Answer:
a) W is a binomial random variable because in each trial there are only two possible outcomes, and the probability of a success is always the same.
b) 0.2013 = 20.13% probability that you win exactly 3 times.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
a. Explain why W is a binomial random variable.
For each time a duck is selected, there are only two possible outcomes. Either it has a star, or it does not. Also, after a duck is selected, it is placed back in the water which means that in each trial, the probability of finding a duck with star is the same. This is why W is a binomial random variable.
b. Find the probability that you win exactly 3 times.
Let W=the number of times you win if you play this game 10 times.
This means that [tex]n = 10[/tex]
The game claims to have 20 ducks with stars among the 100 ducks.
This means that [tex]p = \frac{20}{100} = 0.2[/tex]
We have to find P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013[/tex]
0.2013 = 20.13% probability that you win exactly 3 times.
W is a binomial random variable because in each trial there are only two possible outcomes, and the probability of a success is always the same.
There is 20.13% probability that you win exactly 3 times.
Given that,
In Tsunami Duck Pond there are 100 ducks that get pummeled by tidal waves.
The game claims to have 20 ducks with stars among the 100 ducks.
Let, W = the number of times you win if you play this game 10 times.
We have to determine,
Explain why W is a binomial random variable.
Find the probability that you win exactly 3 times.
According to the question,
A duck is selected, there are only two possible outcomes. Either it has a star, or it does not. Also, after a duck is selected, it is placed back in the water which means that in each trial, the probability of finding a duck with star is the same. This is why W is a binomial random variable.To find the probability that you win exactly 3 times.Let, W=the number of times you win if you play this game 10 times.
Therefore,
The game claims to have 20 ducks with stars among the 100 ducks.
Then, The probability that you win exactly 3 times is,
[tex]P(X =x) = \ ^nC_x \times P^{x} \times (1-p)^{n-x}[/tex]
When, x = 3 and n = 10
Therefore,
[tex]P(X =3) = \ ^{10}C_3 \times (0.2)^{3} \times (1-0.2)^{10-3}\\\\P(X =3) = \ ^{10}C_3 \times (0.2)^{3} \times (0.8)^{7}\\\\\\P(X =3) = \dfrac{10!}{7!. 3!} \times 0.008 \times 0.20\\\\P(X=3) = 0.2013 = 20.13 \ percent[/tex]
There is 20.13% probability that you win exactly 3 times.
To know more about Probability click the link given below.
https://brainly.com/question/23270039
what is the value of 1/2 the power of 6
Answer:0.0156250
Step-by-step explanation: (x)n = (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) = 1/64
What is the perimeter of ABCD?
Answer:
360°
Step-by-step explanation:
Based on what I know that the total of degrees has to be 360°. So, two sides of the rhombus have to have two acute angles and two obtuse angles. So, the Image shows that the 63° is an acute angle. So, multiply 63 by 2 which is 126. Then subtract 126 from 360 which is 234. Then, divide 234 by 2 which is 117. Lastly, add 63 with 63 and 117 with 117 which is 360.
Hopefully, you understand.
Maths-please help Factorise 3y+15
Answer:
3(y + 5)
Step-by-step explanation:
Factorization is a process which is like the opposite of expansion. It involves factoring out the common factors from the given terms.
Thus to factorize 3y + 15, we have to consider the common factor(s) of the two terms. The common factor is 3 because the two terms (i.e 3y and 15) are both divisible by 3 only.
So that:
3y + 15= 3([tex]\frac{3y}{3}[/tex] + [tex]\frac{15}{3}[/tex])
= 3(y + 5)
The outcome of the process is 3(y + 5).
50 points if its correct with brainliest!! How many times smaller will a number become if you decrease it by 20%.
Answer:
1/5 because 20% is equivalent to 20/100
Step-by-step explanation:
or 0.2 Thats what I got- sorry if I am wrong.
Answer: 0.8
Step-by-step explanation:
Decreased by 20percent is multiplying by 80 percent, or 0.8
Are these teams?
5x + 8
lik teams?
Which inequality is represented by the graph? 3 NI 5 6 4 OA. 21 - 5y 3
Answer:
a
Step-by-step explanation:
A home owner purchased the following items to repair a door one box of screws priced at $3.75 one tube of caulk priced at $3.99 two pieces of glass priced at $12.50 each what is the total price of dollars and cents The homeowner paid for these items
Answer: $20.24
Step-by-step explanation: add 3.75+3.99+12.50
22 miles in 12 hour: miles
Answer:
1.67 mph
Step-by-step explanation:
If this helped you please rate this comment, give it a like, and maybe mark it as branliest!
what is the area of this quadrilateral please help FAST!!!
C, 80 square feet.
Have a nice day!
, 4), perp. to y=-2x - 4
Answer:
+1/2
Step-by-step explanation:
If the slope of the given line is -2, the slope of a line perpendicular to the given line is the negative reciprocal of -2, or +1/2.
A dot plot is shown.
Answer:
C i think but I could be wrong
Step-by-step explanation:
Help please! Could you explain it too?
Answer:
a. Not proportional
b. Proportional;
k = ⅞
Step-by-step explanation:
A proportional relationship is usually represented in the format, y = kx. k here represents constant of proportionality. This shows that x and y are directly proportional.
a. y = -2x + 9 is not a proportional equation.
b. y = ⅞x is a proportional equation.
Constant of proportionality: k = ⅞
)) How many solutions does this equation have?
12 + 4t - 14t = -13t - 18
Answer:
t = -10
Step-by-step explanation:
Ok so,
12 - 10t = -13t -18
12 - 10t + 13t = -13t + 13t - 18
12 + 3t = -18
12 - 12 + 3t = -18 - 12
3t = -30
t = -10
hope this helps! have a good day!
Please help due tmr. Find c.
Round to the nearest tenth:
Answer:
c = 14.9 cm
Step-by-step explanation:
Applying the Law of Sines, we would have the following:
c/sin(C) = b/sin(B)
c = ??
C = 180 - (150 + 12) = 18°
b = 10 cm
B = 12°
c/sin(18) = 10/sin(12)
Multiply both sides by sin(18)
c = (10*sin(18))/sin(12)
c = 14.9 cm (nearest tenth)
Tony invests $3,000 dollars in an account earning 12% interest per year. How long will it take
him to make $3960 dollars in simple interest?
3 years
5 years
8 years
11 years
Answer: 11 years
Step-by-step explanation: 3960 divided 12%= 33,000 divided 3000=11
Answer: it will take 11 years
A car dealership increased the price of a certain car by .13% The original price was 38,600.
Answer:
$43,618
Step-by-step explanation:
Find the price of the car after this price increase. Multiplying $38,600 by 1 yields the original price, whereas multiplying it by 0.13 yields the price increase. Thus, we can answer this question by multiplying $38,600 by 1.13:
$38,600*1.13 = $43.618. This is the price for which the dealer sells the car.
The tolerance limits for a circuit breaker are Amperes. This means that any circuit breaker that breaks at an amperage less than 39.5 breaks at too low a level and any that breaks at an amperage greater than 40.5 breaks at too high a level. If a shipment of circuit breakers possesses break points that are normally distributed with mean 39.3 and standard deviation 0.2, then what percentage of the shipment is defective
Answer:
84.13% of the shipment is defective
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Normally distributed with mean 39.3 and standard deviation 0.2
This means that [tex]\mu = 39.3, \sigma = 0.2[/tex]
What percentage of the shipment is defective
Less than 39.5 or greater than 40.5.
Less than 39.5:
This is the pvalue of Z when X = 39.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{39.5 - 39.3}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
Greater than 40.5:
1 subtracted by the pvalue of Z when X = 40.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40.5 - 39.3}{0.2}[/tex]
[tex]Z = 6[/tex]
[tex]Z = 6[/tex] has a pvalue of 1
1 - 1 = 0
Total:
0.8413 + 0 = 0.8413
84.13% of the shipment is defective
I need help! This is due in 30 minutes!!!
Answer:
Complementary
Step-by-step explanation:
You are correct.
Answer:
Complementary
Step-by-step explanation:
b + a = 90 degrees.
complementary is 2 angles that add up to 90 degrees
PLEASE HELP ME 20 POINTS + BRAINLIEST
Answer:
48 ft²
Step-by-step explanation:
The question is only asking for the rectangular part, so you would do 12 • 4 = 48.
Let's say a student scored 33 on a math achievement test for which scores are normally distributed with mean
43 and standard deviation 10.
What proportion of students finished worse than her?
Answer:
15.87%
Step-by-step explanation:
We are given;
x¯ = 33
μ = 43
σ = 10
Let's first find the z-score from the formula;
z = (x¯ - μ)/σ
Thus;
z = (33 - 43)/10
z = -10/10
z = -1
From the table attached the p-value at z = -1 is p = 0.15866 ≈ 0.1587 = 15.87%
Thus, proportion of students finished worse than her is 15.87%
ABCD is a cyclic quadrilateral in which AB parallel to CD if angle D is equals to 70 degree find all the remaining angles
Answer:
angle a is 110
angle B is 110
angle C is 70
What is an equation of the line thatpasses through the point (-1,-3) and is parallel to the line 4x-y=2?
Answer:
Explanation:
First, you put the equation into the standard “slope/intercept” form.
4x -y = 2 subtract 4x from both sides ; -y = -4x + 2 Multiply by -1 :
y = 4x - 2
In this standard form we see that the slope of the line (coefficient of x) is 4. ANY line parallel to this one must thus also have a slope of 4.
y = 4x - a (generic)
ANY other combination of slope multiples and constant terms will therefore also be lines parallel to this one. The one that passes through a specific point will simply have a different constant term.
We find this by putting our point value into the equation:
3 = 4(-2) + a ; 3 = -8 + a ; a = 11
Thus, our “parallel line equation” through the point (-2,3) is:
y = 4x + 11
Answer:
y = 4x + 1
Step-by-step explanation:
first put the equation 4x-y=2 into the form y = mx + b where m is the slope and b is the y-intercept (for example, y = 2x - 1 would have 2 is the slope and -1 is the y-intercept)
4x - y = 2
subtract 4x from both sides
-y = -4x + 2
multiply both sides by -1
y = 4x - 2
That means the slope of this line is 4.
Parallel lines always have the same slope, so the slope of the new line is also 4. You can again put the new equation into the form y = mx + b. You already know that the slope is 4, so y = 4x + b.
Next, you need to find b. You know that (-1, -3) is a solution, so if you plug x = -1 and y = -3 into the equation, it should be true.
You can put that into the equation to solve for b:
-3 = 4 * -1 + b
-3 = -4 + b
1 = b
This means the equation is y = 4x + 1
3- 8 + 4(3x + 3)
+2y
Thanks!!!
Answer:
7+12x+2y
Step-by-step explanation:
3-8+(12x + 12)+2y=
-5+(12x +12)+2y=
7+12x+2y
Answer:
Simplified, your answer should be 12x + 2y + 7
Step-by-step explanation:
Hope this helps! :)
Have a nice day! ♥
The half life of a radioactive kind of cesium is 30 years. How much will be left after 120 years, if you start with 960 grams of it
Answer:
60 grams
Step-by-step explanation:
120 years / half-life of 30 years = it will grow half the size 4 times
960 * 1/2 ^ 4 = 960 * 1/2 * 1/2 * 1/2 * 1/2 = 60 grams
Graph the system of equations:
y = -2x + 5
- 3x + 3y = -12
What would this graph look like? The answer plots at (3,-1) but how would the graph lead up to that point?
Answer:
I posted a picture on the graph and how the two point intercept eachother
Step-by-step explanation:
Hope this Helped
The cost of staying in a hotel is given by the formula C=50d+20, where C is the cost in £ and d is the number of days a person stays. Find the cost of staying for:
a) 6 days
b) 2 weeks
c) If the cost is 120 then how many days the person can stay
Answer:
a) £320
b) £720
c) 2 days
Step-by-step explanation:
The question is all about inputting values and finding a result or rearranging and finding a result.
a) d = 6. C = 50(6)+20 = 320
b) d = 2x7 (7 days a week) C = 50(2x7) + 20 = 720
c) C = 120 ... 120 = 50d+20
100 =50d d = 100/50 = 2
81^3x÷3^4x=729 solve for x
Answer:
Step-by-step explanation:
x=45816 , 1.89552335
Answer:
Answer:
x=0.333333,−0.333333
Step-by-step explanation:
(813)(x) /3^4
x=729
Simplifies to:
6561x2=729
Let's solve your equation step-by-step.
6561x2=729
Step 1: Divide both sides by 6561.
6561x^2 /6561 = 729 /6561
x2= 1 /9
Step 2: Take square root.
x=±√ 1 /9
x=0.333333,−0.333333
In the figure below, AE intersects HR at L, m∠VLH=50° , and ∠HLA≅∠ELR . What is m∠ALR ? A 140° B 90° C 50° D 40°
Step-by-step explanation:
A 140
its obtuse. Hope this helps :)
Find the distance between the two points in simplest radical form.
(3, -8) and (-2,-1)
Jason walked 6 miles in 2 hours. At this same rate, what is the total number of miles Jason could hike in 9 hours?
Answer:
17 hours is the total of miles he walked
Answer:
Step-by-step explanation:
rn = 6 miles in 2 hrs
we want 9 hours
Per hour it will be 3 miles
3 miles = 1 hr
6 miles = 2 hrs
9 miles = 3 hrs
12 miles = 4 hrs
15 miles = 5 hrs
18 miles = 6 hrs
21 miles = 7 hrs
24 miles = 8 hrs
27 miles = 9 hrs
All you basically had to do is multiply the 9 hours with 3 since that's how much you get per mile, and then you get your total of 27 miles
Hope this helped!
Have a supercalifragilisticexpialidocious day!