A typical roulette wheel used in a casino has 38 slots that are numbered 1, 2, 3, ... , 36, 0, 00, respectively The 0 and 00 slots are colored green. Half of the remain ing slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume that each slot has equal probability of 1/38, and we are interested in the number of the slot into which the ball falls.
a. Define the sample space S.
b. Let A = {0, 00}. Give the value of P(A).
c. Let B = {14, 15, 17, 18}. Give the value of P(B).
d. Let D = {x : x is odd}. Give the value of P(D).
Answers
Answer:
Follows are the solution to the given points:
Step-by-step explanation:
For point a:
Space for results All possible outcomes are:
\(\to O = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,}\)
\(17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, \\ 29, 30, 31, 32, 33, 34, 35, 36, 0, 00}\)
For point b:
\(\to P(A) = \frac{ \text{ \# of outcomes in A}}{ \text{ \# Total outcomes}} = \frac{2}{38} = 0.052\)
For point c:
\(\to P(B) = \frac{ \text{ \# of outcomes in B}}{\text{ \# Total outcomes}} = \frac{4}{38} = 0.105\)
For point d:
We consider that in D there are 18 elements (only Odd numbers in the range 1 to 36)
\(\to P(D) = \frac{ \text{\# of outcomes in D}}{\text{\# Total outcomes}} = \frac{18}{38} = 0.473\)
Related Questions
A jet airplane is at an altitude of 30,000 feet. The aircraft is capable of climbing at a rate of 1400 feet per
minute. Approximately how many minutes will it take the jet to climb to 53,000 feet from its current altitude of
30,000 feet?
Answers
Answer:
16.42 mins
Step-by-step explanation:
Take the difference of the altitude you want and current altitude
53,000 - 30,000 = 23,000
Divide the value you got with the constant rate of change
23,000/1400 = 16.42
It will take 16.42 mins
Let's create a simple equation to find the number of minutes the jet will take to climb to 53,000 feet.
x = # of minutes
30,000ft + 1400x = 53,000ft
Subtract both sides by 30,000ft
1400x = 23,000ft
Divide both sides by 1400ft
x = 16.43
It will take the jet approximately 16.43 minutes to reach 53,000ft from 30,000ft
A random sample of vacationers were asked whether they were traveling to another country for their upcoming trip. The resulting confidence interval for the proportion of vacationers traveling abroad is (0.14,0.16). What is the margin of error?
Answers
Answer:
The Margin of error = 0.01
Step-by-step explanation:
Explanation:-
step(i):-
Given confidence interval for the proportion of vacationers traveling abroad
(0.14,0.16)
The 95% of confidence interval for Population proportion with margin of error is determined by
( p⁻ - M.E , p⁻ + M.E)
step(ii):-
The margin of error is determined by
\(M.E = Z_{\alpha } \sqrt{\frac{p(1-p)}{n} }\)
Given Confidence interval is ( 0.14 , 0.16 )
Now
(( p⁻ - M.E , p⁻ + M.E) = (0.14,0.16)
Equating
p⁻ - M.E = 0.14 ...(i)
p⁻ + M.E = 0.16 ...(ii)
Solving (i) and (ii) equations , we get
p⁻ - M.E = 0.14
p⁻ + M.E = 0.16
- - -
- 2 M.E = -0.02
M.E = 0.01
The margin of error = 0.01
Conclusion:-
The margin of error = 0.01
How man 1/3 cups make 3/4 cups
Answers
Answer:
it would take 2.25 1/3 cups if you are looking for an exact answer, or if you are looking for the minimum amount of 1/3 cups necessary to make 3/4 it would be 3.
Step-by-step explanation:
You can solve this by cross multiplying 1/3 and 3/4
You will get 9/4 which simplifies to 2 1/4 or 2.25
The vertices of ΔGHI are G (2, 4), H (4, 8), and I (8, 4). The vertices of ΔJKL are J (1, 1), K (2, 3), and L (4, 1). Which conclusion is true about the triangles?
They are congruent by the definition of congruence in terms of rigid motions.
They are similar by the definition of similarity in terms of a dilation.
The ratio of their corresponding sides is 1:3
The ratio of their corresponding angles is 1:3.
Answers
Answer:
B
Step-by-step explanation:
They are similar by the definition of similarity in terms of a dilation.
What is similarity in terms of dilation in Mathematics?Two figures must have congruent (equal) comparable angle measures and proportional sides in order to be considered similar. Dilations produce comparable numbers because adding the scale factor produces proportional sides while keeping the angle measurement and form constant.
Given
In GHI ,
GH = 3cm [using distance formula]
HI = 5.65 cm
GI = 6 c
In JKL,
JK = 2.2361 cm
KL = 2.8284 cm
JL = 3 cm
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Please look at the photo. Thank you!
Answers
The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x
How to calculate the composite functionsFrom the question, we have the following equations that can be used in our computation:
h(x) = x² + 3
f(x) = 3/4x
From the above, we have
(h o h)(x) = h(h(x))
So, we have
(h o h)(x) = (x² + 3)² + 3
Also, we have
(f o f)(x) = 3/[4(3/4x)]
Evaluate
(f o f)(x) = x
Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x
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I really need help WILL GIVE BRAINLIEST
factor x^2+4x+2^2
Answers
Answer:
2
4
+
6
3
−
8
2
−
2
4
Step-by-step explanation: sorry it is like that I won't let me type straight.
Answer:
(x+2)^2
Step-by-step explanation:
x^2+4x+2^2
Simplify!!!
x^2 + 4x +4
2^2 is also know as squaring when a number is multiplied by itself, 2 x 2
Now time to factor, what you need to look at is the last two numbers and ask...
What two numbers add to give me 4 and multiply to give me 4
We look at the factors of 4: 1,2,2,4
As you can tell 1 and 4 definitely don't work because 1+4=5 or 1-4= -3 and so forth
Therefore 2,2 are the numbers we need!! Lets check just in case
2 +2 gives us 4 or 4x in this case
and 2 x 2 gives 4
Therefore when you factor you place the equation in factored form
(x+2)^2
Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
Answers
Explanation
The square root of a number is “what number times itself”
2 x 2 = 4
3 x 3 = 9
7 is between 4 and 9 so C is the correct answer
a formula in the form y=mx+b models the cost, y, of four-year college x years after 2010. would you expect m to be positive, negative, or zero? explai your answer
Answers
we would expect m to be positive.
In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.
Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.
If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.
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How do I find the volume?
Answers
Answer:
150m^3
Step-by-step explanation:
The formula for the volume a triangular prism, like the one you have, is 1/2 base x height. For your prism the volume would be 1/2 (30 x 10) which equals 150. Now just add the measurment m (meters) and you're set.
A species of animal is discovered on an island. Suppose that the population size Pt of the species can be modeled by the following function, where time t is measured in years. =Pt600+18e−0.45t Find the initial population size of the species and the population size after 8 years. Round your answers to the nearest whole number as necessary.
Answers
we have the function
\(P(t)=\frac{600}{1+8e^{(-0.45t)}}\)Part 1
Find out the initial population
Remember that
The initial value is for t=0
so
substitute in the given function
\(\begin{gathered} P(t)=\frac{600}{1+8e^{(-0.45*0)}} \\ \\ P(t)=\frac{600}{1+8} \\ P(t)=67 \end{gathered}\)the initial population is 67 individuals
Part 2
For t=8 years
substitute in the given function
\(\begin{gathered} P(t)=\frac{600}{1+8e^{(-0.45*8)}} \\ P(t)=492 \end{gathered}\)The answer part 2 is 492 individuals
Gianna drives 5 miles in 10 minutes. If she drove three hours in total at the same rate,
how far did she go?
Before you try that problem, answer the question below.
How many minutes did Gianna drive in total?
Answers
Gianna is 90 miles far away in 3 hours of driving.
She drove in total of 180 minutes.
What is speed?The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.
Given,
Gianna drives 5 miles in 10 minutes
Speed per minute = 5/10 = 0.5 miles/minute
Gianna drove in total for 3 hours
1 hour = 60 minutes
3 hours = 60 × 3 = 180 minutes
Distance Gianna drove in 180 minutes = speed per minute × time
= 0.5 × 180
= 90 miles
Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.
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Simplify (36x^0y^16)^1/2
Answers
Answer:
18y^16
Step-by-step explanation:
Answer:
18y16(the 16 is supposed to be tiny and at the top)
Step-by-step explanation:
An ant colony is built by 200 ants. The number of ants triples each week. How many ants will be in the colony at the end of the eighth week?
Answers
N = N0 * 3^t
where N is the final number of ants, N0 is the initial number of ants, 3 is the rate of growth (since the number of ants triples each week), and t is the number of weeks.
We are given that there are initially 200 ants, so N0 = 200. We want to find N at the end of 8 weeks, so t = 8. Substituting these values into the formula, we get:
N = 200 * 3^8
N = 200 * 6561
N = 1,312,200
Therefore, at the end of the eighth week, there will be 1,312,200 ants in the colony.
multiplication and addition
Answers
Answer:
ok! what do u need help on???
The question is one the picture
Answers
Answer:
y=-1/2x+4
Step-by-step explanation:
The line is going down, which means it's negative. You then do rise over run, go up by 1 and go to the left by 2. To find the y intercept, it's 4 since the coordinate is (0,4).
Form a polynomial whose zeros and degree are given.
Zeros: −2, multiplicity 1; −1, multiplicity 2; degree 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.
f(x) =
Answers
Answer:
Zeros: 5, multiplicity 1; -4 multiplicity 2; degree 3
y=1(x-5)^1(x+4)^2
y=(x+4)^2(x-5)
y=(x^2+8x+16)(x-5)
y=x^3+8x^2+16x-5x^2-40x-85
y=x^3+3x^2-24x-85
Step-by-step explanation:
A triangle has a height that is 2 inches taller than its base and an area of 12 square inches. What are the dimensions of the triangle.
Answers
Answer:
Let the length of the base of a triangle is x inches then the length of its height is
(x+2) inches, accordingly:
Area of the A = x.(x+2)/2 = 12.
or, x^2 + 2.x = 24. or, x^2. + 2.x - 24 = 0.
or, (x+6).(x-4) = 0.
or, x = -6 (not valid), 4.
Thus, base = 4 inches., height = (x+2) = (4+2) = 6 inches. and hypotenuse
=√{4^2+6^2)=√ 52. = 2√13 inches. Answer.
What is the length of side s of the square shown below?
45*
8
90*
Answer is 4v2
Answers
Answer:
4 squareroot 2
Step-by-step explanation:
The answer is 4 squareroot 2
Find the length of the segment with the endpoints (3,-8) and (5,-2).
Answers
g There are students in a kindergarten class. If each kindergartner can have only one task, in how many ways can the teacher assign out the following tasks: line leader, wipe down the tables, pass out papers, water the plants
Answers
Answer:
1 or as many students as she has
Answer:She can divide the 4 tasks by the amount of students in the class.
Step-by-step explanation:
How can I figure out the volume of a compound shape?
Answers
We can divide the compound shape as shown below:
We have divided the shape into two triangles. Therefore, we can calculate the area of both triangles and add the answers together to get the area of the whole shape.
The formula to calculate the area of a triangle is given to be:
\(A=\frac{1}{2}\times b\times h\)Area of Triangle 1:
\(\begin{gathered} b=9\operatorname{cm} \\ h=6\operatorname{cm} \end{gathered}\)Therefore, the area is:
\(A_1=\frac{1}{2}\times9\times6=27\operatorname{cm}^2\)Area of Triangle 2:
\(\begin{gathered} b=3\operatorname{cm} \\ h=2\operatorname{cm} \end{gathered}\)Therefore, the area is:
\(A_2=\frac{1}{2}\times3\times2=3\operatorname{cm}^2\)Area of the Shape:
\(A=27+3=30\operatorname{cm}^2\)The area of the shape is 30 cm².
PLZ needed now plz URGENT!
Answers
Answer:
Realtionship B
Step-by-step explanation:
Relationship A doesn't pass the line test
The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at (n,-2). The distance from point P to point Q is equal to the distance from point P to point R. What is the from point P to point Q? What is the value of N? Explain how you determined the distance from point P to point Q, and the value of N.
Answers
The value of n such that the conditions are met is:
\(n = \frac{2x \pm \sqrt{(-2x) - 4*1*(y + 2)^2} }{2}\)
Where x and y are the coordinates of point P.
How to get the given points?We know that:
Q = (n, -2)R = (0, y) (because R is on the y-axis).P = (x, y)Now, the distance of P to Q is equal than the distance of P to R, then we have that:
\(\sqrt{(x - 0)^2 + (y - y)^2} = \sqrt{(x - n)^2 + (y + 2)^2} \\\\x^2 = (x - n)^2 + (y + 2)^2\)
So we need to solve this for n.
\(x^2 = x^2 - 2xn + n^2 + y^2 + 4y + 4\\\\0 = -2xn +n^2 + (y + 2)^2\\\\\\0 = n^2 - (2x)*n + (y + 2)^2\)
Notice that this is a quadratic of n, the two solutions of n will be:
\(n = \frac{2x \pm \sqrt{(-2x) - 4*1*(y + 2)^2} }{2}\)
Such that, as you can see, the value of n depends on x and y.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
Answers
Answer:
2+2=4
Step-by-step explanation: big brain
HEELLPP plss!!!!!!!!
Solve
Answers
The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−3, 2) and goes to S(2, 2) and continues to T(2, −5). The total length of the walking trail is
units. (Input whole numbers only.) (3 points)
Answers
Answer:
12
Step-by-step explanation:
U.S. Customary unit conversion with mixed number values: One... A cook needs 7 cups of vegetable stock for a soup recipe. How much is this in pints? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
The pints of vegetable stock the chef needs is \(3\frac{1}{2}\).
How many pints does he need?The first step is to determine the unit of conversion of cups to pints.
1 cup = 0.5 pints
To convert cup to pints, multiply 7 by 0.7
7 x 0.5 = 7/2 = \(3\frac{1}{2}\)
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An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sink hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point A on one side of the sink hole and B on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the other ends of the two ropes meet at point C. Then you recreate the same triangle by using the distance from AC and BC and creating new segments CE and CD. The distance DE is 52.2 ft.
a. What type of triangles have you created?
b. How do you know the triangles are congruent?
c. How far across is the sink hole?
d. What is the perimeter of the triangle ABC?
Answers
A) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
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Answer:
Step-by-step expA) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?
A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
lanation:
Helppppppp I WILL GIVE U THE BRAINLEST!!!!
ANSWER ALL THE QUESTIONS!!!
Answers
Circumference is the distance around
diameter is the line that goes from one side through the middle to the other side
origin is (0,0)
pi is 3.14
radius is the line that goes from the center to the side and can go any direction
Hope this helps!!!!
Tori rented a car and drove 325 miles. She decided to fill up the tank before returning the car to the rental company.
She put 11 gallons of gas in the car to fill the tank. She paid $2.85 per gallon for gas. The rental company would have
charged $3.50 per gallon to fill the tank. How much did she save by filling the tank herself?
O $3.50
O $0.65
O $7.15
$29.54
Answers
Answer:
C. $7.15
Step-by-step explanation:
3.5(11)= 38.5
2.85(11)= 31.35
38.5-31.35=7.15