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We will create the equations for this scenario:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
Find z: Monthly administration fee is represented by z, which is the question of this problem.
The amounts of kilowatt hours consumed are 1100 and 1500 respectively.
The cost for each kilowatt hour is denoted by y, although its value is not required for this math problem, we can compute it regardless.
This results in a system of two equations with two unknowns, which can be solved using the substitution method:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
----------------------------
(1) z = 113 - 1100*y [substituting z (right side) into equation (2) instead of z]:
(2) 1500*y + (113 - 1100*y) = 153
-------------------------------------------------
(1) z = 113 - 1100*y
(2) 1500*y + 113 - 1100*y = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y + 113 = 153
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 153 - 113
------------------------------------------------
(1) z = 113 - 1100*y
(2) 400*y = 40
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 40/400
------------------------------------------------
(1) z = 113 - 1100*y
(2) y = 1/10
------------------------------------------------
by placing the calculated value of y back into equation (1), we can find z:
(1) z = 113 - 1100*(1/10)
(1) z = 113 - 110
(1) z = 3 dollars serves as the monthly fee.

Answer:0.246 ft/s

Step-by-step explanation: As the worker starts moving and stops 10 feet away from the side rope connected to the load, it creates a right triangle, as illustrated in the image.

V = s/t... equation 1

S = distance the worker travels while pulling the rope = 10 ft

V = worker's velocity = 2 ft/s

T = time it takes for the worker to cover 10 ft = the same time the load takes to rise = 5 seconds

Using Pythagorean theorem to find the distance from the pulley to the new position of the worker

Square root of (40^2 + 10^2) = 41.23 ft

Distance covered by load = D = 41.23 - 40

= 1.23 ft

Load speed = D/t...equation 2

Substituting D and t into equation 2 gives us

Load speed = 1.23/5 = 0.246 ft/s

Answer:

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)

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

b)

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

c)

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

Where and

We seek the probability:

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

By applying this formula, we can find the probability:

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

Part b

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

Part c

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments: