A random experiment was conducted where a Person A tossed five coins and recorded the number of ""heads"". Person B rolled two dice and recorded the larger number out of the two dice. Simulate this scenario (use 10000 long columns) and answer questions 10 to 13.
Answers
Answer:
(10) Person B
(11) Person B
(12) [tex]P(5\ or\ 6) = 60\%[/tex]
(13) Person B
Step-by-step explanation:
Given
Person A [tex]\to[/tex] 5 coins (records the outcome of Heads)
Person [tex]\to[/tex] Rolls 2 dice (recorded the larger number)
Person A
First, we list out the sample space of roll of 5 coins (It is too long, so I added it as an attachment)
Next, we list out all number of heads in each roll (sorted)
[tex]Head = \{5,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,0\}[/tex]
[tex]n(Head) = 32[/tex]
Person B
First, we list out the sample space of toss of 2 coins (It is too long, so I added it as an attachment)
Next, we list out the highest in each toss (sorted)
[tex]Dice = \{2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6\}[/tex]
[tex]n(Dice) = 30[/tex]
Question 10: Who is likely to get number 5
From person A list of outcomes, the proportion of 5 is:
[tex]Pr(5) = \frac{n(5)}{n(Head)}[/tex]
[tex]Pr(5) = \frac{1}{32}[/tex]
[tex]Pr(5) = 0.03125[/tex]
From person B list of outcomes, the proportion of 5 is:
[tex]Pr(5) = \frac{n(5)}{n(Dice)}[/tex]
[tex]Pr(5) = \frac{8}{30}[/tex]
[tex]Pr(5) = 0.267[/tex]
From the above calculations: [tex]0.267 > 0.03125[/tex] Hence, person B is more likely to get 5
Question 11: Person with Higher median
For person A
[tex]Median = \frac{n(Head) + 1}{2}th[/tex]
[tex]Median = \frac{32 + 1}{2}th[/tex]
[tex]Median = \frac{33}{2}th[/tex]
[tex]Median = 16.5th[/tex]
This means that the median is the mean of the 16th and the 17th item
So,
[tex]Median = \frac{3+2}{2}[/tex]
[tex]Median = \frac{5}{2}[/tex]
[tex]Median = 2.5[/tex]
For person B
[tex]Median = \frac{n(Dice) + 1}{2}th[/tex]
[tex]Median = \frac{30 + 1}{2}th[/tex]
[tex]Median = \frac{31}{2}th[/tex]
[tex]Median = 15.5th[/tex]
This means that the median is the mean of the 15th and the 16th item. So,
[tex]Median = \frac{5+5}{2}[/tex]
[tex]Median = \frac{10}{2}[/tex]
[tex]Median = 5[/tex]
Person B has a greater median of 5
Question 12: Probability that B gets 5 or 6
This is calculated as:
[tex]P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}[/tex]
From the sample space of person B, we have:
[tex]n(5\ or\ 6) =n(5) + n(6)[/tex]
[tex]n(5\ or\ 6) =8+10[/tex]
[tex]n(5\ or\ 6) = 18[/tex]
So, we have:
[tex]P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}[/tex]
[tex]P(5\ or\ 6) = \frac{18}{30}[/tex]
[tex]P(5\ or\ 6) = 0.60[/tex]
[tex]P(5\ or\ 6) = 60\%[/tex]
Question 13: Person with higher probability of 3 or more
Person A
[tex]n(3\ or\ more) = 16[/tex]
So:
[tex]P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Head)}[/tex]
[tex]P(3\ or\ more) = \frac{16}{32}[/tex]
[tex]P(3\ or\ more) = 0.50[/tex]
[tex]P(3\ or\ more) = 50\%[/tex]
Person B
[tex]n(3\ or\ more) = 28[/tex]
So:
[tex]P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Dice)}[/tex]
[tex]P(3\ or\ more) = \frac{28}{30}[/tex]
[tex]P(3\ or\ more) = 0.933[/tex]
[tex]P(3\ or\ more) = 93.3\%[/tex]
By comparison:
[tex]93.3\% > 50\%[/tex]
Hence, person B has a higher probability of 3 or more
Related Questions
If the distance from D to D' is 10 and the distance from A to D is 5, what is the scale factor?
Answers:
1) 3
2) 2
3) 1/2
4) 1/3
Answers
Answer:
2
Step-by-step explanation:
Because 10/5 is 2
The scale factor for the given distances will be 2. The correct option is 2.
To determine the scale factor, we need to compare the distances between corresponding points in two similar figures. In this case, the distances between points D and D' in one figure and points A and D in the other figure are provided.
The scale factor is determined by dividing the distance between corresponding points in the two figures. Therefore, the scale factor can be calculated by dividing the distance from D to D' (10) by the distance from A to D (5):
Scale factor = Distance from D to D' / Distance from A to D = 10 / 5 = 2
Therefore, the correct answer is option 2). The scale factor is 2.
To know more about scale factors follow
https://brainly.com/question/30215044
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Morgan borrowed $0.35 from her mother every time she went to the gas station to buy some chips. Over the summer Morgan went to the grocery store with her mother 9 times. Write an expression using rational numbers to show how much money Morgan borrowed from her mother. Then determine how much Morgan owes her mother.
Answers
Answer:
The money borrowed by Morgan is $ 3.15.
Step-by-step explanation:
Money borrowed by Morgan to buy chips = $ 0.35
Number of times goes to the station = 9
Money borrowed by Morgan in 9 time visit to station
= 9 x $ 0.35
=$ 3.15
What is the slope of the line that passes through the points (3,2) and (-4,3)?
Answers
Answer:
slope = 1/-7
Step-by-step explanation:
We have two points which are (3,2) and (-4,3) .
To find slope , use the slope formula
m = ( y² - y¹ ) / ( x² - x¹)
Where,
m is the slope of line.( y² - y¹ ) = ( 3 - 2 )( x² - x¹) = ( - 4 - 3)substitute the values
m = ( 3 - 2 ) / ( - 4 - 3)
m = 1/-7
Hence, slope of line is 1/-7
A square pyramid has base edges of 4 cm and a slant height of 10 cm, what is its
surface area?
a. 96 cm2
b. 193 cm2
c. 240 cm2
d. 272 cm
Answers
Answer:
96 cm 2
Option A is the correct answer
Step-by-step explanation:
Please mark me as Brainliest
How many bags of concrete are needed to fill the path 1m3 requires 106 x 20kg bags of concrete The pond is 7m diameter and the path around is 2m 50mm deep
Answers
Answer:
300 Bags
Step-by-step explanation:
According to the Question,
Given that, We are laying a concrete border around a circular pond. The pond is 7 metres in diameter and is surrounded by a path 2 metres wide.The radius of the pool = 3.5 m; the overall radius including the border = 3.5 + 2 = 5.5m
The area of the concrete borderoverall area - pool area = border area(A)
A = π×5.5² - π×3.5²
A = 56.55 sq m
The concrete needs to be 50 millimetres deep.the volume of the concrete, change 50 mm to .05 m
56.55 * 05 = 2.8275 cu/meters
We are using premixed bagged concrete.1 cubic metre requires 106 x 20 kg bags.
So For the number of bags106 * 2.8275 = 299.715 ≈ 300bags
300 bags of 20 kg of premixed concrete We needhelp pls help pls help
Answers
Answer:
18.6
Step-by-step explanation:
We know a side and a angle opposite of that side
(AC and Angle B respectively).
We know another side(AB). and are trying to find a angle opposite of it.
Let use Law of Sines rules.
[tex] \frac{ac}{ \sin(angle \: b)} = \frac{ab}{ \sin(angle \: c)} [/tex]
Substitute the values in.
[tex] \frac{22}{ \sin(90) } = \frac{7}{ \sin(x) } [/tex]
Solve for sin x by taking the reciprocal of both sides.
[tex] \frac{ \sin(90) }{22} = \frac{ \sin(x) }{7} [/tex]
Remeber sin 90 =1 and multiply 7 by both sides.
[tex] \frac{1}{22} \times 7 = \sin(x) [/tex]
Take the inverse of sin to find the angle measure.
[tex] \sin {}^{ - 1} (x) = \frac{7}{22} [/tex]
The answer is
18.6
HELP PLEASE THIS IS IMPORTANT FOR MY CLASS!!1.what is the diameter in inches of a circle that has a circumference of 12 inches
Answers
Answer:
3.8 inches
Step-by-step explanation:
12 = 2 x 22/7 x r
84= 2 x 22 x r
42 = 22r
r = 1.9
2r = 3.8inches.
diameter is twice the radius
diameter = 3.8 inches
hope its right. good luck!
which expression gives the volume of a sphere with radius 4
Answers
Answer:
Expression would be (4/3) (π) (4^3)
Equation would be V = (4/3) (π) (4^3)
Step-by-step explanation:
Just plug in the radius into the volume formula!
URGENT: If θ is a second-quadrant angle and cosθ = -2/3, then tanθ = _____.
Answers
In the second quadrant, both cos and tan are negative while only sin is positive.
To find tan, we will use the following property below:
[tex] \large \boxed{ {tan}^{2} \theta = {sec}^{2} \theta - 1}[/tex]
Sec is the reciprocal of cos. If cos is a/b then sec is b/a. Since cos is 2/3 then sec is 3/2
[tex] \large{ {tan}^{2} \theta = {( - \frac{3}{2}) }^{2} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - \frac{4}{4} \longrightarrow \frac{5}{4} } \\ \large{tan \theta = \frac{ \sqrt{5} }{ \sqrt{4} } } \\ \large \boxed{tan \theta = \frac{ \sqrt{5} }{2} }[/tex]
Since tan is negative in the second quadrant. Hence,
[tex] \large{ \cancel{ tan \theta = \frac{ \sqrt{5} }{2} } \longrightarrow \boxed{tan \theta = - \frac{ \sqrt{5} }{2} }}[/tex]
Answer
tan = -√5/2Which expression is equal to 4?
Answers
Answer:
D
Step-by-step explanation:
When taking an esponent to an exponent multiply them
4 ^(1/3)^3 = 4^1 = 4
Find the area of the circle. (Picture attached). Thank you!!
Answers
Answer:
254.5cm²
Step-by-step explanation:
I assumed that the units is cm.
hope it helps!!!
PLSSS HELPPP no linkss plsss im begging
Answers
Answer:
Step-by-step explanation:
It's a quartile question.
Answers
Answer:
D. 8
Step-by-step explanation:
the upper quartile = 8
an angle is 21 degree more than twice its complement find it
QUICK
ASAP now before tomorrow Please
Answers
Answer: 67°
Step-by-step explanation:
Complementary angle refers to the angle that when added together will be equal to 90°.
Let the measurement of the angle's complement be x.
Therefore, the angles are x and 2x + 21. Since it's a complementary angle, therefore,
x + 2x + 21 = 90
3x + 21 = 90
3x = 90 - 21
3x = 69
x = 69°/3
x = 23°
Therefore, the angle will be:
= 2x + 21
= 2(23°) + 21°
= 46° + 21°
= 67°
The angle is 67°.
Simplify the trigonometric expression sin(4x)+2 sin(2x) using Double-Angle
Identities.
A. 8sin(x) cos(x) - 4 sin(x) cos(x)
B. 8sin(x) cos(x)
C. 8sin(x) cos(x) – 8 sin(x) cos(x)
D. 8 sin(x) cos' (x) +8sin(x) cos(x)
Answers
Answer:
[tex]{ \bf{ = \sin(4x) + 2 \sin(2x) }} \\ = { \bf{2 \sin(2x) \cos(2x) + 4 \sin(x) \cos(x) }} \\ { \bf{ = 4 \sin(x) \cos(x) . ({ \cos }^{2} x - { \sin}^{2} }x) + 4 \sin(x) \cos(x) } \\ = { \bf{4 \sin(x) \cos(x) ( { \cos }^{2}x - { \sin }^{2}x + 1) }} \\ = { \bf{4 \sin(x) \cos(x) }(2 { \cos }^{2} x)} \\ = { \bf{8 \sin(x) { \cos}^{3}x }}[/tex]
Choose a strategy and solve. Enter your answer using digits. You may need to use scratch paper or other objects.
Jim is helping his dad cook hamburgers for his family and friends. There are 15 people. Each person wants two hamburgers. Three people want hamburgers with cheese. Two people want hamburgers with mustard. Two people want hamburgers with ketchup. The rest want them plain. How many plain hamburgers will Jim and his dad make?
Answers
Answer They will make 30 hamburgers, 16 of them are plain
Step-by-step explanation:
30-6-4-4=16
given the function k(x) = 3x -2, k(4) equals?
Answers
Answer:
10
Step-by-step explanation:
3(4) -2 = 12 - 2 = 10
The function of f is defined by f(x)=x²-2x-24, find the range of f
Answers
Answer:
[-25, ∞) , {y|y ≥ -25}
Step-by-step explanation:
^^^
Find The Area please help me
Answers
r=3.14 r2
R=3.14x49
A=153
1.
Find the least common multiple.
20 and 12
Answers
Answer:
answer 60
Step-by-step explanation:
The LCM(12, 20) = 60.
I am so lost on this question. I’ve never heard of a matrices so I have no clue where to even start to solve this problem.
Answers
Answer:
thas multiple matrix bro
Step-by-step explanation:
The height of a certain plant can be modeled by the formula h = 4 t + 5 where h is the height in millimeters and t is the time in days.
Answers
Answer:
The dependent variable is h and the independent variable is t
Step-by-step explanation:
Given
[tex]h(t) = 4t + 5[/tex]
Required
The dependent and the independent variable
The [tex]dependent[/tex] [tex]variable[/tex]is the [tex]variable[/tex] whose value [tex]depends[/tex] on another.
In the above equation, the height (h) depends on time (t) for its value
Hence,
The [tex]depe ndent[/tex] [tex]variable[/tex] is h and the [tex]indep endent[/tex] [tex]variable[/tex] is t
look at the image for the question
Answers
Answer:
Answer is y = 6
Step-by-step explanation:
Solve for y.
Answer:
Y=6 I think but I’m not positive.
sorry if I’m wrong.
haha
get it? POSITIVE?
Expand. Your answer should be a polynomial in standard form.
8r^2(r^2-2)=
Answers
Answer:
8r^4 - 16r^2
2Step-by-step explanation:
8r^2(r^2-2)
Multiply everything inside the brackets by the term outside of it.
8r^4 - 16r^2
In triangle RST, angle R is a right angle. If TR = 6 and TS = 8, what is the length of RS
Answers
Answer:
RS = 2[tex]\sqrt{7}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
RS² + RT² = TS² , that is
RS² + 6² = 8²
RS² + 36 = 64 ( subtract 36 from both sides )
RS² = 28 ( take the square root of both sides )
RS = [tex]\sqrt{28}[/tex] = [tex]\sqrt{4(7)}[/tex] = 2[tex]\sqrt{7}[/tex] ≈ 5.3 ( to 1 dec. place )
For the question my answer was -1 but other people were saying the answer was 53. This is my proof that the answer is -1.
Answers
Answer:
53 is the correct answer
Step-by-step explanation:
Your error is the first step
for x = 3
(3x)² = (3 * 3)² = 9² = 81
Complete the square to rewrite y=x2 - 6x + 2 in vertex form. Then state whether the vertex is a maximum or a minimum and give its coordinates.
A. Maximum at (-3, -7)
B. Maximum at (3,-7)
C. Minimum at (3, -7)
D. Minimum at (-3, -7)
Answers
Answer:
C is the Answer
Step-by-step explanation:
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Answer:
C) Minimum at (3,-7)
Step-by-step explanation:
[tex]y=x^2-6x+2[/tex]
[tex]0=x^2-6x+2[/tex]
[tex]0+7=x^2-6x+2+7[/tex]
[tex]7=x^2-6x+9[/tex]
[tex]7=(x-3)^2[/tex]
[tex]0=(x-3)^2-7[/tex]
[tex]y=(x-3)^2-7[/tex]
Because the parabola opens upward, the vertex is the minimum of the function. Therefore, the vertex is the minimum at (3,-7).
Solve for x.
3:12 = x:16
64
4
2 1/4
Answers
Hi!
i think We can set up a proportion to solve this
\frac{3}{12} \frac{x}{16}
12
3
16
x
Cross multiply
3 x 16 = 48
48/12 = 4
The answer is 4
Hope this helps! :)
Which property is shown in the matrix addition below?
0 -5.5
0
5.5
0
0
6
19.4 +-6
-6 -19.4
0
0
0
0
0
0
0 0
Answers
Answer:
additive inverse properties
Find the area of AABC. Round your answer to the nearest tenth.
mZA = 23º, mZC = 39, b = 14.6
a. 44.5
b. 29.7
C. 49.4
d. 77.1
Answers
Answer:
the answer is 77.1
