Answer:
Roots: 3.746 and -13.746
Vertex: (-5, 153)
Step-by-step explanation:
- The roots of the quadratic equation y = ax² + bx + c, are the values of x at y = 0
- Its vertex is (h, k), where, h = , and k is the value of y at x = h
Let us use these facts to solve the question
∵ y = -2x² - 20x + 103
→ Compare it by the form of the equation above
∴ a = -2, b = -20, and c = 103
→ To find its roots equate y by 0
∵ 0 = -2x² - 20x + 103
→ Use your calculator to find the values of x
∴ x = 3.746427842 and x = -13.74642784
→ Round them to 3 decimal places
∴ x = 3.746 and x = -13.746
∴ Roots: 3.746 and -13.746
→ To find its vertex use the rule of h above
∵ a = -2 and b = -20
∵ h = =
∴ h = -5
→ To find k substitute y by k and x by -10 in the equation
∵ k = -2(-5)² - 20(-5) + 103
∴ k = -2(25) + 100 + 103
∴ k = -50 + 100 + 103
∴ k = 153
∴ The vertex of the quadratic is (-5, 153)
∴ Vertex: (-5, 153)
Answer:
(a): Marginal pmf of x
(b): Marginal pmf of y
(c): Mean and Variance of x
(d): Mean and Variance of y
(e): The covariance and the coefficient of correlation
Step-by-step explanation:
Given
<em>x = bottles</em>
<em>y = carton</em>
<em>See attachment for complete question</em>
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Solving (a): Marginal pmf of x
This is calculated as:
So:
Solving (b): Marginal pmf of y
This is calculated as:
So:
Solving (c): Mean and Variance of x
Mean is calculated as:
So, we have:
Variance is calculated as:
Calculate
So:
Solving (d): Mean and Variance of y
Mean is calculated as:
So, we have:
Variance is calculated as:
Calculate
So:
Solving (e): The covariance and the coefficient of correlation
Covariance is calculated as:
Calculate E(xy)
This gives:
So:
The coefficient of correlation is then calculated as:
--- approximated
Answer:
a and b are positive
Step-by-step explanation:
We are given that
We have to find that a and b are positive or negative.
We have
It means b is positive and greater than 4.
Adding 3 on both sides
Hence, a is positive and greater than 4.
Therefore, a and b are positive
Answer:
20
Step-by-step explanation:
The formula for circumference is 2r, where r stands for radius. Therefore, the circumference of this circle can be defined by:
2r
210
20
Hope this helps :) Please contact me if you have any questions!
Answer:
484,000
Step-by-step explanation:
The hundreds place is less than 5 so you round down.