The height (in inches) of a toy that moves up and down on a spring can be modeled by the function y= -(cos x)+2(cos x) (sin x) where x is time in seconds. Within the interval 0 < x < 6, when does the toy reach its minimum height? What is that height?
Answers
The correct option regarding the minimum height reached by the toy is:
A height of -1.76 inches at 5.647 seconds.
How to find the minimum value of the function?The function for the height of the toy in the spring after x seconds is modeled as follows:
y = -cos(x) + 2cos(x)sin(x)
It is a trigonometric function, hence there is no rule to find the minimum value of the function as there is for a quadratic function, for example.
Since there is no rule, we have to sketch the graph of the function in the given domain of 0 < x < 6.
Using a graphing calculator, the graph of the function is given at the end of the answer, with minimum point at (5.647, -1.76), hence the correct option is:
A height of -1.76 inches at 5.647 seconds.
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Related Questions
-3/16, 7/4, -3/8 write in order from least to greatest
Answers
a We have fractions in order to order from least to greatest we will convert the fractions into decimal number
[tex]-\frac{3}{16}=-0.1875[/tex][tex]\frac{7}{4}=1.75[/tex][tex]-\frac{3}{8}=-0.375[/tex]as we can see the least number is -3/8 then -3/16 and the greatest number is 7/4
[tex]undefined[/tex]Holly ate one more brownie, then Tori from the same small pan. Write two equivalent fractions that describe how much Holly eight.
Answers
Holly ate two [tex]\frac{1}{6}[/tex] fractions.
Holly ate 1 more brownie, then Tori
= 1+2
= 3
She ate [tex]\frac{3}{9}[/tex] fraction
Two equivalent fractions = [tex]\frac{3}{9} = 2x[/tex]
[tex]x = \frac{1}{6}[/tex]
Holly ate two [tex]\frac{1}{6}[/tex] fractions.
What are Fractions?
Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.
A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the bottom part represents the denominator, and the top part the numerator. This article's focus is on going to learn the meaning of fractions in mathematics, different sorts of fractions, how to convert fractions to decimals, and a ton of problems that have been solved and well explained.
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Solve the linear system using the elimination method. Type youranswer as an ordered pair in the form (#,#). 6x + 5y = -15-2x – 3y = 17
Answers
1) Solving that linear system using the elimination method, we'll proceed this way.
1.1 Choose one variable to be canceled out firstly. Let's choose the x variable:
6x + 5y = -15
-2x -3y= 17 Multiply this whole equation by 3
6x + 5y = -15
-6x -9y= 51 Add both equations
----------------------
0 -4y =36 Divide both sides by -4
y = -9
2) Now let's plug into any equation, usually the one with smaller numbers y= -9
-2x -3(-9) = 17
-2x +27 = 17 Subtract 17 from both sides
-2x =17-27
-2x = -10 Divide both sides by -2
x= 5
3) So the solution is (5, -9)
-
Distribution Whole Number Multiple Choice
Answers
Distribution of
a(b + c) = ab + ac
Then
36 + 12 is equivalent to
Find composed numbers
36= 3•12
12 = 3•4
THEN ANSWER IS
3• (12 + 4)
Help plllllesessssssssssssssssssssssssssssssssssssssssssssssssss
Answers
Answer: 8 + 7x
Step-by-step explanation:
The perimeter is the same as all the side lengths added together. We will set up an expression, then simplify it by combining like terms.
(4 - x) + (7x - 1) + (6x + 13) + (-8 - 5x)
4 - x + 7x - 1 + 6x + 13 - 8 - 5x
4 - 1 + 13 - 8 - x + 7x + 6x - 5x
8 + 7x
Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.
Printer C prints 115 pages every 5 minutes. Which printer prints the fastest?
Answers
Answer:
Printer B prints the fastest
evaluate x=5 and y=7
y2-x/y+3x
Answers
The answer to the given expression is 2
How to solve variables?To "solve" or "isolate" a variable is to place it on its own side of the equation.
All other variables or constants should be moved to the opposite side of the equation using inverse operations. The operations must be applied to both sides of the equation in order to maintain the equation's balance.
Given : x = 5 and y = 7
To find : [tex]\frac{y^{2} - x }{y + 3x}[/tex]
When we substitute the values mentioned above in this above expression we get;
[tex]\frac{7^{2}- 5 }{ 7+ 3X5}[/tex]
⇒ [tex]\frac{49 - 5}{ 7 + 15}[/tex]
⇒ [tex]\frac{44}{22}[/tex]
On dividing it with 22 we get
[tex]\frac{44}{22}[/tex] = 2
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The age of children in kindergarten on the first day of school is uniformly distributed between 5 and5.76 years old. A first time kindergarten child is selected at random. Round answers to 4 decimalplaces if possible.a. The mean of this distribution isb. The standard deviation isC. The probability that the the child will be older than 5 years old?d. The probability that the child will be between 5.4 and 5.6 years old ise. If such a child is at the 53rd percentile, how old is that child?years old.CalculatorScratchwork Area
Answers
Given the interval of the distribution as
[tex]5-5.76[/tex]a) To find the mean, we will calculate the mid-value of the interval, this is shown below
[tex]\operatorname{mean}=\frac{5+5.76}{2}=\frac{10.76}{2}=5.38[/tex]Hence, the mean is 5.38
b) To find the standard deviation
[tex]\begin{gathered} SD=\sqrt[]{\frac{(b-a)^2}{12}} \\ b=5.76 \\ a=5 \\ SD=\sqrt[]{\frac{(5.76-5)^2}{12}} \\ =\sqrt[]{\frac{0.76^2}{12}}=0.2194 \end{gathered}[/tex]Hence, the standard deviation is 0.2194
c) The probability that the child will be older than 5 years will be
[tex]P(older\text{ than 5 years)=}\frac{5.76-5}{5.76-5}=\frac{0.76}{0.76}=1.0[/tex]Hence, the probability that the child will be older than 5 years is 1.0
d) The probability that the child age is between 5.4 and 5.6 years old will be
[tex]P(\text{ between 5.4 and 5.6 years old)=}\frac{5.6-5.4}{5.76-5}=\frac{0.2}{0.76}=0.2632[/tex]Hence, the probability that the child age is between 5.4 and 5.6 years old is 0.2632
e) If the child is at the 53rd percentile, the age of the child will be
[tex]\begin{gathered} At\text{ 53rd percentile the age}\Rightarrow5+\frac{53}{100}(5.76-5) \\ =5+0.53(0.76) \\ =5.4028 \end{gathered}[/tex]Hence, at the 53rd percentile, the age of the child is 5.4028 years old
Linh buys $11.23 worth of groceries and pays for them with a $20 bill.List her change using the smallest number of coins and bills?
Answers
Given: Linh buys $11.23 worth of groceries and pays for them with a $20 bill.
So, the change will be = 20 - 11.23 = $8.77
triangle DEF is rotated 90 to the right to format the triangle with the side lengths shown below
Answers
Problem
Solution
For this case we can conclude that:
DE = r
DF= s
EF= t
Determine whether the graph represents a function.
Answers
The given graph representing function is a relation.
What is meant by relation and function?A function is a relation that states that there must be only one output for every input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be related with only one y-value.The Cartesian product is a subset of it. Alternatively, a slew of points (ordered pairs). In other words, the connection between the two sets is described as a collection of a ordered pair, where the ordered pair is formed by an object from each set.(INPUT, OUTPUT): An ordered pair is depicted as (INPUT, OUTPUT):For the given question,
For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.
Thus, the graph shows the relation of the function.
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20. A room is 24 feet long and 15 feet wide. How much will it cost to cover the floorwith carpet costing $36 a square yard if an extra 4 square yards must be purchasedfor matching?Answer
Answers
At first, we will change the feet to the yard because the cost of carpet is per square yard
Since 1 yard = 3 feet, then
Divide each dimension by 3 to change it from feet to yard
Since the length of the room = 24 feet, then
The length of the room = 24/3 = 8 yards
Since the width of the room = 15 feet, then
The width of the room = 15/3 = 5 yards
The rule of the area of the rectangle is
Area = Length x width, then
The area of the room = 8 x 5 = 40 square yards
Since we will add extra 4 square yards to it, then
The total area needs to cover = 40 + 4 = 44 square yards
Since the cost of 1 square yard = $36, then
Multiply the area by the cost to find the cost of the carpet
The total cost = 44 x 36 = 1584
The cost of the carpet is $1584
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.60 and the cost of a large greeting card is $4.05. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get x small greeting cards and y large greeting cards?Total cost, 5 small greeting cards and 4 large greeting cards: Total cost, x small greeting cards and y large greeting cards:
Answers
From the given question, we have the following parameters
Cost of a small greeting card = $1.60
The cost of a large greeting card = $4.05.
Cost of 5 small greeting cards = 5(1.60)
Cost of 5 small greeting cards = $8.00
Cost of 4 large greeting cards = 4(4.05)
Cost of 4 large greeting cards = $16.2
Cost of 5 small and 4 large = $8.00 + $16.2
Cost of 5 small and 4 large $24.2
Hence it would cost $24.2 to get 5 small greeting cards and 4 large greeting cards
Similarly;
Cost of x small greeting cards = 1.60x
Cost of y large greeting cards = 4.05y
Cost of small greeting cards and y large greeting cards = 1.60x + 4.05y
Hence it would cost $(1.60x + 4.05y) to get x small greeting cards and y large greeting cards
Which choices are equivalent to the fraction below? Check all that apply.330327O A. 357O B. 34O c. 27D. 33
Answers
Given:
We have given fraction
[tex]\frac{3^{30}}{3^{27}}[/tex]Required:
We have to find the required data which is equal to above fraction solution.
Explanation:
In the above fraction we have same base in numerator and denominator and hence,
when the base is same power are added.
[tex]=3^{30-27}\text{ =3}^3[/tex]Required answer:
Option d is correct.
which is equal to our calculated answer.
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How many times larger is (1.064 x 101) than (7 x 10−1)?
0.152
15.2
6.58
7.448
Answers
Answer:
the correct answer is 15.2
Use the formula for nCr to evaluate the expression. 10c3/6c4
Answers
SOLUTION
The given expression is
[tex]\frac{^{10}C_3}{^6C_4}[/tex]Recall the formula for combination
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]Solving the given expresssion
[tex]\frac{^{10}C_3}{^6C_4}=\frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!}[/tex]This further gives
[tex]\begin{gathered} \frac{10!}{(10-3)!3!}\div\frac{6!}{(6-4)!4!} \\ =\frac{10!}{7!3!}\div\frac{6!}{2!4!} \\ =\frac{10!}{7!3!}\times\frac{2!4!}{6!} \end{gathered}[/tex]This further gives
[tex]\begin{gathered} =\frac{10\times9\times8\times7!}{7!\times3\times2!}\times\frac{2!4!}{6\times5\times4!} \\ =\frac{10\times9\times8}{6\times5\times3} \\ =8 \end{gathered}[/tex]Therefore the solution is 8
The graph shows the number of each kind of book in Hero's personal library. A book is chosen randomly.
What is the probability that the book chosen is an adventure?
Answers
9. Assessment Practice Diego wants to
find 8+ 9. 2.NSO.2.1
Which doubles fact can help him?
A 5+5=10
B6+6=12
C7+7= 14
D 8+8=16
Answers
They can use counters or their fingers, but they can also use doubles facts. If they know 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
What is meant by addition?One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition.
The sum of 5 + 6.
They can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, 5 + 6 = 11.
Estimating other doubles-plus-one facts together, such as 3 + 4, 7 + 8, and 9 + 8.
Repeat the doubles facts so they can use them to solve equations.
They can also use doubles-minus-one facts to enable them solve equations.
Write down 9 + 10 and have your children find the sum.
If they know that 10 + 10 = 20, they know that the sum of 9 + 10 will be one less. Therefore, 9 + 10 = 19.
Practice solving different number sentences together.
Therefore, they can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, the correct answer is option A 5 + 5 = 10.
The complete question is:
Which doubles fact helps you solve 5 + 6 = 11? Circle the number sentence.
A 5+5=10
B6+6=12
C7+7= 14
D 8+8=16
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completed the chart for ordered pairs .Using the equation* reduce all fractions to the lowest terms.Given equation: 10 x- 8y =16x tea chart : __,0,2,__y tea chart: 0,__,__,4fil in the blanks
Answers
-When y = 0 :
10*x -8*0 = 16 (Replacing y=0)
10x = 16 (Multiplying)
x = 16/10 (Dividing on both sides of the equation by 10)
x= 8/5 (Simplifying)
- When x= 0:
10*0 -8*y = 16 (Replacing x=0)
-8y = 16 (Multiplying)
y= 16/(-8) (Dividing on both sides of the equation by -8)
y= -2 (Dividing)
- When x= 2
10*2 -8*y = 16 (Replacing x=2)
20 - 8y = 16 (Multiplying)
20 = 16 + 8y (Adding 8y to both sides of the equation)
20 - 16 = 8y (Subtracting 16 from both sides of the equation)
4 = 8y (Subtracting)
4/8 = y (Dividing on both sides of the equation by 8)
1/2 = y (Simplifying)
- When y= 4
10*x -8*4 = 16 (Replacing y=4)
10 x - 32 = 16 (Multiplying)
10x = 32 + 16 (Adding 32 to both sides of the equation)
10x=48 (Adding)
x = 48/10 (Dividing on both sides of the equation by 10)
x=24/5 (Simplifying)
So, the complete chart would be:
x tea chart : 8/5,0,2, 24/5
y tea chart: 0,-2,1/2,4
Match the terms (picture)
Answers
Answer:
Match that i have the step by step explanations
Step-by-step explanation:
A, F, C, D, E, F, B
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A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Answers
Graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Decorations for the dance cost $120
the club is charging $10 per student that attends.
In the graph, the x axis is labelled with number of students and the y axis with amount of money collected
As they spend $120 for the decorations of the dance the starting point for the money raised is -120, upon charging 2 students the money they will get is 2 x 10 = 20
So the money raised will be
-120 + 20 = -100
The line will pass from point (0, -120) through (2, -100)
Therefore, graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100 is correct.
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Answer:
Step-by-step explanation:
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
9. You are working to determine how much paint you will need to paint your perfectly square room. The
length of the wall is 4y+8. The height of each wall in your room is 4y. What is the area of the first wall
Answers
The area of the wall whose length is 4y+8 and the height is 4y is 16y^2 + 32y.
How area is calculated?
Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2.
The area of a form is computed by dividing its length by its breadth.
It is given that the length of the wall is 4y+8 and height of the wall is 4y.
From this given information, we can conclude that the wall is rectangle.
Formula to calculate the area of rectangle is:
Area of rectangle = length x breadth
Putting the value given in the question:
Area of the wall = (4y+8)(4y)
Area of the wall = 16y^2 + 32y
Therefore, the area of the wall is 16y^2 + 32y
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2. Maryse went for a bike ride. She rode at a constant speed, an she traveled 7 miles in one hour.Maryse wrote the equation y=7x to model her bike ride, where x is the time Maryse spent riding,and y is the distance she traveled.a. Maryse uses her equation to estimate that she rode 14 miles in the first two hours of her trip.Did she use her equation correctly? Explain why or why not. Ensure to write the equation withthe appropriate numbers plugged in.b. Maryse uses her equation to predict that she would travel 40 miles if she rode for four hours.Did she use her equation correctly? Explain why or why not.
Answers
ANSWER
1.) YES! Maryse used her equation correctly.
2.) NO! Maryse did not use her equation correctly.
EXPLANATION
Given:
A bike ride model: y = 7x
where:
1). x is the time Maryse spent riding,
2). y is the distance she traveled
Now, she rode 14 miles in the first two hours of her trip
That is:
y = 7x
where y = 14 miles and x = 2 hours
14 = 7(2)
14 = 14
She indeed used her equation correctly.
When she predicted that she would travel 40 miles if she rode for four hours.
That is:
y = 7x
where y = 40 miles and x = 4 hours
[tex]\begin{gathered} 40\text{ }\ne\text{ 7\lparen4\rparen} \\ 40\ne28 \end{gathered}[/tex]Hence, She indeed used her equation correctly in part one but she did not use her equation correctly in part two.
given angle <afb and <rst are supplementary and the m<afb = 7x - 18 and the m<rst = 72 - 2x what is the value of x? what is the m<afb and m<rst be sure to show your work and all three answers.
Answers
The most appropriate choice for supplementary angle will be given by-
x = 25.2°
∠AFB = 158.4°
∠RST = 21.6°
What is supplementary angle?
Angle is formed when two straight lines meet at a common point.
The common point is the vertex of the angle and the lines are called the arms of the angle.
Two angles are said to be supplementary if their sum is 180°
Here,
∠AFB = 7x - 18
∠RST = 72 - 2x
Sum = 7x - 18 + 72 - 2x
= 5x + 54
By the problem,
[tex]5x +54=180\\5x = 180-54\\5x =126\\x= \frac{126}{5}\\x = 25.2[/tex]
∠AFB = [tex]7 \times 25.2 -18\\[/tex]
= [tex]176.4 - 18\\[/tex]
= [tex]158.4^{\circ}[/tex]
∠RST =
[tex]72 - 2\times 25.2\\72 - 50.4\\21.6^{\circ}[/tex]
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Pam needs 2 yards of blue ribbon she has 0.497 yard she buys 0.91 yard more than she buys 0.4 yard of red ribbon how much more blue ribbon does Pam need?
Answers
Total ribbon Pam needs = 2 yards
Total ribbon Pam purchased = 0.497 + 0.91 + 0.40 = 1.807
The amount of ribbon Pam needs is calculated as,
[tex]\begin{gathered} \text{Amount n}eeded\text{ = 2 - 1.807} \\ \text{Amount n}eeded\text{ = }0.193 \end{gathered}[/tex]Thus the amount of ribbon needed is 0.193 yards .
Robert Key's group medical insurance coverage costs $6,480 a year. His employer, Covington Arts Center, pays 65% of the cost. What is his monthly paycheck deduction for medical insurance?
Answers
Answer:
See below
Step-by-step explanation:
Robert pays 35 % in 12 monthly installments
6480 * .35 / 12 = 189 dollars per month
Convert 50 degrees Fahrenheit to degrees celcius
Answers
10 degrees celsius
Explanations:The formula for converting temperature in degree Farenheit to degree Celcius is:
[tex]\begin{gathered} T_c=\text{ }\frac{5}{9}(T_f-32) \\ \text{Where T}_c=\text{ temperature in degr}ees\text{ celcius} \\ T_f=\text{ temperature in degre}es\text{ Fahrenheit} \end{gathered}[/tex][tex]\begin{gathered} T_c=\text{ }\frac{5}{9}(50\text{ - 32)} \\ T_c=\text{ }\frac{5}{9}\times18 \\ T_c=\text{ 5 }\times2 \\ T_c=10^0C \end{gathered}[/tex]Simplify the following expressions by using the properties of exponents. Assume none of the denominators is zero.
a^3 (2a^2 + 4bc^4)^ 0
Answers
The total value of the exponential expression is a³
What is Exponentiation ?
Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.
Now, The given expression is :
a^3 (2a^2 + 4bc^4)^ 0
From the properties of exponents we know that:
a⁰ = 1
Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1
Hence, The total value of the exponential expression is a³
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Graph 5x + y = 3x + 2(a) Rewrite the equation in slope intercept form. Show your work.(b) Graph the line. If you aren't able to draw on the graph using the technology you have available,then just describe it in words - tell where it is located
Answers
Given the Linear Equation:
[tex]5x+y=3x+2[/tex](a) You need to solve for "y", in order to rewrite it in Slope-Intercept Form, because that form is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, you get:
[tex]\begin{gathered} y=-5x+3x+2 \\ y=-2x+2 \end{gathered}[/tex]Notice that:
[tex]\begin{gathered} m=-2 \\ b=2 \end{gathered}[/tex](b) You can graph the line by finding the x-intercept and the y-intercept. You already know that the y-intercept is:
[tex]b=2[/tex]Then, in order to find the x-intercept, you need to substitute this value of "y" into the equation and then solve for "x":
[tex]y=0[/tex]Because the value of "y" is zero when the line intersects the x-axis.
Therefore, you get:
[tex]\begin{gathered} y=-2x+2 \\ 0=-2x+2 \\ -2=-2x \\ \\ \frac{-2}{-2}=x \\ \\ x=1 \end{gathered}[/tex]Now you know that the line passes through these points:
[tex](1,0),(0,2)[/tex]Hence, you can graph it.
Therefore, the answers are:
(a) Equation in Slope-Intercept Form:
[tex]y=-2x+2[/tex](b) Graph:
You have been given $10,000 to invest. Safe investments, like certificates of deposit, pay about 5.5% interest. The stock market is much riskier but pays about 12%. If you would like to earn about 10% a year on these investments, how much would you invest in CDS and how much should you invest in stocks?
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Answers
Answer:
Let x = amount in low risk account, then 10000-x is amount invested in high risk account. To earn 10% of 10000:
(.10)(10000) = (.055)x + .12(10000-x)
1000 = 1200 -.045x
x = 4444.44 in low risk and 5555.56 in high risk