Answer:
a) 0.1587
b) 0.0475
c) 0.7938
Step-by-step explanation:
Let's start defining our random variable.
X : ''Thickness (in mm) of ancient prehistoric Native American pot shards discovered in a Hopi village''
X is modeled as a normal random variable.
X ~ N(μ,σ)
Where μ is the mean and σ is the standard deviation.
To calculate all the probabilities, we are going to normalize the random variable X.
We are going to call to the standard normal distribution ''Z''.
[(X - μ) / σ] ≅ Z
We normalize by subtracting the mean to X and then dividing by standard deviation.
We can find the values of probabilities for Z in a standard normal distribution table.
We are going to call Φ(A) to the normal standard cumulative distribution evaluated in a value ''A''
a)
Φ(-1) = 0.1587
b)
1 - Φ(1.666) = 1 - 0.9525 = 0.0475
c)
Φ(1.666) - Φ(-1) = 0.9525 - 0.1587 = 0.7938
Answer:
10:40
Step-by-step explanation:
9514 1404 393
Answer:
(X, Y, Z) = (-2, 3, 3)
Step-by-step explanation:
We can subtract the second equation from the first to get ...
Y -Z = 0
We can add the third equation to the first to get ...
Z = 3
Then ...
Y -3 = 0 ⇒ Y = 3
and ...
X -3 -2(3) = -11
X = -2 . . . . . . . . . add 9
The solution is ...
(X, Y, Z) = (-2, 3, 3)
The 9-sided polygon will have a central angle between the vertex and the center of one side of 360°/(2*9) = 20°. Then the apothem is
a = (6 in/2)*cot(20°) ≈ 8.242432 in
The perimeter is 9*6 in = 54 in, so the area is
A = (1/2)Pa = (1/2)*(54 in)*(8.242432 in) ≈ 222.5 in²
(1) Snow fall in last week = inches
Snow fall in today= inches
Let us first change mixed fraction to improper fraction.
Now, make the denominators same.
,
Now, find the difference between 14/4 and 23/4.
So, compared to last week more inches of snow fell today.
(2) Given three times a number, minus nine, equals six times six, divided by four.
Let a number be X.
3X – 9 = 6 × 6/4
(3) To solve the equation:
3X – 9 = 6 × 6/4
3X – 9 = 36/4
3X – 9 = 9
3X = 18
X = 6