The PMF of [tex]X[/tex] is almost geometric in nature. Let [tex]p=\frac{11}{29}[/tex]. Then
[tex]P(X = x) = \begin{cases} p & \text{if }x = 0 \\ (1-p)p & \text{if }x = 1 \\ (1-p)^2 p & \text{if }x = 2 \\ (1-p)^3p & \text{if }x = 3 \\ (1-p)^4 & \text{if }x = 4 \\ 0 & \text{otherwise}\end{cases}[/tex]
Compute the first moment/expected value.
[tex]E(X) = \displaystyle \sum_x x\, P(X=x) \\\\ ~~~~~~~~ = 0\cdot p+1\cdot(1-p)p + 2\cdot(1-p)^2p + 3\cdot(1-p)^3p + 4\cdot(1-p)^4 \approx 1.39349[/tex]
Compute the second moment.
[tex]E(X^2) = \displaystyle \sum_x x^2\, P(X=x) \\\\ ~~~~~~~~ = 0\cdot p+1\cdot(1-p)p + 4\cdot(1-p)^2p + 9\cdot(1-p)^3p + 16\cdot(1-p)^4 \approx 4.01103[/tex]
Compute the variance.
[tex]V(X) = E(X^2) - E(X)^2 \approx 2.06921[/tex]
The standard deviation is the square root of the variance.
[tex]\sqrt{V(X)} \approx \boxed{1.43848}[/tex]
Which of the following represents a rotation of △EFG, which has vertices E(4,−3), F(−7,5), and G(2,8), about the origin by 180°?
Using translation concepts, the vertices of the rectangle after the translation about the origin by 180° will be as follows:
E'(-4,3), F'(7,-5) and G(-2,-8).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The rule for a rotation of 180º about the origin is:
(x,y) -> (-x,-y).
Hence, for triangle EFG, the vertices after the translation will be given as follows:
E'(-4,3), F'(7,-5) and G(-2,-8).
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Answer:
Step-by-step explanation:
Which inequality represents all the solutions of 8(6x-7) <5(9x - 4)?
O A.
OB.
OOO
O C.
OD.
X> 12
x < 12
x> 20
x < 20
Hello,
8(6x-7) <5(9x - 4)
48x - 56 < 45x - 20
48x - 45x < -20 + 56
3x < 36
x < 36/3
x < 12
Help! please answer, an explanation would be great too.
Answer:
the top one as highlighted
Step-by-step explanation:
y=Mx+c is the equation for a straight line
C is the intercept as it is at 0 it can be dropped from the expression as adding or taking away 0 makes no difference to the end value.
m is the slope
find the square by multiplying the polynomial
(4c + 4)²
Answer:
16c² + 32c + 16
Step-by-step explanation:
(4c+4)² =
(4c+4)(4c+4) =
16c² + 16c + 16c + 16 =
16c² + 32c + 16
I think this is the answer you are looking for.
Hope this helped and have a good day
Please help me. I need to find the names for AB, DA, BC, OA, and
Answer:
AB - Diameter
DA - Tangent
BC - Chord
OA - Radius
CAB - Inscribed Angle
Can someone help me please?
Answer: Circumcenter
Step-by-step explanation: The circumcenter is the point where all perpendicular bisectors of a triangle meet. The 3 perpendicular bisectors of the 3 sides of the triangle meet at the point which is labeled in this triangle as H.
i need help on this question !!!
Answer:
C is the right answer I think
What the answers I really need to know I’m doing summer school !!
Based on the geometric figures shown, the three collinear points are:
Point APoint TPoint BWhat are collinear points?Collinear points can be defined as three or more points that all lie on the same straight line (single line). Based on the geometric figures shown in the image below, the three collinear points include:
Point APoint TPoint BAnother name for line AB is line segment BA, AT, BT, TA, TB. Also, a line in plane Z is line segment AT or line l.
Based on the image shown, the intersection of planes Z and W is line segment AT.
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Lou Ann needed to mail 150 invitations to her school play. The invitations came 6 to a package. Which number sentence could be used to find out how many packages Lou Ann needed?
Lou Ann needed 25 packages that contains all the 150 invitations.
Lou Ann needed to mail 150 invitations to her school play. The invitations came 6 to a package.
What is Statistic?The statistic is the study of mathematics which deal with relations between comprehensive data.
Here, 1 package contains 6 invitation
so 1 package = 6 invitations
total invitation= 150 invitations
now number of packages = Total invitation/ 6 invitation = 150/6
=25
Thus the required number of packages is 25.
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Determine two pairs of polar coordinates for (3,-3) when 0
The two pairs of polar coordinates for the given point (3, -3) with 0° ≤ θ < 360° are (3√2, 135°) and (3√2, 315°).
What is a polar coordinate?A polar coordinate is a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).
Next, we would determine the distance (r) and angle (θ) as follows:
r = √(3² + (-3)²)
r = √(9 + 9)
r = 3√2.
θ = tan⁻¹(-3/3)
θ = tan⁻¹(-1)
θ = 3π and 7π/4 (second and fourth quadrants).
Converting to degrees, we have:
θ = 135° and 315°.
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Complete Question:
Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°
Which expressions are equivalent? Check all that apply.
3^9
3^4
-9²
9^9
081¹
Answer:
b, c, and e
Step-by-step explanation:
a. 3^9 = 3 × 3 × 3× 3 × 3 × 3 × 3 × 3 × 3
= 27 × 27 × 27 => 19683
b. 3^4 = 3 × 3 × 3 × 3
= 9 × 9 => 81
c. -9² => 81
d. 9^9 = 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9
= 729 × 729 × 729 => 387420489
e. 81¹ => 81
b, c, and e are all equal to 81
⊱________________________________________________________⊰
Answer:
Step-by-step explanation:
[tex]\LARGE\begin{gathered}\sf{Evaluate \ All \ Expressions \ First} \\ \sf{ 3^9=19683} \\ \sf{ 3^4=81} \\ \sf{-9^2=81, \ or \ -81, \because} \\ \sf{there's \ a \ difference \ between (-9)^2 \ and \ -(9)^2} \\ \sf{(-9)^2=81 \ and -(9)^2=-81} \\ \sf{ 9^9=387,420,489} \\ \sf{0.81^1=0.81\end{gathered}[/tex]
Now, can you see the expressions that are equivalent?
⊰______________________________________________________⊱
Cαlligrαρɦγx =x=x, equals
^\circ
∘
x is 45° (45 degrees.)
To find this out, we first need to understand the properties of a rectangle. A rectangle has opposite sides that are equal, but more importantly, all 4 interior angles of a rectangle are right angles, meaning they are all 90 degrees. These can also be denoted by 4 square boxes in each corner.
When a rectangle is cut diagonally, the rectangle becomes two right triangles, but when joined together, of course make a rectangle. When they are cut diagonally, the triangles are congruent triangles by the Hypotenuse-Leg (HL) Congruence property.
To find the missing x in this angle, we must know that x is apart of a right angle, and if 45 is next to it, x must also be 45 degrees (90-45 = 45)
Hope this helped!
Select the correct answer. Write an expression to represent the sum of three times the square of a number and -7. In your expression, what is the value of the constant? (A. _7 3 B. OC. 1 D. 2 Select the correct answer .
Answer:
A. -7
Step-by-step explanation:
A woven rattan basket can hold up 6 lbs of items. A net bag of 4 oranges weighs 12 ounces. How many bags of oranges can the basket hold ?
[tex]\huge\boxed{8\ \text{bags of oranges}}[/tex]
Let's first find how many ounces the basket can hold.
1 pound is equal to 16 ounces. Multiply that to find how many ounces the basket can hold.
[tex]6\cdot16=96[/tex]
Now, divide the weight held by the basket by the weight of each bag of oranges.
[tex]96\div12=\boxed{8}[/tex]
f¹(-2)=[
f(-4)=
ff¹(-2)) = |
the ratio of boys to girls in a chorus is 5:6. which shows an equivalent ratio. Use a proportion to solve. A 10 boys to 12 girls B 15 boys to 19 girls C 20 boys to 25 girls or D 24 boys to 28 girls
The student body of 115 students want to elect a president and a vice president. How many different ways can they do that
The different ways that the students can elect a president and a vice president will be 13110.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
Given data;
Total no of students = 115
The total number of ways to elect a president = 115
If one person is elected as the president the total number of ways to elect a president = 114
The different ways that the students can elect a president and a vice president are found as;
⇒ 115 ways × 114 ways
⇒ 13110 ways
Hence the different ways that the students can elect a president and a vice president will be 13110.
