In a quadratic equation with the general formula of:
ax^2 + bx + c = 0
The discriminant is equal to b^2 - 4(a)(c). If the answer is a perfect square, then there are two real numbers. If not, then there are no real number root.
The discriminant for this equation is
(-6)^2 - 4(3)(1) = 24
Since 24 is not a perfect square, there are no real number roots.
Answer:
For first lamp ; The resultant probability is 0.703
For both lamps; The resultant probability is 0.3614
Step-by-step explanation:
Let X be the lifetime hours of two bulbs
X∼exp(1/1400)
f(x)=1/1400e−1/1400x
P(X<x)=1−e−1/1400x
X∼exp(1/1400)
f(x)=1/1400 e−1/1400x
P(X<x)=1−e−1/1400x
The probability that both of the lamp bulbs fail within 1700 hours is calculated below,
P(X≤1700)=1−e−1/1400×1700
=1−e−1.21=0.703
The resultant probability is 0.703
Let Y be a lifetime of another lamp two bulbs
Then the Z = X + Y will follow gamma distribution that is,
X+Y=Z∼gamma(2,1/1400)
2λZ∼
X+Y=Z∼gamma(2,1/1400)
2λZ∼χ2α2
The probability that both of the lamp bulbs fail within a total of 1700 hours is calculated below,
P(Z≤1700)=P(1/700Z≤1.67)=
P(χ24≤1.67)=0.3614
The resultant probability is 0.3614
When there's a strong positive, the points are: B. Close together.
<h3>Strong Positive Relationship</h3>
- On a scatter plot, if the data points are close together along the trend line sloping upwards, it means there's a strong positive correlation.
- Strong positive correlation means the two variables change in the same direction.
Therefore, when there's a strong positive, the points are: B. Close together.
Learn more about strong positive relationship on:
brainly.com/question/15552860
Answer:
The answer is B
Step-by-step explanation:
3 to the forth power = 81
3 to the second power = 9
81/9 = 9
We take the distance from points which indicates the location of the park and the mall.
For distance through north and east, we have positive values and negative for west and south.
Mall: (-3, -4)
Park: (3, 5)
The distance is calculate through the equation,
d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)
Substituting,
d = sqrt ((-4 - 5)² + (-3 - 3)²
d = sqrt 117 = 10.82
Thus, the distance between the mall and the park is approximately 10.82 miles.
