a) When Ozzie Foster deposits $2,000 at the end of each year,
amount in account after 25 years = $126571.43
b) If Ozzie had deposited the $2,000 at the beginning of each year,
amount in account after 25 years = $135431.43
What is annuity?An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income stream for retirees.
Given,
Value of each payment P = $2000
Rate of interest per period in decimal r = 7% = 0.07 per year
Number of years n = 25
a) future value of ordinary annuity
FV = P×((1+r)ⁿ−1) / r
FV = 2000×((1+0.07)²⁵−1) / 0.07
FV = 2000×((1.07)²⁵−1) / 0.07
FV = 2000×(5.43 - 1 )/ 0.07
FV = 2000×4.43/ 0.07
FV = 8860/0.07
FV = $126571.43
b) future value of annuity due
FV = (1+r)P×((1+r)ⁿ−1) / r
FV = (1+0.07) × $2000((1+0.07)²⁵ - 1)/0.07
FV = 1.07 × 2000×((1.07)²⁵−1) / 0.07
FV = 1.07 × 2000×(5.43 - 1 )/ 0.07
FV = 1.07 × 2000 × 4.43 / 0.07
FV = 2140 × 4.43 / 0.07
FV = 9480.2 / 0.07
FV = $135431.43
Hence,
a) $126571.43 is the amount in the account when Ozzie Foster deposits $2,000 at the end of each year.
b) $135431.43 is the amount in the account If Ozzie had deposited the $2,000 at the beginning of each year.
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convert the following measurement to the units giving in brackets 0.38km (metres)
Answer:
380m
Step-by-step explanation:
1km=100m
0.38km=
0.38×1000/1=
380m
Twenty less than a number is more than twice the same number . Find the smallest possible value of the number.
The smallest possible value of the number that is an integer is -21
Determining the value of a numberFrom the question, we are to determine the smallest possible value of the number
From the given information, we have that
"Twenty less than a number is more than twice the same number"
Let the number be x
Then,
we can write that
x - 20 > 2x
Now, we will solve for x
x - 20 > 2x
-20 > 2x - x
-20 > x
Therefore,
x < -20
The possible integers are -21, -22, -23, -24, -25, -26, ...
Then,
The smallest integer is -21
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Kayla had a balance of $65 in her savings account before withdrawing $28. What is her new balance? $83 $93 $43 $37
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 9 cm long. A second
side of the triangle is 22.5 cm long. Find all possible lengths for the third side of the triangle.
The Angle Bisector Theorem states that in a triangle, if a line bisects one angle of a triangle and is also a median to the side opposite of that angle, then the ratio of the length of the median to the length of the side opposite the angle bisected is equal to the ratio of the length of the other two medians.
Therefore, if the angle bisector divides the opposite side into segments 6 cm and 9 cm long, the ratio of the length of the median to the length of the side opposite the angle bisected is 6/9.
Let x be the length of the third side of the triangle.
The Angle Bisector Theorem states: (x/22.5) = (6/9)
Solving for x, we get: x = (22.5 * 6/9) = 15
So the length of the third side of the triangle is 15 cm.
This is the only possible length for the third side of the triangle because the Angle Bisector Theorem only holds if the angle bisector is also a median to the side opposite of that angle.
Impulse is a vector quantity ,T or F?
Answer: True
Step-by-step explanation: Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it.
A bakery produces 280 loaves of bread and 95 cakes daily.
explain how you would compute the percent of the baked foods that are cakes.
The percent of the baked foods that are cakes will be 25.33%
How to calculate the percentage?It should be noted that a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %. In this situation, the bakery produces 280 loaves of bread and 95 cakes daily.
The percent of the baked foods that are cakes will be:
= Number of cakes / Number produced daily × 100
= 95 / (280 + 95) × 100
= 95 / 375 × 100
= 25.33%
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Problem is in the attached image pls help thank you!
The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
State Alternate angle theorem?
The angles which are formed inside the two parallel lines, when intersected by a transversal, are equal to its alternate pairs. These angles are called alternate interior angles.
When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.
Angles that are on opposite sides of the transversal are called alternate angles. All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.
In the above-given figure, you can see, two parallel lines intersected by a transversal AB.
So according to the alternate angle theorem,
m∠3 = m∠6
Now moving on to the students' explanations, both logics are correct.
Hence we can say that according to the alternate angle theorem,
m∠3 = m∠6
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PLEAE HELPP WILL MARK BRAINLIEST
Given that my=34°, find the value of the angle b
A 146°
B 56°
C 34°
D 124°
E 68°
Answer: D - 124°
Step-by-step explanation: Since y and a are vertical angles, we can determine that angle a is equal to 34°
90° + 34° = 124°
180° - 124° = 56°
Now we know the last angle in the triangle. Since this angle is on the same line as angle b, subtracting it from 180 would give us angle b
180° - 56° = 124°
Jason is considering purchasing a new machine to make plastic silverware. The machine produced 1,000 pieces of silverware in two hours. one box contains 50 pieces of silverware and sells or $3.00. If the machine costs $9.00 and runs for 24 hours a day, how many days will it take the machine to make enough silverware to pay for itself?
The output voltage of an amplifier is calculated by multiplying the input voltage by the voltage gain of the amplifier. Calculate the output voltage, in millivolts (mV), for a circuit if the input voltage is 45 mV and the gain is 30.
The output voltage, in millivolts (mV), for the circuit would be equal to 1,350 millivolts.
What is an amplifier?An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.
The output voltage of an amplifier= input voltage × gains.
We have been given that input voltage = 45 mV
The gain = 30
Therefore, the output voltage= 45×30
= 1350millivolts.
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Please look at the picture and answer the question thank you
Answer:
( - inf, 5) (9, inf )
Step-by-step explanation:
The arrow(s) at the end of the line indicate that the highlighted green line does not stop at a specific number, hence the use of infinity signs (inf). If the arrow is going to the left on a line, then the value would be negative infinity. If it is going to the right, then it would be positive.
As for the space in between the green arrows pointing separate ways, there are two points, one which is positioned at the number 5 and the other at the number 9. Because there are two separate points which are both solid green, the use of parentheses is needed. The final answer is, as mentioned, ( - inf, 5) (9, inf ).
How do I divide with rational expressions.
The value of the rational expression is q⁴ / 14p⁴
What are rational expressions?A rational expression is the ratio of two polynomials. If f is a rational expression, then f can be written in the form p/q where p and q are polynomials.
Given are rational expressions,
5pq / 16p³ ÷ 35p²q² / 8q⁵
Using identity, a/b ÷ c/d = a/b × d/c
5pq / 16p³ × 8q⁵ / 35p²q²
= 40q⁴ / 560p⁴
= q⁴ / 14p⁴
Hence, the value of the expression is q⁴ / 14p⁴
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HELPPPP ???
Select the correct statement about the system of equations.
the answer is letter d)
if u arrange it correctly it will be -x +2y=2
-½x+y=1
then multiply -½ by the first equation and multiply -1 by the second equation..
then change the signs of the second equation
then cancel x .. then y =1
then substitute y with 1
..it won't be correct
There are 100 cm in 1m. How many sntimeters are there in b m?
Answer:
100,000,000,000cm
Step-by-step explanation:
there are one hundred billion cm in one billion meters.
Place value of the 4 in 2, 487, 492
The table of values represents a quadratic function f(x).
x f(x)
−8 13
−7 6
−6 1
−5 −2
−4 −3
−3 −2
−2 1
−1 6
0 13
What is the equation of f(x)?
f(x) = (x + 5)2 − 2
f(x) = (x + 4)2 − 3
f(x) = (x − 4)2 − 3
f(x) = (x − 5)2 − 2
The correct equation of quadratic equation is,
⇒ f (x) = (x + 4)² - 3
We have to given that;
The table of values represents a quadratic function f(x).
And, Values are,
x f(x)
−8 13
−7 6
−6 1
−5 −2
−4 −3
−3 −2
−2 1
−1 6
0 13
Now, By given options;
f (x) = (x + 5)² - 2
Put x = - 8, f (x) = 13;
13 = (- 8 + 5)² - 2
13 = 9 - 2
13 ≠ 7
From (ii);
f (x) = (x + 4)² - 3
Put x = - 7, y = 6;
6 = (- 7 + 4)² - 3
6 = 9 - 3
6 = 6
Hence, The correct equation of quadratic equation is,
⇒ f (x) = (x + 4)² - 3
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Write the following in polar form
The horizontal axis is the real axis and the vertical axis is the imaginary axis. We find the real and complex components in terms of r
and θ
where r
is the length of the vector and θ
is the angle made with the real axis.
From Pythagorean Theorem :
r2=a2+b2
By using the basic trigonometric ratios :
cosθ=ar
and sinθ=br
.
Multiplying each side by r
:
rcosθ=a and rsinθ=b
The rectangular form of a complex number is given by
z=a+bi
.
Substitute the values of a
and b
.
z=a+bi =rcosθ+(rsinθ)i =r(cosθ+isinθ)
In the case of a complex number, r
represents the absolute value or modulus and the angle θ
is called the argument of the complex number.
This can be summarized as follows:
The polar form of a complex number z=a+bi
is z=r(cosθ+isinθ)
, where r=|z|=a2+b2−−−−−−√
, a=rcosθ and b=rsinθ
, and θ=tan−1(ba)
for a>0
and θ=tan−1(ba)+π
or θ=tan−1(ba)+180°
for a<0
.
Example:
Express the complex number in polar form.
5+2i
The polar form of a complex number z=a+bi
is z=r(cosθ+isinθ)
.
So, first find the absolute value of r
.
r=|z|=a2+b2−−−−−−√ =52+22−−−−−−√ =25+4−−−−−√ =29−−√ ≈5.39
Now find the argument θ
.
Since a>0
, use the formula θ=tan−1(ba)
.
θ=tan−1(25) ≈0.38
Note that here θ
is measured in radians.
Therefore, the polar form of 5+2i
is about 5.39(cos(0.38)+isin(0.38))
.
Which figure below shows the correct vector relationship between voltage and current in a parallel LC circuit?
Therefore , solving the provided vector question we can say that Figure B best describes the voltage and current in parallel LC circuit
what is vector?In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow.
Given :
Vector as given :
Figure A, Figure B , Figure C and Figure D
Voltage and current
parallel LC circuit
=>Iₙ * Eₙ = Iₙ
Size and direction are two independent characteristics of a quantity or phenomena known as a vector.
The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.
Here,
From observation we can say that ,
Figure B best describes the voltage and current in parallel LC circuit
Figure B
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PLEASE HELPPPP IM BEGGING!!!!!!!!!!!!!!!!
Answer: C
Step-by-step explanation:
It's C, as they represent the same ratio.
Gary earned $97,000 as an executive. Gary, who is single, supported his half sister, who
lives in a nursing home. His half sister had no income during the year. Gary received
the following interest: $400 on City of Los Angeles bonds, $200 on a money market ac-
count, and $2,100 on a loan made to his brother.
Gary spent one week serving on a jury and received $50.
Gary received a refund of federal income taxes withheld during the prior year of
$1,200 and a state income tax refund of $140. Gary had itemized deductions last year of
$18,000 which included $1,000 of state income taxes.
Can you please help with this question by putting the information into an Excel spreadsheet to get Taxable Income and Adjusted Gross Income? Thanks
Answer:
Step-by-step explanation:
Sure, here is an example of how the information provided could be organized in an Excel spreadsheet to calculate Taxable Income and Adjusted Gross Income: see in the attached e1 and e2 screenshots.
It's worth noting that the above example is a simplified version, and the actual calculations for tax purposes would depend on the specific tax laws and regulations in the relevant jurisdiction and year. Also, the numbers provided here are not the final Taxable Income, it's only the calculation of Taxable Income based on the information provided.
What is this and how do I solve this? I never seen anything like this.
Answer: This is evaluataion, To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Step-by-step explanation: In this situation you are going to divide the numerator and denominator by 2. For example 2/8 makes 1/4. 1/4 is equivalent to 2/8 but not fully simplified.
Another way to solve this is to reduce to lowest terms. For example, 5/15 is reduced by dividing the numerator and denominator by 5 to get 1/3.
Divide the numerator and denominator to get a decimal form of the fraction or divide 5+2 by 3+6
what is the answer to this problem because i am having trouble.
By using some exponent properties, we can simplify the expression to get:
√(100)² = 100
How to simplify the given expression?Here we will be using two exponent properties, these are:
√a = a^(1/2)
And:
(a^n)^m = a^{n*m}
The given expression here is:
√(100)²
Using the first property, we can rewrite this as:
( 100¹/²)²
And using the second property, we can rewrite as:
( 100¹/²)² = 100²*⁽¹/²⁾ = 100¹ = 100
That is the simplified expression.
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find the exact volume of a waffle ice cream cone with a 9 in diameter and a height of 17 inches
The exact volume of the waffle ice cream cone is 114.75π square inches
Calculating the volume of a coneFrom the question, we are to determine the volume of the waffle ice cream cone
The volume of a cone can be calculated by using the formula,
V = 1/3πr²h
Where V is the volume
r is radius
and h is the height
From the given information,
Diameter = 9 in
∴ Radius, r = 9/2 in = 4.5 in
h = 17 in
Putting the parameters into the formula, we get
V = 1/3 × π × 4.5² × 17
V = 114.75π square inches
Hence, the volume is 114.75π square inches
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I need help with this
Answer:
Step-by-step explanation:
the answer will be option 4
solve for x,y answer
Step-by-step explanation:
here it is earning more money to the doctor said the
Solve the following equation 5x - 1 = 24
Answer:
x = 5
Step-by-step explanation:
5x - 1 = 24
=5x = 24 + 1
=5x = 25
=5x/5 = 25/5
x = 5
Hence the value for x is 5.
Answer:
Step-by-step explanation: 5x - 1 = 24
=> 5x = 24 + 1
=> x = 25/5
=> x = 5
Jasmine claims “to find the lowest common multiple of two numbers, you can multiply them together. For example, 5 × 8 = 40 and the LCM of 5 and 8 is 40”
Is Jasmine correct? Justify your answer.
Answer:
No, Jasmine is not correct. The Lowest Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. Multiplying the two numbers together is not always the correct method to find the LCM.
For example, the LCM of 5 and 8 is 40, but the product of 5 × 8 = 40 is not the LCM.
A more accurate way of finding the LCM is by using the prime factorization of the numbers. By finding the prime factorization of the two numbers, you can take the highest exponent of each prime factor and multiply them together. The result of that multiplication is the LCM of the two numbers.
In this case, the prime factorization of 5 is 5 and 8 is 2^3. The LCM of 5 and 8 is 2^3*5 = 40. So Jasmine's claim that 5 x 8 = 40 and the LCM of 5 and 8 is 40 is not correct.
How to solve x^2 + 12x = 13 using completing the square
Answer: x = 1, -13
Step-by-step explanation:
We will solve this by completing the square, as asked in the instructions. If we do this correctly, we will end up with a perfect square that will allow us to solve more easily.
Given:
x² + 12x = 13
Set the equation equal to 0 by subtracting both sides of the equation by 13:
x² + 12x - 13 = 0
Group the first two terms:
(x² + 12x) - 13 = 0
Add and subtract [tex]\frac{b}{2} ^2[/tex] to the grouped terms:
(x² + 12x + 36 - 36) - 13 = 0
Regroup the terms, move the negative out and simplify:
(x² + 12x + 36) - 49 = 0
Factor the grouped terms (6 is our perfect square here):
(x + 6)(x + 6) - 49 = 0
Add 49 to both sides of the equation and simplify the factors:
(x + 6)² = 49
Square root both sides of the equation:
x + 6 = 7 x + 6 = -7
Subtract 6 from both sides of each equation:
x = 1 x - 13
What Income tax should be on 400 naira at the rate of 2¹/2 kobo per Naira? A. 2 Naira B. 4 Naira C. 5 Naira D. 10 Naira E. 15 Naira
Step-by-step explanation:
A. Hawa Enterprise is a small retail business located in Changlun, Kedah. Follows are information on bank transactions of Hawa Enterprise as at 31 July 2022:
a. Cash on the book was RM34,635.
b. Cash as shown on the bank statement was RM35,296.
c. A deposit of RM3,500, representing cash receipts on 31 July, did not appear on the bank statement.
d. Outstanding cheque include cheques No 2031, No 2558, and No 2783 with the amount respectively RM530, RM1,551 and RM2,100.
e. The bank collected RM810 on a note receivable for Hawa Enterprise. The bank charged a collection fee of RM10 which was credited to Hawa Enterprise’s account.
f. An NSF cheque for RM950 from a customer, En Mansor, was returned with the bank statement.
g. The bank paid correctly an amount of RM3,680 for cheque No 2805 which was recorded in a book as RM3,860. h. Bank service charges for July 2022 amounted to RM50.
REQUIRED:
Prepare the bank reconciliation statement for Hawa Enterprise as at 31 July 2022.
B. Beginning July 2022, Hawa Enterprise has established a petty cash fund for its small expenditures. The following transactions took place during the month of July:
5/7 Established a RM300 petty cash fund with cash withdrawn from the company’s current account.
30/7 The petty cash fund has RM12 remaining and is replenished. Expenditures for July were RM75 for supplies, RM60 (meals), RM80 (postage), RM50 (amenities) and RM25 (freight-in).
REQUIRED:
Prepare the journal entries for the above transactions.
a(b-c)=de Solve for c
Answer:
Step-by-step explanation:
a(b - c) = de
b - c = de/a
-c = de/a - b
c = b - de/a
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