Using proportions, the expression for the final amount is:
150(1+d).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For this problem, we have that:
The increase of d% is equivalent to a multiplication by (1 + d).The increase of 25% is equivalent to a multiplication by 1.25.Hence the equivalent expression is:
120 x 1.25 x (1 + d) = 150(1+d).
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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 70% pure fruit juice?
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
How to use weighted averages to find the correct juice concentration
In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:
70 · 140 = 55 · x + 80 · (140 - x)
70 · 140 = 80 · 140 - 25 · x
25 · x = 10 · 140
x = 56
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
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Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -y)
O (x, y) - (y, x)
O (x, y) -- (-x, -y)
O (x, y) - (-y, -x)
The rule that describes the transformation is (x, y) - (-y, -x).
What is transformation?Transformation is the process of using rules to transform some graphics into something else.When a shape is either reflected, rotated, or translated, the coordinates of the vertices that make up the shape change.The four different forms of transformations—Translation, Reflection, Rotation, and Enlargement—are depicted in the following illustrations.The underlying coordinate system remains fixed while an object transformation modifies the coordinates of each point on the object in accordance with some rule. • A coordinate transformation expresses each point of the object in the new coordinate system by defining it in terms of the old one.The fourth option among the available choices depicts a 180° clockwise or counterclockwise rotation, in which is The vertices' x- and y-coordinates change to their opposites, i.e., x becomes -x and y becomes -y.
The rule that describes the transformation is (x, y) - (-y, -x).
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Burger Corp has $468,500 of assets, and it uses only common equity capital (zero debt). Its sales for the last year were $778,500, and its net income after taxes was $25,000. Stockholders recently voted in a new management team that has promised to lower costs and get the return on equity up to 15%. What profit margin would Burger need in order to achieve the 15% ROE, holding everything else constant?
Answer in % without units (i.e. 17.11% -> 17.1 )
ANSWER: 9.0
BUT I WANT TO KNOW HOW TO SOLVE
The profit margin required to achieve 15% targeted ROE is 9.0%
The ROE means return on equity, it is the return earned on shareholders fund or shareholders equity.
Based on the three-way DuPont approach to computing the ROE, the below formula is very relevant to this analysis:
ROE=net profit margin*assets turnover*equity multiplier
ROE=15%
net profit margin=the unknown now(assume it is X)
assets turnover=sales/total assets
assets turnover=$778,500/$468,500
assets turnover=1.6616862326574200
equity multiplier=total assets/total equity
Note the company is entirely financed by equity(zero debt) which means that total assets is the same as total equity
equity multiplier=$468,500 /$468,500
equity multiplier=1.00
15%=X*1.6616862326574200*1.00
15%=X*1.6616862326574200
X=15%/1.6616862326574200
X=9.0%
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Which of the following numbers is the greatest?
2.5
-2.5
0
-7
Answer:
2.5
Step-by-step explanation:
2.5 is the only positive number amongst the options, so it must be the greatest.
f(x) = x². What is g(x)?
g(x)
f(x) = x²
(3, 1)
The function g(x) is g(x)= (1/3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 1/3 to form g(x).
This means that:
g(x) = f(1/3x)
So, we have:
g(x)= (1/3x)^2
Hence, the function g(x) is g(x)= (1/3x)^2
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I need help with this slope
Answer:
B, C
Step-by-step explanation:
Look at the lower blue point.
Its coordinates are (4, 3).
The x-coordinate, 4, stands for minutes.
The y-coordinate, 3, stands for number of boxes.
This is a slope of 3/4, corresponding to 0.75 boxes per minute, or 3 boxes every 4 minutes.
Answer: B, C
Answer:
3 boxes are filled every 4 minutes.
Step-by-step explanation:
Look at the graph; at the bottom of the graph, it is shown that every __ minutes, __ boxes are filled. If you look at the first shown blue point on the left of the graph, it shows that on the fourth minute, three boxes are filled, as from the axis, you go right four and up three.
If f(x) = 3x4 + 2x3 - x + 15,
what would be the list of
possible rational roots?
Answer: A. ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
Step-by-step explanation:
± [tex]\frac{1, 3, 5, 15}{1, 3}[/tex]
= ± [tex]1, 3, 5, 15, 1/3, 5/3, 5[/tex]
Rearranging, we get:
= ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
How long do you need to invest your money in an account earning an annual interest rate of 4.252% compounded monthly so that your investment grows from $1,018.40 to $10,413.00 over that period of time?
