A person plans to invest a total of $140,000 in a CD at 7% annual interest and in a mutual fund that has a three-year average annual interest of 10% by X and Y represent the money in dollars invested in the CD and the mutual fund respectively how much money should be invested in each account to earn a total of $12,200 in one year

Answers

Answer 1

Final answer:

The student should invest $60,000 in the CD at 7% annual interest and $80,000 in the mutual fund at 10% to earn a total interest of $12,200 in one year. This is determined by setting up and solving a system of linear equations.

Explanation:

The student asked how much money should be invested in a CD at 7% annual interest and a mutual fund with a three-year average annual interest of 10%, given a total investment of $140,000, to earn a total of $12,200 in one year. We can set up a system of equations to solve for X (the amount invested in the CD) and Y (the amount invested in the mutual fund).

Let X be the amount invested in the CD and Y be the amount invested in the mutual fund. We then have the following system of equations:

X + Y = $140,000 (the total investment)0.07X + 0.10Y = $12,200 (the total interest earned in one year)

Solving this system, we subtract the first equation from the second equation multiplied by 0.07:

0.07X + 0.10Y = $12,2000.07X + 0.07Y = $9,800

Subtract the second equation from the first we get:

0.03Y = $2,400

Dividing both sides by 0.03 gives:

Y = $80,000

Substitute Y in the first equation:

X + $80,000 = $140,000

X = $140,000 - $80,000 = $60,000

Therefore, $60,000 should be invested in the CD and $80,000 in the mutual fund to obtain a total interest of $12,200 in one year.

Related Questions

What is the number 0.093 expressed in Scientific notation?
A. 9.3 * 10^2
B. 0.93 * 10^1
C. 9.3 * 10^-3
D. 9.3 * 10^-2

Answers

0.093 expressed in Scientific
=
9.3 x 10^-2

answer
D. 9.3 * 10^-2

Option D is correct. 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex].

To express the number 0.093 in scientific notation, we need to determine the coefficient and exponent.

0.093 can be written as 9.3 multiplied by a power of 10.

Since 0.093 is less than 1, the exponent should be negative.

To shift the decimal point to the right to form the original number, we move it three places to the right:

[tex]0.093 \rightarrow 9.3 \times 10^{-2}[/tex]

Therefore, 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex], option D is correct.

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Verify the identity Cotx/tanx+cotx = 1-sin^2x

Answers

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\\\\ -------------------------------\\\\ \cfrac{cot(x)}{tan(x)+cot(x)}=1-sin^2(x) \\\\\\ \textit{doing the left-side}\implies \cfrac{\frac{cos(x)}{sin(x)}}{\frac{sin(x)}{cos(x)}+\frac{cos(x)}{sin(x)}}\implies \cfrac{\frac{cos(x)}{sin(x)}}{\frac{sin^2(x)+cos^2(x)}{cos(x)sin(x)}}[/tex]

[tex]\bf \cfrac{\frac{cos(x)}{sin(x)}}{\frac{1}{cos(x)sin(x)}}\implies \cfrac{cos(x)}{\underline{sin(x)}}\cdot \cfrac{cos(x)\underline{sin(x)}}{1}\implies cos^2(x)\implies 1-sin^2(x)[/tex]

Write the equation for the following relation. Include all of your work in your final answer. Submit your solution. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}

Answers

First, we will notice that while the value of x increases by 1, the corresponding value of y increases by 4. This means that this is a linear relation.

The general equation for linear equations is : y = mx + c where m is the slope and c is the y-intercept

To get the slope, we will need to use two points. Let's take the first and the last points: (1,0) and (4,12)
The slope is calculated as: (y2-y1) / (x2-x1)
Use the chosen points to substitute in the equation and get the slope as follows:
m = (12-0) / (4-1) = 12/3 = 4

Now, the equation of the line became: y = 4x + c

The given points all satisfy the equation of the line, we can use any of them to substitute in the equation and get the value of c.
For instance, I will use the first point: (1,0)
y = 4x + c
0 = 4(1) + c
c = -4

The equation of the line is:
y = 4x - 4

Plot the x- and y-intercepts to graph the equation. y=−12x−3

Answers

x-intercept: (1/4) ,0
y-intercept: (0, -3)

Keywords

x-intercept, y-intercept, linear equation, graphing tool

we know that

The y-intercept is the value of y when the value of x is equal to zero

The x-intercept is the value of x when the value of y is equal to zero

In this problem we have

[tex]y=-12x-3[/tex]

Step 1

Find the x-intercept

For [tex]y=0[/tex]

find the value of x

[tex]0=-12x-3[/tex]

[tex]12x=-3[/tex]

[tex]x=-0.25[/tex]

The x-intercept is the point [tex](-0.25,0)[/tex]

Step 2

Find the y-intercept

For [tex]x=0[/tex]

find the value of y

[tex]y=-12*0-3[/tex]

[tex]y=-3[/tex]

The y-intercept is the point [tex](0,-3)[/tex]

Step 3

With the point [tex](-0.25,0)[/tex] and the point [tex](0,-3)[/tex]

Plot the linear equation

Using a graphing tool

see the attached figure

therefore

the answer in the attached figure

Two pounds of bananas cost $1.16 what would be the cost of 5pounds s of bananas

Answers

If 2 lb of bananas cost $1.16, then each pound costs $0.58.

0.58 * 5 = 2.9

So 5 lb of bananas will cost $2.90.

Hope this helps!

The cost of 5 lbs of bananas would be $2.90.

The price of one share of a stock fell $12.50 each day for 8 days. Which expression represents this situation?

Answers

12.50 x 8 = 100 This is the answer

" $12.50 x 8 " is an expression to use.

The table shows the steps for solving the given inequality for x.

−3(4−6x)
Select the reason for each step from the drop-down menus.

Answers

step        justification

- 3 (4 - 6x) < x + 5

- 12 + 18x < x + 5                 distributive property (to solve the left side)

-12 + 17x < 5                        subtraction property of equality (to transpose x
                                             from right to left side)

                                              subtraction of like terms (18x - x = 17x)

17x < 17                                addition property of equality (to tranpose - 12
                                              from left to right side)

                                              addition of like terms (12 + 5 =17)

x < 1                                  division property of equality

Answer:step justification

- 3 (4 - 6x) < x + 5

- 12 + 18x < x + 5 distributive property (to solve the left side)

-12 + 17x < 5 subtraction property of equality (to transpose x

from right to left side)

subtraction of like terms (18x - x = 17x)

17x < 17 addition property of equality (to tranpose - 12

from left to right side)

addition of like terms (12 + 5 =17)

x < 1 division property of equality

Step-by-step explanation:

Complete the sentence using one of the words below in 10/6 the 10 is the

Answers

The 10 Is The Numerator

Stuck on this question. Any help would be appreciated.

Answers

Solving the 2nd equation for r results in
10-2h
r = --------------
5
(10-2h)^2
Then r^2 = ----------------
25

Substitute this r and this r^2 into the first equation and simplify. This will result in a formula for V as a function of h (V in terms of h).

2x^5+12x^4+16x^3-12x^2-18x=0

Answers

[tex]2x^5+12x^4+16x^3-12x^2-18x=0 [/tex]

if today is wednsday what day will it be in 100 days and why

Answers

the day would be friday because there are 7 days in a week and in fourteen weeks on wednesday would be 98 days so add two more days which would be friday which is also 100 days

Bonswa. How are you today?

We know that every week (every seven days) it will be Wednesday if today is Wednesday. So, how may weeks are in 100 days? 14. Why? Because 14(7) = 98. So, in order to get to 100 we must add 2. So what is Wednesday plus two more days? Friday. So if today is Wednesday it will be Friday in 100 days. Why? Well, that's how our calendar is set up.

Can someone please solve this?

Answers

multiplicity of a root means, is there that many times.

[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=2\implies &\begin{cases} x-2=0\\ x-2=0\\ x-2=0 \end{cases} \end{cases} \\\\\\ (x-3)(x-2)~~(x-2)(x-2)=\textit{original polynomial} \\\\\\ (x^2-5x+6)~~(x^2-4x+4)=y \\\\\\ x^4-4x^3+4x^2-5x^3+20x^2-20x+6x^2-24x+24=y \\\\\\ 1x^4-9x^3+30x^2-44x+24=y[/tex]

Sampling is ordinarily used when the number of items comprising the population is relatively small.

Answers

I believe this statement is false, and that sampling is used when the number of items in a population are fairly large. One would use a sample to represent some form of measurement or test so that it can be applied to the larger number of same objects.

The ordered pair (2, 1) is a solution of a direct variation equation. Write the equation and identify the constant of variation.

Answers

A direct variation equation takes the form "b = ka," where the k is the constant of variation. In this case, 1 (b) is one-half as large as 2 (a), so the constant will be 0.5. This would allow the equation to be written as "b = 0.5a," and the constant of variation in this equation is 0.5.

Find the maximum and minimum values of the function.
y=7cosx

Answers

The Maximum and Minimum can not be determined on this problem because it isn't a quadratic function. Graphed, the highest point is 7 and lowest is -7 in a repeated mountain shape. Hope this helps.

The range of cos x is -1 to + 1

So maximum of 7 cos x = 7 and minimum is -7.

Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weight of the carrots she bought is 28 kilograms. How many kilograms of carrots will Jennifer get ?

Answers

since they share it equally
28/4=7

Y=2x^2-x-10 write in intercept form

Answers

y-intercept: Let x = 0 and solve for y. Then y =2(0)^2 -(0) - 10 = -10. The y-intercept is (0,-1).

x-intercept: Let y = 0 and solve for x.
Then 0 = 2x^2 - x - 10. a=2, b= -1 and c = -10.
-(-1) plus or minus sqrt[ (-1)^2 - 4(2)(-10)
Then x = ------------------------------------------------------------
2(2)
1 plus or minus sqrt(81) 1 plus or minus 9
x = ----------------------------------- = ---------------------------
4 4

Calculate the 2 x-values. Let's call them "a" and "b." Then the x-intercepts (there are 2) are

(a, 0) and (b, 0)

What is the solution set of the equation
X^2+3x-4=6

Answers

Two solutions were found : x = 5; x = -2. Reformatting the input : Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". Rearrange: Rearrange the equation bAnswer:

Step-by-step explanation:Two solutions were found : x = 5; x = -2. Reformatting the input : Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". Rearrange: Rearrange the equation b

A new iPhone user receives an average of 4.2 phone calls per hour. The calls occur randomly in time so if X = the number of calls received in an hour, then we can assume that X has a Poisson distribution with parameter λ = 4.2. Let Y = the number of phone calls received in a day. Assume all necessary independence in the following.
a. Y also has a Poisson distribution. What is the λ for Y?

b. What is the standard deviation of X?

c. What is the standard deviation of Y?

d. What is the probability that no calls are received in an hour?

e. What is the probability that more than 120 calls are received in a day?

f. What is the probability that Y is between 90 and 110 inclusive? (i.e. 90 ≤ Y≤110)

g. What is the variance of square root of 2Y?

h. Assume this distribution holds for all hours and days and that one call is independent from another. What is the probability that 120 or fewer calls are received for every day of this week? (Assume appropriate independence

Add any comments below.

Answers

Part A:

Given that Y is the number of phone calls received in a day and that a new iPhone user receives an average of 4.2 phone calls per hour.

Thus, the average number of phone calls received in a day is 4.2 * 24 = 100.8

Therefore, the λ for Y is 100.8

Part B:

The standard deviation of a Poisson distribution is given by

[tex]\sigma=\sqrt{\lambda}[/tex]

Thus, the standard deviation of X is given by

[tex]\sigma=\sqrt{4.2}=2.05[/tex]

Therefore, the standard deviation of X is 2.05.

Part C:

The standard deviation of Y is given by

[tex]\sigma=\sqrt{100.8}=10.04[/tex]

Therefore, the standard deviation of X is 10.04.

Part D:

The probability of a Poisson distribution is given by

[tex]P(X=x)=e^{-\lambda} \frac{\lambda^x}{x!} [/tex]

where, x is the number of occurence of the event in the given period.

Thus, the probability that no calls are received in an hour is given by

[tex]P(X=0)=e^{-4.2} \frac{(4.2)^0}{0!} =0.015[/tex]

Therefore, the probability that no calls are received in an hour is 0.015

Part E:

We approximate the Poisson distribution using Normal distribution by noting that for a Poisson distribution

[tex]\mu=\lambda \\ \\ \sigma^2=\lambda \\ \\ \sigma=\sqrt{\lambda}[/tex]

The probability of a normal distribution is given by

[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]

Thus, the probability that more than 120 calls are received in a day is given by

[tex]P(X\ \textgreater \ 120)=1-P(X\leq120) \\ \\ =1-P\left(z\leq \frac{120-100.8}{10.04} \right)=1-P(z\leq1.912) \\ \\ =1-0.97208=0.0279[/tex]

Therefore, the probability that more than 120 calls are received in a day is 0.0279

Part F:

We also approximate this using Normal distribution

The probability of a normal distribution between two value (a, b) is given by

[tex]P(a\ \textless \ X\ \textless \ b)=P\left(z\ \textless \ \frac{b-\mu}{\sigma} \right)-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]

Thus, the probability that Y is between 90 and 110 inclusive is given by

[tex]P(90\leq X\leq 110)=P\left(z\leq \ \frac{110-100.8}{10.04} \right)-P\left(z\leq \frac{90-100.8}{10.04} \right) \\ \\ =P(z\leq0.916)-P(-1.076)=0.82025-0.14103=0.67922[/tex]

Therefore, the probability that Y is between 90 and 110 is 0.67922

Part G:

The variance of aY is given by

[tex]Var(aY)=a^2Var(Y)[/tex]

Thus, the variance of [tex] \sqrt{2} Y[/tex] is given by

[tex]Var( \sqrt{2} Y)=( \sqrt{2} )^2Var(Y)=2(100.8)=201.6[/tex]

Therefore, the variance of [tex] \sqrt{2} Y[/tex] is 201.6

Part H:

We approximate this using Normal distribution

The probability of a normal distribution is given by

[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]

Thus, the probability that 120 or fewer calls are received in a day is given by

[tex]P(X\leq120)=P\left(z\leq \frac{120-100.8}{10.04} \right) \\ \\ =P(z\leq1.912)=0.97208[/tex]

Since, this distribution holds for all hours and days and one call is independent from another. Assuming that there are seven days in a week.

The probability that 120 or fewer calls are received for every day of this week is given by

[tex](0.97208)^7=0.8202[/tex]

Therefore, the probability that 120 or fewer calls are received for every day of this week is 0.8202

what square root lies between 17 and 18

Answers

easy
if x is the number
sqrt x is between 17 and 18

17<√x<18
squaer the whole thing
289x could be 300
it could be sqrt of 300
√300=10√3

one is 10√3

Simplify 3 + c (8n + 4) + 9n

A. 49n + 20
B. 3+33n
C. 25n + 11
D. 19n + 7

Answers

c is the answer to your question

Well first you need to distribute the (c) to the 8n+4. So then you you would get 8nc+4c+9n+3. Not unless that (c) is suppose to be a number.

Point P is reflected across two lines. Point A is its reflection image. Which two lines is point P reflected across?

x = 3 and y = 2

x = -2 and y = 2

x = 3 and y = -3

x = -2 and y = -3

Answers

the correct answer would be x=3 and y=2

Answer: The two lines are x = -2 and y = 2.

Step-by-step explanation: Given that the point P on the co-ordinate plane is reflected across two lines and A is its image after the reflection.

We are to find the two lines across which the point P is reflected.

The co-ordinates of point P are (0, 0) and the co-ordinates of its image A after reflection from two lines are (-4, 4).

From the given figure, we can note that

the first line of reflection is y = 2. Point C(0, 4) is the image after reflection from first line.

The second line of reflection is x = -2. Point A(-4,4) is the final image after second reflection.

Thus, the two lines are x = -2 and y = 2.

State the slope and the y-intercept of each given graph plz help i really dont know how to do this

Answers

For graph 1, the y-intercept is (0,1) and the slope is 1.
For graph 2, the y-intercept is (0,4) and the slope is -1.
For graph 3, the y-intercept is (0,-4) and the slope is -2.
For graph 4, the y-intercept is (0,-3) and the slope is 3/2.
For graph 5, the y-intercept is (0,4) and the slope is 2.
For graph 6, the y-intercept is (0,3) and the slope is -3/2.

(By the way, since the graphs aren't labeled as numbers, I went from left to right, and then down, and then left to right again).

Now, here's the explanation:

Solving for y-intercept is easier than it sounds. All you need to do is mark the point where the line crosses the y-axis (vertical axis).

Solving for slope is just rise/run. For example, in graph one, the points on the line went up one and then to the right one.

So, 1/1 = 1.

When a slope moves down or to the left, it will be negative. However, that's only if the rise OR run is down/left. If both are negative, the two will cancel each other out to make a positive.

Hope this helped!!

If each weighs 2/3 pound, how many potatoes are there in a 50-pound case?

Answers

The number of potatoes that are there in a 50-pound case are 75 potatoes.

In Mathematics and Euclidean Geometry, an expression simply refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Since each potato weighs 2/3 pound, the number of potatoes that are there in a 50-pound case can be modeled by the following expression;

Number of potatoes = 50 ÷ 2/3

Number of potatoes = 50 × 3/2

Number of potatoes = 150/2

Number of potatoes = 75 potatoes.

I don't get why price(max)=$80
Can someone help me

Answers

check the picture below.

as a matter of elasticity, if you sell 100 popsicles for $1, you get a revenue of $100.

However, if your price goes to $5 per popsicle, then folks will begin to find it too expensive and won't be buying 100, but just 15, so, even though $5 is a higher price, 5 * 15 is a much smaller revenue than 1 * 100.

Given four int values x1, x2, y1, y2 write the code to compute the distance between the two point

Answers

In which language?
Please tell me the language java, c++, cetc?

how many square inches does an "11x13" area encompass

Answers

143 square inches

Answer:

143 square inches

Step-by-step explanation:

The area of encompass is given by 11 * 13 inches.

Here the length = 11 inches and the width = 13 inches.

The length and width have different numbers, so the given figure is a rectangle.

Area of a rectangle = length * width

Area of the figure = 11*13

= 143 square inches

The unit for the area is "square"

The units are given in inches, therefore, it is 143 square inches.

Suppose △DEF≅△MNO.
Which congruency statement is true?

A) DF≅NO
B) DE≅MN
C) EF≅MN
D) EF≅MO

Answers

the answer is b. would u like to see steps or are you good?

Final answer:

When triangles are congruent, their corresponding sides and angles are the same. Hence in congruent triangles △DEF and △MNO, side DF is congruent to side MN, thus option B) DE≅MN is the correct answer.

Explanation:

In the case of congruent triangles, the corresponding sides and angles are essentially the same. Therefore, we must match up the corresponding sides. A correct statement would be that side DF, from the first triangle, is congruent to side MN, from the second triangle. Hence the correct option is B) DE≅MN.

Additionally, DE would be congruent to MN, and EF would be congruent to NO, completing the congruence between triangles △DEF and △MNO.

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the sum of 2 3/5 + (-1/5) write in simplest form

Answers

The answer is 2 2/5. Need an explanation

2 2/5 that’s the answer

tep 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________

Answers

Step 4: 3>x. (The sign flips because you divided a negative)
I hope this helps love! :)

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