To demonstrate proportionality between two objects, utilize a table to observe constant ratios, plot points on a graph to confirm a linear relationship passing through the origin, and formulate an equation representing the proportional relationship.
To demonstrate proportionality between two objects, you can use a table, graph, and equation.
Firstly, create a table with corresponding values of the two objects. If they are proportional, their ratios should remain constant.
Secondly, plot the points on a graph with one object on the x-axis and the other on the y-axis.
If the points form a straight line passing through the origin, it indicates proportionality.
Lastly, formulate an equation representing the relationship between the two objects.
For example, if the objects are x and y, and they are proportional, then y = kx, where k is the constant of proportionality.
By analyzing the table, graph, and equation, you can conclusively establish proportionality between the two objects.
Bo has 23 video games for sale. He plans to donate the money he makes from each sale to a local charity. What is the least amount of money in whole dollars Bo should charge for each game in order to raise $100? Explain
In order to raise $100, Bo should charge $5 for each game. In mathematics, "at least one" refers to one or more.
How to calculate least amount of money?He provided the least amount of money of any donor, whether in size, quantity, degree, etc. lowest in importance, standing, or consideration. noun. The smallest possible quantity, degree, or other attribute.
In mathematics, "at least one" refers to one or more. It is frequently employed when existence can be proved but there is no way to know how many possible solutions there are.
Given ,
Let x represent the lowest price per video game.
The number of games available is 23.
Selling video games will need to raise $100 as the minimum amount.
The necessary inequality follows:
total number of games need minimum sum
i.e.[tex]23x\geq 100[/tex]
23 divided by both sides gives us
[tex]x\geq 4.24782608696[/tex]≈5
So, in order to raise $100, Bo should charge $5 for each game.
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There are 25 students in Ms.Morris's class. She wants to divide the class into 3,4,or 5 equal teams with all students on a team. Which number of teams can Ms.Morris make? Explain.
The number of teams Ms.Morris can make would be 5-students groups.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that there are 25 students in Ms.Morris's class. She wants to divide the class into 3,4,or 5 equal teams with all students on a team.
If Ms. Morris wants to divide all the students in 3, 4 or 5 equal teams, then apply a division to know the number of students per group.
If she makes 3-students groups, it would be;
25/3
If she considers 4-students groups, then it would be;
25/4
Thus, it can be seen that she cannot divide a students in parts to have equal groups.
Therefore, she has to make 5-students groups,
25/5 = 5
This means that she can make groups of 5 students each, and she would have equal groups.
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using 3.14 for pi, what is the volume of the sphere to the nearest tenth
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where π can be approximated as 3.14 for simpler calculations. Volume is proportional to the cube of the radius, so if the radius changes significantly, the volume adjusts correspondingly by the cube of the factor of change.
To calculate the volume of a sphere using the value 3.14 for pi, you can apply the formula V = (4/3)πr³. If the radius of the sphere is 'r', you would plug in the value of 'r' into this formula. Next, you would multiply the result by 4/3 and then by 3.14 in place of π to get the volume. It's important to note that the volume of the sphere increases proportionally to the cube of the radius, meaning if the radius changes by a factor of 10, the volume changes by a factor of 10³ or 1000.
carlos has a string that is 24 inches long. he wants to divide it into 3 equal parts. write an equation to find how long each part will be. use ? to represent the unknow number. then solve your equation.
Final answer:
Carlos can divide his 24-inch string into 3 equal parts by solving the equation 3x = 24, which gives each part a length of 8 inches.
Explanation:
Carlos has a string that is 24 inches long and wants to divide it into 3 equal parts. To find how long each part will be, we can represent the unknown length of each part by the variable ? (which we will replace with x for the equation). The equation we can write for this scenario is 3x = 24.
To solve for x, we divide both sides of the equation by 3:
3x / 3 = 24 / 3x = 8So, each part of the string will be 8 inches long.
on saturday, a minor league baseball team gave away baseball cards to each person entering the stadium. one group received 28 baseball cards. a second group received 68 baseball cards. if each person entering the stadium received the same number of cards, what was the greatest possible number of baseball cards that each person could have received?
Answer:
Step-by-step explanation:use the greatest common factor of 28 and 68 would give you 4
If the mean (average) of five consecutive numbers is 21, the smallest of three five numbers will be...
Sarah is keeping up with how many miles her car gets per gallon. She starts with a full tank. After 448 miles, she fills up with 14 gallons. If she plots the points (0,0) and (14,448) on a coordinate plane, what would be the y-value of the point (1,y)?
Using a linear function, it is found that the value is: y = 32.
A linear function has the following format:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change.b is the y-intercept, which is the value of x when y = 0.In this problem, when [tex]x = 0, y = 0[/tex], and thus, the y-intercept is [tex]b = 0[/tex].
Then
[tex]y = mx[/tex]
She also plots the point (14, 448), which means that when [tex]x = 14, y = 448[/tex], and this is used to find m.
[tex]14m = 448[/tex]
[tex]m = \frac{448}{14}[/tex]
[tex]m = 32[/tex]
Hence, the linear function is:
[tex]y = 32x[/tex]
Then, when x = 1, the point is (1,y), and:
[tex]y = 32(1) = 32[/tex]
The y-value is y = 32.
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A car wash detailed 272 cars in 8 hours. At what rate did the car wash detail cars in cars per hour.
Our product is equal to 6+2 what factors are we
3.3k≤9.9 k=? Also what does the solution look like on a graph?
what is the answer to k/3-2k+4=10
In art class mrs Jocelyn
gave everyone a 1 foot stick to measure and cut Vivian measured and cut her stick in to 5 equal pieces Scott measured and cut his into 7 equal pieces Scott is correct
there are 100 degrees on celcius scale from freezing temp to boiling temp of water. there are 180 degrees F scale between these temps. so a change in temp of 10 degrees C on the celsius scale is equilivant to a change of how many degrees on F scale?
Answer:
I got the same answer 30 degress different
a can of juice contains 175 calories per 2.5 servings which of the following is not an equivalent number of calories per serving
To find the equivalent number of calories per serving based on that a can of juice contains 175 calories for 2.5 servings, divide 175 by 2.5 to get 70 calories per serving. Any amount other than 70 calories per serving would not be equivalent.
Explanation:The question is asking to find an equivalent number of calories per serving based on the information that a can of juice contains 175 calories per 2.5 servings. To calculate the calories per serving, we divide the total number of calories by the number of servings, so:
Calories per serving = Total calories ÷ Number of servings = 175 calories ÷ 2.5 servings = 70 calories per serving.
Now, let's say we have several options that represent the number of calories per serving:
70 calories per serving (correct equivalent)60 calories per serving (not an equivalent)75 calories per serving (not an equivalent)80 calories per serving (not an equivalent)From this list, every option except for the first one (70 calories per serving) is not an equivalent number of calories per serving as our calculated 70 calories per serving.
there are threee spider on the wall.There are six ladybugs on the wall.how many spider and ladybugs legs are there on the wall
Explain how mental math can be used to estimate a 15% tip on a taxi ride that costs $23.25
Plz explain, and plz show work
Answer: 3.4875
Step-by-step explanation:
Here, According to the question,
Total amount is $23.25
[tex]100\% = 23.25[/tex]
⇒[tex]1\% = \frac{23.25}{100}[/tex]
⇒[tex]1\%= \frac{0.95}{8}[/tex]
⇒ [tex]15\%= 15\times \frac{0.95}{8}[/tex] ( By multiplying 15 on both sides)
⇒ [tex]15\%= \frac{14.25}{8}[/tex]
⇒ [tex]15\%= 3.4875 [/tex]
Thus, 15% of $23.25 is $3.4875
Given: x - 5 > -10.
Choose the solution set.
Final answer:
To find the solution set for the inequality x - 5 > -10, add 5 to both sides resulting in x > -5; hence the solution set is {x | x ∈ R, x > -5}.
