The value of x that maximizes revenue is x 28.99 and maximum revenue is $1680 (thousand).
The revenue function for a company that sells x (thousand) items is R(x) = x² + 840. To find the value of x that maximizes revenue, we need to differentiate the revenue function, set it equal to zero and solve for x. The maximum revenue can then be calculated by substituting the value of x into the revenue function.
Revenue function: R(x) = x² + 840
To find the value of x that maximizes revenue, we differentiate the revenue function with respect to x:
dR/dx = 2x
Setting this equal to zero, we get:
2x = 0
x = 0
However, this value does not make sense in the context of the problem, as the company cannot sell 0 items. Therefore, we need to consider the critical points of the function, which occur when dR/dx = 0 or is undefined.
dR/dx = 0 when 2x = 0, so x = 0 is a critical point.
dR/dx is undefined when x = ±√840, so these are also critical points.
We can use the second derivative test to determine which critical point corresponds to a maximum. The second derivative of the revenue function is:
d²R/dx² = 2
At x = 0, d²R/dx² = 2 > 0, so this critical point corresponds to a minimum.
At x = ±√840, d²R/dx² = 2 > 0, so these critical points correspond to a minimum.
Therefore, the value of x that maximizes revenue is x = √840 ≈ 28.99 (thousand items).
To find the maximum revenue, we substitute x = √840 into the revenue function:
R(√840) = (√840)² + 840 = 1680
So the maximum revenue is $1680 (thousand).
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T and I Construction is paving a rectangular-shaped parking lot with Hot Asphalt Mix. The parking lot is 100 yards by 44 yards and will have a 9-inch base. If the Hot Asphalt Mix has a density of 140 pounds per cubic foot, about how many tons of mix will be needed to pave the parking lot?
A. ) 77
B. ) 91
C. ) 2079
D. ) 2772
The approximate amount of Hot Asphalt Mix needed to pave the parking lot is 2772 tons. (D)
To calculate the required amount of Hot Asphalt Mix, follow these steps:
1. Convert the dimensions of the parking lot to feet: 100 yards x 3 (feet/yard) = 300 feet and 44 yards x 3 (feet/yard) = 132 feet.
2. Convert the base thickness to feet: 9 inches / 12 (inches/foot) = 0.75 feet.
3. Calculate the volume of the parking lot: 300 feet x 132 feet x 0.75 feet = 29,700 cubic feet.
4. Find the weight of the Hot Asphalt Mix: 29,700 cubic feet x 140 pounds/cubic foot = 4,158,000 pounds.
5. Convert the weight to tons: 4,158,000 pounds / 2000 (pounds/ton) = 2079 tons.
However, the answer options provided do not match the calculated value of 2079 tons. In this case, the closest answer would be option D, 2772 tons.
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Write two numbers that multiply to the value on top and add to the value on bottom.
Answer:
-17 and -5
Step-by-step explanation:
-5 x -17 = 85
-5 + -17 = -22
Add. Hint: Use the place value blocks to help solve
8
+
7
8+78, plus, 7. 8
+
7
=
8+7=start color #0c7f99, 8, end color #0c7f99, plus, start color #ca337c, 7, end color #ca337c, equals
The answer of addition is 94.
What is addition?The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three.
To add 8 and 78, we can start by adding the ones place digits, which are 8 and 7.
8 + 7 = 15
Since 15 is greater than 10, we need to regroup 10 ones as 1 ten and carry it over to the tens place. We can represent this with place value blocks by moving a rod of 10 ones from the ones place to the tens place.
So we have:
8
+78
---
```
8
+78
---
16 (write 6 in the ones place and carry 1 to the tens place)
```
Now we can add the tens place digits, which are 1 (carried over) and 8:
1 + 8 = 9
So the final result is:
8
+78
-----
86
Therefore, 8 plus 78, plus 7 is:
```
8
+78
+ 7
---
94
```
So the answer of addition is 94.
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Choose the diagram that shows the graph of the inequality.
Answer: C
Step-by-step explanation:
Help with the question in photo please
Answer:
AB = 15
Step-by-step explanation:
6(6 + x + 6) = 7(7 + 11)
72 + 6x = 126
6x = 126 - 72 = 54
x = 54/6
= 9.
So AB = 9 + 6 = 15.
Identify each part of the circle given it’s equation.
Each part of the circle given it’s equation should be identified as follows;
Center: (9, 4).Center: (-1, 1).Center: (-6, 0).Center: (2, -13).Center: (-7, -4).Radius: √28What is the equation of a circle?In Geometry, the standard or general form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.Based on the information provided above, we have the following parameters:
Radius, r = √400 units.
Center, (h, k) = (9, 4).
By substituting the given radius and center into the equation of a circle, we have;
(x - h)² + (y - k)² = r²
(x - 9)² + (y - 4)² = (√400)²
(x - 9)² + (y - 4)² = 400.
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Small baskets of tomatoes are sold at a vegetable stand for $3 per basket. Large
baskets of tomatoes are sold at the stand for $5 per basket. Only whole numbers of
baskets may be purchased.
A customer purchases a total of 8 baskets of tomatoes and pays $36.
A. Write and solve a system of equations that models the number of small
baskets (x) and the number of large baskets () that the customer purchases.
Show or explain all your work.
The customer purchased 2 small baskets and 6 large baskets.
Let x be the number of small baskets and y be the number of large baskets that the customer purchases.
We can set up a system of two equations based on the information given:
Equation 1: x + y = 8 (The total number of baskets purchased is 8)
Equation 2 3x + 5y = 36: (The total amount paid for the baskets is $36)
To solve this system, we can use either substitution or elimination method.
Using substitution method:
From Equation 1, we have x = 8 - y.
Substitute this into Equation 2:
3(8 - y) + 5y = 36
24 - 3y + 5y = 36
2y = 12
y = 6
Now, we can substitute y = 6 back into Equation 1 to find x:
x + 6 = 8
x = 2
Therefore, the customer purchased 2 small baskets and 6 large baskets.
Using elimination method:
We can multiply Equation 1 by 3 and subtract it from Equation 2 to eliminate x:
3x + 5y = 36
- (3x + 3y = 24)
2y = 12
y = 6
Now, we can substitute y = 6 back into either Equation 1 or Equation 2 to find x. Let's use Equation 1:
x + 6 = 8
x = 2
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Prove the following two properties of the Huffman encoding scheme. (a) If some character occurs with frequency more than 2=5, then there is guaranteed to be a codeword of length 1. (b) If all characters occur with frequency less than 1=3, then there is guaranteed to be no codeword of length 1
(a) Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency. Therefore, there is guaranteed to be a codeword of length 1 for this character. (b) Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.
(a) Let's assume that some character occurs with frequency more than 2=5.
The two nodes with the lowest frequency are merged into a single node, with the sum of their frequencies as the frequency of the new node.
This process is repeated until all the nodes are merged into a single node, which becomes the root of the tree.
Since the character occurs with a frequency higher than 2=5, it is guaranteed to be merged with another character with the same frequency or a lower frequency.
Therefore, there is guaranteed to be a codeword of length 1 for this character.
(b) Let's assume that all characters occur with frequency less than 1=3.
Consider the binary tree created by the Huffman algorithm. The root of the tree corresponds to the least frequent symbol, which will be assigned the longest codeword.
Since all symbols occur with a frequency less than 1=3, the root of the tree will have a frequency less than 1=3.
This means that the corresponding codeword for the root will be longer than 1 bit. Therefore, there is guaranteed to be no codeword of length 1 for any symbol in this case.
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Barak is going to buy 550 nails from one of these companies.
Nail Company
50 nails
£4. 15 plus VAT at 20%
Hammer Company
25 nails
£2. 95
Special offer
Buy 100 get 25 free
He wants to buy the nails at the cheaper cost.
Where should he buy the nails, from the Nail Company or the Hammer Company?
Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
Let's first calculate the cost of buying 550 nails from each company:
Nail Company:
Cost of 1 nail = £4.15 + (20% of £4.15) = £4.15 + £0.83 = £4.98 (rounded to 2 decimal places)
Cost of 50 nails = £4.98 x 50 = £249
Cost of 550 nails = £249 x 11 = £2739
Hammer Company:
Cost of 1 nail = £2.95/25 = £0.118 (rounded to 3 decimal places)
Cost of 75 nails (buy 100 get 25 free) = 100 x £0.118 x 3 = £35.40
Cost of 550 nails = 550 x £0.118 = £64.90
Therefore, Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
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Eva signs up for dance classes. She pays a onetime registration fee and then the same monthly tuition. Eva pays $110 the first month and at the end of 9 months has paid $670 in all. Which equation can be used to model the tuition and registration fees?
Answer: (670 -110)/8
Step-by-step explanation:
Months: 110 the first month
*Now since she paid 670 in total she subtracts the 110 from the first month which is 560, and now there is an event amound paid in the other months so you divide 560 by 8 since 8 months are left over resulting in $70 each month.
January,
February,
March,
April,
May,
June,
July,
August,
(co 4) from a random sample of 85 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 5.91 hours. what is the 90% confidence interval for the amount of time they spend online each week?
The 90% confidence interval for the amount of time that teens spend online each week is (30.761, 32.839) hours
To find the 90% confidence interval for the amount of time that teens spend online each week, we can use the following formula
CI = x ± z*(σ/√n)
where
x is the sample mean
σ is the population standard deviation
n is the sample size
z is the z-score associated with the desired confidence level
In this case, we have
x = 31.8 hours
σ = 5.91 hours
n = 85
z = 1.645 (for a 90% confidence level, using a z-table or calculator)
Plugging in these values, we get
CI = 31.8 ± 1.645*(5.91/√85)
Simplifying, we get
CI = 31.8 ± 1.039
We can interpret this interval as saying that if we were to take many random samples of 85 teens and compute the confidence interval for each sample, about 90% of these intervals would contain the true population mean.
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Why do Markets behave in the same ways as Individual Consumers?
Answer:
Markets behave the same way as individual customers because markets are made up of individual consumers.
Step-by-step explanation:
Which is true about the relationship between 1 inch and 1 foot?
A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot
Option B is true about the relationship between 1 inch and 1 foot.
What is conversation?
A unit's use depends on the context; for example, a room's area is expressed in meters, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively. Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
There are 12 inches in 1 foot. This means that 1 foot is 12 times longer than 1 inch. Therefore, option B is correct. Option A is incorrect because it states that 1 inch is 12 times as long as 1 foot, which is the opposite of the correct relationship. Option C is incorrect because it states that 1 foot is 6 times as long as 1 inch, which is half of the correct relationship. Option D is incorrect because it states that 1 inch is 6 times as long as 1 foot, which is the opposite of the correct relationship.
Hence, Option B is true about the relationship between 1 inch and 1 foot.
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In 2010, Keenan paid $2,826 in federal income tax, which is 70% less than he paid in 2009. How much did he pay in 2009?
Based on the above, Keenan paid $9,420 in federal income tax in 2009.
What is the income tax?Let X be the amount Keenan paid in taxes in 2009.
According to the problem, Keenan paid 70% less in 2010 than he did in 2009. This means that he paid only 30% of what he paid in 2009, since 100% - 70% = 30%.
We can express this mathematically as:
0.30X = 2,826
To solve for X, we can divide both sides of the equation by 0.30:
X = 2,826 ÷ 0.30
X = 9,420
Therefore, Keenan paid $9,420 in federal income tax in 2009.
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Calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis. calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic.
The cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
To calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis, you would first need to determine the overall proportion of women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week in the sample. Let's say this proportion is 0.20.
Next, you would multiply this proportion by the total sample size to get the expected count. Let's say the total sample size is 500 women. The expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week would be:
Expected count = 0.20 x 500 = 100
To calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic, you would need to subtract the expected count from the observed count for this cell, square the difference, and divide by the expected count. Let's say the observed count for this cell is 80.
Contribution to chi-square = (80 - 100)^2 / 100 = 4
This means that the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
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If r is the annual interest rate of the bank account, then at the end of the year the balance in the account is multiplied by a growth factor of x = 1 + r.
Answer:
Step-by-step explanation:
Yes , that is correct. The growth factor for the balance in the account at the end of the year is calculated by adding 1 to the annual interest rate, which is expressed as a decimal, and multiplying the result by the balance. This gives the formula:
Ending balance = Beginning balance * (1 + r)
where r is the annual interest rate as a decimal.
Problem 68 An outdoor adventure club has 35 members, who are all either rock climbers or skiers. There are 3 more rock climbers than
there are skiers. How many climbers are there?
WHOEVER ANSWERS FIRST GETS BRAINLIEST AND ANSWER FAST FOR WHOEVER GOTS THE HIGHEST BRAILIEST I WILL GIVE THEM THE BRAINLIEST POINT
Answer: 14.5 climbers technically 14 because 1/2 a person is wrong
Step-by-step explanation:
Frank wants to find the area enclosed by the figure at the right the figure on each side has semicircles of a 40 meter by 40 meter square. Find the area by the figure use 3. 14 for pi
The area enclosed by the figure at the right is 2856 square meters.
To find the area enclosed by the figure at the right, we first need to find the area of the square and the two semicircles on each side. The square has sides of 40 meters, so its area is 40 x 40 = 1600 square meters. Each semicircle has a radius of 20 meters (half the side length of the square), so its area is 1/2 x pi x r^2 = 1/2 x 3.14 x 20^2 = 628 square meters. Since there are two semicircles on each side, the total area of all four semicircles is 2 x 628 = 1256 square meters.
To find the total area enclosed by the figure, we add the area of the square and the area of the four semicircles:
1600 + 1256 = 2856 square meters
Therefore, the area enclosed by the figure at the right is 2856 square meters.
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To find the standard deviation of the liquid measure of oil in barrels, the oil company measures 25 randomly selected barrels and find the standard deviation of the samples to be s=. 34. Find the 92% confidence interval for the population standard deviation
The 92% confidence interval for the population standard deviation is (0.199, 0.509).
To find the 92% confidence interval for the population standard deviation, we will use the chi-square distribution. We know that for a sample size of n=25, the degrees of freedom for the chi-square distribution is (n-1) = 24.
The chi-square distribution is a right-tailed distribution, so we need to find the chi-square values that will leave 4% in the right tail (for a total of 92% confidence interval).
From a chi-square distribution table, the chi-square value with 24 degrees of freedom that leaves 4% in the right tail is 41.337. The chi-square value that leaves 96% in the left tail is 13.119.
Using the formula for the confidence interval for the population standard deviation:
lower bound = [tex]sqrt((n-1)*s^2 / chi-square upper)[/tex]
upper bound = [tex]sqrt((n-1)*s^2 / chi-square lower)[/tex]
We can substitute the values we have:
lower bound = [tex]sqrt((25-1)*0.34^2 / 41.337) = 0.199[/tex]
upper bound = [tex]sqrt((25-1)*0.34^2 / 13.119) = 0.509[/tex]
Therefore, the 92% confidence interval for the population standard deviation is (0.199, 0.509).
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Pls help. And please actually answer the question
Answer: y= |x-1| -1
Step-by-step explanation:
Explanation:
This is an absolute value function.
The parent function looks like: y=|x| When transformations take place, we use this function to describe those transformations:
y = a|x-h|+k
where (h, k) is your new vertex
"a" is your stretch
and a - would be placed in the front if there was a reflection
Solution:
Your equation has a new vertex at (1, -1)
There is no stretch and no reflection
Plug into equation:
y= |x-1| -1
¿Como la gastronomia puede ayudarnos a convivir armoniosamente?
Gastronomy is a way of promoting understanding among different cultures, and of bringing people and traditions closer together.
The practise of choosing, preparing, presenting, and consuming exquisite cuisine. The foundation of gastronomy lies in the connections between food, culture, and tradition. Gastronomy has emerged through time as a more potent cultural force than language or other influences among the peoples of the world.
Molecular gastronomy is a relatively recent branch of science that studies the physical and chemical changes that take place during cooking. Molecular cuisine is the name of the new culinary movement based on this emerging discipline.
Nowadays, the world may be broken down into separate gastronomic zones, where different cuisines are popular and similar cooking techniques are used. Throughout much of Southeast Asia, rice is the main food. The abundant and creative use of spices to give meals an extra flavour is what makes Indian and Indonesian cuisine unique. The prevalent ingredient in Mediterranean recipes is olive oil.
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Complete question:
How can gastronomy help us live harmoniously?
James weighs 8712 pounds. he has 2 dogs that each weigh 1314 pounds. how many more pounds does james weigh than both of his dogs combined?
James weighs 6084 more pounds than both of his dogs combined.
To find out how many more pounds James weighs than both of his dogs combined, we first need to calculate the total weight of the dogs. Since he has two dogs that weigh 1314 pounds each, we can find the total weight of the dogs by multiplying 1314 by 2, which gives us 2628 pounds.
Next, we can add the weight of both dogs together to get the total weight of the dogs, which is 2628 pounds. We can then subtract the weight of the dogs (2628 pounds) from James' weight (8712 pounds) to find out how many more pounds James weighs than both of his dogs combined.
Therefore, James weighs 6084 more pounds than both of his dogs combined. This can be calculated by subtracting the weight of the dogs (2628 pounds) from James' weight (8712 pounds), which gives us 6084 pounds.
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The box plots show a summary of push–up scores for Group A and Group B in the same gym class. Both groups have the same number of students. Determine whether each statement is true based on these box plots. Select True or False for each statement. True False At least 50% of students in each group scored more than 165 push–ups. The median score of push–ups of Group A is 10 points greater than the median score of push–ups of Group B. The scores of Group A have less variability than the scores of Group B
Statement 2 is false because while the median score of Group A is higher than Group B, it is not 10 points greater as claimed.
Statement 1 is false because the box plots provide limited information, making it impossible to determine whether at least 50% of students in each group scored more than 165 push-ups.
Statement 3 is false because Group A has more variability in push-up scores than Group B, as indicated by the larger interquartile range (IQR) of Group A.
Looking at the box plots, we can see that the median score of Group A is higher than Group B, but it is not 10 points greater. Therefore, statement 2 is False.
We cannot determine whether at least 50% of students in each group scored more than 165 push-ups. The box plots only show us the quartiles and the minimum and maximum values, so we do not know the exact number of students who scored above 165 push-ups. Therefore, statement 1 is False.
The interquartile range (IQR) of Group A is greater than the IQR of Group B, indicating that Group A has more variability in push-up scores than Group B. Therefore, statement 3 is False.
Hence, All the statement are False.
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2.
Graham wants to take snowboarding lessons at a nearby ski resort that charges $40 per week.
The resort also charges a one-time equipment-rental fee of $99 for uninterrupted enrollment in
classes. The resort requires that learners pay for three weeks of classes at a time.
The function f(x) represents the situation
f(x) =
40x +99
x
Select two choices that are true about the function f(x).
A There is a zero at 0.
B There is an asymptote at y = 40.
C
There is an asymptote at x = 0.
D There is a vertical shift up 99 units.
Options B & C
There is an asymptote at y = 40.
There is an asymptote at x = 0.
Step-by-step explanation:Main concepts:
Concept 1. Zeros of rational functions
Concept 2. Vertical asymptotes of rational functions
Concept 3. Horizontal asymptotes of rational functions
Concept 4. Transformations - vertical shift
Concept 1. Zeros of rational functionsRational functions have zeros at values of x where the numerator is zero, while the denominator is not also zero.
[tex]f(x)=\dfrac{40x+99}{x}[/tex]
Values that make the denominator zero
Note that for the function f(x), x=0 is the only value that will make the denominator zero.
Values that make the numerator zero
To find the value that makes the numerator zero, set the numerator equal to zero, and solve for the value of x that makes it true:
[tex]40x+99=0[/tex]
[tex]40x=-99[/tex]
[tex]x=\frac{-99}{40}[/tex]
So, [tex]x=\frac{-99}{40}[/tex] is the only value that will make the numerator zero
Note that this doesn't simultaneously make the denominator zero, so [tex]x=\frac{-99}{40}[/tex] is a zero (and the only zero) of the function f(x).
Therefore, Option A is NOT a correct answer.
Concept 2. Horizontal asymptotes of rational functionsRational functions have Horizontal Asymptotes if the degree of the polynomial in the numerator is less than or equal to the degree of the polynomial in the denominator.
If the Degree of the denominator is greater, the Horizontal Asymptote is at a y=0.
If the Degrees are equal, the Horizontal Asymptote is at a y-value equal to the ratio of the leading coefficients.
[tex]f(x)=\dfrac{40x+99}{x}[/tex]
Note that for f(x), the degrees of the polynomials in the numerator and denominator are both 1. So, a horizontal asymptote does exist, and it is at a height of the ratio of the leading coefficients.
The leading coefficient of the numerator is 40, while the leading coefficient of the denominator is 1.
The ratio of the leading coefficients, 40/1, so the horizontal asymptote is y=40.
Therefore, Option B is a correct answer choice.
Concept 3. Vertical asymptotes of rational functionsRational functions have Vertical Asymptotes at values of x where the denominator is zero, while the numerator is not also zero (the opposite of finding "zeros" of the function).
Recalling the values that make the numerator and denominator zero from Concept 1:
x=0 is the only value that will make the denominator zero[tex]x=\frac{-99}{40}[/tex] is the only value that will make the numerator zeroSince x=0 doesn't also make the numerator zero, x=0 is a vertical asymptote for the function f(x).
Therefore, Option C is a correct answer choice.
Concept 4. Transformations - vertical shiftRational functions have been vertically shifted if after all the main rational function fraction, there is a number added or subtracted.
I provide an example of a different function (which I'll call g(x)) here:
[tex]g(x)=\dfrac{3}{x}+2[/tex]
Observe that the "+2" is after all of the main fraction, so the graph of 3/x would have been shifted vertically up 2 units.
This is NOT the case for the function f(x) from the question. The "99" is part of the fraction, so it does not represent a vertical shift.
Therefore, Option D is NOT a correct answer choice.
Can you find continuous function & so that when an = f(n) we have SIGMA an = ∫ f(x)dx
[tex]SIGMA an = 1 + 2 + 3 + ... + n = n(n+1)/2 = ∫_1^n f(x)dx = ∫ f(x)dx[/tex]
f(x) = x is indeed a continuous function that satisfies the given condition.
Yes, we can find a continuous function f(x) such that when an = f(n), we have SIGMA an = ∫ f(x)dx.
One such function is f(x) = x.
To see why this works, let's consider a few terms of the series SIGMA an.
When n = 1, we have a1 = f(1) = 1, so the series starts with 1.
When n = 2, we have a2 = f(2) = 2, so the series becomes 1 + 2. When n = 3, we have a3 = f(3) = 3, so the series
becomes 1 + 2 + 3. And so on.
Notice that this series is just the sum of the first n positive integers, which we know is equal to n(n+1)/2.
But if we take the derivative of f(x) = x, we get f'(x) = 1, which means that the integral of f(x) from 1 to n is just n.
So we have:
[tex]∫ f(x)dx = ∫ xdx = 1/2 x^2 + C[/tex]
[tex]∫_1^n f(x)dx = (1/2 n^2 + C) - (1/2 (1)^2 + C) = 1/2 n^2 - 1/2[/tex]
And therefore:
[tex]SIGMA an = 1 + 2 + 3 + ... + n = n(n+1)/2 = ∫_1^n f(x)dx = ∫ f(x)dx[/tex]
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Calcula los siguientes lÃmites página. 115 ejercicio
a) lim n = +[infinity] infinito 6-4n²
----------
2(n)²
b) lim n = +[infinity] infinito 4n²+3n-2
--------------
2n ³ -4n
c) lim n = +[infinity] infinito 2n ³ -4n
---------------
4n
d) lim x = +[infinity] infinito -8x4 +2
------------
2x² +4
a) Para calcular este límite, podemos dividir tanto el numerador como el denominador por n² y luego aplicar la regla de L'Hôpital:
lim n → ∞ [(6 - 4n²)/(2n²)]
= lim n → ∞ [6/(2n²) - (4n²)/(2n²)]
= lim n → ∞ [3/n² - 2]
= -2
Por lo tanto, el límite es -2.
b) Podemos dividir tanto el numerador como el denominador por n³ para simplificar el límite:
lim n → ∞ [(4n² + 3n - 2)/(2n³ - 4n)]
= lim n → ∞ [(4/n + 3/n² - 2/n³)/(2/n² - 4/n²)]
= lim n → ∞ [(4 + 3/n - 2/n²)/(2 - 4/n)]
= lim n → ∞ [(4n + 3 - 2n²)/(2n² - 4)]
= lim n → ∞ [-2n²/(2n² - 4)]
= -1
Por lo tanto, el límite es -1.
c) Podemos dividir tanto el numerador como el denominador por n³ para simplificar el límite:
lim n → ∞ [(2n³ - 4n)/(4n)]
= lim n → ∞ [(2n² - 4)/(4)]
= lim n → ∞ [(n² - 2)/2]
= +∞
Por lo tanto, el límite es +∞.
d) Podemos dividir tanto el numerador como el denominador por x⁴ para simplificar el límite:
lim x → ∞ [-8x⁴ + 2]/[2x² + 4]
= lim x → ∞ [-8 + 2/x⁴]/[2/x² + 4/x⁴]
= -4/1
= -4
Por lo tanto, el límite es -4.
One tire manufacturer claims that his tires last an average of 44000 miles with a standard deviation of 7650 miles. A random sample of 120 of his tires is taken. What is the probability that the average of this sample of tires will last longer than 45000 miles
The probability of a randomly selected tire from this sample having a lifespan greater than 45,000 miles is approximately 0.0639 or 6.39%.
We can use the central limit theorem to approximate the distribution of the sample mean.
In this case, the population mean is 44,000 miles and the population standard deviation is 7,650 miles. We are taking a sample of 120 tires, so the standard deviation of the sample mean is:
σ/√n = 7,650/√120 = 698.68
To find the probability that the sample mean will be longer than 45,000 miles, we need to standardize the sample mean using the formula:
z = (x - μ) / (σ / √n)
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (45,000 - 44,000) / (7,650 / √120) = 1.527
We can then look up the probability corresponding to a z-score of 1.527 in a standard normal distribution table or using a calculator. The probability of a randomly selected tire from this sample having a lifespan greater than 45,000 miles is approximately 0.0639 or 6.39%.
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The tops of two vertical poles of heights 20 m and 15 m joined by a taut wire 12 m long. What is the angle of slope of the wire?
The angle of the tops of two vertical poles of heights 20 m and 15 m joined by a taut wire 12 m long slope of the wire = 24.6 °
Height of the 1st vertical pole = 20m
Height of the second vertical pole = 15m
Difference of their height = 5 m
Length of the taut wire = 12m
Using trigonometry ratio of sin we get
Perpendicular = 5 m
Hypotenuse = 12 m
Sin A = Perpendicular/ hypotenuse
Sin A = 5/12
A = [tex]sin^{-1} (5/12)[/tex]
A = 24.6 °
The angle of slope of the wire = 24.6°
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I need help finding the decimal for these equations.
Answer:
Carlos=1.5041
Mykala=2.6991
William=4.1350
Emily=4.1773
The value of your stock investment decreased by 23% after a stock market crash. What percentage increase in value would the stocks have to rise in order to return to the value they were before the stock market crash? Round your answer to the nearest tenth of a percent
The stocks would need to increase in value by 23% to return to their original value. Rounding to the nearest tenth of a percent, the answer is 23.0%.
Let x be the percentage increase in the value of the stocks needed to return to their original value. Since the value of the stocks decreased by 23%, the new value of the stocks is 100% - 23% = 77% of the original value.
Therefore, we can set up the equation:
(100% + x%) = (77%)*(100%)
Simplifying this equation, we get:
100% + x% = 77%
x% = 77% - 100%
x% = -23%
Since we want to find the percentage increase, we need to take the absolute value of -23%, which is 23%.
Therefore, the stocks would need to increase in value by 23% to return to their original value. Rounding to the nearest tenth of a percent, the answer is 23.0%.
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