Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
There are 6 students, hence n = 6.There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.The probability of one quote being chosen at least two times is given by:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
P(X < 2) = P(X = 0) + P(X = 1).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.05)^{0}.(0.95)^{6} = 0.7351[/tex]
[tex]P(X = 1) = C_{6,1}.(0.05)^{1}.(0.95)^{5} = 0.2321[/tex]
Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9672 = 0.0328[/tex]
0.0328 = 3.28% probability that at least 2 of them choose the same quote.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
The base of the rectangular prism is shaded what is the lateral surface area ( show work pls )
Answer:
126 square feet
Step-by-step explanation:
Lateral Surface Area :
Perimeter of Base x HeightPerimeter :
2(11 + 3)2(14)28 ftHeight : 4.5 ft
Solving :
LSA = PhLSA = 28 x 4.5LSA = 126 square feetWhich of these foods has a high percentage of calories from fats?
A. apples and oranges
B. carrots and eggs
C. bread and celery
D. mayonnaise and nuts
Answer:
D. mayonnaise and nuts
Step-by-step explanation:
Answer:
D. Mayonnaise and nuts
Step-by-step explanation:
Mayonnaise and nuts
How many combinations of 4 books can you choose from 6 books?
Answer:
[tex]\huge\boxed{\bf{^6C_4 = 10combinations}}[/tex]
Step-by-step explanation:
Given:-
6booksTo find:-
How many combinations of 4 books can you choose from 6 books?Ans:-
[tex]\sf \to ^6C_4 = \frac{6!}{4!(6 - 4)!} [/tex]
[tex]\sf \to ^6C_4 = \frac{6!}{4!2!} [/tex]
[tex]\sf \to ^6C_4 = \frac{\cancel6^2*5*\cancel{4!}}{\cancel{4!}\cancel{2!}} [/tex]
[tex]\sf \to ^6C_4 = 2*5 [/tex]
[tex]\sf \to ^6C_4 = 10combinations[/tex]
[tex]\: [/tex]
[tex]\huge\colorbox{blue}{BlackPain} [/tex]
10. Select all true statements.
A. All rectangles are squares.
B. All rectangles are parallelograms.
C. All rhombuses are parallelograms.
D. All squares are rectangles.
E. All squares are rhombuses.
F. All trapezoids are parallelograms.
The correct answers are:
B, D, and E.
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
A rectangle is a parallelogram with all right angles, so yes, every rectangle is a parallelogram.
A square is a parallelogram with all right angles and all congruent sides; since it is a parallelogram with all right angles, every square is a rectangle.
A rhombus is a parallelogram with all congruent sides.
Since a square is a parallelogram with all congruent sides, then every square is a rhombus.
A trapezoid is a quadrilateral with one pair of parallel sides. Since a rhombus is a parallelogram, with 2 pairs of parallel sides, rhombus are not trapezoids.
Find the volume of this prism.
41 cm?
11 cm
Answer:
41cm^2×11cm=451cm^3
Step-by-step explanation:
You need to multiply the surface of the 'base' with height
Answer: 451 cm³
Step-by-step explanation: the rule of the volume is base times height so multiply 41
times 11 so the answer is 451 . The units is to the power of 3 in finding volume of figures . The hexagon is the base and the rectangle is the height so multiply their lengths and don't forget the units . Hope this helps .
Use the information given in the figure to find the length NL. If applicable, round your answer to the nearest whole number. The lengths on the figure are not drawn accurately .
the lenghts on the figure are not
Why is the sample mean an unbiased estimator of the population mean?.
In 2009 the population of the UK estimated at 62 million. In the same year 102,000 people died. Calculate the percentage of people who died in 2009
Answer: 0.165%
Step-by-step explanation: 102,000/62,000,000, × 100%
If you have 34 cookies and eat 7 plus 4/9 how much do you have?
Answer:
26 and 5/9 are left if you eat 7 and 4/9 of 34 cookies.
Step-by-step explanation:
Answer:
15 cookies
Step-by-step explanation:
34-7=27
eat 4/9 of remaining cookies means 27÷9×4= 12 more cookies are eaten
27 - 12 = 15
Please answer the math question thankyou.
Answer:
50 cubic units
Step-by-step explanation:
The formula for volume of cube = length x width x height
so we do
5 x 5 x 2 =
25 x 2 =
50 cubic units
Hope this helps!
- profparis
Principal Time. Rate
$470. 10 days. 9%
Whats the interest?
Interest be I
If interest is daily
I=PRT/100I=470(10)(9)/100I=4230/10I=423$If interest is monthly (30days)
I=(470)(1/3)(9)/100I=470(3)/100I=1410/100I=14.10$Answer:
$ 1.20
Step-by-step explanation:
[tex]\sf Time = 10 \ days = \dfrac{10}{365}=\dfrac{2}{73}[/tex]
[tex]Interest = Principal * time *rate\\\\\\=470*\dfrac{2}{73}*\dfrac{9}{100}\\\\= 1.20[/tex]
= $ 1.20
Which polygon is a pentagon
Answer: In geometry, a pentagon is a five-sided polygon with five straight sides and five interior angles that sum up to
540
°
. A pentagon shape is a plane figure, or flat (two-dimensional) 5-sided geometric shape.
Properties of a Pentagon
1. Pentagons have five straight sides
2. Pentagons have five interior angles, which sum to
540
°
3. The five sides do not intersect
Step-by-step explanation: Hello, I have only told you the properties on how to tell if it's a pentagon, please explain or show some type of image if you still need help!
Answer: it's c
your welcome:)
Step-by-step explanation:
Three-fourths of Mrs.
Brown's class is boys.
Two-thirds of those boys
are wearing tennis shoes.
What fraction of the class
are boys with tennis shoes?
Answer:
3/12
Step-by-step explanation:
2/3 of the 3/4
=3/4×2/3
=6/12
=1/2
this is to say a half of the boys are wearing tennis shoes
since the total number of boys in the class is 3/4
1/2 of the 3/4
=3/12
Twice a number y is more than
-2.5
Answer:
2y >= 5/2
Step-by-step explanation:
When factored, the trinomials x2 + 2x − 15 and x2 + 7x + 10 have one binomial factor in common. What is this factor?
Answer:
(x+5)
Step-by-step explanation:
x^2 + 2x -15 = (x+5)(x-3)
x^2 + 7x + 10 = (x+5)(x+2)
The set of all points in a plane that lie the same distance from a single point in the plane.
Explanation:
Imagine that you have a rope staked into the ground at one end. The other end is allowed to move freely. At this freely moving endpoint, imagine white chalk is spread on the grass. The chalk would draw out a circle. Each point on the white chalk circle is the same distance away from the center.
Another example: we have a campfire and campers gather around it. The fire itself is the center. The campers would be on the edge of the circle if they are the same distance away from the fire (eg: all of them 5 feet away from the fire).
HELPP FOR BRAINLEST RIGHT NOW!!!!
Answer: Counter, 0, 0.
Step-by-step explanation:
Think about a clock. The hand of a clock goes clockwise. When you tighten something (righty tighty) you spin it clockwise. You can rotate an object, lets say a square, clockwise. You can also rotate it counterclockwise, in the other direction. Therefore, you can rotate an object clockwise and counterclockwise.
You can rotate a figure around any point, such as the center of the figure, the origin, or anywhere else. One common place to rotate a figure around, such as a square, is the origin. This is the center of the coordinate plane. This point is not up, down, left, or right at all from the center. This coordinate is (0, 0). Therefore, the next two blank spaces should both be filled with 0.
The blank spaces should look like this:
One direction is clockwise and the other is counterclockwise.
...
This can be any coordinate point such as the origin which is at ( 0 , 0 )
HELP FAST PLEASE I WILL TRY TO MARK BRAINLIEST
950 products
hope it helps...!!!
how do you calculate the average speed of a car that travels one mile at 30 mph and the second mile at 60 mph
Answer:
40mph
Step-by-step explanation:
use the speed = distance/time formula.
1. The first car has a speed of 30mph and travels one mile so the equation can be written as 30mph = 1/t.
Rearrange to get t = 1/30
1/30 of an hour is 2 minutes.
2. The second car has a speed of 60 mph and travels one mile so the equation can be written as 60mph = 1/t
Rearrange to get t = 1/60
1/60 of an hour is 1 minute.
The time it took for the total journey is 1 + 2 = 3 minutes
Writing 3 minutes as a fraction of an hour:
3/60 = 1/20
So using the s = d/t formula to calculate the average speed the formula can be written as (the speed is unknown, time is 1/20 and the distance is 2 miles):
Speed = 2/(1/20) = 2x20/1 = 40
Therefore the average speed of that car is 40 mph.
find the area of a rectangle with length 2/1 4 ft and width 2/1 3
Answer:
5 1/4
Step-by-step explanation:
2 1/4 x 2 1/3 = 21/4 = 5 1/4
Given that 1 millimeter = 1/1000 meters, 2 500 millimeters in meters is?
Answer:
2.5
Step-by-step explanation:
You can do this in an easier way than you may be thinking. You know that 1/000 is 1 mm, therefore to get 2,500, you multiply it by 2.5.
Answer:
[tex]1\ m[/tex]
Step-by-step explanation:
Step 1: Determine the total millimeters
[tex]2 * 500\ mm[/tex]
[tex]1000\ mm[/tex]
Step 2: Covert to meters
[tex]1000\ mm * \frac{1\ m}{1000\ mm}[/tex]
[tex]1\ m[/tex]
Answer: [tex]1\ m[/tex]
What is the interest rate if
$7200 is invested for 2 years and
earns $855?
A rectangular field has an area of 1,764 m2. the width of the field is 13 m more than the length. what is the perimeter of the field? 121 m 144 m 168 m 170 m
The Perimeter of the Field with a rectangular area of 1764 m² and the given width is; D: 170 m
What is the perimeter of the rectangle?We are given;
Area of rectangle; A = 1764 m²
We are told that the width of the field is 13 m more than the length. Thus;
W = L + 13
Thus;
L(L + 13) = 1764
L² + 13L = 1764
Using quadratic equation calculator;
L = 36 m
Thus;
W = 36 + 13
W = 49
Perimeter = 2(L + W)
Perimeter = 2(49 + 36)
Perimeter = 170 m
Read more about Perimeter of Rectangle at; https://brainly.com/question/24571594
Austin is participating in a 30k race. He runs at an average speed of 10 kilometers per hour and walks at an average speed of 6 kilometers per hour. He wants to complete the race in 4 hours. Let x represent the number of hours he runs. Let y represent the number of hours he walks.
What equation in standard form relates x and y to the goal of covering 30 kilometers? (no spaces)
Using the relation between velocity, distance and time, the equation that relates x and y is given by:
x + y - 3 = 0.
What is relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
In this problem, he wants to run 30 km at a rate of 10 km per hour, hence:
[tex]10 = \frac{30}{t}[/tex]
10t = 30
t = 3.
The total time is 3 hours. Considering x as the number of hours he runs and y the number of hours he walks, along with the total time, the equation is given by:
x + y = 3.
In standard form:
x + y - 3 = 0.
More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
Point p divides segment ab in the ratio AP:PB = 8:12. Which letter marks the location of point p?
A. Point k
B. Point L
C. Point M
D. Point N
The point P is located on the second partition, when segment AB is divided into 5 subsegments
How to determine the location of point P?The ratio is given as:
AP : PB = 8 : 12
Simplify the ratio i.e. divide by 4
AP : PB = 2 : 3
The above ratio means that when the segment AB is divided into 5 equal segments, the point P is located on the second partition
Note that the question is incomplete, so I provided a general explanation
Read more about line partition at:
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How many times greater is one mile than one foot?
Answer:
there are 5,280 feet in one miles
so 5,280 times greater
20 POINTS
Which of the following tables does NOT represent a function?
Answer:
C.
Step-by-step explanation:
In a function, one x-value must have just one y-value assigned to it. So in short, C is the only table that does not represent a function because it has two values of Y (-3, and -1) for one value of x (1).
A cylindrical pipe has diameter 20 cm and height 100 cm. How much water can the pipe hold?
Use 3.14 for pi.
Answer:
Step-by-step explanation:
V=pi*r^2*h
V=3.14*100*100
V=31400
Principal. Time. Rate
470. 40 days. 10%
Whats the interest?
Interest is calculated monthly here
Months=1+1/3=4/3monthsP=470R=10Interest:-
I=PRT/100I=470(4/3)(9)/100I=47(12)/10I=47(6)/556.5$Step-by-step explanation:
Interest can be calculated by formula,
» I = Prt
where,
p = principalr = annual interest ratet = time (yrs)Given:
Principal - 470Rate - 10%time - 40 daysTo find:
Interest?Solution:
Time in yrs so :- 40/365 = 8/73
Rate :- 10/100
Calculating Interest
I = Prt» I = 470* 8/73* 10/100
» I = 47* 8/73
» I = 5.15
Triangle Abc has vertices at A(0,4) B(2,10) and C(8,8). It is dilated by a scale factor of 1/4 with the origin used as the center of dilation, to produce the image A' B' C'. What are the coordinates of the verticals of the dilated image A' B' C'
Answer:
Step-by-step explanation: