Suppose that $15,000 is the deposited for five years at 4% APR calculate the interest earned if interest is compounded semiannually round your answer to the nearest cent
Answers
Remember that
The compound interest formula is equal to
\(A=P(1+\frac{r}{n})^{nt}\)where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$15,000
t=5 years
r=4%=0.04
n=2
substitute the given values
\(A=15,000(1+\frac{0.04}{2})^{2\cdot5}\)A=$18,284.92
therefore
The interest is equal to
I=A-P
I=18,284.92-15,000
I=$3,284.92Related Questions
Marc goes to the store with exactly $1.00 in change. He has
at least one of each coin less than a half-dollar coin, but he
does not have a half-dollar coin.
a. What is the least number of coins he could have?
b. What is the greatest number of coins he could
have?
Answers
Answer:
Least amount: 11 coins
Greatest amount: 63 coins
Step-by-step explanation:
If you want the least amount of coins, you need coins of greater value and the opposite for the greatest amount of coins.
The least amount of coins:
3 quarters, 1 dime, 2 nickels, 5 pennies
The greatest amount of coins:
1 quarter, 1 dime, 1 nickel and 60 pennies
PLEASE ANSWER QUICKLY
What is the correct definition for sec 0? A. sec 0 = cos-1 0 B. sec 0 = sin-1 0 C. sec 0 = 1/sin 0 D. sec 0 = 1/cos 0 E. sec 0 = 1/tan 0
Answers
sec(theta) = 1/cos(theta)
I believe that is your option D
(a)Profit function P(x) (b)Find the number items which need to sold in order to maximize profit. (c)Find maximum profit. (d)The price to charge per item order to maximize profit. (e)Find and interpret break even point .
Answers
Answer:
Explanation:
• The cost to produce x T-shirts: C(x)=2x+26, x≥0
,• The price-demand function per shirt: P(x)=30-2x, 0≤x≤15.
The revenue generated from the sale of x T-shirts will be:
\(R(x)=x\times P(x)=x(30-2x)\)The profit earned will be:
\(\begin{gathered} \text{Profit}=\operatorname{Re}venue-\text{Cost} \\ P(x)=R(x)-C(x) \\ =x(30-2x)-(2x+26) \\ =30x-2x^2-2x-26 \\ =-2x^2+30x-2x-26 \\ P(x)=-2x^2+28x-26 \end{gathered}\)Next, we maximize the profit.
This is done by taking the derivative of P(x), setting it equal to 0 and solving for x.
\(\begin{gathered} P^{\prime}(x)=-4x+28 \\ \text{Set P'(x)=0} \\ -4x+28=0 \\ 4x=28 \\ x=7 \end{gathered}\)The number of items that need to be sold to maximize profit, x=7.
Maximum Profit
Substitute x=7 into P(x) to find the maximum profit.
\(\begin{gathered} P(x)=-2x^2+28x-26 \\ \implies P(7)=-2(7)^2+28(7)-26=-98+196-26 \\ =-98+196-26 \\ =72 \end{gathered}\)The maximum profit is $72.
Price to charge
When x=7
\(\begin{gathered} P(x)=30-2x \\ P(7)=30-2(7)=30-14=16 \end{gathered}\)The company needs to charge $16 per item to maximize profit.
Break-Even Point
To break even, the cost must be equal to revenue.
\(\begin{gathered} R(x)=C(x) \\ x(30-2x)=(2x+26) \\ -2x^2+30x-2x-26=0 \\ -2x^2+28x-26=0 \\ 2x^2-28x+26=0 \\ 2x^2-2x-26x+26=0 \\ 2x(x-1)-26(x-1)=0 \\ (2x-26)(x-1)=0 \\ 2x-26=0\text{ or }x-1=0 \\ x=13\text{ or }x=1 \end{gathered}\)If 1 T-shirt is sold, the company breaks even.
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 7.5%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $825. How much was the hotel charge in each city before tax?
Answers
The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.
Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500 (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825 (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.
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Ling wants to determine the average distance she travels each day in her car. She records the odometer reading, which measures the distance the car has traveled, each morning for a week. What is the mean distance Ling travels each day? Show your work.( Will Mark Brainliest if answer is correct)
Answers
Answer: \(10,724.28\)
Step-by-step explanation:
Given
Distance traveled on each consecutive day is given as
\(10150,10211,10424,10769,10884,11155,11477\)
Mean is given by the sum of the observations divided by the total no of observations.
There are 7 observations in total, so the mean is
\(\Rightarrow \mu =\dfrac{10150+10211+10424+10769+10884+11155+11477}{7}\\\\\Rightarrow \mu=\dfrac{75,070}{7}\\\\\Rightarrow \mu =10,724.28\)
thus, the mean is \(10,724.28\)
The mean distance Ling travels each day is \(10724.28 \: \rm miles\) approximately.
How to find the mean value of a data set?The mean value of the data set is the ratio of sum of data set's values to number of values it has.
If the data set consists of values \(x_1, x_2, ..., x_n\), then we get the mean value as:
\(\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}\)
For this case, we have to find the average distance(in miles) from the distance Ling traveled for 7 days.
Thus, we get the average distance he traveled as:
\(\overline{d} = \dfrac{10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477 }{7}\\\\\overline{d} = \dfrac{75070}{7} \approx 10724.28 \: \rm miles\)
Thus, the mean distance Ling travels each day is \(10724.28 \: \rm miles\) approximately.
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8.
Identify the point corresponding to Q.
A. Q′ (−4, 1)
B. Q′ (−1, −4)
C. Q′ (−3, −4)
D. Q′ (−4, −3)
Answers
Answer:
C. Q′ (−3, −4)
D. Q′ (−4, −3)
Step-by-step explanation:
From looking at the graph it looks like the answer would be
Q= (3, -4) if the X-axis goes first
Q= (-4, 3) if the Y-axis goes first
the image is the question
a) c = 22 feet
b) c = 23
c) c = 24
d) c = 30
Answers
The length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
The Pythagorean theorem, which asserts that given a right triangle, the sum of the squares of the two shorter sides (a and b), is equal to the square of the hypotenuse (c), can be used to determine the length of the triangle's hypotenuse (c).
a = 10 feet
b = 20 feet
Using the Pythagorean theorem, we can calculate c as follows:
c^2 = a^2 + b^2
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
To find c, we take the square root of both sides:
c = √500
c ≈ 22.36
Rounding the answer to the nearest whole number, we get c ≈ 22.
Therefore, the length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
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in the pediatric unit of a hospital has 165 beds how many are there if each room holds 3 beds
Answers
Answer:
There are 55 rooms
Step-by-step explanation:
There are 165 beds in the hospital. Each room contains 3 beds. In order to find the number of beds per room, take the total number of beds and divide it by the number of rooms in each bed. 165/3=55. There are 55 rooms in the hospital, all containing 3 beds.
Hope this helps!
In the following diagram,
What is the measure of
∠x
Answers
Answer:
Step-by-step explanation:
BAD = 42
x + 103 + 42 = 180
x = 180 - 145
x = 35
please tell me answer! i’ll give brainliest
Answers
Answer:
Answer: B. It is a perfect square
Step-by-step explanation:
Radical Expressions
Melissa multiplied \(\sqrt{a}\) and \(\sqrt{b}\) and got a rational number.
We are also given that a and b are both natural numbers. It means their product must be not only rational but also a natural number.
We can write that product like:
\(\sqrt{a} \cdot \sqrt{b}=\sqrt{a\cdot b}\)
If the result is a natural number, then the product of a and b must be a perfect square. so the radical disappears.
Answer: B. It is a perfect square
The image of B translated using (x + 2, y + 3) would have what coordinates?
Answers
Answer:
(5, 4)
Step-by-step explanation:
(x + 2, y + 3)
Substitute x and y for that of B's position.(3 + 2, 1 + 3)
(5, 4)
Answer:
B' (5, 4 )
Step-by-step explanation:
the translation rule (x, y ) → (x + 2, y + 3 )
means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then
B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )
Mako runs 10 miles in 2 hours. If he continues at this rate, how many miles
will he run in 5 hours?
A. 50 miles
B. 10 miles
O C. 25 miles
O D. 30 miles
Answers
Answer:
Answer: 25 miles
Step-by-step explanation:
Explanation: He will run 5 hours= 5x5=25
Answer:
25 miles
Step-by-step explanation:
I'll create a set of proportions to figure out the answer (represented by x):
2:10 = 5:x
It looks like our proportion on the left, 2:10, can be simplified by dividing both sides by 2 to get 1:5.
1:5 = 5:x
You can multiply 1 by 5 to get 5, so we should be able to multiply 5 by 5 to get the value of x. 5 times 5 is 25, so the answer to the question is 25 miles.
If you have questions or need clarification on anything, let me know!
-2a-6a-9=-9-6a-2a
help please g
Answers
Answer:
the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).
Step-by-step explanation:
To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:
Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.
Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.
Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).
In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).
whoever answers this correctly gets brainliest
Answers
Answer:
3: D) 11
4: D) 12
7: C) 63
8: A) Adjacent Angles
Step-by-step explanation:
Let's pretend the sides of a triangle are A B and C.
The third side of a triangle is always greater tham A-B and lesser than A+B. This is called the triangle inequality theorem.
For 7 and 8, we have three lines that come together at one point (adjacent angles), and the vertical angle postulate where two mirrored angles will always have the same angle.
factor 49x^2-7^2
and please explain how
Answers
Answer:
\(49x^2-7^2=49(x-1)(x+1)\)
Step-by-step explanation:
Factoring
We need to recall this property of binomials:
\((a-b)(a+b)= a^2-b^2\)
It allows us to factor the difference between two squares as follows.
\(a^2-b^2=(a-b)(a+b)\)
The given expression is
\(49x^2-7^2\)
Comparing with the above expression:
\(a^2=49x^2\)
Taking square root:
\(a = 7x\)
\(b^2=7^2\)
Taking square root:
b=7
Factoring:
\(49x^2-7^2=(7x-7)(7x+7)\)
Now we can see each factor can be taken out the common factor 7:
\(49x^2-7^2=7(x-1)*7(x+1)\)
Multiplying:
\(\boxed{49x^2-7^2=49(x-1)(x+1)}\)
Whats the answer we need help?its been along time since i did this
Answers
Answer:
Try either 33.6 or 24
Step-by-step explanation:
I'm not really sure but it's either one of these two. Good luck
The graph compares the weights in pounds of 100 dogs and cats that are brought in
to a veterinarian's office. Using the medians, how much more does a typical dog weigh than a typical cat?
Answers
Answer:20
Step-by-step explanation:this is wrong
Answer:
40
Step-by-step explanation:
subtract median of dogs and median of cats
Given f(x) = 2x² - 3 and g(x) = x + 1 determine g(f(3)
Answers
Answer:
g(f(3)) = 16
Step-by-step explanation:
Step 1: Define
f(x) = 2x² - 3
g(x) = x + 1
f(3) = x = 3
Step 2: Find f(3)
f(3) = 2(3)² - 3
f(3) = 2(9) - 3
f(3) = 18 - 3
f(3) = 15
Step 3: Find g(15)
g(15) = 15 + 1
g(15) = 16
g(f(3)) = 16
Merrisa is booking a holiday costing £660.
She needs to pay a deposit of of the total cost of the booking
How much does she pay?
Answers
The amount of money she will have to pay for booking of the holidays would be = £220
How to calculate the amount ofr deposit?The total amount of money that will cost Merrisa for booking of holidays = £660
The fraction of the total cost that she needs to deposit = 1/3
Therefore, the actual amount that she needs to deposit = 1/3 of £660
= 1/3× 660
= £220
Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.
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The water level in a burette is 30cm3 if 55 drops of water fall from the burette and the average volume of one drop is 0.12cm3 what is the final water level in the burette ?
Answers
Answer:
The final water level in the burette is \(23.4\ cm^3\)
Step-by-step explanation:
It is given the water level in a burette is \(30\ cm^3\). The burette loses 55 drops, each one with an average volume of \(0.12\ cm^3\).
If each drop has a volume of \(0.12 cm^3\), then 55 drops have a volume of \(55*0.12\ cm^3=6.6\ cm^3\)
The new level of water in the burette is the subtraction of the original contents minus the volume loss.
New volume = \(30\ cm^3-6.6\ cm^3\)
New volume = \(23.4\ cm^3\)
The final water level in the burette is 23.4\ cm^3
What is the value of the expression m - when m = 3?
1/15
13/15
23/15
Answers
The value of the expression when m = 3 is 13/15. So option(2) is correct.
The equation is defined in its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, x + 3 = 4 is an equation, in which x + 3 and 4 are two expressions separated by an 'equal' sign.
Given the expression as shown below:
2/5 m - 1/3
If m is equal to 3, then the expression will be;
2/5(3) - 1/3
6/5 - 1/3
Find the LCM
6/5 - 1/3 = 3(6)-5/15
6/5 - 1/3 = 18-5/15
6/5 - 1/3 = 13/15
Therefore the value of the expression if m = 3 is 13/15
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The length of a rectangle is 5 cm more than its width. If the perimeter is 58cm, calculate:
(a) Write an equation to show the perimeter of the rectangle ?
(b) calculate:
I.width
II.length
III. the area of the rectangle
Answers
The equation to show the perimeter of the rectangle is P = 2(2w + 5)
Writing an equation to show the perimeter of the rectangleFrom the question, we have the following parameters that can be used in our computation:
Length = 5 more than the width
Also, we have
Perimeter = 58
This means that
P = 2(w + 5 + w)
P = 2(2w + 5)
Calculating the dimensions and the areaIn (a), we have
P = 2(2w + 5)
This gives
2(2w + 5) = 58
So, we have
2w + 5 = 29
2w = 24
w = 12
Next, we have
l = 12 + 5
l = 17
Lastly, we have
Area = 17 * 12
Area = 204
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factorise x³-4x²+x+6
Answers
The binomial factors of x³- 4x²+x+6 are (x+2), (x+3), and (x-1).
Using the splitting and grouping the terms:
x³ + 4x² + x - 6
= x³ + 2x² + 2x² + x - 6 [Splitting 4x² = 2x² + 2x²]
= (x³ + 2x²) + (2x² + x - 6)
= x² (x + 2) + (2x² + 4x - 3x - 6)
= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]
= x² (x + 2) + (x + 2) (2x - 3)
= (x + 2) ( x² + 2x - 3)
= (x + 2) ( x² + 3x - x - 3)
= (x + 2) [x (x + 3) - 1 (x + 3)]
= (x + 2) (x + 3) (x - 1)
Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
Answer:
–6x + 15 < 10 – 5x
A number line from negative 3 to 7 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Step-by-step explanation:
Given inequality\(-3(2x-5) < 5(2-x)\)
Solving the inequalityExpand the brackets:
\(\implies -6x+15 < 10-5x\)
Add 6x to both sides:
\(\implies 15 < 10+x\)
Subtract 10 from both sides:
\(\implies 5 < x\)
\(\implies x > 5\)
Therefore, x is bigger than 5.
Graphing the inequalityWhen graphing inequalities on a number line:
< or > = open circle≤ or ≥ = closed circle< or ≤ = shade to the left> or ≥ = shade to the rightTo graph the given inequality on a number line:
place an open circle at 5draw a line starting at 5 and pointing to the rightConclusionTherefore, the correct representations of the given inequality are:
–6x + 15 < 10 – 5xA number line from negative 3 to 7 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
\(\\ \rm\leadsto -3(2x-5)<5(2-x)\)
a(b+c)=ab+ac\(\\ \rm\leadsto -6x+15<10-5x\)
Option C
\(\\ \rm\leadsto -x<-5\)
\(\\ \rm\leadsto x>5\)
Rest are wrong
) Emily baked a cake in 42.5 minutes. She finished making dinner 9 1/10 minutes sooner than the cake. How long did it take her to make dinner? Hint: Change the 9 1/10 to a decimal
Answers
It took Emily 33.4 minutes to make dinner.
Define a mixed number?A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.
To solve the problem, we have to convert the mixed number \(9 \frac{1}{10}\) to a decimal number:
⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)
⇒ \(\frac{91}{10}\) = 9.1
This means that Emily finished making dinner 9.1 minutes sooner than the cake.
To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:
⇒ 42.5 - 9.1 = 33.4 minutes
Therefore, it took Emily 33.4 minutes to make dinner.
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GEOMETRY 80POINTS
ty!
Answers
Answer:
x ≈ 77.79 ft
Step-by-step explanation:
using the sine ratio in the right triangle
sin40° = \(\frac{opposite}{hypotenuse}\) = \(\frac{50}{x}\) ( multiply both sides by x )
x × sin40° = 50 ( divide both sides by sin40° )
x = \(\frac{50}{sin40}\) ≈ 77.79 ft ( to the nearest hundredth )
the dimension of the confirms room or 7.2 M * 11 M what is the area of the conference room
Answers
Step-by-step explanation:
Just multiply the two dimensions to get m^2 area
7.2 m * 11 m = 79.2 m^2
Steven conjectures that for |x|>5, it is true that x^3>125. Is his conjecture correct? Why or why not?
Answers
Answer:
yes
Step-by-step explanation:
it is correct because, since x>5, anything relating x and 5 together will always put x greater than 5.
1.1.3 Quiz: Exponents
Question 2 of 10
Simplify (6^7)³.
Answers
Answer:6^21
Step-by-step explanation:
The owner of a local shop made a list of how much she pays her employees by the hour.
Which measure of central tendency would the store owner use if she wanted to argue that the employees are paid well?
A. the mean
B. the median
C. the mode
D. the range
GIVING BRAINLIST
Answers
Answer: The answer is D
Step-by-step explanation:
I took the quiz