The probability is P(X >= 2).
200 random people, n = 200
Let us consider the Binomial expression
i.e.,
P(X = r) = nCr*p^r*q^(n-r)
Here we have to assume that the 3 initials are equally likely events.
i.e.,
p = 1/3
q = 1 - 1/3
= 2/3
Required probability = P(X >= 2)
= 1 - [P(X = 0) + P(X = 1)]
= 1 - [200C0*(1/3)^0*(2/3)^200 + 200C1*(1/3)^1*(2/3)^199]
= 1 - [1*1*(2/3)^200 + 200*(1/3)*(2/3)^199]
= 1 - [(2/3)^200 + 200*(1/3)*(2/3)^199]
= 1 - (2/3)^200 - 200*(1/3)*(2/3)^199
Probability is truly how possibly something is to happen. every time we're unsure about the final results of an event, we will talk about the possibilities of certain consequences and how probably they are. The evaluation of events ruled by means of possibility is called records.
3 styles of probability
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What’s the length of three pieces of pipe if they all equal 72m
Answer:
72 × 3 = 216m
216 m is the combined length
I need help with this geometry question.
1st transformation: A vertical translation of the figure down by 8 units
2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units
Transformation of coordinatesTransformation is a way of changing the position of an object on an xy-plane.
For the translation
(x, y)-> (x, y-8)
It shows a vertical translation of the figure down by 8 units while the translation;
(x, y - 8) -> (-x, -y)
shows a reflection on both axis and vertical translation up the plane by 8 units
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Describe fully the single transformation which takes shape A to shape B.
You have the correct answer. Apply a 180 degree rotation around the point (0,2)
Reason:
We'll connect corners between figures A and B.
Draw a line from the upper right corner of figure A to the lower left corner of figure B. This line is in red (see diagram below).
Draw another line from the lower right corner to the upper left corner. This line is in blue.
The red and blue lines intersect at the center of rotation (0,2)
The line segments constructed consist of endpoints of "before" and "after". For instance, the upper right corner in figure A rotates to the lower left corner of figure B. This happens because of the 180 degree rotation.
Note: You can do this rotation either clockwise or counterclockwise, and you would get the same result.
Help
x =x=x, equals
^\circ
∘
degrees
The value of x in the straight line shown in the attached diagram is 64°
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
From the image:
x + 26 + 90 = 180° (sum of angles in a straight line)
hence:
x + 116 = 180
x = 64°
The value of x in the straight line shown in the attached diagram is 64°
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Distinguish arithmetic vs geometric sequences
Answer:
Arithmetic sequence
Step-by-step explanation:
The given sequence is arithmetic because it is increases gradually by 5
so the answer is "an arithmetic" and "difference" is equal to "5"
help meee please
20 points
Answer:
16 sq. yds
Step-by-step explanation:
1. Split the shape into 2
The small square is 2(2) = 4
The bigger rectangle is 3(4) = 12
4 + 12 = 16 sq. yds
These questions are in Spanish, someone who knows Spanish, the topic is mathematics, please.
(That solves it in Spanish)
The interest that Marcos will get is 50000.
How to calculate the interest?The following can be deduced from the information given:
Principal = 50000
Interest rate = 12.5%
Time = 8 years
The simple interest will be:
= (PRT/100)
= (50000 × 12.5 × 8)/100
= 50000
The amount that will be obtained after 8 years will be:
= Principal + Interest
= 50000 + 50000
= 10000
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Answer:
The interest that Marcos will get is 50000.
With out calculation the answer, is 1/3 x 7/15 greater or less than 1/3?
Answer:
it might be greater i think
Simplify the following expression.
Answer:
0y^2 + 2z^3 + 3y^3
Step-by-step explanation:
The simplified form of the expression is 0y²+2z³ + 3y³
The given expression is -1/3y² + 2/3 z³ +1/3y² +3y³+4/3z³.
In the expression y, z are the variables.
