The mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is and .
For Discrete Uniform Distribution the probability mass function (pmf) is denoted by P(x)=1/n , where x=1,2,3,...,n.
in the given question
The mean of the Discrete Uniform Distribution is given by [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex]
By substituting the value of P(x)=1/n
[tex]E(x)=\[\sum_{x=1}^{n}\frac{1}{n} *x\][/tex]
[tex]=\frac{1}{n}\[\sum_{x=1}^{n}x\][/tex]
[tex]=\frac{1}{n} (1+2+3+4+...n)[/tex]
[tex]=\frac{1}{n} *\frac{n(n+1)}{2}[/tex] ( as we know that sum of n terms is [tex]\frac{n(n+1)}{2}[/tex] )
=[tex]\frac{n+1}{2}[/tex]
hence , [tex]\mu=\frac{n+1}{2}[/tex] ....(i)
The Variance of the Discrete Uniform Distribution is denoted by Var(x) and is given by [tex]Var(x)=E[(x-\mu)^{2}][/tex]
As we know that [tex]E(x)=\[\sum_{x=1}^{n}p(x)*x\][/tex] similarly for E[(x-μ)²] we get
[tex]E[(x-\mu)^{2}]=E[x^{2} ]-\mu^{2}[/tex]
[tex]=E[x^{2}]-(\frac{n+1}{2} ) ^{2}[/tex] ( we have found [tex]\mu=\frac{n+1}{2}[/tex] ) ....(ii)
For E[x²]
[tex]E(x^{2} )=\[\sum_{x=1}^{n}\frac{1}{n} *x^{2} \][/tex]
[tex]=\frac{1}{n}\[\sum_{x=1}^{n} x^{2} \][/tex]
[tex]=\frac{1}{n} (1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} )[/tex]
We know that [tex]1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} =\frac{n(n+1)(2n+1)}{6}[/tex]
Substituting the value in above equation we get we get
[tex]E[x^{2} ]=\frac{1}{n} *\frac{n(n+1)(2n+1)}{6}[/tex]
[tex]E[x^{2} ]=\frac{(n+1)(2n+1)}{6}[/tex]
Substituting the value of E[x²] back in equation (ii)
We get
[tex]Var[x]=\frac{(n+1)(2n+1)}{6} -( \frac{n+1}{2})^{2}[/tex]
[tex]=\frac{(n+1)(2n+1)}{6} -\frac{(n+1)^{2} }{4}[/tex]
[tex]=(n+1)(\frac{(2n+1)}{6} -\frac{(n+1) }{4})[/tex]
taking LCM as 12 and solving further we get
[tex]=(n+1)(\frac{4n+2-3n-3}{12} )[/tex]
[tex]=\frac{(n+1)(n-1)}{12}[/tex]
[tex]=\frac{n^{2}-1 }{12}[/tex] (using identity of (a+b)(a-b) )
Therefore , the mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is [tex]\frac{n+1}{2}[/tex] and [tex]\frac{n^{2}-1 }{12}[/tex] .
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What are the solutions of the following systems? Explain.
b. 4x+y = 6 12x + 3y = 18
Ana owns a lot that contains 27 acres and is 972' wide. If she buys an adjacent lot that has the same depth but is only 648' wide, how many total acres of land will she own? select one: a. 18 b. 27 c. 45 d. 52
If Ana owns a lot that contains 27 acres and is 972' wide and if she buys an adjacent lot that has the same depth but is only 648' wide then the total acres of land she will own is c.45
First of all, we convert the acres into square feet.
As 1 acre = 43560 square feet
27 × 43560 = 1176120 square feet
Dividing it with 972' to find the depth of the lot she already owns:
1176120 / 972 = 1210 depth
As the adjacent lot has the same depth, therefore;
1210 × 648 = 784080 square feet
Converting square feet into acres by division;
784080 / 43560 = 18 acres
Now we can calculate the total acres of land she will own by addition;
total acres = 27 acres + 18 acres
total acres = 45 acres
Therefore, the total acres of land she will own is calculated to be 45.
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sunil has 40 counters
Answer:
Question:
Sunil has 40 counters. 9 of Sunil's counters are red. (c) What fraction of Sunil's counters are not red?
Answer: 0.775 or 77.5%
Step-by-step explanation:
Based on the given conditions, formulate: (40 - 9) / 40
Calculate the sum or difference: 31/40
= 31/40 = 77.5% or 0.775
What is the equation of the line that passes through the point (4,-3) and has slope 1/2 ?
F. y= (1/2)x+3
G. y= (1/2)x-1
H. y= (1/2)x-5
I. y=x-(1/2)
The equation of the line passing through the point (4 , -3) and has a slope of 1/2 is H. y = (1/2)x - 5.
The equation of a line can be expressed in different forms: standard form, slope-intercept form, and point-slope form
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Given the slope of 1/2 and a point (4 , -3), use the point-slope form to generate the equation of the line by plugging in the values in the equation.
(y - y1) = m(x - x1)
y - -3 = 1/2(x - 4)
y + 3 = (1/2)x - 2
Isolating the variable y in the left side,
y + 3 = (1/2)x - 2
y = (1/2)x - 2 - 3
y = (1/2)x - 5
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Which of the following is equal to 7^1/4?
A. 4√7
B.√7.4
C. 7^4
D. √7
Answer:
[tex] {7}^{ \frac{1}{4} } = \sqrt[4]{7} [/tex]
The correct answer is A.
Find each measure.
m∠ JLK
The measure of the major arc JLK will be 206°. Then the correct option is B.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The measure of the minor arc JK will be 154°.
Then the sum of the major arc and minor arc in a circle is 360°.
Then the major arc JLK will be given as,
JLK + JK = 360°
JLK + 154° = 360°
JLK = 206°
The measure of the major arc JLK will be 206°. Then the correct option is B.
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Under his cell phone plan, Omar pays a flat cost of $61 per month and $5 per
gigabyte. He wants to keep his bill under $70 per month. Which inequality can be
used to determine g, the maximum number of gigabytes Omar can use while staying
within his budget?
O 70 > 5g +61
O 705g + 61
O 70 <5(61+g)
O 70 > 5(61+g)
Submit Answer
Answer:
A. 70>5g+61
Step-by-step explanation:
$5 per gigabyte means $5g
$61 + 5g
he keeps his budget lower than $70 so,
5g + 61 < 70
What is the vertex of the following function?
y=4|x|+1
(4,-1)
(0,1)
(4,1)
(-4,1)
Answer:
(0,1)
Step-by-step explanation:
|x| is minimized when x=0, meaning the vertex is at (0,1).
Determine whether y varies directly with x . If so, find the constant of variation.
y=12 x
The constant of variation in y = (12) x is (12)
y = kx (Where k is the constant)
Here,
⇒ y = (12) x
So, k = (12)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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1/16 x cubed root of 2
Answer:
0.07874506561 or 0.07875
Step-by-step explanation:
cubed root of 2 = 1.25992104989
or 1.260
If f(x)=x-5, then match each of the following.
1.-5
2.0
3.-6
4.-3
5.3
6.-4
f(1)
f(-1)
f(2)
f(0)
f(5)
f(8)
Answer:
Step-by-step explanation:Given f(x)=x-5
f(-1)= -1-5
= -6
f(0)=0-5
= -5
f(1)=1-5
= -4
f(2)=2-5
= -3
f(5)=5-5
=0
f(8)=8-5
= 3
The equation d = 4 - (1/15)t represents your distance from home d for each minute you walk t .
b. Are you walking towards or away from your home? Explain. points on the line.
The graph of the equation is showing that we are walking towards our home. If the equation d = 4 - (1/15)t represents your distance from home d for each minute you walk t .
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We have given d = 4 - (1/15)t
We will use the graph tool and determine the coordinates
(see the attached image)
When t = 0, d = 4 (y-intercept)
This provide the info that at the time t = 0 the house was four units away.
When t = 60 min, d = 0 (x-intercept)
This provide the info that he was already at home at the time t = 60 minutes.
Thus, this slope proves that he was walking towards the house.
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In June, the price of a pair of inline skates is $165.
The price changes each of the next 3 months.
Month
June
July
August
September
Price of Skates
= $165
165
165+ (-12) = $_
165 + 2(-12) = $_
165+3(-12) = $_____
b.
Describe the change in the price of the inline skates for
each month.
alf ach ai
c.
The table at the right shows the amount of money you
save each month to buy the inline skates. Do you have
enough money saved to buy the inline skates in August?
September? Explain your reasoning.
June
July
August
September
$35
$55
$45
$18
The change in price of the inline skates for the month of July is $153, August is $141 and September is $129 and using the mathematical operations we conclude that we cannot buy the inline skates after savings in the month of August
As per the question statement, we are supposed to find the change in price of the inline skates when price of the inline skates for the month of June is $165.
Using mathematical operations,
Price In July =165+(-12)=153 dollars
Price In August =165+2(-12)=165-24=141 dollars
Price In September =165+3(-12)=165-36=129 dollars
Also in the second part of question asks that whether we will be able to buy the skates in the month of August if we save $[tex]35[/tex] in June, $[tex]55[/tex] in July, $[tex]45[/tex] in August and $[tex]18[/tex] in September.
Price of Skates in August = $141
Using mathematical operations,
Total savings tlll August =35+55+45=135$dollars
As the savings is less than the price of Skates in August, we CANNOT buy the inline skates in the month of August.
Mathematical operations: Combinations combining of Addition, subtraction, multiplication or division for solving any given situation using the given numbers and equations.To learn more about such question, click on the link given below:
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Determine whether ΔA B C ≅ ΔX Y Z . Explain. A(3,-1), B(3,7), C(7,7), X(-7,0), Y(-7,4), Z(1,4)
By SSS (Side, side, side) congruency;
⇒ ΔA B C ≅ ΔX Y Z .
Given that;
The vertices of ΔA B C are;
A (3, -1) , B (3, 7) and C (7, 7)
The vertices of ΔX Y Z are;
X (-7, 0), Y (-7, 4), Z (1, 4)
We have to prove that ΔA B C ≅ ΔX Y Z .
What is congruency in triangle?
If all three corresponding sides are equal and all the three corresponding angles are equal in measure, then Two triangles are said to be congruent.
Now,
The vertices of ΔA B C are;
A (3, -1) , B (3, 7) and C (7, 7)
The vertices of ΔX Y Z are;
X (-7, 0), Y (-7, 4), and Z (1, 4)
To prove ΔA B C ≅ ΔX Y Z we use distance formula and prove all sides are equal.
In ΔA B C;
Distance between A and B;
[tex]D_{AB} = \sqrt{(3-3)^2 + (7 -(-1))^2} = \sqrt{64} = 8[/tex]
Distance between B and C;
[tex]D_{BC} = \sqrt{(7-3)^2 + (7 -7)^2} = \sqrt{16} = 4[/tex]
Distance between C and A;
[tex]D_{CA} = \sqrt{(7-3)^2 + (7 -(-1))^2} = \sqrt{80}[/tex]
In ΔX Y Z;
Distance between X and Y;
[tex]D_{XY} = \sqrt{(-7-(-7))^2 + (4 -0)^2} = \sqrt{16} = 4[/tex]
Distance between Y and Z;
[tex]D_{YZ} = \sqrt{(-7-1)^2 + (4 -4)^2} = \sqrt{64}= 8[/tex]
Distance between Z and X;
[tex]D_{ZX} = \sqrt{(1-(-7))^2 + (4 -0)^2} = \sqrt{80}[/tex]Clearly, Distance between sides of ΔA B C and ΔX Y Z are;
[tex]D_{AB} = D_{YZ} \\\\D_{BC} = D_{XY}\\\\D_{CA} = D_{XZ}[/tex]
Hence, By SSS congruency;
⇒ ΔA B C ≅ ΔX Y Z .
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Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 25,50,75,100, ........
The sequence is an arithmetic sequence with d = 25 and the next two terms are 125, 150.
Suppose we are given a sequence: a1, a2, a3, a4, ...
To determine whether the sequence is an arithmetic, geometric, or uncategorized one, we need to check the relation between its consecutive terms.
Arithmetic sequence.
If:
a2 - a1 = a3 - a2 = a4 - a3 = constant
then the given sequence is an arithmetic sequence. Furthermore, the constant d = a2 - a1 is usually called the common difference.
Geometric sequence.
If:
a2/a1 = a3/a2 = a4/a3 = constant
then the given sequence is a geometric sequence. Furthermore, the constant r = a2/a1 is usually called the common ratio.
The given sequence is:
25,50,75,100, ........
Let us check the difference:
50 - 25 = 75 - 50 = 100 - 75 = 25.
We can, then, conclude that the sequence is an arithmetic sequence with d = 25.
To find the next two terms, add 25 to every last terms.
100 + 25 = 125
125 + 25 = 150
Hence the next two terms are: 125, 150.
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Given −47.01 × 6.2, find the product.
Answer:
-291.462
Step-by-step explanation:
My mom is a teacher lol and I have a calculator haha
Marvel consists of calcium, carbon, and oxygen in the ratio 10:3:12
a) How much carbon would you find in a 300kg piece of marvel?
b) what percentage of marble is calcium
How do I work with these ratios I'm confused
Using proportions, it is found that:
a) You would find 36 kg of carbon is a 300 kg piece of marvel.
b) 40% of marble is Calcium.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, the ratio 10:3:12 of calcium, carbon and oxygen means that:
Calcium is 10/25 of the total.Carbon is 3/25 of the total.Oxygen is 12/25 of the total.Hence for item a, the amount is given as follows:
300 x 3/25 = 36.
You would find 36 kg of carbon is a 300 kg piece of marvel.
For item b, the percentage is found as follows:
10/25 = 40%.
40% of marble is Calcium.
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2x-6(x- 3)≥5 solve for x
Answer:
[tex]x \leq \dfrac{13}{4}[/tex]
Step-by-step explanation:
Given inequality:
[tex]2x-6(x-3)\geq 5[/tex]
Expand -6(x - 3):
[tex]\implies 2x-6(x)-6(-3)\geq 5[/tex]
[tex]\implies 2x-6x+18\geq 5[/tex]
Combine like terms 2x - 6x = -4x:
[tex]\implies -4x+18\geq 5[/tex]
Subtract 18 from both sides:
[tex]\implies -4x+18-18\geq 5-18[/tex]
[tex]\implies -4x\geq -13[/tex]
Divide both sides by -1, remembering to reverse the inequality:
[tex]\implies\dfrac{ -4x}{-1}\geq \dfrac{-13}{-1}[/tex]
[tex]\implies 4x\leq 13[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x}{4}\leq \dfrac{13}{4}[/tex]
[tex]\implies x \leq \dfrac{13}{4}[/tex]
Explain why only like radicals can be added or subtracted while unlike radicals can be multiplied or divided, Under what conditiones can unlike radicals not be multiplied on divided?
Answer:
To multiply radicals with different indices, we need to find a common denominator, which is the lowest common multiple (LCM) between the roots. Once we obtain the LCM, we can multiply each root and exponent in the radicand to obtain the LCM, and rewrite as one radical
When we multiply two radicals with the same type of root (both square roots, both cube roots, and so on), we simply multiply the radicands (the expressions under the radical signs) and put the product under a radical sign
You are solving a measurement problem where the numbers 5.2187 x 10−3, 2.05 x 107, and 3.40 x 103 are multiplied. How many significant digits should the product have?
Answer:
3 because you always know your answer by the smalest number which has a digit of 3
Step-by-step explanation:
Type the missing number in this sequence:
-1, -3, -9, ___,
-81
Answer:
-27
there is a pattern of x3 every time :)
The volume of Cube A is 125 cubic inches. The face of Cube B has an area of 121 square inches. Which cube has a
greater side length?
...PLEASE HELPPP
The cube with he greater side length is: cube B.
What is the Volume and Surface Area of a Cube?Volume of a cube = a³
Surface area of a cube = 6a²
Therefore:
Volume of cube A = 125 in.³
125 = a³
√125 = a
a = 5 in.
Side length of Cube A = 5 in.
Surface area of Cube B = 121 in.²
121 = 6a²
√(121/6) = a
√(121/6) = a
10.7 = a
a = 10.7
Side length of cube B = 10.7 in.
Therefore, the cube with he greater side length is: cube B.
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In the diagram below, DGL DF. Use the diagram for questions 1-7.
1. Name the sides of 24.
2. Name the vertex of 22.
3. Give another name for 23.
4. Classify 25.
5. Classify LCDE.
6. If m25 = 42° and m/1 = 117°, find m/CDF.
7. If m/3 = 73°, m/FDE.
H5
D
4
3
G
tay
E
1.
2.
3.
4.
5
Answer:
1. Sides of ∠4 are DC and DG
2. Vertex of ∠2 = Point D
3. Another name for ∠3 = ∠EDG
4. ∠5 is an acute angle
5. ∠CDE is a straight angle
6. m ∠CDF = m∠5 + m∠1 = 42 + 117 = 159°
7. m ∠FDE = 17°
Step-by-step explanation:
For # 7 note that since DG is perpendicular to DF, m ∠GDF = 90°
m ∠GDF = m ∠3 + m ∠FDE
Since m ∠3 = 73°, m∠FDE = 90 - 73 = 17°
Write each equation in slope-intercept form. x-2 y+3=1
The slope - intercept form of the equation x-2 y+3=1 is y = x/2 + 1 .
What is slope - intercept form?Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
The slope - intercept form is y = mx + c
The given equation is
x-2 y+3=1
Subtract 3 from both sides,
x - 2y = -2
Divide the whole equation by 2
x/2 - y = -1
Rearrange the equation -
y = x/2 + 1
So the equation in slope-intercept form is y = x/2 + 1 , where slope is 1/2 and c = 1.
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The equations of four lines are given. Identify which lines are parallel.
Line 1: y=1/2x−6
Line 2: x−2y=−1
Line 3: y=4x+6
Line 4: y+3=1/4(x−6)
Answer:
Line 1 and Line 2 are parallel.
How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 4.33%? Show formulas used
Answer:
Step-by
You have to determine how much more would $10,000 earn in 3 years compounded daily at 1.33% than compounded semiannually at 4.33%.
The first step is to calculate the final amount for both options. To do so, you have to use the following formula:
Where
A is the accrued amount
P is the principal amount
r is the interest rate expressed as a decimal value
t is the time in years
n is the number of compounding periods per year.
→ First, find the accrued amount for P=$10,000, R=1.33%, and t=3 years.
The account compounds daily,
Down
Round...
1. 24.263 to the nearest tenth.
3. 341.276 to the nearest hundredth.
5. 299.61 to the nearest whole number.
6. 4,123.499 to the nearest whole number.
7. 5.246 to the nearest hundredth.
What is the average rate of change, please simplify your answer (PICTURE BELOW)
Answer:
[tex]{ \tt{average \: \triangle = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]
x1 is -1; y1 is -3 [from graph (-1, -3)]x2 is 3; y2 is 5 [from graph (3, 5)][tex]{ \tt{ = \frac{5 - ( - 3)}{3 - ( - 1)} }} \\ \\ = { \tt{ \frac{8}{4} }} \\ \\ = 2[/tex]
ABCD is a rectangle. The length of AC is 4x-8, and the length of BD is 2x+10. What is the length of one of its diagonals?
Answer:
28 units
Step-by-step explanation:
• the diagonals of a rectangle are congruent , then
AC = BD , that is
4x - 8 = 2x + 10 ( subtract 2x from both sides )
2x - 8 = 10 ( add 8 to both sides )
2x = 18 ( divide both sides by 2 )
x = 9
Then
BD = 2x + 10 = 2(9) + 10 = 18 + 10 = 28
the diagonals are 28 units long
Write a unit for:25 pounds in 10 weeks
The unit is 2.5 Pounds per week.
What is a unit?A unit of measurement is a definite magnitude of a quantity that is defined and adopted by convention or law and is used as a standard for measuring the same type of quantity. Any other such quantity can be expressed as a multiple of the unit of measurement. A length, for example, is a physical quantity.So, this is a fraction of 25 Pounds in 10 Weeks.
We want a unit rate with a denominator of one, so we divide the top and bottom by ten.
= 25 Pounds ÷ 10 Weeks= 2.5 Pounds ÷ 1 Week = 2.5 Pounds per weekTherefore, the unit is 2.5 Pounds per week.
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