The greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea would be 63.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Two siblings Edwin and Rhea are both going skiing but choose different payment plans.
Edwin's plan charges $45 for rentals and $5.25 per lift up the mountain.
Rhea's plan was a bundle where her entire day cost $108.
An inequality that models the number of trips, n, up the mountain for which Edwin will pay more than Rhea.
45 + 5.25n > 108
Subtract 45 on both sides
-45 + 45 + 5.25n > 108 -45
5.25n > 63
Divide both sides by 5.25
n > 12
Also,
5.25 x 12
= 63
The greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea would be 63.
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Let’s say you plan to start a lawn-mowing business for a little extra money over the summer. A new lawn-mower costs $450. Between the gas you use and the time is takes to travel (your time is important, after all), you estimate you will incur a cost of approximately $6 per lawn you mow. If you charge $35 for each lawn you mow, how many lawns must you mow before you become profitable?
If you plan on mowing only 3 lawns per day, 5 days per week, over the summer, how long will it take to make a profit of $2,500? Do you think this is a reasonable goal? Why or why not?
Your profit per lawn is [tex]payed \minus cost[/tex] which is [tex]35 \minus 6 = 29[/tex].
If you want to be profitable, you must earn more than the cost of the lawn mower. Each mowing you earn 29$. We must divide using the formula [tex]cost \divide profit = times[/tex] where times is the amount of times you must mow lawns to be profitable. We get [tex]450 \divide 29 = 15.51...[/tex], but you can't only mow parts of a lawn! Therefore, you must mow 16 lawns to be profitable.
Your second part depends on how many weeks are in the summer.
But the answer would look like $435 per week earned, and -$450 one time cost for the lawnmower.
Part A.
You spend $6 per lawn and charge $35 per lawn, so the profit per lawn is $35 - $6 = $29. Let the number of lawns you mow be n. You earn a profit of $29 pewr laun, so you earn a profit of 29n for mowing n lawns.
29n = 450
Divide both sides by 29.
n = 450/29 = 15.517...
You must mow 16 lawns to make profit.
Part B.
3 lawns per day for 5 days per week means 15 lawns per week. Since you make a profit of $29 per lawn, you will make a profit of 15 * $29 for 15 lawns in each week. 15 * $29 = $435.
You want to make $2500 profit, but you must spend $450 on the lawn mower, so you need to earn a total of $2500 + $450 = $2950.
Let n be the number of weeks. In one week, you make $435 in profit. In n weeks, you make 435n in profit.
435n = 2950
Divide both sides by 435.
n = 6.7816...
If you work for 7 weeks, you will make at least $2500 in profit.
Since the summer vacation is longer than 7 weeks, it is a reasonable goal, but you must take into account the time it takes to mow three lawns in one day.
What is the slope of y= 4x + 5
Answer:
Step-byhe slope is 4, or 4/1, and the y-intercept is 5, or (0, 5).step explanation:
[tex]\bf \stackrel{slope}{y=\stackrel{\downarrow }{4}x+5}~\hspace{5em}\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
increase or decrease 32 pages to 28 Pages round to the nearest tenth of a percent
Final answer:
The number of pages decreased from 32 to 28, which is a difference of 4 pages. Dividing by the initial number of pages and multiplying by 100 gives a decrease of 12.5%.
Explanation:
To calculate the percentage change when the number of pages in a document decreases from 32 to 28, we follow these steps:
Find the difference between the two numbers. In this case, it is 32 pages - 28 pages = 4 pages.Divide the difference by the initial number of pages. So, we do 4 pages / 32 pages = 0.125.Multiply the result by 100 to get the percentage. Thus, 0.125 * 100 = 12.5%.Since the number of pages decreased, it is a 12.5% decrease.Therefore, there is a 12.5% decrease when a document goes from 32 pages to 28 pages.
find two consecutive odd integers whose product is 1443
Let's x represents the first odd integer
The next consecutive integer would be represented as x+2.
So x and x+2 being multiplied together will give us 1443:
(x)(x+2)=1443
x^2+2x=1443
x^2+2x-1443=0
By solving the quadratic equation using the quadratic formula, x will equal to 37 and -39.
Since the problem says "integers", so I'm assuming two pairs of consecutive integers would be ok.
With that said you 1st pair will be: 37,39
Your second pair will be: -37,-39.
what is 2 and 3/5 equal to in decimals
2 and 3/5 is equal to 2.6.
Being as the 2 is in front of the fraction, it is the whole number. This means in decimal form, it is to the left of the decimal point. Since there is no "fifths place" in a decimal, you must make it so it can go under the tenths, hundreths, thousanths or another place within the right side of the deciamal point. Simply multiplying 3/5 by 2/2 will give you 6/10. 6/10 as a decimal, is 0.6. Finally, add 0.6 and 2 together. Thus making 2.6 the answer.
I hope this helps!
The equations 2x+7=3 and bx-10=-2 have the same solution for x. Find the value of b.
Solve both equations for x:
2x+7 = 3
2x = -4
x = -2
Plug x into the equation which contains b:
b(-2) -10 = -2
-2b = 8
b = -4
Answer:
b = -4
x = -2
To find the value of b so that the equations 2x+7=3 and bx-10=-2 have the same solution, solve the first equation for x, then use that value to solve for b in the second equation. The value of b is -4.
To find the value of b such that the equations 2x+7=3 and bx-10=-2 have the same solution for x, we need to solve the first equation for x.
Solving the equation 2x+7=3:
Subtract 7 from both sides: 2x = -4
Divide both sides by 2: x = -2
Now that we have the solution x = -2, we can plug this value into the second equation to find b:
bx - 10 = -2
Substitute x with -2: b(-2) - 10 = -2
Multiply b by -2: -2b - 10 = -2
Add 10 to both sides: -2b = 8
Divide both sides by -2: b = -4
Therefore, the value of b is -4.
shen just bought 7 bags of 14 cookies each.he already had 9 cookies in a jar. how many cookies does shen have now??
what is the slope of -1,-7 and 3,9
Answer:
The slope is 4.
Step-by-step explanation:
Use the slope formula.
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] m = \dfrac{-7 - 9}{-1 - 3} [/tex]
[tex] m = \dfrac{-16}{-4} [/tex]
[tex] m = 4 [/tex]
Triangle A’B’C is the image ABC under a translation.
Determine the translation.
Use non-negative numbers.
A translation by ___ units to right/left/up/down
Triangle A'B'C' is the image of triangle ABC under a translation by 3 units right.
Given that, triangle A'B'C' is the image ABC under a translation.
We need to determine the translation.
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions. Since it is just moving the shape from one place to other, there is no change in the shape.
The direction or the path of this change in position of the object can vary i.e., initially the object can move left, then turn right, and so on. While translating, all the points on the shape will shift by the same number of units.
From the given figure we can see triangle ABC is translated by 3 units to the right to get A'B'C'.
Therefore, triangle A'B'C' is the image of triangle ABC under a translation by 3 units right.
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PLEASE HELP,
The formula for finding the area of a sector of a circle is A=πr^2(x/360), where r is the radius of the circle and x is the measure of the central angle of the sector. Solve for x.
x = 360πr^2/A
x = 360A/πr^2
x = Aπr^2/360
x = A/360πr^2
x = [tex]\frac{360A}{\pi r^{2} }[/tex]
multiply both sides by 360 to eliminate the fraction
360A = πr²x ( divide both sides by πr² )
x = [tex]\frac{360A}{\pi r^{2} }[/tex]
Jennifer is planning a holiday. The hotel costs $60 per night and her flights cost $150. She has a budget of $500 for hotel and flights. Up to how many nights can she afford in the hotel?
First add 150 + 60 = 210
Second divide 500 divided by 210 = 2.3
Jennifer can stay up to 2 nights.
Yoko drove 522 miles in 9 hours. At the same rate, how many miles would she drive in 13 hours?
Yoko would drive 754 miles in 13 hours.
First you would have to find how many miles Yoko drives per hour so you divide 522 miles/9 hours to get 58 miles per 1 hour. Then you multiply 58 * 13 to get 754 miles.
Jasper starts the month with $24 in his savings account. At the end of each week, Jasper adds $8 to the account. How much will Jasper have in his account after 10 weeks?
24 + (8·10)
24 + 80
104 dollars after ten weeks
Which variable is most important to the following problem? At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the nurse took the patients temperature again and found it was 105.8 degrees, the highest ever recorded. How long did it take for the patients temperature to reach that high? A: the number of minutes it took for the to reach its peak B: the number of degrees that the temperature changed C: the date on which the previous high was recorded
Answer:
Option A is the important variable.
Step-by-step explanation:
Given is - At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the nurse took the patients temperature again and found it was 105.8 degrees, the highest ever recorded.
The variable that is most important here is A: the number of minutes it took for the to reach its peak.
Firstly it is not mentioned if 10:41 is am or pm.
If its am, then such a temperature rise in less than an hour is very dangerous.
So, the important variable is option A.
Answer:
The answer is B: the number of degrees that the temperature changed.
Step-by-step explanation:
Just took the test
What does 7/18 + 2/27=
The answer would be 25/54
25/54 or .46
7/18+2/27
The figure below shows the penalty box and the goal box of a soccer field. The penalty box is the largest rectangle
Part (A):
The area of the penalty box.
The dimensions of the penalty box are (15x-1) and (5x-7)
The area of rectangle = length * width
∴ The area of the penalty box = (15x-1) * (5x-7) = 75 x² - 110 x + 7
===================================================
Part (B):
The area of the goal box.
The dimensions of the goal box are (7x-1) and (x+3)
The area of rectangle = length * width
∴ The area of the goal box = (7x-1) * (x+3) = 7x² + 20x - 3
=======================================================
Part (C):
The area of the penalty box not coverd by the goal box =
The area of the penalty box - The area of the goal box =
(75 x² - 110 x + 7) - (7x² + 20x - 3) = 68 x² - 130 x + 10
How many 1/5 cup servings are in 3/4 of a cup of ice cream
The bank has accepted Harriet's application for a mortgage to buy a property worth $325,500. She has to make a down payment of 20 percent of the purchase price. What is the loan amount? A. $256,000 B. $258,000 C. $260,400
Answer:
C. $260,400
Step-by-step explanation:
Since Harriet has to pay 20% down, this means she is borrowing 100-20 = 80% of the value.
80% = 80/100 = 0.8; this makes the amount borrowed
0.8(325500) = 260,400
Please!! help me with number 7. and 9.
and I will THANK YOU!!!
7) 12 / 6
(how many party favors can he give to 6 people if he has twelve? each person can get 2)
9) 2(12)
(Each water bottle is two dollars, how many bottles did she buy? 12. 12 bottles at 2 dollars each would be $24)
2 factors of 36 add up to 15 What are they?
Hey there!!
What are the factors of 36?
Ans :- 1 , 36 , 2 , 18 , 3 , 12 , 4 , 9 , 6
Which of these numbers add up to 15 ?
... 12 + 3 = 15
The number are 15.
They add up to 15 and both of these are factors of 36.
Hope my answer helps!!
Find the coordinates of the point of intersection of the graphs of lines with y=−2x+7 and y=0.5x−5.5
the coordinates of the point of intersection of the graphs of lines with
y=−2x+7 and y=0.5x−5.5
to find intersection we solve for x and y
We replace -2x+7 for y in the second equation
−2x+7 =0.5x−5.5
Subtract 0.5x from both sides
-2.5x + 7 = -5.5
Subtract 7 on both sides
-2.5x = -5.5 - 7
-2.5x = -12.5
divide by -2.5 from both sides
x = 5
Plug in 5 for x in y=−2x+7
y=−2(5)+7
y = -10 + 7
y = -3
The point of intersection is (5,-3)
Anna picked 6 apples. Sabrina picked 7 times as many apples. How many apples did Sabrina pick?
Anna picked 6 apples
Sabrina picked 7 times as many apples.
Multiply the two numbers together
6 x 7 = 42
Sabrina picked 42 apples
hope this helps
~Rise Above the Ordinary
Anna picked 6 apples. Sabrina picked 7 times as many apples. How many apples did Sabrina pick?
Times, means to multiply, take the only two numbers in the problem and multiply them together.
6 x 7 = 42
~
Use the equation y = 4x to answer the questions.
The slope is 4 and the Y-Intercept is 0.
In a school election, 34 of the students vote. There are 1464 ballots. Write and solve an equation to find the number s of students.
*(Answer)*= [tex]x+34=1464[/tex]
Hope this helps
BangtanBoyScouts
what is the least common denominator of 5/9 and 11/12?
The LCM of 5/9 and 11/12
is 36
9*4=36
12*3=36
20/36
&
33/36
331 students went on a field trip .six buses were filled and 7 students traveled in cars how many students were in each bus?
331 total students. 7 traveled by car.
331 - 7 = 324 were on buses.
There were 6 buses:
324 / 6 = 54 students on each bus.
a fence is 702 m long. it is cut into three parts. two parts are the same length and the third is 27 m longer than either of the other two. find the length of each part
Answer:
225, 225 and 252 meters
Step-by-step explanation:
Let length of the 2 equal parts be each x m, then:-
2x + x + 27 = 702
3x = 702 - 27 = 675
x = 675/3
x = 225
So lengths of each parts are 225, 225, 252
To find the lengths of the three parts, we let the length of each of the two equal parts be 'x' and set up the equation 3x + 27 = 702. Solving for 'x' gives us that each of the two equal parts is 225 m, and the third part is 252 m.
The student is asking to find the lengths of three parts of a fence that has been cut, with two parts being equal in length and the third part being 27 m longer than the other two. Let's assume each of the two parts that are the same length is 'x' meters. Since the third part is 27 m longer, it would be 'x + 27' meters. According to the problem, the total length of the fence is 702 m.
Therefore, the sum of all three parts is:
x + x + (x + 27) = 702
Simplifying this, we get:
3x + 27 = 702
Subtract 27 from both sides:
3x = 675
Now, divide both sides by 3:
x = 225
So, the two equal parts are each 225 m long, and the third part is 225 + 27 = 252 m long.
is 5.3 repeating rational
Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers. If a number is terminating or repeating, it must be rational if a decimal is both non terminating and non repeating, the number is irrational.
So yes.
Yes, 5.3 repeating is a rational number. It can be written as the fraction 53/9.
Explanation:Yes, 5.3 repeating is a rational number. A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. In this case, we can write 5.3 repeating as the fraction 53/9. The decimal 5.3 repeating means that the digit 3 repeats infinitely, so it can be written as 5.3333... In fraction form, this becomes 53/10 + 53/100 + 53/1000 + ...
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If the equation y = (x - 6)(x + 12) is graphed in the xy-plane, what is the x-coordinate of the parabola’s vertex? Also please show the steps. :)
x- coordinate of vertex = - 3
the vertex lies on the axis of symmetry , which is positioned at the midpoint of the zeros
find the zeros by setting y = 0
(x - 6)(x + 12) = 0 ( equate each factor to zero and solve for x )
x - 6 = 0 ⇒ x = 6
x + 12 = 0 ⇒ x = - 12
x coordinate of vertex = [tex]\frac{- 12+6}{2}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
Write a 2 two column proof. Given: 4y = 2x -10; y = 6 Prove : x = 17
Final answer:
We proved x = 17 given the equations 4y = 2x - 10 and y = 6 through a series of substitution and simplification steps in a two-column proof.
Explanation:
Given the equation 4y = 2x - 10 and the fact that y = 6, we need to prove that x = 17. The process of proving this assertion can be methodically shown through a two-column proof, which lists both the statements and the reasons behind each step.
y = 6 (Given)4y = 2x - 10 (Given)4(6) = 2x - 10 (Substitution of y with 6)24 = 2x - 10 (Simplifying the multiplication)24 + 10 = 2x (Adding 10 to both sides)34 = 2x (Simplifying by combining like terms)17 = x (Dividing both sides by 2 to solve for x)Through these steps, we have shown that, given 4y equals 2x minus 10 and y is 6, we can prove that x equals 17.