Answer:
The probability that a defective rod can be salvaged = 0.50
Step-by-step explanation:
Given that:
A machine shop produces heavy duty high endurance 20-inch rods
On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod.
If such defective rods can be cut so that there is at least 15 consecutive inches without a groove.
Then; The defective rod can be salvaged if the groove lies on the rod between 0 and 5 inches i.e ( 20 - 15 )inches
Now:
P(X ≤ 5) = 
= 0.25
P(X ≥ 15) =
= 0.25
The probability that a defective rod can be salvaged = P(X ≤ 5) + P(X ≥ 15)
= 0.25+0.25
= 0.50
∴ The probability that a defective rod can be salvaged = 0.50
Answer: (1.5, 0)
Step-by-step explanation:
Given : The shape of his satellite can be modeled by 
where x and y are modeled in inches.
Now,the given equation is a equation of parabola.
Here, coefficient of x is positive, hence the parabola opens rightwards.
On comparing this equation with standard equation 
, we get
In standard equation, coordinates of focus=(m,0)
Thus for given equation coordinates of focus=(1.5,0)
Step-by-step explanation:
The simplest method is "brute force". Calculate each term and add them up.
∑ = 3(1) + 3(2) + 3(3) + 3(4) + 3(5)
∑ = 3 + 6 + 9 + 12 + 15
∑ = 45
∑ = (2×1)² + (2×2)² + (2×3)² + (2×4)²
∑ = 4 + 16 + 36 + 64
∑ = 120
∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)
∑ = -4 + -2 + 0 + 2
∑ = -4
4. 1 + 1/4 + 1/16 + 1/64 + 1/256
This is a geometric sequence where the first term is 1 and the common ratio is 1/4. The nth term is:
a = 1 (1/4)ⁿ⁻¹
So the series is:
5. -5 + -1 + 3 + 7 + 11
This is an arithmetic sequence where the first term is -5 and the common difference is 4. The nth term is:
a = -5 + 4(n−1)
a = -5 + 4n − 4
a = 4n − 9
So the series is:
The difference of finish times has a mean of
μ = 105 -98 = 7 . . . . minutes
and a variance of
σ² = 10² +15² = 325 . . . . minutes²
Using a probability calculator, we find the probability to be
p(-5 < x < 5) ≈ 0.2030
For this case we have the following polynomial:
The first thing to do is to place the variables on the same side of the equation.
We have then:
We complete the square by adding the term (b / 2) ^ 2 on both sides of the equation.
We have then:
Rewriting we have:
Therefore, the solutions are:
Answer:
the solution set of the equation is:
