Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 3%, one
paying 5%, and one paying 6% simple interest per year. Cyndee wants to put twice as much in the lowest-yielding, least-risky
account as in the highest-yielding account. How much should she invest in each account to achieve a total annual return of
$2120?
Answers
Answer:
$25,333.33 at 3%$12000 at 5%$12,666.67 at 6%Step-by-step explanation:
Cyndee invests $50,000 in accounts earning 3%, 5%, and 6% annually, for a total annual return of $2120. She puts twice as much in the first account as in the third. You want to know the amount invested in each account.
SetupLet x represent the amount invested in the third account. Then 2x is the amount invested in the first account, and (50000 -3x) is the amount invested in the second account. The total return is ...
0.03(2x) +0.05(50000 -3x) +0.06(x) = 2120
SolutionSimplifying the equation gives ...
-0.03x +2500 = 2120
380 = 0.03x . . . . . . . . . . add 0.03x-2120
12,666 2/3 = x . . . . . . . divide by 0.03
2x = 25,333 1/3
50000 -3x = 12,000
Cyndee should invest 25,333.33 at 3%, $12,000 at 5%, and $12,666.67 at 6%.
Related Questions
You are installing 250 feet of PVC conduit. Each 100-foot section takes 1/2 can of PVC cement, and each 50-ft section takes 1/4 can. How much cement do you need? Your answer should be in the form of a mixed number, with any remaining fraction in its lowest terms.
Answers
While installing 250 feet of PVC conduit given the details we have in the question, The amount of cement needed is 1 1/4 can of PVC cement
How to find quantity of cement neededGiven data
PVC conduit required to be installed = 250 feet
Each 100-foot section takes 1/2 can of PVC cement
Each 50-ft section takes 1/4 can of PVC cement
250 feet will be split into two which is 200 feet and 50 feet. We solve for each separately then add up
solving for 200 feet
200 feet contains how many 100-foot, this is solved as follows:
= 200 / 100
= 2
And each 100-foot takes 1/2 can of PVC cement, therefore:
2 * 1/2 = 1
solving for 50 feet
50 feet takes 1/4 can of PVC cement
= 1/4
The sum: 1 + 1/4 = 1 1/4 ( mix number )
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Geometry please answer quickly I will give brainliest
Answers
Answer:
20 +2x+1=7, hope this is the answer
Someone help ASP YOU GET 30 points and more show work so I’ll be able to understand THANK YOU!!
Answers
Answer: 1. x=4
2. x=12
3. x=-1
Step-by-step explanation:
1. 2(3x-5)=-4x+30
6x-10=-4x+30
6x+4x-10=-4x+4x+30
10x-10=30
10x-10+10=30+10
10x=40
10x/10=40/10
x=4
2. 5x-6-3x=18
5x-3x-6=18
2x-6=18
2x-6+6=18+6
2x=24
2x/2=24/2
x=12
3. -11-5x=6(5x+4)
-11-5x=30x+24
-11-5x+5x=30x+5x+24
-11=35x+24
-11-24=35x+24-24
-35=-35x
x=-1
Combine like terms to simplify the expression:
5x^2-2x+3x^2+7x+10
Answers
Answer:
8x^2-5x+10
you just need to put the ones that are the same together
Khan Question please answer
Answers
Answer: 45 mins
Step-by-step explanation:
Maria and Anita = 30mins
this is 2/3 the time of what Maria takes
so 30 mins is 2/3 so 30 / 2/3 = 45mins
Based on the graph, estimate (to one decimal place) the average rate of change f
Answers
The estimate (to one decimal place) of the average rate of change f is 1.7
How to estimate (to one decimal place) the average rate of change f?The interval is given as
x = 1 to x = 4
This can be represented as
(a, b) = (1, 4)
From the attached graph, we have
f(1) = 2
f(4) = 7
The estimate (to one decimal place) of the average rate of change f is
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(4) - f(1)]/[4 - 1]
So, we have
Rate = [7 - 2]/[4 - 1]
Evaluate
Rate = 1.7
Hence, the estimate (to one decimal place) of the average rate of change f is 1.7
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What are the challenges in mixed research method?
Answers
The seamless integration of quantitative and qualitative data during analysis and interpretation is one of the main issues in mixed research methods.
What is the research about?Mixed Techniques Research is characterized as a subtype of user research that incorporates both qualitative and quantitative research approaches.
The overarching goal and fundamental tenet of mixed methods research is that using both quantitative and qualitative methods together yields a more comprehensive grasp of study issues and complicated phenomena than either method by itself.
In conclusion, the seamless integration of quantitative and qualitative data during analysis and interpretation is one of the main issues in mixed research methods.
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y
X
-9
-6
3
9
x - 1
x
3
у
Answers
Answer:
see explanation
Step-by-step explanation:
-9x = -3y
-6x = 2 1/5y
3x = 0y
9x = 2y
simply the following
2(2x+2y)-14x+7
Answers
Answer:
4 y + -10 x + 7
Step-by-step explanation:
Simplify the following:
2 (2 x + 2 y) - 14 x + 7
2 (2 y + 2 x) = 4 y + 4 x:
(4 y + 4 x) - 14 x + 7
Grouping like terms, 4 y + 4 x - 14 x + 7 = 4 y + (4 x - 14 x) + 7:
4 y + (4 x - 14 x) + 7
4 x - 14 x = -10 x:
Answer: 4 y + -10 x + 7
A ship’s sonar detects a submarine 440 feet below a point on the ocean’s surface 600 ft dead ahead of the ship. To the nearest degree, find the angle x. hurryy!!!
Answers
The angle x to the nearest degree is 40°
Given,
The depth of submarine that a ship's sonar detects = 440 feet
The distance from submarine to ship in oceans surface = 600 feet
We have to find the angle x.
The figure is given below:
Here, we have to use the tangents definition:
That is,
tan θ = opposite side / adjacent side
Here,
tan x = 440 / 600
We want to find x,
So,
x = tan⁻¹ (440 / 600)
x = tan⁻¹ (0.73333)
x = 40.28°
By taking nearest angle, we get x as 40°
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By eating one egg one cupcake and one slice of pizza a child consumes 303 mg of cholesterol. if the child eats three cupcakes in four slices of pizza he or she takes in 93 mg of cholesterol. by eating two eggs in 1 cup cake a child consumes 569 mg of cholesterol. how much cholesterol is in each item?
Answers
The amount of cholesterol that is in each is given as c = 19, E = 275 and P = 9
How to solve for the cholesterolWe have to define the variables as:
E + C + P = 303
3C + 4P = 93,
we have to make pizza, P the subject
4P = 93 - 3C,
P = (93 - 3C) / 4
2E + C = 569,
2E = 569 - C
E = (567-C) / 2
We have to form the equation
(569-C)/2 + C + (93-3C)/4 = 303
We have to multiply the equation by 4
(569-C)2 + 4C + 93-3C = 1212
1138 - 2c + 4c + 93 - 3c = 1212
-C = 1212- 93 -1138
-c = -19
hence c = 19 mg for 1 cupcake
E = (569- 19)/2
275 for 1 egg
P = (93-3C)/4
P = 93 - 57 / 4
= 36 / 4
= 9 for one pizza
Hence we would have c = 19, E = 275 and P = 9
19 + 275 + 9 = 303 (proves it to be correct)
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19+274 + 7 = 300 mg
Yes, it is entirely possible for vou te retire as a millionaire. If your long-term financial goal is te retire as a millionaire and you plan to invest at least $200 per month for 40 years, what rate of return would keep you from ending up a millionaire based on the Building Wealth charts?
Answers
The rate of return that would keep the individual from ending up a millionaire based on the Building Wealth charts is 9.22%
What is most appropriate method in this case?
The most suitable approach to solve for the rate of return in this instance is to make use of a financial calculator , which requires inputs as such the monthly payments, the beginning balance which is the present value and the future value which is $1,000,000 since the individual intends to retire as a millionaire.
N=480(number of monthly payments in 40 years i.e.40*12)
PMT=-200(monthly payment)
PV=0(starting balance is zero)
FV=1000000(the future value is $1,000,000)
CPT(press compute)
I/Y=0.768414778771834%(monthly rate of return)
annual rate of return=0.768414778771834%*12=9.22%
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How do division properties help you evaluate expressions?
Drag a word or number to the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When the Response area of a fraction is equal to −1 and the numerator is nonzero, the value of the fraction is equal to the
Answers
The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.
How to explain the information?It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.
Fractions simply means, numbers that are not whole.
If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.
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Answer:If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.
Step-by-step explanation:
14x^2-9x+11-8x^2+8x^6
Combine like terms
Answers
Answer:
8x^6 + 6x^2 - 9x + 11
Step-by-step explanation:
Well, I combined like terms.
There's only two terms you can combine here anyhow; those being 14x^2 and -8x^2.
given the function f(x)=2/3x-5, evaluate f(9)
Answers
2/(3x-5)
2/(3(9)-5)
1/11 :(
construct a triangle ABC with line AB= 10cm BC=6cm and AC=11cm. Hence measure the values of the angle
Answers
Hence , the construction of the triangle is given below.
AB = 10 cm BC = 6 cm AC = 11 cm
We have to find ∠A, ∠B, and ∠C.
To construct a triangle,
Firstly draw a line segment AB = 10 cm
From A we need a point C at a distance of 6 cm. So with A as the center, draw an arc of 6cm in length from point A.
From B we need a point C at a distance of 11 cm. So with B as the center, draw an arc of 11cm in length from point B.
Mark the point of intersection of the arcs as C.
Meet points C to A and B respectively.
By using a protractor measure the angles of A, B, and C.
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Which of the following Statements are true?
Statement 1: A right triangle can be an equilateral triangle.
Statement 2: An equilateral triangle can be a right triangle.
Answers
Step-by-step explanation:
both statements are wrong.
a right (or right-angled) triangle has a 90° angle. that is all.
an equilateral triangle has 3 equally long sides.
but that also implies that the 3 angles must be equal too.
the sum of all angles in a triangle must be 180°.
if all angles are equally large, that means
180 = 3×angle
angle = 180/3 = 60°.
that means none of the angles can be 90°, so, no right-angled triangle can be equilateral.
and no equilateral triangle can be right-angled.
I need to find the error in the equation
Answers
Answer:
20 - i
Step-by-step explanation:
Addition of complex numbers:In complex number addition/subtraction, add the imaginary part and add the real part separately.
The error is while adding imaginary part, you have to combine the coefficients of the imaginary numbers. So, -3 +2 will give us -1. So, the result is -i.
16 - 3i + 4+ 2i = 16 + 4 -3i + 2i
= 20 - i
Answer:
20 - i
Step-by-step explanation:
The error made during second step:
When adding or subtracting expression, we add or subtract like terms.
(16 - 3i) + (4 + 2i) get rid of parenthesis
16 - 3i + 4 + 2i add/subtract like terms
20 - i (the mistake is made here, instead of "i" they typed i^2)
use the diagram and the given angle measure to find the other 3 measures. m<3=159 degrees
Answers
Answer: hegdbweh wnbdb jsbdjh
Step-by-step explanation:b jbedbd jakdnfcj jsdcnbv
(05.01)Which statement best describes the area of the triangle shown below?
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a square of side length 4 units.
Answers
A statement that best describes the area of the triangle is It is one-half the area of a square of side length 4 units.
What is the area of the triangle?The area of a triangle can be found by the formula:
= 1/2 x base x height
The base is 4 units and the height if 4 units.
Area of the triangle is:
= 1/2 x 4 x 4
= 8 units²
The area of a square of side length 4 units. is:
= 4 x 4
= 16 units²
In conclusion, option B is correct.
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Is 5,707,460 divisible by 10?
Answers
Answer:
Yes
Step-by-step explanation:
Every number is divisible by 10, in this case you just need to tale of the zero at the end. 570,746 is the answer.
In Earnest's yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations also has a total change of 0?
A.It rained 2 inches on Tuesday. Then, it rained 2 inches on Wednesday.
B.It snowed 4 inches last week. Then, 8 inches of snow melted during this week.
C.I put 5 pounds of birdseed in the feeder. Then, birds ate 5 pounds of birdseed.
D.A farmer sold 3 bushels of apples last week. Then, she sold 6 bushels of apples this week.
E.3 feet of growth was cut from a tree branch last year. Then, the tree branch grew 3 feet this year.
F.My family painted a 300 square foot barn on Saturday. Then on Sunday, we painted a 300 square foot garage.
Answers
Explanation:
C is the only answer that gives answer of 0.
+5lbs then -5lbs = 0lbs
All others don’t give same amount.
Option E is a trick,
-3 puts at 0 growth then add 3feet
(PLEASE ANSWER A, B, AND C)
Give each probability as a simplified fraction, decimal, and percent.
If the spinner below is spun once, find each probability.
A. P (4)
B. P (a number less than 10)
C. P (a prime number)
Answers
The probability of P(4) is 1/8. 12.5%, 0.125.
The probability of a number less than 10 is 8/8. 1 , 100%
The probability of a prime number is 1/2. 0.5. 50%.
What is the probability?Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
Probability of spinning 4 = number of possible outcomes / number of sections
1/8 = 0.125 = 12.5%
Probability of spinning a number less than 8 = possible outcomes / total sections
8/8 = 1 = 100%
Probability of spinning a prime number = number of possible outcomes / total sections
Prime numbers between 1 and 8 = : 2, 3, 5, 7
4/8 = 0.5 = 50%
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Assume the statements below are true. If exactly two of the students went to the movies, who did NOT go to the movies?
If Catherine goes to the movies, then Jessika will go.
If Jessika goes to the movies, then Jorge will go.
If Jorge goes to the movies, then Mike will go.
Answers
Answer:Jorge and Mike
Step-by-step explanation:
Nobody goes if Mike goes
an angle measures 101.4 less then the measure of supplementary angles. what is the measure of each angle
Answers
Answer:
39.3°, 140.7°
Step-by-step explanation:
supplementary angles means that together they have 180°.
so, when we have 2 angles, x and y.
x + y = 180
x = y - 101.4
using the second equation in the first
y - 101.4 + y = 180
2y - 101.4 = 180
2y = 281.4
y = 281.4/2 = 140.7°
x = y - 101.4 = 140.7 - 101.4 = 39.3°
so, the starting angle is 39.3°, and every supplementary angle is then 140.7°.
f(x)=2x^2-6
Find f(7)
Answers
Answer:
f(7) = 92
Step-by-step explanation:
f(7) means what is the value of f(x) when x = 7
substitute x = 7 into f(x)
f(7) = 2(7)² - 6 = 2(49) - 6 = 98 - 6 = 92
18:5=5/18 true or false
Answers
i responded to this already but it it is FALSE
Answer: False
Step-by-step explanation: Ratio is A:B = A/B
Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.
Answers
The time it would take from when you threw the ball until it lands on the ground below is equal to 2.16 seconds.
Given the following data:
Height of building = (42.0+A) m = (42.0+9) m = 51 m.
Initial speed of ball = (14.5+B) m/s = (14.5+8) m/s = 22.5 m/s.
Scientific data:
Acceleration due to gravity = 9.8 m/s²
How to determine the time?Generally speaking, when this ball is thrown straight up at a certain speed, it begins to slow down as a result of the effect of downward gravitational acceleration. Consequently, the ball reaches a maximum height where it can't go higher anymore and then starts to fall down due to gravity.
In order to determine the time it would take from when you threw the ball until it lands on the ground below, we would apply the second equation of motion:
S = ut + ½gt²
½gt² + ut - S = 0
Substituting the given parameters into the formula, we have;
0.5(9.8)t + 22.5t - 51 = 0.
4.9t + 22.5t - 51 = 0.
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]t = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-22.5\; \pm \;\sqrt{22.5^2 - 4(0.5)(-51)}}{2 \times 0.5}\\\\t = \frac{-22.5\; \pm \;\sqrt{506.25 + 102}}{2}\\\\t = \frac{-22.5\; \pm \;\sqrt{608.25}}{2}[/tex]
t = 2.16 or -47.16
Since the time cannot be negative, the value of t to three significant figures is equal to 2.16 seconds.
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Complete Question:
Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from when you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.
A=9, B=8
The functions fand g are defined as follows.
g(x)=2x³ +6
f(x)=-4x-1
Find f(7) and g (-3).
Simplify your answers as much as possible.
f(7)=
g(-3)=
Answers
f ( 7 ) = - 4 ( 7 ) - 1
= -28 - 1
= - 29
g ( x ) = 2x^3 + 6
g ( -3 ) = 2 (-3)^3 + 6
= 2 ( -27 ) + 6
= - 54 + 6
= - 48
SLOVE FOR X , really need help it’s due tmrw thanks
Answers
Answer:
3.5
Step-by-step explanation:
21x+6
21/21 6/21
x=3.5