Answer:
B. $25,069
Step-by-step explanation:
An interest of 6% per year, compounded monthly it means that he earns 6/12% = 0.5% of what he has invested every month.
If he invests x money what he will have the first month will be :
Money = x*(1+0.005)
The next month:
Money' = Money*(1+0.005) = x *(1+0.005)(1+0.005) = x* (1+0.005)^2
Therefore in this type of interest the formula is:
Money = x*(1+r)^n
Where:
x is the money invested the first time
r is the interest
n is the number of periods
For this problem:
x = what you have to find
r = 0.005
n = 3 years (1 period is 1 month) then the period is 36 months
Money = 30000
Replacing:
30000 = x * (1+0.005)^36
x = 25,069
Final answer:
To make a $30,000 down payment in three years with an account earning 6% interest compounded monthly, James needs to deposit approximately $25,189.06 today.
Explanation:
Calculating the Present Value for a Future Goal
To achieve a $30,000 down payment in three years with an account that earns 6% interest per year, compounded monthly, we need to calculate the present value of the future goal. Since the interest is compounded monthly, we use the present value formula for compound interest, which is P = A / (1 + r/n)^(nt), where P is the present value, A is the future amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Here, A = $30,000, r = 0.06 (6% converted to decimal), n = 12 (compounded monthly), and t = 3.
So, P = $30,000 / (1 + 0.06/12)^(12*3) = $30,000 / (1 + 0.005)^(36) ≈ $30,000 / 1.191016 = $25,189.06 (rounded to 2 decimal places).
The amount James needs to deposit today is approximately $25,189.06.
To determine her power usage, Keri divides up her day into three parts: morning, afternoon, and evening. She then measures her power usage at 4 randomly selected times during each part of the day. What type of sampling did she use?
Answer:
Stratified Sampling
Step-by-step explanation:
Since Keri divides the day into different strata and each unit is selected from each strata randomly. So, it is Stratified Sampling.
Further, In Stratified Sampling population is divided into several groups such that within the group it is homogeneous and between the group it is heterogeneous. And now a selection of each stratum and unit has an equal chance of selection.
A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 120 gal of a solution of 4% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 6% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?
Answer:
2.5 gal
Step-by-step explanation:
let be x = galons of solution to be drained and replace with bleach
so, we have to substract to the current solution of bleach 0.04*120, x gallons that have a concentration of 0.04 x
and also, we have to add the same gallons of bleach to the solution, that is x
and have to obtain a final concentration of 0.06*120
we can express the problem with the follow equation:
0.04*120 - 0.04*x + x = 0.06*120
solving the equation for x:
4.8+0.96*x=7.2
0.96*x=7.2-4.8
0.96*x=2.4
x =2.5 gallons
True or false?
An even function is one in which f(x) = f(-x) for all x's and odd function is one where g(x) = -g(-x) for all x's.
Answer:
True
Step-by-step explanation:
f is odd if the graph of f is symmetric with respect to the origin.
f is even if and only if f(-x) = f(x) for all x in the domain of f.
I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.
Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisionsa) trueb) flase
Answer:
The given statement is true.
Step-by-step explanation:
Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisions : TRUE statement.
Statistics helps the people to use limited sample to make accurate conclusions about a greater population. In stats we use tables, charts and graphs to present the data to draw some conclusions.
Alex has 360 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer:
90 yd by 90 yd (square)8100 yd²Step-by-step explanation:
When the perimeter of the rectangle is 360 yd, the sum of the lengths of two adjacent sides is 180 yd. If x is the length of one side of the rectangle, then the adjacent side is (180-x). The area is the product of these lengths,
area = x(180 -x)
This describes a downward-opening parabola with zeros at x=0 and x=180. The vertex (maximum) of the parabola is halfway between, at x=90. The adjacent sides of the maximum-area rectangle are the same length: the rectangle is a square with sides 90 yards each.
The area is (90 yd)² = 8100 yd².
The maximum area is achieved when Alex uses the fencing to create a square. Dividing 360 yards by 4 gives each side a length of 90 yards. Thus, the maximum area that can be enclosed is 8100 square yards.
Explanation:Alex is attempting to maximize the area of a rectangular enclosure by manipulating the length and width dimensions. In this circumstance, the maximum area will be achieved when the rectangle is square. This is because for a fixed perimeter, in this case 360 yards, a square provides the largest possible area.
The rectangle will be square if all its sides are equal. Hence, to find the dimensions of the rectangle, divide the total length of the fencing by 4 (as a square has 4 equal sides), i.e., 360 yards/4 = 90 yards. Thus, the rectangle's dimensions will be 90 yards by 90 yards.
To find the maximum area, multiply the length by the width, i.e., 90 yards * 90 yards = 8100 square yards. Therefore, the maximum area that can be enclosed by the fencing is 8100 square yards.
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Norma Jean makes $25 per hour. She works 35 hours per week. She gets a commission of 15% on her total sales. How much should Norma sell to make $4,500 in a single week?
Norma needs to make sales worth $ _____ to make $4,500.
Answer:
$24,166.67
Step-by-step explanation:
Let carry out the breakdown:
So Norman Jean makes a flat rate of $25 per hour, also she works 35 hours per week.
From the above statement Jean will make => 25 × 35 = $875 in a single week without commission.
For Jean to make $4500 in a week, we derive an equation for this:
875 + x = 4500;
x is the amount of commission Jean has to get in a week to make up to $4500 in that week => x = 4500-875; x = $3625.
Let y be the amount of sales Jean has to make to get a commission of x, we derive the following equation: 0.15 × y = x.
y = x ÷ 0.15 => 3625 ÷ 0.15
y = 24166.67.
So for Jean to meet her target of $4500 in a single week, Jean needs to make a sale worth $24,166.67.
The amount of sales that Norma needs to make in a week in order to earn $4500 in a week is; 24167
How to solve algebra word problems?
We are told that;
Norma Jean makes $25 per hour
Total time worked per week = 35 hours
Commision on total sales = 15%
Basic amount earned for the 35 hours in a week = 25 * 35 = $875
Now, if the amount of sales she makes that earns her commision is x, then it means for her to earn $4500 in a single week;
875 + 0.15x = 4500
0.15x = 4500 - 875
x = (4500 - 875)/0.15
x = 24166.67
Approximating to a whole number is;
x = 24167 sales
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A checking account has the following balances:
1. Check register balance of $459.70
2. Bank statement balance of $562.43
3. Two outstanding checks of $76.40 and $29.83
4. Service charge of $3.50.
What is the true balance?
Answer:
The true balance is $562.43
Step-by-step explanation:
1. Check register balance of $459.70
2. Bank statement balance of $562.43
3. Two outstanding checks of $76.40 and $29.83
4. Service charge of $3.50.
The working is shown like -
Subtract the service charge from check register balance
[tex]459.70-3.50=456.20[/tex] dollars
Then add the outstanding checks to this
[tex]456.20+76.40+29.83=562.43[/tex] dollars
Hence, the true balance is $562.43.
Answer:
THIS ANSWER IS CORRECT!!
Step-by-step explanation:
What is the true balance?
$456.20
You have the Check registar balance which includes your outstanding checks. You minus the $3.50 fee to get the true balance.
On three consecutive hands of draw poker a gambler wins $9, loses $20, and then loses another $16. Write an expression using positive and negative numbers to describe this situation and then simplify.
The simplified result is $_____
9 + -20 + -16= 2of course it’s going to be a negative 27 because wen u had a positive u lost 20 and then lost another 16 now u owe 27 which is -27 in your pockets
The simplified result is -$27.
To describe the gambler's situation using positive and negative numbers, we use the following expression:
$9 - $20 - $16
We can simplify this step-by-step:
First, add the positive and negative amounts: $9 - $20 = -$11
Then, subtract the next amount: -$11 - $16 = -$27
Therefore, the simplified result is -$27.
Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 40%, 30%, 20%, and 30% of the time. If a person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that she will receive a speeding ticket?
Answer:
The probability that the person gets a speeding ticket is 0.27
Step-by-step explanation:
The probability that the person receives a speeding ticket is the probability that the person passes through any of the speed limits and the radar is operating at that time.
Let [tex]P(L_1)[/tex] is the probability that the person passes through radar [tex]L_{1}[/tex] and it is operating at that time is
[tex]P(L_{1})=P(1)\times P(2)[/tex]
Where
P(1) is the probability of person passes through [tex]L_{1}[/tex]
P(2) is probability that the radar is operating
[tex]P(L_1)=0.2\times 0.4=0.08[/tex]
Similarly the probabilities are calculated for other radars in the similar manner as
[tex]P(L_2)=0.1\times 0.3=0.03[/tex]
[tex]P(L_3)=0.5\times 0.2=0.1[/tex]
[tex]P(L_4)=0.2\times 0.3=0.06[/tex]
Thus the reuired probability of the reuired event is
[tex]P(E)=P(L_1)+P(L_2)+P(L_3)+P(L_4)\\\\P(E)=0.08+0.03+0.1+0.06=0.27[/tex]
Mrs. Drew wants to build a square sandbox with an area of 400 square feet. What is the total length of wood Mrs. Drew needs to make the sides of the sandbox?
Answer:
80 ft
Step-by-step explanation:
The area can be used to find the side length. The perimeter is the sum of side lengths.
A = s² . . . . . the area of a square is the square of its side length
s = √A . . . . the side length is the square root of the area
s = √(400 ft²) = 20 ft
The perimeter is the sum of the four equal-length sides of the square, so is ...
P = 4s
P = 4(20 ft) = 80 ft
Mrs. Drew needs 80 ft of wood to make the sides of the sandbox.
Final answer:
To build a square sandbox with an area of 400 square feet, each side of the sandbox is 20 feet long, and Mrs. Drew will need a total of 80 feet of wood to construct the sides.
Explanation:
Finding the Total Length of Wood for a Sandbox
The question asks us to determine the total length of wood necessary to build a square sandbox with an area of 400 square feet. To find the length of one side of the sandbox, we take the square root of the area. The square root of 400 square feet is 20 feet, which means each side of the sandbox is 20 feet long. Since the sandbox is square, it has four equal sides.
The total length of wood Mrs. Drew needs for the sandbox is the sum of the lengths of all four sides:
20 feet + 20 feet + 20 feet + 20 feet = 80 feet.
Therefore, Mrs. Drew will require 80 feet of wood to construct the sides of the sandbox.
It's helpful to remember when working with square areas that the perimeter (or total length around the square) is always four times a single side. This is a key concept in geometry and is useful in practical applications such as planning the construction of a sandbox.
HELP ASAP! Algebra II Questions!!
Answer:
The answer to your question is: the last option 5a² + 3b + 6a
Step-by-step explanation:
7a² + 3b + 6a - 2a²
look for like terms
7a² - 2a² 3b 6a
Simplify like terms
5a² + 3b + 6a
On a coordinate plane, a circle has a center at (negative 2, 1). Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0
Final answer:
The correct general form of the equation of a circle with a center at (-2, 1) is x² + y² - 4x + 2y - 4 = 0, as it aligns with the pattern of the standard circle equation upon completion of the square.
Explanation:
The general form of the equation of a circle on a coordinate plane with a center at (-2, 1) can be found using the standard equation of a circle (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Since we do not have the radius given, our primary goal is to expand and arrange the given options to match this standard form and check which one relocates the center to (-2, 1).
The equation that matches this pattern would be x² + y² - 4x + 2y - 4 = 0. Here's why: when you complete the square to revert it back to the standard equation, you'll add 4 to both sides to get (x - (-2))² + (y - 1)² = 4, which indicates a center at (-2, 1) when you compare with the standard equation.
What is the value of A?
Answer:
a = 14
Step-by-step explanation:
Since QR = QP then the triangle is isosceles and
QS is a perpendicular bisector, thus
RS = SP ← substitute values
3a = a + 28 ( subtract a from both sides )
2a = 28 ( divide both sides by 2 )
a = 14
Two cars leave an intersection, one traveling west and the other south. After some time, the slower car is 7 mi nearer to the intersection than the faster car. At that time, the two cars are 13 mi apart. How far did each car travel?
Answer:
Step-by-step explanation:
let x and y be the distances of each car from the intersection after sometime.
let x<y
then y-x=7
and y+x=13
add 2y=20
y=10
x=13-10=3
slower car travels 3 miles and faster car travels 10 miles
A survey was given to 259 people asking where the people like dogs and or cats 186 people said they like dogs 105 people say they like cats 58 said they don't like dogs or cats how many said they like both
Answer:
90
Step-by-step explanation:
There are several ways you can go at this, but the basic idea is that "likes dogs" includes "likes both", as does "likes cats."
That means ...
(likes dogs) + (likes cats) + (likes neither)
= (likes dogs only + likes both) + (likes cats only + likes both) + (likes neither)
= [likes dogs only +likes cats only +likes both +likes neither] + (likes both)
= [total] + (likes both)
In numbers, ...
186 + 105 + 58 = 259 + (likes both)
90 = likes both . . . . . . subtract 259
Anyone know how to solve this
Hey!
----------------------------
Solution:
5 1/5% = 0.052
325 x 0.052 = 16.9
----------------------------
Answer:
D. 16.899...
----------------------------
Hope This Helped! Good Luck!
Answer:
16,9
Step-by-step explanation:
To convert from a percentage to a decimal, move the decimal point twice to the left:
5,2% = 5⅕%
5,2% → 0,052
[tex](0,052)(325) = 16,9[/tex]
I am joyous to assist you anytime.
Latanya leaves her house at 12:30 p.M. And bikes at 12 mi/h to Marta's house. She stays at Marta's house for 90 minute. Both girls walk back to latanya's house at 2.5 mi/h. They arrive at latanya's house at 3:30 p.M. How far is Marta's house from latanya's house?
Answer:
Marta's house is 3.10 miles from Latanya's house
Step-by-step explanation:
Marta's house is at 3.1 miles fron Latanya's house.
How far is Marta's house from latanya's house?From 12:30pM to 3:30pM there are a total of 3 hours, remember that.
Let's say that the distance between the two houses is D, then we can write the equations:
12mi/h*t₁ = D
2.5mi/h*t₂ = D
These are equations of the form:
speed*time = distance
Where t₁ is the time that Latanya takes to arrive to Marta's house, and t₂ is the time that they take to arrive to Latanya's house.
We know that the total time of this is 3 hours, and they spent 90 minutes = 1.5 hours in Marta's house, then:
t₁ + t₂ + 1.5 = 3
t₁ + t₂ = 3 - 1.5 = 1.5
Now we have a system of equations:
12*t₁ = D
2.5*t₂ = D
t₁ + t₂ = = 1.5
We can write:
D/12 = t₁
D/2.5 = t₂
And replace that in the last equation:
D/12 + D/2.5 = 1.5
2.5*D + 12D = 1.5*2.5*12
14.5D = 45
D = 45/14.5
D = 3.10 miles
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Jill had $125 to spend at the mall. She spent 27% of that money on a pair of shoes. Jill spent $___ on the shoes. (Make sure to enter the answer as a decimal number only. Do not enter special characters such as the dollar symbol.)
Answer:
%33.75
Step-by-step explanation:
I put the answer that the other person answered and I got it wrong so here is the right answer!
Answer:
33.75
Step-by-step explanation:
A gecko is in a room that is 12 feet long, 10 feet wide and 8 feet tall. The gecko is currently on a side wall ($10^{\prime}$ by $8^{\prime}$), one foot from the ceiling and one foot from the back wall ($12^{\prime}$ by $8^{\prime}$). The gecko spots a fly on the opposite side wall, one foot from the floor and one foot from the front wall. What is the length of the shortest path the gecko can take to reach the fly assuming that it does not jump and can only walk across the ceiling and the walls?
The shortest path the gecko can take is 20 feet long, consisting of 8 feet along the ceiling and 12 feet along the opposite side wall.
Explanation:Distances:
Gecko to ceiling edge: 1 foot
Ceiling edge to opposite wall edge: 10 feet (room width)
Opposite wall edge to fly: 1 foot
Path calculation:
Ceiling path: 1 foot (to edge) + 8 feet (along edge) = 9 feet
Side wall path: 1 foot (to edge) + 11 feet (remaining wall) = 12 feet
Shortest path:
Add ceiling and wall paths: 9 feet + 12 feet = 20 feet
Therefore, the shortest path for the gecko is 20 feet long.
To make a greeting card, Bryce used 1/8 sheet of red paper, 3/8 sheet of green paper, and 7/8 sheet of white paper. How many sheets of paper did Bryce use?
17. How would you find x and solve for it?
The formula for secant lines is the outside x the overall length is equal to the outside times the overall length of the second line.
A) 5*(x+5) = 6*10
SImplify:
5x +25 = 60
Subtract 25 from both sides:
5x = 35
Divide both sides by 5:
x = 35/5
x = 7
B) 3*8 = 4*(x+4)
Simplify:
24 = 4x +16
Subtract 16 from both sides:
4x = 8
Divide both sides by 4:
x = 8/4
X = 2
A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6 ft/sec. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 45 ft away from the pole?
When the girl is 45 ft away from the pole, the tip of her shadow is moving away from the light at a rate of approximately 4.8 ft/sec.
Given:
Height of the pole (h): 25 ft
Height of the girl (4 ft)
Rate of the girl walking away from the pole (dx/dt = 6 ft/sec)
Distance from the pole to the girl (x = 45 ft, when the girl is 45 ft away from the pole)
Objective:
Find the rate at which the tip of her shadow is moving away from the light (ds/dt) when the girl is 45 ft away from the pole.
Step 1: Set up the Similar Triangles Equation
s/x = h/(x + s)
Step 2: Differentiate both sides with respect to time t:
(1/x) * ds/dt - (s/x^2) * dx/dt = (h/(x + s)^2) * (dx/dt + ds/dt)
Step 3: Substitute Known Values:
Substitute x = 45, dx/dt = 6, and h = 25 into the equation.
(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)
Step 4: Solve for ds/dt:
Combine like terms and isolate ds/dt.
(1/45) * ds/dt - (s/45^2) * 6 = (25/(45 + s)^2) * (6 + ds/dt)
Step 5: Substitute x = 45 into the equation:
(1/45) * ds/dt - (4/2025) = (25/(90 + s)^2) * (6 + ds/dt)
Step 6: Solve for ds/dt:
ds/dt ≈ 4.8 ft/sec
Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans. Use the poisson approximation to the binomial.
a. What is the probability that three loans will be defaulted?
b. What is the probability that at least 3 loans will be defaulted?
