Final answer:
The inequalities that accurately model the situation where Adam needs fewer than 30 cones, with at least a dozen large ones, are y≥12, x+y≤30, and x≥0. These inequalities represent the constraints on large cones, total cones, and the feasibility of small cones respectively.
Explanation:
The student asks about modeling a situation with inequalities where Adam needs both small and large cones for soccer practice, with fewer than 30 cones total and at least a dozen large ones. The variables x represent the number of small cones and y represent the number of large cones. To accurately model this scenario, the following inequalities are correct:
y≥12: Adam needs at least a dozen large cones.
x+y≤30: The total number of cones, both small and large, is less than or equal to 30.
x≥0: The number of small cones can be zero but not negative, as you can't have a negative number of cones.
Thus, the inequalities that model this situation are y≥12, x+y≤30, and x≥0. These inequalities account for the constraints on the number of large cones needed, the total limit on cones, and the feasibility of the number of small cones respectively.
Solve the equation for y. Leave your answer in terms of π.
π=7x−2y
Answer:
The value of the equation for y is [tex]y=\frac{-\pi+7x}{2}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex] \pi=7x-2y[/tex]
We need to solve the equation for y.
Subtract 7x to both sides of the equation.
[tex] \pi-7x=7x-7x-2y[/tex]
[tex] \pi-7x=-2y[/tex]
Divide both the sides by -2.
[tex] \frac{\pi-7x}{-2}=\frac{-2y}{-2}[/tex]
[tex]y= \frac{\pi-7x}{-2}[/tex]
[tex]y=\frac{-\pi+7x}{2}[/tex]
Hence, the value of the equation for y is [tex]y=\frac{-\pi+7x}{2}[/tex].
For his off-road bike, Jackson measures that he needs a brake cable 24 1/8 in. long. The parts catalog shows cables in decimal measurements. Which cable length should he order?
A. 24.125 in.
B. 24.275 in.
C. 24.375 in.
D. 24.775 in.
Answer:
its A
Step-by-step explanation:
Evelyn evaluated 1 and 6/7 - 3/4. Each statement below is a way for Evelyn to check her answer.
Use the drop down menus to complete each statement.
If the sum of her anwser is 3/4 is 1, Evelyn's answer is A. Too high , B. Too low, C. Correct?
If the sum of her answer and 3/4 is 1 and 6/7 , Evelyn's answer is A. Too high , B. Too low, Or C. Correct?
If her answer is minus 3/4 is 1 and 6/7, Evelyn's answer is A. Too high , B.Too low , C.Correct?
The required solutions are as follows,
(a) Evelyn's answer is Too low, Option B is correct.
(b) Evelyn's answer is correct, and Option C is correct.
(c) Evelyn's answer is Too high, Option A is correct.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
According to the question,
Evelyn evaluated 1 and 6/7 - 3/4 as,
= 1 6/7 - 3/4 and add 3/4 later,
= 1 6/7 -3/4 + 3/4
= 1 6/7
So,
If the sum of her answers is 3/4 is 1,
Evelyn's answer is Too low, Option B is correct.
If the sum of her answer and 3/4 is 1 and 6/7
Evelyn's answer is correct, and Option C is correct.
If her answer is minus 3/4 is 1 and 6/7,
Evelyn's answer is Too high, Option A is correct.
Learn more about arithmetic here:
https://brainly.com/question/11424589
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simplify 8(7-1)+4(x+5).
you begin with $25 in a savings account and $50 in the checking account. Each week you deposit $5 into savings and $10 into checking. After how many weeks is the amount in checking twice the amount in savings? write and solve an equation.
PLEZ HELP I NEED HELP BADLYYY!!!
Homer and Bart plan to buy one computer for $499.00 strictly for gaming purposes games cost $49.99 each
PART A ... Define each variable and write an algebraic expression to describe how much they will spend before sales tax based on purchasing the computer and the number of games
PART B .... if they purchase one computer in five games how much do they spend before sales tax
PART C.... Homer and Bart have friends they want to purchase extra controllers each controller costs $24.99 use an algebraic expression to describe how much they spend in total before tax sales when they purchase one computer any number of games in any number of extra controllers
PART D ... what would be the total cost before sales tax if Homer and Bart purchase one computer for games and three extra controllers
A. [tex]\[ T = C + G \times P \][/tex]
B. they will spend $748.95 before sales tax.
C. [tex]\[ T = C + G \times P + K \times R \][/tex]
D. The total cost before sales tax if Homer and Bart purchase one computer, five games, and three extra controllers would be $823.92.
PART A:
Let us define the variables:
- C: Cost of the computer ($499.00)
- G : Number of games
- P : Cost of one game ($49.99)
- T : Total cost before sales tax
The algebraic expression to describe how much they will spend before sales tax based on purchasing the computer and the number of games is:
[tex]\[ T = C + G \times P \][/tex]
PART B:
If they purchase one computer and five games, we substitute G = 5 into the expression:
[tex]\[ T = 499 + 5 \times 49.99 \][/tex]
Now, we can calculate:
[tex]\[ T = 499 + 5 \times 49.99 \]\[ T = 499 + 249.95 \]\[ T = 748.95 \][/tex]
So, they will spend $748.95 before sales tax.
PART C:
Let's define an additional variable:
- K : Number of extra controllers
- R: Cost of one extra controller ($24.99)
The algebraic expression to describe how much they spend in total before sales tax when they purchase one computer, any number of games, and any number of extra controllers is:
[tex]\[ T = C + G \times P + K \times R \][/tex]
If they purchase one computer, five games, and three extra controllers, we substitute G = 5 and K = 3 into the expression:
[tex]\[ T = 499 + 5 \times 49.99 + 3 \times 24.99 \][/tex]
PART D:
Now, we can calculate:
[tex]\[ T = 499 + 5 \times 49.99 + 3 \times 24.99 \]\[ T = 499 + 249.95 + 74.97 \]\[ T = 499 + 324.92 \]\[ T = 823.92 \][/tex]
So, the total cost before sales tax if Homer and Bart purchase one computer, five games, and three extra controllers would be $823.92.
what is the difference between the commutative distributive and associative properties when multiplying?
the sum of two numbers is 90. if 20 is added to 3 times the smaller number, the result exceeds twice the larger by 50. find the number.
After setting up a system of equations and solving them simultaneously, the two numbers are found to be 42 and 48.
To find the two numbers where the sum is 90 and where 20 added to three times the smaller number exceeds twice the larger number by 50, we can set up a system of equations. Let x be the smaller number and y be the larger number. The first equation based on the sum of the numbers will be:
x + y = 90
The second equation derived from the condition involving multiplication and addition will be:
3x + 20 = 2y + 50
Solving these two equations simultaneously, we start by rearranging the first equation to find y:
y = 90 - x
Next, we substitute this expression for y into the second equation:
3x + 20 = 2(90 - x) + 50
Simplify and solve for x:
3x + 20 = 180 - 2x + 50
5x = 210
x = 42
Now substitute x back into the equation for y:
y = 90 - 42
y = 48
The two numbers are 42 and 48.
Tanner collected 360 cans and cans and bottles while fundraising for his baseball team this was 40% of what Reggie collected how many cans and bottles did Reggie collect
Final answer:
To find how many cans and bottles Reggie collected, we consider the 360 cans and bottles Tanner collected as 40% of Reggie's collection. After setting up an equation and solving it, we determine that Reggie collected a total of 900 cans and bottles.
Explanation:
Tanner collected 360 cans and bottles, which was 40% of what Reggie collected. To find out how many cans and bottles Reggie collected, we'll use the concept of percentage. Since 40% equals 0.40 in decimal form, we can represent the total number Reggie collected as 100%, which is 1 when converted to decimal form.
Therefore, if Tanner collected 360 cans and bottles and this is 40% of Reggie's amount, we can set up the equation:
360 = 0.40 × (Total number of cans and bottles Reggie collected)
To solve for the total number, we divide both sides of the equation by 0.40:
Total number of cans and bottles Reggie collected = 360 ÷ 0.40
After the division, we find that:
Total number of cans and bottles Reggie collected = 900
Unit rate for 490 in 3 1/2 hour
I need help with (b) plz help me
pi is an irrational number. could pi = 22/7? why or why not?
tukarkan 0.8 juta kepada nombor bulat
Which of these are NOT examples of the four essential parts of natural selection? Question 2 options: A One offspring of an organism has green fur, and the other has blue fur. This variation in fur color is passed down to their offspring as well. B All offspring of lions will always survive because Earth can always support new organisms. C Cats’ sharp teeth helped them to consume other organisms and survive in their environment. D Jaguars with large jaws made it easier for them to eat certain animals and survive long enough to reproduce.
teresa earns $6.25 per hour. Calculate he wage for the week where she works the following number of hours:
What is the value of the 8 in 381,697?
Tom performed a total of 100 hours of community service. He served at three charities- Salvation Army, Red Cross and Rescue Missiom. The number of hours he served at the Red Cross was 19 hours more than at the Salvation Army. The number of hours he served at the Rescue Mission was 8 hours more than what he served at the Red Cross
Tom volunteered 18 hours at the Salvation Army, 37 hours at the Red Cross, and 45 hours at the Rescue Mission.
Let S represent the number of hours Tom served at the Salvation Army.
The number of hours at the Red Cross is 19 hours more than at the Salvation Army,Since the total number of hours Tom served is 100, we have,
S + R + M = 100
Substitute R and M with the expressions in terms of S:
S + (S + 19) + (S + 19 + 8) = 100
S + S + 19 + S + 27 = 100
3S + 46 = 100
3S = 54
S = 18
So, Tom served 18 hours at the Salvation Army. Now, we find the hours for the other two charities,
R = S + 19In summary, Tom volunteered 18 hours at the Salvation Army, 37 hours at the Red Cross, and 45 hours at the Rescue Mission.
Complete question-
Tom performed a total of 100 hours of community service. He served at three charities – Salvation Army, Red Cross and Rescue Mission. The number of hours he served at the Red Cross was 19 hours more than at the Salvation Army. The number of hours he served at the Rescue Mission was 8 hours more than what he served at the Red Cross. Find the number of hours he volunteered at each charity.
162 water bottles in 9 cases =
Jed made 2 free throws in 5 second how many would he make in one minute
Adam travels 248 miles on Monday and 167 miles on Tuesday. Estimate the total number of miles Adam travels
Answer:
Adam travels total 415 miles.
Step-by-step explanation:
The distance Adam travels on Monday = 248 miles
The distance Adam travels on Tuesday = 167 miles
We have to calculate the total number of miles Adam travels.
Total number of miles Adam travels = distance traveled on Monday + distance traveled on Tuesday
= 248 + 167
= 415 miles
Adam travels total 415 miles.
Considering the one time deposit and monthly rent, the equation y=1200 + 400x can be used to represent y
Answer: $1200
Step-by-step explanation:
THANKS IN ADVANCE!
Jenna multiplied four numbers together and then divided by -2. The result was a positive value.
Which of the following statements MUST be true?
None of the factors were negative.
All of the factors were negative.
An odd number of factors were negative.
An even number of factors were negative.
(1)negative x (2)negative = positive x (3)negative = negative x (4)positive = negative
negative divided by negative = positive
odd number were negative
65.5kg take away 3500 grams
what is 1995298 rounded to the nearest 10000
Seven less than one-third of a number is 5
What is the best estimate of (-3/5)(17 5/6)
[tex]\text{Hey there!}[/tex]
[tex]17\dfrac{5}{6}=17\times6 + 5 =17\times6 \rightarrow102+5 = 107\\\\\text{107 would be your numerator \& 6 would be your denominator.}[/tex]
[tex]17\dfrac{5}{6} = \dfrac{107}{6}[/tex]
[tex]-\dfrac{3}{5}\times\dfrac{107}{6}\\\\5 + 6 = 10\\\\\text{Your new equation is: }\dfrac{-107}{10}\text{Which the mixed number fraction is: }-10\dfrac{7}{10}[/tex]
[tex]\boxed{\boxed{\bf{Answer(s): -10\dfrac{7}{10} \ or \dfrac{-107}{10}}}}\checkmark\\\\\text{Good luck on your assignment and enjoy your day!}\\\\\frak{LoveYourselfFirst:)}[/tex]
which of the following best represents the average rate at which infants can grow in height during the first four years after birth.
*3 inches per month
*3 inches per year
*3 feet per month
*3 feet per year
I'm pretty sure that the answer is three inches PER YEAR because think, there is 12 months in a year so if he grows 3 inches per month for 4 year he/she would be taller than an 8 year old, so per year makes more sense.
The average length of a ladybug can range from 0.08 to 0.4 inch. Find two lengths that are within the given span.
Two lengths within the average range for a ladybug could be 0.2 inches and 0.35 inches, both of which are between the minimum of 0.08 inches and the maximum of 0.4 inches.
The average length of a ladybug can range from 0.08 to 0.4 inch. To find two lengths that are within the given span, we can select any two numbers that fall between these two values. For instance:
The first length could be 0.2 inches, which is exactly in the middle of the range.The second length could be 0.35 inches, which is closer to the upper end of the range but still within the given span.These lengths are examples of measurements that would fall within the typical size range of a ladybug.
Explain how to determine whether to move right or left on a number line when adding rational numbers
Why is 39 rational ????????????????????