92
given 2a² + 5b²
substitute given values for a and b into the expression
2(- 6)² + 5(2)² = (2 × 36 ) + (5 × 4) = 72 + 20 = 92
Answer: The probability of selecting at least one boy (the probability that the 2 students selected are not both girls) is 62/95 or 0.6526
Step-by-step explanation:
From the question, the students to be chosen must be selected from a group of eight boys and twelve girls. This means that the total number of students that these two students must be chosen from is:
8 + 12 = 20 students.
The next step would be to find the probability of selecting a boy:
= Total number of boys/Total number of students
= 8/20
We will also find the probability of selecting one girl from the group
= Total number of girls/Total number of students
= 12/20
To find the probability that the two selected students are not girls is the same as finding the probability of selecting at least one boy. To do this, we will first find the probability of choosing all girls and then subtract it from 1.
The probability of selecting or choosing 2 girls (without replacement)
(12/20) × (11/19)
= 132/380
= 33/95
Then, the probability of selecting at least one boy (the probability that the students chosen are not both girls)
= 1 - (33/95)
= (95/95) - (33/95)
= 62/95 or 0.6526
A) For this problem, we will need to use a normal calculation, in that we find the z-score and the area to the right using Table A.
z = (10 - 7.65) / 1.45
z = 1.62
area to the left for a z-score of 1.62 = 0.9474
area to the right for a z-score of 1.62 = 0.0526
The probability that a randomly selected ornament will cost more than $10 is 0.0526 or 5.26%.
B) For this problem, we will use the binomial probability formula since the problem is asking for the probability that exactly 3 ornaments cost over $10. There are two forms of this equation. One is <em>nCr x p^r x q^n-r</em> and the other is <em>(n r) x p^r x (1 - p)^n-r</em>. I will show both formulas below.
8C3 x 0.0526^3 x 0.9474^5
(8 3) x 0.0526^3 x 0.9474^5
With both equations, the answer is the same. Whichever you are more familiar or comfortable with is the one I would recommend you use.
The probability that exactly 3 of the 8 ornaments cost over $10 is 0.00622 or 0.622%.
Hope this helps!! :)
Answer:
x=11
Step-by-step explanation:
y= 1/4x
5x-8y=33
5x-8(1/4x)=33
x=11
3. If you have to find g(4), then you should substitute x=4 instead of x into the expression of the function 
So:
Answer 3: correct choice is B.
4. If you have to find x such that h(x)=11,, then you should substitute 11 instead of h(x) into the expression of the function 
So:
Answer 4: correct choice is A.