Combine the like terms:
(-1/3+1/3)y²+(2/3+4/3)z³ + 3y³
Simplify each term:
0y²+2z³ + 3y³
Hence, the simplified form of the expression is 0y²+2z³ + 3y³
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what is x over 4 equal to -7
Answer:
-28
Step-by-step explanation:
x/4= -7
4* x/4= -7*4
x= -28
To pay for a fishing boat, mai made a down payment of and took out a loan for the rest. on the loan, she paid monthly payments of for years. (a) what was the total amount mai ended up paying for the fishing boat (including the down payment and monthly payments)? (b) how much interest did mai pay on the loan?
7. Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.
The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5
How to find the equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4
Hence,
perpendicular lines follows the rule below:
m₁m₂ = -1
Hence,
5x - 3y = 4
5x - 4 = 3y
y = 5/ 3 x - 4 / 3
m₁ = 5 / 3
5/3 m₂ = -1
m₂ = - 3 / 5
Hence,
using (-4, 5)
5 = - 3 / 5 (-4) + b
5 = 12 / 5 + b
b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5
Therefore,
y = -3 / 5 x + 13 / 5
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Answer:
3x +5y = 13
Step-by-step explanation:
The equation of a perpendicular line through a given point can be obtained by swapping the x- and y-coefficients of the original line's equation, and negating one of them. The constant in the equation needs to be chosen so the equation will be true at the given point.
Form of perpendicular lineSwapping the coefficients of the given equation, we have ...
3x -5y = c . . . . . for some constant c
Negating the y-coefficient gives a perpendicular line:
3x +5y = c
Particular solutionWe want the equation to be true for (x, y) = (-4, 5), so the constant needs to be ...
3x +5y = 3(-4) +5(5) = -12 +25 = 13
The equation of the perpendicular line is ...
3x +5y = 13
__
Additional comment
This process works for equations given in any form. If you start with point-slope form or slope-intercept form, some manipulation of the result may be required to get to the form you want. Standard-form or general-form equations are the easiest to apply this method to.
Note that equations in standard form want to have a positive leading coefficient. That is why we chose to change the sign of the y-coefficient, rather than the x-coefficient.
Look at the number line below.
←
-2
-1
0
1
What point is marked on the number
line?
Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6 meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.
What is the distance between points M and N?
meters
The distance between points M and N according to the task content is; 9.8 meters.
What is the distance between points M and N?From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints of KL and JL respectively.
Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;
NM/19.6 = 7.4/(2×7.4)
NM = 19.6/2 = 9.8 meters.
This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.
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Answer: 9.8 meters
Step-by-step explanation: Trust Me!! I got the answer correct on Edge.
Q: What is the distance between points M and N?
A: 9.8 meters
You enter a room. 2 dogs, 4 horses, one giraffe, and a duck are laying on a bed. 3 chicken are flying over a chair. How many legs are on the ground?.
Answer:
28 legs are on the ground
find the slope of the line passing through the points (-5, 3) and (7, 9)
[tex] \sf{\red{Answer}}[/tex]
[tex]\sf{m = \frac{1}{2} }[/tex]
[tex] \sf{\purple{Explanation}}[/tex]
[tex] \sf{m = \frac{y_{2}- y_{1}}{m_{2} - m_{1}} }[/tex]
[tex] \sf{m = \frac{9- 3}{7- ( - 5)} }[/tex]
[tex]\sf{m = \frac{6}{7 + 5} }[/tex]
[tex]\sf{m = \frac{6}{12} }[/tex]
[tex]\sf{m = \frac{1}{2} }[/tex]
You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $8 per hour and your sales job pays $119 per hour. You need to earn at least $323 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.
A) h+ s ≥ 40 and 8h + 11s ≥ 323
B) h+ s < 40 and 8h + 11s ≤ 323
C) h + s ≤ 40 and 8h + 11s ≥ 323
D) h + s ≤ 40 and 8h + 11s < 323
Answer:
C
Step-by-step explanation:
you can only work 40 or less hours per week but you must earn greater then or equal to $323.
Reduce to simplest form
- 9/15 + 5/15
Answer: -4/15
Step-by-step explanation: Since the base denominator is the same, all we have to do is add the numerators (the denominators stay the same.)
-9 + 5 = -4 which is -4/15.
(If my answer was helpful, please mark as Brainliest. I'm trying to get to the Expert rank!)
can someone explain what to do
Answer:
8
Step-by-step explanation:
The equation of the parabola can be represented as
[tex]y = a(x + 1)(x - 5)[/tex]
for some constant a.
Since the coefficient of x² is 2, a = 2, so
[tex]y = 2(x + 1)(x - 5) \\ \\ y = 2( {x}^{2} - 4x + 5) \\ \\ y = 2 {x}^{2} - 8x + 10[/tex]
So, the answer is 8.
If P(x + 2) = x² + 3x + 1, then find P(x-1)?
A) x²+3x+1
B) x²-3x+1
C) x-2
D) X-3
Observe that
[tex]x^2 + 3x + 1 = (x^2 + 4x + 4) - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - (x + 2) - 1[/tex]
so that
[tex]P(x+2) = (x+2)^2 - (x+2) - 1 \implies P(x) = x^2 - x - 1[/tex]
Then
[tex]P(x - 1) = (x-1)^2 - (x-1) - 1 \\\\ ~~~~~~~~ = (x^2 - 2x + 1) - (x - 1) - 1 \\\\ ~~~~~~~~ = \boxed{x^2 - 3x + 1}[/tex]
Alternatively, we can avoid find [tex]P(x)[/tex] altogether and instead first write [tex]x-1[/tex] in terms of [tex]x+2[/tex] :
[tex]x - 1 = (x - 1) + 2 - 2 = (x + 2) - 1 - 2 = (x + 2) - 3[/tex]
Then
[tex]P(x - 1) = P((x + 2) - 3) \\\\ ~~~~~~~~ = (x - 3)^2 + 3 (x - 3) + 1 \\\\ ~~~~~~~~ = x^2 - 3x + 1[/tex]
GET BRAINLY! please help me figure this out
Answer: x > -1, see attached.
Step-by-step explanation:
To solve the inequality, we will isolate the x-variable.
Given:
3x - 19 > -22
Add 19 to both sides:
3x > -3
Divide both sides by 3:
x > -1
To graph, we will use an open circle since it is only greater than and not equal to. Then, we will place this circle on -1. Lastly, we will shade to the right of -1, since it is greater than -1.
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
Using translation concepts, the graph of g(x) is given as follows:
It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
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.
In this problem, the parent and translated functions are given, respectively, by:
f(x) = x².g(x) = (x - 5)² + 1.The transformations are as follows:
x -> x - 5, hence the function was shifted right 5 units.y -> y + 1, hence the function was shifted up 1 unit.f(x) has vertex at (0,0), hence g(x) will have the vertex at (5,1). When x = 2, g(x) = (2-5)^2 + 1 = 10, hence the correct statement is:
It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
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Please assist me with this question
Answer:
x+25=180 [Being sum of angle of triangles]x=180 - 25
x=155
NowX+ 144+25=180[ Being sum of angle of a triangles ]x+ 169=180
x=180-169
x=11
PLEASE HELP (ASAP)
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal.
Angle x of the triangle PQR is 53 degrees.
Angle x is gotten by alternate angle relationship.
How to find an angle in a triangle?Line AB is parallel to line CD
Therefore,
AB║CD
Hence,
62 + x = 115(alternate angles)
62 - 62 + x = 115 - 62
x = 53°
We got the angle x degrees from alternate angle relationship.
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Answer:
x = 50
Step-by-step explanation:
Angle <BPR and angle <PRD are supplementary angles so their sum is equal to 180
m<BPR + 115 = 180 subtract 115 from both sides
m<BPR = 65
angles:
<APQ, x, and <BPR form a straight line and so their sum is equal to 180
65 + x + 65 = 180 add like terms
130 + x = 180 subtract 130 from both sides
x = 50
A store pays $140 for a cell phone. The store sells the cell phone for $315. Your classmate says that the markup is 125% because $175$140=1.25. Is your classmate correct? (brainliest for correct answer)
The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the markup, since the store sells the cell phone for $315, hence:
(315 - 140)/140 * 100% = x
x = 125%
The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.
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From the diagram below, we can say that ___.
Select one:
a.
Δ CED is similar to Δ BEA by AA.
b.
Δ CED is similar to Δ BEA by ASA
c.
the two triangles are not similar
Answer: The correct answer is choice A.
Step-by-step explanation:
This is because the triangles have the same angles, but are scaled differently. Thus because of the scale, there can be no correlation between the sides. Because the triangles share point E you can see that both triangles share the same angle but also notice how lines CD and AB are parallel. This makes all angles identical proving the triangles are the same but different sizes. Concluding that choice A is correct.
Triangles L M N and L K N are connected at side L N. A line is drawn from point M to point K and intersects side L N at point P.
Examine this figure. Which two pieces of information, if true, would help to prove that ΔLMP ≅ ΔNMP by HL? Select two options.
Point P is the midpoint of MK.
Line MK is the perpendicular bisector of LN.
ML ≅ MP
ML ≅ MN
PK ≅ PK
The true statement is Line MK is the perpendicular bisector of LN and ML is ≅ MN.
What is perpendicular?Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given:
Δ LMN and Δ LKN are connected at side LN.
As per the information,
Line MK is the perpendicular bisector of LN. and ML ≅ MN.
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Answer: b and d
Step-by-step explanation:
The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
a)0 = –4.9t2 + 19.6t + 24.5
b)0 = –4.9t2 + 24.5t + 19.6
c)19.6 = –4.9t2 + 24.5t
d)24.5 = –4.9t2 + 19.6t
Answer:
s(t) = -4.9t² + 39.2t
Step-by-step explanation:
Given the projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s²
Given
g = -4.9m/s²
v0 = 39.2m/s
s0 = 0m (the initial height)
On substituting into the formula;
s(t) = gt² + v0t + s0
s(t) = -4.9t² + 39.2t + 0
s(t) = -4.9t² + 39.2t
This gives the equation that models the height
Already tried simplifying and dividing, but i didn't get the correct answer. Could a step by step explanation be provided so i know how to do this in the future?
Answer:
[tex]\sf \dfrac{x+2}{x}[/tex]
Step-by-step explanation:
Simplifying the expression:
1. Factorize each expression.
x² + 8x + 15
Sum = 8
Product = 15
Factors = 3 , 5 {When we add 3 & 5 we get 8 and when we multiply 3*5, we get 15}
x² + 8x + 15 = x² + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 3)(x + 5)
x² - 2x - 15
Sum = -2
Product = -15
Factors = 3 , (-5) {When we add 3 + (-5) =2 and when we multiply, 3*(-5) = -15}
x² - 2x - 15 = x² + 3x - 5x - 15
=x(x + 3) -5(x + 3)
= (x + 3)(x - 5)
x² + 5x = x( x + 5)
x² - 3x - 10
Sum = -3
Product = -10
Factors = 2 , (-5) {When we add 2 +(-5) = -3 and when we multiply 2 *(-5) = -10}
x² - 3x - 10 = x² + 2x - 5x - 10
=x(x + 2) - 5(x + 2)
= (x + 2)(x - 5)
2. Use KCF method and simplify.
K - keep the first fraction
C - change division to multiplication
F - Flip the second fraction.
[tex]\sf \dfrac{x^2 + 8x + 15}{x^2 - 2x - 15} \ \div \ \dfrac{x^2 + 5x}{x^2 - 3x - 10}=\dfrac{x^2 + 8x + 15}{x^2-2x - 12}*\dfrac{x^2 - 3x - 10}{x^2 + 5x}[/tex]
[tex]\sf = \dfrac{(x +3)*(x +5)}{(x+3)(x - 5)}*\dfrac{(x + 2)(x - 5)}{x(x+5)} \\\\= \dfrac{x + 2}{x}[/tex]
11. A rectangle is graphed on a coordinate plane. The coordinates for two of the
vertices of the rectangle are (-5,8) and (-5, -6). What is the distance between the
two vertices?
A
2 units
B
C
4 units
10 units
D 14 units
Answer:
D. 14 units
Step-by-step explanation:
d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-x_{1})^{2} }[/tex]
= [tex]\sqrt{(-5 - (-5))^{2} + (-6 - 8)^{2} }[/tex]
= [tex]\sqrt{0^{2} + -14^{2} }[/tex]
= [tex]\sqrt{0 +196 }[/tex]
= [tex]\sqrt{196}[/tex]
= 14