The coordinates of the other trees that must also be on the boundary are (-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).
The coordinates of the other trees that must be on the boundary of the circular orchard, given that the tree at (5, 12) is on the boundary and the center of the orchard is at (0, 0) can be determined as follows.
1. Calculate the radius of the orchard using the distance formula:
sqrt((x2-x1)^2 + (y2-y1)^2).
In this case, (x1, y1) = (0, 0) and (x2, y2) = (5, 12).
2. Radius = sqrt((5-0)^2 + (12-0)^2) = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13.
Now, we know the radius of the orchard is 13. To find the other boundary points, we can use the property of circles that states that the points on the boundary are equidistant from the center.
Since the coordinates are integers and symmetric, we can list the other points as follows:
3. The coordinates of the other trees on the boundary are:
(-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).
These points are also 13 units away from the center, making them equidistant from the center and thus on the boundary of the circular orchard.
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Pentagon on a coordinate plane. will this be a function, relation, function and relation, or neither relation nor function?
A Pentagon on a coordinate plane would be neither a relation nor a function.
This is because it does not have a unique output for every input, which is a requirement for a function. This is because a function must have a unique output for each input, while a pentagon may have multiple points (outputs) for a given x-coordinate (input) due to its shape. Additionally, it does not satisfy the vertical line test, which is a requirement for a relation. Therefore, it is not a relation or a function.
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A velociraptor runs 5m [E] , 10 m [W], 3m [S], & 2m [W] in 10 seconds. Calculate speed & velocity
The velocity of the velociraptor is 0.4 m/s [E] - 0.8 m/s [W] + 0.3 m/s [S] and the speed of the velociraptor is 2 m/s.
To calculate the speed of the velociraptor, we need to divide the total distance traveled by the total time taken:
Total distance = 5m + 10m + 3m + 2m = 20m
Total time = 10 seconds
Speed = Total distance / Total time
= 20m / 10s
= 2m/s
To calculate the velocity of the velociraptor, we need to consider both the magnitude of its speed and its direction. We can calculate the displacement by subtracting the final position from the initial position:
Displacement = (5m [E] + 10m [W] + 3m [S] + 2m [W])
= (5m [E] - 8m [W] + 3m [S])
= 5m [E] - 8m [W] + 3m [S]
Note that we have used negative sign for the distance traveled towards the west.
The time taken is 10 seconds.
Velocity = Displacement / Time taken
= (5m [E] - 8m [W] + 3m [S]) / 10s
= 0.4 m/s [E] - 0.8 m/s [W] + 0.3 m/s [S]
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Sally has seen four movies. The ticket prices were: $13, $8, $10, $10 The next movie she plans to see in is 3D and the ticket price is $34. Circle one of the following that will not change after Sally sees the next movie
The prices of the four movies that Sally has already seen will not change after she sees the next movie.
The ticket prices of the four movies that Sally has already seen are fixed and do not depend on whether she sees another movie or not. Therefore, these prices will remain the same even after she sees the next movie. The price of the next movie that Sally plans to see is $34, which is independent of the ticket prices of the previous movies.
Thus, the cost of the previous movies that Sally has seen will not change after she sees the next movie. In other words, the previous expenses are sunk costs and are irrelevant to future decisions.
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The base of an isosceles triangle is 6 cm and its area is 12 cm². What is the perimeter?
The perimeter of the triangle is 6 + 4√13
Calculating the perimeter of the triangle?Let's denote the length of the congruent sides of the isosceles triangle as x.
The formula for the area of a triangle is A = (1/2)bh, where b is the base and h is the height.
So, we have
A = (1/2)bh
12 = (1/2)(6)(h)
h = 4
Now, using the Pythagorean theorem, we can solve for the length of the congruent sides:
x^2 = 6^2 + 4^2
x^2 = 52
x = √52
The perimeter of the triangle is the sum of the lengths of its sides:
P = 6 + √52 + √52
P = 6 + 2√52
So, we have
P = 6 + 4√13
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When he was 30, Kearney began investing $200 per month in various securities for his retirement savings. His investments averaged a 5. 5% annual rate of return until he retired at age 68. What was the value of Kearney's retirement savings when he retired? Assume monthly compounding of interest
Kearney's retirement savings when he retired at age 68, assuming monthly compounding of interest, was $429,336.69.
How much did Kearney save for retirement?To calculate Kearney's retirement savings at age 68, we need to use the formula for the future value of an annuity due, which is:
FV = PMT x [((1 + r/n[tex])^(n*t)[/tex] - 1) / (r/n)] x (1 + r/n)
Where:
FV is the future value of the annuityPMT is the monthly payment (in this case, $200)r is the annual interest rate (5.5%)n is the number of compounding periods per year (12, for monthly compounding)t is the number of years (38, from age 30 to age 68)Plugging in the numbers, we get:
FV = 200 x [((1 + 0.055/12[tex])^(12*38)[/tex] - 1) / (0.055/12)] x (1 + 0.055/12)
FV = $429,336.69
Therefore, Kearney's retirement savings at age 68 would be approximately $429,336.69, assuming he invested $200 per month in securities with an average annual return of 5.5% and monthly compounding of interest. It's important to note that this calculation assumes that Kearney did not withdraw any money from his retirement savings during the 38-year period. Additionally, the actual value of his retirement savings could be different based on fluctuations in the market and any fees or taxes associated with his investments.
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You want to estimate the number of people in a grocery store who buy milk. which sample is unbiased?group of answer choices70 shoppers at random as they leave the store8 shoppers as they enter the store60 women with children at random80 shoppers in the dairy section at random
80 shoppers in the dairy section at random is a biased sample (d).
To estimate the number of people who buy milk in a grocery store, we need an unbiased sample that represents the entire population. The options provided are 70 shoppers at random as they leave the store, 8 shoppers as they enter the store, 60 women with children at random, and 80 shoppers in the dairy section at random.
The most unbiased sample is selecting 80 shoppers in the dairy section at random because the dairy section is where people are most likely to buy milk, and selecting a random sample of shoppers in that section ensures that we are not introducing any biases.
The other options may introduce biases since they are not necessarily representative of the entire population of shoppers in the store. Therefore, selecting 80 shoppers in the dairy section at random provides the most unbiased estimate of the number of people who buy milk in the grocery store. So d is correct option.
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1. Identify two accounts that are in good standing. Explain what evidence you found on the credit report
to indicate why these are in good standing. (4 points)
The evidence on a credit report that indicates good standing may vary depending on the individual's credit history and financial situation.
What are the accounts that are in good standing? Explain what evidence you found on the credit report.As an AI language model, I do not have access to specific credit reports or personal information of individuals. However, I can provide you with general information on what constitutes good standing on a credit report and some examples of evidence that may indicate good standing.
A good standing on a credit report typically means that a person has been responsible with their credit and has not defaulted on their payments. This may be indicated by a high credit score, a long credit history, and a low debt-to-credit ratio.
Some examples of evidence that may indicate good standing on a credit report include:
A high credit score: A credit score is a numerical representation of a person's creditworthiness. A high credit score, typically above 700, indicates that a person is in good standing and is likely to be approved for credit or loans. A high credit score may be achieved through a consistent history of making on-time payments, a low debt-to-credit ratio, and a diverse mix of credit accounts.
A low debt-to-credit ratio: A debt-to-credit ratio is the amount of debt a person has compared to their available credit limit. A low debt-to-credit ratio, typically below 30%, indicates that a person is not overextended and is able to manage their credit responsibly. This may be achieved through regular payments and not maxing out credit cards.
Overall, the evidence on a credit report that indicates good standing may vary depending on the individual's credit history and financial situation.
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Since 2005, the amount of money spent at restaurants in a certain country has increased at a rate of 6% each year. In 2005, about $410 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2017? About $ billion will be spent at restaurants in 2017 if the trend continues
About $786 billion will be spent at restaurants in 2017 if the trend continues.
To solve this problemWe can use the formula for compound interest:
A = P(1 + r)^n
where:
A is the final amount
P is the initial amount
r is the annual interest rate
n is the number of years
In this instance, we're looking to determine how much will be spent at restaurants in 2017, which is 12 years from now, in 2005. The initial amount was $410 billion in 2005, and the yearly interest rate is 6%. We thus have:
A = 410(1 + 0.06)^12
A ≈ 786.34
Therefore, about $786 billion will be spent at restaurants in 2017 if the trend continues.
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A baker paid $15. 05 for flour at a store that sells flour for $0. 86 per pound.
How many pounds of flour did the baker buy? :)
The baker bought approximately 17.5 pounds of flour.
Let's use algebra to solve the problem. Let x be the number of pounds of flour that the baker bought. We know that the cost of the flour is $15.05 and the price per pound is $0.86. So we can set up the equation:
$15.05 = $0.86 x
To solve for x, we can divide both sides by $0.86:
x = $15.05 ÷ $0.86
x ≈ 17.5
Therefore, the baker bought approximately 17.5 pounds of flour.
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Determine whether each set of measures can be the measures of the sides of a
right triangle. then state whether they form a pythagorean triple.
13. 12, 16, 20
14. 16, 30, 32
15. 14, 48, 50
16.
2 4 6
5' 5' 5
17.2v6,5,7
18. 2v2, 2v7,6
13. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
14. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
15. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
16.They're unfit to be a right triangle's side measures. The forecourt of the longest side( 62 = 36) can not be calculated by adding the places of the two lower sides( 22 42 = 20).
17. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean triadic is formed by them.
18. They're unfit to be a right triangle's side measures.
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the scale is 1 inch=50 miles. 5 inches is what
Answer:
Step-by-step explanation:
you multiply 5 by 50 and that would equal 250
5 x 50 = 250
volume of cylinders
1. The radius of the cylinder is 7. 05 cm
2. The length of the cylinder is 15, 384 meters
3. The radius of the big cylinder is 5. 64 cm
How to determine the valuesThe formula for the volume of a cylinder is expressed as;
V = πr²h
Such that;
r is the radius of the cylinderh is the height1. We have that volume = 2500 cm³
Height = 16cm
Substitute the values, we have;
2500 = π × r² × 16
Divide both sides by 16
r² = 49. 76
Find the square root
r = 7. 05 cm
2. Volume = 20000 cm³/100 = 200 meters
Radius = diameter/2 = 13/2 = 6.5cm = 0. 065 m
Substitute the values
200/0. 013 = h
Divide the values
h = 15, 384 meters
3. Volume = πr²h
Volume = 3.14 × 3.5² × 13
Volume = 500. 045 cm²
Then, substitute the values
500. 045 = 3.14 × r² × 5
r² = 31. 85
find the square root
r = 5. 64 cm
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The union within a company wants its employees to vote for the new pay proposal. over a six day period, the following number of employees cast their vote: 86, 95, 38, 47, 73, 68. which number best describes the average number of employees' votes each day? round your answer to the nearest whole number.
The number that best describes the average number of employees' votes each day is 68.
How we find the average number employees?To find the average number of employees' votes each day, we need to find the total number of votes cast and divide it by the number of days:
Total votes cast = 86 + 95 + 38 + 47 + 73 + 68 = 407
Number of days = 6
Average number of employees' votes each day = Total votes cast / Number of days
= 407 / 6
≈ 67.8
Rounding this to the nearest whole number gives us an average of 68 employees' votes each day.
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A square root function that has been reflected over the x-axis and move up 9
Therefore, the square root function that has been reflected over the x-axis and moved up 9 units is: g(x) = -√(x) + 9.
What is function?In mathematics, a function is a relation between two sets, called the domain and the range, that associates each element in the domain with a unique element in the range. A function is often denoted by a symbol such as f, and is defined by a rule that assigns to each element x in the domain a corresponding value f(x) in the range. Functions can have many different forms and types, depending on the nature of the rule that defines them. Some common types of functions include linear functions, quadratic functions, exponential functions, trigonometric functions, and many others.
Here,
A square root function is a function of the form f(x) = √(x), where the square root of x is taken. To reflect the function over the x-axis, we multiply the function by -1, which changes the sign of the function values.
So, the reflected square root function is g(x) = -√(x). To move the function up by 9 units, we add 9 to the function, which shifts the function vertically upwards.
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Please help with this question. I am offering 40 points. You can use the word box above to answer the questions.
We define [tex]9^{\frac{1}{2} }[/tex] to be the square root of nine. This means that [tex](9^{\frac{1}{2} })^{2}[/tex] must be equal to nine.
By using the properties of exponents to explain why [tex]8^{\frac{1}{3} }=2[/tex];
Statement Reasons_____________________
[tex]8^{\frac{1}{3} }=2[/tex] Given
[tex](8^{\frac{1}{3} })^3=2^3[/tex] Exponent property of equality.
[tex]8^{\frac{1}{3} \times 3}=2^3[/tex] Exponent property of a power.
8 = 8 simplify
What is an exponent?In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.
n is referred to as a superscript or power.
By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:
[tex]9^{\frac{1}{2} }[/tex] = √9 (square root of nine)
[tex](9^{\frac{1}{2} })^{2}=(9^{\frac{1}{2} \times 2})=9^1 = 9[/tex]
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h=-16t^2+27t+3 what is the max height of the soccer ball
To find the maximum height of the soccer ball, we need to determine the vertex of the quadratic function. The vertex is given by the formula:
t = -b/2a
where a = -16 and b = 27 from the given equation:
H = -16t^2 + 27t + 3
Substituting these values into the formula, we get:
t = -27/(2(-16)) = 0.84375
Now that we have the value of t at the vertex, we can find the maximum height by substituting it back into the original equation:
H = -16(0.84375)^2 + 27(0.84375) + 3 = 12.65625
Therefore, the maximum height of the soccer ball is approximately 12.65625 units.
h = -16t^2 + 27t + 3 = -(4t - 27/8)^2 + 921/64
With every number t, h [tex]\leq[/tex] 921/64.
Therefore, the maximum height of the soccer ball is 921/64, or aprroximately 14.4(units)
"=" when 4t = 27/8, or t = 27/32.
Identify the differentiation rule needed in order to find the derivative of
each of the following functions with respect to x.
a) y = sinxcosx
b) y = sin(cosx)
c) y = sin-x
d) y = sinx + cosx
product rule, chain rule, and sum rule are utilized to assess a subordinate of y = sin(x)cos(x), a subsidiary of y = sin(cos(x)), a subordinate of y = sin(-x), a subsidiary of y = sin(x) + cos(x).
a) subordinate of y = sin(x)cos(x) can be assessed by utilizing the product rule.
[tex]y' = (cos(x))(cos(x)) + (sin(x))(-sin(x)) = cos^2(x) - sin^2(x)[/tex]
b) chain rule is used to find the derivative of y = sin(cos(x)):
y' = (cos(x))(cos(cos(x)))
c) chain rule is used to find the derivative of y = sin(-x):
y' = -cos(-x) = -cos(x)
d) derivative of y = sin(x) + cos(x) can be evaluated by using sum rule
y' = cos(x) - sin(x)
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A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the standard deviation of X, the number of draws until the first red marble? 0. 4852 0. 9704 2. 0770 1. 5172
The standard deviation of X to be approximately 0.4852. The correct answer is option (A).
To calculate the standard deviation of X, we need to first calculate the probability of drawing a red marble on the first draw, which is 11/29. The probability of not drawing a red marble on the first draw is 18/29. The probability of drawing a red marble on the second draw, given that we did not draw a red marble on the first draw, is 11/29. Using the formula for the geometric distribution, which models the number of trials until the first success, we can calculate the expected value of X, which is 1/p, where p is the probability of success (11/29 in this case).
Therefore, the expected value of X is 29/11. To calculate the standard deviation of X, we use the formula sqrt(q/p^2), where q is the probability of failure (18/29) and p is the probability of success (11/29). Plugging in these values, we get the standard deviation of X to be approximately 0.4852. Therefore, the correct answer is option A, 0.4852.
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Ella makes a model of a log cabin that is 8 inches long at a scale of 1/2.5 feet. She makes a second model of the same building at a scale of 1/2.5 feet. How much longer is the second model than the first?
Answer: So the second model is 0.2667 feet longer than the first.
Step-by-step explanation: 8 inches * (1/12 feet per inch) * (1/2.5) = 0.1333 feet
So the length of the first model is 0.1333 feet.
The length of the second model is also at a scale of 1/2.5 feet, so its length can be found directly by multiplying the length of the actual building by the scale factor:
Length of second model = 1/2.5 * 1 foot = 0.4 feet
to make next step we can use difference between these numbers by their lengths: Length of second model - Length of first model = 0.4 feet - 0.1333 feet = 0.2667 feet
Match each equation to the situation it represents. Situation Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day. Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month. A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g. Equation 40x600 2400 2400 40x = 600 (600 +40) x = 2400
Each equation should be matched to the situation it represents as follows;
"Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day." ⇒ 2400 - 40x = 600
"Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month." ⇒ 40x - 600 = 2400
"A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g." ⇒ (600 + 40)x = 2400.
How to write a linear function to represent each of the equations?In this scenario and exercise, the independent variable (domain or input value) would be represented by the variable x, and then each of the situations described by the word sentence (problem) would be translated into an algebraic equation or linear function as follows;
Since Leilah studies 40 new cards per day, but hasn't studied 600 of her 2400 flashcards yet, a linear function to model or represent this situation is given by;
2400 - 40x = 600
The rent for Stetson's studio space is $600 per month and he charges his students $40 each hour while earning a profit of $2400 this month, a linear function to model or represent this situation is given by;
40x - 600 = 2400
Since this kit with a total mass of 2400rams contains 600 letter tiles and 40 number tiles, and each of the tiles have the same mass, the required linear function is given by;
(600 + 40)x = 2400.
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Which term can be put in the blank to make the statement below true?
3,000,000=30________________
A. Thousands
B.Ten-Thousands
C.Hundred-Thousands
D.Millions
3 /12 cups of flour for every 3/4 of a cup of milk. How much flour for 1 cup of milk
The amount of cup of flour for 1 cup of milk is 1/3 cup
What is proportion?Proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 4 girls you could write the ratio as: 1 : 4 (for every one boy there are 4 girls).
Another example is if 5 mangoes cost $250, the price of mango will 250 × 1/5 = $50
Similarly, 3/12 cups of flour is for every 3/4 cups of milk
therefore,
1 cup of milk will need 3/12 × 4/3
= 12/36
= 1/3
therefore for 1 cup of milk 1/3 of flour will be needed.
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Is the following data an example of a linear function?
Yes, The given table is an example of a linear function.
Since, The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
To check the following data an example of a linear function.
Now, We can check the slope of given tables as;
⇒ Slope = (3 - (- 2)) / (0 - (- 7))
= (5 / 7)
⇒ Slope = (8 - 3) / (7 - 0)
= (5 / 7)
Thus, This table represent the an example of a linear function.
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Drag each tile to the correct location, Determine the type of fee that will be charged In each situation. Joanne's brokerage firm charged her for providing investment information to help her make informed choices. Pete isn't a regular investor. He hasn't bought or sold any stock this year. His broker charged him an inacovity fee of $75 for the year. John's broker provided him with stock-trading software to manage his trading Lisa sold 50 shares of stock A on a given day. Her broker charged her $12 for this trade Reggie's broker charged him a front-end load of 2. 75% when he purchased a fund. Transaction Fee Non-transaction Fee 2021 Edmentum All rights reserved.
The type of fee that will be charged depends on the specific service provided by the broker to the client. Non-transaction fees are typically charged for account maintenance or access to investment tools, while transaction fees are charged for specific trades or transactions.
To determine the type of fee that will be charged in each situation, we need to consider the specific services that were provided by the broker to the client.
For Joanne, her brokerage firm charged her a fee for providing investment information to help her make informed choices. This type of fee is a non-transaction fee, as it is not related to a specific transaction or trade.
Pete, who hasn't bought or sold any stock this year, was charged an inactivity fee of $75 for the year by his broker. This fee is also a non-transaction fee, as it is not related to a specific trade but rather to the inactivity of the account.
John's broker provided him with stock trading software to manage his trading. This type of service is typically included in a brokerage firm's platform fee, which is a non-transaction fee that covers the cost of maintaining the software and other tools that clients can use to manage their investments.
Lisa sold 50 shares of stock A on a given day and her broker charged her $12 for this trade. This type of fee is a transaction fee, which is charged for each specific trade or transaction that a client makes.
Finally, Reggie's broker charged him a front-end load of 2.75% when he purchased a fund. This fee is a type of sales charge or commission that is applied to the initial investment and is considered a transaction fee.
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17. Which is D = 2zv solved for v? (1 point)
Ov=
2z
D
2z
Ov=D-2z
Ov=
AN
Ov=1
The equation D = 2zv when solved for v is D/2z = v
Which is D = 2zv solved for v?To solve D = 2zv for v, we need to isolate the variable v on one side of the equation. We can do this by dividing both sides of the equation by 2z:
D = 2zv
So, we have
D/2z = v
So the solution for v is v = D/2z.
This equation tells us that v is equal to the ratio of D divided by 2z. In other words, v is proportional to D, and inversely proportional to 2z.
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Taylor has 7 pounds of navel oranges and
6 1/2 pounds of temple oranges. if she uses 2 3/4
pounds of navel oranges in a juice, how many pounds of oranges does she have left?
The total of oranges left by the taylor is about 10 3/4 pounds
To solve this problem, we will start by using adding the weights of the navel oranges and temple oranges to discover the total weight of oranges Taylor has, that's:
total weight = 7 pounds + 6 1/2 poundstotal weight = 13 1/2 poundsNext, we are able to subtract the weight of the navel oranges she uses from the total weight of navel oranges to discover how a lot she has left, which is:
Navel oranges left = 7 pounds - 2 3/4 poundsNavel oranges left = 4 1/4 poundsIn the end, we can add the weight of the navel oranges left to the weight of the temple oranges to find the overall weight of oranges Taylor has left, which is:
total oranges left = Navel oranges left + Temple orangestotal oranges left = 4 1/4 pounds + 6 1/2 poundstotal oranges left = 10 3/4 poundsTherefore, the total of oranges left by the taylor is about 10 3/4 pounds
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A bag contains five red socks and eight blue socks. Lucky reaches into the bag and randomly selects two socks without replacement. What is the probability that Lucky will get different colored socks? Express your answer as a common fraction. I will give brainliest if you give a full explanation, I have the answer but I need to know HOW to solve the problem!!!
A bag contains five red socks and eight blue socks. Lucky reaches into the bag and randomly selects two socks without replacement, the probability that Lucky will get different colored socks is 10/39.
We can divide the issue into two distinct possibilities and multiply them together to find a solution.
Let's start by thinking about the likelihood of choosing a red sock during the initial draw.
The likelihood of choosing a red sock on the first draw is 5/13 due to the fact that there are only five red socks among the total of thirteen socks (five red plus eight blue).
There are now twelve socks left in the bag after the first one is drawn, with four red and eight blue.
On the second draw, there is an 8/12 chance of choosing a blue sock, which is a different colour.
We add the probabilities together to determine the likelihood that both events (drawing a red sock first and a blue sock second) will occur:
(5/13) * (8/12) = 40/156 = 10/39
Therefore, the probability that Lucky will get different colored socks is 10/39.
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Use the indicated table of integrals to evaluate this:
∫√(x-x^2)dx
After evaluating the integral ∫√(x-x²)dx, we get:
∫√u (1 - 2x) du, with the limits of integration 0 to 1/4
To evaluate the integral ∫√(x-x²)dx using the indicated table of integrals, you should look for an entry in the table that matches the given integral's form. Unfortunately, I do not have access to the specific table you are referring to. However, I can guide you on how to approach this problem.
First, you should make a substitution:
let u = x - x², then du = (1 - 2x)dx. To proceed with this substitution, you'll need to rewrite the integral in terms of 'u' and 'du'. Notice that when x = 1/2, u = 1/4.
Therefore, you can change the limits of integration as well: x = 0 corresponds to u = 0, and x = 1 corresponds to u = 0.
Now,
∫√(x-x²)dx = (1/2) ∫(1-4x+4x²-3)⁽¹/²⁾ dx
Now, we can look up the integral in the table of integrals, which indicates that:
∫(1-4x+4x²-3)⁽¹/²⁾ dx = (1/2) [ (x-1)√(1-4x+4x²) + 2arcsin(2x-1) ] + C
Therefore, substituting this result back into the original integral, we get:
∫√(x-x²)dx = (1/2) [ (x-1)√(1-4x+4x²) + 2arcsin(2x-1) ] + C
where C is the constant of integration.
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Miss Marge has a large fish tank in her
office. Does her fish tank hold 100 liters
or 100 mL of water?
Using metric system, we can find that Miss Marge's fish tank holds 100 litres of water.
Define metric system?Everything around us has a quantitative value, from the amount of sugar you put in a cake to the size of a football pitch. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced. The collection of standard units designed to measure length, weight, area, and capacity is known as the metric system of measurement in mathematics. As it uses numbers in powers of 10, it is based on the decimal system.
A litre (L) and millilitres (mL) are two units for measuring capacity in the metric system. A bottle of water holds 1 Liter of water. A millilitre is about 20 drops of water.
So, 100 litres of water will be the correct answer.
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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.
The height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches. The z-score associated with the 96th percentile is 1.75.
To find the z-score associated with the 96th percentile, we can use the following steps:
1. Locate the percentile in a standard normal distribution table or use a calculator that can compute percentiles (e.g., a graphing calculator or an online calculator).
2. For the 96th percentile, we find the corresponding z-score. Using a standard normal distribution table or an online calculator, the z-score is approximately 1.75.
So, 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 following formula:
Height = mean + (z-score × standard deviation)
Here, the mean height is 68.3 inches, the z-score is 1.75, and the standard deviation is 2.9 inches. Plugging these values into the formula:
Height = 68.3 + (1.75 × 2.9) ≈ 68.3 + 5.075 ≈ 73.375 inches
So, the height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches.
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