Answer:
a) 0.0613 b)0.0803
Step-by-step explanation:
Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.
p = 0.025
Let's consider that an applicant is not be able to repay his or her installment loan as a ''success''
p (success) = 0.025
Last month she made 40 loans ⇒ n = 40
For the poisson approximation to the binomial we need to calculate n.p that will be the λ parameter in our poisson approximation
[tex]n.p=40.(0.025)=1[/tex]
λ=n.p=1
Let's rename λ = j
In our poisson approximation :
[tex]f(k,j)=\frac{e^{-j} .j^{k} }{k!}[/tex]
f(k,j) is the probability function for our poisson variable where we calculated j,e is the euler number and k is the number of success :
[tex]f(k,1)=\frac{e^{-1} .1^{k} }{k!}[/tex]
For a) We are looking the probability of 3 success :
[tex]f(3,1)=\frac{e^{-1} .1^{3} }{3!}=0.0613[/tex]
For b) We are looking for the probability of at least 3 success
If ''L'' is the number of success
[tex]P(L\geq 3)=1-P(L\leq 2)[/tex]
[tex]P(L\leq 2)=P(L=0)+P(L=1)+P(L=2)[/tex]
[tex]P(L\leq 2)=f(0,1)+f(1,1)+f(2,1)[/tex]
[tex]P(L\leq 2)=e^{-1} +e^{-1}+\frac{e^{-1}}{2} =e^{-1}(1+1+\frac{1}{2} )[/tex]
[tex]P(L\geq 3)=1-P(L\leq 2)=1-e^{-1}(1+1+\frac{1}{2} )=0.0803[/tex]
The probability that three loans will default is 0.0613
The probability that at least 3 loans will default is 0.0803
Calculations and Parameters:Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.
p = 0.025
Hence, we consider that an applicant is not able to repay his or her installment loan as a ''success''
p (success) = 0.025
Last month she made 40 loans ⇒
n = 40
For the Poisson approximation to the binomial, we need to calculate n.p which will be the λ parameter in our Poisson approximation
n.p= 40.(0.025) =1
λ=n.p=1
Let's rename λ = j
In our Poisson approximation :
f(k,1) = e^-j.j^k/k!
Hence, the probability of 3 success is:
f(3,1)= e^-1.1^3/3!
=0.0613.
The probability of at least 3 successes is:
If ''L'' is the number of successes.
P(L≥ 3) = 1- P(L≤ 2)
P(L≥ 3)= 0.0803.
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A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. What is the correct decision for a hypothesis test using α = .05?
Given : Sample size : n= 16
Degree of freedom = n-1=15
The obtained t-statistic value = 1.94
Since, The treatment is expected to increase scores and the sample mean shows an increase.
Let [tex]\mu_0[/tex] be the population mean before and [tex]\mu[/tex] denotes the population mean after the treatment.
then the related hypothesis will be :-
[tex]\text{Null hypothesis }H_0:\mu_0=\mu\\\\\text{Alternative hypothesis } H_1:\mu_0<\mu[/tex]
Since the alternative hypothesis is left-tailed, so the test is a left tailed test.
The critical value for [tex]\alpha=0.05[/tex]=1.753
Since, the obtained value (1.94) is greater than the critical value (1.753) so we reject the null hypothesis .
Therefore, we have enough evidence to support the alternative hypothesis.
Hence, we conclude that treatment may successful to increase scores and the sample mean shows an increase.
Bao was given $\$1,\!000$ for his birthday. He decided to invest the money in a bank account that earns $10\%$ interest, compounded annually. In dollars, how much total interest will Bao have earned 3 years later?
Bao's initial investment is $1,000, the annual interest rate is 10% or 0.10, and the interest is compounded annually. Plugging in these values into the formula, Bao will earn a total interest of $331 after 3 years.
Explanation:To calculate the total interest Bao will have earned after 3 years, we can use the formula for compound interest: [tex]A = P(1+r/n)^(nt)[/tex] where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, Bao's initial investment (P) is $1,000, the annual interest rate (r) is 10% or 0.10, and the interest is compounded annually (n = 1). We need to find the final amount (A) after 3 years (t = 3).
Plugging in these values into the formula:
[tex]A = 1000(1+0.10/1)^3[/tex]
= $1,331.
Therefore, Bao will earn a total interest of $331 after 3 years.
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Final answer:
Bao will have earned $331 in total interest after 3 years by investing his $1,000 at an annual compound interest rate of 10%.
