Using linear functions, it is found that:
Shop B charges less per hour.The total costs are the same when a pair of skis is rented for 3 hours.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For Shop A, we have that the slope is of 3, as the cost increases by $3 an hour, hence:
yA(x) = 3x + b.
When x = 1, y = 8, hence we find the intercept b as follows:
8 = 3 + b
b = 5.
Hence:
yA(x) = 3x + 5.
For Shop B, the rule is given as follows:
yB(x) = 2x + 8.
Due to the lower slope, we have that:
Shop B charges less per hour.
The costs will be the same when:
yA(x) = yB(x).
Hence:
3x + 5 = 2x + 8
x = 3.
The total costs are the same when a pair of skis is rented for 3 hours.
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university trailer sales company sold utility trailers during a recent year. if the gross annual sales for the company was $, what was the average selling price for each trailer?
The solution for finding out the average selling price for each trailer is given below: Let, The gross annual sales for the company be $GThe number of trailers sold be The selling price of each trailer be SP.
Gross annual sales = number of trailers sold × selling price of each trailer G = n × SP Now, from the given information, we have the value of gross annual sales as $G. However, we do not have the value of n (number of trailers sold) and SP (selling price of each trailer) individually to solve for SP and calculate the average selling price of each trailer.The question doesn't provide information regarding the number of trailers sold or the selling price of each trailer separately to calculate the average selling price of each trailer. Therefore, we cannot calculate the answer to this question. We need one more piece of information to find the solution.
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Six less than seven times a number is negative is twenty
Answer:
7n - 6 = -20
Step-by-step explanation:
HELPPPPPPPPPPPP MEHHHHHHHHHHHHHHHHHHHHHHHHH PLZZZZZZZZZZZZZZZZ GRADES GO OUT TOMMORROW AND I NEED THIS SO I CAN GET MY GRADE UP FROM A D+ PLZZZZZZZZ MY PARENTS WILL MURDER ME
Answer:
6.48
Step-by-step explanation:
17*-.36= -6.12
-6.12+12.6= 6.48
keith has $15 more than jay. if keith has $87, how much money does jay have?
Answer:
Jay has $72
Step-by-step explanation:
$87-$15=$72
Answer: Jay has $72.
Step-by-step explanation: It's basically a subtraction problem. You are subtracting 87-15 and getting 72.
write in factored form 56 - 7p
Answer:
8(7-p)
Step-by-step explanation:
pull out greatest common factor
let r be the region in the first quadrant bounded by the graph of y=2tan(x5), the line y=5−x, and the y-axis. what is the volume of the solid generated when r is revolved about the line y=6
The volume of the solid is 29.865 cubic units.
We have,
To find the volume of the solid generated by revolving region R around the line y = 6, we can use the method of cylindrical shells.
The volume of the solid can be obtained by integrating the area of each cylindrical shell.
Each shell is formed by taking a thin vertical strip of width dx from region R and rotating it around the line y = 6.
Let's denote the radius of each cylindrical shell as r(x), where r(x) is the distance from the line y = 6 to the curve y = 2tan(\(x^5\)).
Since the shell is formed by revolving the strip around y = 6, the radius of the shell is given by r(x) = 6 - 2tan(\(x^5\)).
The height of each cylindrical shell is the difference in x-values between the curve y = 5 - x and the y-axis, which is given by h(x) = x.
The differential volume of each cylindrical shell is given by:
dV = 2π x r(x) x h(x) x dx.
To find the total volume of the solid, we integrate the differential volume over the interval where region R exists, which is determined by the intersection of the curves y = 2tan(\(x^5\)) and y = 5 - x.
The volume V is given by the integral:
V = ∫[a,b] 2π x (6 - 2tan(\(x^5\))) x dx
Setting the two equations equal to each other, we have:
2tan(\(x^5\)) = 5 -x
Let's use numerical approximation to find the intersection points.
Using a numerical solver, we find that one intersection point is approximately x ≈ 1.051.
Now, we can set up the integral to find the volume of the solid:
V = ∫[a,b] 2π (6 - 2tan(\(x^5\))) x dx
Since we are revolving around the line y = 6, the limits of integration will be from x = 0 to x = 1.051.
V = ∫[0,1.051] 2π (6 - 2tan(\(x^5\))) x dx
The integral does not have an elementary antiderivative, so we cannot find the exact value of the integral.
However, we can still approximate the value using numerical methods or software.
Using numerical approximation methods, the volume is approximately V ≈ 29.865 cubic units.
Thus,
The volume of the solid is 29.865 cubic units.
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2.6 + 0.9 show work
Answer:
3.5 is your answer.
Step-by-step explanation:
2.6
0.9+
------
3.5
Answer
3.5
Explanation
2.6 + 0.9
3.5
Good Luck ^-^
food safety guidlines recommend that a beef rib roast should cook for 23 minutes per pound based on 325f oven setting. how many hours should it take to cook a 5.17 pound roast?
It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.
Cooking time in minutes = 5.17 pounds * 23 minutes/pound
Cooking time in minutes = 118.91 minutes
To convert minutes to hours, we divide the total minutes by 60:
Cooking time in hours = 118.91 minutes / 60
Cooking time in hours ≈ 1.98 hours
Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
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What is the type? f(x)=-1/5x³-5+10x²
Muffins are sold by the dozen at a bakery. The table shows the cats for oferent mens of muffins sold at the bakery, Cost of Muffins Domen of Cost (dollars) Muffins 2 17 4 6 51 Explain your thin with equations 34 What is the cost in dollars for 24 dozen muffins? A $408 B $204 Wha С $85 Not here
hello
from the table given, we can establish a relationship bewteen the number of dozens to the cost in dollars
if 2 dozens costs $17
8 dozens costs x
cross multiply and solve for x
\(\begin{gathered} 2\text{ =17} \\ 8=x \\ 2x=8\times17 \\ 2x=136 \\ x=68 \end{gathered}\)what i did above was test if the relationship is correct
now let's find for 24 dozens
if 2 dozens = $17
24 dozen = ?
\(\begin{gathered} 2dz=17 \\ 24dz=x \\ 2x=17\times24 \\ 2x=408 \\ x=\frac{408}{2} \\ x=204 \end{gathered}\)24 dozens of muffins would cost $204
Which equation represents a line that passes through (−2,4) and has a slope of 25?
y−4=−25(x−2)
y−4=25(x+2)
y+12=−5(x−2)
y+4=25(x+2)
Answer:
y−4=25(x+2)
This is the answer.
The original price of new school bag is $352.00. If the school bag is marked down 14% what is the new price?
determine the number of arrangements of the letters in georgiatech such that all the e's are consecutive.
The number of arrangements of the letters in "georgiatech" with all the e's consecutive is 60,480.
To determine the number of arrangements of the letters in "georgiatech" such that all the e's are consecutive, we can treat the three e's as a single unit. So, we have 9 distinct letters: g, o, r, g, i, a, t, c, h, and the "eee" unit.
The total number of arrangements of these 9 letters is 9!. However, within the "eee" unit, the three e's can be arranged among themselves in 3! ways. Therefore, we need to divide the total number of arrangements by 3!.
Hence, the number of arrangements of the letters in "georgiatech" such that all the e's are consecutive is:
9! / 3! = 362,880 / 6
= 60,480
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17 points please help
Answer:
3% of the figure is shaded
Fraction: 3/10
Decimal: 0.3
Hope this helped
x3+y3+z3=k, with k being all the numbers from one to 100
✦ ✦ ✦ Beep Boop - Blu Bot! At Your Service! Scanning Question . . .
Code: Green! Letters, Numbers, and Variables Received! ✦ ✦ ✦
--------------------------------------------------------------------------------------------------------------Question: x3+y3+z3=k, with k being all the numbers from one to 100
--------------------------------------------------------------------------------------------------------------Answer: X = -80538738812075974, Y = 80435758145817515, and Z = 12602123297335631.
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X = -80538738812075974, Y = 80435758145817515, and Z = 12602123297335631.
A university professor does not believe that there is really a difference between the GPA of male and female scholarship athletes, so he looks into how the sample was collected. His investigation shows that the study was given to all of the athletes on the basketball teams exclusively. Based on this information, should the university administration trust the results from this study?
a. Yes, because the results were significant
b. Yes, because a large enough sample was taken
c. No, because not every scholarship athlete part of the study
d. No, because the study was not taken from a random sample of scholarship athletes
Answer: d. No, because the study was not taken from a random sample of scholarship athletes.
Step-by-step explanation:
Since the study only focuses on basketball players, the sample may not be representative of all scholarship athletes in the university. This can cause bias in the results and make it difficult to generalize the findings to the larger population of scholarship athletes. Therefore, the university administration should not fully trust the results of this study.
A teacher wants to buy 9 boxes of granola bars for a school trip. Each box usually costs $7, but many grocery stores are having a sale on granola bars this week. Different stores are selling boxes of granola bars at different discounts.
Answer:
well I think the question's not complete but if that's the question then 9 boxes would cost about $63 dollars. since some stores have a sale, you should add the word 'about' or 'around' with the answer. hope it was helpful ))
The minimum discount teacher will need to buy 9 boxes of granola bars for a school trip is 42.86%.
Complete Question -
A teacher wants to buy 9 boxes of granola bars for a school trip.
● Each box usually costs $7, but many grocery stores are having a sale on granola bars this week, and different stores are selling boxes of granola bars at different discounts.
● This teacher can spend at most $36 on granola bars. Write and solve an inequality to represent the amount that the granola bars could be discounted so that this teacher can stay within his budget.
Given to us
Cost of a box of granola bars = $7Number of boxer teacher wants to buy = 9Budget of teacher = $36Assumption
Let's assume that the discount teacher want is x, therefore, the teacher wants to buy a box of granola bars in (100-x) times the price.
The total cost of 9 boxes of granola barsThe total cost of 9 boxes of granola bars
= Number of boxes x Cost of a box of granola bars
= 9 x $7
= $63
Discount teacher will needAs we know the budget of teachers is only $36, the inequality can be written as,
\((100-x)\%\ of\ \$63 \leq \$36\\\\\dfrac{(100-x)}{100} \times 63 \leq 36\\\\(100-x) \leq \dfrac{36 \times 100}{63}\\\\(100-x)\leq 57.14 \\\\ -x \leq -42.86\%\\\\ x \geq 42.86\%\)
Hence, the minimum discount teacher will need to buy 9 boxes of granola bars for a school trip is 42.86%.
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(-12a^3b^5)/(4a^2b^7)
state any restrictions on the variable(s) if they exist.
PLEASE HELP (30 points)
Answer:
\(a\neq 0 \text{ and } b\neq 0\)
Step-by-step explanation:
So we have the rational expression:
\(\frac{-12a^3b^5}{4a^2b^7}\)
In rational expressions, the restrictions of the expression would be the zeros of the denominator Therefore, set the denominator equal to zero and solve for its zeros:
\(4a^2b^7=0\)
Zero Product Property:
\(4a^2=0\text{ or } b^7=0\\\)
Solve for a and b:
\(4a^2=0 \text{ or } b^7=0\\a\neq 0 \text{ or }b\neq 0\)
Therefore, the restrictions on the variables are that a and b cannot equal zero.
15x⁴-16x³+0x²+8x-17 ÷ (3x²+x+1)
After dividing ( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 ), we get the quotient as 5 x² - 7 x + 4 and the remainder as 11 x - 21.
We are given an expression:
( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 )
We need to perform division of the algebraic expression:
5 x² - 7 x + 4
3 x² + x + 1 √15 x⁴ - 16 x³ + 10 x² + 8 x - 17
15 x⁴ + 5 x³ + 5 x²
______________________
- 21 x³ + 5 x² + 8 x - 17
- 21 x³ - 7 x² - 7 x
______________________
12 x² + 15 x - 17
12 x² + 4 x + 4
______________________
11 x - 21
______________________
Therefore, after dividing ( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 ), we get the quotient as 5 x² - 7 x + 4 and the remainder as 11 x - 21.
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Which system of inequalities is represented by the graph?
The following system of inequalities is represented by the graph
x+y>3
-x+y< -4
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Consider the inequalities:
x+y>3-------(1)
-x+y< -4------(2)
Find x and y intercepts of both by considering them as equations by using equal sign in the place of inequality sign
x+y=3-------(3)
-x+y= -4------(4)
Find x and intercepts of these 2 equations:
we get x intercept when y=0 ( substitute y=0 into the respective equations and find x)
we get y intercept when x=0 ( substitute x=0 into the respective equations and find y)
x intercept of (3) is (3,0)
y intercept of (3) is (0,3)
x intercept of (3) is (4,0)
y intercept of (3) is (0,-4)
plot these points on a the plane and join them with lines
use dotted line and shade under the lines because of less than symbol
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Help me pls asap! :)
Answer:
infinite solutions
4x+ 12 - 4 = 4x + 8
4x + 8 = 4x + 8
what is the inverse of the given relation? y=2x+6
The inverse of our given equation- would be y=x+6/2 and options B is the correct choice.
What is equation?An equation is a mathematical statement that expression the equality of the expression using of the equal sign equation are used to define relationship between differentiation variables can be used to solve for the unknown's values when you problems equation are also used to describe the behavior of the physical system in the represent law of nature.
We have been given an equation y=2x-6 . We are asked to find the inverse of our given equation.
To find inverse of our given equation, we will interchange x and y variables and solve for y as shown below:
x=2y-6
Switch sides:
2y-6=x
Add 6 on both sides:
2y-6+6=x+6
2y=x+6
Divide both sides by 2:
2y/2=x+6/2
y=x+6/2
Therefore, the inverses of our given equation would've be y=x+6/2 and option B is the correct choice.
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Pat found the sum of the first 2021 positive even integers and Ray found the sum of the first 2022 positive even integers. By how much does Ray's sum exceed Pat's sum
The sum of the first 2021 positive even integers is (2021 x 2022). Therefore, Ray's sum exceeds Pat's sum by 2052.
The sum of the first 2021 positive even integers is given by 2+4+6+...+4040. To find this sum, we can use the formula for the sum of an arithmetic series:
S = (n/2)(a + l)
where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term. In this case, n = 2021, a = 2, and l = 4040 (which is the 2021st even integer). So we have:
S = (2021/2)(2 + 4040)
= 2041210
Therefore, Pat's sum is 2041210.
The sum of the first 2022 positive even integers is given by 2+4+6+...+4042. Using the same formula as above, we have:
S = (2022/2)(2 + 4042)
= 2043262
Therefore, Ray's sum is 2043262.
To find by how much Ray's sum exceeds Pat's sum, we can subtract Pat's sum from Ray's sum:
2043262 - 2041210 = 2052
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You have the option to deposit $6500 into an account that pays 3.25% interest, compounded quarterly OR to deposit your money into an account that pays the same interest rate but compounds continuously. Which option yields you more money after 5 years and how much more?
OPTIONS:
Compounded quarterly, $4809.13
Compounded quarterly, $416.23
Compounded continuously, $5.02
Compounded continuously, $878.52
9514 1404 393
Answer:
Compounded continuously, $5,02
Step-by-step explanation:
Compounded quarterly, the amount in the account will be ...
A = 6500(1 +.0325/4)^(4·5) ≈ 7641.89
Compounded continuously, the amount in the account will be ...
A = 6500e^(.0325·5) = 7646.91
So, the account compounding continuously has the higher yield, by the amount of ...
$7646.91 -7641.89 = $5.02
Due to a power outage, the sales clerk manually prepares a sale receipt to her customer. Which one of the following diagrams represents this activity?
a. trapezoid to curvy side rectangle to curved rectangle
b. curved side rectangle to circle to curved rectangle
c. circle to curved side rectangle to curved rectangle
d. trapezoid to curved side rectangle to circle
Based on the given options, the diagram that best represents the activity of a sales clerk manually preparing a sale receipt during a power outage would be option D.
A trapezoid could represent the shape of a receipt, a curved side rectangle could represent the shape of the clerk's desk or the paper she is using, and a circle could represent the shape of a calculator or cash register. Therefore, a trapezoid to a curved side rectangle to a circle could represent the process of the clerk manually calculating and recording the sale amount and inputting it into a calculator or cash register to produce a receipt.
It is important to note that during a power outage, technology-dependent activities such as electronic sales and transactions may be disrupted, and manual methods may have to be used as a backup. This highlights the power of technology in our daily lives and the impact that power outages can have on businesses and individuals.
The question is about selecting the correct diagram that represents the sales clerk manually preparing a sale receipt due to a power outage. Given the options:
a. trapezoid to curvy side rectangle to curved rectangle
b. curved side rectangle to circle to curved rectangle
c. circle to curved side rectangle to curved rectangle
d. trapezoid to curved side rectangle to circle
The appropriate answer for this question cannot be determined based on the provided information. Diagrams typically require visual representation, and the description of the shapes alone is insufficient to convey the activity of preparing a receipt manually. Moreover, the terms "power," "outage," "clerk," "receipt," "trapezoid," "curved," and "curved" don't necessarily correspond to the shapes given in the options.
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a plane flew232 miles from edinburugh airport to liverpool airport. it had an average speed of 174 mog and arrived at 20:15. work out the timw left
The plane departed from Edinburgh at approximately 19:55, taking about 1.333 hours to fly 232 miles to Liverpool, arriving at 20:15.
To calculate the time it took for the plane to fly from Edinburgh Airport to Liverpool Airport, we can use the formula:
Time = Distance / Speed
Given that the distance is 232 miles and the average speed is 174 mph, we can plug these values into the formula:
Time = 232 miles / 174 mph
Time ≈ 1.333 hours
Since we want to determine the arrival time, we need to add the flying time to the departure time. The plane arrived at 20:15, so we can calculate the departure time by subtracting the flying time from the arrival time:
Departure Time = Arrival Time - Flying Time
Departure Time = 20:15 - 1.333 hours
To subtract the decimal part of the flying time, we can convert it to minutes:
0.333 hours * 60 minutes/hour = 20 minutes
Subtracting 20 minutes from 20:15 gives us the departure time:
Departure Time ≈ 19:55
Therefore, the plane departed from Edinburgh Airport at approximately 19:55.
In summary, the plane flew 232 miles from Edinburgh to Liverpool at an average speed of 174 mph, taking approximately 1.333 hours. It departed from Edinburgh at around 19:55 and arrived at Liverpool at 20:15.
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what is happening to this graph when the x values are between -8 and -4
a is it constant
b decreasing
c increasing
i say increasing am i right ?
Answer:
the answer is C increasing. yes of course you are right. please mark me as the brilliant pleasee!
The Probability that Ann will have to wait more than 5 minutes for the next bus is 0.4. What is the Probability that She will not Have to wait more than five minutes
Answer:
0.6
Step-by-step explanation:
The maximum probability is always 1. this to solve this question you need to subtract the probability of waiting for the bus from 1 and get your answer
thus: 1 - 0.4
= 0.6
Which of the following would not be used to describe a slope?
steepness of a line.
ratio of rise to run of a line.
ratio of the horizontal change to the vertical change of a line.
Answer:
C: ratio of the horizontal change to the vertical change of a line
Step-by-step explanation:
A and B are correct.
C is incorrect.
Parker is in the business of manufacturing phones. He must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The equation C=175p+400 can be used to determine the total cost, in dollars, of producing pp phones in a given day. What is the y-intercept of the equation and what is its interpretation in the context of the problem?
9514 1404 393
Answer:
400; building and equipment fixed cost
Step-by-step explanation:
The cost equation has two terms. The constant term (400) is the daily fixed cost of building and equipment. The variable term (175p) represents the cost of producing p phones.
The y-intercept is 400. It is the daily fixed cost of the building and equipment.
Answer:
The y-intercept of the function is 400 which represents the fixed cost for rent and equipment.
Step-by-step explanation:
Since Parker must pay $400 even to make 0 phones, that means $400 is the fixed cost that Parker must pay for rent and equipment regardless of the number of phones produced.
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