By normal curve symmetry
<span>from normal table </span>
<span>we have z = 1.15 , z = -1.15 </span>
<span>z = (x - mean) / sigma </span>
<span>1.15 = (x - 150) / 25 </span>
<span>x = 178.75 </span>
<span>z = (x - mean) / sigma </span>
<span>-1.15 = (x - 150) / 25 </span>
<span>x = 121.25 </span>
<span>interval is (121.25 , 178.75) </span>
<span>Pr((121.25-150)/25 < x < (178.75-150)/25) </span>
<span>is about 75%</span>
The outcomes with neither die showing 2 is 25
<h3>How to determine the outcomes with neither die showing 2?</h3>
The sample sizes of the dice are given as:
Blue die = 6
Red die = 6
The outcomes with neither die showing 2 is
Outcomes = Red die * blue die - (blue die + red die) + 1
So, we have:
Outcomes = 6 * 6 - (6 + 6) + 1
Evaluate
Outcomes = 25
Hence, the outcomes with neither die showing 2 is 25
Read more about dice at:
brainly.com/question/13632618
#SPJ1
Answer:
The corresponding p-value, is p = 1
Step-by-step explanation:
The maximum score SAT score, n = 1,600
The mean of the district's total SAT score distribution = 1,200
The claim of one of the districts principal, is the that mean of the district's total SAT score distribution ≠ 1,200
Using proportions, we have;
p = 1,200/1,600 = 0.75
q = 1 - p = 0.25
The margin of error, E = Z√(p·q/n)
∴ E = 5% = Z×√((0.75 × 0.25)/1,600)
z = 0.05/(√((0.75 × 0.25)/1,600)) ≈ 4.61880
Therefore, the corresponding p-value, p = 1
Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
9514 1404 393
Answer:
84 in
Step-by-step explanation:
The Pythagorean theorem is used to find the length 'b'.
b^2 +12^2 = 37^2
b = √(37^2 -12^2) = √1225 = 35
Then the perimeter is the sum of side lengths:
P = a + b + c = 12 + 35 + 37
P = 84 . . . inches
