How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $12,000 in four years?
Given rate is = 7% or 0.07
Total amount needed = $12000
Time = 4 years
Here, the deposit is compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.
The equation becomes:
P= [tex]\frac{12000}{(1+\frac{0.07}{2})^{2.4}}[/tex]
P = [tex]\frac{12000}{1.035^{8}}[/tex]
Solving it, we get P = $ 9112.93
Hence $9112.93 should be deposited today.
To accumulate $12,000 in four years in an account earning 7% compounded semiannually, approximately $8,289.64 should be deposited today.
Explanation:To find out how much money should be deposited today in an account that earns 7% compounded semiannually to accumulate to $12,000 in four years, we can use the formula for calculating compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal (initial deposit), 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.
Let's substitute the given values into the formula: A = 12,000, r = 7%, n = 2 (compounded semiannually), and t = 4.Now, we can solve for P: 12,000 = P(1 + 0.07/2)^(2*4)By simplifying the equation, we get: 12,000 = P(1.035)^8Divide both sides of the equation by (1.035)^8: P = 12,000 / (1.035)^8 = 8,289.64Hence, approximately $8,289.64 should be deposited today in the account.
Learn more about compound interest here:https://brainly.com/question/14295570
#SPJ3
Five friends are chipping in for a birthday gift for their teacher. David and Jakob each con tribute $13. Stephanie Kate and Janice each contribute eight dollars. What percentage of the total did the girls contribute
Answer:
48%
Step-by-step explanation:
Given that five friends are chipping in for a birthday gift for their teacher.
They were David, Jakob , Stephanie, Kate and Janice
Boys contributed 13 dollar each i.e. a total of 26
Girls contributed 8 each i.e. a total of 24
total contribution =50
Out of total contribution 50, girls total contrbution = 24
Hence percent = 24(100)/50 = 48%
Randy is checking to determine if the expressions 2x+2+4x and 2(3x+1) are equivalent. When x=3, he correctly finds that both expressions have a value of 20. When x=2, he correctly evaluates the first expression to find that 2x+2+4x=14.What is the value of the second expression when x=2 and are the two expressions equivalent?A. The value of the second expression is 7, so the expressions are not equivalent.B. The value of the second expression is 12, so the expressions are not equivalent.C. The value of the second expression is 14, so the expressions are equivalent.D. The value of the second expression is 20, so the expressions are equivalent.
Answer: c. ;]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
Paul's mp3 player has a total of 852 songs. He has 4 different groups of songs. If he puts an equal number of songs in each group,how many songs will be in each group?
Answer:
There will be 213 songs in each group.
Step-by-step explanation:
Suppose, the number of songs in each group is [tex]x[/tex]
As he has 4 different groups of songs, so the total number of songs in all 4 groups will be: [tex](4*x)= 4x[/tex]
Given that, the mp3 player has a total of 852 songs. So, the equation will be........
[tex]4x=852\\ \\ x=\frac{852}{4}=213[/tex]
So, there will be 213 songs in each group.
The equation of a hyperbola is x^2-4y^2-2x-15=0. What is the width of the asymptote rectangle?
Answer: 8
Step-by-step explanation:
x² - 2x + ___ - 4y² = 15 + ___
x² - 2x + 1 - 4y² = 15 + 1
(x - 1)² - 4(y)² = 16
[tex]\frac{(x-1)^{2}} {16} - \frac{4(y - 0)^{2}}{16} = \frac{16}{16}[/tex]
[tex]\frac{(x-1)^{2}} {16} - \frac{(y - 0)^{2}}{4} = 1[/tex]
[tex]r_{x} = 4[/tex] [tex]r_{y} = 2[/tex]
width of rectangle is 2[tex](r_{x})[/tex] = 2(4) = 8
Kim had some candy to give to her four children she fist took two pieces for herself and then evenly divided the rest among her children. Each child received four pieces. With how many pieces did she start?
simplify: 3 times the square root of 5 - 2 times the square root of 7 + the square root of 45 - the square root of 28
2 times the square root of 12
2 times the square root of 2
six times the square root of 5 - four times the square root of 7
six times the square root of 10 - four times the square root of 14
6 on the sq rt 5 - 4 on the sq rt 7
To simplify the given expression, substitute the values of each square root and simplify the expression to get the final result of 1.416.
To simplify the given expression:
3 times the square root of 5 - 2 times the square root of 7 + the square root of 45 - the square root of 28
We can simplify each square root separately:
√5 = 2.236 (approx.)
√7 = 2.646 (approx.)
√45 = 6.708 (approx.)
√28 = 5.292 (approx.)
Substituting these values in the expression:
3(2.236) - 2(2.646) + 6.708 - 5.292
This simplifies to:
6.708 - 5.292 = 1.416
Therefore, the simplified expression is 1.416.
Learn more about Simplifying square roots here:
https://brainly.com/question/13446308
#SPJ12
PLEASE HELP!!! WILL GIVE LOTS OF POINTS IF ANSWERED!!!
Write each equation in slope-intercept form of the equation of a line. Underline the slope and circle the y-intercept in each equation.
a
3x+4y–12=0
Answer:
The slope − intercept form is __
The slope is __
The y − intercept is ( __ , __)
Slope intercept form: y=3/4 - 3
slope:3/4
Y-intercept: -3
Because you subtract 4y from both sides to get it on the other side of the equation. You don’t want it to be 4y=3x-12 though so you would divide both sides by 4 which would give you y=3/4x-3. I hope this is right and it helps
please help on this one?
A i think it could be wrong im only in middle school
This one should be C. Just look at the corresponding letters and plants. It’s easy once you get the numbers and items correctly equaling each other.
Which of the following is a counterexample to the statement "All odd numbers are divisible by 3"?
7 is a prime number
9 is divisible by 3
8 is not divisible by 3
3 is divisible by itself
Answer:
That 9 is divisible by 3.
Step-by-step explanation:
For this case we have the following statement:
"All odd numbers are divisible by 3"
The options given are the following:
a) 7 is odd but not divisible by 3, therefore it is a counterexample of the given statement
b) 9 is odd and is divisible by 3, therefore it is not counter-example
c) 8 is an even number, it is not a counter-example
d) 3 is odd and affirms the given statement.
Therefore, the correct answer is option A.
Answer:
Option A
Matrix M shows the one-way fares for four commuter train routes. If the rail service raised fares by 12% on all routes and days, which formula shows how to find the matrix that would display the new fares?
A) 0.12M
B) M + 0.12
C) M + 0.12M
D) 1 + 0.12M
Answer:
C) M + 0.12M
Step-by-step explanation:
A — calculates the raise, not the new fare
B — adds 12¢ to every fare
C — adds 12% of the current fare to the current fare. This is what you want.
D — adds $1 to the amount of the raise. This is not the amount of the new fare.
Answer: C) [tex]M+0.12M[/tex]
Step-by-step explanation:
Given : Matrix M shows the one-way fares for four commuter train routes.
If the rail service raised fares by 12% on all routes and days.
Then, the proportion of service raised fares on all routes and days. =0.12
Then, the new fares is given by :-
[tex]M+0.12M[/tex]
Hence, the formula shows how to find the matrix that would display the new fares = [tex]M+0.12M[/tex]
Find the interval(s) over which the function is increasing
Answer : (-∞,-1) U (-1, 1)
We need to find the interval(s) over which the function is increasing
We look at the intervals of x where the graph is increasing
Increasing interval of the graph is the part where the graph goes up.
At first the graph starts increasing and it increases till x=-1
So the first increasing interval is -infinity to -1 . We write it as (-∞,1)
Now, we look at the part where the graph changes direction
In the middle inverted U shaped graph , the graph starts increasing at x=-1 and increases till it changes direction. The graph is increasing till x=1
so second increasing interval is x=-1 to 1. we write it as (-1,1)
Now combine both intervals by a 'U' union
(-∞,-1) U (-1, 1)
The interval(s) over which the function that is increasing is (-∞,-1) U (-1, 1)
What is the intervalFrom the question, One need to find the interval(s) over which the function is increasing
Since intervals of x where the graph is increasing Increasing interval of the graph is the part where the graph goes up.
At first the graph starts increasing and it increases till x=-1, So the first increasing interval is -infinity to -1 . We write it as (-∞,1). So, one look at the part where the graph changes direction
In the middle inverted U shaped graph , the graph starts increasing at x=-1 and increases till it changes direction. The graph is increasing till x=1
Since the increasing interval is x=-1 to 1. one then need to write it as (-1,1)
So, The function is increasing for all values of x in the open interval from negative infinity to negative 1, excluding -1, and also in the open interval from -1 to 1, excluding both -1 and 1."
Learn more about interval from
https://brainly.com/question/5661267
#SPJ4
Jane paid $40 for an item after she received a 20% discount. Jane's friend says that this means that the original price was $48. A) How do you think Jane's friend arrived at this amount? B) Is her friend correct? Why or why not?
Answer:
A) She must have used 20% from the $40 instead of the unknown price.
B) No, because: see below explanation.
Step-by-step explanation:
X is the original price.
If $40 is 80% of x, to find 1% of the price, divide $40 by 80.
You will get $0.50 for 1%.
To find the full amount, just multiply that by 100.
0.50*100= 50.
Total: $50.
Hope this helped!
Jane's friend calculated the original price by dividing $40 by 80 and multiplying by 100. However, they made a mistake in their calculations. The correct original price before the 20% discount should be $50.
Explanation:A) It seems that Jane's friend arrived at $48 by considering $40 as 80% of the original price. Since Jane received a 20% discount, it means she paid 80% of the original price. Thus, her friend might have calculated by dividing $40 by 80 and then multiplying by 100 to find the original price.
B) However, her friend's calculation is incorrect. If we indeed divide $40 by 80 and multiply by 100, we get $50, not $48. This means the original price of the item is $50.
To further illustrate this, let's consider the original price to be 'x'. If Jane received a 20% discount, she paid only 80% of 'x'. So, 0.8x = $40. Solving for 'x', we get x = $40 / 0.8 = $50.
Learn more about Discount Calculation here:https://brainly.com/question/35988155
#SPJ3
Which formula can be used to determine the number of different 8-letter arrangements using the letters of the word UNIVERSE?
A.
8!
B.
8P2
C.
8!/2!
D.
8!•2!
A hardcover book sells for 24$ at the bookmart. Ben pays 25.02 for the book. What is the sales tax rate?
Which of the following is the correct expansion of (x + 3)(x - 4)?
A.x2 - 7x + 12
B.x2 - x + 12
C.x2 + 7x - 12
D.x2 - x - 12
Using FOIL (First, Outer, Inner, Last):
(x+3)(x-4)
FIRST: multiply x times x to get x^2.
OUTER: multiply x times -4 to get -4x.
INNER: multiply 3 times x to get 3x.
LAST: multiply 3 times -4 to get -12.
Your expression now looks like:
x^2-4x+3x-12
Combine like terms.
x^2-x-12
The answer is D. x^2-x-12.
I hope this helps :)
At what point on the curve x^2 + y^2 = 9 is the tangent line vertical?
x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3.
This puts the vertices at (-3, 0), (3, 0), (0, -3), and (0, 3).
When is the tangent line vertical? when it passes through the x-axis.
Answer: (-3, 0), (3, 0)
Factor each polynomial completely over the set of complex numbers.
1. a(x)=2x^4-3x^3-24x^2+13x+12
2. b(x)=x^4-2x^3-17x^2+4x+30
3. c(x)=2x^3-5x^2+12x-5
Answer:
1. a(x) = (x-4) (x-1) (2x+1) (x+3)
2. b(x) = (x^2-2) (x-5) (x+3)
3. c(x) = (2x-1) (x^2- 2x + 5)
Do questions 1 and 2 (View picture for question 1 )
1. Milton wants RST to be similar to KLM. where should he place S?
A.(1,3)
B.(1,6)
C.(2,3)
D. (2,6)
2. Evaluate 3 - 4(x + 2) when x = 0
Each number in the first table represents the points scored by a player on the Ace Academy basketball team. Make a frequency distribution, including relative frequency (percent of total: )
1
5
8
10
10
13
3
6
9
10
11
13
3
7
9
10
12
14
4
7
10
10
12
14
For the relative frequencies below, round to the nearest tenth.
Answer:
We know that, the frequency table consists of the number of times the number is appearing.
Also, 'relative frequency is the percent of the total of the frequencies'.
So, the corresponding frequency table is given by,
Points Scored Frequency Relative Frequency (%)
1 1 4.17
3 2 8.33
5 1 4.17
6 1 4.17
7 2 8.33
8 1 4.17
9 2 8.33
10 6 25
11 1 4.17
12 2 8.33
13 2 8.33
14 2 8.33
As, the total of the frequency is 24. So, we get the relative frequency table above.
The relative frequencies of the given data are as follows:
1: 0.043: 0.084: 0.045: 0.046: 0.047: 0.088: 0.049: 0.0810: 0.1711: 0.0412: 0.0813: 0.0814: 0.08.What are the relative frequencies of the given data?Relative frequency is the proportion of the number of occurrences of a particular value to the total number of values.
The frequency of each value are:
Frequency of 1: 1Frequency of 3: 2Frequency of 4: 1Frequency of 5: 1Frequency of 6: 1Frequency of 7: 2Frequency of 8: 1Frequency of 9: 2Frequency of 10: 4Frequency of 11: 1Frequency of 12: 2Frequency of 13: 2Frequency of 14: 2The total number of values = 24
The relative frequency of each value are:
Relative frequency of 1: 1/24 ≈ 0.0417Relative frequency of 3: 2/24 ≈ 0.0833Relative frequency of 4: 1/24 ≈ 0.0417Relative frequency of 5: 1/24 ≈ 0.0417Relative frequency of 6: 1/24 ≈ 0.0417Relative frequency of 7: 2/24 ≈ 0.0833Relative frequency of 8: 1/24 ≈ 0.0417Relative frequency of 9: 2/24 ≈ 0.0833Relative frequency of 10: 4/24 = 1/6 ≈ 0.1667Relative frequency of 11: 1/24 ≈ 0.0417Relative frequency of 12: 2/24 ≈ 0.0833Relative frequency of 13: 2/24 ≈ 0.0833Relative frequency of 14: 2/24 ≈ 0.0833.Read more about relative frequencies
brainly.com/question/30063075
#SPJ4
Sandra saves 12% of her salary for retirement. This year her salary was $3000 more than in the previous year, and she saved $4200. What was her salary in the previous year?
The previous year's salary is x.
This year's salary is x + 3000.
12% of this year's salary is $4200.
12% * (x + 3000) = 4200
0.12(x + 3000) = 4200
x + 3000 = 35,000
x = 32,000
Answer: Her salary in the previous year was $32,000.
Draw a model to represent 3/4 divided by 3/12
The answer you are looking for is 1/3.
First, you must look at the denominators of each fraction, to see if you can simply divide straight across. In this case, you cannot, which means you must multiply by the reciprocal or "flipped" number. Generally when you multiply by the reciprocal, you flip the number with the smaller denominator to multiply.
So, you have 4/3 * 3/12. You then multiply straight across (4 * 3)/(3 * 12), to get an answer of 12/36, which simplified (divided by 3/3) gives you a final answer of 1/3.
I hope this helps!
The required model is attached in the image and the division of 3/4 by 3 /12 is 3.
Given that,
To draw the model to represent 3/4 divided by 3/12.
In mathematics, it deals with numbers of operations according to the statements.
Model hs been attached below for the given problem of division,
= 3 * 4 / 3 * 12
For a rectangle space, drawing 4 column and 12 raws,
Now for 3 / 4 3 of the 4 column to be filled by red, for 3 / 12 every 3 cells in the row have been filled by red.
Calculating number of cells in 3 / 4 = 36
calculating number of cells in 3 / 12 = 12
Now ratio of the cells = 36 / 12 = 3
Thus, the required model is attached in the image and the division of 3/4 by 3 /12 is 3.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
A store sold 55 pairs of shoes for 85.60 each. Later all the proceeds were spent buying 100 scarves. How much does a scaf cost?
Answer:
4.28 $
Step-by-step explanation:
Given that a store sold 55 pairs of shoes for 85.60 each.
Sale proceeds = 55(85.60) = 428 dollars.
Later on 100 scafs were purchased. For that the price was 428 dollars.
The proceeds of 428 dollars were spent buying 100 scarves.
i.e. price of 100 scarves = 428 dollars
Hence price of 1 scarve = 428/100 = 4.28 $
Price of 1 scarve is 4.28 dollars is the answer
What are the coefficients in the expression 24x-3y+7z?
so, the coefficient will 24, -3, and 7. The letters next to the coefficients are called "variable".
What is the apparent solution to the system of equations graphed above?
(3,2)
(2,3)
(0,-3)
(0,2)
The solution of the system of equations is (2, 3), the second option.
What is the apparent solution to the system of equations graphed above?When we have a system of equations, one way of solving it is graphing both equations in the same coordinate axis and then finding the point where the graphs intercept.
Here we can see two lines, and the lines intercept at the point (2, 3), so we can say that the solution of the system is (2, 3), which is the second option.
Learn more about systems of equations at.
https://brainly.com/question/13729904
#SPJ4
A swimming pool in 65.25 feet long and 40.5 feet wide. How much longer is the pool than it is wide?
Okay so you subtract those two and you get 24.75.
You have to find how much more the length is compared to the width
You subtract the length by the width
65.25 - 40.5 = 24.75
The answer is 24.75 feet
BRAINLIEST?!
simplify 9i(2+3i)
Show work
Simplify the expression
(-5+2i)(3-4i)
Show work
Simplify 4i|-28|
Answer:
9i(2+3i) = -27+18i
Step-by-step explanation:
Distribute to get → 9i·2+9i(3i)
Multiply 2 and 9 → 18i+9i(3i)
Simplify → 18i+27i²
Simplify → 18i-27
Reorder → -27+18i
Evaluate 2d+
+32, d, plus, 3 when d=8=d equals, 8.
The value of the expression 2d + 32 is 48 when d equals 8.
The student has provided an expression 2d + 32 and the value for d is given as 8. In order to evaluate the expression, we simply need to substitute the value of d into the expression.
Evaluating the expression:
2d + 32
= 2(8) + 32
= 16 + 32
= 48.
So, the value of the expression when d = 8 is 48.
Leeza did this to solve an equation. Did she makes an error 4x=7+3(2x-5) 4x=7+6x-5
Yes, there was a mistake in applying the distributive property. If you have to perform
[tex] 3(2x-5) [/tex]
you have to multiply both terms in the parenthesis by 3, not just the first one.
So, the correct expansion would be
[tex] 3(2x-5) = 3\cdot 2x - 3 \cdot (-5) = 6x-15 [/tex]
Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 4x=7+3(2x-5).
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, 4x=7+6x-15
4x=6x-8
4x-6x= -8
-2x=-8
x=4
Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.
To learn more about the solution of an equation visit:
https://brainly.com/question/14506845.
#SPJ5
60 boys at a summer camp were asked to complete a survey about their favorite outdoor activity. 18 boys chose biking and 29 boys chose fishing. The remaining boys did not complete the survey. What expression gives the percent of survey participants who chose fishing?
Answer: The percent of survey participants who chose fishing= 61.70%
Step-by-step explanation:
Total number of participants who completed survey= 18 + 29= 47
Now, the number of participants who chose fishing= 29
So,
The percent of survey participants who chose fishing= (the number of participants who chose fishing/the number of participants who completed survey)x100
The percent of survey participants who chose fishing= 29/47x100
The percent of survey participants who chose fishing= 61.70%
Answer:
Step-by-step explanation: 29/18+29 x 100