Answer:
C. 
Step-by-step explanation:
Given that A and B are matrices and
is a scalar, then the distributive property of scalar multiplication over addition is given by;

The distributive property of scalar multiplication over subtraction is

The correct answer is C.
Answer:
(7,-3)
Step-by-step explanation:
y = -3
substitute in the first equation
3x - y^2 = 12
3x - (-3)^2 = 12
3x - 9 = 12
3x = 12 + 9
3x = 21
x = 7
coordinates of intersection (7,-3)
Answer:
Number = 15.
Step-by-step explanation:
Given : If you multiply a number by 3 and then subtract 5, you will get 40.
To find : what is the number.
Solution : We have given if you multiply a number by 3 and then subtract 5, you will get 40.
According to question :
Let the number = x
Multiply is with 3 = 3x
Subtract 5 from it we get 40 .
3x -5 = 40
On adding both sides by 5
3x = 45 .
On dividing both sides by 3
x = 15.
Therefore, Number = 15.
Answer:
Probability that at least 490 do not result in birth defects = 0.1076
Step-by-step explanation:
Given - The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent.
To find - If 500 births were observed rather than only 5, what is the approximate probability that at least 490 do not result in birth defects
Proof -
Given that,
P(birth that result in a birth defect) = 1/33
P(birth that not result in a birth defect) = 1 - 1/33 = 32/33
Now,
Given that, n = 500
X = Number of birth that does not result in birth defects
Now,
P(X ≥ 490) =
=
+ .......+
= 0.04541 + ......+0.0000002079
= 0.1076
⇒Probability that at least 490 do not result in birth defects = 0.1076
————————————-The answer is 3.78