The expected area of a random square which has a side length that is uniform random variable is 1/3.
What is Continuous uniform distribution?A family of symmetric probability distributions includes the continuous uniform distribution and rectangular distribution. The distribution describes an experiment with a random result that falls within predetermined bounds.
The parameters, a and b, which represent the minimum and maximum values, define the bounds. The interval may be closed (for example, [a, b]) or open (for example, (a, b)). common abbreviation for the distribution is U (a, b), where U stands for uniform distribution.
The length of the interval is defined by the difference between the bounds; intervals with the same length on the distribution's support are equally likely.
Let, side of the square = X
we know that the area of a square = side × side
= X × X
= X^{2}
now, by using Continuous uniform distribution,
E[ X^{2} ] = [tex]\int\limits^1_0 X^{2} \, dx[/tex]
= [tex][\frac{1^{3} }{3} - \frac{0^{3} }{3} ][/tex]
= [tex]\frac{1}{3}[/tex]
Hence , the expected area of the square is [tex]\frac{1}{3}[/tex].
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Solve for x in the triangle. Round your answer to the nearest tenth.
The required value of the x in the given right angle triangle is 7.87 unit.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any other angle is a right angle.
In the given triangle,
The given side is 12 unit,
And the angle is 41°.
For any triangle having sides a, b and c and corresponding angles are ∠ A, ∠ B, and ∠ C.
sine formula can be given as,
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]
Since, in the given right angle triangle, one angle is 41° and other angle is 90°.
And their corresponding sides are x unit and 12 unit.
Therefore, sine formula can be applied here,
[tex]\frac{x}{sin41} = \frac{12}{sin90}[/tex]
[tex]\frac{x}{0.656} = \frac{12}{1}[/tex]
x = 7.87
The required value of x is 7.87 unit.
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the coefficient of x in the expansion of (a x)5 (1-2x)6, where a is positive, is 90. find the value of a.
In the given expansion ,the value of a = -4/3 .
Binomial Distribution:
The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments. Each asks a yes-no question and each has its own Boolean outcome: success (probability p) or failure (probability p) (probability q = 1-p. A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.
In general, (A + B)⁵ = A⁵ + 5A⁴ᵇ + 10A²ᵇ*³ + 10A³ᵇ*² + 5AB⁴ + B⁵
So,
(3–2x)⁵= 3⁵ + 5*3⁴*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5.
Multiplying that by (1 + ax) gives:
3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5 + ax(3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5).
In bold, we find the terms of x^2, so the coefficient of x^2 is 10*3^3*(-2)^2+a*5*3^4*(-2) = 360 - 810a
We know that this must equal 1440, so 360–810a = 1440.
Therefore a= -4/3.
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Which equation repreent the line that pae through the point (2, -8) and (-3, 2)?
The Equation represent the line that passes through the points (2, -8) and (-3, 2) is 2x + y + 4 = 0
Two point form is one of the important forms used to represent a straight line algebraically. The equation of a line represents each and every point on the line, i.e., it is satisfied by each point on the line.
The two point formula is used to represent a line algebraically using the coordinates of two points that lie on that line. The formula for two point form can be given as:
(y - y1) = m(x-x1) -----------(1)
where , m is slope of line given by => y2-y1/ x2 - x1
(x, y) is an arbitrary point on the line.
(x1, y1) and (x2 , y2) are coordinates of points lying on the line.
According to the question,
The required line passes through (2,-8) and (-3,2)
Slope : m = 2 - (-8) / -3 -2
=> m = 2+8/-5
=> m = 10/-5
=> m = -2
Substituting the values in equation (1)
(y - (-8)) = -2(x-2)
Solving,
=> y + 8 = -2x + 4
=> 2x + y + 4 = 0 is required equation of line
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A spinner is divided into five equal sections labeled 1, 2, 3, 4, and 5. Another spinner is divided into two equal sections labeled A and B. Nigel will spin each spinner one time.
How many of the possible outcomes have a number less than 3 or an A?
A.) 9
B.) 5
C.) 7
D.) 2
Answer:
Step-by-step explanation
Man its hard...
what is the answer to this problem? Evaluate |-7| + 4
Answer:
11 (PLEASE GIVE BRAINLIYEST)
Step-by-step explanation:
absolute value is distance from zero so |-7|=7
and 7+4 is 11
I need help pleaseee
Answer: 1/10th
Step-by-step explanation:
20 different lengths, 2 are 21.5 = 2/20 reduce to 1/10 so 10%
pls answer this question
Answer:
Step-by-step explanation:
The answer is C
We have to think about what size 0 would look like, if we observe the change between each figures we can find out the figure grows 4 every time, so we know it's always 4 each time. If we take figure 1 and remove all it's 4 green block it will be just left with 1 yellow block, which is figure 0, we have to add 1 every time we increase the size by 1.
How do you solve an equation with 2 answers?
The quadratic formula x = [-b (b2 - 4ac)] / 2a] provides the solutions to the quadratic equation ax2 + bx + c = 0. (2a).
Given,
Equation with two answers are quadratic equations.
Quadratic equation;
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
The solution for quadratic equation;
The quadratic formula x = [-b (b2 - 4ac)] / 2a]gives the solutions to the quadratic equation ax2 + bx + c = 0. (2a). Get the problem into standard form, ax2 + bx + c = 0, and then use the quadratic formula to solve the quadratic equation.
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Which president proposed the creation of the Environmental Protection Agency ?
President Richard Nixon proposed the creation of The Environmental Protection Agency (EPA).
What is the Environmental Protection Agency?
The Environmental Protection Agency is an independent government agency of the United States, which was considered mandatory by the government for environmental issues.
The Agency followed a series of measures to improve air quality, decrease greenhouse gas emissions, forbid water pollution, and invest in oil spill control measures.
The EPA had many obligations in the United States, two of which were to set industry standards to reduce their impact on the environment and investigate air pollution.
How did the EPA launch?
The operation of the agency began on December 2, 1970, after President Nixon had signed an executive order. The order established by the EPA was made official by signing by the committee hearings in the House and Senate.
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30.9 divided by 100
PLEASE I NEED HELP ASAP
Answer:
0.309
Step-by-step explanation:
H(t)= 50- t/5
H(35)=
Please explain it
The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
H(t) = 50 - t / 5
At t = 35, the value of the function will be given as,
H(35) = 50 - 35 / 5
H(35) = 50 - 7
H(35) = 43
The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.
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What is the solution to the system of equations below?
5/2x = y
2x+4/5y=8
A: No solution
B:16/9, 40/9
C: (3, 15/2)
D:(2,5)
Answer:
C
Step-by-step explanation:
[tex]\frac{5}{2}[/tex] x = y → (1)
2x + [tex]\frac{4}{5}[/tex] y = 8 → (2)
substitute y = [tex]\frac{5}{2}[/tex] x into (2)
2x + [tex]\frac{4}{5}[/tex] ([tex]\frac{5}{2}[/tex] ) = 8
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
substitute x = 3 into (1)
y = [tex]\frac{5}{2}[/tex] × 3 = [tex]\frac{15}{2}[/tex]
solution is (3, [tex]\frac{15}{2}[/tex] )
Add 1.5 x 107 to 2.7 x 10.
What is the slope of the line that passes through the points (2, -4) and (5, 2)? Write
your answer in simplest form.
Answer:
used formula
Step-by-step explanation:
y-y1=m(x-x1)
a school show had ticket sales of $1345 the first night and $935 the second night. 180 student tickets were sold and 110 adult tickets were sold on the first night. 100 student tickets were sold and 90 adult tickets were sold. find the price of a student ticket.: * a) $5.75 b) $8.75 c) $6.50 d) $3.50 e) $7.50
A school show had sold the ticket sales of first and second nights. The price of a student ticket is $3.54, a So, the correct answer is option (d).
Total sale on tickets at the first night = $1345
Total sale on tickets at the second night = $935
Let the price of student ticket and adult ticket in school show be "$x" and "$y" respectively. According to problem,
On first night total sale,
180x + 110y = $1345 --(1)
On Second night total sale,
100x + 90y = $935 --(2)
we have to determine the price of student ticket i.e x and price of adult ticket i.e y .. We have a system of linear equation which consists two equations (1) and (2) . Now, we solve these equations using Substitution method,
From equation (2), 100x = 935 - 90y
=> x = (935 - 90y )/100 --(*)
Substitute the value of x in equation (1) 180x + 110y = $1345
=> 180(935 - 90y )/100 + 110y = 1345
Simplify ..
=> 168120 - 16200y + 11000y = 134500
=> 168120 - 134500 = 16200y - 11000y
=> 33620 = 5200y
=> y = 33620/5200
=> y = 6.46
put the value of y in equation (*) we get,
x = (935 - 90× 6.46)/100 = 3.536
Hence, the value of x is $3.536 and value of y is $6.46..
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The students in Franklin's class got to choose whether to visit the zoo or the aquarium. 9 students went to the zoo and 16 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the total number of students?
Write your answer as a fraction. Use a forward slash ( / ) to separate the numerator and denomonator
Answer:
9/25
Step-by-step explanation:
total students = 9 + 16 = 25
ratio = 9/25
Which function is used to calculate maximum value?
Derivatives is used to calculate the maximum value of a function.
We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.
Derivatives
The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.
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Could a scatter graph be used to represent the
data for each of the following? (Yes or No)
a) The heights of different buildings
b) People's favourite sports and their ages
c) The prices of houses and the number of
rooms they have
yes Answer:
Step-by-step explanation: yes
to calculate the expected risk premium on a stock, one must subtract the ________ from the stock’s expected return.
To calculate the expected risk premium on a stock, one must subtract the Inflation rate from the stock’s expected return.
How to complete the blank in the statement?From the question, we have the following parameters that can be used in our computation:
Expected risk premiumStock's expected returnMathematically, the relationship between the expected risk premium and the stock's expected return is represented as follows
Expected risk premium = Stock's expected return - Inflation rate
This means that the Inflation rate must be subtracted from the stock’s expected return to calculate the expected risk premium
Hence, the statement that completes the blank is Inflation rate.
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Help with question 3
Answer:
3.75
Step-by-step explanation:
I BELIVE YOUR ANSWER IS 3.75
Answer:
3.75
Step-by-step explanation:
Help needed was not thought this
Answer:
Yes what is the question
Answer:
what is the question
Step-by-step explanation:
PLEASE HELP MEEEEEEE, GIVING 30 POINTS IF YOU SOLVE (MY THRID TIME REPOSTING THIS)
A rental car company charges $40.50 per day to rent a car and $0.15 for every mile driven. Elizabeth wants to rent a car, knowing that:
She plans to drive 125 miles.
She has at most $210 to spend.
Write and solve an inequality which can be used to determine x, the number of days Elizabeth can afford to rent while staying within her budget.
Answer: 4 days, more below
Step-by-step explanation:
40.50x + 0.15y < 210
(0.15)(125)=18.75
40.50x + 18.75 < 210
40.50x < 191.25
x < 4.7222222...
She can afford to rent the car for 4 days if she drives 125 miles and has 210$ to spend.
Pedro has a balance of $5810 on a credit card with an APR of 16.2%. Paying
off his balance in which of these lengths of time will result in him paying the
least amount of interest?
O 1 Month
2 Months
3 Months
4 Months
The least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month, so option A is correct.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
Pedro has a balance of $5810 on a credit card with an APR of 16.2%,
Calculate the simple interest for one month as shown below,
[tex]SI = P \times r \times t / 100[/tex]
SI = 5810 × 16. 2 × 1 / (12 ×100) [time in year = 1 / 12]
SI = $78.345
SI = 5810 × 16. 2 × 2 / (12 ×100) [For 2 months]
SI = $156.87
Therefore, the least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month.
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Which graph represents y=^3square root x
Why is area in square units?
The number of unit squares needed to completely cover a shape is its area. As a result, it is expressed and measured in square units.
The word "area" refers to a free space. The area of a thing is the amount of space it occupies in two dimensions. A closed figure's surface area is calculated by counting how many unit squares completely encircle the surface. The square unit is frequently expressed as square inches, square feet, etc., and is the accepted unit of area.
Consider, there are several squares with sides that are 1 unit by 1 unit wide in the grid. The surface area of each square is one square unit. Each square is a unit square. As a result, the area is stated and measured in square units.
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9(-2)
Help I don't get it :'(
So, let's think about what it's asking
it next to the parentheses means to distribute, or multiply into.
Multiply 9 * -2
A negative times a positive is a negative.
9 * 2 = 9 + 9 = 18
Make the final answer negative because its a positive and a negative multiplied. A positive and a positive multiplied gives you a positive. A negative and a negative multiplied gives you a positive too.
-18
Write an equation in slope-intercept form of the line.
(Use integers or fractions for any numbers in the equation.)
Answer:
[tex]y=-\frac{1}{2} x+5[/tex]
a certain star is 3.6 x 10^2 light years from the earth. one light year is about 5.9 x 10^12 miles how far from the earth in miles is the star
The earth is 21.24 x 10¹⁴ miles far from the star.
What are the light years?
A light-year is a significant length measure that is used to express astronomical distances. It is around 9.46 trillion kilometers, or 5.88 trillion miles, in length.
We have given,
1 light year = 5.9 x 10¹² miles
Distance of the star = 3.6 x 10² light years
To get this we just convert the distance of the star in light years into miles.
3.6 x 10² light years x( 5.9 x 10¹² miles/1 light years)
We cancel out the lightyears and then we are left with:
3.6 x 10² light years x 5.9 x 10¹² miles
In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.
Coefficients:
3.6 x 5.9 = 21.24
Exponents of 10:
10² x 10¹² = 10⁽²⁺¹²⁾ = 10¹⁴
Then we combine them again to form:
21.24 x 10¹⁴ miles
Hence, the earth is 21.24 x 10¹⁴ miles far from the star.
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Select the correct answer. Which of the following is a solution to 4cos2x − 1 = 0? A. 60° B. 150° C. 210° D. 330°
Answer:
60°A is correct
Given:
Divide by 4
Taking square root both sides
Hence, x=60° is correct
Consider the following table. Is the relationship proportional? Explain your answer.
y
-27
12
57
147
-2
1
4
10
Answer:
The relationship shown in the table is not proportional. A proportional relationship is one in which the ratio of two quantities is always constant. In the table, we can see that the ratio of the values in the y column to the corresponding values in the x column is not constant. For example, the first two values in the y column are -27 and 12, which have a ratio of -27/1 and 12/2, respectively. These ratios are not equal, which indicates that the relationship is not proportional.
Furthermore, if the relationship were proportional, we would expect the values in the y column to increase at a consistent rate as the values in the x column increase. However, this is not the case in the table. For example, the first two values in the x column are 1 and 2, and the corresponding values in the y column are -27 and 12. The difference between these values is -27 - 12 = -39, which is a large negative value. However, the difference between the next two values in the y column is 57 - 147 = -90, which is a much larger negative value. This indicates that the relationship is not proportional, because the differences between the y values do not increase at a consistent rate as the x values increase.
Step-by-step explanation: