Find the measure of each missing angle
1 answer:
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Answer:
f(x) =
Step-by-step explanation:
Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?
There are 3 distinct and real roots given in the question, which means that the function must be a third degree polynomial. The roots are -1, 0, and 2. This means that f(x) = 0 at these points. The general form of the cubic equation is given by:
f(x) = ax^3 + bx^2 + cx + d; where a, b, c, and d are arbitrary constants.
From the given data:
f(-1)=0 implies a*(-1)^3 + b*(-1)^2 + c(-1) + d = -a + b - c + d = 0. (Equation 1).
f(0)=0 implies a*(0)^3 + b*(0)^2 + c(0) + d = 0a + 0b + 0c + d = 0. (Equation 2).
f(2)=0 implies a*(2)^3 + b*(2)^2 + c(2) + d = 8a + 4b + 2c + d = 0. (Equation 3).
f(1)=0 implies a*(1)^3 + b*(1)^2 + c(1) + d = a + b + c + d = -6. (Equation 4).
Equation 2 shows that d = 0. So rest of the equations become:
-a + b - c = 0;
8a + 4b + 2c = 0; (Divide 2 on both sides of the equation to simplify).
a + b + c = -6
This system of equation can be solved using the Gaussian Elimination Method. Converting the system into the augmented matrix form:
• 1 1 1 | -6
• -1 1 -1 | 0
• 4 2 1 | 0
Adding row 1 into row 3:
• 1 1 1 | -6
• 0 2 0 | -6
• 4 2 1 | 0
Dividing row 2 with 2 and multiplying row 1 with -4 and add it into row 3:
• 1 1 1 | -6
• 0 1 0 | -3
• 0 -2 -3 | 24
Multiplying row 2 with 2 and add it into row 3:
• 1 1 1 | -6
• 0 1 0 | -3
• 0 0 -3 | 18
It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• a + b + c = -6
• b = -3
• -3c = 18 (This implies that c = -6.)
Put c = -6 and b = -3 in equation 1:
• a + (-3) + (-6) = -6
• a = -6 + 3 + 6
• a = 3.
So f(x) = (All conditions are being satisfied)!!!
Answer:
And we can use the z scoe formula given by:
And if we find the z score for the limits we got:
And this probability is equivalent to:
Step-by-step explanation:
For this case we can define the random variable X as "number of miles between services" and we know the following info given:
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean is given by:
We select a random sample size of n =44. And we want to find this probability:
And we can use the z scoe formula given by:
And if we find the z score for the limits we got:
And this probability is equivalent to: