The numerical expressions are:
(2 + 4) x 7 = 42
(12 ÷ 3) x 5 = 20
What is a numerical expression?A mathematical expression is made up of integers and mathematical operators including addition, multiplication, subtraction, and division.
A number can be expressed in numerous ways, including word form and numerical form.
A numerical expression is a mathematical statement that only contains numbers and one or more operation symbols. Addition, subtraction, multiplication, and division are examples of operation symbols. It can alternatively be expressed using the radical symbol (square root symbol) or the absolute value symbol.
The numerical expressions are:
(2 + 4) x 7 = 42
(12 ÷ 3) x 5 = 20
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Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.”
7 of the 25 measures are ratings of at most 6, that is, 6 is less than both the mean and the median of the distribution, hence it is not a good description of the center of this data set.
What is a data set?
A data set is a group of related data. In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.
Here, we have
Given: Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.”
From the plot given in this exercise, it is found that only 7 of the 25 measures are ratings of at most 6, that is, 6 is less than both the mean and the median of the distribution.
Hence it is not a good description of the center of this data set.
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Lol I hav no idea I suck at math TvT
Answer:
It's 6444
Step-by-step explanation:
If the answer of the number x multiplied by 2 is 4296 that means that the value of x is 2148.
So if the number is 2148 and we really need to multiplied it by 3 we get 6444.
Hope this helps :)
Pls brainliest...
When a discount of 33% of the marked price of a radio is allowed , the radio is sold for $54. How much discount does Raymond get when buying the radio?
Raymond gets a discount of $27.
Let the marked price of the radio be 'x'.
According to the problem, a discount of 33% is given, which means that the selling price is 67% of the marked price.
So, the selling price of the radio is 67% of x, which is given as $54 in the problem.
Hence, 67% of x = $54
Solving for x, we get x = $80
The discount amount is the difference between the marked price and selling price, which is $80 - $54 = $26.
Therefore, Raymond gets a discount of $26.
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Which of the following fractions are equal to 3/4?
Answer:
6/8, 9/12, 12/16, 15/20
Step-by-step explanation:
If you simplify the fractions it will all equal 3/4.
Simplify by finding the Greatest Common Factor and dividing both numbers by the GCF.
6
Write the sum in expanded form. ∑ = 23 / (i + 23)
i=1
The sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
The sum in expanded form is given by the expression 23 / (i + 23), where i varies from 1 to 6.
The sum in expanded form can be calculated by substituting the values of i from 1 to 6 into the expression 23 / (i + 23) and summing them up.
When i = 1, the expression becomes 23 / (1 + 23) = 23 / 24.
When i = 2, the expression becomes 23 / (2 + 23) = 23 / 25.
When i = 3, the expression becomes 23 / (3 + 23) = 23 / 26.
When i = 4, the expression becomes 23 / (4 + 23) = 23 / 27.
When i = 5, the expression becomes 23 / (5 + 23) = 23 / 28.
When i = 6, the expression becomes 23 / (6 + 23) = 23 / 29.
Therefore, the sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
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The sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
The sum in expanded form is given by the expression 23 / (i + 23), where i varies from 1 to 6.
The sum in expanded form can be calculated by substituting the values of i from 1 to 6 into the expression 23 / (i + 23) and summing them up.
When i = 1, the expression becomes 23 / (1 + 23) = 23 / 24.
When i = 2, the expression becomes 23 / (2 + 23) = 23 / 25.
When i = 3, the expression becomes 23 / (3 + 23) = 23 / 26.
When i = 4, the expression becomes 23 / (4 + 23) = 23 / 27.
When i = 5, the expression becomes 23 / (5 + 23) = 23 / 28.
When i = 6, the expression becomes 23 / (6 + 23) = 23 / 29.
Therefore, the sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
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suppose that n(u ) = 200 , n(e ∪ f ) = 194 , n(e) = 106 , and c n(e ∩ f ) = 73 . find each of the following values. n (e ∪ f)c
N(e ∪ f) = 194.
Using the inclusion-exclusion principle, we have:
n(e ∪ f) = n(e) + n(f) - n(e ∩ f)
We are given n(e ∩ f) = 73 and n(e ∪ f) = 194, so we can rearrange to solve for n(f):
n(f) = n(e ∪ f) - n(e) + n(e ∩ f)
n(f) = 194 - 106 + 73
n(f) = 161
Finally, to find n(e ∪ f), we can substitute the values we have found into the first equation:
n(e ∪ f) = n(e) + n(f) - n(e ∩ f)
n(e ∪ f) = 106 + 161 - 73
n(e ∪ f) = 194
Therefore, n(e ∪ f) = 194.
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1. An online store sells sportswear. Of all online sales, it is known that the amount of each sale is right skewed with mean $55 and standard deviation $19. A sample of 50 sales is randomly selected.(a). Find the mean of the sampling distribution of the mean amount spent per sale for samples of size 50.(b).Find the standard deviation of the sampling distribution from part (a). (Round your answer to three decimal places.)
The following parts can be answered by the concept of standard deviation.
a. The population mean is $55.
b. The standard deviation of the sampling distribution is approximately 2.688 (rounded to three decimal places).
(a) The mean of the sampling distribution of the mean amount spent per sale for samples of size 50 is equal to the population mean. In this case, the population mean is $55.
(b) To find the standard deviation of the sampling distribution, we use the formula:
Standard deviation of the sampling distribution = (Population standard deviation) / sqrt(sample size)
In this case, the population standard deviation is $19 and the sample size is 50. Plugging these values into the formula, we get:
Standard deviation of the sampling distribution = 19 / sqrt(50) ≈ 19 / 7.071 ≈ 2.688
So, the standard deviation of the sampling distribution is approximately 2.688 (rounded to three decimal places).
Therefore,
a. The population mean is $55.
b. The standard deviation of the sampling distribution is approximately 2.688 (rounded to three decimal places).
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The line plot represents data collected from a used bookstore.
Which of the following describes the spread and distribution of the data represented?
The data is almost symmetric, with a range of 9. This might happen because the bookstore offers a sale price for all books over $6.
The data is skewed, with a range of 9. This might happen because the bookstore gives away a free tote bag when you buy a book over $7.
The data is bimodal, with a range of 4. This might happen because the bookstore sells most books for either $3 or $6.
The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4.
The best description of the data on the line plot is: "D. The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4."
What is a Symmetric Data on a Line Plot?A symmetric data on a line plot means that the data is evenly distributed around the center. In other words, the data points on one side of the center are mirror images of the data points on the other side of the center.
For example, the set of data values displayed on the line plot shows that the data points on one side of the line (the center) are balanced by the data points on the other side of the line. This indicates that the data is evenly distributed and has no significant skewness or bias towards one side.
The range of the data = 6 - 2 = $4.
The mode is also $4
Therefore, the correct option is: option D.
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Solve the separable differential equation for u, du/dt = e^5u+5t. Use the following initial condition: u(0) = 15.
Th solution of the given seperable differential equation is :
u = (1/5)ln(25t^2 + e^75)
To solve the separable differential equation for u, we need to separate the variables and integrate both sides.
First, we can write the equation as:
(1/e^5u)du = 5t dt
Now we can integrate both sides:
∫(1/e^5u)du = ∫5t dt
To integrate the left side, we can use u-substitution:
Let u = 5u
Then du = 5e^5u du
Substituting into the integral, we get:
(1/5)∫e^5u du = ∫5t dt
(1/5)e^5u = 5t^2/2 + C
Where C is the constant of integration.
Now we can solve for u:
e^5u = 25t^2 + 2C
Taking the natural logarithm of both sides:
5u = ln(25t^2 + 2C)
u = (1/5)ln(25t^2 + 2C)
Using the initial condition u(0) = 15, we can solve for C:
15 = (1/5)ln(2C)
ln(2C) = 75
2C = e^75
C = (1/2)e^75
Substituting this value of C into our solution for u, we get:
u = (1/5)ln(25t^2 + e^75)
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Question 18 of 26
BACK
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Given
�
(
�
)
=
−
2
�
−
2
f(x)=−2x−2, find
�
−
1
(
�
)
f
−1
(x).
The value of f ⁻¹ (x) would be,
⇒ f⁻¹(x) = - x/2 - 1
We have to given that;
Function is,
⇒ f (x) = - 2x - 2
Now, We can find the inverse of function as;
⇒ f (x) = - 2x - 2
⇒ y = - 2x - 2
Solve for x;
⇒ y + 2 = - 2x
⇒ x = - (y + 2)/2
⇒ x = - y/2 - 1
⇒ f⁻¹(x) = - x/2 - 1
Thus, The value of f ⁻¹ (x) would be,
⇒ f⁻¹(x) = - x/2 - 1
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A park has grass and sand. Find the area of the part with grass.
(Sides meet at right angles.)
Answer:
[tex]26m^{2}[/tex]
Step-by-step explanation:
To solve this problem you find the total area of the entire rectangle and subtract the area of the sand from it. That will give you the area of the grass.
To find the total area you need to do [tex]b*h[/tex], in this case, the base is [tex]2+3+2[/tex] or 7. The height is 5. So to find the area, you have to multiply [tex]7*5[/tex] to get[tex]35m^{2}[/tex].
To find the area of the grass you multiply the [tex]b*h[/tex] or [tex]3*3[/tex] to get the area of 9.
Now the last step is to subtract [tex]35 - 9[/tex], doing so gives you your answer of 26 m
I would love to get Brainliest. I'm trying to get to the Genius status on Brainly.
If the sphere shown above has a radius of 10 units, then what is the approximate volume of the sphere?
Answer:
V = 4188.97
Step-by-step explanation:
Formula for volume of a sphere is 4/3(pi)(r^3)
Using the formula for volume of a sphere, we plug in (4/3 * pi * 10^3).
a federal report indicated that 17 % of children under age 6 live in poverty in washington, an increase over previous years. how large a sample is needed to estimate the true proportion of children under age living in poverty in washington within with confidence? round the intermediate calculations to three decimal places and round up your final answer to the next whole number.
We would need a sample size of at least 1073 children under age 6 in Washington to estimate the true proportion of children living in poverty with 95% confidence and a margin of error of 2%.
To estimate the true proportion of children under age 6 living in poverty in Washington with 95% confidence and a margin of error of 2%, we can use the formula:
n = (Z² * p * q) / E²
where:
Z = the Z-score corresponding to the desired confidence level (1.96 for 95% confidence)
p = the estimated proportion (0.17 based on the federal report)
q = 1 - p
E = the desired margin of error (0.02)
Plugging in these values, we get:
n = (1.96² * 0.17 * 0.83) / 0.02²
n = 1072.45
Rounding up to the next whole number, we would need a sample size of at least 1073 children under age 6 in Washington to estimate the true proportion of children living in poverty with 95% confidence and a margin of error of 2%.
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What is the domain of this function?
(-3, -7)
(-8, 8)
(10, 1)
(9,4)
(7,-4)
(-6, -9)
Answer: (-8, -6, -3, 7, 9, 10)
Step-by-step explanation:
The domain of a function is the set of all possible x-values that correspond to the given ordered pairs.
Therefore, the domain of the function is: (-8, -6, -3, 7, 9, 10)
In Exercises 25-29, the given set is a subset of C[−1,1]. Which of these are also vector spaces? 1F= {f(x) in C[−1,1] : ∫ f(x)dx=0}−1
The given set F = {f(x) in C[-1,1] : ∫ f(x)dx = 0 from -1 to 1} is a vector space.
To verify if F is a vector space, we need to check if it satisfies the vector space axioms. Let f(x) and g(x) be elements of F, and c be a scalar.
1. Closure under addition: ∫ (f(x) + g(x))dx = ∫ f(x)dx + ∫ g(x)dx = 0 + 0 = 0. So, (f(x) + g(x)) is in F.
2. Closure under scalar multiplication: ∫ (cf(x))dx = c∫ f(x)dx = c(0) = 0. So, (cf(x)) is in F.
3. Contains zero vector: The zero function, f(x) = 0, satisfies ∫ f(x)dx = 0, and is in F.
Since F satisfies these axioms, it is a vector space.
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The given set F = {f(x) in C[-1,1] : ∫ f(x)dx = 0 from -1 to 1} is a vector space.
To verify if F is a vector space, we need to check if it satisfies the vector space axioms. Let f(x) and g(x) be elements of F, and c be a scalar.
1. Closure under addition: ∫ (f(x) + g(x))dx = ∫ f(x)dx + ∫ g(x)dx = 0 + 0 = 0. So, (f(x) + g(x)) is in F.
2. Closure under scalar multiplication: ∫ (cf(x))dx = c∫ f(x)dx = c(0) = 0. So, (cf(x)) is in F.
3. Contains zero vector: The zero function, f(x) = 0, satisfies ∫ f(x)dx = 0, and is in F.
Since F satisfies these axioms, it is a vector space.
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Which equation has roots of +_ 3
From the list of options the equation with roots of ±3 is: (d) (x + 0)^2 = 3^2
Which equation has roots of +_ 3The equation that has roots of ±3 is:
(x - 3)(x + 3) = 0
Expanding the left side of the equation using FOIL method, we get:
x^2 - 9 = 0
Therefore, the equation with roots of ±3 is:
x^2 - 9 = 0
Add 9 to both sides
x^2 = 9
Express 9 as 3^2
x^2 = 3^2
So, we have
(x + 0)^2 = 3^2
Therefore, the equation with roots of ±3 is: (d) (x + 0)^2 = 3^2
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The person filling the tank realizes something is wrong with the hose. After 30 minutes
he shuts off the hose and tries a different hose. The second hose flows at a constante
of 18 gallons per minute.
How long does it take to completely fill the tank by using the second hose?
If the person filling the tank realizes something is wrong with the hose. The time it take to completely fill the tank by using the second hose is: 5.56 minutes.
How to find the time?Using this formula find long does it take to completely fill the tank by using the second hose
Let Assume the tank has a capacity of 100 gallons.
Time =Amount of water ÷ rate
Let plug in the formula
Time = 100 gallons ÷ 18 gallons/minute
Time = 5.56 minutes (Approximately)
Therefore it would take 5.56 minutes to fill a 100-gallon tank.
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If the person filling the tank realizes something is wrong with the hose. The time it take to completely fill the tank by using the second hose is: 5.56 minutes.
How to find the time?Using this formula find long does it take to completely fill the tank by using the second hose
Let Assume the tank has a capacity of 100 gallons.
Time =Amount of water ÷ rate
Let plug in the formula
Time = 100 gallons ÷ 18 gallons/minute
Time = 5.56 minutes (Approximately)
Therefore it would take 5.56 minutes to fill a 100-gallon tank.
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can someone help me please im desperate
Explanation: A linear function would be a diagonal line from left to right either moving up or down in direction. An exponential function would be a straight line on the x axis from left or right until it reaches y axis, then a sharp curve up or down. A quadratic function would be a U shape either facing up or down.
Linear equation: y = mx + b
Exponential equation: y = abˣ
Quadratic function: y = axˣ + bx + c
The graph listed in the picture would be a quadratic function according to the explanation.
Area = ?
As in the picture attached.
The area of the shaded area is 0.314m²
How did we reach this conclusion?First let's analyze the shape.
It comprises:
A square whose side length is 1m
Then there is the circle that passes through a corner of the square and is tangent to the opposite two sides of the square. So the region shaded in blue is the region contained by the circle and the square but not common to both shapes.
To get the area of this portion shaded in blue, here is what we must do:
So the Area of the region shaded blue is:
Area of the circle + area of the square - 2 x Area of the overlapping area.
To further help our analysis, we must deconstruct this shape into familiar ones by creating a composite right triangle as shown in the attached image.
Since we have a right triangle, the arc that it subtends will be a 180° arc thus, the hypotenuse of the triangle is the diameter of the circle.
Thus, when we created a right triangle from the shape, we also carved out a semi-circle.
This means that the overlapping areas are:
Area of the composite right triangle + the Area of the Semi Circle.
Since we now have two semi circles, we can cancel out the area of the circle above.
Our new equation for the area shaded in blue becomes:
The area of the square - the area of 2 Right Triangles
Now we can being to compute for the area of the shapes:
Taking the right triangle firs, create a line from the radius bisecting the triangle at 90 degrees. This gives us two equal smaller right triaangles.
Since the ∠90 is bisected, this means that the sides will be r√2 and the height of both right triangles = r (radius)
extending the radius into the opposite direcitn, we now have the diagonal of the square.
Diagonal = r + r√2 = √2
Solving for r we say:
r(1+√2) = √2
r = √2/(1+√2)
To further simplify the above, we can multiply it by the conjugate:
r = √2/(1+√2) x (1-√2)/(1-√2)
Thus,
r = 2-√2
So since the length of the square is 1m, then the area = 1x1 = 1m
The area of the composite triangle =( r√2 x r√2)/ 2 = r²
Since the area of the shaded region as given above is
The area of the square - the area of 2 Right Triangles
Then it's area = 1 - 2r²
We can simplify this further to get:
1-2(2-√2)²
= 8 √2 - 11m²
area of the shaded region ≈ 0.314m²
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Quadrilateral DEFG is a parallelogram. Kaye uses its properties in completing the
table.
The correct answer and the correct option is A.
How to determine the value?It is given that DEFG is a parallelogram.
Draw the diagonals DF and EG. Place point H where DF and EG intersect.
In triangle HGD and HEF
∠HGD ≅ ∠HEF (Alternate Interior angle)
∠HDG ≅ ∠HFE (Alternate Interior angle)
By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.
DG ≅ EF (Opposite sides of parallelogram)
According to ASA postulate, two triangles are congruent if any two angles and their included side are equal in both triangles.
So, by using ASA criterion for congruence we get,
ΔDGH ≅ ΔFEH
Since corresponding sides of congruent triangles are congruent, therefore
GH ≅ EH (CPCTC)
DH ≅ FH (CPCTC)
Option A is correct.
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1) Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = 1/2 + 5/6^x2 − 4/5^x3
The most general antiderivative of f(x) = 1/2 + 5/6x² − 4/5x³ is F(x) = 1/2x + 5/18x³ − 1/5x⁴ + C, where C is the constant of the antiderivative.
To check this answer, we can differentiate F(x) and see if it gives us back f(x). Taking the derivative of F(x), we get f(x) = d/dx (1/2x + 5/18x³ − 1/5x⁴ + C) = 1/2 + 5/6x² − 4/5x³, which matches the original function f(x). Therefore, F(x) is the most general antiderivative of f(x).
The constant of integration, denoted by C, is added because when taking the derivative of a constant, it is equal to zero. Thus, the constant of integration can be any real number, and it is included in the antiderivative to account for all possible functions that have f(x) as their derivative.
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problem 6: what is the bias? your answer should be be two decimal places, example would be 2.23.
if the bias is calculated as 2.234, you would round it to 2.23 since the third digit, 4, is less than 5.
I can explain how to represent a number with two decimal places.
When a number is represented with two decimal places, it means that it has two digits after the decimal point. For example, the number 2.23 has two decimal places, with the digits 2 and 3 after the decimal point.
Once you have calculated the bias or have the number you want to represent with two decimal places, you can round the number accordingly. To round a number to two decimal places:
1. Identify the second digit after the decimal point.
2. Look at the third digit after the decimal point.
3. If the third digit is 5 or greater, add 1 to the second digit. If it is less than 5, leave the second digit unchanged.
4. Remove all digits after the second decimal place.
For example, if the bias is calculated as 2.234, you would round it to 2.23 (since the third digit, 4, is less than 5).
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write a function file [a, b, i] gemetry ( across section, area, orientation) that calculates the perimeter of a beam given the desired cross section
This would calculate the perimeter of a square beam with an area of 25 square units, oriented horizontally.
```
function [perimeter] = geometry(across_section, area, orientation)
% Calculate the perimeter of a beam given the desired cross section
% Define constants for the shape of the cross section
switch across_section
case 'square'
side_length = sqrt(area);
num_sides = 4;
case 'circle'
radius = sqrt(area / pi);
num_sides = 0; % Circles have no sides
case 'rectangle'
aspect_ratio = 2; % Set this to whatever you need for your application
width = sqrt(area / aspect_ratio);
height = width * aspect_ratio;
num_sides = 4;
otherwise
error('Unknown cross section type');
end
% Calculate the perimeter based on the number of sides and shape
switch across_section
case 'circle'
perimeter = 2 * pi * radius;
otherwise
perimeter = num_sides * (width + height);
end
% Adjust the perimeter based on the orientation
switch orientation
case 'horizontal'
% No adjustment necessary
case 'vertical'
% Swap the width and height
temp = width;
width = height;
height = temp;
otherwise
error('Unknown orientation type');
end
end
```
To use this function, you would call it with the desired values for `across_section`, `area`, and `orientation`. For example:
```
perimeter = geometry('square', 25, 'horizontal');
```
This would calculate the perimeter of a square beam with an area of 25 square units, oriented horizontally.
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A fair coin is tossed repeatedly until the first "H" shows up - i.e. the outcome of the experiment is the number of tosses required until the first H occurs (1) What is the sample space for this experiment?(2) Find the probability law for this experiment - i.e. the P(each outcome) [Hint: Use tree diagram representation]
1) The sample space consists of all possible outcomes of coin tosses until the first "H" occurs
2) Probability of each outcome given by (1/2)^(n+1) where n is the number of tails before the first head
1) How to determine the sample space?The sample space for this experiment is the set of all possible outcomes of the coin tosses until the first "H" occurs. This includes all possible sequences of "T" (tails) and "H" (heads), with the restriction that the first "H" must be the last element in the sequence. For example, some possible outcomes are:
"H" (the first toss is heads)
"TH" (the first heads is on the second toss)
"TTTH" (the first heads is on the fourth toss)
2) How to find the probability law for this experiment?To find the probability law for this experiment, we can use a tree diagram to represent all possible outcomes and their probabilities. At each node in the tree, we branch to represent the two possible outcomes of the next coin toss (heads or tails). The probability of each branch is 1/2, since the coin is fair.
Here is the first level of the tree:
H (probability 1/2)
T (probability 1/2)
If the first toss is heads, we have reached the desired outcome and the experiment ends. If the first toss is tails, we continue branching:
T - H (probability 1/2 * 1/2 = 1/4)
T - T (probability 1/2 * 1/2 = 1/4)
If the second toss is heads, the experiment ends with a total of two tosses. If the second toss is tails, we continue branching:
T - T - H (probability 1/2 * 1/2 * 1/2 = 1/8)
T - T - T (probability 1/2 * 1/2 * 1/2 = 1/8)
We can continue this process to generate the full tree, which has an infinite number of levels (since the experiment could theoretically go on forever). However, we can see that each outcome corresponds to a unique path through the tree, and the probability of that outcome is the product of the probabilities along that path. For example, the outcome "TH" has probability 1/2 * 1/2 = 1/4, while the outcome "TTTH" has probability 1/2 * 1/2 * 1/2 * 1/2 = 1/16.
Therefore, the probability law for this experiment is:
P("H") = 1/2
P("TH") = 1/4
P("TTH") = 1/8
P("TTTH") = 1/16
In general, the probability of the outcome "T^nH" (where there are n tails before the first heads) is (1/2)^{n+1}. The probability of the experiment going on forever (i.e. never getting heads) is 0, since the probability of this outcome is the limit of (1/2)^{n+1} as n approaches infinity, which is 0.
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Jetia mixes 5 parts cranberry juice with 8 parts apple juice to make 177 cups of
Answer: 108 cups of cranberry juice. Brainliest?
Step-by-step explanation:
mixed juice. How many cups of cranberry juice did Jetia use?
Let's start by assuming that Jetia used x cups of cranberry juice to make the mixed juice. Then, since the ratio of cranberry juice to apple juice is 5:8, she must have used (5/8)x cups of apple juice.
We know that the total amount of mixed juice is 177 cups, so we can set up an equation based on the total amount of juice:
x + (5/8)x = 177
Simplifying this equation, we get:
(13/8)x = 177
Multiplying both sides by 8/13, we get:
x = 108
Therefore, Jetia used 108 cups of cranberry juice to make the mixed juice.
find the exact value of cos 105 degrees by using the half-angle formula
The exact value of the cos 105 degrees by the using the half angle formula is -0.2588.
To find the exact value of cos(105°) using the half-angle formula, we first need to express 105° as half of another angle. Since 105° is equal to 210°/2,
we can use the half-angle formula for cosine:
cos(x/2) = ±√[(1 + cos(x))/2]
In our case, x = 210°. Now, we need to find the value of cos(210°):
210° lies in the third quadrant, where both sine and cosine are negative. To find the reference angle, subtract 180°:
210° - 180° = 30°
So, cos(210°) = -cos(30°) = -√3/2.
Now, let's plug the value of cos(210°) into the half-angle formula:
cos(105°) = ±√[(1 - √3/2)/2]
Since 105° lies in the second quadrant, where cosine is negative, we choose the negative root:
cos(105°) = -√[(1 - √3/2)/2]
=-0.2588
Explanation:- Here to find the value of the cosine 105 degree by using the half angle formula first we write the half angle formula of the cosine and substituted x=210 degree and simplify.
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Todd spent some time cleaning his room
Jeff spent 11 more minutes cleaning his room room than tod spent.Jeff spent 43
minutes
Answer:
32
Step-by-step explanation:
43-11=32
select all that apply. for r, ≤ is a: a. linear order b. strict partial order c. (non-strict) d. partial order e. well-ordering order
For the relation "≤", the correct options: a. Linear order, d. Partial order, e. Well-ordering order
Hi! I'd be happy to help you with this question. Let's go through each option and determine if it applies to the relation "≤" (less than or equal to).
a. Linear order: A linear order is a partial order in which every pair of elements is comparable. Since "≤" allows us to compare any two elements in a set, it is a linear order.
b. Strict partial order: A strict partial order is a binary relation that is irreflexive (no element is related to itself) and transitive. "≤" is not a strict partial order because it is not irreflexive (an element can be related to itself, e.g., a≤a).
c. (non-strict): This term is incomplete and cannot be properly evaluated. Please provide more context or a complete term.
d. Partial order: A partial order is a binary relation that is reflexive, antisymmetric, and transitive. "≤" satisfies these conditions, so it is a partial order.
e. Well-ordering order: A well-ordering is a linear order in which every non-empty subset has a least element. "≤" satisfies this condition, so it is a well-ordering order.
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Let a, b E N, with a > 0 and b > 0. (a) Let p, q, r, s be the unique integers such thata = qb + r,0 < r < b,b = pr+s,0 < s
The Euclidean algorithm gives gcd(a,b) = gcd(b,r) and gcd(b,r) = gcd(r,s).
The Euclidean algorithm is a recursive algorithm to find the greatest common divisor (gcd) of two integers a and b. It works by repeatedly finding the remainder of the division of the larger number by the smaller number, until the remainder is 0, at which point the gcd is the last non-zero remainder.
When applying the algorithm to a and b with a > b, we can write a = qb + r, where q is the quotient and r is the remainder. Then, we apply the algorithm to b and r to find the gcd(b,r), and so on until we reach 0. At each step, the gcd of the current pair of numbers is equal to the gcd of the previous pair, since any common divisor of the current pair must also divide the previous pair. Therefore, we have gcd(a,b) = gcd(b,r) = gcd(r,s), where s is the final non-zero remainder.
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What is 10% as a whole number??
HELP
Answer: 10
Step-by-step explanation: