Dr Clohessy drives to work every day, and she passes 11 traffic lights. If each traffic light works independently from each other and each have a probability of being green when DR Clohessy drives up to the light of 0.25. Use this information to answer the following questions. a) Define the random variable X of the experiment. b) What is the probability that at least two lights will be green on her morning drive through the 11 traffic lights? c) What is the probability that at least two lights will be green, given that at least one has already been green? d) What is the probability that three lights will be red through the 11 traffic lights? e) Determine the mean of X and standard deviation of X of the number of green traffic lights. f) Now suppose you are interested in the first traffic light that turns red.
Answers
The answer is given in parts:
a) Random Variable X of the experiment is defined as the number of green traffic lights Dr Clohessy passes on her way to work every day.
b) Let X be the number of green traffic lights in the 11 lights that Dr Clohessy encounters. The probability that at least two lights are green is P (X≥2), where X has a binomial distribution with n = 11 and p = 0.25.So,
P (X≥2) = 1 − P (X<2) = 1 − P (X=0) − P (X=1).
P (X=0) = (11C0) (0.25)^0 (0.75)^11 = 0.1176
P (X=1) = (11C1) (0.25)^1 (0.75)^10 = 0.2939
Therefore, P (X≥2) = 1 − P (X<2) = 1 − P (X=0) − P (X=1) = 1 − 0.1176 − 0.2939 = 0.5885.
c) Let A be the event of at least one light is green and B be the event of at least two lights are green. Then P (B|A) represents the probability that at least two lights are green given that at least one is green.
So, P (B|A) = P (A and B) / P (A)
Now,
P (A and B) = P (B) = P (X≥2) = 0.5885.
P (A) = 1 − P (no lights are green) = 1 − (0.75)^11 = 0.946
Therefore, P (B|A) = P (A and B) / P (A) = 0.5885 / 0.946 = 0.6224 ≈ 0.62
d) Let Y be the number of red traffic lights in the 11 lights that Dr Clohessy encounters. The probability that three lights will be red is P (Y=3), where Y has a binomial distribution with n = 11 and p = 0.75.
So, P (Y=3) = (11C3) (0.75)^3 (0.25)^8 = 0.2181
Therefore, the probability that three lights will be red through the 11 traffic lights is 0.2181.
e) Mean of X is µ = np = 11 x 0.25 = 2.75.
Standard deviation of X is σ = √np(1−p) = √11 x 0.25 x 0.75 = 1.369
f) Let Z be the number of traffic lights that Dr Clohessy encounters before the first red light. Then Z has a geometric distribution with p = 0.75.
P (Z=1) = 0.75, P (Z=2) = 0.75 x 0.25 = 0.1875,
P (Z=3) = 0.75 x 0.75 x 0.25 = 0.1055, and so on.
The probability that Dr Clohessy first encounters a red light at the fourth traffic light is:
P (Z≥4) = 1 − (P (Z=1) + P (Z=2) + P (Z=3)) = 1 − 0.75 − 0.1875 − 0.1055 = 0.0120.
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Related Questions
Juliana invested $3,300 at a rate of 6.25% p.a. simple interest.
How many days will it take for her investment to grow to $3,450? 1
days Round up to the next day
Answers
To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest
I = P * r * t.
I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,
Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.
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The expression (x^22) (x^7)^3 is equivalent to x^p. What is the value of p?
Answers
Answer:
x^87
Step-by-step explanation:
Multiplying x^22 and x^7 results in x^29.
Then we have:
(x^29)^3 = x^87
Recall that (a^b)^c = a^(bc) and that a^b*a^c = a^(b + c)
How do I solve this?
Answers
a)
Values of the given angles ∠A = 123° , ∠B = 123° ,∠C = 57.
Given ,
One angle of the figure as 123°.
Now,
∠C and 123° form linear pair.
So,
∠C + 123° = 180°
∠C = 57°
Now,
∠C and ∠B are pairs of interior angles on same side of transversal, thus they are supplementary.
∠C + ∠B = 180°
Substitute the value of ∠C
53° + ∠B = 180°
∠B = 127°
Now,
∠B and ∠A are vertically opposite angles.
Thus,
∠B = ∠A
So,
∠A = 127° .
Hence,
∠A= 127°
∠B = 127°
∠C = 57°
b)
Values of ∠D = 98°, ∠E = 98°, ∠F = 98° .
Given one angle as 82°
Now,
∠F and 82° form linear pair.
So,
∠F + 82° = 180°
∠F = 98°
Now,
∠D and ∠F are corresponding angles. Thus,
∠D = ∠F
∠D = 98° .
Now,
∠D and ∠E are vertically opposite angles.
Thus,
∠D = ∠E
∠E = 98°.
Hence,
∠D = 98°
∠E = 98°
∠F = 98°
c)
Values of ∠G = 75° and ∠H = 75°
Given one angle as 75° .
∠H and 75° are corresponding angles. Thus,
∠H = 75°
Now,
∠H and ∠G are vertically opposite angles.
So,
∠G = 75° .
Hence,
∠G = 75°
∠H = 75°
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An airline ticket costs $40.
The price is increased by 200%.
Work out the absolute increase.
Answers
An airline ticket costs $40. The price is increased by 200 percent. The absolute increase is $80.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Cost of airline ticket = $40.
Increase in price = 200% of $40
Absolute increase = \(\frac{200}{100}* 40 = 80\)
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1,5,9,13 generalize the pattern by finding the nth term
Answers
Answer:
an= a1 +(n-1)*4
Step-by-step explanation:
a1 = 1, a2 =5, a3 = 9, a4= 13,... an= ?
we see that each term is getting bigger so usually that will happen because of addition or multiplication-in our case add 4 to previous term
a1 = 1,
a2 = a1+(2-1) 4 = 1+4 = 5,
a3 = a1 + (3-1)*4 = a1+8 = 1 + 8 = 9,
a4= a1 + (4-1)*4 = a1 + 12 = 1+12= 13,
...
an= a1 +(n-1)*4
N+3/4=1/4 solve for n
Answers
Answer:
N = -1/2
Step-by-step explanation:
We are adding in this, so we need to do the opposite to both sides, to get N by itself.
N + 3/4 - 3/4 = 1/4 - 3/4
N = -2/4 or, simplified, -1/2
25) A father is twice as old as his son. The sum oth of the ages is 99 years. Find their ages.
Answers
Answer:
If the son’s age is x, the father’s age is 2x.
If the son’s age is x, the father’s age is 2x.Ten years ago:
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 52
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 52
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 24
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48
If the son’s age is x, the father’s age is 2x.Ten years ago:(x - 10) + (2x - 10) = 523x + 20 = 523x = 72x = 242x = 48So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.
Hope this answer helps you..!!.
.
Select this answer as the BRAINLIESTf(x)=(-x)^3 -x^2-x+13f(0)f(2)f(-2)f(1)+f(-1)The problem is find the function valuesFind function values
Answers
f(0) = 13
f(2) = -1
f(-2) = 19
f(1) + f(-1) = 24
Explanation:\(f\mleft(x\mright)=\mleft(-x\mright)^3-x^2-x+13\)for f(0): we will substitute x with 0 in the function
\(\begin{gathered} f(0)=(-0)^3-(0)^2\text{ - 0 + 13} \\ f(0)\text{ = 0 - 0 - 0 + 13} \\ f(0)\text{ = 13} \end{gathered}\)for f(2): we wil substitute x with 2 in the function
\(\begin{gathered} f(2)=(-2)^3-(2)^2-2+13 \\ f(2)\text{ = -8 -4-2 + 13} \\ f(2)\text{ = -1} \end{gathered}\)for f(-2): we will substitute x with -2 in the function
\(\begin{gathered} f\mleft(-2\mright)=\mleft(-(-2)\mright)^3-(-2)^2-(-2)+13 \\ f(-2)=(2)^3-4+2+13\text{ = 8-4+2+13} \\ f\mleft(-2\mright)=\text{ 19} \end{gathered}\)for f(1) + f(-1): we will find f(1) and f(-1) seperately, then we will sum the result
\(\begin{gathered} f(1)=(-1)^3-(1)^2-(1)+13 \\ f(1)\text{ = -1-1-1 + 13} \\ f(1)\text{ = 10} \\ \\ f(-1)=(-(-1))^3-(-1)^2-(-1)+13 \\ f(-1)=(1)^3-1+1+13 \\ f(-1)=\text{ 14} \end{gathered}\)\(\begin{gathered} f(1)\text{ + f(-1) = 10 + 14} \\ f(1)\text{ + f(-1) = 24} \end{gathered}\)Select all statements that are true about the intersection of a cone and a plane.
Answers
It will be either Options A, D and E are correct.
What does it mean that a cone intersected a plane?When a plane cuts a solid, such as a cone, cylinder, or sphere, it creates a shape known as a cross-section. Depending on how the plane cuts the cone, the cross-section of a solid, such as a cone, can be a circle, a parabola, or a triangle.
Given:
A cone is intersected by a plane.
A cone that is crossed by a plane
When the cone intersects the plane, we must determine the shape of the cross-section.
When the Plane intersects the cone parallel to the base, the resulting cross-section is circular in shape.
When the plane intersects the cone at an angle, the resulting cross section is of parabola shape.
As a result, choices A, D, and E are correct.
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A manufacturer of spiral notebooks finds that about 8 out of every 500 notebooks are defection. if they produce 2,500 notebooks every day, how many defective notebooks can they expect to find during a 5 day work week?
LINKS AND FUNNY COMMENTS WILL BE REPORTED!
Answers
Answer:
200 notebooks
Step-by-step explanation:
Provided Information:
1) 8 out of every 500 notebooks contain a defect
2) 2500 notebooks are produced per day
We need to find out how many defective notebooks are produced per day:
1) 2500 ÷ 500 = 5
2) 8 x 5 = 40
Next we need to find out how many notebooks are defective per week:
1) 40 x 5 = 200 defective notebooks per week
Which of the following fraction is closest to 0? a. 5/12
b. 2/3
c. 5/6
d. 3/4
Answers
Answer:
(a) 5/12
Step-by-step explanation:
to solve this problem you can make all fractions equivalent with 12 as the denominator
a) 5/12
b) 2/3 = 8/12 Multiply top and bottom by 4
c) 5/6 = 10/12 Multiply top and bottom by 2
d) 3/4 = 9/12 Multiply top and bottom by 3
if you compare numerators, the smallest one is the closest to zero, which would be (a) 5/12
Answer:
A 5/12
Step-by-step explanation:
first you need to round these all to /12 so a is 5/12
12/3 is 4 so multiply 4 by two which means b is 8/12
12/6 is 2 so multiply 5 by two which gives us c = 10/12
12/4 is 3 and multiply 3 x 3 which is 9 so d is 9/12
5 is the lowest decimal/fraction which makes it the closest to 0
whoever can answer BOTH of these question will receive brainliest.
Answers
Second one is 120
PLEASE HURRY TEST QUESTION LIMITED TIME!!
Question- The equation x^2 + y^2 - 4x + 2y= b , describes a circle
(PART A) Determine the y coordinate of the center of the circle
(PART B) The radius of the circle is 7 units. What is the value of b in the equation?
Answers
The y coordinate of the center of the circle is k=-1 and The radius of the circle is 7 units, the value of b in the equation is 49.
What do you mean by circle?A circle is a two-dimensional, symmetrical figure in mathematics. The circle's center is a place inside the circle from which all points on the circle's edge are equally far.
The radius of the circle, abbreviated "r," is the distance from the center of the circle to a point on its edge.
The diameter of the circle, which is the greatest chord of any circle, is equal to the circle's doubled radius.
2 Radius times diameter Half of the circle is represented by the semicircle, and one-fourth by the circle's quadrant.
(PART A) To determine the y-coordinate of the center of the circle, we need to complete the square for both x and y. The equation can be transformed to the standard form for a circle: (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.
First, complete the square for x:
x² - 4x + 4 = 4 + (x² - 4x)
x² - 4x + 4 + 4 = 4 + (x² - 4x) + 4
(x-2)² = (x² - 4x + 4) + 4
Next, complete the square for y:
y² + 2y + 1 = 1 + (y² + 2y) + 1
(y+1)² = (y² + 2y) + 1
Now, substitute the completed squares back into the original equation:
(x-2)² + (y+1)² = b
So, the y-coordinate of the center is k = -1.
(PART B) The radius of the circle is 7 units, so r = 7. Substitute this value and the coordinates of the center into the standard form of the equation:
(x-2)² + (y+1)² = 49
Finally, simplify to find the value of b:
b = 49.
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PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS
Answers
you can substitute x with x and substitute y with y
for example:
x = 2 y = 54
54 = 2 + 52
54 = 54
it’s true
Please answer either or all of them and please show me how you solve it
Answers
Answer:
Step-by-step explanation:
using pythagoras theorem
a^2 + b^2 = c^2
4^2 + y^2 = 21^2
16 + y^2 = 441
y^2 = 441 - 16
y^2 = 425
\(y = \sqrt{425}\)
\(y = 5\sqrt{17}\)
y = 13.2
a^2 + b^2 = c^2
4^2 + x^2 = 7^2
16 + x^2 = 49
x^2 = 40 - 16
x^2 = 33
x = \(\sqrt{33}\)
x = 5.7 m
Convert the following fraction to a decimal: ⅖ *
Answers
Work out the median for each group of numbers.
3, 5, 7, 7, 8, 10, 11, 11, 14
10, 11, 13, 14, 16, 18, 20, 20
3, 4, 6, 6, 6, 7, 8, 9, 10
41, 43, 44, 46, 48, 49, 50, 50, 53, 54
Answers
Answer:
its 11.
hope it helps!!
Answer:
1stone is 8
2nd one is 15
3rd one is 6
4th one is 48.5
TRUE / FALSE. 1:24,000 is an example of a verbal statement. group of answer choices
Answers
Answer:
False.
Step-by-step explanation:
The statement "1:24,000" is not an example of a verbal statement. It is a numerical ratio or scale commonly used in cartography and map scales. Verbal statements typically involve spoken or written language rather than numerical representations. :)
When a random representative sample is drawn from a population, the procedure is deemed to be what type of sample?
Answers
The procedure which is deemed to be the type of sample in discuss is; representative sample are free of bias.
What is a random sampling?Representative sampling and random sampling are two techniques used to help ensure data is free of bias. A representative sample on the other hand is a group or set chosen from a larger statistical population according to specified characteristics. A random sample is a group or set chosen in a random manner from a larger population.
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pls help mepls pls pls pls pls pls
Answers
The expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a expression with a coefficient of 10 and a constant of 5.
The expression with a coefficient of 10 and a constant of 5 is given by -
10x + 5
Therefore, the expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
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Write the equation of the line shown in the table below in slope intercept form.
I"VE BEEN STUCK ON THIS ASSIGNMENT ALL DAY
Answers
Answer:
i think it might be y=0.6x - 2
y=3/5x-2 is the equation of the line shown in the table in slope intercept form
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Let us consider any two values
(5,1) and (10, 4)
m=4-1/10-5
=3/5
Now let us find the y intercept
1=3/5(5)+b
1=3+b
b=-2
So the slope intercept form is y=3/5x-2
Hence, y=3/5x-2 is the equation of the line shown in the table in slope intercept form
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Find the solution point(s) for the system of equations given by y = 2x^2 + 5x – 10 and 4x – y = –11
Answers
Answer:
the solution points for the system of equations are (3, 25) and (-7/2, -7).
Step-by-step explanation:
We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:
Substitute y = 2x^2 + 5x - 10 into the second equation:
4x - (2x^2 + 5x - 10) = -11
Simplifying the left side of the equation:
4x - 2x^2 - 5x + 10 = -11
Rearranging the terms:
2x^2 - x + 21 = 0
Using the quadratic formula:
x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)
x = (1 ± sqrt(169)) / 4
x = (1 ± 13) / 4
Simplifying:
x = 3 or x = -7/2
Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:
For x = 3:
y = 2(3)^2 + 5(3) - 10 = 25
So one solution point is (3, 25).
For x = -7/2:
y = 4(-7/2) + 11 = -7
So the other solution point is (-7/2, -7).
Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).
define the term perpendicular
Answers
Answer:
Perpendicular refers to that which has a right angle in relation to the intersection of two lines or planes. ... As seen in the Cartesian plane, what defines a line as perpendicular is its point of intersection with another line.
Step-by-step explanation:
This is Evaluating Functions.Replace the X values with the number in the question ("Find f( )" )
Answers
Given the following function:
f(x) = 3x - 3
Let's determine the value at f(-3),
This means that we will be replacing all x variables of f(x) by -3.
We get,
f(x) = 3x - 3
f(-3) = 3(-3) - 3
= -9 - 3
f(-3) = -12
Therefore, f(-3) = -12
Given the following function:
f(x) = 3x - 3
Let's determine the value at f(-3),
This means that we will be replacing all x variables of f(x) by -3.
We get,
f(x) = 3x - 3
f(-3) = 3(-3) - 3
= -9 - 3
f(-3) = -12
Therefore, f(-3) = -12
I need to finish please heeelllpppp
Answers
Answer:
Hey you helped me with a different would u mind helping me with more?
Step-by-step explanation:
The value of m, where m is an integer, is located
between 11 and 12 on the number line. What would
be an acceptable value for m?
Answers
Step-by-step explanation:
m>11<12.
This mean the value of m must be greater than 11 but less than 12.
Which statement is true? Question 5 options: A) –|3| = 3 and |4| = 4 B) |–3| = 3 and |–4| = –4 C) |–3| = 3 and –|–4| = –4 D) |–3| = 3 and –|4| = 4
Answers
A and D are true since an absolute value can only be equal to a real number.
if the negative is inside the absolute value it’s positive but if it’s outside the answer will be negative
Select the correct answer. (And pls no link)
Compare the two functions.
f(x)= 1/50(3)^x
g(x)=1/5x^2
Answers
Answer:
20 is right
Step-by-step explanation:
to easy I know maths
Answer:
When your comparing the two functions.
F(x)= 1/50(3)^x
G(x)=1/5x^2
When you compare it i think it would be C
PLEASE DONT QUOTE ME ON THIS
Step-by-step explanation:
Tina paid $6.60 for some $0.15 stamps and some $0.20 stamps. She bought 37 stamps in all. How many of each kind did she buy?
PLS HELP I WILL GIVE BRAINLIEST
Answers
Answer:
Let n be the number of 25 cent stamps.Then, 28 - n must be the number of 29 cent stamps.Tim paid $7.60 the stamps.
0.25n + 0.29(28 - n) = 7.60
This means that n stamps at 25 cents a piece plus (28 - n) stamps at 29 cents a piece sum to $7.60.Solve for m.
0.25n + 8.12 - 0.29n = 7.60
-0.04n = -0.52
n = 13
So, Tim bought 13 25-cent stamps and 28 - 13 = 15 29-cent stamps
Step-by-step explanation:
hope this helps:)
Answer: 16,21
Step-by-step explanation:
There are two ways you can solve this problem using substitution and elimination.
In this answer, I'm going to be using substitution.
First, you make two equations based on the information given.
The two equations are 0.15x+0.2y=6.6 and X+Y=37.
In the second problem subtract y to move it to the other side to get X=37-y.
Now that you got x= make a new equation which should be 0.15(37-y)+0.2y=6.6 use distributive property to get 5.55-.15y+0.2y=6.6.
Then, subtract 5.55 by 6.6 to get 1.05 and 0.2y+-.15y to get 0.05 y.
Now you have 0.05y=1.05 divided 0.05 and 1.05 to get 21.
Now plug 21 into the X+Y=37 equation to get X+21=37 subtract 21 from 37 to get X=16.
So X=16 and Y=21, so the answer is 16,21.
Use the Angle Addition Postulate to find the measure of the unknown angle
Answers
Answer:
103
Step-by-step explanation:
61+42 = 103