The probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]
For this case, we've got:
A coin is flipped 8 times.To find: P(getting exactly 5 heads)Each coin flip is a bernoulli distribution as it has two possible outcomes (assuming any other outcome like coin landing standing straight etc ignored). Take success = getting head in a flip, and failure = not getting success= not getting head = getting tail as the outcome of the flip.
Now, each of those 8 flips are independent in terms of result of each other (assuming coin stays unbiased).
If we take:
X = number of heads out of those 8 flips = number of successes in those 8 bernoulli trials, then:
[tex]X \sim B(n = 8, p)[/tex]
where p is the probability of success = P(Getting head in an unbiased coin with head or tail as only possible outcomes) = 1/2 = 0.5 (as head can come in 1 way, and total outcomes is 2, all equally likely).
Thus, we get:
[tex]X \sim B(n = 8, p=0.5)[/tex]
Now, P(Exactly 5 heads in those 8 flips) = P(X = 5)
Using the probability function of the binomial distribution, we get:
[tex]P(X = 5) = \: ^8C_5(0.5)^5(0.5)^{8-5} = \dfrac{8\times 7\times 6\times 5\times 4}{5 \times 4 \times 3\times 2 \times 1} \times (0.5)^8 \approx 0.219[/tex]
Thus, the probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).
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The angle of elevation to a nearby tree from a point on the ground is measured to be 66^{\circ} ∘ . How tall is the tree if the point on the ground is 68 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
By comparing with a right triangle, we will see that the height of the tree is 62.12ft
How tall is the tree?
We can compare the situation with a right triangle. Such that the hypotenuse measures 68 ft, and an angle measures 66°.
We want to get the height of the tree, which would be the opposite cathetus, then we can use the relation:
Sin(a) = (opposite cathetus)/hypotenuse.
Sin(66°) = H/68ft
Tan(66°)*68ft = H = 62.12ft
The height of the tree is 62.12ft
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For each exercise, identify the error(s) in planning the solution or solving the
problem. Then write the correct solution.
1. Is (-5, -1) a solution of y > - x + 3?
y>-x+3
-13-5+3
-1>-2
-5>4 true (-5, -1) is a solution.
Answer: im sowwy but what are you asking lol srrry ima soopid person
Step-by-step explanation:
A scientist is studying the effect of different types of soll on the height of plants. All plants were of the
same type and were planted at the same time. The scientist randomly selected 50 plants grown in each of
5 different soil types and recorded the heights of the plants in centimeters. The box plots for the soil
samples are shown.
Plant Height (centimeters)
Sample R
Samples
Sample T
Sample U
Sample V
++++
18 19 20 21 22 23 24 25 26 27 28 29 30 31
Which box plot suggests that the median of the population differs substantially from the median of the
population for Sample R?
O A. Samples
OB. Sample T
O C. Sample U
o D. Sample V
Answer:
Sample T ( B)
30 POINTS PLEASE HELP
This table shows a proportional relationship between x and y Find the constant if personality (r). Using the value for r, enter an equation in the form y =rx
Answer:
y=rx x-3
Step-by-step explanation:
answer is 3
What percentage of 3hrs is 45 mins
Answer:
25%
Step-by-step explanation:
First convert 3 hours into minutes by multiplying 3 x 60 min/hr. This is 180 minutes. To find the percentage, divide 45 minutes by 180 minutes and then multiply by 100.
45/180=0.25x100 = 25%
The time 45 minutes is 75 percentage of 3 hours
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the percentage be represented as A
Now , the equation will be
The time be represented as p = 45 minutes
The value of p = 3/4 hours
The value of q = 3 hours
So , the percentage is A = ( p/q ) x 100
Substituting the values in the equation , we get
The percentage A = ( 3/4 ) / 3 x 100
On simplifying the equation , we get
The percentage A = ( 3/12 ) x 100
The percentage A = ( 1/4 ) x 100
The percentage A = 25 %
Hence , the percentage is 25 %
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ANSWER FOR EXTRA POINTS MUST BE CORRECT ANSWER ⭐️⭐️⭐️
you have to substitute the equation. sub y=1x-1 into the other equation.
Answer:
-y = x-1 is a fairly simple equation at least with real integers.
I hope to help you understand the process of solving it so you can apply the thinking to increasingly difficult equations. If this equation is difficult for you, I will try to explain it simply.
let's try a simple trick. If you want to solve for y, then it's helpful to remove the negative from it.
that means you need to do the same thing to the x side, but since x is already positive it needs to change to -x to balance things out.
the equation now reads y = -x+1 because we have reversed the negative and positive values on both sides of the equation.
I hope this helps simplify the thinking behind solving an equation of this nature. The two previous answers above this one are both correct, but may be just a tad more complex than you need at this moment.
Will someone please help me?
Answer:
1. ) Point Y
2.) Side YX, Side YZ
3.) Point X
4.) Side XZ
Hope this helps!
help me plss asp send everything
Answer:
D
Step-by-step explanation:
Since the cost of making backpack is $10 They have a pprfit of $30 for each one(30x)
But they also have $12,000 operaing expenses (-12,000)
And all that should be 980 or more than that (≥)
30x-12,000 ≥ 980
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
Answer:
i cant really see the screen
Step-by-step explanation:
i have attached the question below
Answer:
a. probability of 5/9
b. probability of 3/9
Step-by-step explanation:
All possible outcomes:
1 x 1 = 1
1 x 2 = 2
1 x 3 = 3
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
3 x 1 = 3
3 x 2 = 6
3 x 3 = 9
All outcomes with an even number:
1 x 2 = 2
2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
3 x 2 = 6
All outcomes with a number greater than 5
2 x 3 = 6
3 x 2 = 6
3 x 3 = 9
A savings account balance is compounded annually. If the interest rate is 2% per year and the current balance is $1,377.00 what will the balance be in 15 years?
Help me out and earn Brainliest!!
Step-by-step explanation:
Well there is no direct formula for calculating the orthocentre
well the process of finding the orthocentre is to find the altitudes of all the sides and then find their intersection points
Here in this question
The given triangle represents a right angled triangle with right angled at L(-3,2)
We know that the ortho centre in a right angled triangle is the right angled vertex
-----------------------------------------------------------------------
Hence the required orthocentre is (-3,2) and it is on the Triangle
-----------------------------------------------------------------------
Trevor has 3 baseball cards and 2 football cards. He randomly picks a
card. He then randomly picks a second card from the cards that remain.
What is the probability that Trevor selects only football cards?
Answer:
I would say he has a 25%-50% chance of probability of selecting only football cards.
If right please make brainleist for others to learn from this answer thanks!
Step-by-step explanation:
Which is the correct way to set up the equation to solve for x in this diagram?
Step-by-step explanation:
the products is the 2 parts of the segment lines are the same.
so,
5×8 = 4x
is correct (the second option).
which means
40 = 4x
x = 10
I dont understand this equation
Let's first look only at the numerator: 5x^2 - 5
Consider this question: What do both terms have in common?
The answer is 5, both terms contain a 5, so we can factor it out.
5(x^2 - 1)
Now let's look at the denominator, considering the same question: 3x^2 + 3x
This time, both terms contain a 3 and an x.
3x(x^2 + 1)
Now we are here: [ 5(x^2 - 1) ] / [ 3x(x + 1) ]
In the numerator, the binomial factors out into (x + 1)(x - 1). There is also an (x + 1) in the denominator, so those to binomials cancel out. That leaves us with the following expression:
5(x - 1) / 3x
Correct Answer: C
Hope this helps!
Jenny has six cards.
Each card has a whole number written on it so that the smallest number is 5
the largest number is 24
the median of the six numbers is 14
the mode of the six numbers is 8
Jenny arranges her cards so that the numbers are in order of size.
5,-,-,-,-,24.
(a) For the remaining four cards, write on each line a number that could be on the card.
Mean is the ratio of the sum of data to the ample size. The remaining four cards that could be on the card are 8, 8, 16 and 22
Measure of dispersionMean is the ratio of the sum of data to the ample size. Median is the middle number after rearrangement while the mode is the most occurring number.
Given the sequence of numbers in order of size as 5, _, _, _, _ 24
Since 2 number falls in the middle and the median is 14, hence:
x +y/2 = 14
Since 8 is the mode, we can assume x = 8 in order to determine "y" as shown
8+y/2 = 14
8+y = 28
y = 16
The sequence of numbers will become 5, 8, 8, 16, _ 24 (8 was repeated twice being the mode)
The last unknown number can then be any value between 16 and 24. Using 22 as the last unknown value, the remaining four cards that could be on the card are 8, 8, 16 and 22
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The area of the triangle below is 25.5 square inches. What is the length of the base?
Answer:
i got 8.5
Step-by-step explanation
i have a triangle area calculator lol..
The length of the base of the triangle is B = 8.5 inches
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the area of the triangle be A = 25.5 inches²
Let the height of the triangle be H = 6 inches
Let the base of the triangle be B
Now , area of the triangle = ( 1/2 ) x Length x Base
On simplifying , we get
25.5 = ( 1/2 ) x ( 6 ) x ( B )
On simplifying , we get
3B = 25.5
Divide by 3 on both sides , we get
B = 8.5 inches
Hence , the base of triangle is B = 8.5 inches
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Which property is 3x-6y=2(x-2y)?
Answer:
In fact, there is no such property because you've made a little mistake, I'll write a clear explanation
Step-by-step explanation:
3x-6y= 3 * (x-2y)
and not 2.
it is like dividing by 3, if you want to check try to do it backwards:
3 *(x-2y) = 3x - 6y
The following data shows the number of stage shows 20 students of a class watched in a month:
1 7 4 4 3 2 7 8 1 19 20 22 20 19 16 16 19 13 1 13
Which histogram represents this data?
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 7, the second goes to 6, the third goes to 4, and the last goes to 3.
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 3, the second goes to 4, the third goes to 6, and the last goes to 7.
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 7, the second goes to 3, the third goes to 4, and the last goes to 6.
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 3, the second goes to 7, the third goes to 6, and the last goes to 4.
The histogram that represents this data would be the histogram shown in the image below.
What is a Histogram?In a histogram, bars or bins show the frequency of a range of data points in a data distribution.
Given the data set, 1, 7, 4, 4, 3, 2, 7, 8, 1, 19, 20, 22, 20, 19, 16, 16, 19, 13, 1, 13, the groups and frequency for the data distribution would be:
0 - 5: 7
6 - 11: 3
12 - 17: 4
18 - 23: 6
Therefore, the histogram that represents this data would be the histogram shown in the image below.
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Answer:
if you are confused about the explanation of the person on top... it means the answer is C.
Step-by-step explanation:
creds to the person on top
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.
here it is !
Step-by-step explanation:
must find x and then using x to find y
Simplify: 3[(7 - 5) 2 + (20 - 19) 2] + 14
Answer:
32
Step-by-step explanation:
We first solve everything in the parenthesis. So: (7 -5) = 2 and (20 - 19) = 1. Now we change the equation:
3[(2)2 +(1)2] + 14
Then we multiply inside the brackets: 2 x 2 = 4 and 1 x 2 = 2. So the equation now looks like this:
3[ 4 + 2] + 14
Now we add:
3{6} + 14:
We multiply:
18 + 14
Finaly we add again:
18 + 14 = 32
find the sum of the interior angle
Answer:
dddddddd
Step-by-step explanation:
⭐ Question 3
I have 6 red markers, 3 blue markers, and 1 yellow marker.
What is my probability of pulling a yellow marker with my eyes closed?
Please provide a valid number and reasoning.
Answer:
1/10
Step-by-step explanation:
Because there are 10 markers and only one is yellow. so you have a one in ten chance to pull a yellow marker.
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
Answer:
1/10
Step-by-step explanation:
because there is 10 markers total and 1 of them is yellow
I will mark brainlest
Question 20
- 15 - 12 = -27
Question 21
(-15) x (-2) = + 30
Hope this helps!
Answer:
#20 is correct
#21 30
Step-by-step explanation:
#21 is (-15)(-2)
This is a multiplication problem. A negative × a negative is a positive.
15×2 = 30
-15 × -2 = 30
what is the digit 9 in this number 195,487
Answer:
90,000 is the answer to that question
Answer:
its in the 10,000 digit placement.
Step-by-step explanation:
100, 000
90,000
5,000
400
80
7
Hope this helped! Have a nice day!
Please give Brainliest when you can.
-Jaron, King of Carthya.
The volume of a cylinder is 7271 cm. If the radius is 3 cm, what is the height
of the cylinder?
3 cm
.
O A. 4 cm
B. 12 cm
C. 8 cm
D. 24 cm
Answer:
8 cm
Step-by-step explanation:
Hope it helps............
Write a story problem for the equation 25 ÷ 6.
Alice picked 25 apples from the garden and she wants to share the apples with her 6 friends. She wants to determine how many apples each friend would get.
What is division?Division is a mathematical operation taht entails grouping a number into equal parts using another number. The sign used to denote division is ÷.
Based on the sign in the question, you are to divide 25 by 6. In order to do this, group 25 into 6 groups. The result is 4 remainder 1.
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find the figure of the perimeter. Use 3.14 for pi. The figure is not to scale, round to at least one decimal place. NO LINKS!!!
Answer:
24.8 ft (1 dp)
Step-by-step explanation:
Arc length of semicircle = [tex]\pi r[/tex] (where r is the radius)
Given:
diameter = 4 ft⇒ radius = 4 ÷ 2 = 2ft[tex]\pi[/tex] = 3.14⇒ Arc length = 2 × 3.14 = 6.28 ft
Use Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex] to find the hypotenuse of the right triangle with legs 2 ft and 4 ft:
[tex]\implies 2^2+4^2=c^2[/tex]
[tex]\implies c^2=20[/tex]
[tex]\implies c=\sqrt{20}=2\sqrt{5}\:\sf ft[/tex]
Therefore:
perimeter = 6 + 6.28 + 6 + 2 + 2√5
= 24.75213596...
= 24.8 ft (1 dp)
Perimeter of semicircle
πr2π6.28#Rectangle
2(6+4)2(10)20ft-4(2)=12ftFor triangle
Use Pythagorean theorem
H²=4²+²=16+4=20H=4.5Total Perimeter
12+6.5+6.2824.78ftWHAT IS THE NTH TERM FOR 6 10 14 18 22 26 30
First term, a = 6
Common difference, d = 4
Using the formula :
an = a + (n - 1) d
an = 6 + (n - 1) 4
an = 6 + 4n - 4
an = 2 + 4n
nth term = 2+4n