Explanation:
The student's question involves calculating the amount of interest earned from a compound interest formula over a period of 3 years. To determine the total interest earned by Bao after 3 years, we need to apply the compound interest formula:
[tex]A = P (1 + r/n)^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the original sum of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
For Bao's investment:
P = $1,000
r = 10% or 0.10
n = 1 (since interest is compounded annually)
t = 3 years
Using the formula:
[tex]A = 1000 (1 + 0.10/1)^{(1*3)} = 1000 (1.10)^3 = 1000 * 1.331 = $1,331[/tex]
The total interest earned after 3 years is:
Interest = A - P = $1,331 - $1,000 = $331
So, Bao will have earned $331 in total interest 3 years later.
You are a bus driver and are scheduled to depart from Terminal A at 9:18 a.M. And arrive at Terminal B at 10:03 a.M. You arrive at a stop on your route at 9:58 a.M., and you have 5 more stops remaining, including your arrival at Terminal B. Average travel time between stops is 2 minutes, and loading and unloading takes an average of 1 minute. How many minutes past your scheduled arrival time should you expect to arrive at Terminal B?
You should expect to arrive at Terminal B approximately 17 minutes past the scheduled arrival time, factoring in remaining stops and travel times.
Let's calculate the expected delay in arrival at Terminal B.
Given:
- Scheduled departure from Terminal A: 9:18 a.m.
- Scheduled arrival at Terminal B: 10:03 a.m.
- Arrival at a stop on the route at 9:58 a.m.
- 5 more stops remaining, including the arrival at Terminal B.
- Average travel time between stops: 2 minutes
- Loading and unloading time: 1 minute
1. Total travel time from the current stop to Terminal B:
[tex]\[ 10:03 \text{ a.m.} - 9:58 \text{ a.m.} = 5 \text{ minutes} \][/tex]
2. Remaining stops:
[tex]\[ 5 \text{ stops} \times (2 \text{ minutes travel time} + 1 \text{ minute loading/unloading}) = 5 \text{ stops} \times 3 \text{ minutes per stop} = 15 \text{ minutes} \][/tex]
3. Total time from the current stop to Terminal B, including remaining stops:
[tex]\[ 5 \text{ minutes (travel time to Terminal B)} + 15 \text{ minutes (remaining stops)} = 20 \text{ minutes} \][/tex]
4. Determine how many minutes past the scheduled arrival time at Terminal B this would be:
[tex]\[ 20 \text{ minutes} - (10:03 \text{ a.m.} - 10:00 \text{ a.m.}) = 20 \text{ minutes} - 3 \text{ minutes} = 17 \text{ minutes} \][/tex]
Therefore, you should expect to arrive at Terminal B 17 minutes past the scheduled arrival time.
If the correct answer is indeed 10 minutes, then there might be a misunderstanding or a mistake in the problem statement.
You can expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time. This is calculated based on the average travel time and loading/unloading time for the remaining stops.
To determine how many minutes past your scheduled arrival time you should expect to arrive at Terminal B, let's break down the time required for the remaining stops.
You arrive at a stop on your route at 9:58 AM. You have 5 more stops remaining, including Terminal B.Average travel time between stops is 2 minutes, and loading and unloading takes 1 minute. Therefore, each stop takes 3 minutes on average (2 minutes travel + 1 minute loading/unloading).For 5 stops, the total time required will be 3 minutes per stop × 5 stops = 15 minutes.If you start this 15-minute period at 9:58 AM, the calculation is: 9:58 AM + 15 minutes = 10:13 AM.Your scheduled arrival at Terminal B is 10:03 AM.The delay is then 10:13 AM minus 10:03 AM, which results in a 10-minute delay.Therefore, you should expect to arrive at Terminal B approximately 10 minutes past your scheduled arrival time.
The distance from Los Angeles to Mumbai is 14,000 km. Flights take 22
hours, whilst the return flight from Mumbai to Los Angeles takes only 17
hours because of the direction of the prevailing wind. Assuming the
airplane would fly the same speed in both directions in still air, what is
the average wind velocity?
Answer:
about 93.6 km/h
Step-by-step explanation:
The speed westbound is ...
14000 km/(22 h) ≈ 636.364 km/h
The speed eastbound is ...
14000 km/(17 h) ≈ 823.529 km/h
The difference in speeds is twice the wind speed, so the wind speed is ...
(823.529 -636.364)/2 km/h ≈ 93.6 km/h
To find the wind velocity, first calculate the plane's average speed in still air by averaging its speeds in opposite directions. Then subtract the plane's speed against the wind from its speed in still air. The result is the wind velocity, which in this case is 93.59 km/h.
Explanation:To calculate the wind velocity, we will first need to find out the airplane's speed in still air. This can be calculated by getting the average of the two speeds in opposite directions. You see, when a plane flies from Los Angeles to Mumbai, it takes 22 hours, while the return flight from Mumbai to Los Angeles takes only 17 hours because of wind assistance. Here's how to work it out:
First, calculate the plane’s speed for both directions: For the LA to Mumbai direction it’s 14,000 km / 22 hours = 636.36 km/h, and for the Mumbai to LA direction it’s 14,000 km / 17 hours = 823.53 km/h.Now, get the average speed of the plane in still air. It would be the sum of these two speeds divided by two: (636.36 km/h + 823.53 km/h) / 2 = 729.95 km/h. This is the plane’s speed in an environment without wind.To find the wind velocity, subtract the plane's speed against the wind (LA to Mumbai direction) from the speed in still air. This gives us: 729.95 km/h - 636.36 km/h = 93.59 km/h. Therefore, the average wind velocity is 93.59 km/h.Learn more about Wind Velocity here:https://brainly.com/question/34068902
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At a hotdog stand they serve regular and foot-long hotdogs are the ratio of 3 to 2 based on this ratio how many foot-long hotdogs will be served if there are a total of 80 hotdogs served
To calculate the number of foot-long hot dogs served, divide the total number of hot dogs by the total parts of the ratio (80/5 = 16) and then multiply by the number of parts for foot-long hot dogs (2 * 16 = 32 foot-long hot dogs served).
If the ratio of regular hot dogs to foot-long hot dogs at a hot dog stand is 3 to 2, and there are a total of 80 hot dogs served, we can calculate the number of foot-long hot dogs served using proportional reasoning.
To find out how many foot-long hot dogs are served, first add up the parts of the ratio: 3 parts regular hot dogs + 2 parts foot-long hot dogs = 5 parts total. Since there are 80 hot dogs served in total, we divide this number by the total number of parts to find the value of one part.
80 hot dogs \/ 5 parts = 16 hot dogs per part.
Now, multiply the value of one part by the number of parts for foot-long hot dogs to get the total number of foot-long hot dogs served:
2 parts foot-long hot dogs x 16 hot dogs per part = 32 foot-long hot dogs.
Determine the resulting polynomial:
f(x)=10x−5
g(x)=2x2+4x−4
Find: f(x)⋅g(x)
Only have one question left. Help?
Answer:
50Step-by-step explanation:
[tex]i=\sqrt{-1}\to i^2=-1\\\\(3+\sqrt{-16})(6-\sqrt{-64})\\\\\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\sqrt{-64}=\sqrt{(64)(-1)}=\sqrt{64}\cdot\sqrt{-1}=8i\\\\(3+4i)(6-8i)\\\\\text{use FOIL}\ (a+b)(c+d)=ab+ac+bc+bd\\\\=(3)(6)+(3)(-8i)+(4i)(6)+(4i)(-8i)\\\\=18-24i+24i-32i^2\qquad\text{cancel}\ 24i\\\\=18-32(-1)=18+32=50[/tex]