The probability of x within this range is constant and equal to 1/3. The area under the uniform distribution curve is 1.
The range of the random variable, x, in a uniform distribution from 2 to 5 is [2, 5]. It represents the entire interval of possible values for x.
The probability of the random variable, x, in a uniform distribution is constant over the range. Since it is a uniform distribution, the probability density function is equal for all values within the range. Therefore, the probability of x taking any specific value within the range [2, 5] is the same, and it is given by 1 divided by the length of the range:
Probability of x = 1 / (length of range)
= [tex]P(x) = \frac{1}{5 - 2} = \frac{1}{3}[/tex]
The area of the uniform distribution is represented by the probability density function over the range. Since it is a uniform distribution, the probability density is constant within the range. Therefore, the area under the curve is equal to the length of the range multiplied by the constant probability density:
Area = (length of range) * (probability density) = (5 - 2) * (1 / (5 - 2)) = 3 * (1 / 3) = 1.
Hence, the area of the uniform distribution is 1.
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PLZ HELPPPPPPPP
Two sides of a four-sided figure have negative slopes. Which are the endpoints of the sides of this figure?
1. (–4, –4), (–4, –1), (–1, –4), (–1, –1)
2. (–2, –4), (–1, –1), (1, –1), (2, –4)
3. (1, 1), (2, 4), (5, 4), (4, 1)
4. (1, 4), (2, 1), (5, 1), (4, 4)
Answer:
Think
Step-by-step explanation:
Think its 2.
Which of the following is the equation of a line that is perpendicular to the graph of y = 25x − 1?
A. y = 25x − 4
B. y = −52x − 4
C. y = −25x − 4
D. y = 52x −
Given:
Consider the given equation is
[tex]y=\dfrac{2}{5}x-1[/tex]
To find:
The equation of a line that is perpendicular to the graph of given line.
Solution:
Slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
Equation of given line is
[tex]y=\dfrac{2}{5}x-1[/tex]
Here, slope is [tex]\dfrac{2}{5}[/tex].
We know that, product of slopes of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]\dfrac{2}{5}\times m_2=-1[/tex]
[tex]m_2=-\dfrac{5}{2}[/tex]
The slope of perpendicular line is [tex]-\dfrac{5}{2}[/tex].
Only in option C, the slope of the line is [tex]-\dfrac{5}{2}[/tex].
Therefore, the correct option is C.
From the given option the slope of the line -5/2 is shown by the equation [tex]y=-\dfrac{5}{2}x-4[/tex] that is option B) and this can be determined by using the slope-intercept form.
Given :
Equation -- [tex]y=\dfrac{2}{5}x-1[/tex] ---- (1)
First, determine the slope of the given line by using the slope-intercept form. The slope-intercept is given by the equation:
y = mx + c
Now, compare equation (1) with the above equation.
[tex]\rm m_1 =\dfrac{2}{5}[/tex]
c = -1
For a line to be perpendicular to the other line the product of the slope of both the line is equal to -1, that is:
[tex]\rm m_1m_2 = -1[/tex]
So, the slope of the line perpendicular to the line [tex]y=\dfrac{2}{5}x-1[/tex] is:
[tex]\rm m_2 = -\dfrac{5}{2}[/tex]
So, from the given option the slope of the line -5/2 is shown by the equation [tex]y=-\dfrac{5}{2}x-4[/tex] that is option B).
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In this question, you will build a matrix from the eigenvectors and eigenvalues, instead of the other way around. The matrix A has three eigenvalues: >1 = 8 with eigenvector u₁ = (1,1,0), 12 = -3 with eigenvector u2 = (1,-1, 1) and 13 = 12 with eigenvector uz (1,-1,-2). (a) Normalize the eigenvectors u; to give vi. Enter them in the usual format e.g. [1,2,3]. = 01: v2 = = v3 (b) Recall that you can build an orthogonal matrix P whose columns are that set of orthonormal eigenvectors. Then PT AP D, where D is a diagonal matrix that contains the eigenvalues along the diagonal. We now have P and D, so can find A from the formula A = PDPT. Enter the matrix A as a list of row vectors.
To construct the matrix A using eigenvectors and eigenvalues, we normalize the given eigenvectors to obtain orthonormal vectors. We then form an orthogonal matrix P by arranging the orthonormal eigenvectors as columns. Next, we create a diagonal matrix D with the eigenvalues along the diagonal. Finally, we compute A using the formula A = PDPT.
(a) To normalize the eigenvectors, we divide each vector by its magnitude to obtain unit vectors. The normalized eigenvectors are:
v₁ = [1/√2, 1/√2, 0]
v₂ = [1/√3, -1/√3, 1/√3]
v₃ = [1/√6, -1/√6, -2/√6]
(b) To construct the matrix A, we form an orthogonal matrix P using the orthonormal eigenvectors as columns:
P = [v₁, v₂, v₃] = [[1/√2, 1/√3, 1/√6], [1/√2, -1/√3, -1/√6], [0, 1/√3, -2/√6]]
Next, we create a diagonal matrix D with the eigenvalues along the diagonal:
D = diag, -3, 12])
Finally, we compute A using the formula A = PDPT:
A = PDPT = [[1/√2, 1/√3, 1/√6], [1/√2, -1/√3, -1/√6], [0, 1/√3, -2/√6]] diag([8, -3, 12]) [[1/√2, 1/√3, 1/√6].T, [1/√2, -1/√3, -1/√6].T, [0, 1/√3, -2/√6].T]
Performing the matrix multiplication, we obtain the matrix A:
A = [[4, 0, 0], [0, -1, 0], [0, 0, 12]]
Therefore, the matrix A, constructed using the given eigenvectors and eigenvalues, is:
A = [[4, 0, 0], [0, -1, 0], [0, 0, 12]]
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C(x)=75,000+150x what is the value of x
The rational number which lies between - 1/3 and 1/4
is
(a) 1
(b) - 1
(c) 0
(d) infinite numbers
Answer:
I think that's 1
Step-by-step explanation:
but not sure
Cardi B is buying gifts for her family. She can spend no
more than $60 on all of her gifts.So far she has spent $45.95, and she has one
more gift to buy. Write an inequality that shows how much she can spend on the
final gift. (≥, ≤)
Answer:
x ≥ $14.05
Step-by-step explanation:
I subtracted 45.95 from 60 to find how much she had left, which amounts to 14.05. I used x as the amount she can spend, and the inequality is as such.
Answer: she can spend $14.05
Step-by-step explanation:
$60-$45.95=$14.05
The number of N bacteria in a culture can be modeled through the continuous growth model. If the there were 100 bacteria initially and the
value for kis 0.5, what will the population of the bacteria be in 10 hours, where is the number of hours?
Answer: A. 14,841
Step-by-step explanation:
answers:
Angle 1
Angle 7
Angle 4
Angle 8
Answer:
Step-by-step explanation:
Angle 1 = Angle 7
Angle 4 = Angle 8
Answer:
i need more information
Step-by-step explanation:
Question: Which expression is equivalent to 5(x + 7)
possible answers: A: 5x + 7
B: 35x
C: 5x + 35
D: 5x + 12
Answer:
B
Step-by-step explanation:
You need to multiply both numbers inside the parentheses by 5:
5 times x = 5x
5 times 7 = 35
and then you'll get B
hope this helped UwU
The number of bacteria growing in an incubation culture increases with time according to B() 9800 (3)x, where x is time in days. After how many days will the number of bacteria in the culture be 7,144,200?
After approximately 2.4744 days, the number of bacteria in the culture will reach 7,144,200.
To find the number of days (x) after which the number of bacteria in the culture reaches 7,144,200, we need to solve the equation B(x) = 7,144,200.
The given equation for the growth of bacteria is B(x) = 9800(3)^x.
Setting B(x) equal to 7,144,200, we have:
9800(3)^x = 7,144,200
To solve for x, we can take the logarithm of both sides using base 3 logarithm:
log₃(9800(3)^x) = log₃(7,144,200)
Using logarithmic properties, we can simplify the equation:
log₃(9800) + log₃(3)^x = log₃(7,144,200)
Since log₃(3)^x is equivalent to x (since log₃(3) = 1), we can rewrite the equation as:
log₃(9800) + x = log₃(7,144,200)
Now, we can solve for x by isolating it:
x = log₃(7,144,200) - log₃(9800)
Using a calculator, we can compute the values:
x ≈ 5.2456 - 2.7712
x ≈ 2.4744
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1100 square feet of sod for $1200 OR 1000 square feet of sod for $1100
Answer:
1100 for $1200
Step-by-step explanation: it is
1200/1100 is 1.09
1100/1000 is 1.1
Answer:
Sod installation in an average 1/5-acre, or 8,712 square foot, yard costs $8,715 to $17,430. ... Expect sod installation to cost $1,000 to $6,000 for small yards that are between 1,000 and 3,000 square feet. ... Tulsa, Oklahoma, $1,100-$2,300.
This is my answer i think its correct tell me if it is..........?
Question 4
1 pts
If you double the radius of a circle, then you will quadruple the circumference of the
circle.
O True
False
Subtract ¾ from 5/6
Answer:
1/12
Step-by-step explanation:
the question is asking to subtract a from b, which is the same as asking to find a-b
answer = 5/6 - 3/4
= 10/12 - 9/12 (lowest common multiple of 6 and 4 is 12)
= 1/12
if you dont know how to find lowest common multiple by prime factorisation, you can make the common denominator 6x4 instead which is 24, so
5/6 - 3/4 = 20/24 - 18/24
=2/24 = 1/12
TOPIC: Distributive Property
Can someone tell me what number is being distributed?
Here is the picture of the expression:
-2
Its this number because its the number right outside of the ()
Answer:
-2
Step-by-step explanation:
Step 1: Write expression
3 - 2(x + 1) + 5x - 4
We see here that we have parenthesis around (x + 1) and a number in front of it. If we were to expand this:
3 - 2x - 2 + 5x - 4
We would see that we would distribute a negative 2.
A company produces mopeds and bicycles. It must produce at least 10 mopeds per month. The company has the equipment to produce only 60 mopeds. It also can produce only 120 bicycles. The production of mopeds and bicycles cannot exceed 160. The profit on a moped is $134 and on a bicycle $20. How many of each should be manufactured per month to maximize profit?
(Use x = mopeds; y = bicycles)
3. State the Objective Function in the linear programming problem given:
A. P = 20x + 134y
B. P = 134x + 20y
C. P = 60x + 120y
D. P = 120x + 60y
4. Determine the vertices of the feasible region, given the constraints. (Use Desmos to help with graphing!)
Constraints (for this linear programming problem):
A. (0, 0) F. (160,0)
B. (10,120) G. (60,100)
C. (60, 0) H. (0,120)
D. (60,120) I. (40,120)
E. (10, 0) J. (10,150)
5. How many of each product should be manufactured per month to maximize profit?
A. 60 mopeds, 120 bicycles
B. 160 mopeds, 0 bicycles
C. 60 mopeds, 100 bicycles
D. 40 mopeds, 120 bicycles
PLEASE SHOW WORK.
WILL GIVE BRAINLIEST!
THE PICTURE IS FOR QUESTION 4
Answer:
3. B. P = 134x + 20y
4. J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5. C. 60 mopeds 100 bicycles
Step-by-step explanation:
3. The given information are;
The number of mopeds the company must produce per month = 10
The number of mopeds the company can produce month = 60
The number of bicycles the company can produce per month = 120
The total sum of the produced mopeds and bicycles ≤ 160
The profit on a moped = $134
The profit on a bicycle = $20
Given that the number of moped produced = x and the number of bicycles produced = y
Therefore, we have;
Profit, P = $134 × x + $20 × y
Which gives;
B. P = 134x + 20y
4) From Desmos, using the following constraints;
x + y ≤ 160
10 ≤ x ≤ 60
0 ≤ y ≤ 120 we have;
The vertices of the constraint for the feasible region are;
J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5) We note that since the profit from each moped is more than the profit from the sale of each bicycle, the maximum possible number of moped should be produced, while the rest should be used to produce bicycles
Therefore, given that from the vertices, the maximum possible number of moped = 60, the number of bicycles to be produced should be 160 - 60 = 100 bicycles
Which gives;
C. 60 mopeds 100 bicycles.
3. The objective function should be option B. P = 134x + 20y
4. The vertices of the feasible region, given the constraints should be J(10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5. The number of each product that should be manufactured per month should be option C. 60 mopeds 100 bicycles
Objective function, vertices, and number of each product:3.
Here we assume that the number of mopeds produced = x
and the number of bicycles produced = y
So, the profit equation should be
Profit, P = $134 × x + $20 × y
That provides P = 134x + 20y
4) From Desmos, we used the following constraints;
x + y ≤ 160
10 ≤ x ≤ 60
0 ≤ y ≤ 120 we have;
So, The vertices of the constraint should be
J. (10, 150), I(40, 120), G(60, 100), C(60, 0) and E(10, 0)
5) The maximum no of mopeds should be 60
And, the no of bicycles that need to be produced is
= 160 - 60
= 100 bicycles
That provides 60 mopeds 100 bicycles.
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Solve the equation.
-3n-4n-17=25
n=?
Answer:
n=-6
Step-by-step explanation:
-3n-4n-17=25
-7n-17=25
-7n=42
n=-6
Answer:
n = -6
Step-by-step explanation:
-3n-4n-17=25
Combine like terms
-7n -17 = 25
Add 17 to each side
-7n -17+17 = 25+17
-7n = 42
Divide each side by -7
-7n/-7 = 42/-7
n = -6
I need help please
4. Use the number line to determine the measure of FI.
is in the picture of the questions
simplify the expression, answer quickly
Answer:
[tex]{7}^{3} [/tex]
Step-by-step explanation:
simplify numerator to get
[tex] {7}^{7} [/tex]
simplify denominator to get
[tex] { ({7}^{2} )}^{2} [/tex]
which simplifies to
[tex] {7}^{4} [/tex]
now that it's
[tex] \frac{ {7}^{7} }{ {7}^{4} } [/tex]
the exponents subtract to get our final answer
Answer:
Step-by-step explanation:
(16-9)^7
[(5+2)^2]^2
(16-9)^7
823543
[(5+2)^2]^2
(49)^2
2401
823543/2401 = 343
If the point (x,y) is equidistant from the points (-3,2) and (-5,-4),
prove that x+3y+7=0.
Step-by-step explanation:
i hope u can understand that
Click through and select the graph that represents the function shown in the table.
Answer:
its the last graph
Step-by-step explanation:
It the graph that represents the function given in the table is the graph [3].
What is the point slope form of the equation of a line?
The point slope form of a line is given by -
y - y₁ = m(x - x₁)
Given is a line that passes through the points (-2, 5), (0, 3), (1, 2) and (4, -1).
The general equation of the straight line is -
y = mx + c
where -
m is the slope of line
c is the y - intercept
Now -
We can calculate the slope as follows -
m = (2 - 3)/(1 - 0) = -1/1 = -1
Now, at [x] = 0, [y] = 3
Which is the y - intercept.
The equation of the line will be -
y = - x + 3
We will plot the graph and match it with the given ones.
It can be seen that graph 3 is the correct choice.
Therefore, it the graph that represents the function given in the table is the graph [3]. It is plotted and attached with the answer for reference.
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"Calculate the mean of the following data set of values:
33; 42; 49; 49; 53; 55; 55; 61; 63; 67: 68; 68; 69; 69; 72;
73; 74; 78 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94;
96;100
To calculate the mean of a data set, we need to sum up all the values and then divide by the total number of values.
Sum of the data set = 33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100
Count of values = 31
Mean = (Sum of the data set) / (Count of values)
Now we can substitute the values and calculate:
Mean = (33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100) / 31
After evaluating this expression, we find that the mean of the given data set is approximately 71.29 (rounded to two decimal places).
Therefore, the mean of the data set is 71.29.
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Paul is solving for x. He shows his work as follows:
Step 1: 3x + 2 = 7x - 2
Step 2: 2 = 4x - 2
Step 3: 4 = 4x
Step 4: X = 1
When Paul checks his answer, he thinks he’s made a mistake At which step did Paul make a mistake?
Answer:
This is correct
Step-by-step explanation:
Paul has made no mistakes but he probably is wondering if the 4x that he got in the equation is correct. He might second guess that he shouldn't have subtracted the 3x from the 7x but instead divided the two numbers.
A polygon is shown on a coordinate plane. The vertices are A at negative 6 comma 5, B at negative 6 comma 2, C at negative 2 comma 2, and D at negative 2 comma 6. If the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates. HELPPPPP
Answer:
See below
Step-by-step explanation:
Given a polygon with vertices
A(-6, 5), B(-6, 2), C(-2, 2), D(-2, 6)Translation rule is
T(5, -4)New coordinates are
A' = (-6 + 5, 5 - 4) = (-1, 1)B' = (-6 + 5, 2 - 4) = (-1, -2)C' = (-2 + 5, 2 - 4) = (3, -2)D' = (-2 + 5, 6 - 4) = (3, 2)Answer:his answer is right
Step-by-step explanation:
Help me please I need help!
Answer:
I'd say A because this question is just like y and xays.
Step-by-step explanation:
PLEASE HELP ASAP IM STUCK HELP PLEASE
Answer:
x>-2 and x<5
-2 <x<5
Step-by-step explanation:
We have open circles at -2 and 5 and are between the two numbers so we have and AND statement. It can be written either
x>-2 and x<5
or
-2 <x<5
100,000 is
times
greater than 100.
Please help me I’m in 5th grade and I need help
Answer: 100*1000
Step-by-step explanation:
You would multiply 100 by 1000. So it would be 100*1000 and it would equal 100000.
The function y = 1.5x + 2.25 can be used to determine the cost in dollars for a taxi ride of x miles.
What is the rate of
change of the cost in dollars with respect to the number of miles?
$1.50 per mile
$5.25 per mile
$4.25 per mile
$3.75 per mile
Answer:
the rate of change is $1.50 per mile
Step-by-step explanation:
this is because x is the amount of miles, so if it is $1.50 for every mile then every mile that is traveled you are to pay $1.50
Ryan needs to travel from the lighthouse to the boat dock to go on a dolphin cruise, but he only has
enough gas in his jeep to drive 30 miles. He grabs a map of the island, which shows that the distance
from the lighthouse to the boat dock is 4 inches. The map shows the scale for every half an inch on the
map is really 3 miles on the island. Use proportions to solve for the distance Ryan will need to travel on
the island. Does he have enough gas?
Island Map:
I
4 in
1/2 inch = 3 miles
Answer: 24 miles. Yes
Step-by-step explanation:
1/2in = 3 miles so 1in = 6 miles
6 x 4 = 24 so he will need 24 miles worth of gas to make it.
Answer:
2.25 miles no Ryan does not have enough gas.
Step-by-step explanation:
first draw your proportion
------------------=---------------------
Next fill it out
30 miles 2.25 miles
=
4 inches 3 miles
Then multiply 30 miles by 3 miles and you get 90
After you mutliply 30 by 3 which is 90, divide 90 by 4 and you get 2.25 miles.
Ryan only has enough gas in his jeeep to drive 30 miles he needs to travel 2.25 miles to get to the island, so he does not have enough gas to get to the island.
A fast food restaurant keeps record of the number of customer complaints per week Recently, the location has had 4 complaints per week.Assume that the number of complaints follows a Poisson distribution. What is the probability the restaurant will receive two or more complaints in the next week?
The probability that the restaurant will receive two or more complaints in the next week is approximately 0.907.
Given that a fast food restaurant keeps record of the number of customer complaints per week and it has had 4 complaints per week. Assume that the number of complaints follows a Poisson distribution. We need to find the probability that the restaurant will receive two or more complaints in the next week. To find the probability of two or more complaints in the next week, we need to subtract the probability of zero or one complaint from 1, since the sum of all probabilities is 1.
So ,P(X ≥ 2) = 1 - P(X < 2). Now, the probability of having no complaints P(X = 0) = (e^-λλ^x)/x!
Putting x = 0 and λ = 4,P(X = 0) = (e^-4 4^0)/0! = 0.0183Approximately P(X = 0) = 0.02
Now, the probability of having one complaint P(X = 1) = (e^-λλ^x)/x!
Putting x = 1 and λ = 4,P(X = 1) = (e^-4 4^1)/1! = 0.0733Approximately P(X = 1) = 0.073
So, P(X < 2) = P(X = 0) + P(X = 1)P(X < 2) = 0.02 + 0.073 = 0.093
Therefore, P(X ≥ 2) = 1 - P(X < 2)P(X ≥ 2) = 1 - 0.093P(X ≥ 2) = 0.907
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6: John has a coupon for 20% off any item in a store. What would the final cost be for an item that originally cost $15 if he uses his coupon?
Answer:
12$!❤️
Step-by-step explanation:
