Answer:
9
Step-by-step explanation:
if the opposition of a number is equal to -9.
hence the expression above....
The described picture frame can be visualized into two separate parts. The first area is equal to the area using the outermost dimensions for the length and width.
Area = Length x Height
Area = (20 in) x (14 in)
Area = 280 in²
We are given that the area is only equal to 192 in². We subtract this value from the computed area.
Difference = 280 in² - 192 in²
difference = 88 in²
This area is equal to the area of the hollow space inside the frame. That is equal to,
height = 20 in - 2x
length = 14 in - 2x
The area,
88 = (20 - 2x)(14 - 2x)
Simplify the right hand side of the equation.
88 = 280 - 68x + 4x²
Divide the equation by 4,
22 = 70 - 17x + x²
Transposing,
x² - 17x - 48 = 0
The factors of the equation is 58.2.
Thus, the thickenss is equal to 58.2 in
Answer:
Step-by-step explanation:
In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).
The formula we will use for this problem is the following:
where:
a=0
so the volume becomes:
This can be simplified to:
and the integral can be rewritten like this:
which is a standard integral so we solve it to:
![V=9\pi[tan y]\limits^\frac{\pi}{3}_0](https://tex.z-dn.net/?f=V%3D9%5Cpi%5Btan%20y%5D%5Climits%5E%5Cfrac%7B%5Cpi%7D%7B3%7D_0)
so we get:
![V=9\pi[tan \frac{\pi}{3} - tan 0]](https://tex.z-dn.net/?f=V%3D9%5Cpi%5Btan%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20-%20tan%200%5D)
which yields:
]
A financial analyst wanted to estimate the mean annual return on mutual funds. A random sample of 60 funds' returns shows an average rate of 12%. If the population standard deviation is assumed to be 4%, the 95% confidence interval estimate for the annual return on all mutual funds is
A. 0.037773 to 0.202227
B. 3.7773% to 20.2227%
C. 59.98786% to 61.01214%
D. 51.7773% to 68.2227%
E. 10.988% to 13.012%
Answer: E. 10.988% to 13.012%
Step-by-step explanation:
Given;
Mean x= 12%
Standard deviation r = 4%
Number of samples tested n = 60
Confidence interval is 95%
Z' = t(0.025)= 1.96
Confidence interval = x +/- Z'(r/√n)
= 12% +/- 1.96(4%/√60)
= 12% +/- 0.01214%
Confidence interval= (10.988% to 13.012%)
Group 'em together
a
b
−
a
+
1
−
b
a
b
−
a
=
a
(
b
−
1
)
Notice that there will be a 1 as without it it'll simply be ab
1
−
b
=
1
(
1
−
b
)
Notice that it doesn't match with the upper one... so we'll change the signs
1
(
1
−
b
)
=
−
1
(
b−
1
)
(try to multiply them now!!
Jot them down in one expression
a
(
b
−
1
)
−
1
(
b
−
1
)
You get!!!!!!
(
a
−
1
)
(
b
−
1
)
