(a)The percentage error is 0.123%.
(b)The percentage error is 0.049%.
Find the equation of the tangent line at the point (0,f(0)),
⇒ f(x) = exp(x/500)
⇒ f'(x) = 1/500 exp(x/500)
⇒ f(0) = exp(0/500)
= 1
So the equation of the tangent line at x = 0 is,
⇒ y = f(0) + f'(0)(x - 0) y
= 1 + 1/500x y
= x/500 + 1
Find the equation of the tangent line at the point (100,f(100)),
⇒ f(x) = exp(x/500)
⇒ f'(x) = 1/500 exp(x/500)
⇒ f(100) = exp(100/500)
= exp(1/5)
So the equation of the tangent line at x = 100 is,
⇒ y = f(100) + f'(100) (x - 100)
⇒ y = e^(1/5) - (1/500)(x - 100)
⇒ y = -x/500 + exp(1/5) + 1
Now we can use these two equations to approximate the function f(x) for 0 < x < 100.
For example, when x = 25
⇒ y = x/500 + 1
⇒ y = 25/500 + 1
⇒ y = 1.05
And the actual value of f(25) is,
⇒ f(25) = exp(25/500)
⇒ f(25) = exp(1/20)
⇒ f(25) ≈ 1.0513
So the percentage error is,
⇒ |1.05 - 1.0513| / 1.0513 x 100% ≈ 0.123%
We can repeat the process for x = 50 and find that the percentage error is 0.049%.
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g(x)=2x+1
h(x)=x3−x2
g(h(2))=
Answer:
9
Step-by-step explanation:
g(h(2))= 2(x3-x2)+1 = 2(2^3-2^2)+1 = 2(8-4)+1
=2*4+1 = 9
Tom had an average of 74 runs in 3 matches. if he scored 42 and 31 runs in two resent matches, what is his new average?
Answer:
To calculate Tom's new average, you need to know the total number of runs he scored in the three matches and the total number of runs he scored in the recent two matches.
You can use the following formula to calculate the new average:
New Average = (Total Runs + Recent Runs) / Total Matches
First you need to find the total runs he scored in the first 3 matches:
74 (average) * 3 (number of matches) = 222 runs
Then you need to find the total runs he scored in the recent two matches:
42 (runs in match 1) + 31 (runs in match 2) = 73 runs
Now you can find the new average by adding the total runs in recent two matches and total runs in the first 3 matches and divide it by the total number of matches:
(222 + 73) / 5 = 295 / 5 = 59
So, Tom's new average is 59 runs.
Answer: 59
Step-by-step explanation:
Please refer to the image below:
There are 2 red, 5 green, 3 blue and 4 white points on a circle. Find the
number of line segments which have endpoints of different colors at the
given points.
Answer:
The number of those line segments which have endpoints of different colors is 47.
he mean salary of 150 employees of an organization was found to be Rs 22500 per month.Later on ,after disbursement of salary it was found that salary of two employees was wrongly entered as Rs 25760 and Rs 19590. The correct salaries were Rs 27760 and Rs 18590.Calculate the correct mean salary paid to employees .
The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532.
150 x 22,500 equals the total salary before correction, or Rs.
After rectification, the total salary equals
(150-2)*22500 + 25760 + 18590, or Rs. 339060.
Correct mean pay is equal to Rs. 339060 / 150, or Rs. 22532.
Initial reports stated that the mean wage for 150 workers was Rs. 22500 per month. Further examination revealed, however, that two employees' salary had been put incorrectly as Rs 25760 and Rs 19590, respectively. The two employees' actual pay were Rs. 27760 and Rs. 18590. The total salary before rectification was therefore 150*22,500, or Rs. 337,000. After two employees' pay were adjusted, the total salary was (150-2)*22500.The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532 (150-2)*22500 + 25760 + 18590 = Rs339060. Consequently, it was determined that Rs339060 / 150 = Rs22532 was the proper mean wage paid to employees. After correcting the two incorrectly reported salaries, the average monthly wage for the organization's employees came to Rs22532.
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Solve the equation 2(h+3.5)=-1,h=
Answer: h= -4
Step-by-step explanation:
To solve the equation 2(h+3.5)=-1, we can use the following steps:
Distribute the 2 on the left side of the equation: 2h + 7 = -1
Subtract 7 from both sides of the equation: 2h = -8
Divide both sides of the equation by 2: h = -4
Therefore, the solution to the equation is h = -4
PEPPER-SALT=YUMMy cryptarithm. Each letter corresponds to a digit and different letters correspond to different digits. 40 points. Please help.
The answer of the given question based on cryptarithm the answer is ,
958870 - 214803 = 744067, so the solution is correct.
What is Alphametics?Alphametics, also known as verbal arithmetic or cryptarithm, is a type of mathematical puzzle where letters or symbols are used to represent digits or numbers, and the puzzle solver must determine the correct digit or number to replace each letter or symbol in order to solve the puzzle.
The objective of an alphametic puzzle is to find a unique solution, where each letter or symbol represents a different digit or number, and the arithmetic equation is correct. In some alphametic puzzles, there may be additional constraints, such as leading zeros not being allowed, or certain digits being constrained to specific values.
One possible solution to this cryptarithm is:
9 5 8 8 7 0
- 2 1 4 8 0 3
_________
7 4 4 0 6 7
In this solution, P=9, E=5, R=8, S=7, A=0, L=4, and Y=6.
To check:
PEPPER = 958870
SALT = 214803
YUMMY = 744067
And 958870 - 214803 = 744067, so the solution is correct.
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Please help!!!! Will give brainliest!!!!!
Find the slope and y-intercept of each line
Write an equation for each line in slope intercept form.
Use desmos to verify your equation.
The slope, y-intercept, and equation of each of the lines are:
a. m = 2, b = -1.
y = 2x - 1
b. m = -1; b = 2.
y = -x + 2
c. m = -2/3; b = 1
y = -2/3x + 1
d. m = 1/2; b = -2.
y = 1/2x - 2
How to Write the Equation of a Line in Slope-intercept Form?The slope-intercept form is y = mx + b, where b equals the y-intercept and m is the slope.
a. Slope (m) = change in y/change in x = (3 -(-1))/(2 - 0) = 4/2 = 2
y-intercept (b) = -1.
The equation is: y = 2x - 1
b. Slope (m) = change in y/change in x = (2 -(-2))/(0 - 4) = 4/-4 = -1
y-intercept (b) = 2.
The equation is: y = -x + 2
c. Slope (m) = change in y/change in x = (3 -(-1))/(-3 - 3) = 4/-6 = -2/3
Substitute m = -2/3 and (x, y) = (3, -1) into y = mx + b to find the y-intercept (b):
-1 = -2/3(3) + b
-1 = -2 + b
-1 + 2 = b
1 = b
b = 1
The equation is: y = -2/3x + 1
d. Slope (m) = change in y/change in x = (0 -(-1))/(4 - 2) = 1/2 = 1/2
y-intercept (b) = -2.
The equation is: y = 1/2x - 2
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show your complete work when comparing the following function pairs. provide the c and k values in the formal definition
By providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship, we have
(i) [tex]3^{n/2}[/tex] = O(2^n)
(ii) [tex]8^{\log n}[/tex] = θ([tex]n^2(\log n)^4[/tex] ≤ 3n^3)
(iii) √n + (log n)^5 = O([tex](2)^{1/2\times\log n}[/tex])
We have to compare the following function pairs by providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship
i) The first function is [tex]3^{n/2}[/tex] vs. 2^n
We can write [tex]3^{n/2}[/tex] as
[tex]3^{n/2}[/tex] = [tex](\sqrt{3})^n[/tex]
[tex]3^{n/2}[/tex] = (1.732)^n
Clearly, we get for c = 1 and n ≥ 0, then
0 ≤ 1.732n ≤ 2n
Hence, [tex]3^{n/2}[/tex] = O(2^n)
ii) The second function is [tex]8^{\log n}[/tex] vs. n^2(log n)^4 + 2n^3
We can write it as
[tex]8^{\log n}[/tex] = [tex]n^{\log 8}[/tex]
[tex]8^{\log n}[/tex] = [tex]n^{\log 2^3}[/tex]
[tex]8^{\log n}[/tex] = n^3
For n ≥ 0, c(1) = 1 and c(2) = 3, we have
0 ≤ n^3 ≤ [tex]n^2(\log n)^4[/tex] ≤ 3n^3
Hence, [tex]8^{\log n}[/tex] = θ([tex]n^2(\log n)^4[/tex] ≤ 3n^3)
iii) The third function is [tex](\sqrt{2})^{\log n}[/tex] vs. √n + (log n)^5
We can write [tex](\sqrt{2})^{\log n}[/tex] as
[tex](\sqrt{2})^{\log n}[/tex] = [tex](2)^{1/2\times\log n}[/tex]
For c = 2 and n ≥ 2, we have
0 ≤ √n + (log n)^5 ≤ [tex](2)^{1/2\times\log n}[/tex]
Hence, √n + (log n)^5 = O([tex](2)^{1/2\times\log n}[/tex])
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The complete question is:
Show your complete work when comparing the following function pairs. provide the c and k values in the formal definition when asserting a big O, Ω or θ relationship(e.g. f(n) is O(g(n)) if there exists C>0 and k≥0 such that f(n)≤Cg(n) for all n≥k).
(i) [tex]3^{n/2}[/tex] vs. 2^n
(ii) [tex]8^{\log n}[/tex] vs. n^2(log n)^4 + 2n^3
(iii) [tex](\sqrt{2})^{\log n}[/tex] vs. √n + (log n)^5
when the expression logb32 – logb7, b > 1, is written in the form logba, the value of a, to the nearest hundredth, is
When the expression [tex]log_b{32} - log_b{7}[/tex], b > 1, is written in the form [tex]log_b{a}[/tex], the value of a is 25
We know that a logarithm of a number is nothing but the power to which a number must be raised to get some other values.
We know that the rules for the addition or subtraction (basic algebraic operations)
When the base od logarithms are same, then only we can add or subtract logarithms.
Consider logartithemic numbers : log₂7 , log₃8 and log₂5
Her we can observe that the base of logartithemic numbers log₂7 , log₃8 is different.
Here, the expression [tex]log_b{32} - log_b{7}[/tex]
The base of logartithemic numbers [tex]log_b{32} , log_b{7}[/tex] is equal.
so, we can perform algebraic operation.
[tex]log_b{32} - log_b{7}\\\\=log_b{32-7}\\\\=log_b{25}[/tex]
Comparing above expression with [tex]log_b{a}[/tex] we have,
a = 25
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Use the formula B=kw/h2 to find the body mass index of a man with the given weight and height.
By dividing a person's height in meters by their weight in kilograms (or pounds), the body mass index (BMI) is determined (or feet).
What is meant by body mass index?Body Mass Index (BMI) is calculated by dividing a person's height in meters squared by their weight in kilograms (or pounds) (or feet). A high BMI may be a sign of high body fat.
A person's body mass index (BMI) is calculated by dividing their weight in kilograms by their height in meters squared. Underweight, healthy weight, overweight, and obesity can all be detected using the BMI, which is a low-cost and simple screening approach.
Your risk of developing diseases that can be brought on by having a higher body fat percentage can be determined by your BMI. Your chance of developing certain conditions, including breathing difficulties, heart disease, high blood pressure, type 2 diabetes, gallstones, and some malignancies, increases with your BMI.
a) The formula for the rate of change of the BMI in relation to weight at a constant height is [tex]$B_w=\frac{1}{h^2}$[/tex].
b) Since [tex]$B_w=\frac{1}{h^2}$[/tex] exists always positive, we see that for fixed h, the BMI exists an increasing function of w.
c) Given a fixed weight and height, the rate of change in the BMI is given by [tex]$B_w=\frac{-2 w}{h^3}$[/tex].
d) Since [tex]$B_w=\frac{-2 w}{h^3}$[/tex] exists always negative, we see that for fixed w, the BMI exists a decreasing function of h
The complete question is:
The body mass index (BMI) for an adult human is given by the function [tex]$B=\frac{w}{h^2}$[/tex], where w is the weight measured in kilograms and h is the height measured in meters. (The BMI for units of pounds and inches is [tex]$B=703 \frac{w}{h^2}$[/tex].)
a) Find the rate of change of the BMI with respect to weight at a constant height.
b) For fixed h, is the BMI an increasing or decreasing function of w?
c) Find the rate of change of the BMI with respect to height at a constant weight.
d) For fixed w, is the BMI an increasing or decreasing function of h?
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a father is 7 times as old as his son, and the son is 24 years younger than his father
Father:28
Son: 4
filler since
i need 20 characters
the midpoint of TU is (1,3). point T is (1,5). find U
Point U would be (1, 1)
A pair of fair dice each numbered 1 to 6 i toed. Find the probability of a core of
a. Two odd number
b. A um of 8 or um of 12
C. Both prime or both odd number
The probability of a core of the two odd number be 1/4.
What is meant by probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The outcome of one die has no bearing on the outcome of the other since the two dice are independent.
In this instance, a complex event's probability is calculated by adding its component simple event probabilities.
Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists [tex]$\frac{3}{6}=\frac{1}{2}$[/tex]
The probability that this happens with both dice exists [tex]$\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$[/tex]
It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are
(1, 1), (1, 3), (1, 5)
(3, 1), (3, 3), (3, 5)
(5, 1), (5, 3), (5, 5)
And in fact, 9 good outcomes over 36 total outcomes means
[tex]$\frac{9}{36}=\frac{1}{4}$$[/tex]
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Find the x-intercepts of the function f(x)=x^2-4x-2. Round to the nearest tenth if necessary.
The x- intercept of y = x²-4x-2 is 4.44949 and −0.44949.
What is Intercept?The line's point of intersection with the coordinate axes is known as an intercept. The y coordinate of the intersection point is zero if the line contacts the X axis, and the intercept is known as the x intercept.
The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Given:
To find the x-intercepts of the function, y = x²-4x-2, we need to make the y-value of the function equal to zero,
So, x²-4x-2 = 0
Now, solving the above Quadratic Equation
x²-4x-2 = 0
D = √(-4)² - 4(1)(-2)
D = √16 + 8
D = √24
D = 2√6
So, x= 4 ± 2√6/ 2
x = 4 + 2√6/2 or x = 4- 2√6/2
x = 2 + √6 or x = 2- √6
x = 4.44949 or x = −0.44949
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the glitz jewelry kit contains round beads in 6 different colors plus 100 star-shaped beads. there are 250 beads in all. which equation can you use to find r, the number of round beads in each color?
The number of round beads in the glitz jewelry kit are 25
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Let x be the number of round beads in the glitz jewelry kit. Then the equation is written as,
6x + 100 = 250
Simplify the equation, then the value of 'x' is given as,
6x + 100 = 250
6x = 250 - 100
6x = 150
x = 150/6
x = 25
The number of round beads there in each color will be 25.
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Can I please get help?
Answer:y = -2x + 5
Step-by-step explanation: Slope intercept form is given by the equation y = mx+b where m is the slope and b is the y intercept
1. The slope or m would be -2 because the slope of the live given is -2. We can tell since we can do rise/run or Δy/Δx. We can take two points on the line and use Δy/Δx
Lets use:
(0,4) and (2,0)
Then plug it in so:
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{4-0}{0-2}[/tex]
m = -2
Now we just need b which is fortunatly given to us since b is when x is equal to 0 and it saids in the question "passes through the point (0,5)" so since its (x,y) and x is 0, b is 5.
Finally, after substitution, we get:
y = -2x + 5
The volume of a right cone is 100π
units3. If its height is 12 units, find its diameter.
Answer: 10 units
Step-by-step explanation:
We can use the following formula to determine the diameter of this cone. V is equal to volume, r is equal to radius (half of the diameter), and h is equal to height.
[tex]\displaystyle \boxed{r=\sqrt{3\frac{V}{\pi h}} }[/tex]
Given:
[tex]\displaystyle r=\sqrt{3\frac{V}{\pi h}}[/tex]
Substitute known values:
[tex]\displaystyle r=\sqrt{3\frac{100\pi}{\pi (12)}}[/tex]
Divide:
➜ [tex]\frac{\pi}{\pi}=1[/tex], so we are left with 100 divided by 12
[tex]\displaystyle r=\sqrt{3(\frac{25}{3} )}}[/tex]
Multiply:
➜ When multiplying, we can think of it as [tex]\frac{3}{1} *\frac{25}{3}[/tex]. [tex]\frac{3}{3} =1[/tex], so we are left with 25.
[tex]\displaystyle r=\sqrt{25}[/tex]
Square root:
r = 5, r = -5
Since it's a measure of a shape, it cannot be negative. This means the radius is equal to 5. Now, we will find the diameter.
5 units * 2 = 10 units
Gabriela and William try to do as many pool lengths as possible in 14 minutes. Together they did 56 lengths. Gabriela went 2 lengths less than william How many lengths did William do?
Answer:
29
Step-by-step explanation:
w = # william laps
then w-2 = gabby's laps together they sum to 56
w + w-2 = 56 add 2 to both sides of the equation
2w =58
w = 29 <=====william's laps
Answer: 29
Step-by-step explanation:
Gabriela went w -2 ( 2 lengths less than william)
William went w
Total is 56
So w - 2 + w = 56
Combine like terms: 2w - 2 = 56
Add the two ro both sides: 2 + 2 - 2w = 56 + 2
2w / 2 = 58 / 2
w = 29
May or may not be correct
A sports committee consisting of four rowers, three basketballers and two cricketers sits at a circular table. a. How many different arrangements of the committee are possible if the rowers and basketballers both sit together in groups, but no rower sits next to a basketballer? b. One rower and one cricketer are related. If the conditions in a apply, what is the probability that these two members of the committee will sit next to one another?
(a) Total 288 different arrangements of the committee are possible if the rowers and basketballers both sit together in groups, but no rower sits next to a basketballer.
(b) If the conditions in a apply, 1/24 is the probability that these two members of the committee will sit next to one another.
(a) Considering the four rowers as a single person, the three basketball players as a single person, and the cricketers as two unique people (So, a total of 4 persons).
Number of configurations for a round table of n people = (n-1)!
Number of configurations for a round table of n people = (4-1)!
Number of configurations for a round table of n people = 6 ways
Let's leave out the number of arrangements that the basketball players and rowers will have.
Assuming that a basketball player and a rower are one person, they will sit together = (3-1)! × 2!
Assuming that a basketball player and a rower are one person, they will sit together = 4
There are therefore numerous arrangements for the groups where basketball players and rowers sit together = 2
No. of ways to arrange basketball players in a group = 3!
No. of ways to arrange basketball players in a group = 6
There are numerous number of methods to arrange rowers within a group = 4!
There are numerous number of methods to arrange rowers within a group = 24
Hence, total number of ways = 2×6×24
Total number of ways = 288
No. of ways are 288
b) The definition of an event's probability is as follows:
Probability = No. of Successful Outcomes / Total no. of Outcomes
Number of ways a cricketer can take a seat = 2! = 2 ways
Number of arrangements for the remaining rowers when he is seated next to the cricket player = 3!
Number of arrangements for the remaining rowers when he is seated next to the cricket player = 6 ways
Total number of possible ways = 6×2
Total number of possible ways = 12 ways
Probability = 12/288
Probability = 1/24
Hence, the required probability is 1/24.
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The quadratic function f(x) has a vertex at (1, 6) and opens downward.
If g(x) = (x - 7)2 + 1, which statement is true?
A.
The axis of symmetry of f(x) is x = 1, and the axis of symmetry of g(x) is x = 7.
B.
The axis of symmetry of f(x) is x = 1, and the axis of symmetry of g(x) is x = -7.
C.
The axis of symmetry of f(x) is x = -1, and the axis of symmetry of g(x) is x = -7.
D.
The axis of symmetry of f(x) is x = -1, and the axis of symmetry of g(x) is x = 7.
The statement A is correct option.
What is the vertex of a quadratic function?The vertex of a quadratic equation is the minimum or maximum point of the equation.
Given that, the quadratic function f(x) has a vertex at (1, 6) and opens downward and g(x) = (x - 7)² + 1,
The vertex of f(x) is at (1, 6), we know that a vertical line passing through the vertex is called the axis of symmetry for the parabola.
That mean, axis of symmetry will pass through (1, 6)
Therefore, the axis of symmetry for f(x) is x = 1
And, g(x) = (x - 7)² + 1
= x²+49-14x+1
= x²-14x+50
Vertex = -b / 2a
here, b = -14 and a = 1
Vertex (h, k) = 14 / 2 = 7
To find k, put x = 7 in the equation,
(7-7)²+1 = 1
Therefore, point of the vertex = (7, 1)
That mean axis of the symmetry will pass through (7, 1)
Therefore, axis of the symmetry for g(x) = 7
Hence, the statement A is correct option.
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Let f(x)=-3x-1 and g(x)=x^2+5 find(f•g)(-2)
Answer:
To find (f•g)(-2), we need to first calculate f(-2) and g(-2).
f(-2)=-3(-2)-1=-7
g(-2)=(-2)^2+5=9
Then, we can calculate (f•g)(-2) as follows:
(f•g)(-2)=f(-2)g(-2)=-7*9=-63
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Question in photo. The x and y entered are not correct but the equations are, I just don't know what to do after finding them
Answer:
x = 3. y = 11
Step-by-step explanation:
The two equations are two simultaneous equations, which can be solved by substitution, elimination or graphical method.
Elimination method:
The coefficients of 'x’ or ‘y’ need to be the same with opposite signs. The coefficients of ‘y’ will be focused:
(17x - y = 40) Multiplied by 4
(2x + 4y = 50) Multiplied by 1
68x - 4y = 160
2x + 4y = 50
In the net total, the ‘y’ terms will cancel each other out:
70x = 210
x = [tex]\frac{210}{70}[/tex]
x = 3
The calculated value of x is substituted in any of the equations to determine the value of y:
17(3) - y = 40
51 - y = 40
51 - y - 40 = 0
51 - 40 - y = 0
11 - y = 0
y = 11
can anyone help its for Algebra
If 3,x,12 are in continued proportion, find the value of 'x'
The value of x in the continued proportion is 6
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
3,x,12 are in continued proportion
This means that
x/3 = 12/x
So, we have
x^2 = 36
Take the square roots
x = 6
Hence, the solution is 6
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I need helpppppppppp
Answer: I believe it means that there is no solution
Step-by-step explanation: I believe this because we are given: 5 = 0. In linear graphs when lines are equal to 0 there is no equation or solution
Brayan is painting his living room wall, as
shown in the diagram below. How many
square feet of the wall does he need to
paint?
Answer:
54 square feet
Step-by-step explanation:
First get the area of both rectangles.
The bigger one is 8 by 9
8 times 9 is 72
the smaller one is 3 times 6 which is 18
Now you subtract both of them
72-18 = 54
discuss the significance of the intercept and the coefficient of performance rating using a significance levels of .01, .05, .10 and concepts of strict, regular and weak significance where it applies.
The significance of the intercept and the coefficient of performance rating is defined below.
The significance level is used to determine the strength of evidence for the relationship between the variables.
A significance level of .01 means that there is only a 1% chance that the relationship between the variables is due to chance. A significance level of .05 means that there is a 5% chance that the relationship is due to chance, and a significance level of .10 means that there is a 10% chance that the relationship is due to chance.
If the significance level is .01, the relationship between the variables is considered to be strictly significant, meaning that there is a very low probability that the relationship is due to chance.
If the significance level is .05, the relationship is considered to be regularly significant, meaning that there is a moderate probability that the relationship is due to chance.
If the significance level is .10, the relationship is considered to be weakly significant, meaning that there is a relatively high probability that the relationship is due to chance.
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Could you help me for a second?
There is no relation between the number of people living and the number of pets. The correct option is D.
What is a scatter plot?Scatter plots are used to visually observe and plot relationships between two numerical variables. The values of each individual data point are represented by the dots in a scatter plot.
The scatter plot is showing the data between the number of people living and the number of pets.
In the scatter plot, there is not any perfect relation between the number of people living in a room and the number of pets.
The correct option is D.
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true/false/explain. 1. if x and z are two independent random variables, then var(x - z) = var(x) - var(z) 2. if x ~ n(0,0°), then z =
The variance of the difference of two independent random variables is equal to the sum of the variances, not the difference.
False. So, var(x - z) = var(x) + var(z).
False. If x ~ n(0,0°), then z = 2x ~ n(0,2°), not n(0,4°). This is because the variance of the difference of two variables is the sum of the variance of the individual variables plus twice the covariance between the two variables. Since x and z are independent, the covariance between them is 0, and so the variance of x - z is equal to the sum of the variances of x and z.
If x ~ n(0,0°), then z = 2x ~ n(0,2°). This is because the mean of a random variable multiplied by a constant is equal to the original mean multiplied by the same constant, and the variance of a random variable multiplied by a constant is equal to the square of the constant multiplied by the original variance. So, if x has mean 0 and variance 0°, then z has mean 0 and variance 2°.
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92.- una persona depositó $6 000 en un banco que paga a sus depositantes el 3 nual, capitalizable mensualmente. ¿cuántos años tardará dicho depósito en llegar a $7 500?
It will take 8.8 years for the initial deposit to reach $7,500.
The formula to calculate the number of years it takes for an initial deposit to reach a certain amount with compounding interest is A = P(1+r/n)^nt, where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this example, P = $6,000, r = 3, n = 12 (monthly compounding of interest) and A = $7,500. We can solve for t, the number of years, by rearranging the equation to t = log(A/P)/log(1+r/n). When we plug in the numbers, we find that it will take 8.8 years for the initial deposit to reach $7,500.
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