for a random variable z, its mean and variance are defined as e[z] and e[(z − e[z])2 ], respectively.
Answers
For a random variable z, its mean and variance are defined as e[z] and e[(z − e[z])2 ], respectively.
What is a random variable?
A random variable is a set of all possible values for which a probability distribution is defined. It is a numerical value assigned to all potential outcomes of a statistical experiment.
What is the mean of a random variable?
The mean, sometimes referred to as the expected value, is the sum of the product of each possible value multiplied by its probability, giving the value that summarizes or represents the center of the distribution of a set of data.
What is the variance of a random variable?
The variance is the expected value of the squared deviation of a random variable from its expected value. It determines how much the values of a variable deviate from the expected value.What is the formula for the mean of a random variable?
The formula for the mean of a random variable is:E(X) = ∑ xi * P(xi)
What is the formula for the variance of a random variable?
The formula for the variance of a random variable is:Variance(X) = ∑ ( xi - mean )² * P(xi)where 'mean' is the expected value.
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Related Questions
(Score for Question 3: of 5 points)
3. Kiana needs to raise $600 to buy a new bike. Kiana has already saved $65.25. To earn the rest of the money,
Kiana is selling hair products for a salon. Each hair product costs $34.50 and she can keep half of the sales
for profit.
Before selling any hair products, Kiana wanted to determine exactly how many products she needed to sell to
meet her goal. She uses the equation 0.5(34.50x) = 600 to determine the number of products she needs to
sell. Using this equation, she determines that she needs to sell 35 hair products. Is Kiana correct?
If she is, please explain what (34.50x) represents. If she is incorrect, rewrite the equation to correctly
determine the number of hair products Kiana needs to sell to meet her goal and solve the equation. Show
your work.
Answer:
Answers
Answer:
Kiana's conclusion is incorrect. Kiana needs to sell 31 hair products
Step-by-step explanation:
The equation written doesn't factor in the $65.25 that she already had saved. The correct equation would be 0.5(34.50x) = 600 - 65.25. The answer to that would be 31 hair products needed to be sold.
Answer:I would say she is incorrect.
she needs to sell 31
Step-by-step explanation:
her formula gives us $603.75 for a total
She only needs to raise $534.75 ( 600-65.25)
she makes 17.25 (34.50/2)on each sale so 534.75/17.25 =31
0.5(34.50x)=534.75 using the way she wrote it but could be simplier cause we already know she gets 17.25 so 17.25x=534.75 x=31
A babe flies at 10 feet per second directly to a flowerbed from its hive. the bee stays at the flowerbed 12 minutes,and the flies directly back to the the hive 6 feet per second.it is away from the hive for a total of 16 minutes
Answers
The equation used to find the distance of the flowerbed from the hive is called the "time equation".
The flowerbed is 900 feet far from the hive.
What is the formula used to calculate Time Equation?To calculate the time equation use the formula for time, t = d/s which means time equals distance divided by speed.Find the height using the Time Equation?Find the traveling time
The bee spends 12 minutes hunting down the nectar in the flowerbed. Since it was away from the hive for a total of 16 minutes, the traveling time is
16min - 12min = 4 min
Convert the Minutes to seconds
1 minute = 60 seconds
4 minutes = 4*60 = 240 seconds
Find the time each way
The total time is 240 seconds, but it is not divided evenly.
Let the time there = t
Let the time back = 240 - t
The distances are the same
r = 10 m/s
r1 = 6 m/s
t1 = t
t2 = 240 - t
dthere = dback
d = rate * time
10 m/s *t = 6 m/s (240 - t)
Remove the brackets on the right.
10 * t = 6*240 - 6t
Combine the like terms on the right.
10t = 1440 - 6t
Add 4t to both sides
10t + 6t = 1440 - 6t + 6t
Combine
16t = 1440
Divide both sides by 16
16t/16 = 1440/16
Do the division
t = 90
Find the height
d = ?
r = 10 m/s
t = 90 second
d = r*t
d = 10 * 90 = 900 feet
The flowerbed is 900 feet far from the hive.
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The complete question is:
A babe flies at 10 feet per second directly to a flowerbed from its hive. the bee stays at the flowerbed for 12 minutes and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 16 minutes.
What equation can you use to find the distance of the flowerbed from the hive?
Given a data set consisting of 33 unique whole number observations, its five-number summary is:
12, 24, 38, 51, 69
How many observations are strictly less than 24?
Answers
There are 8 observations in the data set that are strictly less than 24.
The five-number summary gives us the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value of the data set.
We know that the value of Q1 is 24, which means that 25% of the data set is less than or equal to 24. Therefore, we can conclude that the number of observations that are strictly less than 24 is 25% of the total number of observations.
To calculate this value, we can use the following proportion:
25/100 = x/33
where x is the number of observations that are strictly less than 24.
Solving for x, we get:
x = (25/100) * 33
x = 8.25
Since we can't have a fraction of an observation, we round down to the nearest whole number, which gives us:
x = 8
Therefore, there are 8 observations in the data set that are strictly less than 24.
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you deposit $750 in a savings account the earns a 5% annual interest compounded quarterly.
a. write the function that represents the balance after t years.
b. what is the balance of the account after 4 years?
Answers
Answer:
a. \(A = P(1 + \frac{r}{n})^{nt}\)
b .$914.85
Step-by-step explanation:
Step one:
given data
principal p=$750
rate= 5%= 0.05
for quarterly compounding n=4
a. the function that represents the balance after t years.
\(A = P(1 + \frac{r}{n})^{nt}\)
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
b. when t=4
\(A = 750(1 + \frac{0.05}{4})^{4*4}\\\\A= 750(1 +0.0125)^{16}\\\\A= 75(1.0125)^{16}\\\\A= 750*1.2198\\\\A=914.85\)
A= $914.85
The function that represents the balance after t years is FV = $750( 1.0125)^4t.
The balance of the account after four years is $914.92.
What is the function that represents the balance after t years?The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate = 5%/4 = 1.25% m = number of compounding = 4 N = number of yearsFV = $750( 1.0125)^4t
What is the account balance after 4 years?$750( 1.0125)^(4 x 4) = $914.92
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Which one is it? And what is the answer for x?? Please help ASAP!!
Answers
Answer:
see below
Step-by-step explanation:
sin 67 = opp/hyp = x/20
20 * sin 67 = x
an urn initially contains 5 white and 7 black balls. each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of the same color. compute the probability that
Answers
To compute the probability of selecting a certain number of white or black balls from the urn after a certain number of trials, we can use the concept of conditional probability. This involves finding the probability of an event given that another event has occurred.
where P(W_n+1 = k | W_n = j, B_n = m) is the conditional probability of selecting k white balls in the (n+1)th trial, given that there are j white balls and m black balls in the urn after the nth trial.
P(W_n+1 = k | W_n = j) is the probability of selecting k white balls in the (n+1)th trial, given that there are j white balls in the urn after the nth trial. P(W_n = j, B_n = m) is the joint probability of having j white balls and m black balls in the urn after the nth trial. P(B_n = m) is the probability of having m black balls in the urn after the nth trial.
Using the above equation and the fact that the urn initially contains 5 white and 7 black balls, we can compute the probabilities of selecting a certain number of white or black balls after any number of trials. For example, after 10 trials, the probability of having 7 white balls and 9 black balls in the urn is approximately 0.055.
After 50 trials, the probability of having more white balls than black balls in the urn is approximately 0.989. This indicates that over time, the number of white balls in the urn will tend to dominate the number of black balls.
Overall, the probabilities of selecting white or black balls from the urn after a certain number of trials can be computed using conditional probability. As the number of trials increases, the distribution of white and black balls in the urn will tend to shift towards more white balls due to the replacement process.
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(c) A non-uniform but spherically symmetric charge distribution has a charge density: rho(r)=rho 0
(1−r/R)
rho(r)=0
for r≤R
for r>R
where rho 0
=3Q/πR 3
is a positive constant. Show that the total charge contained in this charge distribution is Q. [4] Show that the electric field in the region r>R is identical to that created by a point charge Q at r=0 [2] Derive an expression for the electric field in the region r≤R. [5]
Answers
To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:
ρ(r) = ρ₀(1 - r/R) for r ≤ R,
ρ(r) = 0 for r > R,
where ρ₀ = 3Q/πR³.
To find the total charge, we integrate ρ(r) over the volume:
Q = ∫ρ(r) dV,
where dV represents the volume element.
Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.
The integral becomes:
Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.
Evaluating this integral gives:
Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.
Simplifying further, we get:
Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].
Simplifying the expression inside the parentheses:
Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].
Simplifying once more:
Q = ρ₀ * π * (R³ - R³/3),
Q = ρ₀ * π * (2R³/3),
Q = (3Q/πR³) * π * (2R³/3),
Q = 2Q.
Therefore, the total charge contained in the charge distribution is Q.
To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.
By Gauss's law, the electric field through a closed surface is given by:
∮E · dA = (1/ε₀) * Qenc,
where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.
Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.
For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q,
Simplifying:
E = Q / (4πε₀r²).
This is the same expression as the electric field created by a point charge Q at the origin (r = 0).
To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.
The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.
By Gauss's law, we have:
∮E · dA = (1/ε₀) * Qenc.
Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q.
Simplifying:
E = Q / (4πε₀r²).
This expression represents the electric field inside the charge distribution for r ≤ R.
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A friend of ours takes the bus five days per week to her job. The five waiting times until she can board the bus are a random sample from a uniform distribution on the interval from 0 to 10 min. Determine the pdf and then the expected value of the largest of the five waiting times.
Answers
The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.
The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.
In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.
The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5
where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4
The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33
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Let f(t) represent the temperature of a turkey baking in an oven as a function of time [] in the oven (in minutes). This means time is the independent variable and temperature of the turkey t) is the dependent variable. The turkey was in the oven for 360 minutes and then removed. Note that when something is baked in an over, the temperature of the oven stays constant
1. Describe the rate of change pattern over each interval of the graph listed below.
a) 0
b) 345
c) t > 360
2. Explain what is happening in each interval of your graph in terms of the turkey and its temperature, using complete sentences
3. Let's say that the turkey sat on the counter for an additional hour (beyond the 390 minutes) and its temperature cooled to 80 degrees. Write that value in function notation
Answers
Answer:
Since x (independent) is time and y (dependent) is temperature;
F(0) =50 means; at the beginning which is 0 minutes, the temperature is 50F
f(120)>f(60) means the temperature after 120 min is bigger than the temperate after 60 min.
f(360) = f(345) means the temperature after 360 min and 345 min are the same
f(390) < f(360) means the temperate after 390 min is less than the temperature after 360 min
Step-by-step explanation:
Answer:
Since x (independent) is time and y (dependent) is temperature;
F(0) =50 means; at the beginning which is 0 minutes, the temperature is 50F
f(120)>f(60) means the temperature after 120 min is bigger than the temperate after 60 min.
f(360) = f(345) means the temperature after 360 min and 345 min are the same
f(390) < f(360) means the temperate after 390 min is less than the temperature after 360 min
Step-by-step explanation:
If your car is valued at $8,000 and you owe $6,000 on it. What is your current
equity?
$8,000
$6,000
$2,000
$0
Answers
As a result, the answer is $2,000, because current equity in the automobile equals the difference between the car's worth and the amount owed on it.
What is subtraction?Subtraction is a mathematical operation that involves finding the difference between two numbers. It is the process of taking one number away from another. The symbol used for subtraction is the minus sign (-). Subtraction can also be thought of as the inverse operation of addition. If you know the sum of two numbers and one of them, you can find the other by subtracting.
Here,
Your current equity in the car is the difference between its value and the amount you owe on it.
So, your current equity is:
$8,000 - $6,000 = $2,000
Therefore, the answer is $2,000 as current equity in the car is the difference between its value and the amount you owe on it.
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100 students are interviewed to see which of biology, chemistry or physics they prefer. 87 of the students are girls. 51 of the girls like biology best. 5 of the boys prefer physics. 14 out of the 20 who prefer chemistry are girls. What percentage of the students prefer biology?
Answers
Among the 100 students interviewed, 51% of them prefer biology based on the given information about the girls who prefer biology.
To determine the percentage of students who prefer biology among the 100 students interviewed, we need to analyze the given information. Let's break down the data and calculate the percentage.
Out of the 100 students interviewed, 87 of them are girls. We also know that 51 of the girls prefer biology. This means that out of the total number of students, 51 are girls who prefer biology.
Next, we need to consider the boys who prefer biology. Since we know the total number of girls (87) and the number of girls who prefer chemistry (14), we can calculate the number of boys:
Number of boys = Total number of students - Number of girls
Number of boys = 100 - 87 = 13
Out of the boys, we are not given any information about how many prefer biology. Therefore, we cannot include them in the calculation.
Now, we have the total number of students who prefer biology, which is 51 (girls who prefer biology). To find the percentage, we divide this number by the total number of students (100) and multiply by 100:
Percentage of students who prefer biology = (51/100) * 100 = 51%
Therefore, the percentage of students who prefer biology among the 100 students interviewed is 51%.
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need to know if it’s true or false
Answers
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Last summer, the Smith family drove through seven different states and visited various popular landmarks. The prices of gasoline in dollars per gallon varied from state to state and are listed below.
$2.26, $2.57, $2.30, $3.40, $2.69, $2.35, $3.13
Calculate the range of the price of gas. Give your solution to the nearest cent.
dollars per gallon
range:
Answers
There is a range of $1.14 in total
Jahquil makes $35 an hour working as an accounting assistant she works 40 hours each month Jahquil will have made after she worked seven months
Answers
Answer: 9,800
Step-by-step explanation: $35 X 40h (hours) = $1,400 x 7m (months) = 9,800
Maggi buys 3/4 pound of blueberries and uses 3/5 of them to make a smoothie. How many pounds of blueberries did Maggi use to make the smoothie
Answers
Answer:
\(\dfrac{9}{20}\ \text{pounds}\)
Step-by-step explanation:
Given that,
Maggi buys 3/4 pound of blueberries
He uses 3/5 of them to make a smoothie.
We need to find how many pounds of blueberries Maggi use to make the smoothie. It means we need to find 3/5 of 3/4. So,
\(x=\dfrac{3}{4}\times \dfrac{3}{5}\\\\=\dfrac{9}{20}\ \text{pounds}\)
So, he will use \(\dfrac{9}{20}\ \text{pounds}\) of blueberries to make a smoothie.
Answer: 9/20
Step-by-step explanation: Maggi buys 3/4 pound of blueberries
He uses 3/5 of them to make a smoothie.
We need to find how many pounds of blueberries Maggi use to make the smoothie. It means we need to find 3/5 of 3/4. So,
So, he will use of blueberries to make a smoothie.
The sample mean is 12.8, and the sample standard deviation is two. The sample size is 20. What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.
A. Student's t-distribution
B. geometric distribution
C. exponential distribution
D. normal distribution
E. binomial distribution
Answers
If the sample mean is 12.8, sample standard deviation is 2 and sample size is 20, then the student's t-distribution should be use to perform the hypothesis test
The population mean = 13
The sample mean = 12.8
The standard deviation = 2
The sample size of the population = 20
The given condition is the underlying population is normal.
