His final payment will be $271.66464 at the end of the third year.
What is compound interest?The term "compound interest" refers to interest that is added back to the principal amount during each compounding period.
Compound interest is calculated using the formula
A = P(1+r )ⁿ, where
P = principal balance,
r = interest rate,
n = number of periods.
Given that a man borrows $760 at 4% and of the first year he pays back $270.
Amount owned by him at the end of the first year after repaying $270 = (1+4%)760 - 270
= 1.04×760 - 270
= $520.4
Amount owned by him at the end of the second year after repaying $280 = (1+4%)520.4 - 280
= 1.04×520.4 - 280
= 541.216 - 280
= $261.216
Let his final payment be x.
So, the amount owned by him at the end of the third year will be 0.
⇒ (1+4%)261.216 - x = 0
⇒ 1.04×261.216 - x = 0
⇒ 271.66464 = x
Therefore, his final payment will be $271.66464.
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Which expression is not equivalent to Negative 3 x minus one-half + 4 y?
The expression that is not equivalent is - 2x -0.5 + 6 y + 3 x
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Given the expression -3x - 0.5 + 4y
We are to get the equation equivalent to the expression
2y - 5x - 0.5 + 2y + 2x
4y -3x - 0.5
Hence, the equations are equal
For the expression -2 x -0.5 + 6 y + 3 x
This is equivalent to x + 6y - 0.5
Hence , the expression that is not equivalent is -2 x -0.5 + 6 y + 3 x
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If $15,000 is invested at 6. 5% annual interest compounded annually, how long would it take for the account balance to reach $50,000? Round your answer to the nearest tenth
The account balance invested at 6. 5% annual interest compounded annually will take 19.1 years to reach $50,000.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded annually, and t is the time in number of year
Using this formula, find t, the time it will take the account to reach $50,000 when
B = $15,000
r = 6.5% = 0.065
n = 1
B = P(1 + r/n)^t
$50,000 = $15,000(1 + 0.065/1)^t
(1 + 0.065)^t = $50,000/$15,000
1.065^t = 10/3
t = 19.1 years
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An activity director in a long-term care facility is purchasing recreational supplies. Find the sum of the purchases: 3 bingo games at $13 each, 10 puzzles at $9.00 each, 24 jars of paint at $3.00 each and 2 rolls of paper for $31.00 each.
work out what the values of three consecutive even
integers must be if their sum is 6000.
The values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.
What is an integer?it is defined as a whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0, etc. When it comes to integers, even numbers can be divided by two exactly while odd numbers cannot. 2, 6, 10, 20, 50, and other even numbers serve as examples.
Suppose the value of the three consecutive even integers is n, n + 2, and n + 4
The sum of the integers is 6000.
Sum = n + n + 2 + n + 4
Sum = 3n + 6
Sum=6000
3n + 6 = 6000
3n = 5994
n = 5994/3
n = 1998
The three consecutive even integers are,
n=1998
n+2=1998+2=2000
n+4=1998+4=2002
Thus, the values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.
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please answer with work
The numeric values to the functions are given as follows:
10. 34.
11. 42.
12. 7.5.
To plot the points in item 13, to plot the points, we follow the procedure described below:
Plot A(a,b) on the first quadrant.Plot B(-a,b) on the second quadrant, reflecting point A over the y-axis.Plot C(-a,-b) on the third quadrant, reflecting point B over the x-axis.Plot D(a,-b) on the third quadrant, reflecting point A over the x-axis.How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For item 10, we want to find the numeric value of -9x - 2 at x = -4, hence:
-9(-4) - 2 = 36 - 2 = 34.
For item 11, we want to find the numeric value of 24 - 8x at x = -2.25, hence:
24 - 8(-2.25) = 24 + 18 = 42.
For item 12, we want to find the numeric value of 15x + 9 at x = -0.1, hence:
15(-0.1) + 9 = -1.5 + 9 = 7.5.
For item 13, we have that (a,b) is positive, hence the following procedure is used to plot all points:
Plot A(a,b) on the first quadrant.Plot B(-a,b) on the second quadrant, reflecting point A over the y-axis.Plot C(-a,-b) on the third quadrant, reflecting point B over the x-axis.Plot D(a,-b) on the third quadrant, reflecting point A over the x-axis.More can be learned about the numeric values of a function at brainly.com/question/28367050
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Stock Market At the beginning of the day the stock market goes down 70 1/4
points and stays at this level for most of the day. At the end of the day the stock market goes up 110 1/2
points from the low at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
Question content area bottom
Part 1
The total change in the stock market is
enter your response here points.
The total change in the stock market from the beginning of the day to the end of the day is [tex]40\frac{1}{4}[/tex]
What is the total change?When the value of the stock market goes down, its value has decreased. The decrease in the value of the stock market would be represented with a negative number. A negative number is a number that is less than 0. The sign that is used to represent a negative number is -.
When the value of the stock market goes up, its value has increased. The increase in the value of the stock market would be represented with a positive number. A positive number is number that is greater than 0.
The total change in the stock market is the sum of the decrease and the increase in the stock market.
Total change = increase in the stock market - decrease in the stock market
[tex]110\frac{1}{2} - 70\frac{1}{4}[/tex]
[tex]40\frac{2-1}{4}[/tex] = [tex]40\frac{1}{4}[/tex]
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Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=0.5(1/4) x
4x you had 0.5x are the y -intercept.
How can you tell whether an exponential function is growing or deteriorating?
As the exponential's base is greater than 1, which occurs when those numbers increase, we are seeing exponential growth. When the exponential's base is between 1 and 0, and those numbers decrease, we have exponential decay.You can obviously plot it but if you can also conside that in your function you have 4x
; this tells you that as
x increases (gets bigger) certainly
4x will increase as well (you can consider
4²= 16 and 4³ = 64
). It is true that you have to multiply by
0.5
but nevertheless the entire function will grow anyway!
Graphically:
graph{0.5*(4^x) [-14.24, 14.24, -7.12, 7.12]}
If you want, try to think at the case where instead of having
4x you had 0.5x .
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Which expression is equivalent to -1/2 ( 1/4x - 3/8)?
The expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.
Which expression is equivalent to the expression given as in the task content?It follows from the task content that the expression which is equivalent to that given in the task content be determined.
On this note, by distributing the coefficient of.tne parents; we have;
-1/2 ( 1/4x - 3/8)
= {(-1/2) × (1/4)x} + {-1/2 × -3/8}
= (-1/8)x + 3/16
Ultimately, the expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.
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Find the inverse of each function.
y=log 10 x
The inverse of the function is f ⁻¹(x) = 10ˣ
Given the function is y = log₁₀ x
In relation to the original function f, the inverse function is denoted by the symbol f-1, and both the original function's domain and its range are transformed into the inverse function's domain. By replacing (x, y) with (y, x) with reference to the line y = x, one can obtain the graph of the inverse function.
steps to find the inverse of the function:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now replace y with x.
x = log₁₀ y
change the dependent variables.
f ⁻¹(x) = 10ˣ
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Find the inverse of each function. Is the inverse a function?
f(x)=x²-1
In mathematics, an inverse function is one that "reverses" another function. The inverse function of F(x) = x² - 1 is ±√(x + 1).
What is the inverse function of F(x) =x²-1?The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.
Let the function be f(x) = x² - 1
y = x² − 1
x = y² − 1
simplifying the above equation, we get
y² = x + 1
y = ± √(x + 1)
Because there are two possible values of y for each value of x, there is no inverse function.
The inverse function of F(x) = x² - 1 is ±√(x + 1).
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What is the answer to this \pi =7x-2y
Answer:
In π = 7x - 2y we first isolate y by adding 7x on both sides.
This gives us π + 7x = -2y. Divide 2 on both sides, then we are left with:
y =
Step-by-step explanation:
What is logbase 3√81
Answer:
log3(sqrt(81)) = 2
Step-by-step explanation:
If someone could help soon that would be great
Answer:
a,b,c and no d
Step-by-step explanation:
welcome
Answer:
a, b, and c.
Step-by-step explanation:
Use the line test. :)
The points E(-8,1)(−8,1), F(1,1)(1,1), and G(-3,8)(−3,8) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.
Applying the distance formula, the perimeter of triangle EFG to the nearest tenth is: 25.7 units
What is the Perimeter of a Triangle?The perimeter of triangle EFG with the following points is the sum of all its three sides = EF + FG + EG.
Find the length of each sides of triangle EFG using the distance formula, d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex]:
Given:
E(-8,1)
F(1,1)
G(-3,8)
Using the distance formula:
EF = √[(1−(−8))² + (1−1)²]
EF = √81
EF = 9 units
FG = √[(−3−1)² + (8−1)²]
FG = √65
FG ≈ 8.1 units
EG = √[(−3−(−8))² + (8−1)²]
EG = √74
EG ≈ 8.6 units
The perimeter of triangle EFG = 8.1 units + 9 units + 8.6 units ≈ 25.7 units
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Here are the first 7 terms of a quadratic sequence.
(a) Find an expression, in terms of n, for the nth term of this sequence.
6 11 18 27 38 51
The grid above shows the graph of the parent function f(x)= |x| and a translated functions graph.
Use f(x)=|x| f(x) is shifted left 5 and shifted up 2 to create g (x). write the equation g(x).
The equation of the translated graph from the parent function is g(x) = |x + 2| + 1
How to write the equation of the translated graph?The parent function is given as
f(x)= |x|
From the graph, we can see that the parent function f(x) is translated as follows:
2 units left translation1 unit up translationThe above sequence of translation is represented as
(x, y) = (x + 2, y + 1)
So, we have
g(x) = |x + 2| + 1
Hence, the equation of the translated graph is g(x) = |x + 2| + 1
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translation: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
Answer: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(5, -1)
Step-by-step explanation:
If you want to translate a point 7 units right, you'll need to add 7 to its x-coordinate. If you want to translate a point 1 unit down, you'll need to subtract 1 from its y-coordinate. Do both of these things to perform a translation 7 units right and 1 unit down.
So, we can write,
7 units right means add the +7
1 unit down means subtract the -1
Then,
J(-3, 1) = J'(-3 + 7, 1 - 1)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(-2 + 7, 3 - 1)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(-2 + 7, 0 - 1)
N(-2, 0) = N'(5, -1)
Therefore,
These points to make sure they have shifted 7 units right and 1 unit down.
7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(5, -1)
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Which of the following may fall under the category of collateral? Answer choices: a high salary, a credit card balance of $12,000, an antique vase valued at $125,000, or a previous loan that was repaid in full
The option B , that is , an antique vase valued at $125,000 can be categorized as collateral asset.
What is a collateral asset ?
An asset that a borrower pledges to a lender as a guarantee that the loan will be repaid is known as collateral asset.
We know that the assets that a lender accepts as security for a loan are referred to as collateral. That meant lenders are protected by the collateral in this way. To put it another way, if the borrower stops making loan payments, the lender may be able to sell the collateral to collect some or all of its losses.
So , let's check which of the given option falls under category of collateral.
A.
This is not collateral asset because for a credit card there is no security money given to bank. We only need to pay a maintenance charge and nothing else.
B.
This is a collateral asset.
For an antique vase whose value is $125000 , if the person has purchased this by taking a loan then he would have paid some security money as deposits. If any case he is not able to pay the loan by time the property or the asset becomes collateral which meant the lender may sell the asset to some or all of his losses.
C.
This is not collateral asset because if the loan is repaid in full there will be no extra charges liable on the asset and it can't be categorized as collateral.
Therefore , the option B , that is , an antique vase valued at $125,000 can be categorized as collateral asset.
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1. He is spending more money than he makes.
2. He has to cut back on other expenses.
3. It is a listing of what an individual owns minus what they owe.
4. an antique vase valued at $125,000
5. capital
Explanation: I took the same quick check and got 100%, hope this helps!
Find the sum or difference.
Answer:
The sum is the third answer
Step-by-step explanation:
you add together the numbers that are in the same spot in both matrixes.
-3 + -4 0 + 2
5 + -1 -7 + 8
That would give you
-7 2
4 1
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator 45 to 9
Answer:
[tex]\frac{5}{1}[/tex]
Step-by-step explanation:
45 : 9
= [tex]\frac{45}{9}[/tex] ← divide numerator and denominator by 9 )
= [tex]\frac{5}{1}[/tex] ← in simplest form
Henry is working two summer jobs, washing cars and walking dogs. He can work at most 15 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours washing cars, ww, and the number of hours walking dogs, dd, that Henry can work in a given week.
y=5x 7.5w+7.5d Answer:
Step-by-step explanation:
The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week is , w + d ≤ 15 .
What is an inequality?The relationship between two expressions or values that are not equal to each other is called 'inequality.
here, we have,
Given that w is the number of hours for washing a car and d is the number of hours to walking dogs.
The work hours at most 15 hours altogether between both jobs in a given in a week.
Hence, w + d ≤ 15 is the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week.
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Find the amount in a continuously compounded account for the given conditions.principal: $ 400 annual interest rate: 7.6% time: 1.5 years
The amount in a continuously compounded account is $448.30.
Given that the given conditions are the annual interest rate is $400, time is 7.6% and time is 1.5 years.
Continuous compounding means that the account balance is continuously profitable and transfers that interest back to the balance so that it is also profitable.
To find the amount in a continuously compounded account we will use the formula [tex]A=Pe^{rt}[/tex].
[tex]A=400\times e^{(0.076)(1.5)}[/tex]
Now, we will simplify the above expression, we get
[tex]A=400\times e^{0.114}[/tex]
Now, we will evaluate the value of e that is [tex]e^{0.114}[/tex] is 1.120752, we get
A=400×1.120752
A=448.30
Hence, the amount in a continuously compounded account for the given conditions principal: $ 400 annual, interest rate: 7.6%, time: 1.5 years is $448.30.
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Which of these numbers lies between 4 and 4.5 on a number line? A √13 B √17 C √22 D √28
Therefore √17 will lie between 4 and 4.5 on the number line .
In basic mathematics, real numbers are shown as a graphic of a graduated straight line called a number line. Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.
According to one standard, positive numbers always fall on the right side of zero, whereas negative numbers always fall on the left. The line also contains arrowheads at both ends, signifying that it continues in both the positive and negative directions indefinitely.
Let us find the decimal values of the given numbers.
13 lies between 9 and 16 , therefore √13 lies between 3 and 4 on the number line .
17 lies between 16 and 25 , therefore √17 lies between 4 and 5 on the number line .
22 lies between 16 and 25 , therefore √22 lies between 4 and 5 on the number line .
28 lies between 25 and 36 , therefore √28 lies between 5 and 6 on the number line.
Therefore √17 will lie between 4 and 4.5 on the number line as 4.5² = 20.25.
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Jonathan is buying string to make friendship bracelets. He buys 7 bundles of string in different colors. Each bundle costs $0.56. Tax for the 7 bundles is $0.35. How much money does Jonathan pay in all for the string?
Answer:
4.27
Step-by-step explanation:
1 bundle= $0.56
7bundles=o.56x7=$3.92
Tax=0.35
3.92+0.35=4.27
please help, no troll answers. will give brainliest to correct answers. option answers are
54
46
44
90
Answer:
46
Step-by-step explanation:
A right angle is always equal to 90.
You are given the angle 44 so all you need to do is 90-44 which gives you 46
Hope this helps! Have a great day :)
Answer:
<2 = 46 degrees
Step-by-step explanation:
The angle measuring 44 degrees and <2 are complementary, therefore, they add up to 90 degrees.
Let [tex]x[/tex] be <2
[tex]44 + x = 90 \text{ // Subtract 44 on both sides}\\44 + x - 44 = 90 - 44\\\to x = 46[/tex]
Question 1 (1 point)
Willorie Ford moves to Lake Havasu City Arizona to try out a food truck. She sets up shop
under London Bridge and notices that her business is "seasonal".
On December 1, she makes $450 per day.
On March 1, she makes $800 per day.
On June 1, she makes $450 per day.
On September 1, she makes $100 per day.
On December 1, she makes $450 per day.
Estimate how much she would make on certain days and draw a model.
By this model, she would make $
By this model, she would make $
By this model, she would make $
By this model, she would make $
on February 1. (Round to the nearest dollar)
on May 1. (Round to the nearest dollar)
on July 1. (Round to the nearest dollar)
on August 1. (Round to the nearest dollar)
Step-by-step explanation:
2,250 was made in a month
Find the product of (134−2.4)⋅[0.5⋅(25+2.6)]
Answer: the product is 1816.08
Step-by-step explanation:
The required product of the expression is 1816.08.
Given that,
To determine the product and simplified value of the expression (134−2.4)⋅[0.5⋅(25+2.6)]
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= (134−2.4)⋅[0.5⋅(25+2.6)]
= (131.6) * [0.5 * 27.6]
= 131.6 * 13.8
= 1816.08
Thus, the required product of the expression is 1816.08.
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Oh no! Mike solved the equation below for y:
10x - 3y = 6
Let's help him fix it!
1. Circle the mistake within the problem (on the
whiteboard at the left).
2. Describe his mistake in the box below (be sure to
be specific).
The mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y
How to determine the mistake in the equation solution?The solution of the equation is given as
10x - 3y = 6
+3y +3y
----------------------------
10x = 3y + 6
-6 -6
----------------------------
(10x - 6)/3 = 3y/3
10x - 2 = y
In the above steps, we have the following equation
(10x - 6)/3 = 3y/3
When the above equation is expanded, we have
10x/3 - 6/3 = 3y/3
Evaluate the quotient in the above equation
So, we have
10x/3 - 2 = y
The abvoe equation is different from Mike's result
Hence, the mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y
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I need help with this, can someone help me?
Answer: 5y^2
Step-by-step explanation: hope this helps
Answer: it is the third option
Explanation: as any number with a negative power will be the reciprocal
----> y^-2 = 1/y^2
----> 5 x 1/y^2
----> 5/y^2
i hope this helps
How many ounces of honey would you need to mix with 11 ounces of strawberries?
55 ounces of honey will need to mix with 11 ounces of strawberries.
Question is not complete so lets suppose that,
For each ounce of mix, we use honey five times of a ounces of strawberry.
And then we will find that how many ounces of honey we would to mix with 11 ounces of strawberries.
According to above statement
one ounce of strawberries = 5 ounce of honey
So, for the mix we will need to add honey which will we equal to five times of strawberries.
If we have 11 ounces of strawberries then,
the amount of honey will be = 5 × 11 = 55 ounces
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