Step-by-step explanation:
x^2 -2kx +7k -12 = 0
two equal roots -->Δ = b^2 -4ac = 4k^2 - 4(7k-12)=0 = 4(k^2 - 7k +12)=4(k-4)(k-3)=0
so k =3 and k =4
Answer: Angle ABC = 60, angle CBD = 120 and angle GFH = 60
Step-by-step explanation: Line ABD is parallel to line EFG. Line line CFH is a straight line that cuts across both parallel lines. Therefore, angle FBD and angle HFG are corresponding angles. That means angle FBD equals 3x. Also 3x plus 6X equals 180. That is,
3x + 6x = 180 {Sum of angles on a straight line equals 180}
9x = 180
Divide both sides of the equation by 9
x = 20.
That means angle 6x measures 6(20) and that is 120 degrees.
Also angle 3x measures 3(20) and that is 60 degrees.
Angle ABC + Angle CBD = 180 {Sum of angles on a straight line equals 180}
Angle ABC + 120 = 180
Angle ABC = 180 - 120
Angle ABC = 60
Also angle CBD equals 6x, and x = 20. Therefore angle CBD = 6 x 20
Angle CBD = 120.
And then, angle GFH = 3x, and x equals 20. Hence angle GFH = 60.
Therefore angle ABC = 60, angle CBD = 120 and angle GFH = 60.
Answer:
0.1007
Step-by-step explanation:
Given :
Average gain, μ = 0.8
Standard deviation, σ = 0.7
Number of companies, n = 20
Obtaining the standardized value ;
Zscore = (x - mean) / (σ/√n)
Zscore = (1 - 0.8) / (0.7/√20)
Zscore = (0.2 / 0.1565247)
Z = 1.27775
Using the Z probability calculator :
P(Z > 1.27775) = 0.10067
P(Z > 1.27775) = 0.1007 ( Z probability calculator)
Answer:
Mia has a bag that contains a letter block for each of the 26 letters of the alphabet. She draws a letter block from the bag, writes down the letter, and puts the block back in the bag. She repeats this 26 times. The results show that she drew a vowel (A, E, I, O, or U) 6 times.
Step-by-step explanation:
Short answer: 98
Remark
when you have an average of 71, it's like saying that you took 4 quizzes and got 71 on all of them.
Step One
Find the total point count for the 4 quizzes.
T_4 = 71 * 4 = 284
Step Two
Create an equation that will give you the necessary point count to average 86.
284 + 5*x = 86 * 9
Why did we do this? It is because you have 9 quizzes altogether. All nine must be something that gives a point count of 86 on each quiz. You have to put together 9 such quizzes with a total count of 774.
Step three
Solve the equation.
284 + 5x = 774 Subtract 284 from both sides.
5x = 774 - 284
5x = 490 Divide by 5
x = 490/5
x = 98
You must get an average of 98 on the next 5 quizzes
Answer: 98 <<<<<
