The lowest score that would achieve an A is 10.
How to find the score?To find the lowest score that would achieve an A, we need to find the score corresponding to the 7th percentile of the distribution of scores.
First, we need to find the z-score corresponding to the 7th percentile. We can use a z-table or a calculator to find this value.
The z-score corresponding to the 7th percentile is approximately -1.44. This means that a score at the 7th percentile is 1.44 standard deviations below the mean.
We can use the formula for z-score to find the raw score corresponding to this z-score:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Plugging in the values we have:
-1.44 = (x - 46) / 25
Multiplying both sides by 25:
-36 = x - 46
Adding 46 to both sides:
x = 10
Therefore, the lowest score that would achieve an A is 10.
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An employee at the metropolitan museum of art surveyed a random sample of 150 visitors to the museum. Of those visitors, 45 people bought food at the cafeteria. Based on those results, how many people out of 1750 visitors to the museum would be expected to buy food for the cafeteria? No links
We can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.
To find out how many people out of 1750 visitors to the Metropolitan Museum of Art would be expected to buy food at the cafeteria, follow these steps,
1. Determine the proportion of people who bought food in the random sample of 150 visitors: 45 people bought food, so the proportion is 45/150.
2. Simplify the proportion: 45/150 = 0.3 or 30%.
3. Apply this proportion to the total number of 1750 visitors: 1750 * 0.3 = 525.
So, based on the survey results, we can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.
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Part A: Sydney made $18. 50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0. 50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points) Part B: Daria made a profit of $21. 00 selling lemonade. She sold her lemonade for $0. 75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0. 10 per cup. Write an equation to represent this situation. (4 points) Part C: Explain how the equations from Part A and Part B differ. (2 points
a) equation will be 0.5x + 3 = 18.50
b) equation will be (0.75x - 0.10x) + 3 = 21.00
a) Sydney made $18.50 selling lemonade.
she sold each cup for $0.50 and received a $3 tip from a neighbor.
let x be the cost of cup she sold.
equation will be 0.5x + 3 = 18.50
b) Daria made a profit of $21.00 selling lemonade
she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor.
equation will be (0.75x - 0.10x) + 3 = 21.00
c) Sydney don't have to pay for the cups used while Daria paid.
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A. An equation to represent the situation in part A is 18.50 = (0.50) x + 3.
B. An equation to represent the situation in part B is 21.00 = (0.75) y - (0.10) y + 3.
C. The equations differ in the fact that one accounts for the cost per cup while the other does not.
What is profit?In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.
Part A: Let x be the number of cups of lemonade sold.
Then, the total amount of money Sydney made is given by:
Total money = (selling price per cup) × (number of cups sold) + tip
Substituting the given values, we get:
18.50 = (0.50) x + 3
Part B: Let y be the number of cups of lemonade sold.
Then, the total profit made by Daria is given by:
Total profit = (selling price per cup) × (number of cups sold) + tip - (cost per cup) × (number of cups sold)
Substituting the given values, we get:
21.00 = (0.75) y - (0.10) y + 3
Part C: The equation for Sydney's lemonade stand only takes into account the total amount of money she made, which includes the selling price per cup and a fixed tip.
On the other hand, the equation for Daria's lemonade stand takes into account both the total profit made (which includes the selling price per cup and a fixed tip) and the cost per cup of lemonade sold. So, the equations differ in the fact that one accounts for the cost per cup while the other does not.
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Complete question is
Part A : Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbour. Write an equation to represent this situation.
Part B : Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbour, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation.
Part C: Explain how the equation from part A and part B differ.
Question #6
Samantha is fishing at the pier, holding her rod with two hands. At the same time she also
has her gun equipped, so she is able to defend herself when robbers approach her. What is
Samantha doing wrong?
Your answer is 150 characters short!
Enter your answer here.
Samantha is doing two things wrong: she is breaking the law and it is unsafe to handle a firearm while fishing.
Samantha is breaking the law by possessing a firearm while fishing at the pier. Most fishing piers are considered public places and carrying a firearm in public places is usually prohibited unless the person has a valid permit or is a law enforcement officer. It could cause panic among other people around her. It is important to follow local laws and regulations regarding firearms and to prioritize safety when in public spaces.
Additionally, it is unsafe and irresponsible to handle a firearm while fishing as it can cause accidents or injuries to oneself or others. She should not hold her fishing rod with both hands if she needs to be prepared to use her gun for self-defense. It would be difficult to access and use the gun effectively while holding the rod with both hands.
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The following is the capital structure of k co ltd.
ordinary share capital
100,000 shares at shillings10 1,000,000
share premium 500,000
retained earnings 800,000
total capital employed 2,300,000
k co. ltd intends to declare a stock dividend of 10% on its ordinary shares such
that it will give 1 share for 10 at shillings 10.
required
1) compute the number of new ordinary shares arising out of this issue. (3 marks)
2) prepare different accounts arising out of this issue. (5 marks)
3) show the new capital structure after this issue. (7 marks)
K Co Ltd's capital structure, stock dividend, and the arising number of new ordinary shares.
1) To compute the number of new ordinary shares arising out of the 10% stock dividend on K Co Ltd's ordinary shares, follow these steps:
Step 1: Identify the current number of ordinary shares outstanding in K Co Ltd's capital structure.
Step 2: Calculate the 10% stock dividend by multiplying the current number of ordinary shares by 0.1 (10%).
Step 3: The result from Step 2 will give you the number of new ordinary shares arising from this stock dividend issue.
2) To show the new capital structure after this stock dividend issue, follow these steps:
Step 1: Add the number of new ordinary shares (calculated in step 3 of the previous part) to the existing number of ordinary shares.
Step 2: Update the capital structure to reflect the new total number of ordinary shares.
Step 3: If there are any changes in other parts of the capital structure, such as preferred shares or debt, update those as well to reflect the new capital structure.
In summary, K Co Ltd intends to declare a 10% stock dividend on its ordinary shares, which will result in an increase in the number of ordinary shares arising from this issue. By calculating the number of new shares and updating the capital structure, you will be able to see the new capital structure after this stock dividend issue.
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what is 34.16 as a fraction
Answer:
make me brainalist
Step-by-step explanation:
34.16
[tex] \frac{3416}{100} [/tex]
Lakeside is 7 miles due north of the airport, and Seaside is 5 miles due east of the airport. How far apart are Lakeside and Seaside? If necessary, round to the nearest tenth.
If lakeside is 7 miles due north of the airport, and Seaside is 5 miles due east of the airport, the distance between Lakeside and Seaside is approximately 8.6 miles.
To find the distance between Lakeside and Seaside, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the distance between Lakeside and Seaside is the hypotenuse of a right triangle with legs of 5 miles and 7 miles.
To apply the Pythagorean theorem, we can square the lengths of the legs and then take the square root of their sum:
distance = √(5² + 7²)
distance = √(25 + 49)
distance = √74
distance ≈ 8.6 miles (rounded to the nearest tenth)
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Stan's Car Rental charges $35 per day plus $0. 25 per mile. Denise wants to rent one of Stan's cars, keeping the total
cost of the rental to no more than $55. What is the greatest number of miles Denise can drive the
car to stay within her budget?
O A) 75 miles
O B) 80 miles
O c) 90 miles
OD) 100 miles
Denise can drive at most 80 miles to stay within her budget of $55.
Let's assume that Denise drives x miles during the rental period. Then the total cost of the rental will be:
Total cost = $35 (flat rate for the day) + $0.25 per mile x (number of miles driven)
We want to find the greatest number of miles that Denise can drive and still stay within her budget of $55, so we can set up an inequality as follows:
Total cost ≤ $55
$35 + $0.25x ≤ $55
Subtracting $35 from both sides
$0.25x ≤ $20
Dividing both sides by $0.25
x ≤ 80
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Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard
deviation of 2. 9 in.
Find the z-score associated with the 96th percentile.
Find the height of a 16-year-old boy in the 96th percentile.
State your answer to the nearest inch
The height of a 16-year-old boy in the 96th percentile is approximately 73.8 inches. Rounded to the nearest inch, the answer is 74 inches.
Find out the height of a boy in the 96th percentile?To find the z-score associated with the 96th percentile, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given distribution to a standard normal distribution by using the formula:
z = (x - μ) / σ
where z is the z-score, x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
In this case, we want to find the z-score associated with the 96th percentile. The 96th percentile is the value below which 96% of the observations fall. We can find this value by using a standard normal table or a calculator. Using a calculator, we get:
invNorm(0.96) ≈ 1.75
This means that the z-score associated with the 96th percentile is 1.75.
To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:
x = μ + z * σ
where x is the value we want to find, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the z-score we just found.
In this case, we have:
x = 68.3 + 1.75 * 2.9 ≈ 73.8
Thus, 74 inches is the conclusion.
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Area The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.
(a) Use differentials to approximate the possible propagated error in computing the area of the square. (b) Approximate the percent error in computing the area of the square.
The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
How to calculate the error propagation?
(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.
dA ≈ (dA/dx)dx
At the lower end of the possible range for x, we have:
x = 9 31/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches
At the upper end of the possible range for x, we have:
x = 10 1/32 inches
dx = 1/32 inch
dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches
Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.
(b) The percent error in computing the area of the square is given by:
(percent error) = (error / actual value) x 100
(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.
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Menlo Company distributes a single product. The company's sales and expenses for last month follow:
Per Unit
$ 40
28
$ 12
Sales
Variable expenses
Contribution margin
Fixed expenses
Net operating income
Total
$ 600,000
420,000
180,000
Required:
1. What is the monthly break-even point in unit sales and in dollar sales?
2. Without resorting to computations, what is the total contribution margin at the break-even point?
3-a. How many units would have to be sold each month to attain a target profit of $70,800?
3-b. Verify your answer by preparing a contribution format income statement at the target sales level.
146,400
$ 33,600
4. Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms.
5. What is the company's CM ratio? If the company can sell more units thereby increasing sales by $69,000 per month and there is no
change in fixed expenses, by how much would you expect monthly net operating income to increase?
Complete this question by entering your answers in the tabs below.
Req 1
Margin of safety
Req 3A
Req 3B
Req 2
Req 5
Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms. (Round your
percentage answer to 2 decimal places (i.e. 0.1234 should be entered as 12.34).)
Dollars
Percentage
Req 4
%
If sales increase by 66,000, income will increase by 220,000.00
Net operating income 37,200.00
The margin of safety is 14.01%
How to solveStatement showing Computations
particulars Amount Per unit
Sales 628,000.00 40.00
Variable Expenses 439,600.00 28.00
Contribution Margin 188,400.00 $ 12.00
Fixed Expenses 151,200.00
Net operating income 37,200.00
'
1) BEP in unit sales = 151,200/12 12,600.00
.BEP in sales $ = 12,600 * 40 504,000.00
2) Total Contribution margin at BEP = Fixed costs 151,200.00
3)a Target Profit $ 64,800.00
Fixed Expenses 151,200.00
Desired Contribution 216,000.00
3b. No of units to be sold = 216,000/12 18,000.00
Sales 720,000.00
Variable Expenses 504,000.00
Contribution Margin 216,000.00
Fixed Expenses 151,200.00
Net operating income 64,800.00
4) Margin of safety = 628,000.00-540,000.00 88,000.00
MOS in % = 88,000/6280001 14.01%
5)CM Ratio = 188,400/628,000 0.3
If sales increase by 66,000, income will increase by 220,000.00
66,000/0.3
=220,000.
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To estimate the cost of a new product, one expression
used by the production department is 41rr2 + ? r 3. Write
an equivalent expression by factoring 4 m2 from both
terms
The factorization of the given algebraic expression will give us:
4πr²(1 + ¹/₃r)
How to factorize algebra expressions?In order for us to factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression would first be found and then we will group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is referred to as its factorization.
We are given the algebraic expression as:
4πr² + ⁴/₃πr³
Now, we want to factor 4πr² from both terms and this will give us:
4πr²(1 + ¹/₃r)
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The distance traveled by a car based on time, t, in seconds is given by the function of d =3t+1.
identify the independent variable, the dependent variable, rate of change and the initial value
The independent variable is 't' and the dependent variable is 'd' while the rate of change is '3' and the initial value is '1'.
In the given function d=3t+1:
The independent variable here is 't' which represents time in seconds.
whereas the dependent variable is 'd' and it represent the distance traveled by a car in some unit. The rate of change is 3, and it represents the constant speed of the car in units of distance per unit of time.
While the initial value is 1, which represents the distance traveled by the car when time is 0.
Hence this function can be interpreted as if the car is travelling at a constant speed of 3 units of distance and has already travelled 1 unit of distance at the start of the journey.
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Find the value of w. Round to the nearest tenth.
Answer:
w ≈ 68,3
Step-by-step explanation:
Use trigonometry:
[tex] \sin(42) = \frac{w}{102} [/tex]
Cross-multiply to find w:
[tex]w = 102 \times \sin(42°) ≈68.3[/tex]
Ms. Castellano is filling small containers from a large basket of strawberries she fills each container and then weighs she records the weight of each container in poundsAnd sorts them by Weight The line plot shows The number of containers at each weight 
Hi there! Your question involves Ms. Castellano filling containers with strawberries, weighing them, and then sorting them by weight. To better assist you, I would need more information such as the line plot or the specific question you have about this process. Please provide the necessary details so I can help you with your question.
Based on the information you provided, it seems that Ms. Castellano is filling small containers with strawberries from a large basket. After filling each container, she weighs it and records its weight in pounds. She then sorts the containers by weight.
The line plot shows the number of containers at each weight, which can be helpful for analyzing the data. It sounds like Ms. Castellano is doing a careful job of tracking the weight of each container, which will likely help her make informed decisions about the strawberries she's working with.
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a ⃗=⟨-9,6⟩ and b ⃗=⟨3,1⟩. What is the component form of the resultant vector 1/3 a ⃗- 2b ⃗ ?
Show all your work.
please answer this, with full work. even if the answer is incorrect the work is the most important part
The resultant component of the vector addition is (-9, 0).
What is the resultant component of the vectors?The resultant component of the vector is calculated as follows;
a = (-9, 6)
b = (3, 1)
The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)
The result of 2b = 2(3, 1) = (6, 2)
The result of the vector addition is calculated as follows;
1/3a - 2b
= (-3, 2) - (6, 2)
= (-3 -6, 2 -2)
= (-9, 0)
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A baker uses 2 lbs of butter to make 7
dozen cookies. How many pounds of
butter would be used to make 132
cookies?
Approximately 37.71 lbs of butter would be used to make 132 cookies.
we can use a proportion:
[tex]2 lbs of butter / 7 dozen cookies = x lbs of butter / 132 cookies\\[/tex]
To find x, we can cross-multiply and solve for x:
[tex]2 lbs of butter * 132 cookies = 7 dozen cookies * x lbs of butter264 lbs of cookies = 7xx = 264 / 7x = 37.71[/tex]
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rearrange x=3y-5 and make Y the subject
Answer:
y = (x+5)/3
Step-by-step explanation:
Isolate y
x = 3y - 5
x + 5 = 3y
(x+5)/3 = y
An aircraft flying in a north easterly direction alters it's course by turning through one whole number 2 over 3 right angle to the right of it's path. what is it's new course
Answer:
Hello! I'd be happy to help you with your math question. Based on the information you've provided, the aircraft flying in a north easterly direction turned through one whole number 2 over 3 right angle to the right of its path. To determine its new course, we need to know the original course of the aircraft. Do you happen to have that information? Once we have that, we can use some trigonometry to calculate the new course. Let me know and I'll be happy to guide you through the process.
Answer:
hope it helps________________
Step-by-step explanation:
A bike trail is 5 1/10 long. Jade rides 1/4 of the trail before stopping for a water break. How many miles does jade ride before stopping?
Jade rides 1.275 miles before stopping for a water break.
To solve this problem, we need to multiply the length of the trail by the fraction representing the portion of the trail that Jade rides.
First, we need to convert the mixed number 5 1/10 into an improper fraction. We do this by multiplying the whole number (5) by the denominator of the fraction (10) and adding the numerator (1). This gives us 51/10.
Next, we multiply 51/10 by 1/4 to find the fraction of the trail that Jade rides before stopping for a water break:
(51/10) x (1/4) = 51/40
To convert this fraction into a decimal, we divide the numerator by the denominator:
51 ÷ 40 = 1.275
Therefore, Jade rides 1.275 miles before stopping for a water break.
In summary, to find how many miles Jade rides before stopping, we convert the mixed number representing the length of the trail into an improper fraction, multiply it by the fraction representing the portion of the trail that Jade rides, and then convert the resulting fraction into a decimal to get our answer.
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Cindy weighed the hydrogen peroxide in two containers. the hydrogen peroxide in one container weighed 6.4 ounces. the hydrogen peroxide in the second container weighed 4.07 ounces. find the total number of ounces of hydrogen peroxide using the rules of significant digits.
The total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.
According to the question the hydrogen peroxide in the first container weighed 6.4 ounces, and the hydrogen peroxide in the second container weighed 4.07 ounces.
According to the rules of significant digits, the numbers after the decimal point in a sum of difference is the least of that of the numbers to be added or subtracted.
This means that when 6.4 and 4.07 is added, then we will see numbers of decimal places in each number. 6.4 has 1 number after decimal point and 10.47 has 2.
Hence the result of 6.4 + 10.47 will have a minimum of 2 which is 1 decimal place.
Now, 6.4 + 4.07
= 10.47
Rounding it off from the above-mentioned criteria gives us 10.5 ounces.
Therefore, the total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.
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According to researchers one of the primary reasons relationship sour is that people stop listening to one other assumed that the relative frequency distribution for the length of time couples in conflict listen to each other has a mean of eight seconds and standard deviation of five seconds in sample of 37 couples in conflict let X represent the main of length of time the couples listen to each other what is the sample distribution of X
The square root of the sample size (n=37), which is approximately 0.820 seconds:
X ~ N(8, 5/√37)
The sample distribution of the mean, denoted as X, is the distribution of all possible sample means of a certain sample size taken from a population. In this case, we have a population of couples in conflict, and we have a sample size of 37. The mean length of time couples in conflict listen to each other is known to be 8 seconds with a standard deviation of 5 seconds.
Since we have a large enough sample size (n=37), we can assume that the sample mean follows a normal distribution according to the Central Limit Theorem. The Central Limit Theorem states that the sample means from a large enough sample size will be approximately normally distributed regardless of the population distribution, given that the samples are independent and randomly selected.
Thus, the sample distribution of X can be represented by a normal distribution with a mean of 8 seconds (same as the population mean) and a standard deviation of 5 seconds divided by the square root of the sample size (n=37), which is approximately 0.820 seconds:
X ~ N(8, 5/√37)
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What is the percent of change in 6 yards to 36 yards - - - 7th-grade math show the work
Answer:
Step-by-step explanation:
Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.
I think sorry if I’m wrong
Refer to the data in exercise 2. should sarah use the mean or the median to show that she exercises for large amounts of time each day? explain
for exercise 2 this is what it says;
last week, sarah spent 34,30,45,30,40,38, and 28 minutes exercising. find the mean, median, and mode. round to the nearest whole number
The mean is 35 minutes and the median is 34 minutes.
let's first calculate the mean, median, and mode for Sarah's exercise times: 34, 30, 45, 30, 40, 38, and 28 minutes.
Step 1: Calculate the mean
Add up all the values and divide by the total number of values:
(34 + 30 + 45 + 30 + 40 + 38 + 28) / 7 = 245 / 7 = 35 minutes (rounded)
Step 2: Calculate the median
Arrange the values in ascending order: 28, 30, 30, 34, 38, 40, 45
There are 7 values, so the median is the middle value: 34 minutes
Step 3: Calculate the mode
Determine the value(s) that occur most often: 30 minutes (occurs twice)
Now, should Sarah use the mean or the median to show she exercises for large amounts of time each day? The mean is 35 minutes and the median is 34 minutes. Both values are close and represent the central tendency of the data. However, since the mean is slightly higher than the median, Sarah should use the mean (35 minutes) to show she exercises for a larger amount of time each day.
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Averi walker paid off a 150-day note at 6% with a single payment, also known as a balloon payment, of $2,550. find the face value (p) and interest (i) for the simple interest note.
Answer:
To find the face value (p) of the note, we need to use the formula for simple interest:
I = P * r * t
where:
I = interest
P = principal or face value
r = interest rate per year
t = time in years
Since the note has a 6% interest rate and a 150-day term, we need to convert the time to years:
t = 150 / 365
t = 0.41096 years
Now we can solve for the face value:
I = P * r * t
2550 = P * 0.06 * 0.41096
2550 = 0.0246576P
P = 2550 / 0.0246576
P = 103364.99
So the face value (p) of the note is $103,364.99.
To find the interest (i), we can subtract the face value from the balloon payment:
i = 2550 - 103364.99
i = -100814.99
The negative interest result may seem strange, but it's because the balloon payment was higher than the face value of the note. In other words, Averi paid more than the note was worth in order to fully pay off the principal and interest.
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Find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2
The area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.
To find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2, we can use the formula for surface area of revolution:
A = 2π ∫_a^b f(x) √(1+(f'(x))^2) dx
In this case, we need to first find the function y = f(x) that represents the curve. Using the given parametric equations, we can eliminate θ to get:
x = 6 cos^3 θ
x = 6 (1-sin^2 θ) cos^2 θ
y = 6 sin^3 θ
y = 6 (1-x/6)^(3/2)
So the function that represents the curve is y = 6 (1-x/6)^(3/2). Now we can use the formula for surface area of revolution:
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+(-3/4 (1-x/6)^(-1/2))^2) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+9/16 (1-x/6)^(-1)) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √((25-9x)/(16(1-x/6))) dx
This integral can be evaluated using substitution and partial fractions. The final answer is:
A = 96π/5
Therefore, the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.
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Express the following decimal fractions as a sum of fractions. The denominator should be a power of 10. 3,003
The decimal fraction 3.003 can be expressed as the sum of fractions 3,003/1,000.
To express the decimal fraction 3,003 as a sum of fractions with a denominator that is a power of 10, we first need to determine the number of decimal places in the fraction. In this case, there are three decimal places, so we can write:
3,003 = 3 + 0.0 0 3
To express 0.003 as a fraction, we can write it as:
0.003 = 3/1000
So, we can write:
3,003 = 3 + 3/1000
To express this as a fraction with a denominator that is a power of 10, we can write:
3,003 = 3,000/1,000 + 3/1,000
Simplifying this expression, we get:
3,003 = 3,000/1,000 + 3/1,000 = (3,000 + 3)/1,000 = 3,003/1,000
Therefore, the decimal fraction 3,003 can be expressed as a sum of fractions with a denominator that is a power of 10 as 3,003/1,000.
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Find the area of the region bounded by the curve y=sin(x) and
the x-axis between x=0 and x=4pi."
The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
To find the area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi, we can use the following steps:
1. Determine the function: In this case, the function is y=sin(x).
2. Identify the interval: The interval is from x=0 to x=4pi.
3. Integrate the function over the given interval: We'll integrate y=sin(x) with respect to x from 0 to 4pi.
∫(sin(x) dx) from 0 to 4pi.
4. Find the antiderivative: The antiderivative of sin(x) is -cos(x).
-∫(cos(x) dx) from 0 to 4pi.
5. Apply the fundamental theorem of calculus: We'll evaluate the antiderivative at the upper limit (4pi) and subtract the antiderivative evaluated at the lower limit (0).
[-cos(4pi)] - [-cos(0)]
6. Calculate the values: cos(4pi) = 1 and cos(0) = 1.
[-1] - [-1]
7. Determine the area: The area is the difference between the values calculated in step 6.
[-1 - (-1)] = 0
The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.
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Aleks and Melanie used a protractor to measure the angle below. Aleks thinks the angle measures 50° but Melanie says it is actually 130°. Their teacher confirms that Melanie has the correct answer. What mistake did Aleks make while measuring the angle?
The mistake, Aleks made, while measuring the angle is, he measure the angle from the wrong side of the line.
Angle is a dimensionless vector quantity, that is, it is very important, to take care of the directions, while measuring the angle.
That is, to measure the angle, say ∠ABC, the 0°(reference) line of the protractor, must be on one either AB or BC, to measure the angle rightly.
And since the angles between two lines are supplementary in nature, that is, the two angles will add up to make 180°, that is why, the angle measure by Alek and Melanie, add up to make 180°.
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I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!!
The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.
An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:
(x, y) → (-x, y)
Coordinate = (-1, 1/10) → Coordinate A' = (-(-1), 1/10) = (1, 1/10).
Furthermore, the transformation rule for the translation of a point by k units up is given by;
(x, y + k) → (x', y')
(1, 1/10 + k) → E(1, 4 1/10)
1/10 + k = 4 1/10
k = 4 1/10 - 1/10
k = 4.
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What is the area of the following circle?
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
The area of the circle whose diameter is 14 is approximately 153.94 square units or 49π square units..
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is given as d = 14, we know that the radius is half of the diameter, which is r = d/2 = 7.
Substituting the value of the radius in the formula, we get:
A = πr² = π(7)² = π(49) ≈ 153.94 (rounded to two decimal places using 3.14 for π)
Therefore, the area of the circle is approximately 153.94 square units. Alternatively, the exact answer can be left in terms of π, which would be A = 49π square units.
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