The probability of 45 heads in 100 tosses of a coin given the probability of heads is 50% is 7.1%.
Coin Toss Probability CalculationThe binomial probability formula is used to calculate the probability of getting a certain number of heads (or success) in a certain number of coin tosses (or trials) when the probability of getting a head (or success) in each individual coin toss is known. The formula is:
P(x) = (n choose x) * (pˣ) * (1-p)^(n-x)
Where,
P(x) is the probability of getting x heads (or success) in n coin tosses (or trials)
n is the number of coin tosses
x is the number of heads (or success)
p is the probability of getting a head (or success) in a single coin toss
1-p is the probability of getting a tail (or failure) in a single coin toss
(n choose x) is the binomial coefficient, which is the number of ways to choose x heads (or success) from n coin tosses (or trials)
In this case, the probability of getting 45 heads in 100 tosses of a coin with a probability of heads of 50% can be calculated using the formula: (100 choose 45) * (0.5⁴⁵) * (0.5⁵⁵) which is approximately 0.071, or 7.1%.
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What is the formula for finding the distance between two parallel lines?
[tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex] is the formula used to calculate the distance between two parallel lines. This is derived from the slope-intercept equation.
The two lines that never cross over one another are referred to as parallel lines. When the separation between these two lines is considered constant, then these two lines are parallel.
As a result, the distance between two lines can be determined by considering their perpendicular distance. The two parallel lines can be written using the slope-intercept form as y = mx + c₁ and y = mx + c₂, respectively.
Then, the formula to calculate distance is given by, [tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex]. Here, the intercepts of the two lines are c₁ and c₂, and a and b are the constants or integers.
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in 2009 the average weekly wage of men exceeded that of a woman by $162. the sum of their average wages equaled $1476. write and solve a system of equations to determine the average wage of men and of women in 2009
How do you convert base 10 to base 4?
Answer:
First, divide the number by the base to get the remainder. This remainder is the first, ie least significant, digit of the new number in the other base
Then repeat the process by dividing the quotient of step 1, by the new base. ...
Repeat this process until your quotient becomes less than the base
Step-by-step explanation:
The function g is defined by the following rule. g(x) = 2x +1
The function g is defined by the following rule. g(x) = 2x +1 can be represented in the method given below-
How does this occur?
The function f with g is written as (fg)(x)=f(g(x)), and is understood as f of g of x. The function g will be used in place of any x in the function f, according to this statement (x)
f(x), where x is the input, is a common way to refer to a function. A function can be conceptualized as y = f in general (x).
x= -3 then g(-3) = 2(-3) + 1 = -5If x = -2 then g(-2) = 2(-2) + 1 = -3if x = -1 then g(-1) = 2(-1) + 1 = -1If x = 1 then g(1) then = 2(1) +1 =3This is how by taking various x value we can find the value of g(x) = 2x +1
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Find the missing values so that the area of the product is equal to the
area of its sum.
On solving the provided question, we can say that here, in the equation = (2x+3y)(3y-3)=12x+3y-15. so the missing values are = 3y
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here, in the equation
(2x+3y)(3y-3)=12x+3y-15
so the missing values are
3y
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Why can’t astronomers take a picture of a black hole?
Gravity is so strong that even light cannot escape a black hole.
The nearest black hole is too far away to be seen.
There is no way to detect the locations of black holes.
Black holes are too large to photograph.
Answer:
A
Step-by-step explanation:
edge 2023
solve each system by substitution
y=4x
x-2y=56
Answer:
-8
Step-by-step explanation:
Since it tells you that y=4x you can use that to replace y in the next equation so now it's
X-2(4x)=56
Distribute the -2
X-8x=56
Subtract -8x from x
-7x=56
Divide by -7
X=-8
Answer:
x=−8
y=−32
pspdwdpvprngbpnrpt
One lap around the inide lane of a tandard track i equal to 400 meter. Brad jog one lap around a track in one minute 30 econd. Auming he can maintain thi pace, how long will it take him to run a mile? Round your anwer to the nearet tenth of a minute
Brad takes 6 minutes to run a mile assuming he can maintain the same pace.
Given that,
One lap around the inside lane of a standard track = 400m
Time taken for Brad to jog one lap around a track = 1 minute and 30 secs
We know that one mile = 1609.34 meters = 1600 meters (approximately)
Since Brad can jog 400m in 1 minute and 30 secs
1600 meters = 400*4 meters
Assuming that he can maintain the same pace:
so, the total time taken to run 1 mile = 1 minute 30 secs * 4 = 6 minutes
Hence, Brad takes 6 minutes to run a mile assuming he can maintain the same pace.
Correct question: One lap around the inside lane of a standard track is equal to 400 meters: Brad jogs one lap around a track in one minute and 30 seconds. Assuming he can maintain this pace, how long will it take him to run a mile? Round your answer to the nearest tenth of a minute.
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Need help right now please I don’t understand why this question is so hard
Answer:
A:33
B:22
C:74
Step-by-step explanation:
A:
2x2x2=8
5x5=25
8+25=33
B:
7x7=49
3x3x3=27
49-27=22
C:
8x8=64
square root of 100 is 10
64+10=74
i hope this helps :)
the graph below represents a linear function. which of the following equations models the linear graph above?
What is the exponential form of 5 * 5 * 7 * 7 * 7?
The exponential form of 5 * 5 * 7 * 7 * 7 is [tex]5^{2}[/tex] * [tex]7^{3}[/tex] . Exponential form can be written from the prime factorization of the number.
To get the exponential form of a number we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.
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A fence post that is 5 feet tall casts a 2-foot shadow at the same time that a tree that is 26 feet tall casts a shadow in the same direction. Determine the length of the tree's shadow.
5.2 feet
10.4 feet
12.2 feet
15.4 feet
Answer:
10.4 feet
Step-by-step explanation:
26/5 = 5.2
5.2(2)=10.4
The length of the tree's shadow is 10.4 feet. Option B is correct.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
We can use similar triangles to solve this problem.
The ratio of the height of the fence post to its shadow is the same as the ratio of the height of the tree to its shadow.
(height of fence post) / (length of fence post's shadow) = (height of tree) / (length of tree's shadow)
Substituting the given values, we get:
5 / 2 = 26 / x
where x is the length of the tree's shadow.
Cross-multiplying and solving for x, we get:
x = 26 × 2 / 5
= 10.4 feet
Therefore, the length of the tree's shadow is 10.4 feet.
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1. The function that describes the rigid motion could be (x, y) -
A. (2x, y).
C. (y,-22).
B. (x - 3,y).
D. (x,3).
what is the square root 15v to the 4th power times square root of 2v
the square root 15v to the 4th power times square root of 2v to the 3rd power is 15v^2 x 2v^3, or 30v^5.
What is square root?The square root of a number is a value that, when multiplied by itself, produces the original number. For example, the square root of 16 is 4 because 4 x 4 = 16. In mathematics, the square root of a number is written as a radical symbol, with the number inside the radical symbol. The square root symbol is also known as the radical symbol or radix.
To calculate this, first take the square root of 15v to the 4th power, which is 3v. Then take the square root of 2v to the 3rd power, which is 2v.
Finally, multiply 3v and 2v together to get the final answer of 30v^5.
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Complete questions as follows-
What is the square root 15v to the 4th power times square root of 2v to the 3rd power?
Nadia is a stockbroker. She earns 12% commission each week. Last week, she sold $5,300 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Nadia made commission of $636 last week
She made $33072 commission in 2011.
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given,
Weekly commission of Nadia = 12%
Cost of stocks Nadia sold last week = $5300
Commission made by Nadia last week = 12% of $5300
= (12/100) × 5300
= 12 × 53
Commission made by Nadia last week = $636
No. of weeks in 2011 = 52 weeks
If she averages that same amount each week
Then commission made by her in 2011 = 52 × $636
= $33072
Hence, $636 is the commission made by Nadia last week,
$33072 is the total commission made by Nadia in 2011.
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I need help on filling in the blanks for these shapes
We can see here that the triangles have been attached to the corresponding angles and sides.
(a) ∠A ≅ ∠Y
∠B ≅ ∠Z
∠C ≅ ∠X
(b) Side AB ≅ Side YZ
Side AC ≅ Side YX
Side BC ≅ Side ZY
(c) ΔABC ≅ Δ YZX
What is congruent?Congruent refers to the state of two geometric figures or shapes having the same size and shape. Two figures are congruent if one can be superimposed on the other by a combination of rotation, reflection, and translation.
Congruence is often denoted by the symbol “≅”. Congruence is a fundamental concept in Euclidean geometry, and it applies to many types of geometric figures, including lines, angles, triangles, and polygons.
We can see that the various angles and sides has been shown above.
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Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
Answer:
B and D
Step-by-step explanation:
-2+2=0
What is the y-intercept of y =- 2 5?
Comparing the given expression with the slope-intercept form, the intercept value is calculated. And the value is -2/5.
A line's slope gives information about its steepness or indicates how much y rises as x rises. The equation is typically written as y=mx+b in slope-intercept form. The slope in this equation is represented by the letter m, and the y-intercept is represented by the letter b. The y-intercept is calculated in the subsequent step by comparing the given expression with this.
The given expression is y =- 2/5. Comparing this expression with y=mx+b, we get, m=0, x=0, and b=-2/5. Therefore, the required y-intercept is -2/5.
The complete question is -
What is the y-intercept of y =- 2/5?
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The Chamber of Commerce of a city in central Florida is making brochure to attract tourists. They recorded the high temperatures (in degrees Fahrenheit) for a week in January to be 75, 72, 73, 56, 62, and 71. If you were a tourist planning to visit the area, which of these measures of central tendency would be the best to use as the most accurate indicator of the temperature for planning your wardrobe? Correct mean median mode range
The measure of central tendency that would be the best to use as the most accurate indicator of the temperature for planning your wardrobe is the mean.
What is the mean?The ratio between the sum of all observations and the total number of observations in a data set is known as the mean in statistics. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set.
When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
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Which one of the following triangles has only 2 equal sides.(i) Equilateral triangle(ii) Scalene Triangle(iii) Isosceles Triangle
The correct option is (iii) Isosceles triangle is the one which has only 2 equal sides.
Every triangle is made up of three sides and three angles. A side is opposing an angle or a vertex if none of its ends is at the given angle's vertex. An angle is included between two sides if their common terminus is the angle's vertex.
Triangles are divided into one of three types based on the lengths of its sides: scalene, isosceles, or equilateral. A triangle is scalene if none of its sides are equal (of equal length). The triangle is isosceles if two or more of its sides are equal. A triangle is equilateral if all three of its sides are equal. By definition, all equilateral triangles are also isosceles.
Therefore, the correct answer is option (iii) Isosceles Triangle
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Trevor's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 5 coffees in all, 4 of which were regular. What percentage of the coffees were regular? Write your answer using a percent sign (%)
Answer:
80%
Step-by-step explanation:
since there were 5 coffees but 4 out of it were regular
mathematically
that's 4/5
but to percentage
that's times 100
4/5×100
4×100 all divided by 5
400 divided by 5
80%
Use the quadratic formula to find the solutions to the quadratic equation
below.
x-5x-4 = 0
O A. x =
O
-5+√41
2
B. x = 5±√41
O c. x =
C.
-5+√/29
D. x = 5√2
Answer:
A, B
Step-by-step explanation:
[tex]x^2-5x-4=0 \\ \\ x=\frac{5 \pm \sqrt{(-5)^2-4(1)(-4)}}{2}[/tex]
On simplifying, the correct answers are A and B.
Last week, Darell spent 5 hours doing homework. Bruce did homework for 1/5 as many hours as Darell did. How many hours did Bruce spend doing homework?
The number of hours Bruce spent doing homework last week if he spent 1/5 of Darell's time is 1 hour.
How to solve fractions?Time Darell spent doing homework last week = 5 hours
Time Bruce spent doing homework last week = 1/5 of Darell's time
= 1/5 of 5
= 1/5 × 5
= (1 × 5) / (5 × 1)
= 5/5
= 1 hour
In conclusion, given the fraction of time Bruce spent doing homework last week, that means, he spent 1 hour doing homework.
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factor each expression. You can check your answer by distributing. 8d + 20e
The factorization of given expression is 4(2d+5e).
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given expression is 8d+20e.
In the given expression there are two terms and factors them are
8d= 2×2×2×d
20e= 2×2×5×e
So, the greatest common factor is 4
Now, 4(2d+5e)
Therefore, the factorization of given expression is 4(2d+5e).
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In the triangle below, with right angle Q, suppose that m/R= (3x+2) and m/S= (2x+18).
Find the degree measure of each angle in the triangle.
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer: (-4, 1) (-8, 9)
Explanation: These points are where the two functions meet
8.3 points
What is the leading coefficient in the polynomial 2v³ +4v² + 1?
2
4
1
3
The leading coefficient in the polynomial 2v³ +4v² + 1 will be A. 2
How can you determine a polynomial's leading coefficient?The term with the highest power of x is the leading term in a polynomial. As an illustration, the leading term in 7 + x + 3x² is 3x².
The leading coefficient is the number in front of the variable with the highest power
A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.
In this case, this will be 2v³. The coefficient is 2.
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Can you draw a triangle with sides of length 2cm 3cm and 7cm?
It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.
To check this we firstly add the 2 and 3
2 + 3 < 7
5 > 7
Now we add 2 and 7
2 + 7 > 3
9 > 3
Now we add 3 and 7
7 + 3 > 2
10 > 2
It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).
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What are these two problems fully simplified?
Answer:
1. 3/2 x m^5 x n
2. 54 x m^11 x n^9
Ellie is 1.75 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 20.25 meters. She stands 16.2 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
To find the height of the tree, we can use the tangent of the angle between the top of the tree and the tip of Ellie's shadow to find the height of the tree.
Tangent(theta) = Opposite / Adjacent
Opposite = height of tree
Adjacent = distance between Ellie and the tree
Tangent(theta) = height of tree / 16.2
We know that:
Tangent(theta) = 20.25 / 16.2
We can solve for the height of the tree by multiplying both sides of the equation by 16.2:
height of tree = Tangent(theta) * 16.2
height of tree = (20.25 / 16.2) * 16.2height of tree = 20.25
So, the height of the tree is 20.25 meters to the nearest hundredth of a meter.
Answer: the height of the tree is 20.25 meters to the nearest hundredth of a meter.
Step-by-step explanation: