The problem involves an algebraic expression where Ben, Tracy, and Tran each spend an equal amount, n, on skate rentals that total $15. By setting up an equation, we solve for n, which is $5 per person. This concept is related to understanding budget constraints in financial decision-making.
The student's question about Ben, Tracy, and Tran spending a total of $15 to go skating where they each rented skates for n dollars pertains to algebraic expressions and equations, which is a mathematics concept commonly explored in college-level courses. If we assume that each of them paid an equal amount for the skate rental, represented by n, then we can express the total cost as 3n because there are three individuals.
Given that the total cost was $15, we can set up an equation: 3n = $15. To find the cost of renting skates per person, we solve for n by dividing both sides of the equation by 3, resulting in n = $5. Therefore, each person paid $5 to rent the skates.
Understanding how to solve this problem helps in grasping the concept of budget constraints, as seen in the example of Janet Bain who must decide how to allocate a limited budget of $250 for activities such as skiing and horseback riding. This topic relates to the decision-making processes regarding spending within the constraints of a budget, which is essential in both personal and organizational finance.
Solve each equation. Record your work and check your solution.
a. 5(x-2)+(-9)= -7(1-x)
The solution for equation is x = -6
Solution:
Given equation is:
[tex]5(x-2) + (-9) = -7(1-x)[/tex]
We have to solve the equation
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right
Therefore, solve for brackets in given equation
[tex]5(x-2) + (-9) = -7(1-x)\\\\5x - 10 -9 = -7 + 7x[/tex]
Solve for terms in left hand side of equation
[tex]5x - 19 = -7+7x[/tex]
Move the variables to one side and constants to other side
[tex]7x -5x = -19+7\\\\2x = -12\\\\Divide\ both\ sides\ by\ 2\\\\x = -6[/tex]
Thus the solution for equation is x = -6
This line plot shows something about trails in a state park. What is true about the data in this line plot?
Answer:
2 thirds of the trails are longer than 5 Km
Step-by-step explanation:
A line plot that forms a straight line indicates a direct relationship between the two variables plotted. A graph that shows less deviation from the line of best fit is a good candidate for linear regression. Line graphs are typically used to show trends over time.
Explanation:When considering a line plot or any graphical representation of data such as scatter plots or line graphs, the main goal is to uncover the underlying pattern or relationship presented. If the data, when graphed, forms a straight line, it suggests a direct relationship between the variables involved. This implies that as one variable increases, the other variable either increases or decreases by a consistent rate. For instance, if one plot shows a line from (0,8) to (3,2), there's a decrease as the first variable increases. Conversely, a line from (0,2) to (3,2) or from (0,3) to (3,3) suggests no change, indicating a directly horizontal line and therefore no relationship. When determining good candidates for linear regression, a scattering of points closely aligned in a straight line pattern, with little deviation from the line of best fit, is indicative of such. Linear regression is more accurate when the variance around the line of best fit is minimal, as seen in the second graph described. Line graphs specifically are useful for showing data trends over time, where the x-axis typically represents time and the y-axis represents another variable.
4.) Mr. Souders purchased a car priced at $9800. He paid $500 down and
agreed to a monthly payment of $250 per month for 48 months.
Including the down payment, what is the total cost of the car?
Please show your work.
Answer:
The total cost of the car including the down payment = $12,500
Step-by-step explanation:
The Original price of the car = $9800
The amount paid for down payment = $500
Also, the monthly payment amount = $250
Now, the number of months, the amount is paid = 48 months
So, the TOTAL amount paid in 48 months
= 48 x ( Amount paid each month) = 48 x ( $250)
= $12,000
So, the TOTAL PRICE of CAR paid = Total amount paid in 48 months + The amount paid for down payment
= $12,000 + $500
= $12,500
Hence, the total cost of the car including the down payment = $12,500
State whether the number is a solution to the given inequality
X>-17;-14
Answer:
it is a solution
Step-by-step explanation:
When you put the number where x is, you get ...
-14 > -17 . . . . a true statement
Since this statement is true, x=-14 is a solution.
The number -14 is a solution to the inequality X > -17 in mathematics as it falls within the range of numbers greater than -17.
Explanation:In the realm of mathematics, inequalities define a range of values that can be a solution. In this case, the inequality is X > -17. This means any number greater than -17 is a solution to the inequality. If we consider -14, it falls within this range because -14 is greater than -17. Therefore, yes, -14 is a solution to the given inequality.
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find the x-intercepts and y-intercepts of 10x+6y=-4
The x intercept is [tex](\frac{-2}{5}, 0)[/tex]
The y intercept is [tex](0, \frac{-2}{3})[/tex]
Solution:
Given equation is:
10x + 6y = -4
The x intercept is the point where the line crosses the x axis
The y intercept is the point where the line crosses the y axis
Find x intercept:
Substitute y = 0 in given equation
10x + 6(0) = -4
10x = -4
[tex]x = \frac{-4}{10}\\\\x = \frac{-2}{5}[/tex]
Thus the x intercept is [tex](\frac{-2}{5}, 0)[/tex]
Find y intercept:
Substitute x = 0 in given equation
10(0) + 6y = -4
[tex]6y = -4\\\\y = \frac{-4}{6}\\\\y = \frac{-2}{3}[/tex]
Thus the y intercept is [tex](0, \frac{-2}{3})[/tex]
x−117+120 Simplify the expression
Answer:
Step-by-step explanation:
x-117+120
x+3
brainliest and 100 pts!!!!!!!!!!!!!!!!!!!
Natalie's coach has a stopwatch that records times to the nearest thousandth of a second. Natalie ran a given distance in 25.453 seconds.
What is Natalie's time rounded to the nearest tenth of a second?
Enter your answer in the box.
___s
Answer:
25.5
Step-by-step explanation:
An oil barrel contains 31.6 gallons of oil. One gallon is equal to 3.8 L. How many liters of oil are in the barrel? Round your answer to the nearest tenth.
Final answer:
To convert gallons to liters, use the conversion factor of 1 gallon being equal to 3.8 liters to find that there are approximately 120.1 liters of oil in the barrel.
Explanation:
To convert gallons to liters, we need to use the conversion factor of 1 gallon being equal to 3.8 liters.
Calculate the total liters in the barrel: 31.6 gallons * 3.8 liters/gallon = 120.08 liters
Therefore, there are approximately 120.1 liters of oil in the barrel.
Marta's fruit stand sold x oranges on Thursday and twice as many on Friday. All together, on both days, she sold 108.
Which bar diagram represents the equation?
Answer:
Option A
Step-by-step explanation:
It is given that Marta sold [tex]$ x $[/tex] oranges on Thursday.
She has sold twice as many as on Friday. Therefore, she must have sold [tex]$ 2x$[/tex] oranges on Friday.
And the total amounts to 108.
That is, [tex]$ x + 2x = 108 $[/tex]
Hence, the table which has the total on the top and the entities on the bottom line would be the answer which is Option A.
Answer:
A
Step-by-step explanation:
Thursday is x because she sold x oranges. Friday is 2x because she sold double the amount she sold on Thursday. Then we add them together to make 108.
Which statements are true? Check all that apply.
Please answer :)
Answer:
[tex]\sqrt{1.8}<1.8[/tex]
[tex]\sqrt{1.8}>1[/tex]
[tex]\sqrt{1.8}<\sqrt{1.9}[/tex]
[tex]1.3<\sqrt{1.8}<1.4[/tex]
[tex]\sqrt{1.8}+\sqrt{1.9}[/tex]
Step-by-step explanation:
[tex]\sqrt{1.8} = 1.34[/tex] [tex]\sqrt{1.9} = 1.38[/tex] [tex]\sqrt{1.8}+\sqrt{1.9}=1.34+1.38=2.72[/tex]
[tex]\sqrt{1.9}-\sqrt{1.8}=1.38-1.34=0.04[/tex]
1.
[tex]\sqrt{1.8}<1.8[/tex]
It is true. since 1.34<1.8
2.
[tex]\sqrt{1.8}>1[/tex]
It is true. Since 1.34>1
3.
[tex]\sqrt{1.8}<\sqrt{1.9}[/tex]
It is true. since 1.34<1.38
4.
[tex]1.3<\sqrt{1.8}<1.4[/tex]
It is true. Since 1.3<1.34<1.4
5.
[tex]\sqrt{1.8}+\sqrt{1.9}[/tex]>2
It is true. Since 2.72>2
6.
[tex]\sqrt{1.8}-\sqrt{1.9}>0.1[/tex]
It is false. Since 0.04<0.1
Roxy has some necklaces. Kelly has 4 times more rings than Roxy. Together they have 35. How many necklaces does Roxy have?
Answer:
Roxy has 7 necklaces.
Step-by-step explanation:
35 = n + 4n
35 = 5n
5 = 5
n = 7
The problem is a simple algebra problem related to ratios. By setting up an equation according to the given information, we find that Roxy has 7 necklaces.
Explanation:This is a math problem concerning ratios and simple algebra. Let's denote the number of necklaces that Roxy has as R. Then, Kelly has 4 times more rings, which is 4R. Together they have 35. So, the equation can be set up as:
R + 4R = 35
Combine like terms, you get:
5R = 35
Then, you can solve for R by dividing both sides by 5:
R = 35/5 = 7
So, Roxy has 7 necklaces.
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Can someone explain the differences in discrete vs. continuous data and how these are graphed differently on a histogram?
Answer:
Discrete data means that it is not continuous and is graphed as a line with dashes.Continuous data goes on forever and is usually linear. It is graphed as a straight line all the way through.
Step-by-step explanation:
Hope that helps.
what is an equation for the line that passes through the points (0,-4) (7,11) in slope-intercept form
Answer:
y=15/7x-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(11-(-4))/(7-0)
m=(11+4)/7
m=15/7
y-y1=m(x-x1)
y-(-4)=15/7(x-0)
y+4=15/7(x)
y+4=15/7x
y=15/7x-4
Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using
the scale 1 inch:2 feet.
What is the length of the garden in her model? Show your work, including your proportion.
If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale
model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?
Answer:
Answer:
3 inches
It will fit in the paper.
Step-by-step explanation:
In the scale drawing the 2 feet original length is converted to 1 inch drawing length as Kelly constructs a scale model of the rock garden using the scale 1 inch : 2 feet.
Now the proportion is 1 inch : (2 × 12) inches = 1 : 24 {Since 1 foot is equivalent to 12 inches}
Now, maintaining that scale ratio the 6 feet original length of the garden will be converted to [tex]\frac{1}{24} \times (6 \times 12) = 3[/tex] inches in the drawing.
It is also given that the width of the garden in the scale model is 5 inches and the scale is still 1 inch : 2 feet.
Therefore, the dimensions of the garden in the model is 3 inches by 5 inches and this will fit on a piece of paper that is 8.5 inches by 7 inches. (Answer)
x squared equals x plus 56
Answer: 8 squared equals 8 plus 56
Step-by-step explanation:
What you would do is find a number squared that is greater than 56. I used 8 because 8 squared is 64. So i squared that and got 64, I then subtracted 8 from 64 because you would need to use the same x value in the equation and that lead me t getting 56. All in all x=8.
in Eduardo’s collection, the number of butterflies is 12 more than twice the number of moths. If there are x moths, write an expression to represent the number of butterflies he has.
Answer:
An expression to represent the number of butterflies he has is y = 12 + 2x
Step-by-step explanation:
Let the number of butterflies in Eduardo’s collection be y
Then according to the question
The number of moths = x
The number of butterflies y = 12 + twice the number of moths---------(1)
Twice the number of moths = [tex]2 \times \text{number of moths}[/tex]
Twice the number of moths = 2x -----------------------(2)
Substituting equation (2) in (1)
The number of butterflies y = 12 + 2x
(THIS ONE FIRST)The volume of a cube is 27 cubic inches. Which expression represents s, the length of a side of the cube?
Recall the formula Cube volume = s cubed.
s = RootIndex 3 StartRoot 27 EndRoot
s = 3 + 3 + 3
s = StartRoot 27 EndRoot
s = 3 times 3 times 3 times 3
Yo sup??
The answer to your question is option 1 ie
s=rootindex 3 startroot 27 endroot
because we know that
Volume of cube=s^3
27=s^3
s=27^1/3
Hope this helps.
Answer: A? It’s A
Step-by-step explanation:
Find the diagonal of the rectangular solid. l=4 w=5 h=3
Answer: d≈7.07
Step-by-step explanation:
l=4 w=5 h=3, then d≈7.07
[tex]d=\sqrt{l^{2}+w^{2} +h^{2} } =\sqrt{4^{2}+ 5^{2}+ 3^{2} } =7.07[/tex]
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)
- Cutiepatutie ☺❀❤
a number divided by three less two is at most two
x ≤ 12
Solution:
Let us take the number be x.
A number : x
A number divided by three : [tex]$\frac{x}{3}[/tex]
A number divided by three less two : [tex]$\frac{x}{3}-2[/tex]
A number divided by three less two is at most two : [tex]$\frac{x}{3}-2\leq 2[/tex]
Now, simplify the inequality,
[tex]$\Rightarrow\frac{x}{3}-2\leq 2[/tex]
Add 2 on both sides of the inequality,
[tex]$\Rightarrow\frac{x}{3}-2+2\leq 2+2[/tex]
[tex]$\Rightarrow\frac{x}{3}\leq 4[/tex]
Multiply by 3 on both sides of the equation,
[tex]$\Rightarrow\frac{x}{3}\times3\leq 4\times3[/tex]
[tex]$\Rightarrow x\leq 12[/tex]
Hence x ≤ 12.
Final answer:
The question requires setting up an inequality to express the condition 'a number divided by three less two is at most two.' The solution of the inequality reveals that the number in question is any number less than or equal to 12.
Explanation:
The student's question involves a number theoretical concept that requires setting up and solving an inequality. To understand the requirement of 'at most two' when a number is divided by three and reduced by two, we would establish an inequality as X / (3-2) ≤ 2, where X is the unknown number. This inequality represents the condition mentioned in the question, which restricts the value of X to a certain range after the operations are performed.
When working through the inequality, we aim to isolate X to determine the possible values it can hold. Here, we would start by adding two to both sides of the inequality to remove the subtraction, leading to X / 3 ≤ 4. Multiplying both sides by 3 gives us X ≤ 12. This tells us that the number in question is any number that is less than or equal to 12.
Understanding mathematical operations and the interpretation of numerals in context is necessary to solve such problems. Specifically, discerning the difference between an 'at least' and 'exactly' reading of numerals impacts the formation and solution of such inequalities.
If A = (10, 4) and B = (2, 19), what is the length of Ab?
O
A. 17 units
O
O
B. 12 units
O
C. 23 units
D. 15 units
A gondola plans to pick up 1410 ft3 (110 tons) of iron ore to deliver to a manufacturing plant. The 41-ft gondola has a width of 9.5 ft and a height of 5 ft.
Answer:
Vgondola=lwh
=(41)(9.5)(5)
=1947.5 ft3
Step-by-step explanation:
plz give me brainliest
12 Given: JM MN, L is the midpoint of JN
Prove: JLM NLM
Statements
Reasons
Answer:
Statements and reasons for the proof is shown in the attachment
Step-by-step explanation:
The statements and reasons are as shown in the attached file.
The knowledge of congruency in triangles is applied.
What is the order of this matrix.
Answer:
the order of the matrix is 5 x 3
5 rows and 3 columns
Elijah is looking up to the top of the Washington Monument. If the monument is 555 feet tall and the
angle of elevation from the point on the ground where Elijah is standing to the top is 74', how far is
he standing from the base of the monument?
Answer:
Elijah is standing from the base of the monument 159.14 feet
Step-by-step explanation:
see the attached figure to better understand the problem
In the right triangle ABC
[tex]tan(74^o)=\frac{BC}{AC}[/tex] ----> by TOA (opposite side divided by the adjacent side)
substitute the given values
[tex]tan(74^o)=\frac{555}{AC}[/tex]
solve for AC
[tex]AC=\frac{555}{tan(74^o)}=159.14\ ft[/tex]
therefore
Elijah is standing from the base of the monument 159.14 feet
What plus what equals 24 if the second number subtracted from the first number equals 2?
Answer:
13+11
Step-by-step explanation:
13-11=2 and 13+11=24
Rafeal wants to know if there is a single transformation that will move trapezoid JKLM onto trapezoid PQRS Below
Which Statement is true?
A. A 90 counterclockwise roation of trapezoid JKLM about the origin will move angle L onto angle R
B. A 180 rotation of trapezoid JKLM about the origin will move angle J onto angle R
C. A reflection of trapezoid JKLM across the y-axis will move angle K onto angle R
D. There is no transformation Rafael can use because trapezoids JKLM and PQRS are not congruent
A. A 90° counterclockwise rotation of trapezoid JKLM about the origin will move angle L onto angle R.
Step-by-step explanation:
Since both the trapezoids, trapezoid JKLM and PQRS are congruent, we can do any transformation, may be rotation, reflection and translation.
A 90° counterclockwise rotation of trapezoid JKLM about the origin will move angle L onto angle R is the true statement others are incorrect statements.
When the Preimage is rotated 90° counterclockwise rotation, then its coordinates (x,y) changed into (-y,x)
Nancy joined Movies Extraordinaire for a $8 fee and an agreement to pay $1.99 per movie she rents. The equation for her total cost is y = 1.99x + 8. Predict her total cost if she rents 25 movies.
$57.75
$58.25
$60.85
$65.95
what is a numerator
Answer:
A numerator is the number that you actually have, the top number in a fraction
Step-by-step explanation:
A numerator is the top number on a fraction, such as 1 in 1/2.
I had trouble at this for a while when I was younger, so hopefully this helps (=>ω<=)
Russell randomly surveys seventh-graders in his school and finds that 6 of 30 attend summer camp. If there are 200 seventh-graders in his school, about how many are expected to attend summer camp? Enter your answer in the box.
----------eighth -graders
Answer:
40
Step-by-step explanation:
6 of 30 is the ratio 6 to 30 or 6/30.
6/30 reduces to 1/5
The survey shows that 1/5 of the students attend summer camp.
1/5 of 200 = 1/5 * 200 = 40
Mrs Smith made popcorn for 9 people. Each scoop of popcorn kernels made 2 cups if popcorn. She made 6 scoops total. How much popcorn did each person have if it was divided equally?
A: 3/8
B: 3/4
C: 1 1/3
D: 1 2/3
Answer:a
Step-by-step explanation: