Answer and Step-by-step explanation:
For these system of equations, it would be easier to use the substitution method, as we are have one equation that is being equaled to a variable.
Plug the second equation into the value of b for the first equation.
5a + 3(-2a + 3) = 11
Distribute the 3.
5a - 6a + 3 = 11
Simplify.
-a + 3 = 11
Subtract 3 from both sides of the equation.
-a = 8
Divide both sides by -1.
a = -8
Now, we can plug this value into the second equation.
-2(-8) + 3 = b
Multiply -2 and -8 together.
16 + 3 = b
Add together 16 and 3.
19 = b
<u>a = -8</u>
<u>b = 19</u>
<u></u>
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Answer:
Step-by-step explanation:
Since the life of the brand of light bulbs is normally distributed, we would apply the the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = life of the brand of lightbulbs
u = mean life
s = standard deviation
From the information given,
u = 1300 hrs
s = 50 hrs
We want to find the probability that a light bulb of that brand lasts between 1225 hr and 1365 hr. It is expressed as
P(1225 ≤ x ≤ 1365)
For x = 1225,
z = (1225 - 1300)/50 = - 1.5
Looking at the normal distribution table, the probability corresponding to the z score is
0.06681
For x = 1365,
z = (1365 - 1300)/50 = 1.3
Looking at the normal distribution table, the probability corresponding to the z score is
0.9032
Therefore
P(1225 ≤ x ≤ 1365) = 0.9032 - 0.06681 = 0.8364
$60 I think
Use a calculator just in case I’m wrong
Answer:
b)
Step-by-step explanation:
A is invertible if and only if det(A)≠0. Let's compute the determinant of A and find the values k for which it is nonzero.
Using Sarrus's rule, we obtain that
Note that the determinant is a quadratic equation on k, which can be factored as above.
Now the determinant is only zero if k=5 or k=2 (the zeroes of the quadratic polynomial). Therefore, if k≠2,5 the determinant is nonzero so A is invertible.
