Answer:
60
Step-by-step explanation:
To get to 300 from 15 you times 15 by 10 and then by 2, do the same for the number of students who like icecream
The probability of a baby being a boy is 0.514.
Nine baby births are selected and we have to find the probability that at last one of them is a girl.
P(At least one out of 9 is baby girl) = 1 - P(No baby girl)
= 1 - P(All 9 are baby boy)
= 1 - (0.514)^9
= 1 - 0.0025
= 0.9975
The probability that at least one out of 9 selected births is baby girl is 0.9975
Answer:
See below
Step-by-step explanation:
<em>Vector argument</em>
Vector DF is (5, -4) - (5, 5) = (0, -9).
Vector EG is (2, 2) - (8, 2) = (-6, 0).
The dot-product of these two vector is (0, -9)•(-6, 0) = 0·(-6) + (-9)·0 = 0.
When the dot-product of two vectors is zero, those vectors are at right-angles to each other. Therefore diagaonal DF ⊥ diagonal EG.
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<em>Alternate argument</em>
The x-coordinates of points D and F are the same, so diagonal DF is a vertical line. The y-coordinates of points E and G are the same, so diagonal EG is a horizontal line. Vertical lines are perpendicular to horizontal lines, so DF ⊥ EG.
Answer: x=-1, y=2, z=-3
Step-by-step explanation:
[1] 2x + 3y - 4z = 16
[2] -x + 2y - z = 8
[3] 2x - y - 2z = 2
Solve by Substitution :
Solve equation [3] for the variable y
[3] y = 2x - 2z - 2
Plug this in for variable y in equation [1]
2x + 3•(2x-2z-2) - 4z = 16
8x - 10z = 22
Plug this in for variable y in equation [2]
-x + 2•(2x-2z-2) - z = 8
3x - 5z = 12
Solve equation [2] for the variable x
3x = 5z + 12
x = 5z/3 + 4
Plug this in for variable x in equation [1]
8•(5z/3+4) - 10z = 22
10z/3 = -10
10z = -30
Solve equation for the variable z
10z = - 30
z = - 3
By now we know this much :
x = 5z/3+4
y = 2x-2z-2
z = -3
Use the z value to solve for x
x = (5/3)(-3)+4 = -1
Use the x and z values to solve for y
y = 2(-1)-2(-3)-2 = 2
