Answer:
We can use the formula |a × b| = |a| |b| sin θ to solve for the magnitude of the cross product |a × b|, where θ is the angle between vectors a and b. In this case, we have |a × b| = 1 and θ = π/4, so we can write:
1 = |a| |b| sin(π/4)
Simplifying, we have:
|a| |b| = √2
Now, we need to find the dot product a · b. We know that:
a · b = |a| |b| cos θ
where θ is the angle between vectors a and b. Since we're given the angle between a and b, we can substitute θ = π/4 and use the value we found for |a| |b|:
a · b = (√2) cos(π/4) = (√2)/2
Therefore, a · b is equal to (√2)/2.
Step-by-step explanation:
Synthetic Division to Find Zeros
if f(x)=x^3−3x^2+16x+20 and x+1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answer:
Step-by-step explanation:
Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.
We set up synthetic division as follows:
-1 | 1 -3 16 20
| -1 4 -20
|_____________
1 -4 20 0
The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:
x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))
= (4 ± sqrt(-64)) / 2
= 2 ± 2i√2
Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.
Please help! Need answers as soon as possible!
1. Time taken to fill one community pool is 2hours 24 minutes.
2. Time taken to audit 30 files is 4 hours 41 minutes.
3. The time taken to erect is 54/7 hours or 7 hours 43 minutes
Define the time and work?Time and work is a branch of mathematics that deals with the calculation of the amount of time required to complete a job or task by a worker or a group of workers working at a certain rate.
1. Job: Fill one community pool Rate Time Work Completed
Reserve water tower 1/6 x x/6
City water pipes 1/4 x x/4
Solution: Fill one community pool; [tex]\frac{x}{6} + \frac{x}{4} = 1[/tex]
Simplify, x = 12/5 hours or 2hours 24 minutes
Time taken to fill one community pool is 2hours 24 minutes.
2. Job: Work together Rate Time Work Completed
Mr. Dupree 12/5 x 12x/5
Ms. Carmichael 16/4 x 16x/4
Solution: If they work together, time taken to audit one file is
[tex]\frac{12x}{5} + \frac{16x}{4} = 1[/tex]
Simplify, x = 5/32 hours
So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes
Time taken to audit 30 files is 4 hours 41 minutes.
3. Job: Work together Rate Time Work Completed
Macon Construction 100/8 x 100x/8
Thomson Masonry 200/12 x 200x/12
Solution: If they work together, time taken to complete a work
[tex]\frac{100x}{8} + \frac{200x}{12} = 1[/tex]
Simplify, x = 6/175
Macon Construction 2 hours before so,
remaining work = 250 - (100×2hour/8) = 225 feet
then, the time taken to erect 225 feet rock facing by together is
6/175 × 225 = 54/7 hours or 7 hours 43 minutes
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1. Time taken to fill one community pool is 2hours 24 minutes. 2. Time taken to audit 30 files is 4 hours 41 minutes. and 3. The time taken to erect is 54/7 hours or 7 hours 43 minutes.
Define the audit?An audit is an independent review of financial statements and related documents in order to confirm their accuracy and compliance with relevant regulations.
1. Job: Fill one community pool Rate Time Work Completed
Reserve water tower 1/6 x x/6
City water pipes 1/4 x x/4
Solution: Fill one community pool;
Simplify, x = 12/5 hours or 2hours 24 minutes
Time taken to fill one community pool is 2hours 24 minutes.
2. Job: Work together Rate Time Work Completed
Mr. Dupree 12/5 x 12x/5
Ms. Carmichael 16/4 x 16x/4
Solution: If they work together, time taken to audit one file is
Simplify, x = 5/32 hours
So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes
Time taken to audit 30 files is 4 hours 41 minutes.
3. Job: Work together Rate Time Work Completed
Macon Construction 100/8 x 100x/8
Thomson Masonry 200/12 x 200x/12
Solution: If they work together, time taken to complete a work
Simplify, x = 6/175
Macon Construction 2 hours before so,
remaining work = 250 - (100×2hour/8) = 225 feet
then, the time taken to erect 225 feet rock facing by together is
6/175 × 225 = 54/7 hours or 7 hours 43 minutes
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Linda deposits $50,000 into an account that pays 6% interest per year, compounded annually. Bob deposits $50,000 into an account that also pays 6% per year. But it is simple interest. Find the interest Linda and Bob earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits. Year First Second Third Interest Linda earns (Interest compounded annually) Interest Bob earns (Simple interest) Who earns more interest? Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount.
Answer:
Step-by-step explanation:
To calculate the interest earned by Linda for the first year, we can use the formula:
A = P(1 + r/n)^(nt)
Where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
For the first year, we have:
A = $50,000(1 + 0.06/1)^(1*1) = $53,000
So, the interest earned by Linda for the first year is:
Interest = $53,000 - $50,000 = $3,000
For the second year, we can use the same formula with t = 2:
A = $50,000(1 + 0.06/1)^(1*2) = $56,180
Interest = $56,180 - $53,000 = $3,180
For the third year, we can use the same formula with t = 3:
A = $50,000(1 + 0.06/1)^(1*3) = $59,468.80
Interest = $59,468.80 - $56,180 = $3,288.80
Now, to calculate the interest earned by Bob for each of the first three years, we can use the formula:
Interest = Prt
Where P is the principal amount, r is the annual interest rate, and t is the time in years.
For the first year, we have:
Interest = $50,0000.061 = $3,000
For the second year, we have:
Interest = $50,0000.061 = $3,000
For the third year, we have:
Interest = $50,0000.061 = $3,000
As we can see, Linda earns more interest than Bob for each year, as her interest is compounded annually, while Bob's interest is simple interest. Therefore, the answer is:
Linda earns more.
Answer:
Linda earns $9550.8 interest and bob earns $9000 interest
Step-by-step explanation:
Linda takes compound interest: C.I. = Principal (1 + Rate)Time − Principal
interest= 50,000(1+6/100)³
=59550.8 - 50000
Linda earns $9550.8 interest in 3 years.
bob takes simple interest: S.I = prt/100
interest = 50,000*6*3/100
Bob earns $9000 in 3 years.
thus, Linda earns more interest than bob.
Sixth grade >
E.12 GCF and LCM: word problems 288
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Learn with an example
pumpkin seeds
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Franklin wishes to plant pumpkins and sunflowers, so this morning he bought packs of seeds
at a local gardening shop. Pumpkin seeds were sold in packages of 4 seeds, while sunflower
seeds were sold in packs of 8. If Franklin bought the same number of each type of seed, what
is the smallest number of pampkin seeds he must have bought?
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Therefore, the answer is that Franklin must have bought at least 4 packs of pumpkin seeds to have an equal number of pumpkin and sunflower seeds.
What do you mean by LCM?LCM stands for Least Common Multiple. It's the lowest positive number that's a multiple of two or further given figures. In other words, it's the lowest number that all the given figures divide into unevenly.For illustration, the LCM of 2 and 3 is 6, because 6 is the lowest number that's a multiple of both 2 and 3. Another illustration, the LCM of 4, 6, and 8 is 24, because 24 is the lowest number that's a multiple of all three of those figures.LCM is a useful conception in calculation, especially when dealing with fragments, because it helps us find a common denominatorGiven by the question.
Sure! Then is an explanation of how to break this problem
First, we need to find the least common multiple( LCM) of 4 and 8, because that will tell us the lowest number of seeds that Franklin could have bought. To find the LCM, we can list the multiples of each number until we find one that they've in common
Multiples of 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
Multiples of 8 8, 16, 24, 32, 40, 48, 56, 64.
The first multiple that appears in both lists is 8, so the LCM of 4 and 8 is 8.
Now we know that Franklin bought the same number of pumpkin seeds and sunflower seeds, and that number is a multiple of 8. So, we just need to find the lowest multiple of 8 that's also a multiple of 4. That is 8 itself, because it's formerly a multiple of 4.
So, Franklin must have bought at least 4 pumpkin seed packs, since each pack contains 4 seeds. Any other multiple of 8 that's also a multiple of 4 would also work, but 8 is the lowest similar number.
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Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Round your final answer to three decimal places. Intermediate calculations should be rounded to a minimum of four places. n = 15, p = 0.4 a. Find P(2). Round to three decimal places. b. Find P(2 or fewer). Round to the three places.
a. The value of P(2) is 0.022
b. The value of P(2 or fewer) is 0.027
From the question; n = 15, p = 0.4
a. We have to determine P(2).
P(X = x) = ⁿCₓ·Pˣ·(1 - P)ⁿ⁻ˣ
P(X = 2) = ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²
We can write ⁿCₓ = [tex]\frac{n!}{x!(n - x)!}[/tex]
P(X = 2) = [tex]\frac{15!}{2!(15 - 2)!}[/tex] · (0.16) · (0.6)¹³
P(X = 2) = [tex]\frac{15\times14\times13!}{2\times1\times13!}[/tex] · (0.16) · (0.6)¹³
P(X = 2) = (15 × 7) · (0.16) · (0.6)¹³
After simplification
P(X = 2) = 0.022(approx)
b. We have to determine P(2 or fewer).
P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)
P(x ≤ 2) = ¹⁵C₀·(0.4)⁰·(1 - 0.4)¹⁵⁻⁰ + ¹⁵C₁·(0.4)¹·(1 - 0.4)¹⁵⁻¹ + ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²
After simplification like above
P(x ≤ 2) = 0 + 0.005 + 0.022
P(x ≤ 2) = 0.027
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she works a 35
-hour week earning $17.10
an hour.
How much does she earn in one year? (Use 52
weeks in one year.)
$
Answer:
$31122.00
Step-by-step explanation:
We know
She works 35 hours a week, earning $17.10 an hour.
17.10 x 35 = $598.50 a week
How much does she earn in one year?
We Take
598.50 x 52 = $31122.00
So, she earns $31122.00 one year.
PLease soemone help me you would make my life and day just answer true or false. I will give you 20 points just please answer the question with a true or false.
Answer: first 4 are false last one is true
Step-by-step explanation:
FILL IN THE BLANK Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look ______ than it would if it were outside the cloud.
Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look dimmer than it would if it were outside the cloud.
Interstellar clouds are vast, dense regions of dust and gas that exist between stars. These clouds contain tiny solid particles of dust, which scatter and absorb light as it passes through them.
When we observe a star that is located near the edge of an interstellar cloud, the light from that star has to pass through a greater amount of dust before it reaches our eyes or telescopes. The dust scatters and absorbs some of the light, causing the star to appear dimmer than it would if it were outside the cloud.
This effect is similar to how the sun appears dimmer when it is viewed through a thick layer of clouds or fog. In both cases, the amount of light that reaches us is reduced due to the presence of a barrier that scatters and absorbs some of the light.
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A doctor collects data on all the men in his practice. They have an average age of 45 years, with a standard deviation of 15 years. They have an average systolic blood pressure of 150 mmHg, with a standard deviation of 10 mmHg. The two variables have correlation r=0.7.
a) Using regression, calculate the predicted systolic blood pressure for a man in the practice who is i) 30 years old ii) 45 years old iii) 50 years old
b) The above predictions all are subject to error. The average size of such errors is about ___ mmHg, and 95% of the predictions we make using regression will be correct to within about ___ mmHg.
c) A man is selected at random from the practice. He is 60 years old, which means that he is ___ SD(s) above the average age of men in the practice. Another way of expressing his relative age is that he is at the ___ percentile of age among all men in the practice.
d) Using regression, we can predict the man from part (c) will have a blood pressure that is ___ SD(s) above average. Therefore, he is predicted to be at the ___ percentile of blood pressure.
(A) This means that the systolic blood pressure 100 is less than average blood pressure and 150is higher than the average blood pressure.
(B) The average size of such errors is about 125 mmHg, and 95% of the predictions we make using regression will be correct to within about 90 mmHg.
(C) He is 60 years old, which means that he is 1.7857 SD(s) above the average age of men in the practice.
(D) The percentile corresponding to -0.6 as27.43. this means that 27.43% of people with blood pressure reading above 125.
(A) We have to find the z statistics of systolic blood pressure 100 and 150.
We have:
z₁₀₀ = 100 -125/14
= -1.7857
And, Z₁₅₀ = 150-125/14
= 1.7857
So, the systolic blood pressure 100 is -1.7857 standard deviation to the left of the mean 125.
And, the systolic blood pressure 150 is 1.7857 standard deviation to the left of the mean 125.
This means that the systolic blood pressure 100 is less than average blood pressure and 150is higher than the average blood pressure.
(B) The above predictions all are subject to error. The average size of such errors is about 125 mmHg, and 95% of the predictions we make using regression will be correct to within about 90 mmHg.
-2.5 = x -125/14
⇒ x = -2.5 × 14 +125
⇒ x = 90.
(C) A man is selected at random from the practice. He is 60 years old, which means that he is 1.7857 SD(s) above the average age of men in the practice. Another way of expressing his relative age is that he is at the 96% percentile of age among all men in the practice.
(D) The z score is: z = 0.6
The percentile corresponding to -0.6 as27.43. this means that 27.43% of people with blood pressure reading above 125.
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The absolute value function, shifted to the left 2 units.
This is the absolute value function shifted to the left 2 units:
| x+2 | = {
x+2 if x >= -2,
-(x+2) if x < -2
}
What is function?In mathematics, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule or a set of rules that assigns each input value exactly one output value. Functions can be represented using equations, graphs, or tables. They are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and finance.
Here,
The absolute value function is defined as:
| x | = {
x if x >= 0,
-x if x < 0
}
To shift the function to the left 2 units, we can replace x with (x+2):
| x+2 | = {
x+2 if x+2 >= 0,
-(x+2) if x+2 < 0
}
Simplifying further, we get:
| x+2 | = {
x+2 if x >= -2,
-(x+2) if x < -2
}
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Complete question:
The absolute value function is defined as:
| x | = {
x if x >= 0,
-x if x < 0
}
Find the function when shifted to the left 2 units.
Determine the values of A, B, and C when y - 7 = 3(x - 4) is written in standard form, Ax + By = C.
Answer:
To convert the equation y - 7 = 3(x - 4) to standard form Ax + By = C, we need to rearrange it so that it has the form Ax + By = C, where A, B, and C are constants.
y - 7 = 3(x - 4)
y - 7 = 3x - 12 (distribute the 3)
3x - y = 7 - 12 (move y to the left-hand side)
3x - y = -5
Now we have the equation in standard form, where:
A = 3
B = -1
C = -5
Therefore, the values of A, B, and C are 3, -1, and -5, respectively.
Consider the function f (x) = -2/3x + 5.
What is f(-1/2)?
Enter your answer, as a simplified fraction, in the box.
f(-1/2) =
Answer: f(-1/2) = 16/3
Step-by-step explanation:
Substituting -1/2 for x in the given function:
f(-1/2) = (-2/3)(-1/2) + 5
f(-1/2) = 1/3 + 5
f(-1/2) = 16/3
Therefore, f(-1/2) = 16/3.
Ms. Do Bee, the 8th grade mathematics teacher gives exams that are 20 multiple choice questions. Each question has for possible answers. Ms. Do Bee has a standing offer. if you get every question wrong, your grade on the exam is A.
a) supposed (especially having done no studying) you simply guess I each question. Find the probability you get none correct. Explain where this probability comes from.
b) does Ms. Do Bee’s offer make sense? Why or why not? explain.
In response to the stated question, we may state that As a result, the probability of correctly answering none of the 20 questions is roughly 0.0000262, or 0.00262%.
What is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
The likelihood of getting any one question accurate is 1/4 if you merely guess on each question. The binomial distribution formula may be used to calculate the chance of correctly answering none of the 20 questions:
P(X=0) = (n choose X) * pX * (1-p) (n-X)
[tex]If n=20, X=0, and p= 1/4\\P(X=0) = (20 pick 0) (20 choose 0) * (1/4)^0 * (3/4)^20\\P(X=0) = 1 * 1 * 0.0000262\\P(X=0) = 0.0000262[/tex]
As a result, the probability of correctly answering none of the 20 questions is roughly 0.0000262, or 0.00262%.
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Team A scored twice as many points as Team B. If the total number of points scored by both teams was 12, find the number of points scored by each team.
Answer:
Step-by-step explanation:
Let x be the number of points scored by Team B.
Then, Team A scored twice as many points, or 2x.
The total number of points scored by both teams is 12, so we can set up the equation:
x + 2x = 12
Combining like terms, we get:
3x = 12
Dividing both sides by 3, we get:
x = 4
So Team B scored 4 points, and Team A scored twice as many, or 8 points.
After y - 4x = 12 is put in slope-intercept form, what is the slope?
-4
-1/4
-3
4
Rewrite without absolute value for the given condition: y=|x−3|+|x+2|−|x−5|, if 3 < x < 5
When 3 < x < 5, y can be expressed as y = 3x - 6 without absolute value notation.
What is absolute value notation ?
Absolute value notation is a mathematical notation used to represent the magnitude or distance of a real number from zero. It is denoted by vertical bars or pipes around the number. For example, the absolute value of x is written as |x|.
When 3 < x < 5, the expression |x-3| evaluates to x-3, the expression |x+2| evaluates to x+2, and the expression |x-5| evaluates to 5-x. Therefore, we can rewrite the expression y = |x-3| + |x+2| - |x-5| as:
y = (x-3) + (x+2) - (5-x)
Simplifying this expression, we get:
y = 3x - 6
Therefore, when 3 < x < 5, y can be expressed as y = 3x - 6 without absolute value notation.
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francesca bought 27 keychains of two different kinds to make goodie bags for her birthday party. leather keychains were three dollars and beaded keychains for two dollars. she spent $73. how many keychains of each kind did she buy
Answer: Supergirl = 19 and Wonder Woman = 8
Step-by-step explanation:
Let g represent the quantity of Supergirl keychains and w represent the quantity of Wonder Woman keychains.
Qty Cost
Supergirl g $3g
Wonder Woman w $2w
Total 27 $73
Qty: g + w = 27 → -2(g + w = 27) → -2g - 2w = -54
Cost: 3g + 2w = 73 → 1(3g + 2w = 73) → 3g + 2w = 73
g = 19
Input g = 19 into one of the original equations to solve for w:
g + w = 27
(19) + w = 27
w = 8
if y is given and you need to find third derivative of y (given as y'''), what are the steps: explain what one needs to do and say it in your words.
The steps for finding out the third derivative of y (given as y''') are explained and given below.
To find the third derivative of y (y'''), you would need to differentiate the function y three times with respect to the independent variable. Here are the steps:
Start by differentiating y once to get the first derivative, y'.
Differentiate y' again to get the second derivative, y''.
Finally, differentiate y'' to get the third derivative, y'''.
You can use the chain rule, product rule, quotient rule, and other differentiation rules as needed to find each derivative.
Here's an example of finding the third derivative of y for the function y = x^4 + 2x^3 - 5x:
y' = 4x^3 + 6x^2 - 5
y'' = 12x^2 + 12x
y''' = 24x + 12
So the third derivative of y is y''' = 24x + 12.
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The difference between a number and -17 is equal to the product of the number and 25
Answer:
Let's call the unknown number "x".
According to the problem:
x - (-17) = 25x
Simplifying:
x + 17 = 25x
Subtracting x from both sides:
17 = 24x
Dividing by 24:
x = 17/24
Therefore, the unknown number is 17/24.
PLS HELP FAST 40 POINTS + BRAINLIEST!
An 800 seat multiplex cinema is divided into 3 theatres. There are 270 seats in
Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many
seats are in Theatre 2?
Answer:
340 seats in Theatre 2
Step-by-step explanation:
let n be the number of seats in Theatre 3 then the number of seats in theatre 2 is n + 150
summing and equating gives
27 0 + n + 150 + n = 800
420 + 2n = 800 ( subtract 420 from both sides )
2n = 380 ( divide both sides by 2 )
n = 190
then
number of seats in Theatre 2 = n + 150 = 190 + 150 = 340
Answer:
Theatre 3 has 190 seats, and Theatre 2 has 190 + 150 = 340 seats.
Step-by-step explanation:
Let x be the number of seats in Theatre 3.
Then the number of seats in Theatre 2 is x + 150.
And the total number of seats in the multiplex is 270 + x + (x + 150) = 800.
Simplifying the equation, we get
2x + 420 = 800
2x = 380
x = 190
Therefore, Theatre 3 has 190 seats, and Theatre 2 has 190 + 150 = 340 seats.
What is the equation of the line graphed?
Answer:
The simplest possible equation for the line on the graph would be x = - 2
(a) What is the expanded form of (a + b) 2? (b) The length of a rectangular mat is 3x-y meter and its breadth is 3-*meter. Find the area of the mat.
Answer: 9x - 3x* - 3y + y* square meters
Step-by-step explanation:
(a) The expanded form of (a + b) 2 is:
(a + b) 2 = a2 + 2ab + b2
(b) The area of the rectangular mat is:
Area = Length × Breadth
Given that the length is 3x - y meters and the breadth is 3 - * meters.
So, the area of the rectangular mat can be calculated as:
Area = (3x - y) × (3 - *)
= 9x - 3x* - 3y + y*
Therefore, the area of the rectangular mat is 9x - 3x* - 3y + y* square meters.
Answer:
Step-by-step explanation:
Find the absolute maximum and minimum values of the function f(x,y) = x^2+y^2-2x
The function f(x,y) has only minimum value at (1,0) is -1 and maximum value does not exist.
The given function is f(x,y)=x²+y²-2x
First find the partial derivative with respect to x and y
f'(x)=2x-2
f'(y)=2y
f'(x)=0=f'(y)
2x-2=0
x=1
and y=0
Now we will cheak maxima and minima at (1,0)
f''(x,y)=2 and f"(x,y)=2 and f"(x,y)=0( derivative of first order of x with respect to y)
We know that
rt-s²≥0 and r positive then f is minimum and r negative maximum
r=2 , t=2 and s=0
rt-s²≥0 and r is positive so f(x,y) is minimum at (1,0)
f(1,0)=1-2=-1
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HELP ME ASAP PLEASE!!!!!!!!!
Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
A random sample of 14
deer mice in a rich forest habitat gives an average body length of ¯=91.1
mm.
The standard deviation for the given mean length x is found to be: 2.138.
Explain about the standard deviation ?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Here, the standard deviation enters the picture; it gauges how variable a set of values is, or how dispersed they are from the average. The differential between each value and the group average serves as the basis for the standard deviation.
Given data:
mean μ = 86
standard deviation σ = 8
number of sample n = 14
average body length x = 91.1
The population standard deviation is divided by that of the square root of both the sample size to calculate the standard deviation of the sampled distribution of the sample mean.
So,
σₓ = σ / √n
σₓ = 8 / √14
σₓ = 2.138
Thus, the standard deviation for the given mean length x is found to be: 2.138.
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The complete question is-
Deer mice (Peromyscus manicul.atus) are small rodents native of North America. Their adult body lengths (excluding tail) are known to vary approximately Normally, with mean 86 mm and standard deviation 8 mm. Deer mice are found in diverse habitats and exhibit different adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of x = 91.1 mm. Assume that the standard deviation σ of all deer mice in this area is also 8 mm.
What is the standard deviation of the mean length x?
Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using
limits.
Y=(1/6) ^-x
Answer:
The given function is an exponential growth function, not an exponential decay function because as the exponent x increases, the value of y also increases instead of decreasing.
To describe its end behavior using limits, we need to find the limit of the function as x approaches infinity and as x approaches negative infinity.
As x approaches infinity, the exponent -x approaches negative infinity, and the base (1/6) is raised to increasingly larger negative powers, causing the function to approach zero. So, the limit as x approaches infinity is 0.
As x approaches negative infinity, the exponent -x approaches infinity, and the base (1/6) is raised to increasingly larger positive powers, causing the function to approach infinity. So, the limit as x approaches negative infinity is infinity.
Therefore, the end behavior of the function is that it approaches zero as x approaches infinity and approaches infinity as x approaches negative infinity.
find average speed that was traveled from city a to city p if trip took a half an hour to travel 23 miles
Step-by-step explanation:
Speed = distance / time
you are given distance = 23 miles and time = .5 hr
distance / time = 23 miles / .5 hr = 46 mph
Suppose that the random variable X has the continuous uniform distribution | 1,0
For the random variable X, the mean of "X-3" is -5/2 and variance of "X-3" is 1/12.
We have to find the mean and variance of the quantity "X-3" , for the random variable X;
⇒ Let y = x-3,
So, Mean of y = E(y),
⇒ E(y) = E(x-3) = E(x) - 3,
⇒ E(x) = [tex]\int\limits^1_0 {x}f(x) \, dx[/tex] = [tex]\int\limits^1_0 {x.1} \, dx[/tex];
⇒ E(x0 = [x²/2]¹₀ = 1/2.
So, E(y) = (1/2) - 3 = -5/2.
⇒ Variance of y is = Var(x-3)
⇒ Variance of y = Var(x) - 0 ...because Var(3) = 0 as the variance of constant is 0.
⇒ We know that, Var(x) = E(x²) - (E(x))²;
⇒ E(x²) = [tex]\int\limits^1_0 {x^{2} f(x)} \, dx[/tex] = [tex]\int\limits^1_0 {x^{2} .1} \, dx[/tex] = [x³/3]¹₀ = 1/3,
So, Var(x) = (1/3) - (1/2)²
⇒ Var(x) = 1/3 - 1/4 = 1/12.
Therefore, the required Mean is -5/2 and the variance is 1/12.
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The given question is incomplete, the complete question is
Suppose that the random variable X has the continuous uniform distribution,
f(x) = {1, 0 ≤ x ≤ 1
{0, otherwise
Suppose that a random sample of n=13 observations is selected from this distribution.
Find the mean and variance of the quantity x-3.
FILL IN THE BLANK.When the group leader uses the skill of _______ he/she is easing the group out of emotional interaction and into cognitive reflection
When the group leader uses the skill of reframing, he/she is easing the group out of emotional interaction and into cognitive reflection.
Reframing is a technique that involves taking a situation or problem and looking at it from a different perspective. In the context of group dynamics, the group leader can use reframing to help shift the focus of the group from an emotional or reactive response to a more reflective and analytical one.
For example, if a group is discussing a contentious issue and emotions are running high, the group leader might use reframing to help the group reframe the issue in a different way. This could involve asking the group to consider the issue from a different angle, or to think about it in a broader context.
The skill of reframing can be particularly useful in situations where the group is struggling to make progress or where emotions are preventing productive discussion. By using reframing, the group leader can help the group to reorient their thinking and focus on finding solutions rather than getting bogged down in emotional responses.
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A brand new stock is called an initial public offering or IPO. Remember that in this model the period immediately after the stock is issued offers excess returns on the stock(ie it is selling for more than its actually worth). One such model for a class of internet IPOS predicts the percentage overvaluation of a stock as a function of time, as R(t)=2501^2/e^3t where R(t) is the overvaluation in percent and t is the time in months after issue. Use the information provided by the first derivative and second derivate, and asymptotes to prepare advice for clients as to when they should expect a signal to buy or sell (Inflection point), the exact time when they should buy or sell(max/min) and any false signals prior to an as- ymptote. Explain your reasoning. Make a rough sketch of the function.
The Function of maximum or minimum for t is infinity.
What is first and second subsidiary test?While the principal subordinate can let us know if the capability is expanding or diminishing, the subsequent subsidiary. tells us in the event that the primary subsidiary is expanding or diminishing. On the off chance that the subsequent subsidiary is positive, the first.
To analyze the function R(t) = 2501² / e(3t), we can take the first and second derivatives:
R'(t) = -7503 * 2501² / e(3t)
R''(t) = 22509 * 2501² / e(3t)
To find the inflection point, we can set R''(t) = 0 and solve for t:
22509 * 2501² / e(3t) = 0
t = ln(0) / -3 = undefined
Since there is no real solution to this equation, there is no inflection point for this function.
To find the maximum or minimum, we can set R'(t) = 0 and solve for t:
-7503 * 2501² / e(3t) = 0
t = infinity
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