Given:
[tex]\begin{gathered} D_{\text{iamteter of the tire}}=62cm \\ N_{\text{umber of revolution}}=10revolutions \end{gathered}[/tex]To Determine: The distance travelled
The distance travel in 1 revolution is the circumference of the tire.
The circumference of a circle is calculated by the formula below
[tex]\begin{gathered} C_{\text{ircumference of a circle }}=2\pi r \\ 2r=d \\ \text{Therefore} \\ C_{\text{ircumference of a circle }}=\pi d \end{gathered}[/tex]Substituting for diameter in the formula to get the distance travelled in 1 revolution as below
[tex]D_{is\tan ce\text{ travelled in 1 revolution}}=\pi\times62cm=62\pi cm[/tex]Therefore the distance in 10 revolution would be
[tex]\begin{gathered} D_{is\tan ce\text{ travelled in 10 revolutions}}=10\times62\pi cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}=620\pi cm=1947.787cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}\approx1948cm \end{gathered}[/tex]Hence, the distance travelled by the bicycle in 10 revolutions to the nearest cm is 1948cm
4lemons are bought for RS 40 and sold 3 for RS24 find profit percent or loss percent
Since the buying price is RS 40
Since the selling price is RS 24
If the selling price is less than the buying price, then it is a loss
To find the percent of loss Divide the loss by the buying price, then multiply the answer by 100%
[tex]\begin{gathered} \text{Loss= 40 - }24 \\ \text{Loss = }16 \end{gathered}[/tex]The percent of the loss is
[tex]\begin{gathered} \text{Percent Loss}=\frac{16}{40}\times100\text{ \%} \\ \text{Percent Loss = 40\%} \end{gathered}[/tex]The percent of loss is 40%
Name the order pair that is solution set in the following system.
Answer:
(1, 2)
Explanation:
The solution of the system is the intersection point of the lines. In this case, the intersection point is (1, 2), so the solution set is the order pair (1, 2)
The system of inequalities, r+ y > 10 * + y 2 Select the region that contains solutions to the system of inequalities modeled in the graph below O Region A Solutions to the system of inequalities lie in one ofthe regions shown on the coordinate plane. O Region B Region O Region D B A С Previous
we know that
inequality 1
The solution is the shaded area above the solid line x+y=10
Inequality 2
The solution is the shaded area below the solid line -x+y=-2
therefore
the solution of the system of inequalities is the region C
An animal food must provide 60 units of vitamins and 65 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 8¢, a gram of meat byproducts 9¢, and a gram of grain 10¢.
(a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost?
(b) What is the minimum cost?
x1 x2 s1 s2 s3 z
2.5 5 1 0 0 0 __
4.5 3 0 1 0 0 __
5 10 0 0 1 0 10
__ __ 0 0 0 1 0
There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual.
When pivoting on the second row of the dual, the mixture would contain __ grams of soybean meal, __ grams of meat byproducts, and __ grams of grain. When pivoting on the third row of the dual, the mixture would contain __ grams of soybean meal, __ grams of meat byproducts, and __ grams of grain.
The minimum cost is $__
Answer: its A i hope this helps <3
Step-by-step explanation:
Until June 2002 the simple interest rate on Stafford loans to college students was 5.39%% while the students was still in college how much interest would a student pay on a $1,500 loan for 2 years
The amount that a student would pay in interest on a $1,500 loan for 2 years is $161.70
What is simple interest?
Under simple interest loan arrangement, the same amount of interest is paid every year for the entire duration of the loan as the interest is determined as the loan principal multiplied by interest rate as well as multiplied by the loan duration expressed in years as indicated below:
I=PRT
I=the interest on the Stafford loans in dollars=unknown
P=Stafford loans principal=$1500
R=annual rate of interest on the loan=5.39%
T=the loan period in years=2
I=$1500*5.39%*2
I=$161.70
Over the period of 2 years, the interest on the student's loan is $161.70
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In the diagram below, GPK = 18x + 5 and KPH = 14x + 15. Solve for the measure of angleGPK.PH
We can say that the two triangles are identical, then, the angle GPK is equal to the angle KPH, then we write the following equation:
[tex]\begin{gathered} \angle GPK=\angle KPH \\ \\ 18x+5=14x+15 \\ \\ 4x=10 \\ \\ x=\frac{10}{4}=\frac{5}{2}=2.5 \end{gathered}[/tex]Now we know the value of x, we can return to the equation and find the value of the angle GPK
[tex]\begin{gathered} \angle GPK=18x+5 \\ \\ \operatorname{\angle}GPK=18\cdot\frac{5}{2}+5 \\ \\ \operatorname{\angle}GPK=9\cdot5+5 \\ \\ \operatorname{\angle}GPK=45+5 \\ \\ \angle GPK=50 \end{gathered}[/tex]Therefore, the measure of the angle GPK is equal to 50 degrees
A tennis racket at Sport City costs $180and is discounted 15%. The same modelracket costs $200 at Tennis World and is onsale for 20% off. Which store is offering thebetter deal? Explain.
We can find the discounted price of the tennis racket at Sport City by finding the 100% - 15% = 85% of the total price. We can do this by multiplying the total price by the decimal form of 85%:
[tex]180(85\%)=180(0.85)=153[/tex]then, we have that the price of the racket at Sport City is $153
Doing the same but with the price at Tennis World, we get:
[tex]\begin{gathered} 100\%-20\%=80\% \\ \Rightarrow200(80\%)=200(0.80)=160 \end{gathered}[/tex]since the price of the tennis racket is $160 at Tennis world, we can clearly see that Sport City offers a better deal (since 153 < 160)
Explain how to evaluate f(2) to a student that is absent today.
Answer:
f(x) is a function. For example f(x) = 2x + 1
If you were to say evaluate f(2), you would plug in the '2' to 'x'.
So in the example I gave, f(2) = 2(2) + 1
f(2) = 4 + 1
f(2) = 5
8. Let g(x) = 8 – 2xa) Find g(3)
2
1)In this case, let's plug in 3 from the domain set into the function g(x):
g(3) =8-2(3)
g(3) =8-6
g(3) =2
2) So 2 is the value in the Range when 3 is plugged in from the Domain set.
Answer:
[tex]g(3)=2[/tex]
Step-by-step explanation:
GivensWe are given a function:
[tex]g(x)=8-2x[/tex]
We are asked to find g(3).
SolveFirst, substitute 3 as x in g(x):
[tex]g(x)=8-2x\\\\g(3)=8-2x[/tex]
Then, substitute 3 as x in the function:
[tex]g(3)=8-2x\\\\g(3)=8-2(3)[/tex]
Simplify the function by multiplying 2(3):
[tex]g(3)=8-2(3)\\\\g(3)=8-6[/tex]
Then, simplify by performing the final necessary arithmetic:
[tex]g(3)=8-6\\\\g(3)=2[/tex]
Final AnswerTherefore, g(3) = 2.
Consider the function:f(x) = -5x + 5Step 1 of 2: Find the value of f(-2).
Given:
[tex]f(x)=-5x+5[/tex][tex]f(-2)=-5(-2)+5[/tex][tex]f(-2)=10+5[/tex][tex]f(-2)=15[/tex][tex]f(5)=-5(5)+5[/tex][tex]f(5)=-25+5[/tex][tex]f(5)=-20[/tex]BRAINLIST TO BEST ANSWER
solve these problems
Answer:
11: 4.64 m
12: 61.6 in
Step-by-step explanation:
formula for an area of a triangle is base times height divided in half and 2.9 times 3.2 is 9.28 and divided by 2 you get 4.64
formula for a trapezoid is base 1 plus base 2 in half times height and 12 plus 10 is 22 divided by 2 it is 11 and 5.6 times 11 is 61.6
What’s the correct answer answer asap for brainlist I really need help
Answer:
A. clouds
Step-by-step explanation:
hope it helps :)
Reasoning Awat withdraws $17 from his bank account once each day for four days. What integer represents the change in the amount in the account? Use pencil and paper. Find the integer that would represent the change in the amount in the account if Awat deposits $17 into his bank account once each day for four days. Explain the difference between the integer for the withdrawals and the integer for the deposits…
The integer that represents the change in Awat's account is $-68.
The difference between the integers that represents withdrawal and deposits is the integer that represents withdrawals is negative while the integer that represents deposits is positive.
What is the integer that represent withdrawals?In order to determine the total withdrawals in four days, multiply the daily withdrawals by the number of days. Multiplication is the arithmetic operation that is used to determine the product of two or more numbers.
Total withdrawals = daily withdrawal x number of days
$17 x -4 = $-68
When there is a withdrawal, the value of the money in the account would decline. Thus, this would be represented with a negative number. A negative number has a negative sign in front of it. When there is a deposit, the value of the money in the account would increase. Thus, this would be represented with a positive number.
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Looking to receive full help on this practice question, thank you.
-42
Explanation
the determinant of a 2 X 2 matrix is given by:
[tex]\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix}=ad-bc[/tex]so, the determinant of the matrix
[tex]\begin{bmatrix}{-6} & {0} \\ {4} & {7}\end{bmatrix}[/tex]would be
[tex]\begin{gathered} \begin{bmatrix}{-6} & {0} \\ {4} & {7}\end{bmatrix}=\left(-6*7\right)-\left(4*0\right)=-42-0=-42 \\ so \\ det\left(\right?\begin{bmatrix}{-6} & {0} \\ {4} & {7}\end{bmatrix}=-42 \\ \end{gathered}[/tex]therefore, the answer is
-42
I hope this helps you
Which of the following would be enough information to know that ABC~MNP?
Answer:
[tex]\textsf{(2) \quad $m \angle A=m \angle M$ and $\dfrac{AB}{MN}=\dfrac{AC}{MP}$}[/tex]
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are the same size and the corresponding sides are in the same ratio.
Therefore, if triangle ABC is similar to triangle MNP then their corresponding angles are congruent:
m∠A = m∠Mm∠B = m∠Nm∠C = m∠PSimilarly, if triangle ABC is similar to triangle MNP then their corresponding sides are in the same ratio:
[tex]\implies \dfrac{AB}{MN}=\dfrac{BC}{NP}=\dfrac{AC}{MP}[/tex]
SAS Triangle Similarity
If two sides of one triangle are in the same ratio to the corresponding sides of another triangle, and their included angles are congruent, then the triangles are similar.
∠A is the included angle of sides AB and AC.
∠M is the included angle of sides MN and MP.
Therefore, the only statement that shows that two corresponding sides are in the same ratio and their included angles are congruent is:
[tex]\textsf{(2) \quad $m \angle A=m \angle M$ and $\dfrac{AB}{MN}=\dfrac{AC}{MP}$}[/tex]
A line is defined by the equaton y=-x=+3. which shows the graph of this line
The slope and y-intercept of the line whose equation is given as y=(-x+3) is -1 and 3 respectively.
As per the question statement, we are supposed to find the slope and y-intercept of the line whose equation is given as y = -x + 3
We know slope-intercept form of line: y = mx + c, where "m" is the slope of the line and "c" is the y-intercept.
Comparing the given equation with y = mx +c
We get slope, m = -1
and y- intercept, c = 3
Hence, the The slope and y-intercept of the line whose equation is given as y= -x + 3 , is -1 and 3 respectively.
Slope: The value of slope gives an indication of the steepness of a straight line and is calculated by taking the tangent of the angle on x-axis.y-intercept: The graph's intersection with the y-axis is known as the y-intercept of that very line.To learn more about slope and y-intercepts of a line, click on the link given below:
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Not good at math at all so I rlly don’t know much of anything, could really use the help.
Given
Stack of 39 pennies is exactly as tall as 31 pennies
Find
the correct options
Explanation
No the two stacks will have different volume.
The two stacks will have same height but the area of cross section of the penny stack is smaller than that of nickel stack
Final Answer
option (b) is correct
A ball is thrown in the air. Its path is modeled by the equation ℎ(t) =− 16t^2 + 56t, where h represents the height of the ball in cm and t represents time in seconds since the ball was thrown. When is the ball at its highest point? What is the highest point?
Check the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+56}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 56}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (56)^2}{4(-16)}\right) \implies \left( - \cfrac{ 56 }{ -32 }~~,~~0 - \cfrac{ 3136 }{ -64 } \right) \\\\\\ \left( \cfrac{7}{4}~~,~~49 \right)\implies \stackrel{seconds\qquad feet}{\left(1\frac{3}{4} ~~ ~~,~ ~~ ~49 \right)}[/tex]
What is the volume of the sphere shown below with a radius of 6?617.8--A. 2885 cu. unitsB. 1625 cu unitsC. 485 cu. unitsD. 1445 cu units
The radius of sphere is r = 6.
The formula for the volume of sphere is,
[tex]V=\frac{4}{3}\pi r^3[/tex]Substitute the value in the formula to determine the volume of sphere.
[tex]\begin{gathered} V=\frac{4}{3}\pi\cdot(6)^3 \\ =\frac{4}{3}\pi\cdot216 \\ =288\pi \end{gathered}[/tex]Answer: Option A
2.Make a table & Graph the function f(x) = 2)*х-1012y
We are given the function
f(x) = 2(1/2)^1
Firstly, let f(x) = y
Then, y = 2(1/2)^x
To find y, substitute the value of x into the function.
y = 2(1/2)^x
Find y, when x = -1
y = 2(1/2)^-1
y = 2 ( 1/ 1/2)
y = 2(2 x 1 / 1)
y = 2 x 2
y= 4
When x = -1 , y = 4
find y, when x = 0
y = 2(1/2)^0
In mathematics, anything raise to the power of zero is 1
Therefore, (1/2)^0 = 1
y = 2 x 1
y = 2
When x = 0 , y = 2
find y, when x = 1
y = 2(1/2)^1
y = 2 * 1/2
y = 2/2
y = 1
when x = 1, y= 1
find y, when x = 2
y = 2(1/2)^2
(1/2)^2 = (1/4)
y = 2(1/4)
y = 2x 1/4
y = 2/4
y = 1/2 or 0.5
When x = 2, y= 1/2 or 0.5
The new table becomes
x y
-1 4
0 2
1 1
2 1/2
POSSIBLThe midpoint of FG is M(1,0). One endpoint is F(8,-2).Find the coordinates of endpoint G.GO
The formula for determining the midpoint of a line is expressed as
(x1 + x2)/2 , (y1 + y2)/2
x1 and y1 represents the coordinates of the starting point of the line
x2 and y2 represents the coordinates of the end point of the line
The given line is FG. It means that the starting point is F and the end point is G. From the information given,
x1 = 8, y1 = - 2
x2 = ?, y2 = ?
For Midpoint coodinates, x = 1, y = 0
Therefore,
(8 + x2)
A sound receiving dish used at outdoor sporting events is constructed in the shape of a paraboloid, with its focus 5 inches from the vertex. Determine the exact width (in inches) of the dish if the depth is to be 2 feet.
First, lets remember that a paraboloid is just a parabola that was rotated around the Y axis. So lets find the equation from our parabola that is been rotated. We know that the focus is in the point (0,5), so we can find our equation:
[tex]y=\frac{x^2}{4\times5}\rightarrow y=\frac{x^2}{20}[/tex]Just to remember, a parabola that has focus in (0,P) has equation as:
[tex]y=\frac{x^2}{4\times p}[/tex]We can draw our parabola:
So we want to find the width knowing that the depth is 2 feet our 24 inches. That means that he wants to know the X that make the Y be 24, so lets find it:
[tex]y=\frac{x^2}{20}\rightarrow x^2=24\times20\rightarrow x=\pm\sqrt[]{480}\rightarrow x^{\prime}\cong21.908\text{ and }x\~\~^{}\cong-21.908[/tex]~(P ∨ (P ⊃ Q))
A.tautology
B.contradiction
C.contingent
D.None of the above
The statement ~(p v (p ^ q)) is classified as follows:
C. contingent
What are tautologies and contradictions?When a logic statement is always true, no matter the inputs, it is called a tautology. Otherwise, when a statement is always false, no matter the inputs, it is called a contradiction.
If the statement can be either true or false, depending on the boolean values of the inputs, the statement is called contingent.
The statement given in this problem is as follows:
~(p v (p ^ q))
From the precedence of operations, it is found that:
p ^ q can be either true or false, true if p = q = 1, false otherwise.p v (p ^ q) is false if p = q = 0 and true otherwise. ~(p v (p ^ q)) is the negation of the above statement, that is, true if p = q = 0 and true otherwise.Since the statement can be either true or false, depending on the boolean values of p and q, it is classified as contingent, and option c is correct.
Missing informationThis problem is incomplete and could not be found on any search engine, hence I will consider that it asks to classify the statement ~(p v (p ^ q)).
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Al gave correct answers to 11 of the 20 questions on the driving test. What percent of the questions did he get correct?
Given:
Al gave correct answers to 11 of the 20 questions on the driving test.
So, the percent of the correct answers =
[tex]\frac{11}{20}\cdot100=11\cdot5=55\%[/tex]so, the answer will be
the percent of the questions did he get correct = 55%
A cash register contains $20 bills and $100 bills with a total value of $1260. If there are 23 bills total, then how many of each does the register contain?
$20 bill answer
$100 bill answer
According to the solving Each register held eight $20 bills, thirteen $100 bills.
What is a linear equation?A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
What makes an equation linear?A line in the Euclidean plane is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from.
According to the given data:x=number of $20bills
y=number of $100 bills
20x+100y
=1460 20x+100(-x+21)
=1460 20x-100x+2100
=1460 -80x
=-640 x
=8
-8+21 =13
y=13
20x+y=21 --&g t;
y=-x+21
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Suppose that the value of a stock varies each day from $10.82 to $20.17 with a uniform distribution.Find the third quartile; 75% of all days the stock is below what value? (Enter your answer to thenearest cent.)
start by subtracting the maximum and the minimun vaue
[tex]\max -\min =9.35[/tex]now divide that into 4
[tex]\frac{9.35}{4}=2.3375[/tex]since is the third quartile mutipli that by 3
[tex]2.3375\cdot3=7.0125[/tex]round to 7.01
add that to the minimun value
10.82+7.01=17.83
Tonya is a real-estate agent with a commission rate of 7%. She wants to earn a commission of $12,900. What is the minimum amount of real estate she needs to sell? Round to the nearest
dollar.
well, she needs to sell $"x", which oddly enough is the 100%.
now, we also know that 7% of "x" is $12900, which is what Tonya takes home.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 12900& 7 \end{array} \implies \cfrac{x}{12900}~~=~~\cfrac{100}{7} \\\\\\ 7x=1290000\implies x=\cfrac{1290000}{7}\implies x\approx 184286[/tex]
Amortize Premium by Interest Method
Shunda Corporation wholesales parts to appliance manufacturers. On January 1, Year 1, Shunda Corporation issued $22,000,000 of five-year, 9% bonds at a market (effective) interest rate of 7%, receiving cash of $23,829,684. Interest is payable semiannually. Shunda Corporation’s fiscal year begins on January 1. The company uses the interest method.
a. Journalize the entries to record the following:
Question Content Area
1. Sale of the bonds. Round amounts to the nearest dollar. For a compound transaction, if an amount box does not require an entry, leave it blank.
blank
- Select -
- Select -
- Select -
- Select -
- Select -
- Select -
Question Content Area
2. First semiannual interest payment, including amortization of premium. Round to the nearest dollar. For a compound transaction, if an amount box does not require an entry, leave it blank.
blank
- Select -
- Select -
- Select -
- Select -
- Select -
- Select -
Question Content Area
3. Second semiannual interest payment, including amortization of premium. Round to the nearest dollar. For a compound transaction, if an amount box does not require an entry, leave it blank.
blank
- Select -
- Select -
- Select -
- Select -
- Select -
- Select -
Question Content Area
b. Determine the bond interest expense for the first year. Enter amounts as positive numbers. Round amounts to the nearest dollar.
Annual interest paid $
fill in the blank 6502c1ff4fd7045_1
Premium amortized
fill in the blank 6502c1ff4fd7045_2
Interest expense for first year $
fill in the blank 6502c1ff4fd7045_3
Question Content Area
c. Explain why the company was able to issue the bonds for $23,829,684 rather than for the face amount of $22,000,000.
The bonds sell for more than their face amount because the market rate of interest is
the contract rate of interest. Investors
willing to pay more for bonds that pay a higher rate of interest (contract rate) than the rate they could earn on similar bonds (market rate).
The journal entries for the bonds transactions of Shunda Corporation are as follows:
Journal Entries:1. Debit Cash $23,829,684
Credit Bonds Payable $22,000,000
Credit Bonds Premium $1,829,684
2. Debit Interest Expense $834,039
Debit Bonds Premium $155,961
Credit Cash $990,000
3. Debit Interest Expense $828,580
Debit Bonds Premium $161,420
Credit Cash $990,000
b. Bond Interest Expense for the first year is as follows:
Annual interest paid = $1,980,000
Premium amortized = $317,381
Interest Expense = $1,662,619
c. The bonds sell for more than their face amount because the market rate of interest is less than the contract interest rate. Investors are willing to pay more for bonds that pay a higher rate of interest (contract rate) than the rate they could earn on similar bonds (market rate).
Transaction Analysis:Face value of bonds = $22,000,000
Bonds Proceeds = $23,829,684
Bonds Premium = $1,829,684 ($23,829,684 - $22,000,000)
Coupon interest rate = 9%
Semi-annual interest payment = $990,000 ($22,000,000 x 9% x 1/2)
Effective market interest rate = 7%
1. Cash $23,829,684 Bonds Payable $22,000,000 Bonds Premium $1,829,684
2. Interest Expense $834,039 Bonds Premium $155,961 Cash $990,000
3. Interest Expense $828,580 Bonds Premium $161,420 Cash $990,000
1st Semiannual Interest Payment:Interest Payment at 4.5% $990,000
Interest Expense = $834,039 ($23,829,684 x 3.5%)
Amortized Premium = $155,961
Bond's carrying value = $23,673,723 ($23,829,684 - $155,961)
2nd Semiannual Interest Payment:Interest Payment at 4.5% $990,000
Interest Expense = $828,580 ($23,673,723 x 3.5%)
Amortized Premium = $161,420
Bond's carrying value = $23,512,303 ($23,673,723 - $161,420)
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You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 1050 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 5 units each, and you can spare at most 1,700 units of shelf space for the texts. If the used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, how many of each type of text should you purchase to maximize profit?
calculus text(s):
history text(s):
marketing text(s):
What is the maximum profit the program can make in a semester?
Using linear programming, the amounts of each book that you should purchase are given as follows:
Calculus: 850.History: 0.Marketing: 0.The maximum profit will be of $850.
How to maximize a function given it's constraints?To maximize the function, we have to find the numeric values at the intercepts of the most restrictive constraints, as the maximum value is the highest numeric value. This strategy is called linear programming.
In the context of this problem, the variables are given as follows:
Variable x: number of calculus books purchased.Variable y: number of history books purchased.Variable z: number of marketing books purchased.The used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, hence the profit function is defined as follows:
P(x,y,z) = 10x + 4y + 8z.
The constraint related to budget limitations, as an equality, is given by:
x + y + z = 1050.
The most restrictive constraint is from shelf-space limitations, and is given as follows:
2x + y + 5z = 1700.
Hence the intercepts are given as follows:
(850, 0, 0) as 2x = 1700 -> x = 850.(0, 1700, 0), as y = 1700.(0, 0, 340), as 5z = 1700 -> z = 340.The numeric value of the profit function at each of these intercepts is:
P(850,0,0) = 10(850) = 8500.P(0, 1700, 0) = 4(1700) = 6800.P(0, 0, 340) = 8(340) = 2720.Hence, due to the maximum numeric value, the maximum profit will be of $850, when 850 calculus books are purchased.
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The temperature of water in a lake decreases 12 degree in 3 hours. How much temperature does water decrease every hour on average? Represent the quotient as a rational number.
We have a rate of 12 degrees every 3 hours, then, to find the rate for every hour we just divide this rate by 3.
[tex]-\frac{12^o}{3h}=-\frac{4^o}{h}[/tex]We have a rate of decrease of 4 degrees/h.
