A) list roots and multiplicity.B) domain and range C) degree : 4 D) equation (show work by solving for a)
Answers
ANSWER :
A. (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain : (-∞, ∞)
C. Range : (-16, ∞)
D. Degree : 4
E. f(x) = (x + 3)(x + 1)(x - 1)(x - 3)
EXPLANATION :
From the problem, we have a graph in the illustration.
A. Roots are the points in which the graph intersects the x-axis.
Multiplicity means how many times the graph intersects at the specific point.
Roots :
The graph intersects at (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain and Range.
Domain is the set of x-values in the graph.
Range is the set of y-values in the graph.
From the graph,
Domain :
x values are all real numbers. (-∞, ∞)
Range :
y values are from y = -16 to the positive infinity. That will be (-16, ∞)
C. Degree : 4
D. The equation of a function with a degree of 4 is given by :
[tex]f(x)=a(x-b)(x-c)(x-d)(x-e)[/tex]where a = coefficient
b, c, d and e are the roots of the function.
Since we already solved for the roots, that will be :
b = -3, c = -1, d = 1 and e = 3
The equation will be :
[tex]f(x)=a(x+3)(x+1)(x-1)(x-3)[/tex]Plug in the given point (0, 9) then solve for the value of "a"
[tex]\begin{gathered} 9=a(0+3)(0+1)(0-1)(0-3) \\ 9=a(3)(1)(-1)(-3) \\ 9=9a \\ a=\frac{9}{9} \\ a=1 \end{gathered}[/tex]The equation will be :
[tex]f(x)=(x+3)(x+1)(x-1)(x-3)[/tex]Related Questions
12 is 58% of what number?
Also can you explain how to solve these problems?
Answers
Answer:
20.68976
Step-by-step explanation:
Convert the percentage into decimal :
58% = 0.58
0.58 × x = 12
Divide both sides by 0.58 :
x = 12÷0.58
x = 20.689655...
x = 20.68976
So the method to these types of question is to make the question into an equation by converting the percentage into a decimal, rearrange to make the unknown number the subject and solve .
Hope you understood and have a good day
Determine whether the pair of polygons is similar using properties of similar polygons. Explain your reasoning.
Answers
The polygons are similar
What is a polygon?
A polygon (/pln/) in geometry is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain (or polygonal circuit). A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides. The vertices (plural: vertex) or corners of a polygon are the spots where two edges meet. A solid polygon's interior is sometimes referred to as its body. A polygon having n sides is known as an n-gon. A simple polygon is one that does not cross itself. Mathematicians are frequently interested simply in the bounding polygonal chains of simple polygons, and they frequently define a polygon in this manner.
The sides ratio is same in both polygons i.e. 1:2
and all the angles of the two polygons are congruent
So, the polygons are similar
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Yaritza finds some nickels and pennies in her change purse. How many coins does she have if she has 140 nickels and 130 pennies? How many coins does she have if she has nn nickels and pp pennies?
Answers
As per given by the question,
There are given that 140 nickels and 130 pennies.
Now,
The number of nickels is 140 and number of pennies is 130.
So,
The total number of coin is:
[tex]140+130=270[/tex]Hence, 270 coins does she have if she has 140 nickels amd 130 pennies.
And,
The total coint that have n nickels and p pennies is:
[tex]n+p[/tex]The asnwer is:
[tex]\begin{gathered} (a)\text{ 270 coins} \\ (b)\text{ n+p coins} \end{gathered}[/tex]What are the six trigonometric ratios, and how are some of them related to each other(which are reciprocals of which)?
Answers
Consider the following right triangle:
In this triangle
x = adjacent side to the angle theta.
y = opposite side to the angle theta.
h= hypotenuse.
Now, by definition, we have the following trigonometric ratios:
[tex]\cos(\theta)=\frac{adjacent\text{ side to the angle }\theta}{hypotenuse}\text{ =}\frac{x}{h}[/tex][tex]\sin(\theta)=\frac{opposite\text{ side to the angle }\theta}{hypotenuse}=\frac{y}{h}[/tex][tex]tan(\theta)=\frac{opposite\text{ side to the angle }\theta}{adjacent\text{ side to the angle }\theta}=\text{ }\frac{y}{x}=\frac{y\text{ /h}}{x\text{ /h}}\text{ =}\frac{\sin(\theta)}{\cos(\theta)}[/tex]and according to the above trigonometric ratio, we get:
[tex]cotan(\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]On the other hand, we get the following reciprocals:
[tex]csc(\theta)=\frac{1}{\sin(\theta)}[/tex]and
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]we can conclude that the correct answer is:
Answer:The six trigonometric ratios:
[tex]\cos(\theta)=\frac{adjacent\text{ side to the angle }\theta}{hypotenuse}\text{ }[/tex][tex]\sin(\theta)=\frac{opposite\text{ side to the angle }\theta}{hypotenuse}[/tex][tex]tan(\theta)=\frac{opposite\text{ side to the angle }\theta}{adjacent\text{ side to the angle }\theta}=\text{ }\frac{\sin(\theta)}{\cos(\theta)}[/tex][tex]csc(\theta)=\frac{1}{\sin(\theta)}[/tex][tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex][tex]cotan(\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]Write the correct equation for the following statement.
The quotient of x and seven is twelve
Answers
To get quotient we divide
in this case we divide x by 7 to get the quotient 12 as A RESULT
[tex]x \div 7 = 12[/tex]
HOPE THIS HELPS.
I believe you start with 2.4 million has initial start value? Not sure cause it worded weirdly and English not very good
Answers
2,466,000
Here, we want to know what is to be used as the initial value
The general exponential equation should be in the form;
[tex]P=I(1+R)^n[/tex]where P is the population at a certain year
I is the initial population which is 2,466,000 in this case
R is the rate of increase
n is the number of years
a submarine is situated at 45 feet below sea level and sing 75 ft what is the new position of the submarine?
Answers
Given
a submarine is situated at 45 feet below sea level
the submarine sink 75 ft
so, the new position will be = 45 + 75 = 120 feet below
given:m<6=m<8b l l cprove:a l l b
Answers
1) From the data, we can see that
[tex]\angle6=\angle8[/tex]is given.
2) Next,
[tex]\angle6=\angle7[/tex]since they are alternate angles.
3) By substitution, these means that
[tex]\angle7=\angle8[/tex]4) Finally, a || b since
[tex]\angle7=\angle8[/tex]this is because, angle 7 and angle 8 are corresponding angles.
Corresponding angles are angles that are on the same corner at each intersection. For instance, 2 and 6
4 and 8, 1 and 5, 3 and 7
In our case, 7 and 8 are corresponding angles
Tamarisk Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company's current truck (not the least of which is that it runs). The new truck would cost $56,619. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $8,100. At the end of eight years, the company will sell the truck for an estimated $28,500. Traditionally, the company has used a general rule that it should not accept a proposal unless it has a payback period that is less than 50% of the asset's estimated useful life. Thomas Anderson, a new manager, has suggested that the company should not rely only on the payback approach but should also use the net present value method when evaluating new projects. The company's cost of capital is 8%.
Answers
The cash Payback period is 6.66 years and the Net present value of the proposed investment is $5,329 (to see the calculation please refer the attached image.)
Computation of Payback Period
Cash Payback Period = Cost of truck/Annual cost savings.
Given that-
Cost of truck = $56,619
Annual cost savings = $8,100
Putting values, we get-
Cash payback period = ($56,619/$8,100) cash payback period
cash payback period = 6.66 years.
To calculate the PVF at 8% below is the formula
P = (1/[tex](1+r)^{n}[/tex])
Where,
P = the Present Value Factor.
r = the interest rate
n = the number of periods over which payments are made.
To calculate the Present Value = PVF at 8% x Amount.
Hence, As the Net Present Value is positive, Tamarisk corporation should purchase the truck.
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1. What would the slope of a line that is parallel to the line in the graph be?
(4,3)
X
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line above, since a parallel line will have the same slope anyway
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{ -4 }{ -3 } \implies {\Large \begin{array}{llll} \cfrac{ 4 }{ 3 } \end{array}}[/tex]
What’s the correct answer answer asap for brainlist
Answers
Answer: A
Step-by-step explanation:
Jane spends $15 each time she travels the toll roads. She started the month with $240 in her toll road account. The amount, A (in dollars), that she has left in the account after r trips on the toll roads is given by the following function.
How much money does Jane have left in the account after 8 trips on the toll roads?
(b) How many trips on the toll roads can she take until her account is empty?
Answers
$120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.
What is Equation?
Two or more expressions with an equal sign is called equation.
Given that Jane spends $15 each time she travels the toll roads..
Jane started the month with $240 in her toll road account.
The amount, A (in dollars), that she has left in the account after r trips on the toll roads is given by the following function
A(r)=240-15r.
Now for 8 trips the amount she left is
A(8)=240-15(8)
=240-120
=120
So $120 money does Jane have left in the account after 8 trips on the toll roads.
$240/15
=16.
She has to make 16 trips to make her account empty.
Hence $120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.
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Enter the value of b when the expression 1/2x + b is equivalent to 1/4(2x+3)
Answers
Answer:
b = 3/4
Step-by-step explanation:
[tex]\frac{1}{2}x + b=\frac{1}{4} (2x+3)[/tex]
Distribute.
[tex]\frac{1}{2}x + b=\frac{1}{2} x+\frac{3}{4}[/tex]
Subtract 1/2x from both sides to isolate the b.
[tex]b=\frac{1}{2} x+\frac{3}{4}-\frac{1}{2}x[/tex]
1/2x and -1/2x cancel each other out.
[tex]b=\frac{3}{4}[/tex]
So b = 3/4
Mr. Shepard,The band teacher wanted to know if a certain type of Instruments are more appealing Who won grade level or another he conduct a survey and compiled the chart
Answers
So complete If I were to multiply 23 by 15, I would get 38
if one gender finds a certain sort of instrument more attractive than the other. In order to find out his pupils' choices, he organized a poll. The findings are shown in the table below. What percentage of girls preferred woodwind instruments? So girls who prefer woodwind instruments over boys would receive instruments? So, 30 2 19 would be the result. The same thing is said at the beginning of this one as well, but it asks for the number of ladies who prefer string instruments, which is 23 out of all the pupils that performed and preferred string instruments. So complete If I were to multiply 23 by 15, I would get 38.
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complete question:
'Mr Keen, a band teacher wanted to know if certain types of instruments are more appealing to one gender or the other. So he conducted a survey of his students preferences. The results are complied in the chart below: What is the ratio of the number of girls preferring woodwind instruments to the number of boys preferring woodwind instruments? * Instruments Boys Girls 15 23 Strings Woodwind 19 30 Brass 27 13 Percussion 32 25 Your answer P Mr Kccn; band tcacher wantea t0 know certain types 0i instumenlsare morc appealing [O onc gender or the other So he conducted & survey of his students preferences; Thc results are complied In Ihe chart below: What is the ratio of the number of girls preferring woodwind instruments t0 the number of boys preferring woodwind instruments? Inatuuments Roys he Strings Woodwlnd Brass Percusslon Your answer Mr Keen; band teacher wanted t0 know if certain types of instruments are more appcaling to ore gender or the other: So he conducted survey of his students preferences, The results are complied in the chart below: What is the rallo of the number of girls preferring string instrurents to the total number of students preferring strings Instruments?
A railroad crew can lay 7 miles of track each day. They need to lay 196 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function.
L (d) = 196 - 7d
(a). How many days will it take the crew to lay all the track?
(b) How many miles of track does the crew have left to lay after 19 days?
Answers
The number of miles of track does the crew have left to lay after 19 days is 63 miles.
The given equation is L (d) = 196 - 7d.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
a) Number of days will it take the crew to lay all the track = 196/7
= 28 days
b) Number of miles of track does the crew have left to lay after 19 days
L (d) = 196 - 7d
Put d=19 in the given equation
We get L=196 - 7(19)
= 196 - 133
= 63 miles
Therefore, the number of miles of track does the crew have left to lay after 19 days is 63 miles.
