Answer:
Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.
Step-by-step explanation:
The coin theoretically could give a very large number of tails first so each person's probability is made up of an infinite series.
P(1st person wins) = P(H) + P(TTTH) + P(TTTTTTH) + . . . etc
= 1/2 + (1/2)^4 + (1/2)^7 + (1/2)^10 + . . .
This is a geometric series with first term a = 1/2 and common ratio r = 1/8
Using formula a/(1 - r) this is (1/2)/(7/8) = 4/7
P(2nd person wins) = P(TH) + P(TTTTH) + P(TTTTTTTH)
= (1/2)^2 + (1/2)^5 + (1/2)^8 + . . .
Geometric series with sum (1/4)/(7/8) = 2/7
P(3rd person wins) = P(TTH) + P(TTTTTH) + P(TTTTTTTTH) + . . .
= (1/2)^3 + (1/2)^6 + (1/2)^9 + . . .
Geometric series with sum (1/8)/(7/8) = 1/7
Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.
Hope this helped!
130 students choose to attend one of three after school activities: football, tennis or running. There are 58 boys. 49 students choose football, of which 27 are girls. 27 students choose tennis. 24 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.
Answer: [tex]\dfrac{27}{65}[/tex]
Step-by-step explanation:
There are 130 students.
There are 58 boys --> 72 girls
A) 49 chose football: 27 are girls --> 22 are boys
B) 72 girls: 24 chose running, 27 chose football --> 21 girls chose tennis
C) 27 students chose tennis: 21 are girls --> 6 are boys.
D) 58 boys: 22 chose football, 6 chose tennis --> 30 boys chose running.
[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&22&27&49\\Tennis&6&21&27\\\underline{Running}&\underline{\quad 30\quad}&\underline{\quad 24\quad}&\underline{\quad 54\quad}\\Total&58&72&130\end{array}}[/tex]
Total running = 30 boys + 24 girls = 54
Total students = 130
[tex]\dfrac{\text{Total running}}{\text{Total students}}=\dfrac{54}{130}\quad \rightarrow \large\boxed{\dfrac{27}{65}}[/tex]
Which of the following is a key property of the quadratic parent function?
Answer: B
Step-by-step explanation:
Quadratic parent function is y=x^2 which means the vertex is the origin because if you input 0 into the function you will get an output of zero. (0,0) is the origin which is where the graph intersect.
please help !!!!!!!!
Answer:
x=3 y=11
Step-by-step explanation:
2x+3=9
2x=6
x=3
y-4=7
y=11
X^4 -33x^2-108 which of the following is equal to the polynomial given above? A. (X+36)(x+v3i)(x-3) B. (X-36)(x+v3i)(x+3)
Answer:
Answer D I believe :)
Step-by-step explanation:
x^4-33x^2-108
rewrite as a difference
x^4+3x^2-36x^2-108
factor out x^2
x^2(x^2+3)-36x^2-108
factor out -36
x^2(x^2+3)-36(x^2+3)
factor out x^2+3
(x^2+3)(x^2-36)
factor x^2-36
(x^2+3)(x-6)(x+6)
set x^2+3 equal to 0
x^2+3=0
solve for x
x=+/-[tex]\sqrt{3}[/tex]i
set at factors
(x+6)(x-6)(x+[tex]\sqrt{3}[/tex]i)(x-[tex]\sqrt{3}[/tex]i)
I hope this helps.
Please help
Factorise completely 36ab - 18b+6a-3
Answer:
[tex]3(6b-1)(2a-1)[/tex]
Step-by-step explanation:
[tex]36ab-18b+6a-3\\18b(2a-1)+3(2a-1)[/tex]
Taking (2a-1) as common
[tex](18b+3)(2a-1)[/tex]
=> [tex]3(6b-1)(2a-1)[/tex]
Answer:
[tex]3(6b+1)(2a-1)[/tex]
Step-by-step explanation:
[tex]36ab - 18b+6a-3[/tex]
Factor the two groups.