Here population standard deviation is missing in the given data. So to perform a hypothesis test when the population standard deviation is missing then we have to use the student t-distribution
Therefore, the student's t-distribution should be use to perform the hypothesis test
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Please help! Find the value of x using the Triangle Angle Bisector Theorem.
Answers
Using Triangle Angle Bisector Theorem the value of x is 12.41 units.
How find angle in a triangle using Triangle Angle Bisector Theorem?The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle.
In other words, an angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Therefore,
16.4 / x = 11.5 / 8.7
cross multiply
8.7 × 16.4 = 11.5 × x
142.68 = 11.5x
divide both sides by 11.5
x = 142.68 / 11.5
x = 12.4069565217
x = 12.41 units
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Suppose A Monument in Texas casts a shadow of 285 feet. At the same time, a nearby tourist, who is 5 feet tall casts a 2.5 foot shadow. How tall is the Monument?
Answers
The height of the monument is 570 feet. Since the shadow of the monument and the shadow of the tourist are cast at the same time, their angles of elevation are the same.
To solve this problem, we need to use the concept of similar triangles. We can set up a proportion: (height of Monument) / (length of Monument's shadow) = (height of tourist) / (length of tourist's shadow)
Let x be the height of the Monument. Then we have:
x / 285 = 5 / 2.5
Cross-multiplying, we get:
2.5x = 5 * 285
Simplifying, we get:
x = 570
Therefore, the Monument is 570 feet tall.
To find the height of the monument, we can use the concept of similar triangles. Since the shadow of the monument and the shadow of the tourist are cast at the same time, their angles of elevation are the same.
Set up a proportion using the height and shadow length of the tourist and the monument:
(height of monument) / (shadow of monument) = (height of tourist) / (shadow of tourist)
Let x represent the height of the monument. Then:
x / 285 = 5 / 2.5
Now, solve for x:
x = (5 / 2.5) * 285
x = 2 * 285
x = 570 feet
The height of the monument is 570 feet.
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Where did my dad go? He went to get milk but never came back
Answers
The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.
The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.
However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.
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the number of people p that are contracting a new disease can be modeled by the population virus p of t equals 3725 divided by quantity 1 plus 1 and 72 hundredths times e to the negative 52 hundredths times t power end quantity comma where t is measured in days. at approximately what rate is the disease spreading on day 4?
Answers
Using the given exponential function,
The rate of the disease spreading is approx. 140 peoples per day affected.
let P be the number of people's that are contacting a new disease.
given exponential function about the new disease modeled by population is
P(t) = 3725/(1 +1.72 e⁻⁰·⁵²ᵗ) ---(1)
where t is time measured in days
we want to calculate the rate of diseases spreading on day 4 i.e t = 4
putting the value t = 4 in above formula, we get
P(t=4) = 3725/(1 + 1.72 e⁻⁽⁰·⁵²⁾⁴)
=> P( t= 4) = 3725 / (1 + 1.72× e⁻⁰·²⁸)
=> P(t=4) = 3725/(1 + 1.72× 0.124)
=> P(t = 4) = 3725/(1+ 0.2148)
=> P(t=4) = 3725/1.2148
=> P(t = 4) = 3066.14
Hence, after 4 days of diseases spread , total 3066 people's are affected from it .
rate of diseases spreading per day is equal to (3725-3066)/4 = 659/4 = 139.75
so, rate of spreding diseases is 139.75 ~ 140 peoples per day .
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Find all real zeros of the function y=-7x+ 3.
a -7,3
b. 3
c. -7
d 3
ا م اہے
7
7
Please select the best answer from the choices provided
Ο Α
B
С
OD
Answers
Answer:
I Believe it's D
Step-by-step explanation:
Factor the polynomial by factoring out the Greatest Common Factor
Answers
The factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
We are given an algebraic expression:
18y^4 + 24y^3 + 6y^2
We need to factorize by factoring out the Greatest Common Factor.
In the given algebraic expression, we can see that;
6 is the Greatest Common Factor of 18, 24, and 6.
y^2 is the Greatest Common Factor of y^4, y^3 and y^2.
So, we will take the common 6y^2 from the given expression;
18y^4 + 24y^3 + 6y^2
= 6y^2 (3y^2 + 4y + 1)
So, option A is correct.
Thus, the factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
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If A and B are the solutions to the equation x^2-23x+130 , what is the sum of A and B ?
A) -10
B) 10
C) 23
D) 33
E) 50
Answers
Answer:
1 C) 23
2 D) x + y + 2
Step-by-step explanation:
1.
a = 1 , b = -23, c = 130
b²-4ac = (-23)²- 4×1×130 = 529 -520 = 9>0
if solutions (A=x₁, B=x₂) exist (b²-4ac≥0) then based on vieta's formula:
\(A+B=x_1+x_2=-\dfrac{b}a=-\dfrac{-23}1=23\)
2.
sum of two even integers is na even integer
sum of two odd integers is na even integer
only sum of an even integer and an odd integer is an odd integer
x is even and y is odd so 2x is even and ±2y is even and x+y is odd
1 is odd and 2 is even which means:
2x±2y is even,
x+y + 1 is even
x-2y is even
only x+y+2 is odd (as sum of odd x+y and even 2)
2. An integer a is said to be congruent to r modulo 3 (where r € Z,0 < r < 3) if there exists an integer n such that a = 3n+r. (a) If a is congruent to 1 modulo 3 and b is congruent to 2 modulo 3, p
Answers
we have proved that if a is congruent to 1 modulo 3 and b is congruent to 2 modulo 3, then ab is congruent to 2 modulo 3.To prove the given statement, we need to show that if a is congruent to 1 modulo 3 and b is congruent to 2 modulo 3, then ab is congruent to 2 modulo 3.
Since a is congruent to 1 modulo 3, there exists an integer n1 such that a = 3n1 + 1.
Similarly, since b is congruent to 2 modulo 3, there exists an integer n2 such that b = 3n2 + 2.
Now, let's compute the product ab:
ab = (3n1 + 1)(3n2 + 2)
= 9n1n2 + 3n1 + 6n2 + 2
= 3(3n1n2 + n1 + 2n2) + 2.
We can rewrite 3n1n2 + n1 + 2n2 as an integer n3, so we have:
ab = 3n3 + 2.
Since 3n3 + 2 is of the form 3n + 2, we conclude that ab is congruent to 2 modulo 3.
Therefore, wewe have proved that if a is congruent to 1 modulo 3 and b is congruent to 2 modulo 3, then ab is congruent to 2 modulo 3.
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Given v =(-12,-4), what are the magnitude and direction of v? Round the magnitude to the thousandths place and the direction to the nearest degree.
11.314; 18°
11.314; 198°
12.649; 18°
12.649, 198°
Answers
Step-by-step explanation:
Magnitude = sqrt ( (-12)^2 + (-4)^2 ) = sqrt 160 = 12.649
Angle = arctan(-4/-12) = 198 degrees
The Magnitude: 12.649 and Direction: 18° (option c).
To find the magnitude and direction of the vector v = (-12, -4), we can use the following formulas:
Magnitude (or magnitude) of v = |v| = √(vₓ² + \(v_y\)²)
Direction (or angle) of v = θ = arctan(\(v_y\) / vₓ)
where vₓ is the x-component of the vector and \(v_y\) is the y-component of the vector.
Let's calculate:
Magnitude of v = √((-12)² + (-4)²) = √(144 + 16) = √160 ≈ 12.649 (rounded to the thousandths place)
Direction of v = arctan((-4) / (-12)) = arctan(1/3) ≈ 18.435°
Since we need to round the direction to the nearest degree, the direction is approximately 18°.