The time needed for the investment to become $10,413 is 54.7 years
How long before $1,018.40 grows to $10,413.00?Number of years = (In FV / PV) / r
FV = future valuePV = present valuer = interest rater = 4.252/12 = 0.354%
(In 10, 413 / 1,018.40) / 0.00354 = 656.73 months = 54.7 years
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101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1
Distribute the summation over the sum.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]
Now plug in the known sums and simplify.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]
someone please help me on this question
i need detailed step by step explaination with reasoning
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Correct option - C[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Area left for flowers = Area of flower garden - Area of bird bath.
Area of flower garden [ rectangle ] :
[tex]\qquad❖ \: \sf \:length \times width[/tex]
[tex]\qquad❖ \: \sf \:3 \times 2[/tex]
[tex]\qquad❖ \: \sf \: 6\: \: {m}^{2} [/tex]
Area of bird bath [ Circle ] :
[tex]\qquad❖ \: \sf \: \pi{r}^{2} [/tex]
[tex]\qquad❖ \: \sf \:3.14 \times ( \frac{1}{2} ) {}^{2} [/tex]
[tex]\qquad❖ \: \sf \:3.14 \times \frac{1}{4} [/tex]
[tex]\qquad❖ \: \sf \:0.785 \: \: m {}^{2} [/tex]
Area left for flowers :
[tex]\qquad❖ \: \sf \:6 - 0.785[/tex]
[tex]\qquad❖ \: \sf \:5.215 \: \: m {}^{2} [/tex]
[tex]\qquad❖ \: \sf \: \approx5.22 \: \: m {}^{2} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct option - CTwo cars start at the same time, but travel in opposite directions. One car's average speed is 80 miles per hour (mph). At the end of 2 hours, the two cars are 220 miles apart. Find the average speed in mph of the other car.
The speed of an object is the relationship between the distance covered by the object and the time taken. Thus, the average speed of the other car is 30 mph.
The speed of an object is the relationship between the distance covered by the object and the time taken. The expression for speed is given as;
speed = [tex]\frac{distance covered}{time taken}[/tex]
⇒ distance = speed x time taken
In the given question, the distance of the first car after 2 hours can be determined as:
distance = 80 mph x 2 h
= 160 miles
The distance covered by the first car after 2 hours is 160 miles.
Thus, since the total distance between the two cars after 2 hours is 220 miles, then;
distance covered by the second car = 220 miles - 160 miles
= 60 miles
The distance covered by the second car is 60 miles.
So that the average speed of the other car is;
speed = [tex]\frac{60}{2}[/tex]
= 30 mph
The average speed is 30 miles per hour (mph).
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A tank originally contains 100 gallon of fresh water. Then water containing 0.5 Lb of salt per gallon is pourd into the tank at a rate of 2 gal/minute, and the mixture is allowed to leave at the same rate. After 10 minute the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at end of an additional 10 minutes.
Let [tex]S(t)[/tex] denote the amount of salt (in lbs) in the tank at time [tex]t[/tex] min up to the 10th minute. The tank starts with 100 gal of fresh water, so [tex]S(0)=0[/tex].
Salt flows into the tank at a rate of
[tex]\left(0.5\dfrac{\rm lb}{\rm gal}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = 1\dfrac{\rm lb}{\rm min}[/tex]
and flows out with rate
[tex]\left(\dfrac{S(t)\,\rm lb}{100\,\mathrm{gal} + \left(2\frac{\rm gal}{\rm min} - 2\frac{\rm gal}{\rm min}\right)t}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = \dfrac{S(t)}{50} \dfrac{\rm lb}{\rm min}[/tex]
Then the net rate of change in the salt content of the mixture is governed by the linear differential equation
[tex]\dfrac{dS}{dt} = 1 - \dfrac S{50}[/tex]
Solving with an integrating factor, we have
[tex]\dfrac{dS}{dt} + \dfrac S{50} = 1[/tex]
[tex]\dfrac{dS}{dt} e^{t/50}+ \dfrac1{50}Se^{t/50} = e^{t/50}[/tex]
[tex]\dfrac{d}{dt} \left(S e^{t/50}\right) = e^{t/50}[/tex]
By the fundamental theorem of calculus, integrating both sides yields
[tex]\displaystyle S e^{t/50} = Se^{t/50}\bigg|_{t=0} + \int_0^t e^{u/50}\, du[/tex]
[tex]S e^{t/50} = S(0) + 50(e^{t/50} - 1)[/tex]
[tex]S = 50 - 50e^{-t/50}[/tex]
After 10 min, the tank contains
[tex]S(10) = 50 - 50e^{-10/50} = 50 \dfrac{e^{1/5}-1}{e^{1/5}} \approx 9.063 \,\rm lb[/tex]
of salt.
Now let [tex]\hat S(t)[/tex] denote the amount of salt in the tank at time [tex]t[/tex] min after the first 10 minutes have elapsed, with initial value [tex]\hat S(0)=S(10)[/tex].
Fresh water is poured into the tank, so there is no salt inflow. The salt that remains in the tank flows out at a rate of
[tex]\left(\dfrac{\hat S(t)\,\rm lb}{100\,\mathrm{gal}+\left(2\frac{\rm gal}{\rm min}-2\frac{\rm gal}{\rm min}\right)t}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = \dfrac{\hat S(t)}{50} \dfrac{\rm lb}{\rm min}[/tex]
so that [tex]\hat S[/tex] is given by the differential equation
[tex]\dfrac{d\hat S}{dt} = -\dfrac{\hat S}{50}[/tex]
We solve this equation in exactly the same way.
[tex]\dfrac{d\hat S}{dt} + \dfrac{\hat S}{50} = 0[/tex]
[tex]\dfrac{d\hat S}{dt} e^{t/50} + \dfrac1{50}\hat S e^{t/50} = 0[/tex]
[tex]\dfrac{d}{dt} \left(\hat S e^{t/50}\right) = 0[/tex]
[tex]\hat S e^{t/50} = \hat S(0)[/tex]
[tex]\hat S = 50 \dfrac{e^{1/5}-1}{e^{1/5}} e^{-t/50}[/tex]
After another 10 min, the tank has
[tex]\hat S(10) = 50 \dfrac{e^{1/5}-1}{e^{1/5}} e^{-1/5} = 50 \dfrac{e^{1/5}-1}{e^{2/5}} \approx \boxed{7.421}[/tex]
lb of salt.
The terms 1/64, 1/32, 1/16 form a geometric progression (GP) If the sum of the GP is (2^36 – 2^-6), find the number of terms
If [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio of the series, then the sum of the first [tex]n[/tex] terms is
[tex]S_n = a + ar + ar^2 + \cdots + ar^n[/tex]
Multiply by [tex]r[/tex] on both sides, then subtract that from and solve for [tex]S_n[/tex].
[tex]rS_n = ar + ar^2 + ar^3 + \cdots + ar^{n+1}[/tex]
[tex](1-r)S_n = a - ar^{n+1}[/tex]
[tex]S_n = \dfrac{a(1-r^{n+1})}{1-r}[/tex]
Use the given first and second terms of the sequence to find [tex]a[/tex] and [tex]r[/tex].
[tex]a = \dfrac1{64}[/tex]
[tex]ar = \dfrac1{32} \implies \dfrac r{64} = \dfrac1{32} \implies r = \dfrac{64}{32}=2[/tex]
Solve for [tex]n[/tex].
[tex]S_n = \dfrac{1-2^{n+1}}{64(1-2)} = 2^{36} - 2^{-6}[/tex]
[tex]\dfrac{2^{n+1} - 1}{2^6} = 2^{36} - 2^{-6}[/tex]
[tex]2^{n-5} - 2^{-6} = 2^{36} - 2^{-6}[/tex]
[tex]\implies n-5 = 36 \implies \boxed{n = 41}[/tex]
Solution for the attached question below
The solution to the question is 265.
What is the logarithm of a number?Logarithm of a number A is the exponent or power or index n, a given number called the base B would be raised to give the number A.
So n is the logarithm of A to base B.
Analysis:
log 2( log2(x-9)) = 3
log2(x-9) = [tex]2^{3}[/tex]
log2(x-9) = 8
x-9 = [tex]2^{8}[/tex]
x-9 = 256
x = 256 + 9
x = 265
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On a ΔABC, mΔA=80, mΔB=60
Find mΔC
The measure of angle C (m ∠C) is 40°
Calculating angles in a triangleFrom the question, we are to determine the measure of angle C (m ∠C)
In any given triangle, the sum of all the angles is 180°
Thus,
In ΔABC, the angles sum up to 180°
That is,
∠A + ∠B + ∠C = 180°
From the given information,
m ∠A = 80°, m ∠B = 60°
Thus,
80° + 60° + m ∠C = 180°
140° + m ∠C = 180°
m ∠C = 180° - 140°
m ∠C = 40°
Hence, the measure of angle C (m ∠C) is 40°
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PLS HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELP
Answer:
let the first and second table box as 12345 and abcde
1,a
2,c
3,e
4,b
5,d
Step-by-step explanation:
you can use
y=mx+b form m is slope , b is y intercept
m with variable x and b without any variable I.e it is real value
Which choice is a term in this expression? -3x − 7(x + 4)
Answer:
Mate im sorry for replying here but i need points to ask a question.
Using the table, what is the average daily balance of the credit card for the July 1 - July 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Day 1112126 Activity − Payment Purchase Payment Adjustment −−500+750−700 Closing Balance 2500200027502050
To solve, multiply each closing balance by the number of days at that balance, add all of these together and then divide by the total number of days in the billing period.
($2500×10)+($2000×10)+($2750×5)+($2050×6)31≈$2291.94
The average daily balance of the credit card is 2291.94
What is the average daily balance?
The average daily balance can be determined by dividing the total daily balance of month by numbers of days in month.
We can find average daily balance as shown below:
Average daily balance = total balance of the month/total number of days in the month
Total balance = (2500*10) +(2000*10) +(2750*5) +(2050*6)
= 25000+20000+13750+12300
= 71,050
Number of days = 31
Average daily balance = 71,050/31
= 2291.9354
Round to the nearest cent
= 2291.94
Hence, the average daily balance of the credit card is 2291.94
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guys can you help me with this i just dont understand how to plot it so u just have to tell me how
Answer:
no
Step-by-step explanation:
Answer:
Step-by-step explanation:
6(3x-5)≤2(9x+7)+10
divide by 2
3(3x-5)≤9x+7+5
3(3x-5)≤9x+12
divide by 3
3x-5≤3x+4
-5≤4
which is true.
I’m confused on c and d please help me
Answer:
C is 27 and d is 16
Step-by-step explanation:
count how many cubes are on the first level and multiple but how many it goes up too
Mohinder needs to create a 5 character password. He wants each of the first, third, and fifth characters in the password to be one of the letters A to E and second and fourth characters to be one of the numerals 0 through 9. If each of the characters in the password must be unique how many passwords are possible
The number of unique passwords is 5400
How to determine the number of unique passwords?The characteristics of the password are given as:
Number of characters = 5First, third, and fifth characters in the password = One of the letters A to ESecond and fourth characters = one of the numerals 0 through 9Since the characters in the password must unique, we have the following possibilities
First character = Any of 5 charactersSecond characters = Any of 10 digitsThird character = Any of remaining 4 charactersFourth characters = Any of remaining 9 digitsFifth character = Any of remaining 3 charactersSo, the number of unique passwords is
Password = 5 * 10 * 4 * 9 * 3
Evaluate the product
Password = 5400
Hence, the number of unique passwords is 5400
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n an element’s square on the periodic table, the number with the greatest numerical value represents the
Adam eats 20 % of a pizza, Bethany eats another 1/3 of the pizza, and Charlie eats the remaining 14 slices. How many slices total did the pizza originally have?
The pizza originally have 30 slices.
What is linear equation?
An equation in which the highest power of the variable is one is known as linear equation.
We will find number of pizza slices as shown below:
Let pizza originally have x slices.
Adam eats 20% of a pizza
= 0.2x
Bethany eats 1/3 of pizza
=1/3(x)
Charlie eats the remaining 14 slices
0.2x+1/3(x)+14=x
14 = x - 0.2x - 1/3(x)
14 = x - x/5 - x/3
14 = (15x - 3x - 5x)/15
14*15 = 7x
By dividing both sides by 7, we get
30 = x
x = 30
Hence, the pizza originally have 30 slices.
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The circumference of a circle is 15π in. What is the area, in square inches? Express your answer in terms of \piπ.
Answer:
the area would be 176.7
Step-by-step explanation:
You know the area of a circle is A = pi×r^2, so you need the radius.
You know C = 2pi×r, so r = C/(2pi)
r = 15pi / 2pi = 7.5
A = pi(7.5)^2 = 56.25pi ~ 176.715 square inches.
The area of the circle is about 176.7 square inches.
The radius of the circle is 7.5 inches. Therefore, the area of the circle will be 56.25π square inches.
What is the circumference and area of a circle?Let r be the radius of the circle. Then the area of the circle will be given as,
A = πr² square units
The circumference of the circle will be given as,
C = 2πr units
The circumference of a circle is 15π inches. Then the radius of the circle is calculated as,
15π = 2πr
r = 7.5 inches
The area of the circle is calculated as,
A = π x 7.5²
A = 56.25π square inches
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Simplify the following
Answer:
[tex]6 + ( \frac{4}{3} + ( \frac{5}{6} - \frac{1}{3} ))[/tex]
[tex] = 6 + ( \frac{4}{3} + ( \frac{5 - 2}{6})) [/tex]
[tex] = 6 + ( \frac{4}{3} + \frac{3}{6})[/tex]
[tex] = 6 + ( \frac{8 + 3}{6})[/tex]
[tex] = 6 + \frac{11}{6} [/tex]
[tex] = \frac{6}{1 } + \frac{11}{6} [/tex]
[tex] = \frac{36 + 11}{6} [/tex]
[tex] = \frac{47}{6} [/tex]
[tex] = 7 \frac{5}{6} [/tex]
Blossom company , a machinery dealer leased manufacturer equipment to Mays corporation on January 1, 2017. The lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year . The first payment is received on January 1, 2017 . Blossom had purchased the machine during 2016 for $75000 collectibility of lease payments is reasonable predictable, and no important uncertainties surround the amount of cost yet to be incurred by blossom se the annual rentel to ensure a 8% rate of return . The machine has an economic life of 8 years with no resiidaul value and reverts to blossom at the termination of the lease.A. Compute the amount of the lease receivable
The amount of the lease receivable will be $146999.
What are lease receivable?It should be noted that lease receivables means all the payments under the operative documents in respect of:
(i) the Purchaser Basic Rent,
(ii) the Maximum recourse amount,
(iii) the Purchaser Balance and
(iv) any purchase by the Lessee of the Properly up to the amount of the Capital then outstanding.
In this case, the lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year and the first payment is received on January 1, 2017.
The lease receivable will be:
= PVAD8%,7 × Lease payment
= 5.62288 × 26143
= $146999
In conclusion, the lease receivable is $146999.
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POINTS, AND BRAINLIEST
The identification of parts A,B andC is illustrated below with their various reasons given.
What is an equilateral triangle?An equilateral triangle is the triangle that has all its sides equal in length and each angle is made up of angle 60°.
Part A = The similar triangle are RGE and PBE
Part B = The triangles selected are similar because it was formed by an interception of the parallel lines of the rectangle GCPR.
Part C= All the sides of the equilateral triangle are the same therefore the distance from B to E and from P to E is the same with BP which is 225ft.
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In the diagram the origin is at the center of a cube that has edges 6 units long. The x-,y-, and z-axes are perpendicular to the faces of the cube give the coordinates of the corner at point A.
Answer:
the third answer (-3, -3, 3)
Step-by-step explanation:
the dotted lines indicate that these lines (or part of lines) are invisible due to being inside or behind the cube.
so, we know that A is the left-back-upper corner of the cube.
the x-axis goes front-back. front is positive.
the y-axis goes left-right. right is positive.
the z-axis goes up-down. up is positive.
since the origin (0, 0, 0) is the center of the cube, and the sides are all 6 units long, the corners can have only -3 or +3 coordinates (half of a side length on either side of the origin) in each direction.
as we said : left-back-upper corner.
left means negative y.
back means negative x.
upper means positive z.
so, the coordinates of A are
(-3, -3, 3)
Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
The linear equations are given as follows:
For diagonal AC: [tex]x + y = 0, -3 \leq x \leq 3[/tex].For diagonal BD: [tex]x - y = 0, -3 \leq x \leq 3[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For diagonal AC, the line contains points (-3,3) and (3,-3), hence the line is:
y = -x.
In standard form:
[tex]x + y = 0, -3 \leq x \leq 3[/tex].
For diagonal BD, the line contains points (3,3) and (-3,-3), hence the line is:
y = x.
In standard form:
[tex]x - y = 0, -3 \leq x \leq 3[/tex].
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Match the expressions to their solutions or equivalents. -1/9 / (-1/3)
The quotient of the given expression is 1/3
Difference and division of fractionsFractions are written as a ratio of two integers
Given the expression below'
-1/9 / (-1/3)
Change the division to multiplication
-1/9 * -3/1
1/9 * 3/1
1/3
Hence the quotient of the given expression is 1/3
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