Overall, finding the mean and variance of a random variable Y that is associated with another random variable X requires some knowledge of probability theory and calculus. However, by following the steps outlined above, we can arrive at an answer that is both accurate and concise.
When it comes to the question of finding the mean and variance of a random variable, Y, that is associated with another random variable X, it's important to take a few steps to calculate those values. Here's how to do it:
- Start with the formula for the expected value of Y: [tex]E(Y) = E(g(X))[/tex]. In this case, we want to find the expected value of Y, so we need to find the function g(X) that relates X to Y. The problem tells us that X represents the length of a punched part, and Y represents the number of parts that can be cut from a 12-foot rod. So we can say that Y = h(X), where h(X) = 12/X. This means that the expected value of Y is E(Y) = E(12/X).
- To find E(Y), we need to find E(12/X).
We can use the formula for the expected value of a function of a continuous random variable:[tex]E(g(X)) = ∫g(x)f(x)dx,[/tex]where f(x) is the probability density function of X. The problem doesn't give us a specific probability density function for X, but it does tell us that X is a random variable. So we can assume that X follows some distribution, such as a normal distribution or a uniform distribution. Depending on the distribution of X, we can use the appropriate formula to find E(12/X).
- Once we have found E(Y), we can use the formula for the variance of a random variable: Var(Y) = E(Y^2) - [E(Y)]^2. To find E(Y^2), we need to find E(h^2(X)). Since h(X) = 12/X, we can say that [tex]h^2(X) = 144/X^2. So E(h^2(X)) = E(144/X^2).[/tex]We can use the same method as before to find [tex]E(144/X^2)[/tex], and h^2(X) = 144/X^2. So E(h^2(X)) = E(144/X^2).then plug that into the formula for Var(Y).
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carbon-14 dating wood deposits recovered from an archaeological site contain 19% of the c-14 they originally contained. how long ago did the tree from which the wood was obtained die? (assume the half life of carbon-14 is 5,730 years. round your answer to the nearest whole number.)
The tree from which the wood was obtained died 13,729 years ago, considering the exponetial function that models the situation.
How to model an exponential function?The standard definition of an exponential function is given by the equation presented as follows:
[tex]A(t) = A(0)b^{\frac{t}{n}}[/tex]
The parameters of the exponential function with format above are given as follows:
A(0) is the initial value.b is the rate of change of the function.n is the time needed for the rate of change.The half-life of carbon-14 is 5,730 years, hence the parameters b and n have the values given as follows:
b = 0.5, n = 5730.
Then the exponential function for the amount of the substance after t years is given as follows:
[tex]A(t) = A(0)(0.5)^{\frac{t}{5730}}[/tex]
19% of the substance remained, hence the time is obtained as follows:
[tex]0.19A(0) = A(0)(0.5)^{\frac{t}{5730}}[/tex]
[tex](0.5)^{\frac{t}{5730}} = 0.19[/tex]
t = 5730 x log(0.19)/log(0.5)
t = 13,729 years.
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symmetrical balance which has similar shapes repeated on either side of a vertical axis is also called:
Symmetrical balance, also known as bilateral symmetry, is a type of balance in which two halves are mirror images of each other. This type of balance can be found in both visual art and in nature.
In visual art, symmetrical balance is achieved when similar shapes, colors, lines, and textures are repeated on either side of a vertical axis. This creates an even distribution of visual elements and creates a sense of harmony and equilibrium. In nature, symmetrical balance is created when there is a symmetrical arrangement of organs and features in plants and animals.
Symmetrical balance is often used to create a sense of order and balance in visual works of art, as well as to emphasize the balance of nature in landscapes. It can also be used to convey a sense of unity and tranquility, as the repetition of similar elements creates an overall feeling of calmness and symmetry. Symmetrical balance is an important element in many types of artwork, and it is used in all kinds of visual art, including paintings, photographs, sculptures, and more.
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A plant in my garden is growing 2/3 of a foot every 3/4 of a month. How much does it grow per month?
The plant is growing 0.89 feet per month.
To calculate how much a plant grows per month, you need to first convert the measurements into one unit of measurement.
Since the plant is growing 2/3 of a foot every 3/4 of a month,
we can first convert the fractions of a foot and a month into decimal equivalents.
2/3 of a foot is 0.67 feet, and 3/4 of a month is 0.75 months.
We can then calculate the amount of growth per month by dividing the amount of growth per 3/4 of a month by the amount of time that is 3/4 of a month (0.75).
The equation is 0.67 feet / 0.75 months = 0.89 feet per month.
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GIVING BRAINLIEST AND MANY POINTS FOR CORRECT ANSWER!!
Let's say you decide to go for a walk. You start out at home and walk 500 meters total, making a few turns here and there. You stop for a moment and realize you have ended up only 100 meters east of where you started.
What distance did you travel?
What was your displacement?
Answer:
500 meters.
Step-by-step explanation:
To save up for a car, you work at a trampoline park after school and at a landscaping company on the weekends. You must work at least 4 hours per week at
the trampoline park, and the total number of hours you work at both jobs, in a week, cannot be greater than 15.
Write a system of linear inequalities to model the number of hours that you could work at each location in a week.
Let x = #hours at trampoline park, let y = #hours landscaping
The system of linear inequalities to model the number of hours that you could work at each location in a week is:
x ≥ 4
x + y ≤ 15
What is system of linear inequality?
A system of linear inequalities is a set of two or more linear inequalities with the same variables. It describes a region in the coordinate plane that satisfies all of the inequalities in the system.
In this case, we are trying to model the number of hours that someone could work at two different jobs.
The first inequality given is that the person must work at least 4 hours per week at the trampoline park. Let x be the number of hours worked at the trampoline park. This can be represented as:
x ≥ 4
The second inequality given is that the total number of hours worked at both jobs cannot be greater than 15. Let y be the number of hours worked at the landscaping company. Then, the total number of hours worked can be represented as:
x + y ≤ 15
Together, these two inequalities form a system of linear inequalities that model the possible number of hours that the person can work at each job in a given week.
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Who can help me? This is solving cube root equation help ?
Answer:
22: 2
23: -7
25: 6
26: 3
Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!
Step-by-step explanation:
For 22: 2 * 2 * 2 = 8, therefore, 2
For 23: -7 * -7 * -7 = -343. This results in a negative number because there is is an odd number of negative numbers (follows the odd-even negative rule).
For 25: Multiply both sides of the equation by -1/2 to get z^3 = 216. The cube root of 216 is 6
For 26: Add 11 to both sides to get 2h^3 = 54. Divide both sides by 2 to get h^3 = 27. Cube root of 27 is 3.
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Harold walks once round a circle with diameter 100 metres.
There are 6 points equally spaced
on the circumference of the circle.
a) Find the distance Harold walks between
b) What is the mean distance covered by Harold
when walking from one point to the next?
m (1)
Harold therefore walks an average distance of 10 metres when moving from one location to another.
what is circle ?All the points in a plane that are equally spaced from a fixed point known as the centre make up a circle, which is a geometric form. The radius of a circle is the separation between any two points on the circle and its centre. A circle's diameter is defined as a line segment whose endpoints are on the circle and which goes through the centre of the circle. Circles are helpful in many areas of mathematics and science due to a number of significant characteristics.
given
A circle with a dimension of 100 metres has a circumference of d, where d is the diameter. As a result, this circle's diameter is:
C = d = (100) = 100 m
Harold will walk from one spot to the next after completing 1/6
of the circle's circumference because the circle's circumference has six points that are all equally spaced apart. As a result, Harold travels the following distance between each location:
Distance equals 1/6 * C * 1/6 * 100 * (50/3) metres.
b) The average of the distances between each location, which we just discovered to be (50/3) metres, represents the average distance that Harold covers when moving from one place to another. The circle has six evenly distributed points, so the average distance travelled by Harold is:
(Total distance travelled) / Mean distance (Number of segments)
Total distance travelled equals the distance between two adjacent locations on the circle, which is C/2, or (1/2) 100 metres, or 50 metres.
Segment count equals number of marks - 1 (i.e., 6 - 1 = 5).
The average distance Harold travels while strolling is as follows:
Typical distance is calculated as (Total distance travelled) / (Number of segments), which equals (50) / 5 = 10 metres.
Harold therefore walks an average distance of 10 metres when moving from one location to another.
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Pls i need help on this question
The length of the missing side is 3√17 ft. Option B is the correct option.
What is the hypotenuse?
The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
The △ABC is a right-angled triangle.
Thus the sum of squares of the legs of the triangle is equal to the square of the hypotenuse.
The hypotenue is 13 ft.
Assume that the missing leg is equal to x.
The legs of the triangle are x and 4ft.
Apply Pythagorean theorem:
13² = 4² + x²
x² = 169 -16
x² = 157
x = √(3×3×17)
x = 3 √17
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anderson went to the restaurant traveling 15 mph and returned home traveling 12 mph. if the total trip took 9 hours, how long did anderson travel at each speed?
Anderson traveled 15 mph to go to the restaurant and 12 mph to get home. Anderson went at 15 mph for 3 hours and at 12 mph for 6 hours. if the entire trip took 9 hours.
The given speed Anderson, the total time taken, and asked to find the time traveled at each speed:
Speed, [tex]S_1[/tex] = 15 mph
Speed, [tex]S_2[/tex] = 12 mph
Total time, [tex]t[/tex] = 9 hours
Time traveled with speed 1,
[tex]t_1[/tex] Time traveled with speed 2, [tex]t_2[/tex]
To solve the given problem, let's use the following formula:
Total [tex]t[/tex] (time) = [tex]t_1[/tex] ( time 1) + [tex]t_2[/tex] (time 2)
Now, time 1 can be represented as
[tex]t_1[/tex] (time 1) = [tex]d[/tex] (distance) / [tex]S_1[/tex] (speed 1)
Similarly, time 2 can be represented as:
[tex]t_2[/tex] (time 2) = [tex]d[/tex] (distance) / [tex]S_2[/tex] (speed 2)
Here, we need to find the time traveled at each speed. Let's use these equations to solve the given problem.
Time traveled with speed 1, [tex]t_1[/tex] = [tex]d[/tex] / [tex]S_1[/tex]
Time traveled with speed 2, [tex]t_2[/tex] = [tex]d[/tex] / [tex]S_2[/tex]
As we know the total time, we can find the value of d in terms of [tex]t[/tex].
So, [tex]d[/tex] = [tex]S_1[/tex] * [tex]t_1[/tex] = [tex]S_2[/tex] * [tex]t_2[/tex]
From the above equation, we can write: [tex]t_1[/tex] / [tex]t_2[/tex] = [tex]S_2[/tex] / [tex]S_1[/tex] [tex]t_2[/tex]
= [tex]t[/tex] - [tex]t_1[/tex]
Substitute the value of [tex]t_2[/tex] in equation(1):
[tex]t_1[/tex] / ([tex]t[/tex] - [tex]t_1[/tex] ) = [tex]S_2[/tex] / [tex]S_1[/tex][tex]t_1[/tex] [tex]S_1[/tex]
= ([tex]t[/tex] - [tex]t_1[/tex] ) [tex]S_2[/tex] .[tex]t_1[/tex] . [tex]S_1[/tex] + [tex]t_1[/tex] [tex]S_2[/tex]
= [tex]tS_1[/tex][tex]t_1[/tex]
= [tex]tS_1[/tex] / ( [tex]S_1[/tex] + [tex]S_2[/tex] ) [tex]t_2[/tex]
= [tex]t[/tex] - [tex]t_1[/tex]
= [tex]tS_2[/tex] / ( [tex]S_1[/tex] + [tex]S_2[/tex] )
Therefore, Anderson traveled at 15 mph for 3 hours Anderson traveled at 12 mph for 6 hours.
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Which number line best represents the solution to the problem below -x-8<16
The solution set of the inequality -x - 8 < 16 is graphed in the number line at the end of the answer.
Which number line represents the solution of the inequality?Here we want to see which number line represents the solution set of the inequality:
-x - 8 < 16
First, let's solve the inequality by isolating x, then we will get:
-x - 8 < 16
-8 - 16 < x
-24 < x
That is the inequality solved, the graph of this will be an open circle at x = -24 and then a line that goes to the right, like in the image posted at the end of this answer.
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Find Sum to infinity of the given series: a. 1 + 2x + 3x² + 4x³+... to ∞ (|x| <1)
The sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1.
How do we calculate?The formula for the sum of an infinite geometric series when |x| < 1 is given as:
S = a/(1-r)
We have a = 1 and r = x/1.
S = 1/(1-x) + 2x/(1-x)² + 3x²/(1-x)³ + 4x³/(1-x)⁴ + ...
we multiply both sides of this equation by (1-x)²,
S(1-x)² = (1-x) + 2x + 3x²(1-x) + 4x³(1-x)² + ...
S(1-x)² = 1 + x + x² + x³ + ... eqn (1)
Using the formula for the sum of an infinite geometric series when |x| < 1, we have:
1/(1-x) = 1 + x + x² + x³ + ...
Substituting this into equation (1), we get:
S(1-x)² = 1/(1-x)
S = 1/[(1-x)²]
In conclusion, the sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1
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What is the value of the missing side
length?
5.6
x
3.4
Answer:
the missing value of the side length is 19.04
Would a line through these two points A and B be a good fit for the data? Why or why not?
(Please don’t mind the other words! TvT
what is the center of dilation
The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:
Step-by-step explanation:
after a (not very successful) trick or treating round, candice has 12 tootsie rolls and 10 twizzlers in her pillow case. her mother asks her to share the loot with her three younger brothers. (a) how many different ways can she do this?
Using the stars and bars technique, Candice can distribute her 24 pieces of candy among her four siblings in 2,925 different ways. If she must give each sibling at least one of each type of candy, there are 67,200 ways to distribute the candy among the four siblings.
(A) To solve this problem, we can use the technique of stars and bars. We have a total of 24 pieces of candy to share among four children. We can represent this using 24 stars, with 3 bars to separate the stars into four groups, one for each child. For example, the following arrangement represents giving 6 pieces of candy to the first child, 10 pieces to the second child, 3 pieces to the third child, and 5 pieces to the fourth child:
*****|**********|***|****
The number of ways to arrange the stars and bars is equal to the number of ways to choose 3 positions out of the 27 possible positions for the stars and bars. Therefore, the number of different ways that Candice can share her candy with her three younger brothers is:
C(27, 3) = 27! / (3! * 24!) = 2925
(B) Now, we need to ensure that each child receives at least one Tootsie roll and one Twizzler. We can give each child one of each candy to start, and then distribute the remaining 13 Tootsie rolls and 7 Twizzlers using the stars and bars technique. We have 13 Tootsie rolls and 7 Twizzlers to distribute among four children, which can be represented using 13 stars and 3 bars for the Tootsie rolls, and 7 stars and 3 bars for the Twizzlers. The number of ways to arrange the stars and bars for each type of candy is:
C(16, 3) = 560 for the Tootsie rolls
C(10, 3) = 120 for the Twizzlers
To find the total number of ways to distribute the candy, we can multiply the number of ways for each type of candy:
560 * 120 = 67200
Therefore, there are 67,200 different ways for Candice to share her candy with her three younger brothers after her mother asks her to give at least one of each type of candies to each of her brothers.
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Complete question:
After a (not very successful) trick or treating round, Candice has 15 Tootsie rolls and 9 Twizzlers in her pillow case. Her mother asks her to share some of the loot with her three younger brothers.
(A) How many different ways can she do this?
(B) How many different ways can she do this after her Mother asks her to give at least one of each type of candies to each of her brothers?
Roberto plays on the school baseball team. In the last 10 games, Roberto was at bat 44 times. While at bat, Roberto got 11 hits and struck out 33 times. What is the experimental probability that Roberto will get a hit during his next time at bat?
The experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.
The experimental probability of an event is calculated by dividing the number of times the event occurred by the total number of trials.
In this case, the event is "getting a hit" and the number of times it occurred is 11. The total number of trials is 44, which represents the number of times Roberto was at bat.
Experimental probability of getting a hit = Number of times Roberto got a hit / Total number of times at bat
Experimental probability of getting a hit = 11 / 44
Experimental probability of getting a hit = 0.25 or 25%
Therefore, the experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.
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Patrick owns a business that makes chandeliers. He wants to make
greater than 470 chandeliers. The company made 163 chandeliers so
far. If 10 chandeliers can be made in an hour, how long will it take to
reach Patrick's goal?
Write a two-step inequality, using the values provided in the problem,
that represents this situation. Use x as the variable.
Patrick's goal will reached by 30.7 hours
The inequality is 163 + (10x) > 470
How to write the inequalityLet's use x to represent the number of hours it will take to reach Patrick's goal.
First step: The total number of chandeliers made must be greater than 470.
163 + (10x) > 470
Second step: Solve for x by isolating it on one side of the inequality.
10x > 307
x > 30.7
Therefore, it will take more than 30.7 hours to reach Patrick's goal of making greater than 470 chandeliers.
The inequality can be written as: 163 + (10x) > 470
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What is the volume of this rectangular prism?
1
마
13
3
cm
cm
cm
how many different 5-digit sequences can be formed using the digits 0, 1,...,6 if repetition of digits is allowed?
In the following question, among the conditions given, With digit combinations, there are 16,807 different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed.
To solve this problem, we can use the fundamental counting principle or multiplication rule. It states that if there are m ways to do one thing, and n ways to do another thing, then there are m*n ways to do both things. Therefore, to find the number of different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed, we can multiply the number of choices at each position. Since repetition is allowed, each of the five positions has 7 possible digits (0, 1, 2, 3, 4, 5, or 6). Thus, the total number of possible 5-digit sequences is:7 × 7 × 7 × 7 × 7 = 7^5 = 16,807Therefore, there are 16,807 different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed.
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There are 16,807 different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed.
To find out the number of different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed, we can use the fundamental principle of counting or multiplication principle.The fundamental principle of counting states that if there are n different ways of performing the first task, and for each of these n ways of performing the first task there are m different ways of performing the second task, then the total number of different ways of performing both tasks is n x m.
To apply this principle to this problem, we can consider each digit in the 5-digit sequence as a task. The first task is to choose a digit from 0, 1,...,6, which can be done in 7 ways since there are 7 digits to choose from. Similarly, for each of the first 5 digits, there are 7 ways to choose a digit from 0, 1,...,6, so the total number of different 5-digit sequences that can be formed with repetition of digits allowed is 7 x 7 x 7 x 7 x 7 = 7^5 = 16,807.
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there are 75 people at the city swim park today. everyone in the park was wearing swim suits or sunglasses, some people had both. how many people had swim suits on but not sunglasses, if you know 63 people have swim suits on and 43 have sunglasses?
If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.
To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.
We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:
total = swim suits + sunglasses - both
Substituting in the given values, we get:
75 = 63 + 43 - x
Simplifying, we get:
x = 31
Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:
63 - 31 = 32
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That answer is wrong
Answer: why is it wrong
Step-by-step explanation:i said so
Write an equation in point-slope form of the line that passes through the given
point and with the given slope m.
8. (3, -4); m = 6
9. (4, 2); m= -=
10. (-2, -7); m=1
11. (4, 0); m =
-1
Answer:
y - (-4) = 6(x - 3)
y - 2 = -3(x - 4)
y - (-7) = 1(x - (-2))
y - 0 = -1(x - 4)
its special angles, please show work
Answer:
H=25
I=36
Step-by-step explanation:
There are 3.2 liters of iced tea in a pitcher. How many milliliters of iced tea are in the pitcher?
Answer:3200
Step-by-step explanation:
there are 1000 ml per liter
What inequality describes the number of weeks for which halimah will put money in the bank
The inequality "w < 30" describes the weeks for which Halimah will put money in the bank instead of buying an oud. It means she must save for less than 30 weeks to have less than $300 saved.
Let's assume the number of weeks Halimah saves money is represented by the variable "w".
Halimah saves $10 per week, so the total amount of money she saves after "w" weeks is:
Total amount saved = $10 x w
According to the problem, Halimah will put the money in the bank instead of buying an oud if she saves less than $300. Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is:
$10 x w < $300
Simplifying the inequality:
w < 30
Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is "w < 30".
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Complete question:
Halimah saves $10 per week for w weeks to buy an oud. If she saves less than $300, she will put the money in the bank instead of buying an oud.
What inequality describes the number of weeks for which Halimah will put money in the bank?
Factor:
[tex]8 {x}^{2} + 2x - 3[/tex]
Please show the steps on how you got it!
Answer:
(2x - 1) (4x + 3)
Step-by-step explanation:
8x² + 2x - 3
= 8x² - 4x + 6x - 3
= 4x (2x - 1) + 3 (2x - 1)
= (2x - 1) (4x + 3)
So, the factor is (2x - 1) (4x + 3)
I need help with this please
Work Shown:
1 km = 1000 m
5*(1 km) = 5*(1000 m)
5 km = 5000 m
Step-by-step explanation:
let x= m
1 km=1000m
5km= x.m
1km.x/1km=5000.km/1km
x=5000m
therefore 5km=5000m
Ricardo throws a stone off a bridge into a river below.
The stone's height (in meters above the water), x seconds after Ricardo threw it, is modeled by
w ( x ) = − 5 ( x − 8 ) ( x + 4 )
How many seconds after being thrown will the stone reach its maximum height?
Therefore , the solution of the given problem of equation comes out to be the stone will reach its maximum height 2 seconds after being thrown.
What is an equation?Variable words are widely used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic figures. Think about the information that y + 7 provides. When paired with construct y + 7, elevating results in b + 7 in this circumstance rather than another method that may divide 12 equal two halves.
Here,
The height of the stone above the water is given by the function:
=> w(x) = -5(x-8)(x+4)
To find the time when the stone reaches its maximum height, we need to find the vertex of the parabola that represents this function. We can do this by using the formula:
=> x = -b / 2a
where a = -5 and b = -5(8+(-4)) = -20.
Substituting these values into the formula, we get:
=> x = -(-20) / 2(-5) = 2
Therefore, the stone will reach its maximum height 2 seconds after being thrown.
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Given the function g(x) = 5x - 12, find the value of g(-2)
Answer:-22
Step-by-step explanation:
g(x)=g(-2) means that, x=-2:
so, we have to write -2 instead of every x,
5*(-2)-12=-10-12=-22
The cross product of two vectors in R3 is defined by (a1, a2, a3) × (b1, b2, bз) = (a2b3 — aзb2, aзb1 — a1bз, a12 — ab1). Letv = (-1,3, 0). Find the matrix A of the linear transformation from R3 to R3 given by T(x) = V x X.
The given cross product formula is slightly incorrect. The correct cross product of two vectors in R3 is defined by (a1, a2, a3) × (b1, b2, b3) = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1). We are given vector v = (-1, 3, 0) and asked to find the matrix A of the linear transformation [tex]T(x) = v × x.[/tex]
Let x = (x1, x2, x3) be a vector in R3. Then, using the cross product formula, we have:
T(x) =[tex]v × x = (-1, 3, 0) × (x1, x2, x3) = (3x3 - 0x2, 0x1 - (-1)x3, (-1)x2 - 3x1)[/tex]
T(x) =[tex](3x3, x3, -x2 - 3x1)[/tex]
Now, we can express the linear transformation as a matrix A multiplied by the vector x:
[tex]A * (x1, x2, x3) = (3x3, x3, -x2 - 3x1)[/tex]
The matrix A can be found by comparing the components of the vectors:
A = | 0 -3 0 |
| 0 0 1 |
|-3 -1 3 |
So, the matrix A of the linear transformation from R3 to R3 given by T(x) = v × x is:
A = | 0 -3 0 |
| 0 0 1 |
|-3 -1 3 |
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