Answer:
k = 8
Step-by-step explanation:
Since the roots of the equation 3x² + 2x + k are x₁ and x₂ and 2x₁ = 3x₂.
By the roots of an equation, ax² + bx + c , where its roots are x₁ and x₂. It follows that sum of roots are x₁ + x₂ = -b/a and product of roots are x₁x₂ = c/a.
Comparing both equations, a = 3 b = 2 and c = k.
So, x₁ + x₂ = -b/a = -2/3 and x₁x₂ = c/a = k/3
x₁ + x₂ = -2/3 and x₁x₂ = k/3
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
Since 2x₁ = -3x₂, and -2x₁ = 3x₂substituting this into equations (1) and (2) above, we have
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
3x₁ + (-2x₁) = -2 and x₁(3x₂) = k
3x₁ - 2x₁ = -2 and x₁(3x₂) = k
x₁ = -2 and x₁(-2x₁) = k
x₁ = -2 and -2x₁² = k
Substituting x₁ = -2 into -2x₁² = k, we have
-2x₁² = k
-2(-2)² = k
2(4) = k
8 = k
So, k = 8
Answer:
A - 28 5/4
B - 29 1/4
D - 117/4
Step-by-step explanation:
<h2>
Answer with explanation:</h2>
Formula for plus-four confidence interval :
, where n= Sample size.
= Sample proportion and 
z* = Critical z-value.
Let p be the proportion of puppies area found with early hip dysplasia.
As per given , we have
n= 42
Since confidence interval is not given , so we assume it as 95% .
z-critical value for 95% confidence is 1.96.
Then, the required confidence interval will become :
Hence, the plus four confidence interval for p = (0.0484, 0.256)
Interpretation: We are 95% sure that the true proportion of puppies area found with early hip dysplasia lies in (0.0484, 0.256).
Answer:
no
Step-by-step explanation:
Answer:um i belevie it is 300
Step-by-step explanation:
hope this helps
