In normal distribution the area above 66 for a n(60, 10) is 0.726
What is normal distribution?
In probability theory and statistics, the Normal Distribution, which is also called the Gaussian Distribution, is the most significant continuous probability distribution. It is also called a bell curve. In this distribution a large number of random variables are either nearly or exactly represented. Moreover, it can be used to approximate other probability distributions,
From the given data n(60, 10) so mean = 60 and standard deviation= 10
Now x≥ 66
so the z-score will be (66-60)/10
= 6/10
= 0.6
Now P(z>0.6)= 1- P(z< 0.6)
= 0.726
So, in normal distribution the area above 66 for a n(60, 10) is 0.726.
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help solve this graph please
The graph of the exponential function across the interval is attached below
How to graph the exponential functionTo graph the function y = 3ˣ over the interval 1 ≤ x ≤ 2, you can follow these steps:
Choose a suitable scale for the x-axis and y-axis. Since the function grows rapidly, you may need to use a logarithmic scale on the y-axis to show the entire graph.
Plot some key points of the function. To do this, you can choose some values of x within the given interval and calculate the corresponding values of y. For example:
When x = 1, y = 3^1 = 3
When x = 1.5, y = 3^1.5 = 5.2
When x = 2, y = 3^2 = 9
Connect the plotted points with a smooth curve. Since the function is exponential, the curve will be a smooth upward curve that gets steeper and steeper as x increases.
Label the axes and add any necessary annotations or markings. For example, you may want to label the plotted points with their coordinates or add gridlines to help read off values from the graph.
Kindly find the attached graph below
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suppose that 8% of the patients tested in a clinic are infected with hiv. furthermore, suppose that when a blood test for hiv is given, 97% of the patients infected with hiv test positive and that 4% of the patients not infected with hiv test positive. what is the probability that a patient testing positive for hiv with this test is infected with hiv? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
The likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4%
To illuminate this issue, we will utilize Bayes' hypothesis. Let's characterize the taking after occasions:
A: the persistent is contaminated with HIV
B: the persistent tests positive for HIV
We need to calculate P(A|B), the likelihood that an understanding is contaminated with HIV given that they tried positive for HIV.
By Bayes' hypothesis:
P(A|B) = P(B|A) * P(A) / P(B)
where
1. P(B|A) is the likelihood of testing positive for HIV given that the persistent is tainted with HIV (97%)
2. P(A) is the predominance of HIV within the clinic (8%)
3. P(B) is the likelihood of testing positive for HIV, which can be calculated utilizing the law of adding up to likelihood:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
where
1. P(B|A') is the likelihood of testing positive for HIV given that the persistent isn't tainted with HIV (4%)
2. P(A') is the complement of A, i.e., the likelihood of a quiet not being tainted with HIV (1 - 8% = 92%)
Substituting the values we have:
P(B) = 0.97 * 0.08 + 0.04 * 0.92 = 0.0736
P(B) = 0.0736
Hence,
P(A|B) = 0.97 * 0.08 / 0.0736 ≈ 0.104
P(A|B) = 0.104
So the likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4% (adjusted to three decimal places).
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1. a national organization sets out to investigate the change in prevalence of hiv since the last census in 2010. a total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be hiv positive. assume that the data from the census indicated that the prevalence of hiv in the particular population was 7.5%. a) is the sample size large enough to justify the use of the z formula? show your calculation to support your answer. (3 points)
Yes, the sample size of 4,706 is large enough to justify the use of the z formula.
To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.
One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.
In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.
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(ASAP) Tell whether the transformation appears to be a rigid motion. Explain.
Yes, the transformation is a rigid motion because the angle measures and the distances between the vertices of the image are the same as the corresponding angle measures and distances in the preimage.
Why is the transformation a rigid motion?Since the shape and size are the same in both the preimage and the image, and only the position has changed, this transformation is considered a rigid motion. Rigid motions, such as translations, rotations, and reflections, preserve the shape and size of the original figure.
Assuming the shape has been bent, it means that the angle measures and distances between the vertices have been altered. But this is not the case.
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What proportion p of adults received a parking ticket in the last year? In a survey of 400 adults selected using random digit dialing, 40 received a parking ticket in the last year. The standard error for the proportion P hat of adults receiving a parking ticket is0.30.0.00023.0.015.
The proportion (p) of adults who received a parking ticket in the last year is 0.1 or 10%.
The standard error for the proportion (P hat) is given as 0.015, which provides a measure of the precision of our estimate.
To find the proportion (p) of adults who received a parking ticket in the last year, we will use the information provided in the survey.
Determine the number of adults who received a parking ticket (given as 40).
Determine the total number of adults surveyed (given as 400).
Now, calculate the proportion (p) using the formula:
p = (number of adults with parking tickets) / (total number of adults surveyed)
p = 40 / 400
p = 0.1
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given the plot of computing time ~ n, what is the best description of this computational complexity?
A computation time expression ~ n, of means that the computation time increases in proportion to the size of the input.
This presents a computational complexity of O(n). Here 'O' stands for 'Big O Notation' and is used to denote an upper bound on the computational complexity of the algorithm.
That's, the algorithm's computational complexity is straightforwardly corresponding to the measure of the input information.
This shows that as the input estimate increments, the computational time will increment at the same rate.
Linear time complexity is considered to be very efficient, and many algorithms aim to achieve this level of complexity. This is a relatively efficient computational complexity and is common in algorithms that require only one pass through the input data.
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HELP i NEED to get my grades up
1. A cylinder has a radius and height of 2.0×10^7
feet and 4.0×10^5
feet respectively. What is the approximate volume of the solid? Leave your answer in terms of π
. Use scientific notation.
2. A cone has a diameter and length of 1.0×10^7
inches and 5.0×10^5
inches respectively. What is the approximate volume of the solid? Leave your answer in terms of π
. Use scientific notation. Round your significant figure to the nearest hundredth.
The approximate volume of the solid is 1.6 × 10^23 π cubic feet.
The approximate volume of the solid is 8.17 × 10^20 π cubic inches.
We have,
1.
The volume V of a cylinder is given by V = πr²h,
where r is the radius and h is the height.
Substituting r = 2.0 × 10^7 feet and h = 4.0 × 10^5 feet.
V = π (2.0 × 10^7)² (4.0 × 10^5)
Simplifying,
V = 1.6 × 10^23 π cubic feet (using scientific notation and leaving the answer in terms of π)
2.
The volume of a cone is given by V = 1/3πr²h,
where r is the radius, h is the height, and we are given the diameter (d = 2r).
Substituting,
d = 1.0 × 10^7 inches, r = d/2 = 5.0 × 10^6 inches, and
h = 5.0 × 10^5 inches, we get:
V = 1/3 π (5.0 × 10^6)² (5.0 × 10^5)
Simplifying,
V = 2.6 × 10^20 π cubic inches
(using scientific notation and leaving the answer in terms of π)
Rounding to the nearest hundredth,
V = 8.17 × 10^20 π cubic inches.
Thus,
The approximate volume of the solid is V = 1.6 × 10^23 π cubic feet.
The approximate volume of the solid is V = 8.17 × 10^20 π cubic inches.
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
The appropriate measure of center for the data on the tickets sold is C. The median is the best measure of center, and it equals 19.
Why is the median best ?In a box plot, the median is represented by the horizontal line that divides the box into two equal parts. The median is the middle value of the dataset when it is ordered from smallest to largest.
The median is the best measure of center for a box plot. The median is represented by the line inside the box, which in this case is at 19 on the number line.
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Answer:
ccccccccccccccccccccccccc
Step-by-step explanation:
I am an even whole number. I am greater than 0 and I am also less than 20. If you multiply me by 2 the product will be less than 3.
Let h(x) be the number of hours it takes
a new factory to produce x engines. The
company's accountant determines that
the number of hours it takes depends on
the time it takes to set up the machinery
and the number of engines to be
completed. It takes 6.5 hours to set up
the machinery to make the engines and
about 5.25 hours to completely
manufacture one engine. The
relationship is modeled with the
function b(x)=6.5+5.25%
1. Determine the x and y-
intercepts of the function.
2. Is the function increasing or
decreasing?
Based on the information, the y-intercept is (0, 6.5).
The function is increasing.
How to calculate the interceptBased on the information, we can use the variable x. This will be:
0 = 6.5 + 5.25%x
-6.5 = 5.25%x
x = -6.5 / 5.25% ≈ -123.81
There's no x intercept due to the negative value which doesn't make sense in this scenario.
In order to find the y-intercept, we set x = 0 and evaluate b(x):
b(0) = 6.5 + 5.25% × 0 = 6.5
Therefore, the y-intercept is (0, 6.5).
The function b(x) is increasing since the coefficient of x is positive (5.25%). This means that as the number of engines produced (x) increases, the time it takes to manufacture the engines also increases.
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What is 270% of 136ft?
Answer:
367.2
Step-by-step explanation:
Basically 270% is 2.7 so if you multiply 2.7 by 136 you will get 367.2
Question 5
Karin has $83,555 in a retirement account right now. Suppose she deposits $3,000 this year and then increases that by 7.5% each subsequent year. The account earns 9.8%. Find her future account value after 20 years.
The solution of the given problem of percentage comes out to be Karin's future account value would therefore be about $313,425.67 after 20 years.
What are percentages?In statistics, a figure or metric that may be presented as a percentage or 100 is denoted by the abbreviation "a%". Other unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this.
Here,
Using the compound interest calculation, we can determine Karin's account worth in 20 years:
=> A = P(1 + r)ⁿ
P =$83,555 (current balance), as given.
(Annual interest rate) r = 9.8% = 0.098
20 years, n
Let's use the following formula to determine the future account worth for each year:
Year 1: P = $83,555 (balance as of now)
(Annual interest rate) r = 9.8% = 0.098
Given that this is the first year, n equals 1.
=> A = $83,555(1 + 0.098)¹
=> A = $83,555(1.098)
=>A = $91,785.09
Year 2: P = $6,225 (current balance after deposit) = $3,000 + $3,225.
(Annual interest rate) r = 9.8% = 0.098
n = 1 year
=> A = $6,225(1 + 0.098)¹
=> A = $6,225(1.098)
=> A = $6,834.44
After 20 years, the current balance is
=> P = $12,873.51 + (20 - 1)($3,000 + 7.5% of $3,000)
= $12,873.51 + $71,132.10 = $83,005.61.
The yearly interest rate is 9.8%, or 0.098.
20 years, n
=> A = $83,005.61(1 + 0.098)²⁰
=> A = $83,005.61(3.778)
=> A = $313,425.67
Karin's future account value would therefore be about $313,425.67 after 20 years.
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Find the value of x. Round to the nearest degree.
A right triangle is drawn with an angle that is labeled x degrees. The leg opposite of the labeled angle is 7. The hypotenuse is 9.
Rounding to the nearest degree, we get x = 53 degrees.
We can use the inverse sine function (sin⁻¹) to find the value of x.
From the sine rule,
sin(x) = opposite/hypotenuse
[tex]sin(x) = 7/9\\x = sin^{-1}(7/9)[/tex]
Using a calculator, we find that x is approximately 53.13 degrees. Rounding to the nearest degree, we get x = 53 degrees.
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The selling price for peanut butter is $3. 79 and the cost is $2. 84
Answer: Profit = .95 or 95 cents
Step-by-step explanation:
What is the question here?
If it is profit then the answer is 3.79-2.84
The graph of the function f(x) = (x +2)(x + 6) is shown below. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). What is true about the domain and range of the function?
The domain is all real numbers, and the range is all real numbers greater than or equal to -4. So, correct option is A.
The given function f(x) = (x + 2)(x + 6) is a quadratic function, and its graph is a parabola that opens upwards. We are given that the vertex of the parabola is at (-4, -4), and it passes through the points (-6, 0) and (-2, 0).
The domain of a function is the set of all possible input values for which the function is defined. Since this is a polynomial function, it is defined for all real numbers. Therefore, the domain of the function f(x) is all real numbers.
The range of a function is the set of all possible output values that the function can take. Since the parabola opens upwards and its vertex is at (-4, -4), the lowest point on the graph is at (-4, -4), and it extends infinitely upwards. Therefore, the range of the function f(x) is all real numbers greater than or equal to -4.
Hence, the correct option is A).
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Complete question is:
The graph of the function f(x) = (x +2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (- 6, 0), has a vertex at (- 4, - 4), and goes through (- 2, 0).
What is true about the domain and range of the function?
A) The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
B) The domain is all real numbers greater than or equal to
–4, and the range is all real numbers.
C) The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.
D) The domain is all real numbers greater than or equal to
–4, and the range is all real numbers such that –6 ≤ x ≤ –2.
Please PLEASE HELP ME this is due in 7 minutes and it the last question PLEASE
Answer:
(3,0)
Step-by-step explanation:
the point (5,-5) a translation of 2 units left would be equivalent to x-2.
(5-2,-5)
5 units up is equivalent to y+5
therefore
(5-2,-5+5)
yields
(3,0)
Justine takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut she makes is 5 inches long and the width of the paper is 3 inches. What is the paper's length? inches
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins,16% are pennies and 42% are dimes There are 6 more nickels than pennies. How much money does the bag contain?.
The bag contains 4.63 dollars.
To find :
Total amount of the coins bag contains.
Solution:
According to the given statement, a bag contains 50 coins.
Number of pennies = 16% of 50
= 0.16 × 50
= 8 pennies
Number of dimes = 42% of 50
= 0.42 × 50
= 21 dimes
Number of nickels = 6 more than pennies
= 8 + 6
= 14 nickels
Number of quarters = Rest of the coins
= 50 - (8 + 21 + 14)
= 50 - 43
= 7 quarters
Since,
1 penny = 0.01 dollar
8 pennies = 0.01 × 8 = 0.08 dollar
1 dime = 0.10 dollar
21 dimes = 0.10 × 21 = 2.1 dollar
1 nickel = 0.05 dollar
14 nickel = 0.05 × 14 = 0.70 dollar
1 quarter = 0.25 dollar
7 quarter = 0.25 × 7 = 1.75 dollars
Total value of the coins in the bag = 0.08 + 2.10 + 0.70 + 1.75
= 4.63 dollars
Hence, The bag contains 4.63 dollars.
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The population of Log Village is 1800 in 2010, and the population increases each year by 9%. What equation is used to determine the population, y, of Log Village x years after 2010?
The equation that will be used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ
What is equation?
An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.
The population of Log Village is 1800 in 2010, and the population increases each year by 9%.
Initial population(p)= 1800
rate of increase(r)= 9%
Time(t)= x years.
The formula for the population after n years is p(1+r/100)ⁿ.
To determine the equation for the population after x years we have to put the values in the above expression.
So putting all the values we get,
The population, y, of Log Village x years after 2010 is
y= 1800( 1+9/100)ˣ
y= 1800(1.09)ˣ
Hence, The equation that will be used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ
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how many pattern block triangles would i need to make 4 hexagons
Answer:
4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles
Step-by-step explanation:
Pattern blocks are a set of geometric shapes commonly used in math education. The set typically includes six different shapes: triangle, rhombus, trapezoid, hexagon, square, and equilateral triangle. Each hexagon in a pattern block set is made up of six equilateral triangles.
To make 4 hexagons using pattern blocks, we would need to calculate the total number of equilateral triangles required. Since each hexagon is made up of 6 equilateral triangles, we can multiply the number of hexagons by 6 to get the total number of equilateral triangles needed.
4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles
So, you would need 24 pattern block triangles to make 4 hexagons using pattern blocks.
Answer:
Let's use pattern blocks to visualize the situation and say that a hexagon is 1 whole. Since 3 rhombuses make a hexagon, 1 rhombus represents and 2 rhombuses represent . We can see that 6 pairs of rhombuses make 4 hexagons, so there are 6 groups of in 4.
a variable needs to be eliminated to solve the system of equations below.
x-7y= -45 -x+8y=51
Eliminate x by adding the two equations, yielding [tex]y = 6[/tex]. Then, substitute y into either equation to solve for x, obtaining [tex]x = -3[/tex]. The solution is [tex](-3,6)[/tex].
