Answers
a) The linear function giving the cost after x months is given as follows: C(x) = 88 - 8x.
b) The cost of the shoes after 8 months is given as follows: $24.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.Each month, the balance decays by $8.00, hence the slope m is given as follows:
m = -8.
Hence:
y = -8x + b.
When x = 1, y = 80, hence the intercept b is given as follows:
80 = -8 + b
b = 88.
Hence the function is:
C(x) = 88 - 8x.
The cost after 8 months is given as follows:
C(8) = 88 - 8(8) = 88 - 64 = $24.
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Related Questions
Use spherical coordinates to find the volume of the solid.The solid between the spheresx2+y2+z2=a2 and x2+y2+z2=b2,b>aand inside the cone z2=x2+y2
Answers
Answer:
The volume of the solid is ([tex]π/3)(b^3 - a^3).[/tex]
Step-by-step explanation:
To find the volume of the solid, we need to set up the triple integral in spherical coordinates. We first note that the cone [tex]z^2 = x^2 + y^2[/tex] is symmetric about the z-axis and makes an angle of π/4 with the z-axis. We can then use the bounds of integration for the spherical coordinates as follows:
ρ: from a to b (the distance from the origin to the surface of the spheres)
θ: from 0 to 2π (the azimuthal angle)
φ: from 0 to π/4 (the polar angle)
The volume element in spherical coordinates is given by ρ^2 sin φ dρ dθ dφ. The integral for the volume of the solid is then:
[tex]V = ∫∫∫ ρ^2 sin φ dρ dθ dφ[/tex]
The bounds of integration for the integral are:
ρ: a to b
θ: 0 to 2π
φ: 0 to π/4
Substituting in the bounds and the volume element, we get:
[tex]V = ∫₀^(π/4)∫₀^(2π)∫ₐ^b ρ^2 sin φ dρ dθ dφ[/tex]
Evaluating the integral, we get:
[tex]V = (1/3)(b^3 - a^3) (π/4)[/tex]
Thus, the volume of the solid is ([tex]π/3)(b^3 - a^3).[/tex]
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You are asked to estimate the water flow rate in a pipe of radius 2m at a remote area location with a harsh environment. You already know that velocity v varies along the radial location, but you do not know how it varies. The flow rate Q is given by
Q = ∫(0 to 2) 2 π r v dr
To save money, you are allowed to put only two velocity probes (these probes send the data to the central office in New York by satellite). Radial location r is measured from center of the pipe, i.e., r = 0 is the center of the pipe, and r = 2m is the pipe radius. The radial locations you will suggest for the two velocity probes for the most accurate calculation of the flow rate are
0.42, 1.42
0.00, 1.00
0.42, 1.58
0.58, 1.58
Answers
To estimate the water flow rate in the pipe, we need to measure the velocity at two radial locations and then use the integral formula to calculate the flow rate. The formula tells us that the flow rate is equal to the integral of 2πrv with respect to r, where r is the radial location, v is the velocity, and the limits of integration are 0 to 2 (since the pipe has a radius of 2m).
Since we don't know how the velocity varies along the radial location, we need to choose two locations that will give us the most accurate estimate of the flow rate. The best locations to choose are where the velocity varies the most, which is usually near the center and near the edge of the pipe.
Based on this, the two radial locations that would give us the most accurate calculation of the flow rate are 0.42 and 1.58. These locations are close to the center and the edge of the pipe, respectively, and will give us a good estimate of how the velocity varies along the radial location.
Therefore, the answer is 0.42, 1.58.
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Suppose the trip take 3 hours and 15 minutes of driving time for the 124-mile round trip. What is the average speed of the buses in miles per hour?
Answers
The average speed of the buses is approximately 19.08 miles per hour.
We have,
If the trip takes 3 hours and 15 minutes of driving time, that's a total of 3.25 hours.
The distance traveled is 124 miles round trip, so the distance traveled in one direction is half of that or 62 miles.
To find the average speed of the buses in miles per hour, we can use the formula:
average speed = distance/time
where distance is in miles and time is in hours.
So, the average speed of the buses in miles per hour is:
Average speed
= 62 miles / 3.25 hours
= 19.0769 miles per hour (rounded to 4 decimal places)
Therefore,
The average speed of the buses is approximately 19.08 miles per hour.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
0.625
0.750
0.875
Answers
The theoretical probability of the spinner not landing on blue is 3/4
Determining the theoretical probability of the spinner not landing on blueFrom the question, we have the following parameters that can be used in our computation:
Colors = 4 i.e. purple, yellow, blue and red
Blue = 1
Not blue = 3
So, we have
Theoretical probability = Not Blue /Colors
Substitute the known values in the above equation, so, we have the following representation
Theoretical probability = 3/4
Hence, theoretical probability is 3/4
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Use the figure to find the Surface Area.
32 sq. units
64 sq. units
85 1/3 sq. units
Answers
The surface area of the sphere is 64π square units.
Option B is the correct answer.
We have,
Surface area of a sphere = 4πr² ______(1)
Now,
Radius = 4 units
Substituting in (1)
The surface area of a sphere
= 4πr²
= 4 x π x 4²
= 4π x 16
= 64π square units
Thus,
The surface area of the sphere is 64π square units.
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F(x)=-4x^2+10x-8
What is the discriminant of f?
How many distinct real number zeros does f have?
Answers
The discriminant of f(x)is -28, and f(x) has no distinct real number zeros.
The expression[tex]b^{2}- 4ac[/tex] gives the value of discriminant of the quadratic function with the form f(x) = [tex]ax^{2} + bx + c[/tex]. This result is obtained through using this formula on the quadratic function, where f(x) = [tex]-4x^{2}+ 10x - 8[/tex]: [tex]b^2 - 4ac = (10)^2 - 4(-4)(-8)[/tex] = 100-128 = -28. Hence, -28 is the discriminant of f(x).
The discriminant informs us of the characteristics of the quadratic equation's roots. There are two unique real roots if the discriminant index is positive. There is just one real root (with a multiplicity of 2) if the discriminator is zero. There are only two complicated roots (no real roots) if discrimination is negative.
Given that f(x)'s discriminant is minus (-28), we can conclude that there are no true roots. F(x) contains two complex roots as a result. This is further demonstrated by the fact that the parabola widens downward and does not cross the x-axis, as indicated by the fact that the coefficient of the [tex]x^{2}[/tex] term in f(x) is negative.
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What is 2/5 as a decimal?
Answers
Answer:
The answer to this question is --> 0.40
Step-by-step explanation:
simply do the division.
as a fraction is basically nothing else than a division of the upper number by the lower number.
2 divided by 5
2/5 = 0.4
remember, how division works :
first the outmost left digit(s) divided by the digits of the right number. we use the same number of digits on both sides.
2 / 5 = 0
the first step gives us a 0, because 2 cannot be divided by 5.
then we pull down the next digit from the left side.
if we don't have any (as in this case), we simply pull a 0.
20 / 5 = 0.4
when we pull digits on the left side after the decimal point, then the result gets the decimal point exactly at that position.
20/5 = 4, so the 4 goes into the first position after the decimal point.
and therefore, the final result is
2/5 = 0.4
Question 6 Suppose a Pharmaceutical company manufactures a specific drug and needs to perform some quality assurance to ensure that they have the correct dosage, which is supposed to be 500 mg. In a random sample of n=125 units of the drug, there is an average dose of x=499.3 mg with a standard deviation of =6 mg. What is the likelihood that the drugs produced will actually contain a dosage of 500 mg?
Answers
If in a random sample of n=125 units of the drug, there is an average dose of x=499.3 mg with a standard deviation of =6 mg the likelihood of the drugs produced containing a dosage of 500 mg is fairly high.
Based on the information provided, we can use the concept of the standard error of the mean to determine the likelihood that the drugs produced will contain a dosage of 500 mg.
The formula for the standard error of the mean is:
SE = s/√n
Where:
s = standard deviation of the sample
n = sample size
Substituting the values given, we get:
SE = 6/√125
SE = 0.54
This means that the sample mean of 499.3 mg is 0.54 units away from the true population mean of 500 mg.
To determine the likelihood of the drugs produced containing a dosage of 500 mg, we can use a confidence interval. A 95% confidence interval for the mean dosage can be calculated as:
Mean dosage ± 1.96(SE)
Substituting the values given, we get:
499.3 ± 1.96(0.54)
499.3 ± 1.06
The 95% confidence interval for the mean dosage is (498.24, 500.36).
Therefore, there is a 95% chance that the true population means dosage falls within this interval. Since the interval includes the value of 500 mg, we can conclude that the likelihood of the drugs produced containing a dosage of 500 mg is fairly high.
In a random sample of n=125 units of the drug, there is an average dose of x=499.3 mg with a standard deviation of =6 mg is very high.
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The height in feet of an arrow is modeled by the equation h(t) = (1+2r)(18-81),
where is seconds after the arrow is shot.
a. When does the arrow hit the ground? Explain or show your reasoning.
b. From what height is the arrow shot? Explain or show your reasoning.
Answers
The arrow would hit the ground after 2.25 seconds.
The height from which this arrow was shot is 18 feet.
How to determine the time when the arrow would hit the ground?Based on the information provided, we can logically deduce that the height (h) in feet, of this arrow above the ground is related to time by the following quadratic function:
h(t) = (1 + 2t)(18 - 8t)
Generally speaking, the height of this arrow would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:
0 = (1 + 2t)(18 - 8t)
(18 - 8t) = 0
8t = 18
By dividing both sides of the equation by 8, we have:
Time, t = 18/8
Time, t = 2.25 seconds.
Next, we would determine the height from which this arrow was shot by substituting time (t) with zero;
h(0) = (1 + 2(0))(18 - 8(0))
h(0) = 1(18)
h(0) = 18 feet.
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Complete Question:
The height in feet of an arrow is modeled by the equation h(t) = (1+2t)(18-8t),
where t is seconds after the arrow is shot.
a. When does the arrow hit the ground? Explain or show your reasoning.
b. From what height is the arrow shot? Explain or show your reasoning.
Which graph represents the inequality \(y>x^2-3\)?
Answers
A graph that represents the inequality y > x² - 3 include the following: A. graph A.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Since the leading coefficient (value of a) in the given quadratic function y > x² - 3 is positive 1, we can logically deduce that the parabola would open upward. Also, the value of the quadratic function f(x) would be minimum at -3.
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An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B. When the kinetic energy of the object is a minimum, the object is locatedA. A either A or BB. 1/3 of distance from A to BC. 1/√2 times the distance from A to B D. 1/4 of distance from A to BE. Midway between A and B
Answers
The correct option is D. 1/4 of the distance from A to B.
D. 1/4 of distance from A to B.
The potential energy of a spring varies with the displacement of the object from its equilibrium position. At the equilibrium position, the potential energy is at a minimum, and the kinetic energy is at its maximum. As the object moves away from the equilibrium position, the potential energy increases and the kinetic energy decreases until the object reaches the maximum displacement point, where the potential energy is at a maximum and the kinetic energy is at a minimum.
In the case of a vertical spring, the equilibrium position is the midpoint between the two extreme points, A and B. At this point, the object has zero potential energy and maximum kinetic energy. As the object moves away from the equilibrium position towards point A, its potential energy increases and its kinetic energy decreases until it reaches point A, where the potential energy is at a maximum and the kinetic energy is at a minimum. Therefore, the object is located at point A when the kinetic energy is at a minimum.
Since the spring is ideal and massless, the potential energy is proportional to the square of the displacement from the equilibrium position. The kinetic energy is proportional to the square of the velocity of the object. At point A, the velocity of the object is zero, and hence the kinetic energy is at a minimum. Therefore, the object is located at point A when the kinetic energy is a minimum.
The distance from A to B is divided into four equal parts, and the object is located at the first quarter point from A to B, which is 1/4 of the distance from A to B. Therefore, the correct option is D. 1/4 of the distance from A to B.
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Suppose a normal distribution has a mean of 79 and a standard deviation of
7. What is P(x286)?
OA. 0.975
B. 0.84
O C. 0.025
D. 0.16
Answers
The value of P(x286) is 0.16, the correct option is D.
We are given that;
Mean=79
Standard deviation=7
Now,
To calculate the probability for a normal distribution, you need to convert the raw score x into a standard score z using the formula z = (x - mean) / standard deviation12. Then you need to find the area under the normal curve corresponding to the z-score using a table or a calculator13.
The z-score for x = 86 is:
z = (86 - 79) / 7 = 1
Using a table or a calculator, we can find that the area under the normal curve to the left of z = 1 is about 0.8413. This means that P(x < 86) ≈ 0.8413.
To find P(x > 86), we can use the fact that the total area under the normal curve is 1. So, P(x > 86) = 1 - P(x < 86) ≈ 1 - 0.8413 = 0.1587.
Therefore, by the given mean the answer will be 0.16.
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In government data, a household consists of all occupants of a dwelling unit. Choose an American household at random and count the number of people it contains. Here is the assignment of probabilities for the outcome. (The probability of finding 3 people in a household is the same as the probability of finding 4 people.) What probability should replace "?" in the table? Remember: there is a larger version of the charts on my website!answer choicesa. 0.04b. 0.09c. 0.32d. 0.16
Answers
Based on the information given, we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people. Therefore, the probability that a randomly chosen American household contains 2 or 5 people is 1/6.
To determine the probability that should replace "?" in the table, we first need to recognize that the sum of probabilities for all possible outcomes must equal 1. Given that the probability of finding 3 people in a household is the same as the probability of finding 4 people, let's denote that probability as x.
Since the "?" represents the remaining probability, we can set up an equation:
x + x + ? = 1
The sum of the probabilities for all possible outcomes must equal 1. We know that there are 4 possible outcomes (households with 2, 3, 4, or 5 people).
Simplifying the equation:
3x + ? = 1
Since we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people, we can set up another equation:
Now, let's plug in the answer choices and see which one gives us a valid probability distribution:
a) 0.04:
2x + 0.04 = 1
2x = 0.96
x = 0.48 (Invalid, since x should be the probability for finding 3 or 4 people and it's greater than the maximum probability value of 1)
b) 0.09:
2x + 0.09 = 1
2x = 0.91
x = 0.455 (Invalid for the same reason as options a)
c) 0.32:
2x + 0.32 = 1
2x = 0.68
x = 0.34 (Valid, as it falls within the probability range of 0 to 1)
d) 0.16:
2x + 0.16 = 1
2x = 0.84
x = 0.42 (Invalid for the same reason as options a)
Based on the calculations, option c (0.32) should replace "?" in the table, as it creates a valid probability distribution with the given conditions.
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2-1/3-2/+1 in its simplest fraction
Answers
Answer:
7/3
Step-by-step explanation:
2-1/3-2/+1 in its simplest fraction is equal to 7/3.
HELP.
Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.
Answers
The formula for finding the slope and length of a segment indicates;
Slope of [tex]\overline{QR}[/tex] = -7, length of [tex]\overline{QR}[/tex] = 5·√2
Slope of [tex]\overline{RS}[/tex] = -1, length of [tex]\overline{RS}[/tex] = 5·√2
Slope of [tex]\overline{ST}[/tex] = -7, length of [tex]\overline{ST}[/tex] = 5·√2
Slope of [tex]\overline{TQ}[/tex] = -1, length of [tex]\overline{TQ}[/tex] = 5·√2
What is the formula for finding the length of a segment?The length of a segment on a coordinate plane can be found using the distance formula for finding the distance, d, between two points (x₁, y₁), and (x₂, y₂), which can be expressed as follows;
d = √((x₂ - x₁)² + (y₂ - y₁)²))
The slope of [tex]\overline{QR}[/tex] = (3 - (-4))/(5 - 6) = -7
The length of [tex]\overline{QR}[/tex] = √((3 - (-4))² + (5 - 6)²) = 5·√2
The slope of [tex]\overline{RS}[/tex] = (8 - 3)/(0 - 5) = -1
The length of [tex]\overline{RS}[/tex] = √((8 - 3)² + (0 - 5)²) = 5·√2
The slope of [tex]\overline{ST}[/tex] = (8 - 1)/(0 - 1) = -7
The length of [tex]\overline{ST}[/tex] = √((8 - 1)² + (0 - 1)²) = 5·√2
The slope of [tex]\overline{TQ}[/tex] = (-4 - 1)/(6 - 1) = -1
The length of [tex]\overline{TQ}[/tex] = √((-4 - 1)² + (6 - 1)²) = 5·√2
The quadrilateral QRST can best be described as a rhombus
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the lengths of full-grown scorpions of a certain variety have a mean of 1.96 inches and a standard deviation of 0.08 inch. assuming the distribution of the lengths has roughly the shape of a normal disribution, find the value above which we could expect the longest 20% of these scorpions.
Answers
We can expect the longest 20% of these scorpions to be above a length of approximately 2.0272 inches.
To find the value above which we could expect the longest 20% of these scorpions, we need to use the z-score formula. First, we need to find the z-score that corresponds to the 80th percentile, which is the complement of the top 20%. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 80th percentile is 0.84.
Next, we use the formula z = (x - mu) / sigma, where z is the z-score, x is the value we are trying to find, mu is the mean, and sigma is the standard deviation. We plug in the given values and solve for x:
0.84 = (x - 1.96) / 0.08
0.0672 = x - 1.96
x = 2.0272
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For the scale model of an airplane Jamie is building, 4 feet is proportional to 6 inches. If the length of the airplane Jamie is modeling is 20 feet, what will be the length of his model ?
Answers
4 feet / 6 inches = 20 feet / x
Cross-multiplying, we get:
4 feet * x = 6 inches * 20 feet
Simplifying, we get:
4x = 120
Dividing both sides by 4, we get:
x = 30 inches
Therefore, Jamie's airplane model will be 30 inches long.
,n > Question 2. (18 marks] If pmf of a random variable is given by 4 f(X=n)= n(n+1)(n+2) a. Show that Ë F(X = n)=1 b. Show that E[x]=2
Answers
If pmf of a random variable is given by 4 f(X=n)= n(n+1)(n+2)
the answer to part (a) is:
Ë F(X = n) = 9n(n+1)
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
a. To show that the cumulative distribution function (CDF) F(X) satisfies Ë F(X = n)=1, we need to show that the sum of the probabilities of all possible values of X is equal to 1.
The probability mass function (PMF) is given by:
f(X=n) = 4n(n+1)(n+2)
The CDF is defined as:
F(X=n) = P(X ≤ n)
We can calculate F(X=n) by summing up the probabilities of all values less than or equal to n:
F(X=n) = Σ f(X=i), for i = 0 to n
Substituting the given PMF:
F(X=n) = Σ 4i(i+1)(i+2), for i = 0 to n
Expanding the sum:
F(X=n) = 4(0)(1)(2) + 4(1)(2)(3) + 4(2)(3)(4) + ... + 4n(n+1)(n+2)
F(X=n) = 4 [ (0)(1)(2) + (1)(2)(3) + (2)(3)(4) + ... + (n)(n+1)(n+2) ]
Notice that the sum inside the brackets is a telescoping sum, which can be simplified as:
[(k-1)k(k+1) - (k-2)(k-1)k] = 3k(k-1)
Thus,
F(X=n) = 4 [ 3(0)(-1) + 3(1)(0) + 3(2)(1) + ... + 3(n)(n-1) ]
F(X=n) = 4 [ 3(0 + 1 + 2 + ... + (n-1)) ]
F(X=n) = 4 [ 3(n-1)n/2 ]
F(X=n) = 6n² - 6n
Therefore, Ë F(X = n) is given by:
Ë F(X = n) = Σ F(X=n) * P(X=n), for all n
Substituting the given PMF:
Ë F(X = n) = Σ [ 6n² - 6n ] * 4n(n+1)(n+2), for all n
Expanding the sum and simplifying:
Ë F(X = n) = 24 [ (n+2)(n+1)n(n-1)/4 - (n+1)n(n-1)(n-2)/4 ]
Ë F(X = n) = 24 [ (n-1)n(n+1)(n+2)/4 - (n-2)(n-1)n(n+1)/4 ]
Ë F(X = n) = 24 [ (n-1)n(n+1)(n+2) - (n-2)(n-1)n(n+1) ] / 4
Ë F(X = n) = 6n(n+1)(n+2) - 6n(n+1)(n-1) / 4
Ë F(X = n) = 6n(n+1)[ (n+2) - (n-1) ] / 4
Ë F(X = n) = 6n(n+1) * 3 / 4
Ë F(X = n) = 9n(n+1)/2
Substituting n = 0 and n = ∞ to get the bounds of the sum, we get:
E[X] = 2(0)(5(0)+8) / 3 + 2(∞)(∞+1)(5(∞)+8) / 3
Since the second term diverges to infinity, we can conclude that the expected value of X does not exist (i.e., it is undefined).
Therefore, the answer to part (a) is:
Ë F(X = n) = 9n(n+1)/
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If pmf of a random variable is given by 4 f(X=n)= n(n+1)(n+2)
the answer to part (a) is:
Ë F(X = n) = 9n(n+1)
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
a. To show that the cumulative distribution function (CDF) F(X) satisfies Ë F(X = n)=1, we need to show that the sum of the probabilities of all possible values of X is equal to 1.
The probability mass function (PMF) is given by:
f(X=n) = 4n(n+1)(n+2)
The CDF is defined as:
F(X=n) = P(X ≤ n)
We can calculate F(X=n) by summing up the probabilities of all values less than or equal to n:
F(X=n) = Σ f(X=i), for i = 0 to n
Substituting the given PMF:
F(X=n) = Σ 4i(i+1)(i+2), for i = 0 to n
Expanding the sum:
F(X=n) = 4(0)(1)(2) + 4(1)(2)(3) + 4(2)(3)(4) + ... + 4n(n+1)(n+2)
F(X=n) = 4 [ (0)(1)(2) + (1)(2)(3) + (2)(3)(4) + ... + (n)(n+1)(n+2) ]
Notice that the sum inside the brackets is a telescoping sum, which can be simplified as:
[(k-1)k(k+1) - (k-2)(k-1)k] = 3k(k-1)
Thus,
F(X=n) = 4 [ 3(0)(-1) + 3(1)(0) + 3(2)(1) + ... + 3(n)(n-1) ]
F(X=n) = 4 [ 3(0 + 1 + 2 + ... + (n-1)) ]
F(X=n) = 4 [ 3(n-1)n/2 ]
F(X=n) = 6n² - 6n
Therefore, Ë F(X = n) is given by:
Ë F(X = n) = Σ F(X=n) * P(X=n), for all n
Substituting the given PMF:
Ë F(X = n) = Σ [ 6n² - 6n ] * 4n(n+1)(n+2), for all n
Expanding the sum and simplifying:
Ë F(X = n) = 24 [ (n+2)(n+1)n(n-1)/4 - (n+1)n(n-1)(n-2)/4 ]
Ë F(X = n) = 24 [ (n-1)n(n+1)(n+2)/4 - (n-2)(n-1)n(n+1)/4 ]
Ë F(X = n) = 24 [ (n-1)n(n+1)(n+2) - (n-2)(n-1)n(n+1) ] / 4
Ë F(X = n) = 6n(n+1)(n+2) - 6n(n+1)(n-1) / 4
Ë F(X = n) = 6n(n+1)[ (n+2) - (n-1) ] / 4
Ë F(X = n) = 6n(n+1) * 3 / 4
Ë F(X = n) = 9n(n+1)/2
Substituting n = 0 and n = ∞ to get the bounds of the sum, we get:
E[X] = 2(0)(5(0)+8) / 3 + 2(∞)(∞+1)(5(∞)+8) / 3
Since the second term diverges to infinity, we can conclude that the expected value of X does not exist (i.e., it is undefined).
Therefore, the answer to part (a) is:
Ë F(X = n) = 9n(n+1)/
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Find the area of the rectangle.
5.5 in
20.45 in
Answers
Answer:112.475
Step-by-step explanation:
5/8x + 1/2 ( 1/4x + 10)
Answers
Answer:5+3x/4
Step-by-step explanation:
Answer:2x+1
1
Step-by-step explanation:
PLEASE HELP ME SOLVE THIS ONE QUESTION , I HAVE SOLVED I) IT IS II) I NEED HELP WITH
5. A is the point (1,5) and B is the point (3,9).M is the midpoint of AB
i) M = (2,5)
ii)Find the equation of the line that is perpendicular to AB and passes through M.
Give your answer in the form : y=mx+c
Answers
I)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 +1}{2}~~~ ,~~~ \cfrac{ 9 +5}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 14 }{2} \right)\implies (2~~,~~7)[/tex]
II)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line AB
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 4 }{ 2 } \implies 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 2 \implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2} }}[/tex]
so we're really looking for the equation of a line whose slope is -1/2 and it passes through (2 , 7)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{2}) \\\\\\ y-7=- \cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x+8 \end{array}}[/tex]
Given vector u equals open angled bracket negative 12 comma negative 5 close angled bracket and vector v equals open angled bracket 3 comma 9 close angled bracket comma what is projvu?
open angled bracket negative 27 over 10 comma negative 81 over 10 close angled bracket
open angled bracket negative 54 over 5 comma negative 9 over 2 close angled bracket
open angled bracket negative 243 over 169 comma negative 729 over 169 close angled bracket
open angled bracket negative 972 over 169 comma negative 405 over 169 close angled bracket
Answers
The value of the vector [tex]proj_{vu}[/tex] is <-972/169, -405/169>. (option d).
The projection of one vector onto another vector can be thought of as the shadow of one vector onto another in the direction of the second vector. Mathematically, the projection of vector v onto vector u can be calculated as follows:
[tex]proj_{vu}[/tex] = (v · u / ||u||²) x u
Here, · denotes the dot product of two vectors, and ||u|| denotes the magnitude or length of vector u.
Now, let's apply this formula to the given vectors u and v:
u = <-12,-5>
v = <3,9>
To calculate [tex]proj_{vu}[/tex], we first need to find the dot product of vectors u and v:
u · v = (-12 x 3) + (-5 x 9) = -36 - 45 = -81
Next, we need to find the magnitude of vector u:
||u|| = √((-12)² + (-5)²) = √(144 + 25) = √169 = 13
Now, we can substitute the values we have found into the formula for [tex]proj_{vu}[/tex]:
[tex]proj_{vu}[/tex] = (-81 / (13²)) x <-12,-5> = <-81/13, -405/169>
Therefore, the answer to the given question is option (d): [tex]proj_{vu}[/tex] = <-972/169, -405/169>.
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Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10 each and short-sleeved shirts are $5 each. The club can spend no more than $165. What are the minimum and maximum numbers of long-sleeved shirts that can be purchased?
Answers
Answer:
Assume "x" represents the number of long-sleeved shirts and "y" represents the number of short-sleeved shirts.
According to the information provided, at least 25 members will receive a shirt. As a result, we may express the equation as:
x + y 25...........(1)
In addition, the club's budget cannot exceed $165. Each long-sleeved shirt costs $10, while each short-sleeved shirt costs $5. As a result, the total cost is stated as:
10x + 5y 165...........(2)
The minimum and maximum quantity of long-sleeved shirts that can be purchased must be determined.
To determine the bare minimum of long-sleeved shirts, we may assume that each of the 25 members will receive a short-sleeved shirt. As a result, equation (1) becomes: x + 25 25 x 0
As a result, the bare minimum of long-sleeved shirts that can be purchased is 0.
To determine the maximum number of long-sleeved shirts, we must solve equations (1) and (2) concurrently. We may do this by using the replacement approach.
We may deduce from equation (1): y ≥ 25 - x
When we substitute this number for "y" in equation (2), we get:
10x + 5(25 - x) ≤ 165
When we simplify this equation, we get:
5x ≤ 40
x ≤ 8
As a result, the total number of long-sleeved shirts that can be ordered is eight.
As a result, the lowest number of long-sleeved shirts available for purchase is 0 and the maximum number of long-sleeved shirts available for purchase is 8.
Find f(x) if f(2) = 2 and the tangent line at x has slope (x - 1) 2x
Answers
The function f(x) is [tex]\frac{2}{3}x^3 - 76x^2 + 150x + 2.67[/tex].
To find f(x), we need to integrate the given slope (x-1)(2x-150) with respect to x, because the slope of a tangent line to a function is the derivative of that function. A line's slope is a gauge of its steepness. Between any two points on the line, it is calculated as the ratio of the change in the vertical coordinate (rise) to the change in the horizontal coordinate (run).
So, we have:
f'(x) = (x-1)(2x-150)
Integrating both sides with respect to x:
[tex]f(x) = ∫(x-1)(2x-150) dx[/tex]
[tex]f(x) = \int (2x^2 - 152x + 150) dx[/tex]
[tex]f(x) = \frac{2}{3}x^3 - 76x^2 + 150x + C[/tex]
where C is an arbitrary constant of integration.
To determine the value of C, we can use the given condition f(2) = 2:
[tex]f(2) = \frac{2}{3}(2)^3 - 76(2)^2 + 150(2) + C = 2[/tex]
Simplifying:
C = 2 - (8/3) + 304 - 300 = 2.67
Therefore, the function f(x) is:
f(x) = [tex]\frac{2}{3}x^3 - 76x^2 + 150x + 2.67[/tex].
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Suppose follows the standard normal distribution calculate the following probabilities using ALEKS Chitarunt your own decimal places (a) P(2> -175) - 0 (0) P(2 5 1.82)=0 (C) P(-109
Answers
The calculated probabilities are approximately:
(a) P(Z > -1.75) = 0.9599
(b) P(Z ≤ 1.82) = 0.9656
(c) P(Z < -1.09) = 0.1379
We have,
To calculate probabilities using the standard normal distribution, with the given values
(a) P(Z > -1.75), (b) P(Z ≤ 1.82), and (c) P(Z < -1.09):
1. Identify the Z-score for each probability:
(a) Z > -1.75
(b) Z ≤ 1.82
(c) Z < -1.09
2. Use a standard normal distribution table, calculator, or software (such as ALEKS) to find the probability associated with each Z-score:
(a) P(Z > -1.75) = 1 - P(Z ≤ -1.75)
(b) P(Z ≤ 1.82) = P(Z ≤ 1.82)
(c) P(Z < -1.09) = P(Z ≤ -1.09)
3. Look up the probabilities in the standard normal distribution table or calculate them using a calculator or software:
(a) P(Z > -1.75) = 1 - 0.0401 = 0.9599 (approx.)
(b) P(Z ≤ 1.82) = 0.9656 (approx.)
(c) P(Z < -1.09) = 0.1379 (approx.)
Thus,
The calculated probabilities are approximately:
(a) P(Z > -1.75) = 0.9599
(b) P(Z ≤ 1.82) = 0.9656
(c) P(Z < -1.09) = 0.1379
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In a recent school year, 91,863 of the students were girls and 80,492 of the students were boys. Among the girls, 19,598 dropped out of school, and among the boys, 31,419 dropped out. A student is chosen at random. Create a table to help you answer the question. Boys Girls Total Dropped Did not drop Total Given that the student is male, what is the probability that he did not drop out? Write your answer as a decimal rounded to 2 decimal places.
Answers
The probability that a male student did not drop out of school is 0.28 (rounded to 2 decimal places).
To answer the question, we need to use conditional probability. We are given that a student is male, and we need to find the probability that he did not drop out of school.
From the information given, we can fill in the table:
The probability of a student being a boy is:
P(boy) = number of boys / total number of students = 80,492 / 172,355 = 0.4666 (rounded to 4 decimal places)
The probability that a boy did not drop out is:
P(did not drop | boy) = number of boys who did not drop out / total number of boys = 49,073 / 80,492 = 0.6100 (rounded to 4 decimal places)
Therefore, the probability that a student is male and did not drop out of school is:
P(male and did not drop) = P(did not drop | boy) * P(boy) = 0.6100 * 0.4666 = 0.2847 (rounded to 4 decimal places)
So the probability that a male student did not drop out of school is 0.28 (rounded to 2 decimal places).
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HELPPPPPP!!!!!!!!!!!!!
Answers
Haha I remember this back in 7th grade good times the answer is y=1/3x+
write the recursive rule for the sequence shown in each table.
position, n 1 2 3 4 5
term, f(n) 5 18 31 44 57
1 2 3 4 5 6 7
65 54 43 32 21 10 -1
1 2 3 4 5 6 7
-9 6 21 36 51 66 81
1 2 3 4 5 6 7 8
17 13 9 5 1 -3 -7 -11
Answers
The recursive rule for the sequence given is aₙ = aₙ₋₁ + 13.
Given that, a sequence,
position, n = 1 2 3 4 5
term, f(n) = 5 18 31 44 57
We need to write the recursive rule for the sequence,
So,
a₁ = 5, a₂ = 18
18-5 = 13
a₃ = 31, a₄ = 44
44-31 = 13
Therefore,
We see that, the preceding term is 13 less than the succeeding term,
We can write,
aₙ = aₙ₋₁ + 13
Hence, the recursive rule for the sequence given is aₙ = aₙ₋₁ + 13.
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44 students complete some homework and the histogram shows information about the time taken. work out the estimate of the interquartile range. in the working you must show the upper and lower quartiles.
Answers
It can be seen that the range is 19 minutes
How to solveFrom the given data, we can see:
1.4 × 5 = 7
0.8 × 10 = 8
1.4 × 10 = 14
1 × 15 = 15
15 + 14 + 8 + 7 = 44
44 ÷ 4 = 11
LQ of 44=11
LQ = 10 minutes
11 × 3 = 33 UQ = 29 minutes
Therefore, it can be seen that the range is 19 minutes
Range is the aggregate of conceivable output values in a function. Any inputs within its domain can be used to compute the range, which is viewed as a pivotal aspect when assessing the behavior and properties of functions. Additionally, it is regularly incorporated in describing the spread and variability of data sets in statistics.
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The tree diagram represents an
experiment consisting of two trials.
S
A
B
.4 C
6
13
D
C
D
Answers
The required probability is P(A and C) is 0.2 which is represented in the tree diagram.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The given tree diagram represents an experiment consisting of two trials.
The tree diagram represents an experiment consisting of two trials. In this case, the probability of event A and event C occurring is represented by the intersection of branches A and C in the tree diagram.
This probability can be calculated by multiplying the probability of each individual event together.
As per the given question, we have
P(A) = 0.5
P(C|A) = 0.4
So, P(A and C) = 0.5 × 0.4 = 0.2
Thus, the required probability is P(A and C) is 0.2
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