1) For a quadratic equation, we'll have two answers typically. We're looking for two numbers that when multiplied give -64, and when added give -12. This is a bit of trial and error, but you go about it by systematically factoring -64 in all possible combinations: 64=-2*32=2*-32=-4*16=4*-16=-8*8. Of these, I can 'see' that I can make -12 with 4 and -16. So the factorization of the equation becomes:
(x-16)(x+4)=0, so x=16 or x=-4.
Answers B and D are correct.
For (2), same trick applies. Rewrite as x²-8x-48=0. Factor as (x+4)(x-12)=0 because 4*-12=-48 and 4-12=-8. The other solution is x=12.
4x + 8 = 2x + 6
-2x ----- -2x
2x + 8 = 6
----- -8 ---8
2x = -2
÷-2 ÷-2
x = -1
Hope this helps!
Answer: A
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p = x/n
Where x = number of success
n = number of samples
For the first treatment,
x = 35
n1 = 50
p1 = 35/50 = 0.7
For the second treatment,
x = 16
n2 = 40
p2 = 16/40 = 0.4
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.005 = 0.995
The z score corresponding to the area on the z table is 2.576. Thus, the z score for 99% confidence level is 2.576
Margin of error = 2.576 × √[0.7(1 - 0.7)/50 + 0.4(1 - 0.4)/40]
= 2.576 × 0.10099504938
= 0.26
Confidence interval = 0.7 - 0.4 ± 0.26
= 0.3 ± 0.26
Option A is correct
Answer:9
Because,
Two number six’s is twelve.
And if you add twelve and negative three it would equal nine
Or subtract three from twelve
Step-by-step explanation:
sec² x − 2 = 0
sec² x = 2
cos² x = ½
cos x = ±√½
x = π/4, 3π/4, 5π/4, 7π/4