What is equation?An equation is a mathematical statement that uses symbols, numbers, and variables to show that two expressions are equal, typically with an equal sign between them.
A variable is a quantity or symbol that can take on different values in a mathematical expression, equation, or formula, typically represented by a letter.
To eliminate a variable in a system of equations, we want to find a way to add or subtract the two equations so that one of the variables is eliminated.
In this case, we can eliminate the variable x by adding the two equations
[tex]x- 7y = -45[/tex]
[tex](-x +8y = 51)[/tex]
[tex]y = 6[/tex]
Now that we have found the value of y, we can substitute it into either of the original equations to solve for x. Let's use the first equation
[tex]x-7y = -45\\x- 7(6) = -45\\x = -45+42\\x = -3[/tex]
Therefore the solution to the system of equations is [tex]x= -3[/tex] and[tex]y= 6[/tex]
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the solution to the system of equations is (x, y) = (-3, 6).
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
To eliminate the variable x, we can add the two equations together. This will result in the x variable being eliminated, leaving us with an equation in terms of y:
(x - 7y) + (-x + 8y) = -45 + 51
Simplifying and solving for y, we get:
y = 6
Now that we know the value of y, we can substitute it into one of the original equations to solve for x. Using the first equation:
x - 7(6) = -45
Simplifying and solving for x, we get:
x = -3
Therefore, the solution to the system of equations is (x, y) = (-3, 6).
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What was a typical number of points for scored in 2008, (and all the rest of them)
The typical number of points from the histogram for scored in 2008 is 11 points.
The typical number of points from the histogram for scored in 2016 is 9 points
What is a histogram?A histogram is described as an approximate representation of the distribution of numerical data.
We take note of the following pints while determining the number of points:
Identify the graph that represents the number of points during 2008.Look at the bars and identify the tallest one, as well as the number of points this represents.This would be considered the typical number of points or the most common number of points.Learn more about histogram at:
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1
Find the side lengths for the triangle with the following
measurements.
If your answer is not an integer round it to the nearest
hundredth.
side c = 50 and angle B = 21 degrees
side a =
side b=
The value of side a and b for the given triangle is 46.68 units and 17.92 units.
What is law of sines?A triangle's angles and side lengths are related by the law of sines, a trigonometric identity. It asserts that the ratio of the sine of one angle to the length of the side opposite that angle is constant for all three angles for any triangle with sides a, b, and c and opposing angles a, b, and c:
If a/sin(A) = b/sin(B) = c/sin(C), then
As long as at least one angle and its matching side length are known, this can be used to solve for unknown angles or side lengths in a triangle.
For the given triangle we have:
cos B = a / c
Thus, substituting the values we have:
cos 21 = a / 50
a = 46.68 units.
Now, sin B = b/50
Sin 21 = b / 50
b = 17.92 units.
Hence, the value of side a and b for the given triangles is 46.68 units and 17.92 units.
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The complete question is:
4PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
9.3 ft
Step-by-step explanation:
Write an equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞.
The equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞ is y = √(x - 3) - 2.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields of mathematics, science, engineering, and economics. They can be written in various forms, such as standard form, slope-intercept form, point-slope form, and more.
Here,
To shift the parent function y = √x to the right by 3 units and down by 2 units, we use the transformation:
y = √(x - 3) - 2
This equation has a domain of 3 ≤ x < ∞, since we subtract 3 from x inside the square root function. The range is -2 ≤ y < ∞, since we subtract 2 from the square root function.
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A deck of standard playing cards holds 52 unique cards.
36 of these cards are numbered cards (numbered 2-9), 4
of these cards are aces, and 12 of these cards are face
cards (jack, queen, and king). If you play a card game and
draw half of the face cards, one ace, and one fourth of the
numbered cards, how many cards do you have? How
many of each card type of card do you have? Cite
evidence from the problem.
PLS HELP
The total number of cards drawn is 16 and As a result, we have the following:
6 face cards, Aces 1, 9 numbered cards
How to determine the type of each card?Because there are 12 face cards, half of them are 6 face cards.
There are 4 aces, so we draw 1.
There are 36 numbered cards in total, therefore one-fourth of them are 9 numbered cards.
We draw a total of 6 + 1 + 9 = 16 cards.
We may use the information provided in the problem to determine how many of each card type we have. We chose:
6 face cards make up half of the deck.
1 ace: 1 ace
9 numbered cards are one-fourth of the numbered cards.
As a result, we have:
6 face cards
Aces: 1
9 numbered cards
We can also ensure that the total number of cards drawn (16) corresponds to the number of cards in a regular deck by subtracting the cards we drew from the total number of cards: a deck of playing cards (52)
There are 52 - 16 = 36 cards left.
This means that there are 36 - 6 - 1 - 9 = 20 undrawn cards in the deck.
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The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds.1-e^x/lamda
The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.573.
Given that the time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds.
We know that the exponential probability distribution function is given by
f(x) = λ e^(-λx)
Where λ is the rate parameter of the distribution and is equal to 1/mean in this case. So, λ = 1/14.
Now, we need to find the probability that the arrival time between vehicles is 12 seconds or less. Mathematically, we can express this as:
P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] λ e^(-λx) dx
Integrating this expression, we get:
P(X ≤ 12) = [-e^(-λx)]_[0,12] = -e^(-λ12) + e^(-λ0)
Since e^(-λ×0) is equal to 1, we have:
P(X ≤ 12) = 1 - e^(-λ×12)
Substituting the value of λ, we get:
P(X ≤ 12) = 1 - e^(-12/14)
P(X ≤ 12) ≈ 0.573
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The given question is incomplete, the complete question is:
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds . What is the probability that the arrival time between vehicles is 12 seconds or less?
There is a raffle with 250 tickets, each costing $16. One ticket will win a $240 prize, one ticket will win a $130 prize, one ticket will win a $120 prize, one ticket will win a $70 prize, and the other tickets will win nothing. If you buy a ticket, what is the expected profit?
If you buy a ticket, you can expect to make a profit of approximately $0.96 on average.
To calculate the expected profit, we need to consider the probability of winning each prize and the value of each prize.
The probability of winning each prize can be calculated by dividing the number of winning tickets by the total number of tickets. There is 1 winning ticket for each prize, so the probability of winning each prize is:
$240 prize: 1/250
$130 prize: 1/250
$120 prize: 1/250
$70 prize: 1/250
The value of each prize is already given, so we can multiply the probability of winning each prize by its value and sum the results to find the expected profit:
Expected profit = (1/250 x $240) + (1/250 x $130) + (1/250 x $120) + (1/250 x $70) - ($16)
Expected profit = $0.96
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Drag the tiles to the correct boxes to complete the pairs *Not all tiles will be used*
Match the correct volume formula with each described figure
1. V = 1/2 * pi * x ^ 3;
2. V = x ^ 3;
3. V = 1/3 * x ^ 3;
4. V = 1/2 * pi * x ^ 3;
5. V = 1/2 * x ^ 3;
6. V = pi * x ^ 3
A. a prism with a height of x cm and a square base with side length of x cm
B. a cylinder with a radius of x and height of cm
C. a pyramid with a height of x cm and a square base with a side length of x cm
D. a cone with a radius of x cm and height of x cm
A. a prism with a height of x cm and a square base with side length of x cm = option 2
B. a cylinder with a radius of x and height of cm= option 6
C. a pyramid with a height of x cm and a square base with a side length of x cm = option 3.
How to match the correct formula with the statements given ?For statement A=
The formula for a square based prism= a²h
where a= X
h = X
Vol = x³
For statement B;
The formula for a cylinder=πr²h
where r= X, h= X
Vol= π×x³
For statement C;
The formula for a square based pyramid= 1/3a²h
a = X
H = X
Vol = 1/3 * x³
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A ran a 20-mile race that she completed in 2.5 hours.
If A ran at a constant speed for the entire race,what was her speed in miles per hour?
SHOW YOUR WORK
Answer:
The answer for speed is 8 miles/hr
Step-by-step explanation:
speed =distance/time
s=20/2.6
s=8miles/hr