On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to th

Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

Multiply both sides by 10:

Next, factor the quadratic:

Solving for x gives:

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

Hence, the valid solution is x=70.

Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:

The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.

The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.

Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.

b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.

The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.