An automobile manufacturer is concerned about the possibility of a fault in the engine of a particular model of one of its cars. This fault could potentially cause the engine to fail to start. The average number of cars per year that experience this fault is 4 cars. If the probability that 10 or more cars experience this fault in a year is at least 0.01, the manufacturer will issue a recall. Will the manufacturer issue a recall for this engine fault

The probability of 10 or more cars experiencing the fault, 0.00813 is less than 0.01, hence, the manager will not issue a recall for this engine fault.

Step-by-step explanation:

This is Poisson distribution problem

Poisson distribution formula is given by

P(X = x) = (e^-λ)(λˣ)/x!

where λ = mean = 4 cars developing faults per year.

x = variable whose probability is required = 10 or more cars

Meaning we require

P(X ≥ x) = Σ (e^-λ)(λˣ)/x! (Summation From x to the end of the variables)

But Mathematically,

P(X ≥ 10) = 1 - P(X ≤ 9) (since only whole number values are allowed for X)

Therefore,

P(X ≥ 10) = 1 - P(X ≤ 9) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) ++ P(X=9)]

P(X ≥ 10) = 1 - P(X ≤ 9) = 1 - 0.99187 = 0.00813

P(X ≥ 10) = 0.00813 < 0.01, Hence the manager will not issue a recall for this engine fault.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1