The work required to pump out half of the water from the aquarium is approximately 2000 J.
The volume of the aquarium is V = (6 m) x (1 m) x (1 m) = 6 cubic meters. Since the density of water is 1000 kg/m3, the mass of the water in the aquarium is m = ρV = 1000 kg/m3 x 6 m3 = 6000 kg.
To pump out half of the water, we need to remove 1/2 x 6000 kg = 3000 kg of water. Since work is force times distance, we need to calculate the force required to lift this mass of water a distance of 1 m (the height of the aquarium).
The force required is F = mg = (3000 kg) x (9.8 m/s2) = 29,400 N. The work done is W = Fd = (29,400 N) x (1 m) = 29,400 J.
To approximate the required work by a Riemann sum, we can divide the height of the aquarium into n subintervals of width Δx, and choose a sample point xi* in each subinterval.
The force required to lift the water in each subinterval is approximately constant, so the work required to lift the water in each subinterval is approximately F(xi*)Δx. The total work required is therefore approximately given by the Riemann sum:
nlim ∑ F(xi*)Δxi= nlim ∑ (1000 x 6 x Δxi x xi*)i=1
Taking the limit as n goes to infinity, this Riemann sum becomes the integral:
∫0^1 1000 x 6 x x dx
Evaluating this integral gives:
∫0^1 6000 x^2 dx = [2000 x^3]0^1 = 2000 J
Therefore, the work required to pump out half of the water from the aquarium is approximately 2000 J. This approximation becomes more accurate as the number of subintervals n becomes larger.
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which one of the following are parametric equations for the tangent line to the curve at the point ( )?
The parametric equations for the tangent line to the curve
x = 26+27, t = 10+6t, z = 27+27t
In the given question points are given and we have to find the parametric equations for the tangent line to the curve.
given r(t) = <t³-1 , t²+1 , t³>
taking differentiation
r'(t) = <3t² , 2t , 3t² >
parameters corresponding to point at the point (26, 10, 27)
t²+1 = 10
=> t² = 9
=> t = √9
=>t=3
r'(t) at t = 3 is
r'(t) = <27, 6, 27 >
So the parametric equations for the tangent line to the curve
x = 26+27
t = 10+6t
z = 27+27t
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The complete question is :
Find the parametric equations for the tangent line to the curve
x = t³ - 1,
y = t² + 1,
z = t³
at the point (26, 10, 27). Use the variable t for your parameter.
Earline needs to save $367.50 for her summer vacation. She plans on saving $52.50 per week. In 6 weeks, will she have enough money? Explain.
Hint: write a multiplication equation
No, Earline won't have enough money in six weeks
How to calculate the amount of money that Earline will have in six weeks?Earline needs to save $367.50 for her summer vacation
She plans on saving $52.50 per week
The amount of money that Earline will get in six weeks can be calculated as follows
= 52.50 × 6
= 315
$315 is lesser that $367.50
Hence Earline will not be able to save enough money in six weeks
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Which point on the number line is approximately 13/17
Answer:
C
Step-by-step explanation:
Cause 13/17 is 0.76 so c is nearer to 1 about 0.76
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{13}{17}}\\\\\mathsf{\rightarrow 13\div17}\\\\\mathsf{\rightarrow 0.764705882352941}}\\\\\mathsf{\approx 0.764\approx 0.75\ (in\ this\ case)}}[/tex]
[tex]\huge\text{Therefore your answer should be:} \\\\\huge\boxed{\mathsf{Point\ C.}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The balance, B, in dollars, in a bank account depends on the amount deposited, A dollars, the annual interest rate, r %, and the time, t, in months since the deposit, so B=f(A,r,t).
(a) Is f an increasing or decreasing function of: The answers to chose from are after the ? mark.
A? ? increasing decreasing neither increasing nor decreasing somtimes increasing and sometimes decreasing
r? ? increasing decreasing neither increasing nor decreasing somtimes increasing and sometimes decreasing
t? ? increasing decreasing neither increasing nor decreasing somtimes increasing and sometimes decreasing
(b) Interpret the statement f(1000,4,18)?1822 by writing a sentence, including units. Then use your sentence to complete the following: The options to chose from are after the ? mark.
The units of 1000 are: ? percent months dollars dollars/month percent/month
The units of 4 are: ? percent months dollars dollars/month percent/month
The units of 18 are: ? percent months dollars dollars/month percent/month
The units of 1822 are ? percent months dollars dollars/month percent/month
As per the information provided, this all indicates that the function f is becoming more of a function r at end.
Three different factors affect the function that determines the balance in this account: the initial deposit amount, the interest rate compounded on this account, and the amount of time the money is kept in the account. The account balance changes if any one or all of these three values is altered.
Let us examine how the interest rate affects this balance. When money is kept in an interest-bearing account, the interest is added as a percentage of the balance to the value of the account. Accordingly, a higher interest rate would result in a larger sum being added to the balance because a larger portion of the balance would be deposited.
Thus, this indicates that the function f is becoming more of a function r at end.
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Note that the correct question is:
The balance, B, in dollars, in a bank account depends on the amount deposited, A dollars, the annual interest rate, r%, and the time, t, in months since the deposit, so B = f(A, r, t).
Is f an increasing or decreasing function of r? Explain your answer.
How many ways can you make change for 70 cents using only nickels, dimes, and quarters?
The number ways can make change for 70 cents using only nickels, dimes, and quarters is,
7 dimes, 0 nickels
6 dimes, 2 nickels
5 dimes, 4 nickels
4 dimes, 6 nickels
3 dimes, 8 nickels
2 dimes, 10 nickels
1 dime, 12 nickels
0 dimes, 14 nickels
What is the combination?In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.
Formula for selection of a objects from the n objects,
N = ⁿCₐ
To find the number of ways to make change for 70 cents using only nickels, dimes, and quarters, we can use a combination of systematic listing and counting.
One approach is to consider the number of quarters used to make the change, which can be 0, 1, or 2, since using more than 2 quarters would exceed the total value of 70 cents.
Here are the possible combinations of coins to make change for 70 cents:
Using 0 quarters:
7 dimes, 0 nickels
6 dimes, 2 nickels
5 dimes, 4 nickels
4 dimes, 6 nickels
3 dimes, 8 nickels
2 dimes, 10 nickels
1 dime, 12 nickels
0 dimes, 14 nickels
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HURRY 100 PTS AND BRAINLIEST!!! Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 8 feet.
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 17 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Answer:
Part A: PR ≈ 16.06
Part B: QR≈ 9.60
Step-by-step explanation:
Part A)
The length of rod PR can be found using the Pythagorean theorem.
In this case, rod PQ is one leg, rod QR is the other leg, and rod PR is the hypotenuse. So, we have: PQ^2 + QR^2 = PR^2
Substituting the given lengths, we have:
14^2 + 8^2 = PR^2
Solving for PR, we get:
PR^2 = 14^2 + 8^2 = 196 + 64 = 260
Taking the square root of both sides, we have:
PR = √260
PR ≈ 16.06
Part B)
If the length of rod PR is adjusted to 17 feet, we can use the Pythagorean theorem to find the new height QR.
PQ^2 + QR^2 = 17^2
Substituting the given length of PQ, we have:
14^2 + QR^2 = 17^2
Expanding both sides, we have:
196 + QR^2 = 289
Subtracting 196 from both sides, we have:
QR^2 = 289 - 196 = 93
Taking the square root of both sides, we have:
QR = √93
QR ≈ 9.60
In the given diagram the value of x is
Answer:
15
Step-by-step explanation:
A right angle is 90 degrees
90 - 45 = 45
The remaining angle of 3x is equal to 45 degrees.
45/3 = x x=15
Each person in a group buys a ticket, a medium drink, and a large popcorn. Write an expression in simplest form that represents the amount of money the group spends at the movies. Interpret the expression.
Ticket $7.50
DRINKS
Small: $1.75
Medium: $2.75
Large: $3.50
POPCORN
Small: $3.00
Large: $4.00
Answer: 14.25x is the expression
It represents the total combined cost everyone paid.
=======================================================
Explanation:
Add up the price of a ticket, a medium drink, and a large popcorn.
7.50+2.75+4.00 = 14.25
Each person spends $14.25 for those three items.
If x is the unknown number of people, then 14.25x represents the total amount spent by everyone combined.
Example: x = 10 people, so 14.25x = 14.25*10 = 142.50 dollars total is spent by everyone combined.
what is equivalent to 2/100
Answer:
1/50
Step-by-step explanation:
Divide 2/100 by 2 to get the simplest form.
Graph the line. Y = -3×
Answer:
here it is
Step-by-step explanation:
-3 represents the slope. Since its 3/1, this means which point on the slope is 3 to side and 1 either up or down. Since the slope is negative, it goes down.
The formula for a slope is y = mx + b. Since we don’t have the b, that means it is 0. B represents the y intercept or when the line crosses the y axis.
select the net number of atp produced from eight molecules of glucose during the process of glycolysis
The net number of ATP produced from eight molecules of glucose during glycolysis is 32 ATP molecules.
Glycolysis is a metabolic pathway that breaks down glucose into two molecules of pyruvate, which in turn produces ATP. Each molecule of glucose yields two molecules of ATP and two molecules of NADH. Each NADH molecule, in turn, produces three more ATP molecules when it is oxidized in the electron transport chain. Therefore, the total number of ATP produced from one molecule of glucose is four. When eight molecules of glucose undergo glycolysis, the total number of ATP produced is 4 x 8 = 32 ATP molecules. hence 32 ATP molecules produced during the process of glycolysis.
The complete question is : select the net number of ATP produced from 8 molecules of glucose during the process of glycolysis is
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A cliff-jumper of mass 68.0 kg stands on the edge of a cliff and possesses 16,800 J of potential energy. How high up is this lunatic from the base of the cliff?
The cliff-jumper is standing 24.7 meters (or about 81 feet) above the base of the cliff.
What is potential energy (PE)?
The potential energy formula is affected by the force operating on the two objects. The formula for gravitational force is P.E. = mgh, where m is mass in kilograms, g is gravity's acceleration (9.8 m/s2 at the earth's surface), and h is height in meters.
The potential energy (PE) possessed by the cliff-jumper of mass m at height h above the base of the cliff is given by the formula:
PE = mgh
where g is the acceleration due to gravity (9.81 m/s²).
In this problem, the cliff-jumper has a mass of 68.0 kg and possesses 16,800 J of potential energy. We can use the formula above to find the height h:
PE = mgh
h = PE / (mg)
Substituting the given values, we get:
h = 16800 J / (68.0 kg x 9.81 m/s^2)
h = 24.7 meters (rounded to two decimal places)
Therefore, the cliff-jumper is standing 24.7 meters (or about 81 feet) above the base of the cliff.
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Describe how technology improvements have changed the way we find and apply for jobs. How do you plan to use social media to find a job in the future?
Answer:
Technology improvements allow someone to look up jobs and be able to apply. This is much easier than going around yourself as it takes less time and effort. With technology we are capable of looking at ads of jobs and finding jobs in and around your area. Places such as indeed and linkedin have options for filters to allow you to adjust your search to salaries and areas that suit you.
Hope this helps, have a lovely day! :)
show that if a and b are square, upper triangular matrices. then so is ab. (hint: the ith column of ab is a suitable linear combination of the columns of a)
Hence, if i > j, then (AB)ij is a sum of products of zeros, and is therefore zero. This means that all the entries below the main diagonal in the matrix AB are zero. Therefore, AB is also an upper triangular matrix.
To show that if a and b are square, upper triangular matrices, then so is ab, we need to prove that all the entries below the main diagonal in the matrix ab are zero.
Let A and B be square, upper triangular matrices of size n x n.
Then the (i,j)th entry of AB is given by:
(AB)ij = Σk=1n AikBkj
For i > j, we have:
(AB)ij = Σk=1n AikBkj = Σk=1j AikBkj + Σk=j+1n AikBkj
Since A is upper triangular, we have Aik = 0 for k > i.
Therefore, the first sum above is non-zero only for k ≤ i. Since B is also upper triangular, we have Bkj = 0 for k > j.
Therefore, the second sum above is non-zero only for k > j.
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T/F If you want to compare the value 3 to the value 5 to see if 3 is greater than 5, you would enter the following formula: =3>5.
Answer:
Step-by-step explanation:
The answer is TRUE, If you want to compare the value 3 to the value 5 to see if 3 is greater than 5, you would enter the following formula: =3>5.
What critical value t* would you use for a confidence interval for the population mean in each of the following situations?
a) A 95% confidence interval based on n = 10 randomly selected observations.
b) A 99% confidence interval from an SRS of 20 observations.
c) A 90% confidence interval based on a random sample of 77 individuals.
Answer: a) A 95% confidence interval based on n = 10 randomly selected observations would use a t*-value from the t-distribution with (n - 1 = 9) degrees of freedom.
b) A 99% confidence interval from an SRS of 20 observations would use a t*-value from the t-distribution with
Step-by-step explanation:
ASAP!!!! Sixty-eight percent of U.S. adults oppose hydraulic fracturing (fracking) as a means of increasing the production of natural gas and oil in the United States. You randomly select six U.S. adults. Find the probability that the number of U.S. adults who oppose fracking as a means of increasing the production of natural gas and oil in the United States is (a) exactly 2, (b) less than four, and (c) at least three
The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.
What is the probability?Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as
[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]
The probability that the number of U.S. adults who oppose exactly 2 is given as,
P(2) = ⁶C₂ x (0.68)² x (1 - 0.68)⁴
P(2) = 0.0727
The probability that the number of U.S. adults who oppose less than four is given as,
P(x < 4) = ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ + ⁶C₂ x (0.68)² x (1 - 0.68)⁴ + ⁶C₃ x (0.68)³ x (1 - 0.68)³
P(x < 4) = 0.0137 + 0.0727 + 0.2061
P(x < 4) = 0.2925
The probability that the number of U.S. adults who oppose at least three is given as,
P (x ≥ 3) = 1 - ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ - ⁶C₂ x (0.68)² x (1 - 0.68)⁴
P (x ≥ 3) = 1 - 0.0137 - 0.0727
P (x ≥ 3) = 0.9136
The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.
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PLEASE HELP ME WITH THIS WORKSHEET! Answer all parts.
1.
A company makes two types of electronic devices: laptops and tablets. Its business
plan says that it must produce from 70 to 130 laptops, and from 50 to 110 tablets,
per day. The total number of devices it must make per day according to the plan
ranges from 150 to 220. Given that x is the number of laptops made per day, and y
is the number of tablets made, what are the daily constraints that the plan places on
the company?
2. The company sells all the electronic devices. It makes its profit is $65 for every laptop sold and $45 for every tablet sold. what is the objective function for maximizing profit?
3. Insert an image of a graph showing the feasible region.
4. What are the vertices of the feasible region?
5. Evaluate the objective function at the vertices of each feasible regions.
6. How many laptops and how many tablets for the company make to maximize profit?
7. What is the maximum profit?
The maximum profit that the company will be left with is $11,450 from the laptops and tablets.
What does the word "profit" mean?Your profit is the amount left over after paying all necessary business expenses. The three main categories of profit are gross, operational, and net. Gross revenue is the most profitable. After paying for the items and services that were sold, the remaining balance is shown.
1.The daily constraints on the company according to the plan are:
70 <= x <= 130 (number of laptops produced)
50 <= y <= 110 (number of tablets produced)
x + y >= 150 (total number of devices produced)
x + y <= 220 (total number of devices produced)
2.The objective function for maximizing profit is:
Profit = 65x + 45y
4.The vertices of the feasible region are:
(70, 80)
(70, 110)
(100, 50)
(110, 40)
(130, 20)
(130, 30)
(130, 50)
(100, 110)
5.Evaluating the objective function at the vertices of each feasible region:
(70, 80): Profit = 65(70) + 45(80) = $8,150
(70, 110): Profit = 65(70) + 45(110) = $9,500
(100, 50): Profit = 65(100) + 45(50) = $8,750
(110, 40): Profit = 65(110) + 45(40) = $8,950
(130, 20): Profit = 65(130) + 45(20) = $9,350
(130, 30): Profit = 65(130) + 45(30) = $9,800
(130, 50): Profit = 65(130) + 45(50) = $10,700
(100, 110): Profit = 65(100) + 45(110) = $11,450
6.To maximize profit, the company should make 100 laptops and 110 tablets.
7.The maximum profit is $11,450.
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Determine for what value of a is the expression x2+2x-a divisible by x+4
The expression x^2 + 2x - a is divisible by x + 4 when a = 6x.
What is polynomial long division?
A long division polynomial is an algorithm for dividing polynomial by another polynomial of the same or a lower degree.
By using the long division method:
x + 4 | x^2 + 2x - a
-x^2 - 2x + 4x
-------------------
-a + 6x
-x^2 - a + 6x
-------------------
2x - a
-x^2 - 2x + 4x
-------------------
0
The remainder is 0 a = 6x.
Hence, the expression x^2 + 2x - a is divisible by x + 4 when a = 6x.
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Let XY be a random draw from the following box of tickets0 0 1 1 21 2 0 1 0Find E(X+Y)^2
We can start by finding the expected value of X and Y separately: (X) = (0+0+1+1+2+1+0+1+0)/9 = 6/9 = 2/3, E(Y) = (0+0+1+1+2+0+1+0+0)/9 = 5/9
Next, we can expand (X+Y)^2: (X+Y)^2 = X^2 + 2XY + Y^2
Taking the expected value of both sides, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2)
To find E(XY), we can create a table of the possible values of X and Y, and their corresponding probabilities: [table in the attatchment]
So, we have:
E(XY) = 0*(3/9) + 0*(2/9) + 0*(1/9) + 0*(2/9) + 1*(1/9) + 2*(1/9) + 0*(1/9) + 2*(1/9) + 4*(1/9) = 1
Next, we need to find E(X^2) and E(Y^2): E(X^2) = (0^2+0^2+1^2+1^2+2^2+1^2+0^2+1^2+0^2)/9 = 8/9
E(Y^2) = (0^2+0^2+1^2+1^2+2^2+0^2+1^2+0^2+0^2)/9 = 5/9
Putting it all together, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2) = 8/9 + 2*1 + 5/9 = 23/9. Therefore, the answer is 23/9.
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10. Solve the equation 0.5p - 3.45 = -1.2.
Answer:
p = 4.5
Step-by-step explanation:
0.5p - 3.45 = -1.2.
0.5p = -1.2 + 3.45
0.5p = 2.25
0.5p/0.5 = 2.25/0.5
p = 4.5
therefore p is equal to 4.5
find the center, transverse axis, vertices, and foci of the hyperbola. ((x) with superscript (2)/121) - ((y) with superscript (2)/144)
Option C, center at (0, 0) transverse axis is x - axis vertices at (-11, 0) and (11, 0) foci at ([tex]-\sqrt{265}[/tex], 0) and ([tex]\sqrt{265}[/tex], 0) is the correct option.
The transverse axis is a line segment with vertices as its endpoints that traverses the hyperbola's center. The transverse axis's containing line is where the foci are located. The co-vertices serve as the endpoints of the conjugate axis, which is perpendicular to the transverse axis.
The transverse axis is located on the y-axis because of the equation's form, which is y^2a^2-x^2b^2 = 1. The vertices act as the graph's y-intercepts since the hyperbola is centered at the origin. Set x=0 and then solve for y to discover the vertices. Hence, the formula for a hyperbola with foci along the x-axis is x^2a^2-y^2b^2 = 1. The solution can be seen on the attached image below.
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Question correction:
See attached image below.
according to a recent pew research center report, many american adults have made money by selling something online. in a random sample of 4579 american adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met. construct a 98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year. (0.1859, 0.2133) (0.1899, 0.2093) (0.1994, 0.1998) (0.1880, 0.2112) (0.1937, 0.2037)
98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year by using z-score. The correct answer is (0.1859, 0.2133)
The point estimate for the proportion of American adults who earned money by selling something online in the previous year is:
p-hat = 914/4579 = 0.1995
To construct a 98% confidence interval for the population proportion, we can use the formula:
p-hat ± z*(sqrt(p-hat*(1-p-hat)/n))
where z is the z-score associated with the desired confidence level (98% corresponds to a z-score of 2.33), and n is the sample size. Plugging in the values, we get:
0.1995 ± 2.33*(sqrt(0.1995*(1-0.1995)/4579))
Simplifying this expression, we get:
(0.1859, 0.2133)
Therefore, the correct answer is (0.1859, 0.2133). This means we are 98% confident that the true proportion of American adults who earned money by selling something online in the previous year lies between 0.1859 and 0.2133.
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Determine whether these sequences of vertices are paths in this directed graph.
a) a, b, c, e
b) b, e, c, b, e
c) a, a, b, e, d, e
d) b, c, e, d, a, a, b
e) b, c, c, b, e, d, e, d
f ) a, a, b, b, c, c, b, e, d
To determine whether these sequences of vertices are paths in this directed graph:
A) path is a series of edges that starts at a vertex and moves along a graph's edges from vertex to vertex.
B) "A circuit begins at the same vertex and terminates there.".
C) "The number of edges determines length.".
D) "A path or circuit is simple if there are no repeated instances of the same edge."
E) No path
F) No path
In most cases, "a simple path" means that you can only enter or exit a vertex once (in the case of cycles, you do both but only once, i. e. It's still ok because there is only one entrance and exit). The phrase "simple path" can mean: simple curve, a continuous injective function from a real number set interval or, more generally, to a topological or metric space.
In graph theory, a simple path is a path through a graph without repeating vertices.
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Note that the graph is: (check attached image)
Please helppppppp meeee
The range, given the cost of surfboard rentals, would be $ 140.
The interquartile range of the cost of surfboard rentals is $ 56.
There is an outlier which is the cost of 6 days of rentals which is $ 168.
How to find the range and interquartile range ?To find the range, the formula is :
= Largest cost - Lowest cost
To find these costs, find the cost of the days of rentals :
1 day : 2 days 3 days :
= 28 x 1 = 28 x 2 = 28 x 3
= $ 28 = $ 56 = $ 84
6 days :
= 28 x 6
= $ 168
The range is therefore :
= 168 - 28
= $ 140
To find the Interquartile range, first find the First Quartile and the Third Quartile after ordering the costs:
Order of costs :
28, 28, 28, 56, 56, 56, 84, 84, 84, 168
First quartile position :
= 1 / 4 x ( n + 1 )
= 1 / 4 x ( 10 + 1 )
= 3 rd position which is $ 28
Third quartile position :
= 3 / 4 x ( n + 1 )
= 3 / 4 x ( 10 + 1 )
= 8 th position which is $ 84
The Interquartile range is :
= 84 - 28
= $ 56
The outlier is the cost of 6 days which is $ 168. This is a rental as it is much larger than other costs.
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Suppose that 3y - 5 = 45 and y = 3x - 2.
Which of the following equations is equivalent to 3y - 5=45, but written
only in terms of x?
a) 15x-10=40
b) 9x-6=50
c) 9x-6=40
d) 15x-10= 50
An equation that is equivalent to 3y - 5=45, but written only in terms of x include the following: B. 9x - 6 = 50.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
3y - 5 = 45 .......equation 1.
y = 3x - 2 .......equation 2.
By using the substitution method to substitute equation 2 into equation 1, we have the following:
3(3x - 2) - 5 = 45
9x - 6 - 5 = 45
9x - 6 = 45 + 5
9x - 6 = 50.
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Use sigma notation to write the Taylor series about x=x0 for the function. e^−x,x0=−1.
Taylor series =∑k=0∞
Answer:
Step-by-step explanation:
To write the Taylor series for the function f(x) = e^(-x) about x = x0 = -1, we first need to find the k-th derivative of f(x) and evaluate it at x = -1.
f(x) = e^(-x)
f'(x) = -e^(-x)
f''(x) = e^(-x)
f'''(x) = -e^(-x)
f''''(x) = e^(-x)
...
The k-th derivative alternates between e^(-x) and -e^(-x), depending on the parity of k.
To evaluate the k-th derivative at x = -1, we substitute -1 into the k-th derivative expression and simplify:
f^k(-1) = (-1)^k * e^1
Now we can write the Taylor series using the formula:
f(x) = f(x0) + (x - x0) f'(x0) / 1! + (x - x0)^2 f''(x0) / 2! + (x - x0)^3 f'''(x0) / 3! + ...
Plugging in the values we obtained earlier, we have:
f(-x0) = e
f'(-x0) = -e
f''(-x0) = e
f'''(-x0) = -e
f''''(-x0) = e
...
Substituting these values into the formula, we get:
f(x) = e - (x + 1)e + (x + 1)^2 e / 2! - (x + 1)^3 e / 3! + (x + 1)^4 e / 4! - ...
Using sigma notation, we can write this as:
f(x) = ∑_{k=0}^∞ (-1)^k (x + 1)^k e / k!
where ∑_{k=0}^∞ represents the sum from k = 0 to infinity.
Kelly had $450 in a game of Monopoly.
She landed on another person's space and now she only has $100.
Round to the nearest whole number.
Answer: She lost 78% percent of her money.
450-100 is 350. This means that Kelly lost 350 dollars.
350/450 is 0.777777778. Rounded to the next whole number the percent is 78%. This means Kelly lost 78% of her money.
I hope this helped & Good Luck <3 !!
Use the following set definitions to specify each set in roster notation. Except were noted, express elements as Cartesian products as strings. A ={a}
B= {b, c } .
C = {a, b, d} a. Ax (B UC) b. Ax (BnC)
c. ( AxB) U (Ax C) d. (Ax B) n (Ax C) e. P(A x B) P(A) x P(B). Use ordered pair notation for elements of the Cartesian product.
Cartesian product are A.{aa, ab, ac, ad} B. {ab} C. {aa, ab, ad} D.{ab}
Given the set notations A = {a} B = {b, c} C = {a, b, d}
BUC = {a, b, c, d}
B∩C = {b}
a) A × (BUC) = {aa, ab, ac, ad}
b) A × (B ∩ C) = {ab}
c) (A × B) ∪ (A × C)
A × B = {ab, ac} and A × C = {aa, ab, ad}
(A × B) ∪ (A × C) = {aa, ab, ac, ad}
d) For (A × B) ∩ (A × C)
(A × B) ∩ (A × C) = {ab}
The symbol ∩ represents the intersection of sets. For example, the intersection of two sets X and Y can be expressed as X ∩ Y.
The union of two sets P and Q is denoted by P ∪ Q. This is the set of all distinct elements contained in P or Q. The symbol used to represent the union of sets is ∪. The intersection of two sets P and Q is denoted by P ∩ Q. This is the set of all distinct elements in both P and Q. The symbol for the set intersection is ∩. The intersection of two given sets, H. P and Q, is the set containing all elements common to both P and Q.
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