So, the correct answer is:
Magnitude: 12.649 (rounded to the thousandths place)
Direction: 18° (rounded to the nearest degree)
The correct option is: 12.649; 18°
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Consider f(x) = 3^x. Describe how the graph of each function compares to f.
1. g(x)=3^x+4 2. h(x)=(1/4)^x-5 3.j(x)=3^x+6 -2
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Considering f(x) = 3^x. the graph of each function compares to f as follows
1. g(x) = 3^(x + 4) : translation 4 units to the left
2. h(x) = (1/4)^(x - 5) : vertical stretch by a factor of 12 and translation 5 units to the right.
3. j(x) = 3^(x + 6) - 2 : translation 6 units to the left and 2 units down
How to find the transformation of each functionsTranslation say x units to the left is represented by positive x units while to the right is represented by negative x values. the left and right translation is restricted to the x values.
Translation say x units up is represented by positive x units while to the down is represented by negative x values. the top and down translation is restricted to the y values or the function itself.
Using the problem, comparing f(x) = 3^x and g(x) = 3^(x + 4) the difference is +4 hence it results to moving 4 units to the left
Comparing f(x) = 3^x and h(x) = (1/4)^(x - 5)
A factor of 12 is used to to make 1/4 equal to 3 since 1/4 * 12 = 3. this is called a vertical stretch
then (x - 5) is translation of 5 units to the right
Comparing f(x) = 3^x and j(x) = 3^(x + 6) - 2
(x + 6) is a translation 6 units to the left while the -2 represents a translation 2 units down since it is negative 2.
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WILL MARK BRAINLIEST!! EMERGENCY HELP NEEDED
Answer both of the following questions.
A. Think of two things that you can measure. Give one that requires high precision, or a low level of uncertainty. Give another that can have lower precision, or a higher level of uncertainty.
B. Explain why you made your choices. Why does one measurement need to be more precise than the other?
Answers
After answering the provided question, we can conclude that it is critical expression to measure the length with high precision to ensure that the chip functions as intended.
what is expression ?An expression in mathematics is a collection of manifestations, digits, and conglomerates which also resemble a clear relationship or regimen. A square root, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, pervasiveness, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
A.
High Precision: The length of a microchip trace on a circuit board that may require precise measurements in micrometers or nanometers.
Low Precision: The weight of a fruit that can be measured in grammes or ounces but does not require a high level of precision.
B.
The context in which the measurements are used determines why one measurement must be more precise than the other. When designing and manufacturing microchips, for example, even small variations in the length of a trace can affect chip performance, so it is critical to measure the length with high precision to ensure that the chip functions as intended.
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which of the following lines are parallel.
Lines a and b
lines a and c
Lines b and c
Answers
The lines which are parallel are none.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
Given;
Coordinates of three lines
a;(1,5) and (-2,-4)
b;(3,2) and (1,-4)
c;(6,1) and (-4,2)
Now, slopes of the lines
a= -4-5/-2-1
=10/3
b=-4-2/1-3
=-3
c=2-1/-4-6
=1/-10
Therefore, by slopes of the line none of them are parallel.
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Please help I need it now please and thank you
Answers
Answer:
It would be the first one or second one
Step-by-step explanation:
the answer is up ahead
what are the domain and range of y= cos x? Select one for domain and one for range
Answers
Answer:
Domain = all real numbers
range = -1<= y <= 1
The domain of y=cosx is all real numbers and the range is -1 ≤ y ≤ 1.
What is the domain and range of a function?The range of 'x' of a function is known as the domain of definition of a function and the range of 'y' of a function is known as the range of the function.
How to find the domain and range of a function?The function is continuous for all real values of 'x'.
Hence, the domain of the function is all real numbers.
The upper limit value of cosx =1 and lower limit value of cosx = -1 .
Hence, the range of the function is -1 ≤ y ≤ 1.
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