The standard deviation for the given mean length x is found to be: 2.138.
Explain about the standard deviation ?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Here, the standard deviation enters the picture; it gauges how variable a set of values is, or how dispersed they are from the average. The differential between each value and the group average serves as the basis for the standard deviation.
Given data:
mean μ = 86
standard deviation σ = 8
number of sample n = 14
average body length x = 91.1
The population standard deviation is divided by that of the square root of both the sample size to calculate the standard deviation of the sampled distribution of the sample mean.
So,
σₓ = σ / √n
σₓ = 8 / √14
σₓ = 2.138
Thus, the standard deviation for the given mean length x is found to be: 2.138.
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The complete question is-
Deer mice (Peromyscus manicul.atus) are small rodents native of North America. Their adult body lengths (excluding tail) are known to vary approximately Normally, with mean 86 mm and standard deviation 8 mm. Deer mice are found in diverse habitats and exhibit different adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of x = 91.1 mm. Assume that the standard deviation σ of all deer mice in this area is also 8 mm.
What is the standard deviation of the mean length x?
a homogeneous wire is bent into the shape shown. determine the x coordinate of its centroid by direct integration. express your answer in terms of a.
The x coordinate of the centroid of the wire with y=kx^(3/2) and x and y intercept a is 0.546a. The y coordinate is 8a/5.
To find the centroid of the wire, we need to find the area and first moments of the wire, which are given by:
Area, A = ∫y dx, where x ranges from -a to a
First moment with respect to x, Mx = ∫xy dx, where x ranges from -a to a
Then the x coordinate of the centroid is given by:
xc = Mx / A
We can start by finding the area:
A = ∫y dx = ∫kx^(3/2) dx = (2/5)kx^(5/2) + C
At x = a, y = 0, so C = - (2/5)ka^(5/2)
At x = -a, y = 0, so A = 2(2/5)ka^(5/2) = (4/5)ka^(5/2)
Now we need to find the first moment with respect to x:
Mx = ∫xy dx = ∫kx^(5/2) dx = (2/7)kx^(7/2) + C'
At x = a, y = 0, so C' = - (2/7)ka^(7/2)
At x = -a, y = 0, so Mx = 0
Therefore, the x coordinate of the centroid is:
xc = Mx / A = 0 / [(4/5)ka^(5/2)] = 0
This means that the centroid lies on the y-axis. To find its y coordinate, we can use the formula:
yc = ∫x dy / A = ∫x (dy/dx) dx / A
Using the equation y = kx^(3/2), we can find dy/dx:
dy/dx = (3/2)kx^(1/2)
Substituting this into the formula for yc and simplifying, we get:
yc = (4/5)ka^(5/2) / (5/8)ka^(5/2) = (8/5)a
Therefore, the coordinates of the centroid are (0, 8/5 a), and the y coordinate is (8/5)a.
To find the x coordinate of the centroid, we need to use the formula:
xc = (1/A) ∫x y dx
We already found the expression for the area A, so we just need to evaluate the integral:
xc = (1/A) ∫x y dx = (1/A) ∫x kx^(3/2) dx
Integrating this by substitution with u = x^(1/2), we get:
xc = (2/5a^(5/2)) ∫u^4 du = (2/5a^(5/2)) (u^5/5) + C
where C is a constant of integration.
At x = a, y = 0, so u = a^(1/2) and C = -(2/25)a^(5/2).
At x = -a, y = 0, so the contribution to the integral is zero.
Therefore, the x coordinate of the centroid is:
xc = (2/5a^(5/2)) (u^5/5) - (2/25a^(5/2)) = (2/25)a(5√2 - 1)
Plugging in a = 1, we get:
xc = 0.546a
So the x coordinate of the centroid is 0.546 times the x and y intercept value a.
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_____The given question is incomplete, the complete question is given below:
a homogeneous wire is bent into the shape shown of graph y = kx^(3/2), x and y intercept is 'a'. determine the x coordinate of its centroid by direct integration. express your answer in terms of a. Also find y- coordinate.
What is the difference between the questionnaire and an interview?
