You decide to put $100 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
Answer:
170.202 years
Step-by-step explanation:
From the compound interest formula, that has interest rate in times per year but compounds monthly we have
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A is the amount you want to save, P is the principal (what you put down, in this case 100), r is the anual interest rate, n is 12 i.e the times it compounds, and t is the amount of years it will take. So we have data for all variables but t.
Solving for t we have
[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]
taking logs
[tex]log(\frac{A}{P})=nt \,log(1+\frac{r}{n})[/tex]
finally
[tex]t = \frac {log(\frac{A}{P}) }{ n[log(1 + \frac{r}{n})]}[/tex]
replacing and calculating we get t=170.202
solve the system of equations solve for x
y=6x+12
solve for y
y=x+47
To solve the system of equations xy = 6x + 12 and yy = x + 47, we can rearrange the equations, isolate one variable, and substitute it into the other equation. Then, solve for the variables. The solution is x = 282 / (270 - y) and y = (270 - xy) / 6.
Explanation:To solve the given system of equations,
xy = 6x + 12
yy = x + 47
We can start by rearranging the equations:
xy - 6x = 12
yy - x = 47
Next, we can isolate one variable in terms of the other variable and substitute it into the other equation:
x = (yy - 47)
xy - 6(yy - 47) = 12
Simplifying the equation:
xy - 6yy + 282 = 12
Combining like terms:
-6yy + xy = -270
Now, we can solve this equation for y in terms of x:
y = (270 - xy) / 6
Re-substituting the value of y back into one of the original equations:
(270 - xy) / 6 * x = 47
Simplifying and solving for x:
270x - xy = 282
x(270 - y) = 282
x = 282 / (270 - y)
So, the solution to the system of equations is:
x = 282 / (270 - y)
y = (270 - xy) / 6
Mark shoots arrows at a target and hits the bull's-eye about 40% of the time. find the probability that he hits the bull's-eye on the fourth shot
The probability of Mark hitting the bull's-eye on the fourth shot, assuming he misses the first three times, is 8.64%. This is calculated as the product of the probabilities of each event occurring independently.
Explanation:This is indeed a problem related to probability, particularly, this pertains to the concept of an independent event in statistics. Mark's success in shooting an arrow accurately to the target is an independent event because the outcome of one shot doesn't affect the outcome of other shots.
In Mark's case, he hits the bull's-eye about 40% of the time, i.e. his success rate P(Success) is 0.40 and his failure rate P(Failure) is 0.60. Since the question asked about the probability of him hitting the bull's-eye on the fourth shot, we should look at the first three shots being failures and only the fourth being a success.
This leads us to the calculation: P(FFFH) = P(F) x P(F) x P(F) x P(H) = (0.60)*(0.60)*(0.60)*(0.40) = 0.0864 or 8.64% chance.
So, there's an 8.64% chance that Mark will hit the bull's-eye on the fourth shot given that he misses the first three.
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The probability that Mark hits the bull's-eye on his fourth shot, given he typically hits the bull's-eye 40% of the time, is 0.0864 or 8.64%
Explanation:The problem is about the probability that Mark hits the bull's-eye on the fourth shot given that he hits the bull's-eye about 40% of the time. In these cases, for the first three shots, he should not hit the bull's-eye (probabilty of 60%) and on the fourth trial, he should hit the bull's-eye (probability of 40%). Therefore, we multiply the individual probabilities together to find the answer.
Step 1: Find the probability that he does not hit the bull's-eye in the first three trials. This is (0.6)*(0.6)*(0.6) = 0.216.
Step 2: Find the probability that he hits the bull's-eye on the fourth trial. This is simply 0.4.
Step 3: Multiply the two probabilities together to find the final answer. This gives us 0.216*0.4 = 0.0864.
So, the probability that Mark hits the bull's-eye on the fourth shot is 0.0864, or 8.64%.
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What are the dimensions of the rectangle of greatest area that can be formed with 200 feet of fence?
Dimensions are 50 feet by 50 feet.
Let the length = x
the width = y
So the perimeter = 2(x+y)=200
or, x+y=100
or, y=100-x
So the area is = A = xy = x(100-x).
For greatest area A' = 0 and A" < 0.
[tex]A= x(100-x)\\A=100x-x^2\\A'=100-2x\\A''=-2[/tex]
We set A'=0 to find x.
[tex]100-2x=0\\2x=100\\x=50[/tex]
For x=50, A"=2 < 0
It means for x=50, y=100-50=50 the rectangle will have the greatest area.
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if f(4)=183.07 when r=0.04 for the function f(t)=Pe* then what is the appropriate value of P?
Show work please
Which line is a line of symmetry for this regular polygon?
line g
line h
line i
Line g is a line of symmetry of this regular polygon.
We have regular polygon as shown in the figure.
We have to determine which line is a line of symmetry for this regular polygon.
What do you understand by the Symmetry of any plane figure?A plane figure is symmetric about a line if it is its own image when flipped across the line. The reflection line is the line of symmetry.
According to the question, we have a Regular Polygon.
According to the concept of Symmetry of any plane figure -
if we fold this polygon about the line g then both the sides will overlap.
The lines i and h do not fulfill this condition.
Hence, line g is a line of symmetry of this regular polygon.
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ALGEBRATIC EXPRESSIONS HELP
the product of 4 and a number is increased by 7
product means multiply
increased by means add
so product of 4 and a number would be 4n
than add 7
so you have 4n+7
Find the distance between the points 1,4 and (-2,-1
What is 31/8 as a decimal
Greta is opening a savings account. She starts with $100 and plans to add $59 each week. Write an equation she can use to calculate the amount of money she will have after any number of weeks. How much money will she have after 1 year?
The graph of a combination of line segments that passes the vertical line test is a ?
Nonlinear function (A)
The graph of a combination of line segments that passes the vertical line test is a Non Linear function.
What is vertical line test?The vertical line test states that a graph represents a function if and only if all vertical lines intersect the graph at most once.
The vertical line check is a graphical approach of determining whether or not a curve inside the aircraft represents the graph of a function by means of visually examining the variety of intersections of the curve with vertical lines.A vertical line intersects with them only once, making them features.Parabolas that face upward and downward are capabilities.They may be functions because a vertical line intersects the curve no extra than once.
If a vertical line intersects a curve on an xy-plane greater than once then for one price of x the curve has multiple value of y, and so, the curve does now not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.
The vertical line take a look at helps to find it a given curve represents a function or now not. If the vertical line cuts the graph of the equation at simplest one factor, then it's miles a characteristic, and if cuts the graph of the characteristic at a couple of point, then it does not constitute a characteristic. A vertical form is a shape with layers stacked on top of every other, with a fixed layer top, for instance a spherical tower where the radius corresponds to the datapoint.
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(01.07)
Name the algebraic property demonstrated in the example below:
(2 + x) + y = 2 + (x + y) (1 point)
Commutative Property of Addition
Associative Property of Addition
Distributive Property
Transitive Property
What’s the temperature difference between -5 degrees and 25 degrees?
A.20 degrees
B.25 degrees
C.30 degrees
D.35 degrees
difference between -5 and 25 is
25 + 5 = 30 degrees
answer is C.
How do you find how many solutions a system of equations has?
The average height of a female draft is 4.6 meters. Was her height in centimeters.
Final answer:
To convert the average height of a female giraffe from meters to centimeters, multiply 4.6 meters by 100, resulting in 460 centimeters.
Explanation:
To convert the average height of a female giraffe from meters to centimeters, we need to use the conversion factor where 1 meter is equivalent to 100 centimeters. If the average height is 4.6 meters, then we need to multiply this value by 100 to find the height in centimeters
Step-by-step calculation
This conversion process, from meters to centimeters, simplifies the representation of the average height of a female giraffe. Utilizing the conversion factor, where 1 meter equals 100 centimeters, the calculated result of 460 centimeters provides a more practical and commonly used metric. Such conversions are valuable for ensuring consistency in measurement units and facilitating communication across different contexts, enhancing our understanding of the physical dimensions of giraffes in a more accessible manner.
The folding chair can be set in different positions that change the angles formed by its parts. As angle 1 increases, how does the relationship change between the back of the chair and the front leg of the chair?
A. As the measure of increases, the distance between the back of the chair and the front leg of the chair increases.
B. As the measure of increases, the distance between the back of the chair and the front leg of the chair decreases.
C. As the measure of increases, the distance between the back of the chair and the front leg of the chair remains constant.
Final answer:
In the context of a folding chair, as angle 1 (between the backrest and the seat) increases, the distance between the back of the chair and the front leg correspondingly increases due to the lever-like movement of the backrest.
Explanation:
When considering the geometry of a folding chair and the angles formed by its parts, it's important to visualize the chair as a system of linked levers. As angle 1 increases, which is the angle between the backrest of the chair and the seat, the relationship between the back of the chair and the front leg changes. If we assume that the front leg stays still and the back of the chair moves backward to increase the angle, the distance between the back of the chair and the front leg increases. This movement can be seen as the backrest acting like a lever, where increasing the angle effectively moves the lever away from the pivot point at the front leg.
Therefore, the correct answer in the context of a folding chair is: A. As the measure of angle 1 increases, the distance between the back of the chair and the front leg of the chair increases.
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
Find the slope of each of the lines below:
Simplify. 7/3+3(2/3−1/3)^2
All of these are fractions except the three and the exponent
7/3 +3(2/3 -1/3)^2 =
2/3 -1/3 = 1/3 now you have
7/3 +3(1/3)^2
1/3^2 = 1/9
7/3 +3(1/9)
3*1/9 = 1/3
7/3 + 1/3 = 8/3, which can be changed to 2 2/3
What must you add to the expression x2+bxx2+bx to complete the square?
We are given the incomplete expression:
x^2 + b x
Now to complete the square, we need to add the square of the half of b, that is:
(b / 2)^2
or
b^2 / 4
Therefore the complete expression is:
x^2 + b x + (b^2 / 4)
Suppose that you have the option to buy an item with either cash or credit. Under which condition would you use credit?
Answer:
By having or building a good credit history.
Step-by-step explanation:
When an item is to bought by you on credit , for you to have or build a good credit history , Buying something with credit means that you are buying something with money you don't have at that very time
Later on, you will have to give back this money borrowed to a person,an interest will be paid for lending it.
Angela enjoys swimming and often swim a at a steady pace to burn calories. At this pace, Angela can swim 1,700 meters in 40 minutes. What is Angela's unit rate?
What is the x coordinate in the solution of the system of equations y =-2/3x and 4x - 9y =-40
The x-coordinate in the solution of the given system of equations is -4.
Explanation:The x-coordinate in the solution of the given system of equations can be found by substituting the value of y from one equation into the other equation and solving for x. Let's solve the system of equations:
Start with the equation y = -2/3x. Substitute this into the second equation:
4x - 9(-2/3x) = -40
Now simplify and solve for x:
4x + 6x = -40
10x = -40
x = -4
So, the x-coordinate in the solution of the system of equations is -4.
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Which example supports the given conjecture? the sum of two odd numbers is an even number.
a. 0 + 3 = 3
b. 2 + 6 = 8
c. 5 + 7 =12
d. 4 + 9 = 13?
Perform the indicated operation.
4/11 x 10/8
To solve the operation 4/11 x 10/8, multiply the numerators and denominators separately. The result is 0.45454545454.
Perform the indicated operation: 4/11 x 10/8
Multiply the numerators: 4 x 10 = 40
Multiply the denominators: 11 x 8 = 88
The result is 40/88 = 0.45454545454
How much pasta will each person get if 6 people share 2/3 lb of pasta equally?
Each person would get 1/9 lb of pasta if 6 people were to share 2/3 lb of pasta equally.
Explanation:In the given question, 6 people are sharing 2/3 lb of pasta equally. This implies that we are performing an operation of division. You would divide 2/3 by 6 to find out how much each person gets. Here's how you can do it:
First, write the fraction 2/3 as the division of two numbers 2 divided by 3. Now divide 2 by 6 which equals 1/3. Now, divide 1/3 by 3. Therefore, each person will get 1/9 lb of pasta. Learn more about division here:
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the diagram shows the dimensions of a teepee. find the volume of the building to the nearest cubic unit. use 3.14 for pi. height is 17 ft and width is 20 ft.
f (x)=4x-7 when f (x)=8
Partway through the season, a basketball coach promises his team that he will take them to a water park if they reach 1,000 points as a team by the end of the season. So far, they have scored 424 points. There are 9 games left in the season. Fill in the values for a, b, and c to create an equation that can be used to find the average number of points, x, the team needs to score in each of the remaining games to meet their goal.
1. In ∆ABC the angle bisectors drawn from vertexes A and B intersect at point D. Find ∠ADB if: m∠A = α , m∠B = β
2.Angle bisectors of the angles ∠A and ∠B of a triangle ∆ABC intersect each other at point M. Find m∠AMB, if m∠A = 58°, m∠B = 96°.
The measure of an angle formed by the intersection of two angle bisectors in a triangle is the semisum of the two angles being bisected. So, in both situations, ∠ADB and ∠AMB will be (α + β)/2.
Explanation:In a triangle, the angle formed by the intersection of two angle bisectors is always equal to the semisum of the two angles being bisected. Therefore, in ∆ABC, the measure of ∠ADB (∠ formed by the intersection of the bisectors from ∠A and ∠B) will be (α + β)/2.
For example, if angle A is 40° (let's represent it by α) and angle B is 60° (let's represent it by β), the ∠ADB will be (40 + 60) / 2, which equals 50°.
In the second problem, the measure of ∠AMB will also be equal to the average of ∠A and ∠B, so m∠AMB = (58° + 96°) / 2 = 77°. This rule applies to any triangle ABC, regardless of the type of triangle.
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Answer:
Hi, sorry, but my computer is glitching and I can't put in the answer for some reason.... I'm REALLY sorry...
Step-by-step explanation: