A company’s profits (P) are related to increases in a worker’s average pay (x) by a linear equation. If the company’s profits drop by $1,500 per month for every increase of $450 per year in the worker’s average pay, what is the slope of the graph of the equation?
Since the company’s profits drop by $1,500 per month for every increase of $450 per year in the worker’s average pay, the slope of the graph of the equation is -40.
In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
Based on the information provided, we can logically deduce that the rise and run are as follows;
Rise = 12 × -1500 = 18,000 units (its negative because the profit drops)
Run = 450 units.
By substituting the given data into the formula for the slope of a line, we have the following:
Slope (m) = rise/run
Slope (m) = -18000/450
Slope (m) = -40.
PLEASE HELP NO ONE WILL HELP ME! I NEED PROS! TYSM! For f(x) = 3 x 5 − 5 x 3 + 3 . Determine the interval(s) on which f(x) is concave up and on which f(x) is concave down AND indicate where f(x) has inflection point(s). (If there are none, please tell me). Also, indicate where f(x) has local maximum and local minimum points. Also, can you please help me determine the interval(s) on which f(x) is increasing and on which f(x) is decreasing.
The number 272 is a palindrome because it reads the same forward or backward How many numbers from 10 to 1000 are palindromes
A european outlet supplies 220 v (rms) at 50 hz. how many times per second is the magnitude of the voltage equal to 220 v
Explains how many times per second the magnitude of the voltage equals 220 V in a European outlet at 50 Hz frequency.
Explanation:The frequency at which the magnitude of the voltage is equal to 220 V is:
Convert the given 220 V (rms) to peak voltage: 220 V x √2 = 311.13 VSince the voltage alternates sinusoidally, it will reach 311.13 V twice per cycle (positive and negative peaks).For a 50 Hz frequency, the number of times the magnitude of the voltage equals 220 V will be 2 x 50 = 100 times per second.For children between the ages of 18 months and 29 months, there is approximately a linear relationship between height and age. the relationship can be represented by ŷ = 63.80 + 0.61x where y represents height (in centimeters) and x represents age (in months). joseph is 23.5 months old and is 80 centimeters tall. what is joseph's residual?
a.78.135
b.112.600
c.5.865
d.1.865
e.-32.600 f) none of the above
Answer: Joseph's residual is 1.86 (option d).
Step-by-step explanation:
Hi, to answer this question we have to replace the variable "x" for Joseph’s age (23.5 months) in the equation given:
y = 63.80 + 0.61x.
y = 63.80 + 0.61 (23.5)
y = 63.80 + 14.335 = 78.135
Now, we subtract the amount obtained to Joseph's height ( 80 centimeters).
Mathematically speaking:
80 - 78.135 = 1.865
So, Joseph’s residual is 1.86 (option d).
If you bike for 60km at 30km/h and return at 20km/h what is your average speed for the whole trip
2/5 of the students in your class are in band. Of these, 1/4 play the saxophone. What fraction of your class plays the saxophone?
At Travis's Hats, 60% of the 25 hats are baseball caps. How many baseball caps are there?
Alana spent 21 dollars of her 300 dollar paycheck on a gift . What percent of her paycheck was spent on the gift
Thr profits in December were 5 times the profits in June. If Decembers profit were $3455 how much were thw profits in June?
an office has an area 120 square meters and a width of 12 meters write an equation to represent the area
The mean water temperature downstream from a discharge pipe at a power plant cooling tower should be no more than 100°f. past experience has indicated that the (population) standard deviation of temperature is 2°f. the water temperature is measured on nine randomly chosen days, and the average temperature is found to be 98°f. if you were to do a hypothesis test using the data from this problem to test the hypothesis that the population mean temperature is 97 degrees f, which test statistic would you need to use?
Actually in this case we will make use of the z test statistic. In which we calculate for the z score and then use the standard normal distribution tables to find for the P value at the calculate z score.
z = (x – u) / s
z = (97 – 98) / 2
z = -0.5
The z value should be greater than 1.65 to for the null hypothesis to be accepted. Hence rejected.
What is the selling price if the actual cost is $720 and 43% markup on selling price
What is a normal distribution with a mean of 0 and a standard deviation of 1 called?
A normal distribution with a mean of 0 and a standard deviation of 1 called The Standard normal distribution or z - distribution.
What is Standard normal distribution?A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.
Given that a normal distribution with a mean of 0 and a standard deviation of 1
In the given condition, the normal distribution is called Standard normal distribution or z - distribution or Gaussian distribution.
Hence, the normal distribution with a mean of 0 and a standard deviation of 1 called Standard normal distribution or z - distribution or Gaussian distribution.
For more references on Standard normal distribution, click:
https://brainly.com/question/14916937
#SPJ2
the difference between two integers is 13 and their sum is 87. What are the two integers
it would be 50 and 37
a company must select 4 candidates to interview from a list of 12, which consist of 8 men and 4 women.
How many selections of 4 candidates regardless of gender?
How many selections are possible, if 2 women must be selected?
How many selections are possible, if at least 2 women must be selected?
Evaluate the polynomial xyz^2-z when x=6, y=-4, and z=-2
Write the whole number as an equivalent fraction with the indicated denominator.
Ben is 8 years older than Sarah 10 years ago Ben was twice as old as Sarah how old are Ben and Sarah today
How do u solve 24tenths-1 one 3 tenths
two pumps of different sizes, working together, can empty a fuel tank in 3 hours. the larger pump can empty the tank in 4 hours less than the smaller one. if the larger pump is not working, how long will it take the smaller pump to do the job alone?
To find the time it takes for the smaller pump to empty the tank alone, we need to first determine the rate of the smaller pump and solve an equation involving the rates of both pumps.
Explanation:Let's denote the rate at which the smaller pump can empty the tank as x gallons per hour. Since the larger pump can empty the tank in 4 hours less than the smaller pump, its rate would be x+4 gallons per hour.
Working together, the total rate at which they can empty the tank is the sum of their individual rates:
x + (x+4) = 1/3 gallons per hour.
Solving this equation will give us the rate of the smaller pump (x), and we can then calculate how long it would take the smaller pump to empty the tank alone.
Final answer:
To find the time it takes for the smaller pump to empty the tank alone, we calculate the combined rate of both pumps and set up an equation based on their separate rates. After solving, we find that it takes the smaller pump 6 hours to empty the tank by itself.
Explanation:
To solve this problem, we can set up a system of equations based on the rates at which the pumps work. Let's denote the time it takes the smaller pump to empty the tank alone as x hours. According to the problem, the larger pump can do this in x - 4 hours. When working together, they can empty the tank in 3 hours.
If the smaller pump's rate is 1/x tanks per hour and the larger pump's rate is 1/(x-4) tanks per hour, the combined rate when they work together is the sum of their individual rates, which is 1/3 tanks per hour.
We can set up the equation as follows:
1/x + 1/(x-4) = 1/3
To solve for x, find a common denominator and combine terms:
(x-4 + x)/(x(x-4)) = 1/3
Multiply all terms by the common denominator x(x-4) to clear the fractions:
2x - 4 = x(x-4)/3
Multiply both sides by 3 to get rid of the fraction:
6x - 12 = x2 - 4x
Rearrange the equation to set it to zero and solve for x:
x² - 10x + 12 = 0
By factoring, we find that x equals 6 or 2. However, since x - 4 must be greater than zero (a pump can't empty a tank in negative time), we discard the solution x = 2 and keep x = 6 hours as the correct answer.
Therefore, the smaller pump will take 6 hours to empty the tank alone.
The ratio is boys to girls is 3:5. If there are 24 boys how many girls are in the class
A multivitamin tablet contains 0.16g of vitamin C. How much vitamin C does a bottle of 60 tablets contain?
how to slove multistep equation 2/5(x-2)=-3
Find the laplace transform of f(t)={0,(t−4),0≤t<4t≥4
The Laplace transform of f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].
Sure, let's find the Laplace transform of the piecewise function [tex]\( f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} \).[/tex]
Define the function for all ( t ):
[tex]\[ f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} = (t - 4)u(t-4) \][/tex]
where u(t) is the unit step function.
Use the definition of the Laplace transform:
[tex]\[ \mathcal{L}\{f(t)\} = \int_0^\infty f(t)e^{-st} dt \][/tex]
Break the integral into two parts based on the piecewise definition of f(t) :
[tex]\[ \mathcal{L}\{f(t)\} = \int_0^4 0 \cdot e^{-st} dt + \int_4^\infty (t - 4)e^{-st} dt \][/tex]
Solve each integral separately:
[tex]\[ \int_0^4 0 \cdot e^{-st} dt = 0 \][/tex]
[tex]\[ \int_4^\infty (t - 4)e^{-st} dt = \int_4^\infty te^{-st} dt - 4\int_4^\infty e^{-st} dt \][/tex]
Integrate:
[tex]\[ = \left[ -\frac{1}{s}te^{-st} \right]_4^\infty - \left[ -\frac{4}{s}e^{-st} \right]_4^\infty \][/tex]
[tex]\[ = \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) - \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) \][/tex]
[tex]\[ = \frac{4}{s}e^{-4s} \][/tex]
Combine the results:
[tex]\[ \mathcal{L}\{f(t)\} = \frac{4}{s}e^{-4s} \][/tex]
So, the Laplace transform of f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].
The Laplace transform of the given piecewise function f(t) is found using the Heaviside step function and shifting theorem, yielding[tex]\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]
To find the Laplace transform of the function f(t), we'll break it down into two parts: one for t < 4 and another for [tex]\( t \geq 4 \).[/tex]
For t < 4 , f(t) = 0 , so its Laplace transform is simply 0.
For [tex]\( t \geq 4 \), \( f(t) = (t - 4)^3 \)[/tex]. We'll use the property of the Laplace transform that states [tex]\( \mathcal{L}\{t^n\} = \frac{n!}{s^{n+1}} \). So, for \( f(t) = (t - 4)^3 \)[/tex], we get:
[tex]\[ \mathcal{L}\{(t - 4)^3\} = \frac{3!}{s^{3+1}} \\\[ = \frac{6}{s^4} \][/tex]
Now, we can combine both parts:
[tex]\[ \mathcal{L}\{f(t)\} = 0 \quad \text{for } t < 4 \\\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \quad \text{for } t \geq 4 \\\text{Therefore, the Laplace transform of}\; \( f(t) \) is:\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]
Suppose you go shopping for a new futon bed for your apartment/home. The model you really like happens to be on sale for $675. It's original price is $900. What percent of the original price will you save if you purchase it?
Answer:
[tex]25\%[/tex]
Step-by-step explanation:
Given: you go shopping for a new futon bed for your apartment/home.The model you really like happens to be on sale for [tex]\$675[/tex]. It's original price is [tex]\$900[/tex].
To Find: What percent of the original price will you save if you purchase it.
Solution:
Original price of model [tex]=\$900[/tex]
discounted price of model on sale [tex]=\$675[/tex]
Now,
money saved by buying model from sale [tex]=\text{original price}-\text{price on sale}[/tex]
[tex]900-675[/tex]
[tex]\$225[/tex]
percentage of the original price saved [tex]=\frac{\text{Amount saved}}{\text{original price of model}}\times100[/tex]
putting values
[tex]\frac{225}{900}\times100[/tex]
[tex]\frac{225}{9}[/tex]
[tex]25\%[/tex]
[tex]25\%[/tex] of original price can be saved if model is purchased from sale.
Beth purchased a computer, and its value depreciated exponentially each year. Beth will sketch a graph of the situation, where x represents the number of years since she purchased the computer, and y represents its value that year.
Beth will only sketch the graph in the quadrant or quadrants for which it makes sense to.
In which quadrant or quadrants will Beth sketch the graph?
1. Quadrants I and IV only
2. Quadrant I only
3. Quadrants I, II, III, and IV
4. Quadrants I and II only
Please help, thank you
So we need a quadrant where x is positive and y in positive. It is the first quadrant.
Answer choice 2 is right.
ANSWER: Answer Choice #2 (Quadrant I only)
which statement describes the function below f(x)=2x^3-3x+1
The given function is f(x)=2x^3+2x^2-x. In this case, the highest degree among the terms is 3. According to the Fundamental Theorem of Algebra, the number of zeros or roots of the equation is equal to the highest degree among the terms. Hence for every value of y, there are 3 equivalent x's. The answer thus is B. It is a many-to-one function.
In six test runs, a truck operated 8, 10, 15, 7, 9, and 11 miles with one gallon of gasoline. at the 95% level of confidence, is this sufficient evidence to show that the truck is operating at a mean rate of about 13.1 miles per gallon (confidence interval)
Anne is comparing savings accounts. One account has an interest rate of 1.2 percent compounded yearly, and one account has an interest rate of 1.2 percent compounded monthly. Which account will earn more money in interest?
Final answer:
An account with an interest rate of 1.2 percent compounded monthly will earn more money than one compounded yearly because of how compound interest works, earning 'interest on interest' throughout the year.
Explanation:
The student's question asks which savings account would earn more money, one with an interest rate of 1.2 percent compounded yearly, or one with the same interest rate but compounded monthly. When interest is compounded, it means the bank pays interest on both the original amount of money and any interest that account has already earned. With compounded interest, you end up earning interest on interest.
For the account with yearly compounding at a rate of 1.2 percent, the formula to calculate the amount after one year would be A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate (decimal), n is the number of times interest is compounded per year, and t is the time in years. In this case, n is 1 because the interest is compounded annually. Therefore, the amount after one year would be A = P(1 + 0.012/1)^(1×1) or A = P(1.012).
For the monthly compounded account, the same formula applies, but n would be 12 because the interest is compounded monthly. So, the amount after one year would be A = P(1 + 0.012/12)^(12×1).
When you perform these calculations, the account with the monthly compounding will yield a slightly higher amount than the annually compounded account because interest is being added more frequently. Each month's interest is then earning interest in the following months, leading to a process known as 'interest on interest'. Though the difference may not be substantial for small amounts and low interest rates, over longer periods, or with higher rates and balances, the difference can become significant.