Harrison has an account with the balance of $155.59 this account has an interest rate of 9.4 % compound annually and the initial investment was two years ago. How much was the initial investment?
Answers
To answer this problem, we need to use the compound interest formula, which is
\(A=P(1+\frac{r}{n})^{nt}\)Where A represents the final amount, P represents the principal(initial investment), r represents the interest rate in decimals, n represents the number of times interest is compounded per unit t, and t the amount of time.
We have the final balance of Harrison's account, which is our value A
\(A=155.59\)The interest rate is 9.4%. To convert a percentage to a decimal, we just divide the percentage value by 100.
\(r=9.4\%=\frac{9.4}{100}=0.094\)The initial investment was two years ago, therefore, the time period is 2.
\(t=2\)And since the interest is compounded anually and the time period unit is year, we have
\(n=1\)Plugging all those values in the formula, we have
\(155.59=P(1+\frac{0.094}{1})^{1\cdot2}\)Solving for P, we have
\(\begin{gathered} 155.59=P(1+\frac{0.094}{1})^{1\times2} \\ 155.59=P(1.094)^2 \\ P=130.001102908... \\ P\approx130.00 \end{gathered}\)The initial investment was $130.00.
Related Questions
Three people spend money on a vacation. The expression −1,0263 represents the amount of money each person spends on the vacation. Which expression is equivalent to −1,0263 ?
Answers
Answer:-(-1,026/3
Step-by-step explanation:
6.
Identify the axis of symmetry of the parabola.
A. x = 3
B. y = −3
C. y = 3
D. x = −3
Answers
Answer:
D.
Step-by-step explanation:
D. x = −3
Letter d is the answer
A sweater normally costs
$50 dollars. If someone
purchases it for $30, what
percent of the total cost
was taken off of the regular
price?
Answers
Answer:
I think 40%
Step-by-step explanation:
Answer:
I think 20%. If we subtract we will get that was taken
Maggie's brother is 12 years younger than twice her age. The sum of their ages is 30.
How old is Maggie?
Answers
Maggie's age is 14 and her brother's age is 16.
Step-by-step explanation:This is a classic problem of linear equations systems.
1. Setting up the equations.
Let "m" be the age of Maggie.
Let "b" be the age of Maggie's brother.
"Maggie's brother is 12 years younger than twice her age", hence:
Equation 1: \(2m-12=b\)
"The sum of their ages is 30." Hence:
Equation 2: \(m+b=30\)
2. Solve "equation 2" for b.\(m+b=30\\ \\b=30-m\)
3. Take the expression found for b in step 2 and plug it in as b on equation 1.\(2m-12=30-m\)
4. Add m to both sides of the equation.\(2m+m-12=30-m+m\\ \\3m-12=30\)
5.Add 12 to both sides of the equation.\(3m-12+12=30+12\\ \\3m=42\)
6. Divide both sides by 3.\(\frac{3m}{3} =\frac{42}{3} \\m=14\)
Hence, Maggie's age is 14.
7. Use Maggie's age to find her brother's age through equation 2.\(14+b=30\\ \\b=30-14\\ \\b=16\)
8. Verify."Maggie's brother is 12 years younger than twice her age. "
a. Find the double of Maggie's age.
14 * 2=28
b. Subtract 12.
28-12= 16
Is this the age of Maggie's brother? Yes.
c. Add up Maggie and her brother's age.
"The sum of their ages is 30."
14+16=30. Is the sum of their ages 30? Yes.
9. Present your results.
Maggie's age is 14 and her brother's age is 16.
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URGENT PLEASE HELP !!
In a recent election, there were six candidates and 4700 total votes. The circle graph below summarizes the votes by candidate.
The central angle for the Choi slice is 93.6°. How many of the votes did Choi get?
Answers
Based on the central angle for the Choi slice of 93.6°, the number of votes that Choi got was 1,222.
How is the number of votes determined?The central angle representing Choi's votes is converted to a percentage of the total by dividing it by 360 degrees, and multiplying by 100.
The percentage is applied (multiplication) to the total votes of the six candidates to get Choi's total votes in the recent election.
The central angle for Choi = 93.6°
The total degrees of a circle = 360°
The fraction or percentage of the circle Choi got = 0.26 or 26% (93.6°/360°)
The total number of votes for the six candidates = 4,700
The number of votes Choi got = 1,222 (0.26 x 4,700)
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Ezra works two summer jobs to save for a laptop that costs at least $1100 he charges $15/hr to mow lawns and $10 an hour to walk dogs. Recall the inequality that represents this situation: 15x + 10y >_ 110
is (60,20) a solution? How do you know? What does this power represent?
Answers
Answer:
The inequality that represents this situation is 15x + 10y ≥ 1100, since Ezra needs to earn at least $1100 to buy the laptop.
To check if (60, 20) is a solution to this inequality, we need to substitute x = 60 and y = 20 into the inequality and see if it is true:
15(60) + 10(20) ≥ 1100
900 + 200 ≥ 1100
1100 ≥ 1100
Since 1100 ≥ 1100 is true, this means that (60, 20) is a solution to the inequality. This means that if Ezra works 60 hours mowing lawns and 20 hours walking dogs, he will earn enough money to buy the laptop.
The point (60, 20) represents the combination of hours worked for mowing lawns (x) and walking dogs (y) that will result in Ezra earning enough money to buy the laptop. The x and y values are the inputs or variables, while the inequality 15x + 10y ≥ 1100 is the constraint that must be satisfied. The solution (60, 20) is the output or result of the system of inequalities, and represents the combination of hours worked that will satisfy the constraint.
Figure A is similar to Figure B. What must always be true?
a.
The corresponding side lengths of A and B are proportional.
c.
The corresponding side lengths of A and B are equal.
b.
The corresponding side lengths of A are twice the corresponding side lengths of B.
d.
The corresponding side lengths of A are half the corresponding side lengths of B.
Answers
Option (a) is the correct answer. When two figures are similar, it means they have the same shape but different sizes.
How to solve the question?
In other words, their corresponding angles are congruent, and their corresponding side lengths are proportional.
Option (b) and (d) suggest that the corresponding side lengths of A and B are related by a constant factor (either 2 or 1/2). However, this is not necessarily true for all similar figures. The constant of proportionality can be any positive real number.
Option (c) suggests that the corresponding side lengths of A and B are equal, which means that A and B are not just similar but congruent. This is not necessarily true for all similar figures, as similar figures can differ in size.
Therefore, option (a) is the only answer that must always be true for similar figures. The corresponding side lengths of similar figures are proportional, which means that if one side of figure A is twice as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 2:1. Similarly, if one side of figure A is three times as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 3:1. This proportional relationship holds true for all pairs of corresponding sides in similar figures
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Option (a) is the correct answer. The corresponding side lengths of A and B are proportional, must always be true if Figure A is similar to Figure B.
How to find if the figure is similar?When two figures are similar, their corresponding angles are congruent, and their corresponding side lengths are proportional. This means that if we take any two corresponding sides of the figures, the ratio of their lengths will be the same for all pairs of corresponding sides.
Option b and d cannot be true, as they both suggest a specific ratio of corresponding side lengths, which is not necessarily true for all similar figures.
Option c is not necessarily true, as two similar figures can have corresponding side lengths that are not equal but still have the same ratio.
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write as a polynomial. a(a+9b)^2
Answers
First, you square (a+9b) which will become (a^2+81b^2)
Then, you multiply it by a and you will get a^3+81ab^2
what is the answer to 8x²+7y²-3x²+5y²=12
Answers
Answer:
-5x/12y
Step-by-step explanation:
What reasons can be given for the steps in solving the equation for x ?
Answers
The reasons for the steps are given below.
The value of x is -4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
-2(4x + 3) = 26
[ The distributive property of multiplication over addition ]
-2(4x) + -2(3) = 26
-8x - 6 = 26
[ Adding 6 on both sides ]
-8x - 6 + 6 = 26 + 6
-8x = 32
[ Divide -8 into both sides ]
-8x/-8 = 32/-8
x = -4
Thus,
The reasons for the steps are given above.
x = -4
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Hiii this due today can you draw a digram for 5 times 20 please THIS IS DUE TODAY THANK You
Answers
Answer:
draw the diagram and multiply 5x20
what is the sum of 2,888 and 74
Answers
Answer:
2962
Step-by-step explanation:
2 8 8 8
+ 7 4
----------------
2 9 6 2
2962
Step-by-step explanation:2888 +
74
---------
2962
8 + 4 = 12
8 + 1 + 7 = 16
8 + 1 = 9
What is the solution to the equation
2x=5
Answers
Answer:
5/2 or 2.5
Step-by-step explanation:
Divide both sides by 2.
A rectangle has a height of 362 and a width of 464 + 26 -6 what is the area?
Answers
Answer:
175,208 square units
Step-by-step explanation:
Lets calculate the width first:
464 + 26 - 6 = 484
The area is equal to the length times the width, so
362 x 484 = the area
= 175,208 square units
What is the factored form of the
polynomial? x^2+ 19x + 60
Help
Answers
Answer:
(x+15)(x+4)
Step-by-step explanation:
The mean life of a television set is 96 months with a variance of 225. If a sample of 76 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by greater than 1.3 months?Round your answer to four decimal places.
Answers
Answer:
0.4496
Step-by-step explanation:
Mean u = 96
Sd² = 225
Sd = √225
= 15
n = 76
Bar x is the mean
Bar x follows an approximately normal distribution
sd/√n = 15/√76
= 1.720618
The probability that bar x would differ from mean by less than -1.3
P(-1.3<z<1.3)
P(-1.3/1.720618 <z <1.3/1.720618)
= P(-0.756 < z < 0.756)
= P(z<0.756)-p(z<-0.756)
= 0.7752-0.2242
= 0.5504
To get the probability
1-0.5504
= 0.4496
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answers
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = \(\frac{sum}{count}\)
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = \(\frac{168}{7}\) = 24
1 point
Francis heard that a car stereo system was on sale for 30% off. If the sale price was $57.75, what was the original price of the stereo?
Answers
Answer:
The original price of the sterio was $82.50
Caroline is saving up to buy a new video game .she already has $45 and can save an additional $9 per week using money from her after-school job how much total money you would Caroline have after 9 weeks of saving? also write an expression that represents the amount of money Caroline would have saved in W weeks .
Answers
So, since W is weeks... and you have 9 weeks, you do (9x9)+45.
Then you get 81+45, which is 126. She will have $126 after 9 weeks
Which statement best explains how elasticity and incentives work together? An elastic good, such as a game, is more likely to respond to incentives. An inelastic good, such as a game, is more likely to respond to incentives. An elastic good, such as a game, is less likely to respond to incentives. An inelastic good, such as a game, is less likely to respond to incentives.
Answers
which statement best explains how elasticity and incentives work together
- answer: A. an elastic good, such as a game, is more likely to respond to incentives.
Incentives are applied to items that have high elasticity to increase the
number prospective consumers.
The statement that best explains how elasticity and incentives work together is; An elastic good, such as a game, is more likely to respond to incentives.Reasons:
Elasticity in quantity demanded is an indication that the quantity demanded
changes appreciably when other factors changes, such as the price of the
commodity.
A commodity that has elastic demand changes the quantity demanded
rapidly following a small change in another factor.
Examples of items that have elasticity are; Luxury goods, and some non-
essential goods such as a game, or a pleasure ride.
Due to the sensitivity of consumers to such items, consumers may be
made to order such items based on incentives and demand for elastic
goods can be made to increase due to added incentives.
Therefore, the correct option is; An elastic good, such as a game, is more
likely to respond to incentives.
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Researchers from a large community college in California are interested in understanding the demographics of students enrolled in their online classes. The researchers collected the following data for the 2017/2018 school year.
Male Female Total
Online Only 2,000 7,000 9,000
Online and in class 8,000 1,000 9,000
Total 10,000 8,000 18,000
What does the data suggest about the relationship between sex and enrollment?
a. Females are more likely to enroll in Online Only courses than males.
b. Females are more likely to enroll in Online and In Class courses than males.
c. There are more females enrolled at the community college than males.
d. Females are equally likely as males to enroll in an Online Only course.
Answers
Answer:
a. Females are more likely to enroll in Online Only courses than males.
Step-by-step explanation:
Given
The collected data
Required
Which of the options is true
(a): Female more likely in online only courses
In online courses, we have:
\(Female = 7000\)
\(Male = 2000\)
By comparison:
\(7000 > 2000\)
Hence, this statement is true
Other options are false
Write equivalent fraction with the given denominator.
