The set {x∈R:[tex]x^2\geq 0[/tex]}^c is the empty set, as there are no real numbers that are not included in the set of all real numbers.
To find the set {x∈R:[tex]x^2\geq 0[/tex]}^c, we first need to understand what the statement [tex]x^2\geq 0[/tex] means. This inequality simply states that any real number squared is always non-negative. Therefore, the set {x∈R:[tex]x^2\geq 0[/tex]} is equivalent to the set of all real numbers.
Now, to find the complement of this set, we need to look for all the elements that are not in the set of all real numbers. Since the universal set is R, which is the set of all real numbers, the complement of {x∈R:[tex]x^2\geq 0[/tex]} will be the empty set, since there are no real numbers that are not included in the set of all real numbers.
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HELP!! Please!! i will write brainuiest.
Answer:
20
Step-by-step explanation:
16 / 20 = 0.80
0.80 = 80%
Let p represent the regular price of one poster. Which equation represents
Sunita's purchase?
5(p-3)=63
What is the regular price of one poster?
$
Answer:
p=$16.5
Step-by-step explanation:
By using the distributive Property, you can say:
5p-15=63
Then add 15 on both sides to make the equation balanced:
5p=78
Then divide by 5:
p=78/5=$16.5
for infinity car wash, the arrival rate is 9 / hour and the service rate is 16 / hour. the arrival and service distributions are not known so we can't use the m/m/1 formulas. if the average waiting time in the line is 23 minutes, then how many customers (waiting and being served) are at the carwash
The approximate number of customers (waiting and being served) at the carwash is 3.
To determine the number of customers (waiting and being served) at the carwash, we can use Little's Law, which states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time spent in the system.
In this case, the average arrival rate is 9 customers per hour, and the average waiting time is given as 23 minutes (which is equivalent to 23/60 = 0.3833 hours).
Using Little's Law, we can calculate the average number of customers in the system:
Average number of customers = Average arrival rate * Average time spent in the system
Average number of customers = 9 customers/hour * 0.3833 hours
Average number of customers = 3.4497 customers
Since we can't have fractional customers, we round the value to the nearest whole number.
Therefore, the approximate number of customers (waiting and being served) at the carwash is 3.
It's important to note that this calculation assumes steady-state conditions and that the arrival and service distributions are not known.
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find an expression for the general term of the series and give the range of values for the index.
ex2 = 1+x2+x4/2!+x6/3!+x8/4!+......
the series ex2 converges for all real values of x.
The general term of the series ex2 = 1 + x^2 + x^4/2! + x^6/3! + x^8/4! + ... is given by:
an = xn/(n!) for n ≥ 0, where n is an even integer.
Here, xn represents the term with exponent n in the series.
Therefore, the range of values for the index n is all even non-negative integers starting from 0.
Note that n! (n factorial) in the denominator of the general term ensures that each term after the first term (which is 1) is smaller than the preceding term, as n increases.
what is integer?
An integer is a whole number that can be positive, negative, or zero. It does not include fractions or decimals. Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on. The set of integers is denoted by the symbol Z.
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The small submarine is at –1,320 feet in relation to sea level. The submarine needs to be 180 feet below sea level in 60 minutes.
How far must the submarine travel?
The small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.
To determine the distance that the small submarine must travel to reach 180 feet below sea level, we need to use some basic math.
First, we need to determine the distance between the current position of the submarine (-1,320 feet) and its target depth (-180 feet below sea level). To do this, we subtract the target depth from the current depth:
-1,320 ft - (-180 ft) = -1,140 ft
This means that the submarine needs to travel 1,140 feet down in order to reach its target depth.
Next, we need to figure out how long it will take the submarine to travel that distance. We know that it has 60 minutes to do so, so we can use the formula:
distance = rate x time
We know the distance (1,140 feet), so we need to solve for rate. Rearranging the formula, we get:
rate = distance / time
Plugging in the values we know, we get:
rate = 1,140 ft / 60 min = 19 ft/min
So the small submarine needs to travel at a rate of 19 feet per minute in order to reach its target depth of 180 feet below sea level in 60 minutes.
In summary, the small submarine must travel 1,140 feet and maintain a speed of 19 feet per minute in order to reach a depth of 180 feet below sea level within 60 minutes.
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the sum of the percent frequencies for all classes in a frequency distribution will always equalT/F
The statement "the sum of the percent frequencies for all classes in a frequency distribution will always equal" is True.
The sum of the percent frequencies for all classes in a frequency distribution will always equal 100%. This is because the percent frequency for each class is calculated by dividing the frequency of that class by the total number of observations and then multiplying by 100. Therefore, when we add up all the percent frequencies for all the classes, we get the total percentage of observations, which must be 100%.
In a frequency distribution, percent frequencies are calculated by dividing the frequency of each class by the total number of observations and then multiplying by 100. Since all observations are accounted for in the distribution, the sum of the percent frequencies for all classes will always equal 100%.
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a local internet company, with customers in 15 towns is considering offering several streaming services in a bundle with internet. before launching the new bundle they want to find out whether customers would pay the extra $50 per month they plan to charge. an intern randomly selects 20 customers from each town surveys these customers and analyses the combined data. the sampling design is
The sampling design used in this scenario is cluster sampling.
Cluster sampling involves dividing the population into groups or clusters (in this case, the 15 towns) and randomly selecting entire clusters to be included in the sample. In this case, the intern randomly selected 20 customers from each town, which means that the clusters were the towns themselves.
Cluster sampling is a practical and efficient sampling method when it is difficult or expensive to access individual elements of the population. By selecting entire clusters, the sampling process becomes more manageable, and it can reduce costs and logistical challenges.
However, it's important to note that cluster sampling introduces the possibility of within-cluster similarity, meaning that individuals within the same cluster may have similar characteristics or behaviors. This can affect the variability of the sample and the generalizability of the findings to the entire population. It is important to consider this potential bias and account for it in the data analysis and interpretation.
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obsa has two prism shaped container. one has a volume of2 1/3 cubic feet, and the other has a volume of 4/3 cubic feet. how many smaller prisms would it take to fill the larger?
Obsa will need 2 smaller prisms to fill the larger prism, with each smaller prism having a volume of 4/3 cubic feet.
To find out how many smaller prisms it would take to fill the larger one, we need to first determine the volume of the larger prism. We know that the larger prism has a volume of 2 1/3 cubic feet, which can also be expressed as 7/3 cubic feet.
Next, we need to find out how many of the smaller prisms will fit into the larger one.
To do this, we can divide the volume of the larger prism by the volume of the smaller prism.
The smaller prism has a volume of 4/3 cubic feet, so:
(7/3 cubic feet) / (4/3 cubic feet) = 7/4
This means that it will take 7/4 smaller prisms to fill the larger prism.
However, since we can't have a fraction of a prism, we need to round up to the nearest whole number.
Therefore, it will take 2 smaller prisms to fill the larger prism. One prism will fill up 4/3 cubic feet, and the other will fill up 4/3 cubic feet, totaling to 8/3 cubic feet, which is just a bit more than the 2 1/3 cubic feet of the larger prism.
This means that it takes 1 and 3/4 smaller prisms to fill the larger container.
However, since we cannot have a fraction of a prism, we need to round up to the nearest whole number, which is 2.
Therefore, it would take 2 smaller prisms to fill the larger prism-shaped container.
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If angle 5=91-2x and angle 10=5x find the value of x
The value of x for the same angle based on the information is 13.
How to calculate tie angleIn Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle
Since angles 5 and 10 are the same, we can set them equal to each other:
91 - 2x = 5x
Simplifying this equation, we can add 2x to both sides:
91 = 7x
Then, we can divide both sides by 7 to solve for x:
x = 13
Therefore, the value of x for the same angle is 13.
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Which value is closest to 81120 ? 8 8 1/2 8 3/4 9
Answer:
Step-by-step explanation:
it is 83/49 because I searched it up.
What multiplies to -63 and adds to -18
To find two numbers that multiply to -63 and add to -18, we can start by listing all the factors of -63:
1, -1, 3, -3, 7, -7, 9, -9, 21, -21, 63, -63We can see that -9 and 7 are the only two factors that add up to -2.
Therefore, the two numbers that multiply to -63 and add to -18 are -9 and 7.
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Which of the following best describes the possible values for a chi-square statistic?
a. Chi-square is always a positive whole numbers.
b. Chi-squarc is always positive but can contain fractions or decimal values.
c. Chi-square can be either positive or negative but always is a whole number.
d. Chi-square can be either positive or negative and can contain fractions or
decimals.
Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.
However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.
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Harley-Davidson Inc. Currently has $750,000 in accounts receivable, and its days sales outstanding (DSO) is 55 days. It wants to reduce its DSO to 35 days by pressuring more of its customers to pay their bills on time. If this policy is adopted, the company’s average sales will fall by 15%. What will be the level of accounts receivable following the change? Assume a 365-day year
The level of accounts receivable will be $479,452.05.
If Harley-Davidson Inc. reduces its DSO to 35 days by pressuring more of its customers to pay their bills on time, the company’s average sales will fall by 15%. To calculate the level of accounts receivable following this change, we need to use the formula for DSO:
DSO = (Accounts Receivable / Average Daily Sales) x Number of Days in Period
We know that the current DSO is 55 days, and the company wants to reduce it to 35 days. Therefore, we can assume that the current average daily sales are:
Average Daily Sales = Annual Sales / 365
DSO = (Accounts Receivable / Average Daily Sales) x Number of Days in Period
55 = ($750,000 / (Annual Sales / 365)) x 365
Solving for Annual Sales, we get:
Annual Sales = $1,095,890.41
If the company’s average sales will fall by 15%, then the new Annual Sales will be:
New Annual Sales = $931,507.85 ($1,095,890.41 - 15%)
Using this new Annual Sales figure, we can now calculate the new level of accounts receivable following the change:
35 = (New Accounts Receivable / (New Annual Sales / 365)) x 365
New Accounts Receivable = $479,452.05
Therefore, if Harley-Davidson Inc. reduces its DSO to 35 days by pressuring more of its customers to pay their bills on time and its average sales fall by 15%, the level of accounts receivable will be $479,452.05.
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y[tex]y\leq -\frac{1}{2} x^2+4x+7[/tex]
The graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.
y≤-1/2x² + 4x + 7
The inequality is a quadratic function in standard form.
To graph it, we can find the vertex and the x-intercepts.
The vertex is at the point (h, k) where h = -b/2a and k = f(h), and f(x) = -1/2x² + 4x + 7.
a = -1/2, b = 4, and c = 7,
so h = -b/2a = -4/(-1) = 4, and
k = f(h) = -1/2(4)² + 4(4) + 7 = 15.
So the vertex is at (4, 15).
Now let us find the x-intercepts by setting y value as 0 and solve for x:
0 ≤ -1/2x² + 4x + 7
1/2x² - 4x - 7 ≤ 0
x² - 8x - 14 ≤ 0
We find roots by using the quadratic formula
x = (8 ± √8² - 4(1)(-14))) / 2
x = 4 ± √18
So the x-intercepts are 0.34 and 7.66.
Hence, the graph of the inequality is a downward-opening parabola that passes through (0, 7) and (8, -9). The shaded region is below the curve.
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Explain the graph of the inequality y≤-1/2x² + 4x + 7?
Another measure of central tendency is the trimmed mean. It is computed by determining the mean of a data set after deleting the smallest and largest observed values. Compute the trimmed mean for the data given in the accompanying table. Is the trimmed mean resistant to changes in the extreme values in the given data?
0.81 0.88 0.82 0.90 0.84 0.84
0.91 0.94 0.86 0.86 0.88 0.87
0.89 0.91 0.86 0.87 0.88
0.83 0.96 0.87 0.93 0.85
0.91 0.91 0.86 0.89 0.84
0.88 0.88 0.89 0.76 0.83
0.90 0.88 0.84 0.93 0.90
0.88 0.92 0.85 0.84 0.86
The trimmed mean is ___?___ ( round to the nearest thousandth as needed)
Is the trimmed mean resistant to changes in the extreme values for the given data?
Multiple choice
a. No, because the trimmed mean varies substantially when the extreme values change.
b. yes, because changing the extreme values does not change the trimmed mean.
To compute the trimmed mean for the given data, we need to first delete the smallest and largest observed values, which are 0.76 and 0.96 respectively. Then we calculate the mean of the remaining 28 values.
The trimmed data set after deleting the smallest and largest values is:
0.81 0.88 0.82 0.90 0.84 0.84 0.91 0.94 0.86 0.86 0.88 0.87 0.89 0.91 0.86 0.87 0.88 0.83 0.91 0.91 0.86 0.89 0.84 0.88 0.88 0.89 0.83 0.90 0.88 0.92 0.85 0.84 0.86
The sum of these values is 24.39, and the trimmed mean is 24.39/28 = 0.871 (rounded to three decimal places).
The trimmed mean is considered to be a resistant measure of central tendency because it is less affected by extreme values compared to the mean. In this case, even though we deleted the smallest and largest values, the resulting trimmed mean is very close to the mean of the original data set (which is 0.8716). Therefore, the trimmed mean is resistant to changes in extreme values in the given data.
The answer is (b) yes, because changing the extreme values does not change the trimmed mean.
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Whic if the following functions is graphed
The piecewise function graphed in this problem is defined as follows:
y = x + 6, x ≤ 1.y = x² + 3, x > 1.What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The definitions for this problem are given as follows:
Up to x = 1.Greater than x = 1.For the function up to x = 1, the function is a linear function with slope of 1 and intercept of 6, hence:
y = x + 6, x ≤ 1.
For the function greater than x = 1, the quadratic function y = x² + 3 is defined, hence:
y = x² + 3, x > 1.
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Answer ASAP please!!
Select the correct answer.
In a sequence described by a function, what does the notation f(3) = 1 mean?
A.
The first term in the sequence has a value of 3.
B.
The third term in the sequence has a value of 1.
C.
The common ratio of the sequence is 3.
D.
The common difference of the sequence is 3.
Answer: b
Step-by-step explanation: b
This question is really confusing me, thank you so much if you can explain it to me, I would really appreciate it.
Factor completely.
9j² - 25k6
Enter your answer in the blanks in order from left to right.
(Oj − Okº) (Oj + k)
-
Blank # 1
Blank # 2
Blank # 3
Blank #4
Blank # 5
Blank # 6
Step-by-step explanation:
(3j - 5k^3) ( 3j + 5k^3) = 9j^2 - 25k^6
For what values of r will the area of the shaded region be greater than or equal to half of the area of the larger rectangle
(The larger rectangle has a length of 12 cm and a width of 8 cm)
(the shaded region has a length of r and a width of 6cm)
The values of r where the area of the shaded region be greater are values at least 8
Calculating the values of r where the area of the shaded region be greaterFrom the question, we have the following parameters that can be used in our computation:
The larger rectangle has a length of 12 cm and a width of 8 cm)The shaded region has a length of r and a width of 6cmThe area of the larger rectangle is
Area = 12 * 8
Area = 96
The area of the shaded region is
Area = r * 6
Area = 6r
When the shaded region is greater than or equal to half of the area of the larger rectangle, we have
6r ≥ 1/2 * 96
This gives
r ≥ 1/12 * 96
Evaluate
r ≥ 8
Hence, the values of r are r ≥ 8
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SECTION 11 17. Half the sum of the present ages of a mother and daughter equal to the clipference bhen their ages now. In lour's time the mother's age will be exactly twice the daughter's ag Calculate their present ages
Answer:
Step-by-step explanation:
let the present age of mother and daughter be x and y
[tex]\frac{1}{2} * (x + y) = x - y\\x + y = 2x - 2y\\x = 3y --- (1)\\[/tex]
[tex]x+4 = 2(y+4)\\3y+4 = 2y + 8\\y = 4\\x = 3y = 12[/tex]
Age of mother = 12 yrs
Age of daughter = 4 yrs
Can somebody pls answer this question fast
The solution of the expression is,
⇒ 0 + (7/11)√5
We have to given that;
Expression is,
⇒ (7 + √5) / (7 - √5) - (7 - √5) / (7 + √5)
Take LCM we get;
⇒ (7 + √5)² - (7 - √5)² / (7 - √5) (7 + √5)
⇒ (49 + 5 + 14√5) - (49 + 5 - 14√5) / (7² - √5²)
⇒ (28√5) / (49 - 5)
⇒ 28√5 / 44
⇒ 7√5 / 11
⇒ 0 + (7/11)√5
Thus, The solution of the expression is,
⇒ 0 + (7/11)√5
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uppose that the time it takes to get service in a restaurant follows an expo- nential distribution with mean 10 minutes. find the 75th percentile of the wait time.
The 75th percentile of the wait time in a restaurant, assuming it follows an exponential distribution with a mean of 10 minutes, can be found using the inverse of the exponential cumulative distribution function.
In an exponential distribution, the probability density function (PDF) is given by f(x) = λe^(-λx), where λ is the rate parameter. The mean of the exponential distribution is equal to 1/λ. In this case, we are given that the mean is 10 minutes, so λ = 1/10.
To find the 75th percentile, we need to find the value x for which P(X ≤ x) = 0.75. In other words, we want to find the value of x such that 75% of the wait times are less than or equal to x.
Using the exponential cumulative distribution function (CDF), we can solve for x by setting P(X ≤ x) = 0.75 and solving for x. The formula for the exponential CDF is F(x) = 1 - e^(-λx).
Setting 1 - e^(-λx) = 0.75, we can solve for x to find the 75th percentile of the wait time.
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What is the angle measured counterclockwise, from the positive x-axis to the ray from through (-5, 12)
The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.
To find the angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12), follow these steps:
Step 1: Determine the coordinates of the given point. In this case, it is (-5, 12).
Step 2: Calculate the horizontal (x) and vertical (y) distances from the origin (0, 0) to the point. The horizontal distance is -5 and the vertical distance is 12.
Step 3: Calculate the angle using the arctangent function (tan^(-1)). The arctangent function takes the ratio of the vertical distance to the horizontal distance as its argument. So, angle = tan^(-1)(12 / -5).
Step 4: Compute the arctangent value using a calculator or an online tool. Angle ≈ tan^(-1)(-2.4) ≈ -67.38 degrees.
Step 5: Convert the angle to a positive value measured counterclockwise from the positive x-axis. Since the angle is measured in the second quadrant, subtract the angle from 180 degrees: 180 - 67.38 ≈ 112.62 degrees.
The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.
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mike has under 1/4 of a tank of gas, and he decides to fill up his gas tank. his gas tank holds 16 gallons. the gas cost $3.59 per gallon. approximately, how much will it cost mike to fill up his car?
Mike has under 1/4 of a tank of gas, and he decides to fill up his gas tank. his gas tank holds 16 gallons. the gas cost $3.59 per gallon. It will cost Mike $43.08 to fill up his car.
To help you with your question, we first need to determine the amount of gas Mike needs to fill up his car. Since he has less than 1/4 of a tank, let's assume he has exactly 1/4 of a tank for simplicity.
Mike's car has a 16-gallon gas tank, so:
1/4 * 16 gallons = 4 gallons already in the tank.
To fill up the tank, Mike needs to add:
16 gallons - 4 gallons = 12 gallons.
The gas costs $3.59 per gallon, so to find the total cost:
12 gallons * $3.59 = $43.08.
Approximately, it will cost Mike $43.08 to fill up his car.
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Rodarius wants to make a special gift for the raffle. He has 120 mini footballs and 30 signed autographs from the Titans. What is the most amount of gift packages he can make so that each recipient gets an equal number of footballs and autographs? PLSSS ANSWERR ILL GIVE POINTSS
The maximum number of gift packages that Rodarius can make is 30. Each gift package will contain 4 mini footballs and 1 signed autograph from the Titans.
To determine the maximum number of gift packages Rodarius can make so that each recipient gets an equal number of footballs and autographs, we need to find the greatest common factor (GCF) of the two numbers, 120 and 30.
The prime factorization of 120 is:
120 = 2³ x 3 x 5
The prime factorization of 30 is:
30 = 2 x 3 x 5
To calculate the GCF, multiply the product of the common factors by the lowest exponent:
GCF = 2 x 3 x 5 = 30
So the maximum number of gift packages that Rodarius can make is 30. Each gift package will contain 4 mini footballs and 1 signed autograph from the Titans.
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Write x2 + 4x − 5 = 0 in the form of (x − a)2 = b, where a and b are integers.
a
(x + 4)2 = 9
b
(x + 4)2 = 5
c
(x + 2)2 = 9
d
(x + 2)2 = 3
Answer:
C. (x+2)2=3
Step-by-step explanation:
Take the root of both sides and solve.
Both x2+4x-5=0 and (x+2)2=3 have the solution of x=1,-5
have a great day and thx for your inquiry :)
From the sum of 2/9 and -3/7 subtract the difference of 3/7 & -13/23
The final result of the expression is -12,173/10,083. First, let's find the sum of 2/9 and -3/7. To add fractions, we need a common denominator. The least common multiple of 9 and 7 is 63.
To simplify the given expression, let's break it down step by step:
The sum of 2/9 and -3/7 is:
(2/9) + (-3/7)
To add these fractions, we need a common denominator, which is the least common multiple (LCM) of 9 and 7, which is 63.
(2/9) + (-3/7) = (2 * 7)/(9 * 7) + (-3 * 9)/(7 * 9)
= 14/63 - 27/63
= (14 - 27)/63
= -13/63
The difference of 3/7 and -13/23 is:
(3/7) - (-13/23)
Again, we need a common denominator, which is the LCM of 7 and 23, which is 161.
(3/7) - (-13/23) = (3 * 23)/(7 * 23) - (-13 * 7)/(23 * 7)
= 69/161 + 91/161
= (69 + 91)/161
= 160/161
Now, we subtract the second result from the first result:
(-13/63) - (160/161)
To subtract fractions, we need a common denominator, which is the LCM of 63 and 161, which is 10,083.
(-13/63) - (160/161) = (-13 * 161)/(63 * 161) - (160 * 63)/(161 * 63)
= -2,093/10,083 - 10,080/10,083
= (-2,093 - 10,080)/10,083
= -12,173/10,083.
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How to find the maximum volume of a cylinder inscribed in a sphere of radius r?
To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.
Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.
Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.
To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:
d/dx (2πr^3) = 6πr^2 = 0
This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.
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I will give brainilest and 100 points!!!!
harry potter is in his dorm in gryffindor and needs to visit 4 places. hermione computes the time it takes to travel between any two places in minutes and labels it on the graph. in what order should harry travel to visit each place once then return to gryffindor in the least amount of time?
To determine the order in which Harry Potter should visit the 4 places and return to Gryffindor in the least amount of time, we need to look at the graph provided by Hermione.
We can start by looking for the shortest distances between each location. Once we have identified the shortest distances, we can then use this information to determine the most efficient order for Harry to visit each place.
It's important to note that there may be multiple routes that Harry can take to visit all 4 places, but we want to find the one that will take the least amount of time. To do this, we can start by identifying the shortest distance between two locations and continue to do this until we have identified the shortest path to all 4 locations.
Once we have determined the order in which Harry should visit each location, we can then calculate the amount of time it will take for him to travel between each place and return to Gryffindor. This will give us a total time for the entire journey.
We can say that determining the most efficient route for Harry to visit the 4 places and return to Gryffindor in the least amount of time requires careful analysis of the graph provided by Hermione. By identifying the shortest distance between each location and using this information to create the most efficient route, we can minimize the amount of time Harry spends traveling between each place. Once we have identified the order in which Harry should visit each location, we can then calculate the amount of time it will take him to travel between each place and return to Gryffindor. By doing this, we can determine the total amount of time it will take for Harry to complete his journey.
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