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SOMEONE PLEASE HELP ME ANSWER THIS I PROMISE ITS EASY
Answer:
x = 1 19/21 the one is in front of the 19/21
Step-by-step explanation:
Exact form: x = 40/21
Decimal form: x = 1.90476190
Mixed number form: x = 1 19/21.
Answer:
Let's solve your equation step-by-step.
[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]
Step 1: Simplify both sides of the equation.
[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]
[tex]\tt{ 14 = \dfrac{3}{5}(7) + \dfrac{3}{5}(10)}[/tex]
(Distribute)
[tex]\tt{ 14 = \dfrac{21}{5} x + 6 }[/tex]
Step 2: Flip the equation.
[tex]\tt{ \dfrac{21}{5} x + 6 = 14}[/tex]
Step 3: Subtract 6 from both sides.
[tex]\tt{ \dfrac{21}{5} x + 6 - \blue{6} = 14 - \blue{6}}[/tex]
[tex]\tt{ \dfrac{21}{5} = 8}[/tex]
Step 4: Multiply both sides by 5/21.
[tex]\tt{ \left( \dfrac{5}{21}\right) \times \left(\dfrac{21}{5}x \right) = \left(\dfrac{5}{21}\right) \times (8)}[/tex]
[tex]\\[/tex]
[tex]\large\tt\purple{ x = \dfrac{40}{21}}[/tex]
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help me get these 10 questions u will have 100 points EZ
Figure AAA is a scale image of Figure BBB.
What is the value of xxx?
Quick!
HELP ASAP!!!!!!!!!!
Given: ABCD is a parallelogram, BE bisects AC and DF bisects AC.
Prove: triangle BEC is congruent to triangle DFA.
Answer:
1.) & 2.) BC and AD are congruent and parallel because in parallelogram opposite sides are equal and parallel
4.) <BCE≅<DAF because they are alternating interior angles bisected by line CA
5.) & 6.) The line BE/DF which bisects the <B/<D iS perpendicular to diagonal CA which forms the right angle
7.) Because sum of any two adjacent angles are 180
8.) This follows ASA Postulate which means that if 2 pair of angles is congruent given that they share a same side, the triangle formed will also be congruent.
Step-by-step explanation:
Take the side CA as the same side of both triangles. This side also participates on the aforementioned angles on the given. The angles <BCE≅<DAF shares the side CA which makes the angles <DFA and <BEC congruent to each other. Therefore, the two right triangles are congruent
what is the answer of these two according to this piecewise function?
f(1)=?
f(5)=?
[tex]f(1)=1^2+4\cdot1+6=1+4+6=11\\f(5)=5^2+4\cdot5+6=25+20+6=51[/tex]
The area of ∆ABC is 100 square centimeters. The area of ∆DEF is square centimeters.
The area of the similar triangle named ∆DEF is; 4 square centimeters.
How to find the area of a similar triangle?
We are given that ∆ABC is similar to ∆DEF.
The perimeter of ∆ABC is five times the perimeter of ∆DEF. Thus;
(Perimeter of ΔABC) = 5(Perimeter of ΔDEF)
Thus;
(Perimeter of ΔABC)/(Perimeter of ΔDEF) = 5
Thus, we can say that;
Scale factor, K = 5.
Since the area of ∆ABC is 100 square centimeters, Then;
(area of ∆ABC)/(area of ∆DEF) = K²
100/(area of ∆DEF) = 5² = 25.
(area of ∆DEF) = 100/25 = 4.
Thus, the area of ∆DEF is 4 square centimeters.
Complete Question is;
∆ABC is similar to ∆DEF. The perimeter of ∆ABC is five times the perimeter of ∆DEF. The area of ∆ABC is 100 square centimeters. The area of ∆DEF is square centimeters
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write the equation of a line that is perpendicular to y=3x-2 that passes trough the point (-9,5)
[tex]\huge\boxed{y-5&=-\frac{1}{3}(x+9)}[/tex]
First, we'll find the slope of the new line. The first line has a slope of [tex]3[/tex]. Take the negative reciprocal of this (Flip the numerator and denominator, then multiply by [tex]-1[/tex]) to get [tex]-\frac{1}{3}[/tex] for the new slope.
Then, we'll use the point-slope form to make the new equation, where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-5&=-\frac{1}{3}(x-(-9))\\y-5&=-\frac{1}{3}(x+9)\end{aligned}[/tex]
HELP HELP HELP HELP
HELP HELP HELP
Answer:
[tex]\sqrt{16} = 4\\[/tex]
Step-by-step explanation:
the distance formula for graph = [tex]\sqrt{x^{2} + y^{2} }[/tex]
(simplified version)
[tex]\sqrt{0^{2} + (-4)^{2} } \\\\\\\sqrt{0 + 16} \\\\\\\sqrt{16}\\\\= 4[/tex]
I hope its right TT I just looked it up here:
https://byjus.com/maths/distance-between-two-points-formula/
you should double check here as well
For f(x)=2x+1 and g(x)=x^2-7, find
◯ A.
B.
C.
D.
2x+1
3²-9
x²-7
2x+1
2x+1
ラ
x²-7
2x+1
x=-1212
(1)
(木)
Answer:
-1468955
Step-by-step explanation:
please don't forget to write down the correct questions and formula.
find f(x) of g(x)
f(x)=2x+1 and g(x)=x²-7
F of G = 2(x²-7)+1
= 2x²-14+1
= 2x²-13
according to the question x=-1212
so there for f(x) of g(x)=2(-1212)²-13
=-1468955
Write a rational expression that satisfies the following condition: non permissible values x=y, +-2
The rational expression that satisfies x = y +-2 is 2xy/(x + y)(x² - 4).
How to illustrate the expression?It should be noted that non permissible value is the value of the variable which make the denominator of the rational expression equal to zero.
Based on the information, x + y gives x - y = 0.
x = 2 gives x - 2 = 0
x = -2 gives x + 2 = 0
Ths denominator according to the condition illustrated will be (x - y)(x - 2)(x + 2) = (x - y)(x² - 4)
Then, the rational expression can be written by taking the numerator and denominator. An example will be 2xy/(x + y)(x² - 4).
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What is 2.3g as a percentage of 5.98g ? (Round the nearest whole number)
Answer:
38%
Step-by-step explanation:
2.3/5.98 x 100
= 0.38 x 100
= 38%
I write down three different positive whole numbers that add to 96. The sum of any two is divisible by the third.
What is the largest of these three numbers?
Simple
They are 64 ,0,32Sum of all three
64+0+32=96Sum of first two
64+0=64Divide by
64/322Yes Verified
Quick algebra 1 assignment for 50 points!
Experts please help, Only answer if you know the answer! :)
See below for the demonstration of (e) graphing a line using x- and y-intercepts
The graphing method to demonstrateTo solve this question, we make demonstrate (e) graphing a line using x- and y-intercepts
The learning goalsAt the end of this exercise, you should be able to graph a line using x- and y-intercepts
A brief overviewA linear equation is represented as:
Ax + By = C
Where:
y-intercept = C/Bx-intercept = C/AThis means that we plot the points (0,C/B) and (C/A, 0) on a graph and then connect the points using a straight line.
Once this is done, the line has been graphed.
For instance, a line parallel to 3x + 8y = 16 will have a slope of -3/8
An original problem to solvePlot the graph of the following equation using the intercepts
2x + 4y = 10
We have:
2x + 4y = 10
Set x = 0 to determine the y-intercept
4y = 10
Divide by 4
y = 2.5
Set x = 0 to determine the x-intercept
2x = 10
Divide by 2
x = 5
So, we have:
(5, 0) and (0, 2.5)
Plot the above points and connect the points (see attachment for graph)
An original problem to solve by another studentPlot the graph of the following equation using the intercepts
3x + 6y = 18
We have:
3x + 6y = 18
Set x = 0 to determine the y-intercept
6y = 18
Divide by 6
y = 3
Set x = 0 to determine the x-intercept
3x = 18
Divide by 3
x = 6
So, we have:
(6, 0) and (0, 3)
Plot the above points and connect the points (see attachment for graph)
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