A coin toss bet is placed between two friends such that the person who wins four tosses first is the winner. What is the total number of possible ways in which the bet can play out
Answers
Answer:
who wins four tosses first is the winner.
possible cases-7 tosses, 6 tosses, 5 tosses, 4 tosses
We get cases of Win of Head first-4 tosses
All 4 must be Head
Number of ways = 1
5 tosses-5th must be Head
there are 3 Head out of 4 in ⁴C₃ = 4 Ways
6 tosses-6th must be Head
there are 3 Head out of 5 in ⁵C₃ = 10 Ways
7 tosses-7th must be Head
there are 3 Head out of 6 in ⁶C₃ = 20 Ways
Cases of Head wins = 1+ 4 + 10 + 20 = 35
similarly cases when Tails Wins = 35
Total Possible cases = 35 + 35 = 70
70 is total number of possible ways in which the bet can play out.
Step-by-step explanation:
I hope that this helps u out..
Related Questions
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Note: Figure is not drawn to scale.
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
OA.
21 m
OB.
32 m
29 m
34 m
OC.
OD.
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After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.
The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted measurement regarding the distance around the outside of a two-dimensional shape. In this system the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m
grace thought of a number, added 7, multiflied by 3, took away 5 and divided by 4 to give an answer of 7
Answers
Answer:
Step-by-step explanation:
To find the number that Grace thought:
We'll represent the unknown number as "x."
"Added 7": This can be represented as (x + 7).
"Multiplied by 3": This becomes 3 * (x + 7).
"Took away 5": This is represented as 3 * (x + 7) - 5.
"Divided by 4": This gives (3 * (x + 7) - 5) / 4.
"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.
Now we can solve for x:
(3 * (x + 7) - 5) / 4 = 7
Multiply both sides by 4 to eliminate the denominator:
3 * (x + 7) - 5 = 28
Simplify the left side:
3x + 21 - 5 = 28
Combine like terms:
3x + 16 = 28
Subtract 16 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Therefore, the number that Grace thought of is 4.
82 people were surveyed as to how many TVs they had in their homes.
What was the range in the number of TVs owned by these households?
Number of TVs per Household Frequency
0 1
1 10
2 24
3 21
4 16
5 9
6 1
Answers
Answer:
The range is 23
Step-by-step explanation:
You need to find the biggest number, and then find the smallest number. Then you need to subtract them.
y=x2^+9x+7 in vertex form
Answers
Answer: (-9/2,-53/4)
Step-by-step explanation:
Answer:
\(y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}\)
Step-by-step explanation:
Vertex form of a quadratic equation:
\(\boxed{y=a(x-h)^2+k}\)
where:
(h, k) is the vertex.a is the leading coefficient.To find the vertex form of a quadratic equation, complete the square.
Given quadratic equation:
\(y=x^2+9x+7\)
Add and subtract the square of half the coefficient of the term in x to the right side of the equation:
\(\implies y=x^2+9x+\left(\dfrac{9}{2}\right)^2+7-\left(\dfrac{9}{2}\right)^2\)
\(\implies y=x^2+9x+\dfrac{81}{4}+7-\dfrac{81}{4}\)
\(\implies y=x^2+9x+\dfrac{81}{4}-\dfrac{53}{4}\)
Factor the perfect square trinomial formed by the first 3 terms:
\(\implies y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{53}{4}\)
Q3. Given that the area of sector below is 85cm^2 work out its radius, marked p on the
diagram.
Give your answer correct to 1 decimal place
Answers
The radius of the circle, marked p on the diagram, is approximately 5.8 cm.
What is radius?Radius is a term used in geometry to describe the distance from the center of a circle to any point on the circumference. It is a line segment that has its two endpoints at the center of the circle and at any point on the circumference.
The area of a sector is equal to the fraction of the circle's area that the sector occupies multiplied by the area of the entire circle.
Therefore, the area of the sector is equal to (θ/360) × πr^2.
Since the area of the sector is given as 85 cm^2, we can rearrange the equation to get:
85 = (θ/360) × πr^2
Rearranging further, we get:
r^2 = (85 × 360)/(πθ)
Taking the square root of both sides, we get:
r = √((85 × 360)/(πθ))
Since the angle θ is not given, we cannot solve for r. However, we can approximate the angle θ to be equal to 360° since the sector occupies the entire circle.
Therefore, the radius of the circle is equal to:
r = √((85 × 360)/(π × 360))
r = √(85/π)
r ≈ 5.8 cm
Therefore, the radius of the circle, marked p on the diagram, is approximately 5.8 cm.
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Need help please, fast, here i screenshot!!
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The equation g(x) = (x - 4) (x + 2) is in the factored form.
The x-intercepts are x = -2 and x = 4.
The axis of symmetry is x = 1.
Vertex is (1, -9).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
g(x) = (x - 4) (x + 2)
This is in the factored form.
Now,
From the graph,
The x-intercepts are x = -2 and x = 4.
The axis of symmetry.
x = -b/2a
x = 2/2
x = 1
i.e
g(x) = (x - 4) (x + 2)
g(x) = x² + 2x - 4x - 8
g(x) = x² - 2x - 8
a = 1, b = -2, and c = -8
Now,
g(x) = x² - 2x - 8
g(x) = x² - 2x + 1 - 1 - 8
g(x) = (x² - 2x + 1) - 9
g(x) = (x - 1)² - 9
This is in the form of f(x) = a(x - h)² + k
So,
Vertex = (h, k) = (1, -9)
Thus,
The statements are completed above.
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The data manager for a state political party gathered data to determine how many citizens would support the party’s senate candidate. He polled citizens in 30 similarly sized senate districts and found a sample mean of 70,438 citizens. Statewide data shows that the population standard deviation is 645.3. What is the approximate 90% confidence interval for this situation?
Answers
The approximate 90% confidence interval for this situation is given as follows:
(70244, 70632).
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the rule presented as follows:
\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)
In which:
\(\overline{x}\) is the sample mean.z is the critical value.n is the sample size.\(\sigma\) is the standard deviation for the population.From the z-table, the critical value for a 95% confidence interval is given as follows:
z = 1.645.
The parameters are given as follows:
\(\overline{x} = 70438, \sigma = 645.3, n = 30\)
The lower bound of the interval is given as follows:
\(70438 - 1.645 \times \frac{645.3}{\sqrt{30}} = 70244\)
The upper bound of the interval is given as follows:
\(70438 + 1.645 \times \frac{645.3}{\sqrt{30}} = 70632\)
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Philip has been experimenting with new recipes at his bakery for the past 8 months. This month, he tried a recipe for lavender vanilla muffins and gave samples to his customers. He asked them to rate the muffins on a scale of 1 to 10 stars. The median rating was 7 stars, and the interquartile range was 4 stars. ) What can you conclude from these data and statistics? Select all that apply. () No customer gave the muffins fewer than 8 stars. A typical rating for the muffins was 7 stars. The middle 50% of customer ratings had a range of 4 stars. Submit
Answers
- A typical rating for the muffins was 7 stars, since the median rating was 7 stars.
- The middle 50% of customer ratings had a range of 4 stars, since the interquartile range was 4 stars.
- We cannot conclude that no customer gave the muffins fewer than 8 stars, as the median is not necessarily equal to the mean, and it is possible that some customers rated the muffins below 8 stars. Therefore, this statement is not necessarily true.
PLZ, HURRY WILL GIVE BRAINILEST TO CORRECT ANSWER!
Write the fraction in the simplest form.
8/10
A. 16/20
B. 2/5
C. 4/5
D. 2/10
Thank you if u help UVU
Answers
You welcome
What is the approximate area of the shaded region? Use 3.14 for 7.
1 in
6 in
4 in
A. 23 square inches
B. 27.14 square inches
C. 22.43 square inches
OD. 20.86 square inches
Answers
The Area of the shaded region is 20.86 in²
What is the area of circle?The area of a circle is calculated using the formula A = πr², where "A" is the area of the circle.
We know,
Area of Rectangle = l × w, where l = length and w = width
Area of Circle = \(\pi r^{2}\), where r = radius.
find the area of the rectangle,
length = 6 in and width = 4 in
Area of Rectangle = 6 × 4 = 24 inch²
Here given the circle radius is 1 inch, and we use π as 3.14
Area of Circle = \(\pi r^{2}\)
Area of Circle = 3.14 × 1² = 3.14 in²
The area of the shaded region as per figure below is:
Area of the shaded region = Area of Rectangle - Area of Circle
Area of the shaded region = 24 - 3.14 = 20.86 in²
Therefore, the answer is D. 20.86 square inches.
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can you please help me
Answers
Given:
Radius of the sphere, r = 16 ft
Let's find the surface area and volume of the sphere.
• Surface Area:
To find the surface area of the sphere, apply the formula below:
\(SA=4\pi r^2\)Thus, we have:
\(\begin{gathered} SA=4\pi\ast16^2 \\ \\ SA=4\pi\ast256 \\ \\ SA=1024\pi \\ \\ SA=3216.99ft^2 \end{gathered}\)Therefore, the surface area of the sphere is 1024π square ft.
• Volume:
To find the volume of the sphere, apply the formula below:
\(V=\frac{4}{3}\pi r^3\)Thus, we have:
\(\begin{gathered} V=\frac{4}{3}\pi\ast16^3 \\ \\ V=\frac{4\pi\ast4096}{3} \\ \\ V=\frac{16384\pi}{3} \\ \\ V=17157.28ft^3 \end{gathered}\)Therefore, the volume of the sphere is 17157.28 cubit ft
ANSWER:
\(\text{ S = (1024}\pi)ft^2\)\(V=(\frac{16384}{3}\pi)ft^3\)
Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
Answers
The coordinates of pre-image point H is (c) (3, 2)
How to determine the coordinates of pre-image point H?The graph represents the given parameter
On the graph, we have the coordinate of point H' (i.e. the image) to be
H' = (-3, -2)
The transformation rule is given as
Rotation 180° about the origin
Mathematically, this is represented as
(x, y) = (-x, -y)
This implies that:
H = (3, 2)
So, the coordinates are (3, 2)
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What should be subtracted from minus 3 / 4 so has to get 5 / 6 ?
Answers
Answer:
Step-by-step explanation:
Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and
6,which is 12.
3*3/4*3=9/12
5*2/6*2=10/12
Step 2:Subtract 9/12 from 10/12,which is 1/12.
Bob grew 1,102 plants with 29 seed packets. With 94 seed packets, how many total plants can Bob have in his backyard? Assume the relationship is directly proportional.
Answers
If the relation between number of plants and the number of seed packets is directly proportional and x is the number of plants can Bob have for 94 seed packets, you can write;
\(\frac{x}{94}=\frac{1102}{29}\)By solving for x in the previous expression and simplifying, you get:
\(\begin{gathered} x=\frac{1102}{29}\cdot94 \\ x=3572 \end{gathered}\)Hence, Bob could have 3572 plants if he uses 29 seed packets.
If the domain of the function y=4x+1 is 0
Answers
Compute 292,000 divide 100.
Answers
The division 292,000 divide 100. results to 2920.
What is Division?Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.
Given:
292,000 divide 100.
We know division with zero in the denominator is different and easy.
As, 292000 have three and 100 have two zeroes.
So, the two zero of hundred cancels out the two zeroes of 292000.
So, 292000/ 100
= 2920
Hence, the division results to 2920.
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What is the rental cost? Step by step.
Answers
The rental cost in dollars per square foot is $11,00
What is the rental cost in dollars per square foot?Cost of renting 1.250 square feet = $13, 750 per month
Rental cost per square foot = Total renting cost / total renting area
= $13, 750 per month / 1.250 square feet
= $11,000
Hence, $11,000 is the rental cost in dollars per square foot.
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Help pls i dont understand this
Answers
The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The total number of water bottles the company manufactured in February, March, and April.
In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.
Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.
This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.
Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
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Write the equation of the circle graphed below.Write standard equation of a circle
Answers
EXPLANATION
The equation of a circle with center (h,k) and radius r is the following:
\((x-h)^2+(y-k)^2=r^2\)In this case, the center is at (5,0) and the radius is diameter/2=8/2=4
Therefore, the equation is as follows:
\((x-5)^2+(y-0)^2=4^2\)Computing the power:
\((x-5)^2+y^2=16\text{ \lbrack EQUATION OF THE CIRCLE\rbrack}\)The solution is:
(x-5)^2 + (y-0)^2 = 16
The graph is the following:
the formula for the area a of a circle of radius r is
Answers
Expressed as a single fraction, 3/4x - 2/5x is equal to
Answers
The single fraction is 7x/20
What is a fraction?A fraction can be defined as the part of a whole variable, number or element.
The different types of fractions are;
Simple fractionsMixed fractionsProper fractionsComplex fractionsImproper fractionsWhat are algebraic expressions?Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.
They are made of operations such as multiplication, addition, subtraction, division, etc
Given the expression;
3/4x - 2/5x
Find the LCM
15x - 8x/20
7x/20
Thus, the value is 7x/20
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what is an equivalent expression for 1/4x
please help ASAP.
Answers
Answer:
x/4
Step-by-step explanation:
Find the areas of the figures below. Can you find more than one method for each shape?
Please explain how you solved this. I am struggling.
Answers
Using area formula,
a. Area of the trapezium = 47.5m².
b. Area of parallelogram = 54inches².
Define area?The area of a thing is the amount of space it occupies in two dimensions. It is a way to count how many unit squares completely round the surface of a closed figure. The standard unit of area is the square unit, which is usually expressed as square inches, square feet, etc.
a. Sides of the trapezium are, a = 5m and b = 14m.
Height, h = 5m.
Area of the trapezium = (a+b)/2 × h
= (5 + 14)/2 × 5
= (19× 5)/2
= 95/2
= 47.5m².
b. Height of parallelogram = 6inches.
Base of parallelogram = 9inches.
Area = b × h
= 6 × 9
= 54inches².
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f(x) = 4x – 6. Which steps are a correct way to find f(2)?
Answers
Answer:
Step-by-step explanation:
f(x) means the same thing (just about) as y. Think of it as the y value.
f(2) means that wherever you see an x on the right, you make it into a 1.
So f(2) means 4(2) - 6 = 8 - 6 = 2
A us the correct answer. Everything else cannot be made to produce 2 or at least not the right way
Answer:
ITS A trust i did this
Step-by-step explanation:
Please help me with my work
Answers
Answer:
y = \(-\frac{2}{3}x + 1\)
Step-by-step explanation:
When y = mx + b
I. Find m.value
If m = (y2 - y1) / (x2 - x1)
= ( -1 - 3) / (3 + 3)
= -4/6
m = -2/3
II. Find b.value
If y = mx + b, when y is 3, x is -3 and m is -2/3
3 = -2/3(-3) + b
3 = -2(-1) + b
3 = 2 + b
3-2 = b
b = 1
That makes y = -2/3(x) + 1
Choose the term that is a number that describes the middle of a data set.
a.) Outlier b.) Spread c.) Shape d.) Center
Answers
Answer:
center
Step-by-step explanation:
2. The area of a figure is 207 m². If the
dimensions are multiplied by what will
be the area of the new figure?
Answers
EXREAMLY URGENT!! WILL FOREVER THANK YOU!!!! PLS JUST TAKE A LOOK!!!!! 20. What is the area of triangle XWZ?
Answers
Answer:
72√3
Step-by-step explanation:
30 60 90 triangles are what you start out with.
Step 1: 30-60-90
x = 12
WZ = 12√3
Step 2: Area formula
A = 1/2(12)(12√3)
*Since the 2 30-60-90 triangles are congruent, both segments of the base are 12
Plug it into the calc and you should get A = 72√3 as your final answer!
) Find the average gold medal winnings of those NOCs who have been
awarded fewer than ten bronze medals.
Count the number of those NOCs that have been awarded ten or more
silver medals.
This question requires the construction and interpretation of a pie chart based
on the data throughout this task.
a) Create a suitable and fully labelled pie chart to show the total medal
winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games.
Interpret the pie chart produced in Question 8a). Discuss two probable
justifications for the behaviour of the data.
Answers
a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:
Obtain the data for the medal winnings of the Top 10 NOCs
Find the average gold medal winnings of those NOCs who have beenawarded fewer than ten bronze medals.?Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)
Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option
Add a title and labels to the chart to show the NOCs and their corresponding medal winnings
b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:
Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.
Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.
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2/9 - 2/15 as a fraction in lowest terms
Answers
The numerator and the denominator have no common prime factors.
Their prime factorization:
2 is a prime number;
9 = 32;