Answer:
55 boxes
Step-by-step explanation:
Using Linear Equations:The linear equation provided is: [tex]y=78x+8840[/tex] and since we want to check if we can carry 60 boxes, we just need to weight by substituting in "60" as x and then comparing that to the limit of 13200 pounds.
[tex]y = 78(60)+8840\\\\y=4680+8840\\\\y=13,520[/tex]
This of course is over the limit of 13200 pounds but we can set up an inequality and solve for "x"
[tex]78x+8840 < 13200[/tex]
From here we subtract 8840 from both sides
[tex]78x < 4,360[/tex]
Now divide both sides by 78
[tex]x < 55.89[/tex]
now of course we can't have 55.89 boxes, so we want to round down as we can't have 56 boxes as that would go over the limit, but we can have 55 boxes.
the two equal sides of an isosceles triangle are given as (x 2) cm and the third side is (x 6) cm. if the perimeter of the triangle is 385 cm, find x.
If the two sides of isosceles triangle are (x+2) cm and third side is (x+6) cm. if perimeter is 385 cm, then the value of x is 125 .
We know that the Perimeter of the triangle is equal to the sum of the lengths of all its sides.
the two sides of isosceles triangle are = (x+2) cm ;
the length of third side of triangle is = (x+6) cm ;
So , we have:
⇒ x + 2 + x + 2 + x + 6 = 385
Simplifying and solving for x:
⇒ 3x + 10 = 385 ;
⇒ 3x = 385 - 10 ;
⇒ 3x = 375 ;
⇒ x = 375/3 = 125
Therefore , the value of x for the isosceles triangle is 125 .
The given question is incomplete , the complete question is
The two equal sides of an isosceles triangle are given as (x+2) cm and the third side is (x+6) cm. if the perimeter of the triangle is 385cm, find the value of x.
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12. Town A has 4.563 residents.
Town A has 127 more than
4 times the number of residents
of Town B. How many residents
does Town B have?
Answer:
1109
Step-by-step explanation:
4563 = 4b + 127 Subtract 127 from both sides
4436 = 4b Divide both sides by 4
1109 = b
explains in detailed steps how the algorithm implemented in the identified procedure works. your explanation must be detailed enough for someone else to recreate it.
The detailed steps how the algorithm implemented in the identified procedure works is:
Set the index of the list's first element in the list index variable, i. (0).Continue iterating while increasing I by one with each iteration as long as it is less than or equal to the index of the last member in the list.Return true right away if the element we're looking for equates to the ith element in the list.Return false if the iteration fails to discover a match.i. Outlines the two instances of the method that were mentioned in written response 3c. Each call must take a separate argument(s) that direct the algorithm to run a different section of code.
List as first call Includes ("Alice," "Maya," "Will," "Alice")Call two: list Includes ("Alice," "Maya," "Will," "Akram")ii. Specifies the condition(s) each call to the process is testing.
Conditions put to the test by the initial callchecks to see if the list contains an element with the value "Alice."The second call examines the following condition(s):checks to see if the list contains an element with the value "Akram."iii. Shows the outcome of each call.
The first call's outcome was true.The second call's outcome was false.Learn more about Algorithm:
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Iced tea 3/16, Fruit juice, 4/16 Water 7/16 Soda 2/16. What combination of beverages makes up 3/4 of the student votes?
Answer: Iced tea, Water, and Soda, or 12/16
Step-by-step explanation: 3/4 of 16/16 is 12/16, and 7/16+3/16+2/16=12/16
Fabiola's special seasoning mix has two ingredients. The recipe uses 5 parts thyme
and 3 parts parsley. If she is making 40 tablespoons of the mix, how many
tablespoons of parsley does she need?
A 3 tbsp
C 9 tbsp
B 5 tbsp
D 15 tbsp
D) 15 tablespoons of parsley she needs.
How to find the number of tablespoons?Let's call the number of tablespoons of parsley she needs "x". We know the recipe uses 5 parts thyme to 3 parts parsley, so the total number of parts is 5 + 3 = 8.
Since she's making 40 tablespoons of the mix, each part is equal to 40 / 8 = 5 tablespoons.
So x, the number of tablespoons of parsley, is equal to 3 parts * 5 tablespoons/part = 15 tablespoons.
The answer is D) 15 tablespoons of parsley she needs.
Therefore, we can say she needs 15 tablespoons of parsley.
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Pls help and do it as fast as you can
Answer:
what can i do please send me a question?
The third option from the top is correct
use the spinner to identify the probability to the nearest hundredth of the pointer landing on a non-shaded area. 0.66 0.26 0.34 0.60
Option A is the correct answer. The probability of the nearest hundredth of the pointer landing on a non-shaded area is 0.66.
An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle. It contains a total of 360° degrees all the way around the center.
To know the Probability of the non-shaded area first we have to add the shaded area.
The sum of the shaded angles 48°+45°+122°+52° =145°.
As we know that the total angle of a circle=360°.
Now divide the sum of the shaded angles by the total angle of the circle.
i.e=145°/360°
non-shaded area=0.66
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3 4/5 + 5 3/4= PLEASEEEEE
Find the radius of a pencil with a volume of 110 π mm³, a cone height of 3mm, and a cylinder height of 10 mm.
The radius of the pencil is 3.32mm
How to determine the radius of the pencilThe formula for determining the volume of a cylinder is expressed as;
V = πr²h
Given that the parameters are;
V is the volume of a cylinderπ takes the value 3. 14 or 22/7r is the radius of the cylinderh is the height of the cylinderFrom the information given, we have that;
The volume of the cylinder = 110 π mm³
The height of the cylinder = 10mm
Now, substitute the values, we get
110π = πr² × 10
Multiply the values
110π = 10πr²
Divide both sides by the coefficient of r², we get;
r² = 110π/10
r² = 11
Find the square root of both sides
r = 3. 32mm
Hence, the value is 3.32mm
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in triangle abc, m is the midpoint of ab, n is the midpoint of ac, and g is the intersection of bn and cm. the area of triangle gmn is 6. find the area of triangle gbc.
The area of the triangle GBC for the given condition of midpoint with a given area of ΔGMN = 6 equals 24.
In triangle ABC,
M is the midpoint of AB , N is the midpoint of AC
⇒ MN is parallel to BC
G is the intersection of BN and CM.
⇒ G is the centroid.
Centroid divides the line segment BN and CM in the ratio
BG : GN = 2 : 1
CG : GM = 2 : 1
In ΔGMN and ΔGBC ,
MN || BC , BN and CM are transversal.
∠NMG ≅∠BCG ( alternate angles)
∠MNG ≅ ∠CBG ( alternate angles)
∠MGN ≅∠BGC ( vertically opposite angles )
By AA corollary,
ΔGMN is similar to ΔGBC
BG : GN = CG : GM
Area of triangle GMN = 6
Area of ΔGBC / Area of ΔGMN = Square of the sides
⇒ Area of ΔGBC / 6 = ( 2 / 1 )²
⇒ Area of ΔGBC = 4 ( 6)
⇒ Area of ΔGBC = 24
Therefore, the area of the triangle GBC is equal to 24.
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I need full working pleaseee, I'll rate it brainliest
On integrating the function ∫4/(2x-1) dx, the value is obtained as 2 ln (2x + 1) + C.
What is Integration?
The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.
The integral is given as - ∫4/(2x-1) dx
Substitute u = (2x - 1) → du/dx = 2 → dx = 1/2 du -
⇒ 2 ∫ 1/u du
The standard integral is -
⇒ ln (u)
Plug in solved integrals -
⇒ 2 ∫ 1/u du
⇒ 2 ln (u)
Undo the substitution u = (2x - 1) -
⇒ 2 ln (2x + 1)
Apply the absolute value function to arguments of logarithm functions in order to extend the antiderivative's domain -
⇒ 2 ln (2x + 1) + C
Therefore, the value is obtained as 2 ln (2x + 1) + C.
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-3(t+6)=0 Need it for my homework
Answer: t= -6
Step-by-step explanation:
-3(t+6)=0
-3t+-18=0
-3t=18
-t=6
t= -6
It is only appropriate and possible to calculate the variance and standard deviation as measures of variability for variables measured using a(n) scale of measurement. O ordinal O ratio O interval or ratio O ordinal or nominal
Variance and standard deviation are measures of variability that are appropriate and possible to calculate for variables measured on an interval or ratio scale of measurement.
Interval scales have a true zero point, meaning that a difference of zero on the scale represents a lack of the characteristic being measured (e.g. temperature measured in degrees Celsius). Ratio scales are similar to interval scales, but also have a meaningful zero point, meaning that a value of zero on the scale represents a complete absence of the characteristic being measured (e.g. height measured in meters).
Variance and standard deviation can be calculated for interval and ratio variables because these scales provide meaningful differences and ratios between values. The calculation of variance involves finding the average squared difference between each value and the mean of the values, while standard deviation is the square root of the variance. Both variance and standard deviation provide information about how spread out the values of a variable are and are useful in statistical analysis.
On the other hand, nominal and ordinal scales only provide categories or rank order for values, without any meaningful differences or ratios between values. As such, it is not appropriate or possible to calculate variance or standard deviation for variables measured on nominal or ordinal scales.
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The length of a rectangle is three times linger that the width. The perimeter of the rectangle is 40 inch. What is the length of the rectangle in inches
Answer:
Step-by-step explanation:
L=3W
P=2L+2W
40= 2 (3W)+2W
40=6W+2W
8W=40
W=40/8
W=5 in
L=15 in (3W= 3*5=15)
Can anyonee help me with this question
Answer:
5
Step-by-step explanation:
The first says 4 and 4
They added 4 to the previous cumulative, which was nothing and thru got the cumulative of 4+0=4
The second says 10 and 14
Same thing. Adding 10 to the previous cumulative, which was 4, you get 4+10=14
Let's follow the rules for this next one
We have ? and 19
Adding ? to the previous cumulative, which was 14, you get 14+?=19
Making ? = 5 because that what 19-14 is
Q. 5. A newspaper boy buys magazines for Rs.13 each and sells them for Rs.18 each. He cannot return the unsold magazine. The past record of sales is as follows:. Sales Prob. 23 .05 24 .10 25 .15 26 .30 27 .20 28 .10 i) Prepare the opportunity loss table ii) Select the optimal act using expected opportunity loss criterion. iii) Find EVPI 29 .05 30 .05
Thus, 25 newspapers are required to make the most profit.
How to find the calculation?Profit is the amount of money you have after covering business expenses.
Gross, operational, and net profits are the three basic categories of profit.
Profit potential, p = S p C + C b
S p = Selling price
C = Unit cost of purchase
C b Goodwill lost per unit due to backorders or shortages
p ′ = 12 − 8 + 1.5
= ₹ 5.5
l = C - C b + C h, where C is the loss per unit.
A = Scrap value/unit
holding cost/unit = C
l = 8 − 2 + 0
l = ₹ 6
p ( S − 1 ) ≤ p /p + l ≤ p ( s )
At this point, p / p + l = 5.5 / 5.5 + 6 = 0.4783 = 47.83 %
Thus, 25 newspapers are required to make the most profit.
The Complete Question.
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Which of the following is NOT divisible by 8?
A. 1,406
B. 1,488
C. 3,608
D, 5,016
Answer: A
Step-by-step explanation:
How many inches are in 71.12 cm, show your work!
In 71.12 centimeters, there are 28 inches.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
We have a measurement in centimeters,
= 71.12
And we know 1 inch = 2.54 centimeters
So,
In inches, the mesurement = 71.12/2.54
= 28 inches.
Therefore, the required result is 28 inches.
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mary is 5 feet tall and her shadow is 12 feet long flagpole she is standing next to cast a shadow 42 feet
Mary is 5 feet tall and her shadow is 12 feet long flagpole. She is standing next to cast a shadow 42 feet. The height of the flag pole is 17.5 feet.
Mary is 5 feet tall and her shadow is 12 feet long flagpole.
She is standing next to cast a shadow 42 feet.
ΔABC ≅ ΔADE
Using the Similarity Theorem
BC/ED = AC/AD
From the diagram the value of BC = x, ED = 5 feet, AC = 42 feet and AD = 12 feet
Now putting the value
x/5 = 42/12
Multiply by 5 on both side, we get
x = 210/12
x = 17.5
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The complete question is:
Mary is 5 feet tall and her shadow is 12 feet long flagpole. She is standing next to cast a shadow 42 feet. The height of the flag pole is.
What’s the answer to 41
The probability of earning a total of exactly 10 points in 2 turns is 1/8.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:
(4, 6) or (6, 4)
The probability of getting a 4 in first try and 6 in second try is:
(4, 6) = 1/4 * 1/4 = 1/16
The probability of getting a 6 in first try and 4 in second try is:
(6, 4) = 1.4 * 1/4 = 1/16
The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:
(4, 6) or (6, 4) = 1/16 + 1/ 16 = 2/16 = 1/8
Hence, the probability of earning a total of exactly 10 points in 2 turns is 1/8.
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A company charges a 5 flat fee plus 3 per window to wash windows. Might someone have to pay exactly 87 to have their windows washed explain
Someone can't pay exactly 87 to have their windows washed.
How to find the exact amount someone have to pay for the company services?A company charges a 5 flat fee plus 3 per window to wash windows. Therefore, let's find if someone can pay exactly 87 units to have there window washed.
Hence, using equation,
y = 5 + 3x
where
x = number of windows washedy = total costUsing the equation, let's find if someone can use exactly 87 units for the service.
87 = 5 + 3x
87 - 5 = 3x
82 = 3x
divide both sides by 3
x = 82 / 3
x = 27.33
Therefore, someone can't use exactly 87 units because the number of windows washed is in decimal.
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the 1st, 4th and 8th terms of an arithmetic sequence, with common difference d, d is not equal to 0, are the first three terms of a geometric sequence, with common ratio r. given that the 1st term of both sequences is 9 find the values of d and r.
The value of common difference, d is equals to the one. The value of common ratio, r is equals to the 4/3.
We have, an arithmetic sequence and second is geometric sequences. The common difference between the two consecutive terms of AP sequence is "d" and d ≠ 0 and the common ratio between two consecutive terms of geometric sequence is "r". Let the AP sequence is represented by aₙ and G.P sequence is represented by Tₙ. First term of both sequences = 9 , i.e., a₁ = a = T₁ = 9
The nth term of A.P is written as
aₙ = a + (n - 1)d so, a₄ = a + 3d and a₈ = a + 7d
The nth term of G.P is , Tₙ = ar⁽ⁿ⁻¹⁾
so, T₂ = ar , T₃ = ar²
Now, a₄ = T₂ => ar = a + 3d
=> 9r = 9 + 3d --(1)
a₈ = T₃ => ar² = a + 7d
=> 9r² = 9 + 7d --(2)
from(1) and (2) , 3(r - 1) = d , 9r² = 9 + 7(r -1)3
=> 9r² = 9 + 21r - 21
=> 9r² = 21r - 12
=> 9r² - 21r + 12 = 0
=> r = 1, 4/3
then, plugging the value of r in equation (1),
d = 3( r - 1)
=> d = 3( 0) when r = 1
=> d = 0, but it is not possible as d≠0
and d = 3( 4/3 - 1) = 1 when r = 4/3
So, required values of d and r are 1 and 4/3.
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The radius of a circle is multiplied by 1/4. Which of the following describes the effect of this change on the area? The area Is multiplied by 1/8
The area Is multiplied by 1/16
The area Is multiplied by 4
The area Is multiplied by 1/4
If the radius of a circle is multiplied by 1/4, then its area is multiplied by 1/16.
The formula for the area of a circle is given by:
A = πr²
Where:
r = the radius of the circle.
Notice that the area is directly proportional to the square of the radius, or:
A ∝ r²
Let:
r₁ = initial radius of the circle
r₂ = final radius of the circle
A₁ = initial ara of the circle
A₂ = final area of the circle
It is mentioned that: r₂ = 1/4 r₁
A ∝ r²
A₂/A₁ = (r₂/r₁ )²
A₂/A₁ = (1/4 )²
A₂/A₁ = 1/16
Hence, the area is multiplied by 1/16.
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An agricultural engineer selected a random sample of 30 farms in the United States to construct a 95 percent confidence interval for the mean size, in acres, of farms in the United States. The resulting interval was (367, 558). Which of the following is an appropriate interpretation of the 95 percent confidence level?(A) Approximately 95% of the farm sizes in the sample are between 367 acres and 558 acres.(B) Approximately 95% of all farm sizes in the United States are between 367 acres and 558 acres.(C) Approximately 95% of all random samples of size 30 from the population will have a mean farm size between 367 acres and 558 acres.(D) Approximately 95% of all random samples of size 30 from the population will produce intervals that contain the mean size of farms in the United States.(E) Approximately 95% of all random samples of size 30 from the population will produce intervals that contain the sample mean.
Answer:
Step-by-step explanation:
The correct interpretation of the 95% confidence level is (D) Approximately 95% of all random samples of size 30 from the population will produce intervals that contain the mean size of farms in the United States.
In other words, if we repeatedly take random samples of size 30 from the population of farm sizes in the United States and construct 95% confidence intervals for the mean size in each sample, approximately 95% of those intervals will contain the true mean size of farms in the United States. The interval (367, 558) is just one of those intervals, and it is not a statement about the farm sizes in the sample or the farm sizes in the entire population.
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For the year ending April 30, Urology Medical Services Co. mistakenly omitted adjusting entries for (1) $1,400 of supplies that were used, (2) unearned revenue of $6,600 that was earned, and (3) insurance of $9,000 that expired. Indicate the combined effect of the errors on (a) revenues, (b) expenses, and (c) net income for the year ended April 30.
(a). Revenues = $6,600.
(b). Expenses = $10400
(c). Net income = $3800
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
For the year ending April 30,
Urology Medical Services Co. mistakenly omitted to adjust entries for (1) $1,400 of supplies that were used,
(2) unearned revenue of $6,600 that was earned,
and (3) insurance of $9,000 that expired.
(a). Revenues = $6,600.
(b). Expenses = ($1,400 + $9,000).
= $10400
(c). Net income =
($10,400 – $6,600).
= $3800
Therefore, all the required values are given above.
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Show that a system consisting of exactly one linear equation can have no solution, one solution, or infinitely many solutions. Give examples.
The system does not have any solution 0=2, The one solution exactly has one solution is, [tex]x=2[/tex] and the infinity many solutions is, [tex]y=2-x\end{aligned}$$[/tex].
The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1, then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
A system consisting of exactly one equation can have no solution. for example.
[tex]2 x[/tex][tex]=\frac{1}{2}(4 x+2)+1[/tex]
on we solve this, we get,
[tex]$$\begin{aligned}& 2 x=\frac{1}{2}(4 x+2)+1 \\\Rightarrow & 2 x=2 x+1+1 \\\Rightarrow & 2 x-2 x=2 \\\Rightarrow & 0=2\end{aligned}$$[/tex]
which is not true.
hence the system does not have any solution.
One Solution: -
Consider the system.
[tex]$$3x+3=9$$[/tex]
On sowing we get,
[tex]$$\begin{aligned}& 3 x+3-3=9-3 \\& \Rightarrow 3 x=6 \\& \Rightarrow \frac{3 x}{3}=\frac{6}{3} \\& \Rightarrow x=2\end{aligned}$$[/tex]
which has exactly one solution.
infinity many solutions: -
Consider the system of two variables.
[tex]$$2x+2 y=4$$[/tex]
On solving we get,
[tex]$$\begin{aligned}& 2 x+2 y=4 \\\Rightarrow & 2 x+2 y-2 x=4-2 x \\\Rightarrow & 2 y=4-2 x \\\Rightarrow & \frac{2 y}{2}=\frac{4-2 x}{2} \\\Rightarrow & y=2-x\end{aligned}$$[/tex]
Now, we can choose any value of [tex]$x$[/tex] and we will get the corresponding value of [tex]$y$[/tex]. So, there exists infinitely many solutions to the system.
Therefore, the system does not have any solution is 0=2, The one solution exactly has one solution is [tex]x=2[/tex] and the infinity many solutions is [tex]y=2-x\end{aligned}$$[/tex].
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Michaela and Aleah play on the same basketball team. In one game Michaela scored one-fifth of the team’s points and Aleah scored one-tenth's of the team’s points. Together the scored a total of 42 points. How many points did the team score? Solve algebraically
THESE ARE 2 DIFFERENT Q'S
In still water Derek can paddle his canoe at 6.5 km/h. On a river the canoe travels faster downstream than upstream because of the current. In the morning Derek travels upstream and takes 5 hours and then in the afternoon Derek travels downstream the same distance and takes 2 hours. What is the speed of the current? Answer to the nearest tenth. Solve algebraically.
1) The number of points that they scored is;
Michaela scored; 28 points
Aleah scored; 14 points.
2) The speed of the current is; 2.79 km/ hr
How to solve Algebra Word Problems?1) Let s represent the team score and as such we have;
Michaela scored s/5 (one fifth of the team's points)
Aleah scored s/10 (one tenth of the team's points)
These total scores is 42. Thus;
s/5 + s/10 = 42
Multiply through by 10 to get;
2s + s = 420
3s = 420
s = 420/3
s = 140
The team scored 140 points.
Thus;
Michaela scored;
140/5 = 28 points
Aleah scored;
140/10 = 14 points.
2) Let the speed of current be x km/ hr
Thus;
Upstream speed = ( 6.5 - x) km/ hr
Downstream speed = ( 6.5 + x) km/ hr
Distance = Speed * Time
Thus;
5(6.5 - x) = 2(6.5 + x)
32.5 - 5x = 13 + 2x
7x = 19.5
x = 2.79 km/ hr
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Assume that you just won $35 million in the Florida lottery, and hence the state will pay you 20 annual payments of $1.75 million each beginning immediately. If the similar risk to the lottery earnings (e.g., the rate on 20-year U.S. Treasury bonds) is 6 percent, what is the present value of your winnings? (Note: provide answer in full dollars/cents form, e.g., $123.45)
The present value of your winnings is $20.07 million.
What is Present Value?Present value is the value right now of some amount of money in the future.
For example, if you are promised $110 in one year, the present value is the current value of that $110 today.
Given:
The present value of an annuity is determined by:
PV = P [ 1- [tex](1+ r)^{-n[/tex] / r]
With annual payments (P) of $1.75 million, for a period (n) of 20 years at a discount rate (r) of 6 percent, the present value is:
PV = 1.75 [ 1- [tex](1+ 0.06)^{-20[/tex] / 0.06]
PV = 1.75 [ 1- 0.31180472688 / 0.06]
PV = 1.75 x 11.4699
PV = $20.07 million
Hence, the present value is $20.07 million.
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Widgets'R'Us created a monthly expense equation, E = 1.48q + 4,830. The company plans to sell their widgets to retailers at a price of $3.98. How many widgets must be sold to reach the breakeven point?
Using the expense and revenue equations above, if Widgets'R'Us sells 5,430 widgets, what will their profit be?
a) The number of widgets that Widgets"R'U must sell to reach the break-even point is 2,082 units.
b) Using the expense and revenue equations, if Widgets'R'Us sells 5,430 widgets, their profit will be $8,745.
What is the profit equation?The profit equation is total revenue minus total costs.
The profit equation shows that profit is a function of the difference between the total revenue realized from sales and services less the total costs involved in rendering the services or delivering the goods.
At the break-even point, the total revenue equals the total costs. Therefore, there is no profit or loss.
The total cost function, E = 1.48q + 4,830
The total revenue function, R = 3.98q
To break even, the quantity to be sold, q, 1.48q + 4,830 = 3.98q
-2.32q = -4,830
q = 2,082
When q = 5,430:
Profit = 3.98q - (1.48q + 4,830)
= 3.98(5,430) - (1.48 x 5,430 + 4,830)
= 21,611.4 - (12,866.4
= 8,745
= $8,745
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A parabola can be drawn given a focus of ( 5 , 3 ) and a directrix of x = − 1 x=−1. What can be said about the parabola?
The equation of a parabola can be drawn given a focus of (5, 3 ) and a directrix of x = − 1.
The equation of the parabola is:
x² - 10x - 8y + 17= 0
What is a parabola?A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.
The equation of a parabola:
y = a(x-h)^2 + k
We have,
The standard form:
(x - h)² = 4p (y - k)
where the focus is (h, k + p) and the directrix is y = k - p.
Now,
(h, k + p) = (5, 3)
h = 5
k - p = -1
k + p = 3
Now,
k - p = -1
k = -1 + p
substituting
k + p = 3
-1 + p + p = 3
-1 + 2p = 3
2p = 3 + 1
2p = 4
p = 2
k = -1 + 2
k = 1
Now,
The equation of the parabola.
(x - h)² = 4p (y - k)
(x - 5)² = 4 x 2 (y - 1)
(x - 5)² = 8 (y - 1)
x² - 10x + 25 = 8y - 8
x² - 10x - 8y + 25 - 8 = 0
x² - 10x - 8y + 17= 0
Thus,
The equation of the parabola is
x² - 10x - 8y + 17= 0
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