Explanation:
The student is asking for the solution set for the inequality x - 5 > -10. To solve for x, we need to isolate the variable on one side of the inequality. Add 5 to both sides of the inequality to achieve this:
x - 5 + 5 > -10 + 5x > -5This means that the value of x must be greater than -5. We can represent this solution set as {x | x ∈ R, x > -5}, where R represents the set of all real numbers.
Comparing this solution to the given options, it is clear that the correct solution set is the second one: {x | x ∈ R, x > -5}.
clydesdale horse weighs as much a shetland pony and an american saddledred combined
10-5y=1x
Please show work on how to solve for Y
Convert 3/5 to a percent
When the Santos family stopped at the diner, they had traveled 36 miles from their home. At the gas station, the trip meter read 79 miles. How far did they travel from the diner to the gas station?
Suppose f(x) = 4x – 2 and g(x) = -2x + 1. Find the value of f(g(3)).
Value of f(g(3)) is -22.
What is a function?Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given
f(x) = 4x – 2
g(x) = -2x + 1
Value of f(g(3))
g(x) = -2x + 1
g(3) = -2(3) + 1
g(3) = -6 + 1
g(3) = -5
f(g(3)) = f(-5)
f(x) = 4x – 2
f(-5) = 4(-5) - 2
f(g(3)) = -20 -2
f(g(3)) = -22
Hence, value of f(g(3)) is -22.
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what what what is an equation for 2 1/4 + 6 2/10
A store sells 12-packs of ballpoint pens for $1.09 each and composition books for $2.79 each. Cindy buys m packs of ballpoint pens and n composition books. The store offers a 5% discount for every 50th customer who makes a purchase. If Cindy gets the 5% discount, which expression will represent Cindy’s bill?
A. 0.05 − 1.09m + 2.79n
B. 1.05 + 1.09m + 2.79n
C. 1.05(1.09m + 2.79n)
D. 0.95(1.09m + 2.79n)
The expression that will represent Cindy’s bill is 0.95(1.09m + 2.79n). Hence, the correct option is D. 0.95(1.09m + 2.79n).
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
It is given that store sells 12-packs of ballpoint pens for $1.09 each.
The store also sells composition books for $2.79 each.
Cindy buys 'm' packs of ballpoint pens and 'n' composition books.
So, the equation for this becomes
1.09m + 2.79n
Cindy gets a 5% discount, so she has to pay 95% of the regular price.
Then the expression that will represent Cindy’s bill,
0.95(1.09m + 2.79n)
Hence, the correct option is D. 0.95(1.09m + 2.79n).
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Bob makes 4% commission on his sales as a real estate agent. If Bob sells a house for $249,000, How much money does he get to keep?
A mountain climber climbed down a cliff 50 feet at a time.He did this 5 times in one day.What was the overall change in his elevation
Answer:
The overall change is -250 feet. 50 times 5 is 250 feet, and the mountain climber descended. Therefore, the change is -250 feet in elevation.
Step-by-step explanation:
Answer:
the overall changes is -250 its descended 50×5=250
Step-by-step explanation:
Adding 3/8 to a number increases it by 5% of its original value. What is the original number?
The lemonade stand at the county fair sells the lemonade at a price of two cups for $3.60. Complete the table at right to find what Paula’s family will pay to buy lemonade for all eight members of the family.
The cost of 8 cups of lemonade would be $14.40
Calculating the price for the table givenPrice of lemonade :
2 cups = 3.60price per cup:
3.6 / 2 = 1.80for 3 cups:
1.8 × 3 = 5.40for 4 cups:
1.8 × 4 = 7.20for 5 cups:
1.8 × 5 = 9for 6 cups:
1.8 × 6 = 10.8for 7 cups:
1.8 × 7 = 12.60for 8 cups:
1.8 × 8 = 14.40Therefore , the cost of 8 cups of lemonade is $14.40
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The school purchased 100 trophies to give to the honor roll students. If one trophy cost $4.32, how much would it cost for all of the trophies
Why is an increase 20-40 100% but a decrease of 40-20 is 50%