Answer:
2nd option
Step-by-step explanation:
to find f(h(x)) substitute x = h(x) into f(x) , that is
f(h(x))
= f(2x + 3)
= 2x + 3 - 7
= 2x - 4
Answer: The total volume of the the cubes in the tower is 792 cubic centimetres (792 cm³)
Step-by-step explanation: We shall call the volume of the cube at the bottom VB, the volume of the cube at the middle VM, and the volume of the cube at the top VT. The tower is made up of cubes at different levels and at the bottom the cube measures 8 centimetres. The cube at the middle measures 2 cm less than the bottom cube, hence middle cube equals 8 minus 2 which equals 6 cm. The top cube measures 2 cm less than the middle cube, hence the top cube equals 6 minus 2 which equals 4 cm. The volume of each cube is given as;
Volume = L³
The length of a cube measures the same on all sides, that is, length, width and height. The length on all sides therefore of the bottom cube is 8 cm. The volume equals;
VB = 8³
VB = 512 cm³
The length on all sides of the middle cube is 6 cm (measures 2 cm shorter than the bottom cube). The volume of the middle cube equals;
VM = L³
VM = 6³
VM = 216 cm³
The length on all sides of the top cube is 4 cm (measures 2 cm shorter than the middle cube). The volume of the top cube equals;
VT = L³
VT = 4³
VT = 64
From the calculations shown, the total volume of the cubes in the tower is given as;
Total volume = VB + VM + VT
Total volume = 512 + 216 + 64
Total volume = 792 cm³
Total volume is 792 cubic centimetres.
Answer:
Step-by-step explanation:
I have 30 coins, all nickels, dimes, and quarters, worth $4.60. There are two more dimes than quarters. How many of each kind of coin do I have.
..
let quarters be x
dimes = x+2
...
dimes + quarters = x+x+2=2x+2
...
nickels = 30-(2x+2)
...
5(30-(2x+2))+10(x+2)+25x=460
5(30-2x-2)+10x+20+25x=460
150-10x-10+10x+20+25x=460
160+25x=460
-160
25x=460-160
25x=300
/25
x=300/25
x=12 ---- quarters
x+2= 12+2=14 dimes
30-(2x+2)=4 nickels
...
check
4*5+14*10+12*25=20+140+300=460
There are 22 roses in the vase
probability of first selecting a red rose = 8/22 = 4/11
P( second one is red) = 7/21 = 1/3
these probabilities are multiplied because the individual picks are independent
so the answer is 4/11 * 1/4 = 4/33
Answer:
A sample size of at least 1,353,733 is required.
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:
98% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
You would like to be 98% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required?
We need a sample size of at least n.
n is found when M = 0.001.
Since we don't have an estimate for the proportion, we use the worst case scenario, that is 
So
Rounding up
A sample size of at least 1,353,733 is required.