[tex]18b(2a-1)+3(2a-1)[/tex]
Take 2a - 1 common.
[tex](18b+3)(2a-1)[/tex]
Factor 18b + 3.
[tex]3(6b+1)(2a-1)[/tex]
∫1/(1+sinx^2 +2cos^2x)
Answer:
Im not sure, is this correct?
Explain please --
Find the measure of angle A to the nearest degree.
a. 26
b. 27
c. 63
Explanation:
We'll use the tangent ratio to connect the opposite and adjacent sides with the reference angle
tan(angle) = opposite/adjacent
tan(A) = 14/7
Then use the arctangent function (aka inverse tangent) to fully isolate A
A = arctan(14/7)
A = 63.4349 degrees approximately; make sure your calculator is in degree mode
Round this to the nearest whole number to get 63.
F(x) = 3x+2 what is f(5)
Answer:
f(5) = 17Step-by-step explanation:
f(x) = 3x + 2
To find f(5) substitute 5 into f(x)
That's
f(5) = 3(5) + 2
= 15 + 2
= 17
Hope this helps you
Answer:
17
Step-by-step explanation:
You just plug 5 into the equation
f(5)= 3(5)+2
=15+2
=17
Hope this helped! :)
PRST is a trapezium. PQR and PTU are
straight lines. Find the values of x and y.
Answer:
x = 56 degrees
y = 62 degrees
Step-by-step explanation:
Given TS || PR
x = 56 ................. corresponding angles TS, PR parallel sides of trapezium.
VSK = x ...................... correspoinding angles given TU || SV
y = 118 - VSK .......... given VSR = 118
= 118 - 56
= 62
Which is a qualitative graph? On a coordinate plane, a line with positive slope goes through points (negative 1, 0) and (0, 3). On a coordinate plane, points are at (0, 2), (1, 3), (2, 2.5), (3, 3), (4, 4), and (4.5, 5). A graph has time on the x-axis and height on the y-axis. The graph increases to point A, increases to point B, and then decreases to point C. A graph has time on the x-axis and height on the y-axis. Segment A increases, segment B is increases, and segment C decreases.
Answer:
(-1,0), (0,3) and (2,2.25)
Step-by-step explanation:
The qualitative graph is as follows:
A(-1,0) ------> B(0,3) ------> C(2,2.25)
Hence, slope = (2.25 - 0)/(2 - (-1)) = 2.25/3
∴ slope = 0.75
Except for the option graph on a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), all the graph is qualitative. Options B, C, and D are correct.
What is a qualitative graph?The kind of graph that shows the quality curve such as decreasing and increasing events, is called a qualitative graph or curve.
Here,
1. On a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), since this graph does not represent any data as well as also constantly increasing between two points so it is not a qualitative graph.
Similarly,
Graphs B, C, and D have an increasing and decreasing order, so all are qualitative graphs.
Thus, except for graph A all the graphs are qualitative graphs.
Learn more about qualitative graphs here:
https://brainly.com/question/21981889
#SPJ6
Tucker was asked to solve the equation 5x + 3 = 6x + 1. He did not know if his first step should be to add 5 negative x-tiles, or 1 negative unit tile, to both sides. What advice would you give Tucker to help him decide on his first step?
Answer:
He should use the negative 1 unit tile.
Step-by-step explanation:
He should do this because in this equation you wish to isolate the variable on one side, and it would be better to first take away any constants. Afterwards, the variable would be next.
Answer: It does not matter which he does first. Either way, zero pairs will be created on both sides, which will isolate the variable to determine x. Adding the x-tiles and then the unit tile, or visa versa, will give the same solution.\
Explanation: that's what i put and i got it right
PLZZZZZ MARK ME BRAINIEST
Find the indicated functional value for the ceiling function: f(1.5)?
Answer:
The correct answer is 2Step-by-step explanation:
The ceiling function is a python programming function that rounds a decimal point number to the nearest whole number.
Given the function expression f(1.5), the ceiling function will round 1.5 to the nearest whole number which is 2
PLEASE HELP!! ASAP
The two square pyramids are similar. The side length of the smaller pyramid is 3/4 the side length of the larger pyramid. Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid? Answer choices: 9/16 or 16/9
Simplify each expression.
1) 3(8Z² - 52 - 7)
2) 8d(2d-4)
6) 6(5x - 4)
7) 6q- 4
Answer:
1) 24Z^2 - 177.
2) 16d^2 - 32d.
6) 30x - 24.
7) 6q - 4.
Step-by-step explanation:
1) 3(8Z^2 - 52 - 7)
= 3(8Z^2 - 59)
= 24Z^2 - 177
2) 8d(2d - 4)
= (8d * 2d) - (8d * 4)
= 16d^2 - 32d
6) 6(5x - 4)
= (6 * 5x) - (6 * 4)
= 30x - 24
7) Already simplified. 6q - 4.
Hope this helps!
List some typical benefits an employee might receive on top of their wage?
Answer:
paid vacation
paid medical
401k
Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
i just took the test
an orphanage bought 119 1/4 m of cloth to stitch dresses for kids. The dress for one kid requires 2 1/4m of cloth. How many dresses of the size can be stitched
Answer:53 dresses
Step-by-step explanation:
First of all..if one kid required 2 1/4m of cloth,what about 119 1/4m of cloth?
So u take 119 1/4m of cloth and divide it by 2 1/4m of cloth.
Then change the mixed numbers into improper fractions.
So the question will be 477/4 m divided by 9/4 m.
The second improper fraction (9/4)m will be reciprocated to be (4/9)m.
Afterwards,take 477/4 m and multiply it by 4/9 m.
The result will be 53 dresses.
what is the value of "c" by completing the square. x^2 - 14x +
Answer:
[tex]\large\boxed{\sf \ \ 49 \ \ }[/tex]
Step-by-step explanation:
Hello,
we need to get the discriminant = 0 meaning
[tex]\Delta = b^2-4ac = 0\\\\<=>14^2-4c=0\\\\<=>c=\dfrac{196}{4}=49[/tex]
And then the square is
[tex]x^2-2\cdot 7\cdot x+7^2=(x-7)^2[/tex]
Hope this helps
Simplify: 14 - 2+ 8 = 2 *3
helppp meeee
Answer:
20=6?
Step-by-step explanation:
14-2+8=2*3
14-2+8=6
12+8=6
20=6?
Answer:
These to equations aren't equivalent.
Step-by-step explanation:
14-2+8=2*3
12+8=6
20=6
Hope this helps ;) ❤❤❤
You need to find the volume of the plastic sphere that holds the gum in your gumball machine. If the diameter is 2 feet, what is the volume? Use 3.14 to approximate pi. Round your answer to the nearest hundredth.
Answer:
The volume is
4ft³Step-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{ 3} [/tex]
where r is the radius
π = 3.14
From the question we were given the diameter and
radius = diameter/ 2
diameter = 2 feet
radius = 2/2 = 1 feet
So the volume of the sphere is
[tex]V = \frac{4}{3} (3.14)(1) ^{3} [/tex]
[tex] = \frac{4}{3} \times 3.14[/tex]
V = 4.186
We have the final answer as
V = 4 ft³ to the nearest hundredth
Hope this helps you
My age if I am half as old as two more than twice Mack's age if Mack is m years old.
Answer:
You are m + 1 years old.
Step-by-step explanation:
Let's say that you are x years old, and Mack is m years old.
x = 1/2( two plus twice m)
x = 1/2(2 + 2m)
x = 1 + m
x = m + 1
Hope this helps!
pls answer asap i need this answer quick plus the full explanation #7
in a certain town there are 30000 registered voters, of whom 12000 are Democrats. A survey organization is about to take a simple random sample of 1000 registered voters. a) the expected value for the percentage of Democrats in the sample is
Answer:
400.
Step-by-step explanation:
The following data were obtained from the question:
Total number of Registered voters = 30000
Total number of Democrats = 12000
Next, we shall determine the percentage of Democrats in the registered voters.
This can be obtained as follow:
Percentage of Democrats = number of Democrats / Total number of registered voters x 100
Percentage of Democrats = 12000/30000 x 100
Percentage of Democrats = 40%
Now, we can obtain the expected value of percentage of Democrats in the 1000 sample as follow:
Percentage of Democrats = 40%
Total number of Sample = 1000
Number of Democrats in the sampl=..?
Percentage of Democrats = number of Democrats in sample / Total number of sample x 100
40% = number of Democrats in sample/1000
Cross multiply
Number of Democrats in sample
= 40% x 1000
= 40/100 x 1000
= 400
Therefore, the expected number of Democrats in the sample is 400.
What the answer question
its b the answer is b
Answer:
the answer on the B
Step-by-step explanation:
Multiply. √3 ⋅ √5 ⋅ √7 Enter your answer, in radical form, in the box.
Answer: square 105
Step-by-step explanation: Confirming answer
A radical expression is an expression containing a square root, mostly a square root.
The value of √3.√5.√7 in radical form is √105.
What is a radical expression?A radical expression is an expression containing a square root, mostly a square root.
We have,
√3.√5.√7
We can multiply the numbers together.
= √(3 x 5 x 7 )
= √(15 x 7)
= √105
Thus the value of √3.√5.√7 in radical form is √105.
Learn more about radical form here:
https://brainly.com/question/27272065
#SPJ2
At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
Solve sin 20 = COS CE-30)
Answer:
CE = 100°
Step-by-step explanation:
Using the cofunction identity
sin x = cos(90 - x)
Given x = 20°, then 90° - 20° = 70° thus
CE - 30 = 70° ( add 30 to both sides )
CE = 100°
Thus
sin20° = cos(100 - 30)° = cos70°
Answer:
CE = 100
have a nice day!
Step-by-step explanation:
In a recent study, volunteers who had 8 hours of sleep were three times more likely to correctly on a math test than were sleep-deprived participants.
1) Identify the sample used in the study.
A) The sample is the math questions in the study.
B) The sample is the responses of the volunteers in the study.
C) The sample is the amount of sleep the volunteers got in the study.
D) The sample is the sleep-deprived participants in the study.
2) What is the sample's population?
A) The population is the collection of all the math questions from the math test.
B) The population is the collection of the responses of all individuals who completed the math test.
C) The population is the collection of all the individuals who completed the math test.
3) Which part of the study represents the descriptive branch of statistics?
1) Identify the sample used in the study: B) The sample is the responses of the volunteers in the study
2) What is the sample's population: B) The population is collected of the response of all individuals who completed the math test
3) Which part of the study represents the descriptive branch of statistics:
individuals who are not sleep deprived will be more likely to answer math questions correctly than individuals who are sleep deprived.
hope i helpd
-lvr
The base of a regular pyramid is a hexagon.
Which best describes the relationship between the lines with equations 5x +y = 4 and 20.0 + 4y = 16?
Answer:
There is no relationship, except they do intersect at the point (1, -1). Hope this helps :)
Brainliest?
Both given lines are going to intersect at ( 1,-1 ) that's it.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
Given that
Line 1 ; 5x +y = 4
Line 2 ; 20 + 4y = 16 ⇒ y = -1
At y = -1 the first line is
5x - 1 = 4 ⇒ x = 1
So,
It is clear that line 1 has a point ( 1 .-1 ) and line 2 also passes
through it hence there will an intersection.
For more about line segment
https://brainly.com/question/25727583
#SPJ5