So we have 10 painters and sculptors all together. There are also 22 people in total. That means we have a 10/22 chance it will be one of those artists. This fraction can be reduced to 5/11.
Solve for y:
x + y = 0
Subtract x from both sides:
Answer: y = -x
The range of sinx is [-1; 1]
The range of 3sinx is [-3; 3]
The range of 3sinx + 3 is [0; 6]
Answer: y ∈ [0; 6]
Answer:
9m ×5m
Step-by-step explanation:
Area of a rectangle= length ×width
Let the width be W meters and the length be L meters.
2 equations can be written from the given information:
45= WL -----(1)
L= W +4 -----(2)
Substitute (2) into (1):
45= W(W +4)
<em>Expand:</em>
45= W² +4W
<em>-45 on both sides:</em>
W² +4W -45= 0
<em>Factorise:</em>
(W +9)(W -5)= 0
W+9=0 or W-5=0
W= -9 or W= 5
(reject)
Substitute W= 5 into (2):
L= 5 +4
L= 9
∴ The dimensions of the garden is 9m ×5m.
xBar ± z * sx / sqrt(n)
where xBar is the sample
mean
z is the zscore for having
α% of the data in the tails, i.e., P( |Z| > z) = α
sx is the sample standard
deviation
n is the sample size
For sample size
calcualtions we need the following. The width of the interval, from one end
point to the center is:
z * sx / sqrt(n) =
w and solving for n gives:
<span> n = (z * sx / w) ^ 2 </span>
remember that n needs to
be an integer. Always take the ceiling, i.e., round up. If you round down then
the width of the interval will not be correct, it will be too wide. By rounding
up, the interval will be more narrow than asked for, but this is a good thing.
It means there is more precision in the estimate.
<span> here we have </span>
z = 2.05
w = 0.04 * 152 = 6.08
n = (z * sx / w) ^ 2 n =
(2.05 * 26 / 6.08)^2
n = 76.8506
Round of the answer since
n must be an integer.
<span>n = 77 </span>
