The acceleration of the wagon is 3.2 m/s².
Explanation:To find the acceleration of the wagon, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force applied to it divided by its mass. In this case, the net force is 64 N (the horizontal force applied) and the mass of the wagon is 20 kg. So the acceleration can be calculated as follows:
A = F/M = 64 N / 20 kg = 3.2 m/s²
Therefore, the acceleration of the wagon is 3.2 m/s².
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(8.166×10^8)×(1.515×10^9)
If you work for an hourly wage, your gross pay is a function of the number of hours that you work. Your hourly wage is $8 per hour. Assuming you work 40 hours per week, what is the practical domain and the practical range of the function? a. The practical domain is 0 through 8. The practical range is 0 through 32. b. The practical domain is 0 through 320. The practical range is 0 through 40. c. The practical domain is 0 through 40. The practical range is 0 through 320. d. The practical domain is 0 through 32. The practical range is 0 through 8.
Answer:
The correct option is C.
Step-by-step explanation:
It is given that gross pay is a function of the number of hours that you work.
Let y represents the gross pay and x represents the number of hours. So, the value of x and y can be negative.
Hourly wage = $8 per hour.
The weekly gross pay function is
[tex]y=8x[/tex] .... (1)
Domain is the set of inputs and ranges is the set of outputs.
It is given that you work 40 hours per week. It means the value of x lies between 0 to 40.
Domain = [0,8]
Substitute x=40 in equation (1), to find the gross pay when number of hours is 40.
[tex]y=8(40)=320[/tex]
Range = [0,320]
The practical domain is 0 through 40. The practical range is 0 through 320.
Therefore the correct option is C.
The practical domain for the function representing gross pay is the range of hours worked, 0 to 40 hours. The practical range is the corresponding gross pay, from $0 to $320, based on an $8 per hour wage for up to 40 hours of work. So correct answer is option C.
To determine the practical domain and range of the function that represents your gross pay based on an hourly wage of $8 per hour, we must consider the possible number of hours you can work in a week and the corresponding earnings. Given that you work 40 hours per week, the practical domain (which represents the number of hours worked) would be any value from 0 to 40 hours, since you cannot work negative hours and we're assuming a standard full-time workweek.
The practical range (which represents the gross pay) is calculated by multiplying the number of hours worked by the hourly wage. Therefore, the range would be 0 (if you work 0 hours) to $320 (if you work 40 hours), because 40 hours times $8 per hour equals $320.
So, the correct answer from the given options is Option C.
Practical domain: 0 through 40.
Practical range: 0 through 320.
it costs $150 to be a member of a music club. A member of the club pays $5 per music lesson. A nonmember pays $15 per music lesson. How many music lessons must a member and a non member take so the cost for each is the same?
The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
It costs $150 to be a member of a music club. A member of the club pays $5 per music lesson. A nonmember pays $15 per music lesson.
Let x be the number of music. Then the equation is given as,
15x = 5x + 150
Simplify the equation, then we have
15x - 5x = 150
10x = 150
x = 15
The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.
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rotate 270 clockwise around the origin (8,0)(11,-5)(14,-2)
What is 128/56 simplified⁉️
After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets and had a total of $700 profit. Which equation models the total profit, y, based on the number of tickets sold, x?
I need Help with my multi step equations!
A 25-foot streetlight casts a showdown 20feet long.If Melanie is standing at the end of the shadow casted by a 60. -foot tall building,how far is she from the building.
By setting up a proportion based on the similar triangles created by the streetlight and the building, we can find that Melanie is standing 48 feet away from the building.
To solve the problem of determining how far Melanie is standing from the building using the shadows, we can use similar triangles. We are given a 25-foot streetlight that casts a 20-foot shadow and a 60-foot tall building. The goal is to find the length of the shadow cast by the building, which will tell us how far Melanie is from the building.
By setting up a proportion based on the similar triangles, we have:
Height of the streetlight / Length of streetlight's shadow = Height of the building / Length of the building's shadow.25 feet / 20 feet = 60 feet / x feet.To find the value of x, we cross multiply:25x = 60 * 20.x = (60 * 20) / 25.x = 1200 / 25.x = 48 feet.Therefore, Melanie is standing 48 feet away from the building.
When sales representatives for a pharmaceutical company drive out of town meetings that require an overnight stay, they receive $175 for lodging plus $0.70 per mile driven. How many miles did Joe drive if his company reimbursed him $329 for an overnight trip?
Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.
Joe was given $329 for an overnight trip because he drove a distance of 220 miles
Word ProblemGiven Data
Amount rep receive = $175Added amount per mile driven = $0.70Reimbursed/Total = $329The Mathematical relation for this scenario is
Total amount = Amount Receive+ 0.7*Distance driven
let the distance driven be x
Substituting our given data into the relation we have
329= 175+ 0.7*x
329-175 = 0.7x
154 = 0.7x
divide both sides by 0.7
x = 154/0.7
x = 220miles
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Tran drove his car at a constant speed of 55 mph.
Which is an equation for the distance Tran drove?
A. 55d=t
B. d=55t
C. t/d=55
D. 55/d=t
Plz help I think the answer is D am not sure.
The correct equation for the distance Tran drove at a constant speed of 55 mph is B. d = 55t.
In this equation:
"d" represents the distance in miles that Tran drove.
"t" represents the time in hours.
So, the distance "d" is equal to Tran's constant speed of 55 mph multiplied by the time "t" in hours, which is why the equation is written as d = 55t.
Option D is not the correct equation because it has the variables and constants in the wrong order.
The correct order is distance (d) on the left side of the equation, followed by the constant speed (55) and then the time (t) on the right side of the equation.
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Which number line correctly shows 2 2/5, 2 4/5, and 11/5?
I really need help with this one...
what is rounding and estimate 253,495 - 48,617=
Answer:
205000
Step-by-step explanation:
Given : 253,495 - 48,617
To Find : What is rounding and estimate
Solution:
To Estimate a difference by rounding.
1 ) Round each term that will be subtracted
2 )Subtract the rounded numbers
Round off of 253,495 = 253000
Round off of 48,617 = 48000
So, 253000 - 48000 = 205000
Hence The rounding and estimate 253,495 - 48,617= 205000
What is 68√ in simplest radical form?
Answers are appreciated! :D
The correct option is d. 8 oz. can of juice is most convenient to meet this requirement.
First, let's convert 240 milliliters to ounces because the answer choices are in ounces.
1 milliliter is approximately equal to 0.0338 ounces.
So, 240 milliliters is approximately \( 240 \times 0.0338 \) ounces, which is about 8.112 ounces.
Now, let's examine the options:
a. 5 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.
b. 4 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.
c. 12 oz. can of juice: More than enough juice. It's more than the required 8.112 ounces.
d. 8 oz. can of juice: Exactly the amount needed. It matches the required 8.112 ounces, which is the closest to the calculated amount of 8.112 ounces.
Therefore, the 8 oz. can of juice is the most convenient option to meet the requirement of having 240 milliliters of juice every 2 hours.
What is x for 7x plus 4 over 6 equals negative 4
A vat contains 21.12 L of cleaning solution. Kenyon pours the solution into 0.44-L containers.
How many containers of solution does he create?
Answer:
48
Step-by-step explanation:
what happens when the slope is doubled?
4 girls and 4 boys run. Then 2 more children run. The same number of girls and boys run. How many of each run
A whale dives at a speed of 3 feet per second. What is the change in position of the whale relative to where it started after 12 seconds?
These are the round-trip distances that city buses traveled on different routes each month. Calculate the total distance, in miles, that buses travel each route in one year.
350 3/5 miles to Parkville
346 3/10 miles to Green City
134 1/5 miles to Evergreen Town
327 4/5 miles to Jefferson
413 7/10 miles to Clinton City
Michelle bought 76 pounds of cocoa powder for her bakery. Every day she used the same amount of cocoa powder to make bakery items. After 10 days, Michelle was left with 20.2 pounds of cocoa powder. On average, how many pounds of cocoa powder did Michelle use each day?
5.58 pounds
7.45 pounds
9.62 pounds
12.6 pounds
Which fraction is equivalent to [tex] \frac{30}{35} [/tex]?
6/7 because if you divide 30/35 by 5 it will leave at 6/7
Which of the following is a multiple of 4?
A. 620
B. 891
C. 734
D. 626
What is the value of the expression? 3.2(2.3)−4.8 Enter your answer in the box as a decimal.
3.2(2.3) - 4.8
Simplify.
(3.2 × 2.3) - 4.8
Simplify.
(7.36) - 4.8
Simplify.
2.56
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What is the point slope form of the line with slope −14 that passes through the point (−2, 9) ?
a.y+2=−14(x−9)
b.y−9=−14(x+2)
c.y−2=−14(x+9)
d.y+9=−14(x−2)
its not d its the +2 one
solve the equation by completing the square 5x(x+6)=-50
To solve the equation 5x(x+6) = -50 by completing the square, we first isolate the quadratic term and then add the square of half the coefficient of x to both sides of the equation. Taking the square root gives us the solution x = -3 + i and x = -3 - i.
Explanation:
To solve the equation by completing the square, we first need to isolate the quadratic term on one side of the equation. So, let's distribute the 5x to get 5x^2 + 30x = -50. Next, we move the constant term to the other side and divide the equation throughout by the leading coefficient to get x^2 + 6x + 10 = 0.
Now, we can complete the square by adding the square of half the coefficient of x (which is 3) to both sides of the equation. This gives us (x + 3)^2 + 10 - 9 = 0, which simplifies to (x + 3)^2 + 1 = 0.
Taking the square root of both sides, we get x + 3 = ±√(-1), which means x = -3 ± i. Hence, the solution to the equation is x = -3 + i and x = -3 - i.
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Need to show work for problem x+9.72=21
MAXIMUM POINTS!!!!! PLEASE HELP
A popular cellular phone family plan provides 1,500 minutes. It charges $89.99/month for the first two lines and $9.99/month for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.
divide 9x^2 square root by square root 18y^2