5050 flips expect to make before running out of coins .
Let's approach this problem using the concept of geometric distribution.
The probability of getting heads on any given coin flip is 1/2, assuming a fair coin.
So the probability of getting tails on a given flip is also 1/2.
The number of flips it takes to get the first head is a geometric distribution with a probability of success p = 1/2.
The expected number of flips until the first head appears is 1/p = 2 flips.
After the first head appears, there will be 99 coins left to flip.
The expected number of flips until the next head appears is still 2, since the probability of getting heads on any given flip is still 1/2.
So the expected number of flips until the second head appears (and the number of coins remaining drops to 98) is 2+1 = 3 flips.
Similarly, the expected number of flips until the third head appears (and the number of coins remaining drops to 97) is 2+1+1 = 4 flips.
We can generalize this pattern: after k heads have been obtained, the expected number of additional flips until the next head appears (and the number of coins remaining drops to 100-k) is k+1 flips.
Using this formula, we can calculate the expected number of flips to obtain all 100 heads:
E(number of flips) = (2 + 3 + 4 + ... + 101)
= (1 + 2 + 3 + ... + 100) + 100
= (100 x 101 / 2) + 100
= 5050
Therefore, we expect to make 5050 flips before running out of coins to flip and obtaining all 100 heads.
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4 women and 5 men are eligible to be in a committee of three. find the probability that the committee has exactly two woman.
The probability that the committee has exactly two woman is 0.1758.
Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.The ratio of the favorable outcomes to the all possible outcomes.
Given that, 4 women and 5 men are eligible to serve on a committee.
A committee of 3 is randomly selected.
Choosing 2 women out of 3 women is
³[tex]C_{2}[/tex]
= 3
Choosing 1 men out of 5 men is
5C1
= 5
Total number of eligible person is = (4+5)=9
Choosing 3 member out of 9 member is
9C3
=84
The required probability is
=3*5/84
0.1785
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a factor of 24 is chosen at random what is the probalility as a decimal that its a 2 digit numbers
Answer:
1/4 as fraction
0.25 as decimal
= 0.25
Step-by-step explanation:
Factors of 24 starting at 1 are:
1 x 24 = 24
2 x 12 = 24
3 x 8 = 24
4 x 6 = 24
Then the pattern repeats in decreasing orders of products of numbers . 6 x 4, 8,x 3 etc which are duplicates of the ones shown above
Factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24
There are 8 factors
Out of the 8 factors, only two - 12 and 24 are two digit numbers
P(factor is a 2 digit number = # two-digit numbers/Total # factors
= 2/8
= 1/4
= 0.25
Answer:
1/4 as a fraction
0.25 as decimal
0.25
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Bronze is a mixture of copper and tin. The copper and tin are mixed in the ratio 9:1 by weight.
a. How much copper is there in a bronze brooch weighing 360 g?
b. Another bronze brooch contains 670.5g of copper.
How much does it weigh altogether?
a. The amount of copper in a bronze of 360g is 324g
b. The mass of bronze with 670.5g of copper is 745g
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
The ratio of copper to Tin is 9:1. The total ratio is 10
a.therefore the amount of copper = 9/10 × 360
= 324g
b. The mass of copper = 670.5g
therefore the mass of the bronze =
= 9/10× y = 670.5
9y = 670.5 × 10
9y = 6705
y = 6705/9
y = 745g
therefore the total mass of the bronze is 745g
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Kyle and Tina both think they figured out how to get Triangle ABC to transform to Triangle A'B'C', however they both did it in different ways. Kyle used a sequence of transformations, but Tina was able to do it in just one transformation. Assuming both students are correct, explain what each of them did in order to complete the problem.
Kyle: Rotation about the origin, then reflection across the x axis
Tina: Reflection over the line y = x
What is reflection in geometry?In geometry, reflection refers to a transformation that involves flipping a shape or object over a line, often called the "line of reflection".
This transformation preserves the size and shape of the original object, but changes its orientation by reversing the positions of all its points across the line of reflection.
Considering the image, rotation about the origin, then reflection across the x axis when compare with Reflection over the line y = x. will yield similar result.
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in a magnetometry experiment, after a minute of collecting data the statistical noise was reduced to 1 picotesla. for how many more minutes should data be collected in order to reduce the random error by a factor of 10
In a magnetometry experiment, It will take 1 more minute for data be collected in order to reduce error the statistical noise by a factor of 10.
To reduce the random error by a factor of 10, we need to reduce the statistical noise to 1/10 picotesla. Since the statistical noise was initially 1 picotesla, this means we need to reduce it by a factor of 10.
We can use the following formula to calculate the time needed to reduce the statistical noise by a certain factor:
t = (log (final noise / initial noise)) / (log (reduction factor))
Here, the final noise is 1/10 picotesla, the initial noise is 1 picotesla, and the reduction factor is 10.
Plugging in these values, we get:
t = (log (1/10 / 1)) / (log (10))
t = (log (1/10)) / (log (10))
t = -1 / 1
t = -1
The negative value of t doesn't make sense in this context, so we need to take the absolute value:
t = |-1|
t = 1
Therefore, it will take 1 more minute to reduce the statistical noise by a factor of 10.
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____The given question is incomplete, the complete question is given below:
Reduction of the standard error
In a magnetometry experiment, after a minute of collecting
data the statistical noise was reduced to 1 picotesla.
For how much longer should data be collected in order
to reduce the random error by a factor of 10?
The length of a marathon is 138,435 ft. Each stride, or step, by a particular runner is 3 ft long. Does the number of strides the runner takes fit evenly into the length of the race? Explain.
Answer:
Yes
Step-by-step explanation:
length 138,435 ÷ 3 ft stride = 46,145 equally
Use Evcel fo find the probabinty that in 112 trials with probabinty0.42of success that there are 30 or fewer suce ses. Round to 6 decimaiplaces Type your answer hern
The probability that there are 30 or fewer successes in 112 trials with a probability of 0.42 of success is 0.874763 rounding to 6 decimaiplaces.
To use the Excel spreadsheet programme to calculate the likelihood that 30 or fewer successes occur in 112 trials with a success probability of 0.42, follow these steps:
In Excel, create a new spreadsheet with the first column labelled "Number of Successes" and the second column labelled "Probability."
Enter "0" in the first row of the "Number of Successes" column.
Enter "1" in the second row of the "Number of Successes" column.
Continue to input numbers in the "Number of Successes" column in ascending order until you reach 30.
Enter the following formula in the field next to the "0" in the "Probability" column: =BINOM.DIST (0,112,0.42,TRUE)
Enter the following formula: =SUM (B1:B31)
The result in the cell where you input the formula in step 8 will be the chance of 30 or fewer successes in 112 trials with a success rate of 0.42.
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Find 6x3/5. Use model at the right to find the product
The multiplication of the given fraction 6 × 3/5 is 15 or 3 3/5
How to multiply fraction?Fraction refers to numbers which comprises of a numerator and a denominator. A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.
6 × 3/5
multiply the numerator and denominator separately
= (6 × 3) / (1 × 5)
= 18/5
= 3 3/5
Therefore, 3 3/5 is the solution to the multiplication of the fraction.
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The function P(n) = 108 + 10 log(n) gives the
total sound power in decibels when n drill presses are operating in a factory. What is the total sound power, to the nearest decibel, when three drill presses are operating?
112.8 is the the total sound power, when three drill presses are operating
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.
We need to find the total sound power, to the nearest decibel, when three drill presses are operating
We have to consider n as 3
P(3) = 108 + 10 log(3)
=108+10×0.477
=108+4.77
=112.77
Hence, 112.8 is the the total sound power when three drill presses are operating
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Sarah used an equation to solve the problem below. Justify each step of her work. About 11% of people are left handed. How many people would you expect to be left handed in a class of 30 students?
Answer:
To solve the problem, Sarah used the equation:
Left-handed people = (11/100) * Total people
Step 1: Plug in the total number of people (30) into the equation.
Left-handed people = (11/100) * 30
Step 2: Simplify the right side of the equation.
Left-handed people = (11/100) * 30
Left-handed people = 3.3
Step 3: Round the answer to the nearest whole number.
Left-handed people = 3
So, Sarah expects 3 people in a class of 30 to be left-handed. Each step of Sarah's work is justified because she used the percentage formula to find the number of left-handed people in a class and rounded the answer to the nearest whole number.
Select all the equations that are equivalent. 52 = 8n + 4 4(2n + 1) = 52 4 = 52 – 8n 4n = 48 n = 6
Answer:
all of these equations except 4n = 48
Step-by-step explanation:
your equations are
52 = 8n+4
4(2n+1) = 52
4 = 52-8n
4n = 48
n = 6
let's solve these equations!
52 = 8n + 4
48 = 8n
n = 6
4(2n+1) = 52
8n + 4 = 52
8n = 48
n = 6
4 = 52-8n
-48 = -8n
n=6
4n = 48
n = 12
all of these equations simplify to n = 6 except for 4n = 48, so they're all equivalent
If 70% of a number is 224 and 95% of the same number is 304, find 25% of that number.
Using the information given in the problem to set up two equations and by solving them
25% of the number is 80.
What is an equation?An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side can contain variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.
According to the given informationLet's call the number we're looking for "x". We can use the information given in the problem to set up two equations:
0.7x = 224 (equation 1)
0.95x = 304 (equation 2)
We want to find 25% of the same number, which can be written as 0.25x. We can solve for x using either equation 1 or equation 2 and then plug that value into 0.25x to find the answer.
Let's solve for x using equation 2:
0.95x = 304
x = 304/0.95
x = 320
Now that we know x is 320, we can find 25% of that number:
0.25x = 0.25(320) = 80
So 25% of the number we were looking for is 80.
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4 Statistic Homework Questions! Will Give Brainliest!
a student committee has 6 membersâ€""4 undergraduate and 2 graduate students. a subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. what is the probability that there will be no graduate students on the subcommittee?
The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in
(4 choose 3) = 4 ways.
The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in
(6 choose 3) = 20 ways.
Therefore, the probability that there will be no graduate students on the subcommittee is:
Number of subcommittees with only undergraduate students / Total number of possible subcommittees
= 4 / 20
= 1/5
= 0.2
So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
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x + y = -5 is it a solution
Answer: The equation X + y = -5 represents a straight line in a two-dimensional plane. To determine whether a specific point (X, y) is a solution of the equation, you can substitute the values of X and y into the equation and see if it holds true. If the equation is satisfied, then the point (X, y) is a solution. If the equation is not satisfied, then the point (X, y) is not a solution.
For example, if X = 2 and y = -7, then the equation becomes:
2 + (-7) = -5
-5 = -5
Since the equation holds true, the point (2, -7) is a solution of the equation X + y = -5.
Step-by-step explanation:
an online coupon service has offers for free samples. part: 0 / 20 of 2 parts complete part 1 of 2 (a) how many different requests are possible if a customer must request exactly free samples? the number of different requests is .
The number of possible requests for free samples is 5^1 = 5. This means that the customer has 5 different requests that they can make for free samples.
The number of possible requests for free samples can be calculated using the combination formula. The combination formula is used to calculate the number of combinations with repetitions of size “n” taken from a set of “r” elements . The formula is: [tex]C(n,r) = n^r[/tex] In this case, n = number of requests (1 request) and r = number of free samples offered (let’s say, 5). Therefore, the number of possible requests for free samples is[tex]5^1 = 5.[/tex]This means that the customer has 5 different requests that they can make for free samples.
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EFGHI~ WVUTS. Find EI and ST.
I
E 16
16
H
Submit
24
24
G
T
S
U
Write your answers as decimals or whole numbers.
EI =
ST=
18
W
18
The side lengths on the similar polygons are given as follows:
EI = 16.ST = 27.What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:
18/16 = 18/EI = ST/24.
Hence the length of EI is given as follows:
EI = 16.
The length of ST is obtained as follows:
18/16 = ST/24
16ST = 18 x 24
ST = 18 x 24/16
ST = 27.
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Maggie made 4 valentines in 6 hours.
What is the RATE of valentines made PER hour?
Jamie burned 480 calories in an exercise
class on Monday. She took a different class
the next day and burned 7/8 as many
calories as she did on Monday. How many
calories did she burn on Tuesday?
Answer: Jamie burned 420 calories on Tuesday
Step-by-step explanation:
Cross method is best for this question
Let x = calories burnt on tuesday
480 is 100%
x is 7/8 (or 87.5%)
∴
(480*87.5%) ÷ 100%
= 420 ÷ 100%
= 420
Therefore, Jamie burned 420 calories on Tuesday
Which choice names a chord of circle F?
FE
BA
A and F
FD
Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ? 1. ? 2. ? 3. ? 4. ? 5. ? 6. ? 7. ? 8
The differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.
1. y' = x: This differential equation corresponds to a phase line with a slope of 1, since the y' term is equal to the x term.
2. y' = -x: This differential equation corresponds to a phase line with a slope of -1, since the y' term is equal to the negative of the x term.
3. y' = [tex]x^2[/tex]: This differential equation corresponds to a phase line with a slope of 2x, since the y' term is equal to the x squared term.
4. y' = [tex]-x^2[/tex]: This differential equation corresponds to a phase line with a slope of -2x, since the y' term is equal to the negative of the x squared term.
5. y' =[tex]x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]3x^2[/tex], since the y' term is equal to the x cubed term.
6. y' = [tex]-x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-3x^2[/tex], since the y' term is equal to the negative of the x cubed term.
7. y' = [tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]nx^(n-1)[/tex], since the y' term is equal to the x to the power of n term.
8. y' = -[tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-nx^(n-1),[/tex] since the y' term is equal to the negative of the x to the power of n term.
In summary, the differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.
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Complete question:
Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ?
1. y' = x
2. y' = -x
3. y' = [tex]x^2[/tex]
4. y' = [tex]-x^2[/tex]
5.y' =[tex]x^3[/tex]
6.y' = [tex]-x^3[/tex]
7. y' = [tex]x^n[/tex]
8. y' = -[tex]x^n[/tex]
if the sum of two consecutive even numbers is 42 find the number
Answer:
20 and 22
Step-by-step explanation:
if the sum of two consecutive even numbers is 42 find the number
42 - 2 = 40 remove the difference (2)
40 : 2 = 20 find the smallest number
20 + 2 = 22 find the largest number
------------------------------------
(20 + 22 = 42)
A triangle has a perimeter of 9x 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle? x 13 x − 1 8x − 7 17x − 1
The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.
Perimeter of the triangle is equal to
= 9x + 6
First side of the triangle = 5x
Second side of the triangle = 3x - 7
Let 'n' be the third side of the triangle
perimeter of the triangle = 9x + 6
⇒ 5x + 3x - 7 + n = 9x + 6
⇒ n + 8x - 7 = 9x + 6
⇒ n = 9x -8x + 6 + 7
⇒ n = x + 13
Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.
The above question is incomplete , the complete question is :
A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?
a. x + 13 b. x − 1 c. 8x − 7 d. 17x − 1
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-11x-11 ≥ −6+13x
X <
NEED THIS ASAP
Find m/EFG.
m/EFG
Answer: 41 degrees
Step-by-step explanation:
121-39=82
82/2=41
Is the answer 126.26? Area of compound figures?
Answer:
Step-by-step explanation:
HELP ASAP, WILL GIVE BRAINLIEST
Where is the above note played on the guitar?
Open second string
Open third string
Second string, first fret
Third string, second fret
Answer:
Second string, first fret.
Step-by-step explanation:
A composite figure is shown. A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 8 feet. The portion from a point to a vertical line created by two vertices is 4 feet. Which of the following represents the total area of the figure?
44 ft2
400 ft2
440 ft2
484 ft2
The solution is 440 ft² because the overall size of the image is 528 sq ft, which in itself is closest approaching 440 square feet.
What does parallel shape mean?Parallel forms are defined as having at least two even more parallel lines. If two lines never cross, they are considered to be parallel. There are different parallel shapes, however any parallel sides require an equitable distribution of sides in the shape.
Sum of the measurements of the two main sides divided by height equals the area of a trapezoid.
Let's refer to the longer parallel side's length as "L." The figure's height is 22 feet, while the shorter parallel side's length is 16 feet.
Area = (L + 16) / 2 * 22
We also knows that the distance between a point and the vertical line formed by two studs is 4 feet and the distance between a vertex and the opposing height is 8 feet. The Pythagorean theorem may be used to determine the length of the greater parallel side, L, since these two lengths create a right triangle.
L² = (8 + 4)² = 64
L = 8
We can now calculate the overall area using the formula for a trapezoid's area.
Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528
The solution is 440 ft² because the overall size of the figures is 528 sq ft, that is closest towards 440 sq ft.
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I NEED HELP!!!!!!
Workers install 840 chairs at a constant rate. After 5 days, the workers still have to install 240 chairs. How much time does it take to install the chairs from start to finish?
Let's call the time it takes to install all the chairs from start to finish "t". The workers install 840 chairs per day, so in "t" days they will have installed 840 * t chairs.
At the end of 5 days, they still have 240 chairs to install, so they have installed 840 * 5 chairs so far. We can use this information to write an equation:
840 * t - 840 * 5 = 240
Expanding and simplifying the equation gives us:
840t - 4200 = 240
Adding 4200 to both sides gives us:
840t = 4440
Finally, dividing both sides by 840 gives us:
t = 5.2857142857...
So it takes approximately 5.29 days to install all the chairs from start to finish.
Some of the world's smallest horses
include: Thumbelina, who stands
17 inches tall; Black Beauty, who stands
18 inches tall; and Einstein, who stands
14 inches tall.
a. How much taller is Black Beauty
than Thumbelina?
Black Beauty stands one inch taller than Thumbelina, measuring 18 inches in height compared to Thumbelina's 17-inch stature.
Black Beauty is 1 inch taller than Thumbelina.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Thumbelina, who stands 17 inches tall
Black Beauty, who stands 18 inches tall.
Einstein, who stands 14 inches tall.
We have to find how tall is Black Beauty than Thumbelina.
To find out, we can subtract Thumbelina's height from Black Beauty's height:
Black Beauty's height - Thumbelina's height
= 18 inches - 17 inches = 1 inch
Therefore, Black Beauty is 1 inch taller than Thumbelina.
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