0 – 53n = - 159
-53n = -159
53n = 159
n = 3
Now, substitute n value in (1) ⇒ 6m + 3 = 27 ⇒ 6m = 24 ⇒ m = 4
Hence, matt earns $4 and $3 for 1 load of laundry and 1 load of dishes respectively.