Let daniel's age = d and let jessica's age = j
let your current age = x and your wife's current age = y
x = 5d (given in question)
∴ x - 5d = 0
x + 21 = 2(d+21) (given in question)
∴ x + 21 = 2d + 42
∴ x - 2d = 21
We can solve these two rearranged equations simultaneously by multiplying the first equation by -1 and adding them. This gives us the following:
3d = 21
∴ d = 7
This means that daniel is currently 7 and (if we substitute d = 7 into one of the equations) you are 35. We use a similar method for your wife's and jessica's current ages.
y = 7j (given in question)
∴ y - 7j = 0
y + 8 = 3(j + 8)
∴y + 8 = 3j + 24
∴ y - 3j = 16
If we use a similar method of elimination we get this:
4j = 16
∴ j = 4
Hence, from this we can concur that daniel is 7 and jessica is 4.
Answer:
Margin of error at 90% is 0.024
Margin of error at 99% is 0.037
Step-by-step explanation:
Sample size = 1076
A poll found that 64% of a random sample of 1076 adults said they believe in ghosts.
So, No. of adults said they believe ghosts = 
So, x = 688
n = 1076
z at 90% confidence is 1.64
So, margin of error at 90% is 0.024
Find the margin of error needed to be 99% confident.
z at 99% confidence is 2.58
So, margin of error at 99% is 0.037
9514 1404 393
Answer:
164π cm²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr²
The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...
1/2A = (1/2)(π)(d/2)² = (π/8)d²
The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.
The total area will be ...
area of largest + area of middle-size - area of smallest
= (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²
The area of the shape is 164π cm².
Answer:
What is the longest side?
square root of 1700
What is the square of the longest side?
1700
What is the sum of the squares of the two shorter sides?
1700
Does the window frame form right triangles?
Yes, the sum of the square of the two shorter sides equals the square of the longest side.