Answers
Answer:
20/10
Step-by-step explanation:
2x10=20
Answer:
2 = 20/10
Step-by-step explanation:
The problem wants you to write a fraction that is equalavent to 2, but that has 10 as the denominator. I chose 20, because 2 x 10 = 20.
The lines given by the equation y = 9 - 1/3x and y = mx + b are perpendicular and intersect at a point on the x axis. What is the value of b?
Answers
Answer:
• Since these lines are perpendicular, their product of their gradients is negative one:
\( \dashrightarrow \: { \tt{m_{1} \times m _{2} = - 1 }}\)
• m1 is gradient of first line.
• m2 is gradient of second line.
\( \dashrightarrow \: { \tt{ - \frac{1}{3} \times m_{2} = - 1}} \\ \\ \hookrightarrow \: { \underline{ \tt{ \: \: m _{2} = 3 \: \: }}}\)
• since they intersect at a point on x-axis, y = 0
• Considering the first line: y = 9 - ⅓x
\(\dashrightarrow \: { \tt{0 = 9 - \frac{1}{3} x}} \\ \\ { \tt{x = 9 \times 3 = 27}}\)
point is (27, 0)
• Considering the second line: y = mx + b
\(\dashrightarrow \: { \tt{0 = (3 \times 27) + b}} \\ \\ { \tt{b = - 81}}\)
What are the domain and range of the function represented by the set of
ordered pairs?
K(-10, -6), (-4, -10), (3, 8), (9, -2)}
Answers
Answer:
A
Step-by-step explanation:
Domain is the first number in the ordered pairs and range is the second number. (I'm sorry if it's wrong)
Hope it helps!
Pleaseee help me I’ll give brainliest find the sum of 4x^2-7 and 6x^2-5
Answers
Answer:
10x² - 12
Step-by-step explanation:
4x² - 7 + 6x² - 5
10x² - 12
A bowl of soup at 95!C (too hot) is placed in a 22!C room. One minute later, the soup has cooled to 83!C. When will the temperature be 49!C (just right)?
Answers
Answer:
in 3 minutes and 50 seconds
Step-by-step explanation:
soup = 95c
after 1 minute = 83c
after 2 minutes = 71c
after 3 minutes = 59
soup cools down 0.2c in 1 seconds
so 10 seconds = 2c
in 3 minutes and 50 seconds = 49c
The temperature 49°C of soup bowl will be after 5.54 minutes
Newton law of coolingAccording to Newton's law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundingsThe formula is as follow:\((T-T_{s} )=(T_{0} -T_{s} )e^{-kt}\)
What are the steps to solve this problem?Given\(T =\) 83°C and 49°C
\(T_{s} =\) 22°C
\(T_{0} =\) 95°C
We have to find value of t for that first we will find value of k and applying all values in formula we get,(83-22)=(95-22)\(e^{-k}\)
∴ k = -ln (61/73)
Now,
(49-22) = \(e^{ln(61/73)t}\)
∴ t = \(\frac{ln (27/73)}{ln(61/73)}\)
∴ t = 5.54 minutes
So, after 5.54 minutes temperature will be 49°C
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Assume that t varies jointly as r and q2². If t=320 when r=5 and q = 4, what is the value of q when r= 1 and t= 196?
q=
Answers
Step-by-step explanation:
\(t = k(r)( {q}^{2} )\)
\(320 = k(5)( {4}^{2} )\)
\(320 = 80k\)
\(k = 4\)
\(196 = 4(1)( {q}^{2} )\)
\(49 = {q}^{2} \)
\(q = 7\)
Selected financial data for Amberjack Corporation follows.
Answers
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Define Decimal place?
A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32 etc. In the figure given above, the decimal point separates the whole number 42 from the fractional part . In words, it is written as Forty Two Point Eight Five.One decimal place to the left of the decimal point is the ones place. One decimal place to the right of the decimal place is the tenths place. Keep your eye on the 9 to see where the decimal places fall.Rounding a decimal number to two decimal places is the same as rounding it to the hundredths place, which is the second place to the right of the decimal point. For example, 2.83620364 can be round to two decimal places as 2.84, and 0.7035 can be round to two decimal places as 0.70.To learn more about decimal place refers to:
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solve for x and y triangle
Answers
Answer:
y=7, x=5
Step-by-step explanation: hope this helps
A and B are mutually exclusive events. P(A) = 0.20 and P(B) =
0.50.
What is P(A or B)?