Phyllis invested 800 dollars into two different accounts, a portion earning a yearly interest rate of
4
percent per year compounded monthly and the rest earning a rate of
6
percent per year compounded quarterly

After 12 years the investments were worth $1579.05. How much money did she invest at each rate

Answers

Answer 1

The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.

Calculation of the total capital invested

The time the investment lasted= 12 years.

Simple interest = 1579.05 - 800= $779.05

The principal capital= $800

Rate of the both capital invested;

= SI × 100/P ×T

= 779.05 × 100/800 × 12

= 77,905/9600

= 8.11%

To find the amount of money that Phyllis invested at each given rate,

Rate 1 = 4/8.11× 800

= 3200/8.11

= $394.57

Rate 2 = 6/8.11× 800

= 4800/8.11

= $591.86

The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.

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Related Questions

Find the equation of the exponential function represented by the table below:
Y
8
0
1
2
3
3
12
48
192

Answers

no I dont feel like it is the answer

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101.
Find the substance's half-life, in days. Round your answer to the nearest tenth.

Answers

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.

What is the formula for half-life?

Exponential decay obeys the equation

[tex]m(t) = m_0 e^{-kt}[/tex]

where t = time, days

Given:

Initial mass, m₀ = 8 g

Decay constant, k = 0.101

For half-life, the mass is m = m₀/2.

Therefore,

[tex]m(t) = m_0 e^{-kt}[/tex]

e^{-0.101t} = 1/2

-0.101t = ln 0.5

t = ln 0.5/-0.101

t = 2.98

Therefore, The half-life is 2.98 days.

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7,000 dollars is placed in a savings account with an annual interest rate of 3%. If no money is added or removed from the account, which equation represents how much will be in the account after 7 years?

Answers

Answer:

See below

Step-by-step explanation:

Interest   3%   in decimal form is  .03

  interest in ONE year    7000 * .03

         interest in SEVEN years   7000 * .07 * 7

           this is added to the original deposit of 7000

              to become   7000 + 7000 * .03 * 7

                                        or  7000 ( 1 + .03*7 )

                                              or   7000 ( 1.21 ) = $ 8470

IF the interest is compounded

   the money in the account will be    7000 ( 1+.03)^7  

A company orders 24 boxed lunches from a deli for $177.60. If each boxed lunch
costs the same amount, what is the unit cost of each boxed lunch?

Answers

It’ll cost $44.40 per box
Because 177.60 divided by 4 is 44.40

Answer: $7.40

Step-by-step explanation:

You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.

Work out the length of
x.
Give your answer rounded to 3 significant figures.

Answers

The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.

What is a Pythagoras theorem?

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The right-angle triangle is given below.

The given triangle is an isosceles right triangle.

P = B = x

Then we have

1.8² = x² + x²

2x² = 3.24

 x² = 1.62

   x = 1.27 cm

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Sophia determined that the expression Negative (4 x minus 5) + 2 (x minus 3) is equivalent to –2x – 5 by using the steps below.


Expression: Negative (4 x minus 5) + 2 (x minus 3)
Expression: –2x – 5
Step 1:
Choose a value of x
Choose x = 1.
Choose x = negative 1.
Step 2: Substitute
Negative (4 (1) minus 5) + 2 (1 minus 3)
Negative 2 (negative 1) minus 5
Step 3: Evaluate
Negative (4 (1) minus 5) + 2 (1 minus 3) = negative (negative 1) + 2 (negative 2) = negative 3
Negative 2 (negative 1) minus 5 = 2 minus 5 = negative 3
Step 4:
Compare
Since –3 = –3, the two expressions are equivalent.

Which explains whether Sophia is correct?
She is correct because the value of the two expressions are the same in Step 3.
She is correct because she substituted opposite values in Step 1.
She is not correct because she did not substitute the same number in both expressions in Step 1.
She is not correct because she did not perform the correct order of operations in Step 3.

Answers

The correct statement is:

"She is not correct because she did not substitute the same number in both expressions in Step 1."

Is Sophia correct?

First, let's see if Sophia is correct.

She starts with the expression:

-(4x - 5) + 2*(x - 3) = -2x - 5

Expanding the left side:

-4x + 5 + 2x - 6 = -2x - 5

-2x -1 = -2x - 5

So the constant term is different.

Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).

"She is not correct because she did not substitute the same number in both expressions in Step 1."

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simplify (4x^3)^2 (3x^5)

Answers

Answer:

16x^6(3x^5)

48x^11

PLEASE HELP!!!!!!!!!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!!!!!A moving-van rental company uses the polynomial 110 + 0.65(m – 200) to calculate the rental charges if a customer drives a van more than 200 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 200 miles in one day.

Answers

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $110 per hour. The mechanics worked for a combined total of 35 hours, and together they charged a total of $3550. How long did each mechanic work?

Firstmechanic:hours
Secondmechanic:hours

Answers

Answer:

1st mechanic:20hours

2ndmechanic:15hours

Step-by-step explanation:

1stmechanic:20hours=20x95

                                   =$1900

2nd mechanic:15hours=15x110

                                     =$1650

total=$1900+$1650

       =$3550

The y-intercept is the place where a line crosses the y-axis. hat is true about the y-intercept?
A. It always has an x coordinate of 0.
B. It always has any coordinate of 0
C. Both x and y coordinates are 0.

Answers

Answer:

It always has an x coord of 0

The first step that we must take before attempting to solve a problem is to understand what it is asking for and what is given to us to help solve the problem.  Looking at the problem statement, we can see that they are asking what is true about the y-intercept.  We are given the information that the y-intercept is the place where a line crosses the y-axis.

Now that we have collected all that information, let us move onto understanding and solving the problem.  So first of all, using the information that was given to us, we know that the y-intercept is the place where a line crosses the y-axis.  The y-axis occurs where the x-coordinate is 0 and the x-axis occurs where the y-coordinate is 0.  Therefore, the option that would best fit the description that we have would be option A, it always has an x coordinate of 0.

what is the answer ???

Answers

Answer: Heyaa!~

                  - Write 63 as the product of prime factors -

Since, the prime factors of 63 are 3, 7. Therefore, the product of prime factors = 3 × 7 = 21.

              - Write the prime factors in ascending order -

                     I think it would be 3/7

         -   what's the highest common factor of 63 and 105   -

                21,  divides both 63 and 105, i.e., 21.

             Hopefully this helps you! ^^^

HELP!!!!!! 100 POINTS!!!!!!
Kyle and Lauren teach swimming lessons during the summer. Kyle has 8 classes with g students in each class and 6 classes with h students in each class. Lauren has 5 classes with g students in each class and 10 classes with h students in each class.

If Kyle has a total of 62 students and Lauren has a total of 70 students, which equation shows the solution to the system of equations that represents this situation?

Answers

The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

Kyle and Lauren teach swimming lessons during the summer. Kyle has 8 classes with g students in each class and 6 classes with h students in each class. Lauren has 5 classes with g students in each class and 10 classes with h students in each class.If Kyle has a total of 62 students and Lauren has a total of 70 students,

The equation made by the given situation is:-

For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-

8g   +  6h  =  62

Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-

5g  +  10h  =  70

Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

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what is the volume of the solid

Answers

Answer:

A.264

Step-by-step explanation:

((Area Of triangle*height)=Volume

Area of triangle is the base of the triangle multiplied by height of triangle divided by 2

((8*6)/2)*11=264

EASY POINTS LM is the midsegment of & ABC. If IM is 8 centimeters long, how long is AC

Answers

I think it's 12 because here it comes out

6-2 6 grade home work

Answers

Answer:

list five solution to the energy crisis of nepal

What additional piece of information would prove △LMK≅△NMK by Side Angle Side?

Answers

Answer:

angle M

Step-by-step explanation:

if you are using side angle side the two sides may be

line LK and NK

and angle M

I need help I don’t understand please help

Answers

put 8 on the y axis and 7 on the x axis for the first one and -2 on the y axis and 10 on the x axis for the second one ( you can see the y and x axis on the graph)

What is the solution to this equation? (1/27)2-x =9^3x

Answers

Answer:

 x = -2

Step-by-step explanation:

Prime factorize, 27 and 9

27 = 3 *3 * 3 = 3³

  9 = 3*3 = 3²

[tex]\sf \left(\dfrac{1}{27}\right)^{2-x}=9^{3x}\\\\[/tex]

 [tex]\left(\dfrac{1}{3^3}\right)^{2-x}=9^{3x}\\\\(3^{-3})^{2-x}=(3^2)^{3x}\\\\3^{(-3)*(2-x)}=3^{2*3x}\\\\3^{-6+3x} = 3^{6x}[/tex]

Bases are same, so now compare the exponents

     -6 + 3x = 6x

            3x = 6x + 6

       3x - 6x = 6

             -3x = 6

               x  = 6/(-3)

               [tex]\sf \boxed{\bf x = -2}[/tex]

Exponent law:

         [tex](x^m)^n=x^{m*n}\\\\\left(\dfrac{1}{a^{m}}\right)=a^{-m}\\[/tex]

Bulls can develop respiratory issues as they get older. This may compromise their ability to breath properly which affects their energy level and overall health. A researcher wishes to conduct a study to find which of two injection therapies, Therapy A or Therapy B, is more effective in improving respiratory health. A total of 180 bulls that are at least 12 years old will be randomly selected from ranches in the state of Texas. The researcher will get consent from all owners, treat the bulls for eight months and evaluate changes in respiratory health.

Part A: How would the study benefit from adding a control group? (2 points)

Part B: What is the best way to randomly place the bulls into the Therapy A, Therapy B, and control groups? (4 points)

Part C: The researcher wants to use a blocking variable to place the bulls into groups instead of doing it randomly. He decides to block either by breed or ranch. Explain which would be the best blocking method. (4 points)

Answers

The study benefit from adding a control group as it would help in the correlation

What is a control group?

A control group is s used to establish a cause-and-effect relationship by isolating the effect of an independent variable.

The best way to randomly place the bulls into the Therapy A, Therapy B, and control groups is random testing. The best blocking method will be breeding.

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the perimeter of a rectangular field is 302 yards. if the length of the field is 92 yards what is its width

Answers

Answer:

the width is 59

Step-by-step explanation:

302/2-92=59

Hi there !
What is a Pythagoras theorem ?
Nonsense = Reported
Thank you​

Answers

Answer:

Hi! I think you are referring to the Pythagorean Theorem.

Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.

The formula is a squared + b squared = c squared

If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:

3 squared + 4 squared = x squared

(Let x =  the longer side)

3 squared = 9

4 squared = 16

9+16 = x squared

25 = x squared

x =  5

So there you go, that's the Pythagorean theorem.

Let me know if this helped!

Answer:

a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Step-by-step explanation:

add 6370 square to 6370 square

Answers

i’m not sure if this is what you meant

A recipe calls for (1 3/8) cups of sugar to make 2 dozens cupcakes. How much sugar is needed to make 60 cupcakes?

Answers

Answer:

55/16 cups or 3.4375 cups

Step-by-step explanation:

there are 5 dozens (12) in 60, so there are 2.5 2 dozens in 60, so you would multiply 1 3/8 by 2.5 to find how many cups are needed in 60 cupcakes because 1 3/8 cups is for 2 dozen cupcakes

What are the zeros of the quadratic function f(x)=8^2-16-15

Answers

Answer:

C)

Step-by-step explanation:

f(x)=[tex]8x^{2} -16x-15[/tex]
[tex]8x^{2} -16x-15=0[/tex]
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]  ,  a=8, b= - 16, c= - 15

[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4*8*(-15)} }{2*8} = \frac{16+-\sqrt{736} }{16} =\frac{16+-4\sqrt{46} }{16} = 1 +- \frac{\sqrt{46} }{4} = 1+- \frac{\sqrt{23} \sqrt{2}}{2\sqrt{2} \sqrt{2} } =1+-\frac{\sqrt{23} }{2\sqrt{2} } = 1+-\frac{\sqrt{23} }{\sqrt{8} }[/tex]

Which statement best describes Inflation?
О А. Inflation decreases the amount of goods and services that can be purchased with a dollar.
Inflation Increases the amount of goods and services that can be purchased with a dollar.
Inflation increases the purchasing power of a dollar.
O C.
OD.
Inflation decreases the prices of goods and services.
O E. Inflation doesn't affect the prices of goods and services but increases wages.

Answers

Answer:

A

Step-by-step explanation:

Inflation decreases the amount of goods and services that can be purchased with a dollar.

SHOW ALL WORK PLEASE!!!!!!!

The rat population in a major metropolitan city is given by the formula n(t)=89e^0.02t where t is measured in years since 1992 and n(t) is measured in millions

What was the rat population in 1992?

What does the model predict the rat population was in the year 2003?

Answers

Answer:

See below ~

Step-by-step explanation:

What was the rat population in 1992?

⇒ t represents the years after 1992

⇒ So, in 1992, t = 0

⇒ Apply in the formula

⇒ n(0) = 89e^(0.02 × 0)

⇒ n(0) = 89e⁰

⇒ n(0) = 89,000,000

The rat population in 1992 was 89,000,000.

===========================================================

What does the model predict the rat population was in the year 2003?

⇒ Number of years after 1992 : 2003 - 1992 = 11

⇒ Substitute for t in the formula

⇒ n(11) = 89e^(0.02 × 11)

⇒ n(11) = 89e^(0.22)

⇒ n(11) = 89 × 1.24607673

⇒ n(11) = 110,900,829 rats

The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.

Answer:

(a) 89,000,000 rats

(b) 110,900,829 rats

Explanation:

Given equation:

n(t)=89e^0.02t

To find the initial population (1992):

insert t = 0

n(0) = 89e^0.02(0) = 89 million ≈ 89,000,000

To find the rat population in 2003 (after 11 years):

insert t = 11

n(11) = 89e^0.02(11) = 89e^0.22 ≈ 110,900,829

Given: ABCD is a parallelogram.

Prove: ∠A ≅ ∠C and ∠B ≅ ∠D

Parallelogram A B C D is shown.

By the definition of a ▱, AD∥BC and AB∥DC.

Using, AD as a transversal, ∠A and ∠
are same-side interior angles, so they are
. Using side
as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary.

Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠
.

Answers

A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.

How to show the proof?

In the given figure, AB||DC. AD is the transversal, such that:

∠A + ∠D = 180-degrees.

The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.

From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.

From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.

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Match each graph with the function it represents.

Answers

A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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Solve for x
(2^2/x) (2^4/x) = 2^12

Answers

[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12} [/tex]

Now, since the base on both sides are equal, therefore their exponents are equal as well ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6}{x} = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{6}{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{1}{2} [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:x = 0.5[/tex]

Hope you got the required Answer ~

can you please help me? 2.1.3

Answers

[tex]~~~~~~2I_2 - A\\\\\\=2\begin{bmatrix}1&0\\0&1 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2&0\\0&2 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2-4&0-2\\0-3&2+3 \end{bmatrix}\\\\\\=\begin{bmatrix}-2&-2\\-3&5 \end{bmatrix}[/tex]

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