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A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin if its radius is r=5.4 ft, the height of the cylindrical portion is h=7.7 ft, and the overall height is H=16.7 ft?
Answers
The Volume of a Compound Solid
The figure consists of a cylinder and a cone, both with the same radius of r=5.4 ft. The height of the cylinder is h=7.7 ft and the total height (of cone and cylinder) is H = 16.7 ft. This means the height of the cone is hc = 16.7 - 7.7 = 9 ft.
The volume of a cylinder of height h and radius r is:
[tex]V_{\text{cyl}}=\pi\cdot r^2\cdot h[/tex]The volume of a cone of height hc and radius r is:
[tex]V_{\text{cone}}=\frac{\pi\cdot r^2\cdot h_c}{3}[/tex]Calculate the volume of the cylinder:
[tex]\begin{gathered} V_{\text{cyl}}=\pi\cdot(5.4ft)^2\cdot7.7ft \\ V_{\text{cyl}}=705.388ft^3 \end{gathered}[/tex]Calculate the volume of the cone:
[tex]V_{\text{cone}}=\frac{\pi\cdot(5.4ft)^2\cdot9}{3}=274.827ft^3[/tex]Now we add both volumes:
V = 705.388 + 274.827 = 980.215 cubic feet
Rounding to the nearest tenth:
V = 980.2 cubic feet
a realtor make 6% commission on each sale how much commission will the realtor earn for selling a $140,000 home
Answers
Answer:
1&3239282882819&;&39303847
Answer:
$8,400
Step-by-step explanation:
6%x140,000
Suppose Rachel and Nadia buy a house and have to take out a loan for $183500. If they qualify for an APR of 3.75% and choose a 30 year mortgage, we can find their monthly payment by using the PMT formula. If Rachel and Nadia decide to pay $1500 per month, we can use goal seek to see how many years it will take to pay off the loan. Use the PMT function and goal seek (as needed) to answer the following questions about Rachel and Nadia's mortgage. a. What is their monthly payment on the 30 year loan? $ 15 year loan, what will the new monthly payment be?
Answers
We have that the PMT formula is given by:
[tex]\text{PMT}=p(\frac{\frac{r}{n}}{1-(1+\frac{r}{n})^{-ny}})[/tex]Where p is the initial principal (Loan ammount), r is the interest rate period, n is the total number of payments or periods, y is the number of years, PMT is the monthly payment.
Now, replacing the data in the formula, we will get:
*The payment will be due for 30 years, that is 12 months each year [That is our n] and y will be 30, r is 0.0375.
p will be $183500, that is:
[tex]\text{PMT}=(183500)(\frac{\frac{0.0375}{12}}{1-(1\pm\frac{0.0375}{12})^{-(12)(30)}})[/tex]Then, we will have that the monthly payment for the 30 years, should be:
[tex]\text{PMT}=849.8171105[/tex]If she wishes to pay $1500 each mothn, we then replace in the formula:
[tex]1500=(183500)(\frac{(\frac{0.0375}{12})}{1-(1+\frac{0.0375}{12})^{-12y}}[/tex]Now, solving for Y, we will have:
[tex]-12y=\frac{\ln(\frac{593}{960})}{\ln(\frac{321}{320})}\Rightarrow y\approx12.86643229[/tex]From this, we have that if they pay a monthly morgage of 1500, they would take 13 years to pay the total cost.
If they wanted to pay the morgage in 15 years, then we replace in the formula as follows:
[tex]\text{PMT}=(183500)(\frac{(\frac{0.0375}{12})}{1-(1\pm\frac{0.03755}{12})^{-12(15)}})[/tex]That is:
[tex]\text{PMT=1334.453182}\Rightarrow PMT\approx1334.45[/tex]They would have to pay $1334.45 each month in order to pay the morgage in 15 years.
The measures of the angles of a triangle are 2x, 3x, and 4x. What is the degree measure of the largest angle of the triangle?o 20°o 60°o 80°o 100°
Answers
ANSWER
[tex]80\degree[/tex]EXPLANATION
We want to find the measure of the largest angle of the triangle.
The sum of angles in a triangle is 180 degrees. This means that:
[tex]2x+3x+4x=180[/tex]Simplify the equation and solve for x:
[tex]\begin{gathered} 2x+3x+4x=180 \\ 9x=180 \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]The largest angle is 4x. Therefore, the measure of the largest angle is:
[tex]\begin{gathered} 4\cdot20 \\ 80\degree \end{gathered}[/tex]-5x + 3 > (-7x) - 12
Answers
Solve the inequality
-5x + 3 > (-7x) - 12
We want to move the variables to the left side and the numbers to the right side. The (-7x) can be eliminated from the right side by adding 7x on both sides.
Add 7x to both sides:
-5x + 3 + 7x > -12
We need to move the 3 from the left to the right side. So we subtract 3
Subtract 3 to both sides:
-5x + 7x > -12 - 3
Joining like terms:
2x > -15
Solving:
x > -15/2
The solution is every real number greater than -15/2
In interval notation, it can be written as:
[tex]\mleft(-15/2,+\infty\mright)[/tex]The left parentheses are used because the endpoint is not included in the solution
If the endpoint was included, we'd use a bracket [
Ana has two plants. From Monday to Tuesday, plant A grew 5 cm more than plant B. If the sum of the length of the two plants on Tuesday is 41 cm, how long is each plant on Tuesday?
Answers
Write a system of equations using A and B as the variables
The first equation is the sum of the lengths of the plants
[tex]A+B=41[/tex]The second equation is the relation of growth that plant A grew 5cm more than plant B
[tex]A=B+5[/tex]Insert the second equation into the first one to solve for B
[tex]\begin{gathered} A+B=41 \\ (B+5)+B=41 \end{gathered}[/tex]Solve the equation for B
[tex]\begin{gathered} 2B+5=41 \\ 2B=41-5 \\ 2B=36 \\ B=\frac{36}{2} \\ B=18 \end{gathered}[/tex]Use the value of B in the second equation to find the value of A
[tex]\begin{gathered} A=B+5 \\ A=18+5 \\ A=23 \end{gathered}[/tex]Plant A is 23 cm long on Tuesday and plant B is 18 cm long on Tuesday.
Final Grade An instructor gives four 1-hour exams and one final exam, which counts as three 1-hour exams. Find a student's grade if she received 66, 81, 99 and 86 on the 1-hour exams and 85 on the final exam. Round your answer to one decimal place if necessary.
Answers
Answer:
83.9
Explanation:
The final exam counts as three 1-hour exams. Therefore, the student's scores written in terms of 1-hour exams will be:
• One-Hour Exam: 66, 81, 99 and 86
,• Final Exam: (85 x 3)
We take the average to find the student's grade:
[tex]\begin{gathered} \text{Final Grade}=\frac{66(1)+81(1)+99(1)+86(1)+85(3)}{1+1+1+1+3} \\ =\frac{332+255}{7} \\ =\frac{587}{7} \\ =83.857 \\ \approx83.9 \end{gathered}[/tex]The student's grade will be 83.9 correct to one decimal place.
which of the following graphs match the indicated rotation? Point “R” Rotated 90 degrees about the origin.
Answers
The rule for a 90° rotation about the origin is:
[tex](x,y)\rightarrow(-y,x)[/tex]then, if we select one of the points of the figure, A(-2,1), and apply the transformation,
[tex]A(-2,1)\rightarrow A^{\prime}(-1,-2)[/tex]do the same for the other three points,
[tex]\begin{gathered} B(3,3)\rightarrow B^{\prime}(-3,3) \\ C(4,0)\rightarrow C^{\prime}(0,4) \end{gathered}[/tex]select the graph with all three points.
Answer:
The correct answer is option 4.
Which of the following is the correct mathematical expression
for:
The sum of x and 5
Answers
Answer:
Yes
Step-by-step explanation:
Yes
Given points J(2,5), A(5,4), and R(4,2), graph AJAR and its reflection image across the given line.Ry-axis
Answers
after a reflection across the x-axis:
[tex]\begin{gathered} J\to(x,-y)\to J^{\prime}=(2,-5) \\ A\to(x,-y)\to A^{\prime}=(5,-4) \\ R\to(x,-y)\to R^{\prime}=(4,-2) \end{gathered}[/tex]which function can be used to find y, total amount saved in, x weeks
Answers
Input data
Points
A = (0, 50)
B = (30,110)
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
[tex]\begin{gathered} m=\frac{110-50}{30-0} \\ m=\frac{60}{30} \\ m=2 \end{gathered}[/tex]Now, what about b, the y-intercept?
[tex]\begin{gathered} b=y-mx \\ b=50-2\cdot0 \\ b=50 \end{gathered}[/tex]The equation of the line that passes through the points
[tex]y=2x+50[/tex]find the surface area of a square pyramid with side length 3km and slant height 5km
Answers
Explanation
the surface area of a square pyramid is given by:
[tex]\begin{gathered} sa=A+\frac{1}{2}ps \\ \text{where A is the area of the base} \\ p\text{ is the perimeter of the base} \\ s\text{ is the }slant\text{ heigth} \end{gathered}[/tex]so
Step 1
area of the base
the baseis a square, so the area is
[tex]\begin{gathered} Area=side^{^2} \\ Area_{base}=3km\cdot\text{ 3}km \\ Area_{base}=\text{ 9(}km^2) \end{gathered}[/tex]Step 2
perimeter of the base
the perimeter of a square is given by:
[tex]\begin{gathered} \text{Perimeter}=\text{ 4}\cdot side \\ sp \\ \text{Perimeter}=\text{ 4}\cdot3km\text{ =12 }km \\ \text{Perimeter}=12km \end{gathered}[/tex]Step 3
finally, let
[tex]\text{slant heigth=5}km[/tex]now, replace in the formula
[tex]\begin{gathered} sa=A+\frac{1}{2}ps \\ sa=9(km^2)+\frac{1}{2}(12km)(5km) \\ sa=9(km^2)+30(km^2) \\ sa=39(km^2) \end{gathered}[/tex]therefore, the answer is
[tex]\text{ 36 }km^2[/tex]I hope this helps you
Find slope and y-intercept12x = 2y+1
Answers
12x = 2y+1
First, express in slope-intercept form
y= mx +b
Where:
m = slope
b= y -intercept
So, we have to solve for y:
12x=2y+1
-2y= -12x+1
y= (-12x+1)/-2
y = 6x-1/2
So:
Slope = 6
Y-intercept = -1/2 or -0.5 (decimal form)
Need help please and also explain it
15 points if help
Answers
Answer:
60
Explanation:
1/2 of 80 is 40. 1/4 of 80 is 20. Add them and you get 60.
At the ice cream factory you manage you have a rush order for 1200 gallons of wainut fudge ice cream. One machine can produce 100 gallons of ice cream every 80 minutes. If you start production on that machine at 6:00 am, about what time will be production run end end?
Answers
Given that the machine takes 80 minutes to produce 100 gallons of ice cream, so the rate of production (r) is given by,
[tex]\begin{gathered} r=\frac{100}{80} \\ r=1.25\text{ gallons/min} \end{gathered}[/tex]So the time required to produce 1200 gallons of the ice cream is calculated as,
[tex]\begin{gathered} t=\frac{1200}{r} \\ t=\frac{1200}{1.25} \\ t=960\text{ min} \end{gathered}[/tex]Thus, 960 minutes are required for producing 1200 gallons of ice cream.
Converting into hours,
[tex]\begin{gathered} 960\text{ minutes=}\frac{960}{60}\text{ hours} \\ 960\text{ minutes=}16\text{ hours} \end{gathered}[/tex]The time 16 hours after 6:00 am will be 22:00 which corresponds to 10:00 pm.
Therefore, the product run will end at 10:00 pm.