Answer: Questionnaire refers to a research instrument, in which a series of question, is typed or printed along with the choice of answers, expected to be marked by the respondents, used for survey or statistical study. It consists of aformalisedd set of questions, in a definite order on a form, which are mailed to the respondents or manually delivered to them for answers. The respondents are supposed to read, comprehend and give their responses, in the space provided.
A ‘Pilot Study’ is advised to be conducted to test the questionnaire before using this method. A pilot survey is nothing but a preliminary study or say rehearsal to know the time, cost, efforts, reliability and so forth involved in it.
The interview is a data collection method wherein a direct, in-depth conversation between interviewer and respondent takes place. It is carried out with a purpose like a survey, research, and the like, where both the two parties participate in the one to one interaction. Under this method, oral-verbal stimuli are presented and replied by way of oral-verbal responses.
It is considered as one of the best methods for collecting data because it allows two way exchange of information, the interviewer gets to know about the respondent, and the respondent learns about the interviewer. There are two types of interview:
Personal Interview: A type of interview, wherein there is a face to face question-answer session between the interviewer and interviewee, is conducted.
Telephonic Interview: This method involves contacting the interviewee and asking questions to them on the telephone itself.
An instructor is administering a final examination. She tells her class that she with give an A grade to the 10% of the students who earns the highest marks. Past experience with the same examination has yielded grades that are normally distributed with a mean of 70 and a standard deviation of 10. If present class runs true to form, what numerical score would a student need to earn an A grade?
To earn an A grade, a student needs to score at least 82.8 , calculated using the inverse normal cumulative distribution function with a mean of 70, a standard deviation of 10, and a 10th percentile of 0.10.
Given that the grades are normally distributed with a mean of 70 and a standard deviation of 10.
We need to find the score which is at the 10th percentile of the distribution.
Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile.
From the table, we can see that the z-score is approximately -1.28.
Using the formula for standardizing a normal distribution:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values, we have:
-1.28 = (x - 70) / 10
Solving for x, we get:
x = (-1.28 * 10) + 70
x = 82.8
Therefore, a student would need to earn a score of approximately 82.8 to receive an A grade.
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Please help me, can’t figure out which one is actually correct for Jackson
If Jackson feels confident that he can score higher than 69 on the final exam, then he should take it. Otherwise, he would be better off not taking the final exam.
What is probability?
Probability is a branch of mathematics that deals with the study of random events or phenomena. It is the measure of the likelihood or chance of an event or set of events occurring.
If Jackson does not take the final exam, the average of his three highest scores would be:
(72 + 73 + 70)/3 = 71.67.
If Jackson takes the final exam, there are two possibilities:
If Jackson scores lower than any of his previous exam scores, then his lowest score will be dropped, and his grade will be calculated based on his four highest scores, which would be:
(73 + 72 + 70 + X)/4.
where X is his score on the final exam. In this case, taking the final exam would not benefit Jackson, as his grade would be based on his three highest scores (72, 73, and 70) regardless of his performance on the final exam.
If Jackson scores higher than any of his previous exam scores, then his lowest score will be the lowest of his first four exams, and his grade will be calculated based on his four highest scores, which would be:
(73 + 72 + X1 + X2)/4.
Therefore, If Jackson feels confident that he can score higher than 69 on the final exam, then he should take it. Otherwise, he would be better off not taking the final exam.
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Which number line represents the solutions to NEED HELP
Answer:
Step-by-step explanation:
|x-a|=b
x-a=±b
x=a±b
|x-2|=6
x-2=±6
either x-2=6
x=2+6=8
or
x-2=-6
x=2-6
x=-4
d
Help please! I have no idea!!!! PLEASEE
To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0.
What is graph?
In mathematics, a graph is a visual representation of a set of data, typically as a set of points or lines on a coordinate plane. Graphs are used to represent various types of data, such as numerical values, functions, relationships, and patterns.
Assuming that the graph is a coordinate plane with the x-axis and y-axis, do the following:
To highlight the point (9, 8) on the graph in red, locate the point (9, 8) on the coordinate plane and mark it with a red color.
To highlight the point (20, f(20)) on the graph in green, you need to know the value of f(20) first. Once you have that value, locate the point (20, f(20)) on the coordinate plane and mark it with a green color.
To highlight the line y = 5 on the graph in blue, draw a straight line passing through all points whose y-coordinate is 5. This line should be parallel to the x-axis and should be marked with a blue color.
Therefore To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0. This line should be parallel to the x-axis and should be marked with a black/grey color.
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John plans to practice piano at least 2 hours this weekend.
If he practices 1 hours on Saturday and 14 hours on Sunday, will he meet his goal?
Answer:
Yes
Step-by-step explanation:
Yes because 1+14=15 hours and that is more than two
A cyclist rides off from rest, accelerating at a constant rate for 3 minutes until she reaches 40 kmh-1. She then maintains a constant speed for 4 minutes until reaching a hill. She slows down at a constant rate over one minute to 30 kmh-1. then continues at this rate for 10 minutes.
At the top of the hill she reduces her speed uniformly and is stationary 2 minutes later.
How far has the cyclist travelled?
Answer:
The cyclist has travelled a distance of 931.888 meters.
Let G
be a group. Say what it means for a map φ:G→G
to be an automorphism. Show that the set-theoretic composition φψ=φ∘ψ
of any two automorphisms φ,ψ
is an automorphism. Prove that the set Aut(G)
of all automorphisms of the group G
with the operation of taking the composition is a group.
a) An automorphism of a group G is a bijective map φ:G→G that preserves the group structure. That is, φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹ for all a, b ∈ G.
b) The set-theoretic composition φψ of any two automorphisms φ, ψ is an automorphism, as it preserves the group structure and is bijective.
c) The set Aut(G) of all automorphisms of G, with the operation of composition of maps, is a group. This is because it satisfies the four group axioms: closure, associativity, identity, and inverses. Therefore, Aut(G) is a group under composition of maps.
An automorphism of a group G is a bijective map φ:G→G that preserves the group structure, meaning that for any elements a,b∈G, we have φ(ab) = φ(a)φ(b) and φ(a⁻¹) = φ(a)⁻¹. In other words, an automorphism is an isomorphism from G to itself.
To show that the set-theoretic composition φψ is an automorphism, we need to show that it satisfies the two conditions for being an automorphism. First, we have
(φψ)(ab) = φ(ψ(ab)) = φ(ψ(a)ψ(b)) = φ(ψ(a))φ(ψ(b)) = (φψ)(a)(φψ)(b)
using the fact that ψ and φ are automorphisms. Similarly,
(φψ)(a⁻¹) = φ(ψ(a⁻¹)) = φ(ψ(a))⁻¹ = (φψ)(a)⁻¹
using the fact that ψ and φ are automorphisms. Therefore, φψ is an automorphism.
To show that Aut(G) is a group, we need to show that it satisfies the four group axioms
Closure: If φ,ψ∈Aut(G), then φψ is also in Aut(G), as shown above.
Associativity: Composition of maps is associative, so (φψ)χ = φ(ψχ) for any automorphisms φ,ψ,χ of G.
Identity: The identity map id:G→G is an automorphism, since it clearly preserves the group structure and is bijective. It serves as the identity element in Aut(G), since φid = idφ = φ for any φ∈Aut(G).
Inverses: For any automorphism φ∈Aut(G), its inverse φ⁻¹ is also an automorphism, since it is bijective and preserves the group structure. Therefore, Aut(G) is closed under inverses.
Since Aut(G) satisfies all four group axioms, it is a group under composition of maps.
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the graph shows the preimage shaded in grey and the image outlined in black. what is the scale factor of the dilation?
The scale factor of dilation of the shaded in gray to the shaded in black is 3
Calculating the scale factor dilationGiven that
The preimage = shaded in gray
The image = shaded in black
From the graph, we have the following values on the image and the preimage
The preimage = shaded in gray = 4
The image = shaded in black = 12
The scale factor of dilation is then calculated as
Scale factor = shaded in black/shaded in gray
So, we have
Scale factor = 12/4
Evaluate
Scale factor = 3
Hence, the scale factor dilation is 3
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TRUE/FALSE.For a Binomial experiment, the second moment about mu is given by the second derivative of (p+qeAt) with respect to t evaluated at t-0.
False. The second moment about mu for a binomial experiment is not given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0.
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q=1-p.
The second moment about mu is a measure of the variability of the binomial distribution, and is given by the formula[tex]E[(X-mu)^2][/tex] , where X is the random variable, mu is the mean, and E is the expected value operator.
To calculate the second moment about mu for a binomial distribution with parameters n and p, we can use the formula npq, where np is the mean and q=1-p. This formula can also be derived using the properties of variance, which state that [tex]Var(X)=E[X^2] - (E[X])^2.[/tex]
Therefore, the statement that the second moment about mu for a binomial experiment is given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0 is false. This statement does not relate to the binomial distribution or its properties, and is not a relevant formula for measuring the variability of a binomial experiment.
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Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes f(x) = g(x). f: initial value of 500 decreasing at a rate of 6% g: initial value of 90 increasing at a rate of 6%
The value of x that makes f(x)g(x) is x
Answer:
Step-by-step explanation:
u got this
how do you find the simplest radical form for this please help me i got a (f) and i really need help that’s why i’m up this late trying to do all of my missing assignments.
Answer:
[tex]14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} }[/tex]
Step-by-step explanation:
[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} }= \sqrt{196} \times \sqrt{ {x}^{3} } \times \sqrt{ {y}^{4} } \times \sqrt{ {z}^{9} } \\ \sqrt{196} = 14 \\ \sqrt{ {x}^{3} } = {x}^{ \frac{3}{2} } \\ \sqrt{ {y}^{4} } = {y}^{2} \\ \sqrt{ {z}^{9}} = {z}^{ \frac{9}{2} }[/tex]
A fractional exponent is not necessarily simpler so just take out the 1st and 3rd parts of the term which simplify nicely:
[tex] \sqrt{196 {x}^{3} {y}^{4}{z}^{9} } = 14 {y}^{2} \sqrt{ {x}^{3} {z}^{9} } [/tex]
Daisy cream is sold in a bulk of 76 cups of cream. Kremlin cream is sold in a bulk of 4 1/2 gallons of cream. Mable cream is sold in a bulk of 40 pints. Which one has the most cream?
Answer:
Step-by-step explanation:
it is mable
Correct to 3 significant figures, the of 18.75-(2.11)2
Answer: 14.5
Step-by-step explanation:
When there is a decimal point, you start counting from the left any number that is not zero. If the zero is at the end, then you count it.
For example, if the answer is 0.000145 then the number of significant figures is still three because you start counting from the first nonzero number from the left.
If the answer is 14.50, then the number of significant figures is four because you start counting from the first nonzero number from the left.
14.53 is the answer to the equation but because you want to correct it to 3 significant figures, you round down because 3 is less than 5 and 14.5 ends up being the final answer.
Solve the system of equations x + y = 8; y = x ^ 2 - 4
The solution to the system of equations is (x, y) = (-4, 12) or (3, 5).
What are systems of equations?simultaneous equations, or system of equations Two or more equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a distinct solution. Even then, a solution is not assured.
According to the given information:We can solve this system of equations by substitution or elimination. Here, we will use substitution:
Substitute y in the first equation with its expression from the second equation:
x + (x^2 - 4) = 8
Now, we have a quadratic equation in x:
x^2 + x - 12 = 0
Factor the quadratic equation:
(x + 4)(x - 3) = 0
So, either x + 4 = 0 or x - 3 = 0:
x = -4 or x = 3
Substitute each value of x into either equation to find the corresponding value of y:
If x = -4, then y = (-4)^2 - 4 = 12
If x = 3, then y = 3^2 - 4 = 5
Therefore, the solution to the system of equations is (x, y) = (-4, 12) or (3, 5).
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Please help me with this question
The slope-intercept version of the equation for the tangent line to f(x) at the position (-5, -1) is y = (-1/5)x -2. Thus,
m = -1/5
y = (-1/5)x -2
What can you infer from a tangent line?A tangent line is a straight line that οnly has οne cοntact with a functiοn. (See earlier.) The instantaneοus rate οf change οf the functiοn at that exact place is shοwn by the tangent line. At each given pοint οn the functiοn, the slοpe οf the tangent line is equal tο the derivative οf the functiοn at that same lοcatiοn.
We must determine the derivative οf the functiοn and evaluate it at x = -5 in οrder tο determine the slοpe οf f(x) = 5/x at the pοint (-5, -1).
f(x) = 5/x
f'(x) = [-5/x²]
When we enter x = -5, we obtain:
f'(-5) = [-5/(-5)²] = -1/5
As a result, the tangent line to f(x) at the point (-5, -1) has a slope of -1/5.
y - y1 = m(x - x1)
y - (-1) = (-1/5)(x - (-5))
y + 1 = (-1/5)(x + 5)
y = (-1/5)x -10/5
y = (-1/5)x -2
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The sum of the ages of father and son at present is 45 years. If both live on until the son's age becomes equal to the father's present age, the sum of their ages then will be 95 years. Find their present ages.
Answer:
father age 45 son age 0 this is answer
I need help with this question.. :')
The equation of the line passing through A and B is y = (4/5)x - (2/5).
What is the line example's equation?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.
The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:
y - y1 = m(x - x1) (x - x1)
where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.
To calculate the slope, we can use points A (3, 2) and B (8, 6).
m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5
So the equation for the line connecting A and B is:
y - 2 = (4/5)(x - 3) (x - 3)
This equation can be simplified by multiplying both sides by 5:
5y - 10 = 4x - 12
Then we can rearrange it to form the slope-intercept equation, y = mx + b:
5y = 4x - 2
y = (4/5)x - (2/5)
As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).
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If
f(x) = 2x² + 3x - 6, determine the value of f(2).
Answer:
8
Step-by-step explanation:
2x² + 3x - 6
plug in x with 2
2(2)^2+3(2)-6
2(4)+6-6
8+6-6
14-6
8
PLEASE HELP !
Use the figure below to answer the questions
From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.
What are rays, line segment and line?A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.
The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.
A line is a collection of points that extends in two opposing directions and is endlessly long and thin.
From the given figure we observe that,
1. Two line segments are LA and EP.
2. Two rays are EC and AH.
3. Two lines are b and AP.
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consider the following scores: 13, 18, 9, 27, 15, 15, 28, 5, 16, 21, 23, 29, 15, 15 what z-score would be earned by a person who had scored 25 points?
A person who scored 25 points in this dataset would have a z-score of 0.99.
The mean can be calculated by adding up all of the scores and dividing by the number of scores:
(13 + 18 + 9 + 27 + 15 + 15 + 28 + 5 + 16 + 21 + 23 + 29 + 15 + 15) / 14 = 18
The standard deviation can be calculated using the formula:
sqrt(sum((x - mean)^2) / (n - 1))
where x is each score in the dataset, mean is the mean of the dataset, and n is the number of scores.
Using this formula, we get:
sqrt (((13-18) ^2 + (18-18) ^2 + (9-18) ^2 + (27-18) ^2 + (15-18) ^2 + (15-18) ^2 + (28-18) ^2 + (5-18) ^2 + (16-18) ^2 + (21-18) ^2 + (23-18) ^2 + (29-18) ^2 + (15-18) ^2 + (15-18) ^2) / (14 - 1))
= 7.05
Now we can calculate the z-score of a scores of 25 using the formula:
z = (x - mean) / standard deviation
where x is the score, we are interested in, mean is the mean of the dataset, and standard deviation is the standard deviation of the dataset.
Plugging in the values, we get:
z = (25 - 18) / 7.05 = 0.99 (rounded to two decimal places)
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A bag with 6 marbles has 2 blue marbles and 4 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is red?
Write your answer as a fraction in simplest form.
Step-by-step explanation:
Hey mate, if there are no red balls inside the bag then the probabililty will be obviously 0
12. What is the height of the trapezoid in yards? (Hint: Use the formula
A = 1/2h (b 1, + b2,) (Lesson 2)
Answer:
height = 7 yards
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the 2 parallel bases
here b₁ = 12 , b₂ = 9 and A = 73.5 , then
[tex]\frac{1}{2}[/tex] h(12 + 9) = 73.5 ( multiply both sides by 2 to clear the fraction )
h(21) = 147
21h = 147 ( divide both sides by 21 )
h = 7 yards
A home has gone up in value over several
decades and is now worth 1354% of its
original sale price of $23,000. What is the
value now?
Answer:
$31,142
Step-by-step explanation:
To convert a percentage into a decimal, you move the decimal two places to the left. 1354% converted into a decimal is 13.54.
$23,000 * 13.54 = $31,142
10. You buy a 1-pound box of oatmeal. You use of the box, then divide the
remainder into 4 equal portions. How many pounds are in each portion?
Therefore, each portion will be (1-x)/4 pounds.
What are pounds?Pounds (lb) is a unit of measurement of weight or mass commonly used in the United States, United Kingdom, and other countries that have adopted the Imperial system of measurement. One pound is equal to 0.453592 kilograms (kg). The symbol for pound is "lb", which comes from the Latin word libra. In everyday use, pounds are often used to measure the weight of objects, people, and animals, as well as food and other goods sold by weight.
Given by the question.
If you have used x pounds of the 1-pound box of oatmeal, then the remaining amount is 1 - x pounds.
You then divide this remainder into 4 equal portions, which means each portion will be (1-x)/4 pounds.
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The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 30 minutes, what is the probability that X is less than 38 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)
Answer:
0.718 = 71.8% probability that X is less than 38 minutes
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x)=\mu e^{-\mu x}[/tex]
In which [tex]\mu=\frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X\leq x)=\int\limits^a_0f ({x)} \, dx[/tex]
Which has the following solution:
[tex]P(X\leq x)=1-e^{-\mu x}[/tex]
If X has an average value of 30 minutes
This means that [tex]m=30,\mu=\frac{1}{30}[/tex]
What is the probability that X is less than 38 minutes?
[tex]P(X\leq 38)=1-e^{-\frac{38}{30} }[/tex]
0.718 = 71.8% probability that X is less than 38 minutes
Milly took a loan of N$900 with simple interest for as many years as the rate of interest. If she paid N$324 as
interest at the end of the loan period, what was the rate of interest?
Answer:
Let's assume that the rate of interest is r (in decimals), and the time period is also r years. Then we can use the simple interest formula:
I = P * r * t
where I is the interest paid, P is the principal amount (the loan amount in this case), r is the rate of interest per year, and t is the time period in years.
Substituting the given values, we get:
324 = 900 * r * r
Simplifying, we get:
r² = 324/900
r² = 0.36
Taking the square root of both sides, we get:
r = ±0.6
Since the rate of interest cannot be negative, we can take r = 0.6. Therefore, the rate of interest is 0.6 or 60% per year.
6u^2+17u-10
factor please
Answer:
(2u - 1) (3u + 10)
Step-by-step explanation:
Let's Check
(2u - 1) (3u + 10)
6u² + 20u - 3u + 10
6u² + 17u + 10
So, (2u - 1) (3u + 10) is the correct answer.
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Answer:
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Step-by-step explanation:
The total surface area of the pyramid can be calculated using the formula for the lateral surface area of a pyramid:
Lateral surface area = (1/2) × perimeter of base × slant height
Since the base is an equilateral triangle, the perimeter is 3 times the length of one side:
Perimeter of base = 3 × 40 feet = 120 feet
Lateral surface area = (1/2) × 120 feet × 50 feet = 3000 square feet
To paint 75% of the pyramid, the painter needs to paint:
0.75 × 3000 square feet = 2250 square feet
Since the painter can paint 100 square feet in 18 minutes, the time required to paint 2250 square feet can be calculated as:
2250 square feet ÷ 100 square feet per 18 minutes = 225 ÷ 10 × 18 minutes = 405 minutes
Therefore, the painter would need 405 minutes or 6 hours and 45 minutes to paint 75% of the pyramid.
