"There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter." is correct statement. Therefore, the answer is option C.
The problem asks us to choose 5 students out of a class of 26 to present homework problems. Since the order in which the students present the problems does not matter, we need to use the combination formula. The combination formula is used to calculate the number of ways to choose a subset of k elements from a set of n elements without regard to order, and it is denoted by nCk.
Option A, "There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters," is incorrect because the order in which the students are chosen does not matter.
Option B, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters," is incorrect because we are choosing 5 students out of 26, and the order in which they are chosen does not matter.
Option D, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter," is also incorrect because the order in which the students are chosen does not matter.
Therefore, the answer is option C.
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Complete question is:
In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems?
A) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters.
B) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters.
C) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter.
D) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.
If the points A,B and C have the coordinates A (5,2), B (2,-3) and C (-8,3) show that the triangle ABC is a right angled triangle.
Answer:
Step-by-step explanation:
To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.
We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's find the length of each side of the triangle:
AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34
BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136
CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170
Now, let's check if the Pythagorean theorem is satisfied:
AC² = AB² + BC²
170 = 34 + 136
Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.
We know that,
the distance between two points=√(x2-x1)²+(y2-y1)²
∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²
=√(9+25)
= √(34)
∴ The length of side AB = √(34)
Again,
The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]
= √(100+36)
= √136
∴ The length of side BC =√136
Also,
The distance between points A and D, AC= √(-8-5)²+(3-2)²
= √(169+1)
= √170
∴ The length of side AC=√170
Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170
Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,
AC²=170
BC²=136
AB²=34
Clearly, 170=136+34
or, AC²=AB²+BC²
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A man drove 14 miles directly east from his home, made a left turn at an intersection, and then traveled 7 miles north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
If a, b, c are in H.P.; prove that b+ca+ca+b ac' ab bc are also in A.P.
If a, b, c are in Harmonic Progression, b+ca+ca+b ac' ab bc are in Arithmetic Progression.
How to prove Harmonic Progression and Arithmetic Progression?Given a, b, c are in H.P.:
1/a + 1/b = 2/c
Multiplying both sides by abc:
bc + ac = 2ab
Adding c to both sides:
bc + ac + c = 2ab + c
Rearranging the terms:
c + ab = ac + bc
Adding the terms b + ca and ca + b to both sides:
b + ca + ca + b + ac' + ab + bc = ac + bc + b + ca + ca + b
Simplifying:
b + ca + ca + b + ac' + ab + bc = 2ac + 2b
Dividing both sides by 2:
(b + ca + ca + b + ac' + ab + bc)/2 = ac + b
Hence, b+ca+ca+b ac' ab bc are in A.P.
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What did Maleuvre write about Gauguin's views on Polynesian women?
Answer:
Step-by-step explanation:
Observation of the real life and way of life of the peoples of Oceania are intertwined in them with local myths.
Find the area of each of the figures
In the given diagram, the areas of the figures are as follows:
Area of the rectangle is 1/6 cm²
Area of the parallelogram is 12 m²
Calculating the area of a plane shapeFrom the question, we are to calculate the areas of the given plane shapes
From the diagram, we have a rectangle and a parallelogram
The area of a rectangle is given by the formula
Area = l × w
Where l is the length
and w is the width
From the given information,
l = 1/2 cm
w = 1/3 cm
Thus,
Area = 1/2 cm × 1/3 cm
Area = 1/6 cm²
Hence, the area of the rectangle is 1/6 cm²
For the parallelogram
The area of a parallelogram is given by the formula
Area = b × h
Where b is the base length
and h is the perpendicular height
From the given information,
b = 6 m
h = 2 m
Thus,
Area = 6 m × 2 m
Area = 12 m²
Hence, the area of the parallelogram is 12 m²
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Can someone help me with my accounting assignment please?
The State Cash Flow Statement using the direct method.
OP INV FIN
Personnel emolument 2,000,000
CRF charges 1,000,000
Statutory revenue allocation 20,000,000
Proceeds from sale of fixed assets 100,000
Purchase of marketable securities 50,000
Purchase & construction of fixed assets 500,000
Share of VAT 200,000
Share of excess crude oil 100,000
Internally generated revenue 10,000,000
Gratuities and pension 15,000,000
Miscellaneous income 50,000
Overhead expenses 36,000
Recurrent grant made 20,000
Miscellaneous expenses 10,000
Servicing & repayment of public debts 100,000
Grants & subventions from NGO 200,000
Proceeds from loan & other borrowings 300,000
Dividends received 100,000
12,234,000 -450,000 500,000
Net Cash Flow for the year ended 31 December 2006: 12,284,000
How was the cash Flow Statement using the direct method solved?To prepare the State Cash Flow Statement using the direct method, we'll classify cash flows into three categories: Operating Activities (OP), Investing Activities (INV), and Financing Activities (FIN). Then, we'll calculate the net cash flow for each category and add them together to find the net cash flow for the year.
Operating Activities:
(-2,000,000 - 1,000,000 + 20,000,000 + 200,000 + 100,000 + 10,000,000 - 15,000,000 + 50,000 - 36,000 - 20,000 - 10,000) = 12,234,000
Investing Activities:
(100,000 - 50,000 - 500,000) = -450,000
Financing Activities:
(-100,000 + 200,000 + 300,000 + 100,000) = 500,000
Net Cash Flow for the year ended 31 December 2006:
12,234,000 (Operating Activities) - 450,000 (Investing Activities) + 500,000 (Financing Activities) = 12,284,000
The above answer is in response to the question below;
The following information has been extracted from the records of WELFARE STATE of Nigeria for the year ended 31 December 2006:
Personnel emolument 2,000,000
CRF charges 1,000,000
Statutory revenue allocation 20,000,000
Proceeds from sale of fixed assets 100,000
Purchase of marketable securities 50,000
Purchase & construction of fixed assets 500,000
Share of VAT 200,000
Share of excess crude oil 100,000
Internally generated revenue 10,000,000
Gratuities and pension 15,000,000
Miscellaneous income 50,000
Overhead expenses 36,000
Recurrent grant made 20,000
Miscellaneous expenses 10,000
Servicing & repayment of public debts 100,000
Grants & subventions from NGO 200,000
Proceeds from loan & other borrowings 300,000
Dividends received 100,000
You are required to:
Prepare the State Cash Flow Statements for the year ended 31 December 2006 using the direct method approach (ICAN May 2008)
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Draw and describe the plane section that results from the following cut: a cylinder cut parallel to the base.
When a cylinder is cut parallel to its base, the plane section that results is a circle. This circle will have the same radius as the cylinder's base. The center of the circle will be located at the center of the cylinder's base. This type of cut will create a circular cross-section that is parallel to the base of the cylinder.
What is -2 - 1 3\7 please help
Answer:
Step-by-step explanation:
To solve this expression, we need to first combine the integer part of -2 and -1, which gives us -3. Then, we need to combine the fractional parts of -1 and 3/7.
To do this, we find a common denominator, which is 7, and convert -1 to an equivalent fraction with denominator 7 by multiplying both the numerator and denominator by 7, which gives us -7/7.
Now we can add -7/7 and 3/7 to get -4/7.
Therefore, -2 - 1 3/7 = -3 - 4/7, which can also be written as -3 4/7 or -23/7 in improper fraction form
In 2015, there were roughly 1 x 10° high school football players and 2x 10° professional football players in the United States. About how many times more high school football players were there?
The number of times more high school football players were there is 500.
Given that, in 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States.
Here, the number of times more high school football players were there
= 1×10⁶/2×10³
= 1×10³/2
= 1000/2
= 500
Therefore, the number of times more high school football players were there is 500.
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"Your question is incomplete, probably the complete question/missing part is:"
In 2015, there were roughly 1×10⁶ high school football players and 2×10³ professional football players in the United States. About how many times more high school football players were there?
Describe how the following functions are transformed from the parent function
f(x)=|x|-3
f(x)= - |x - 4|
f(x)= 1/3 |x|
f(x)= -2 |x-1|
Answer:
Each of these functions is a transformation of the parent function f(x) = |x|. The transformations include shifting the graph up or down, stretching or compressing the graph vertically, reflecting the graph across the x-axis, and shifting the graph left or right. The vertex of each graph is located at a different point.
Step-by-step explanation:
- The function f(x) = |x| - 3 is a transformation of the parent function f(x) = |x|. The "-3" at the end of the function shifts the graph 3 units down. This means that the vertex, or lowest point, of the graph is at (0, -3) instead of (0, 0).
- The function f(x) = -|x - 4| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-4" inside the absolute value function shifts the graph 4 units to the right. This means that the vertex of the graph is at (4, 0) instead of (0, 0).
- The function f(x) = (1/3)|x| is a transformation of the parent function f(x) = |x|. The "1/3" in front of the absolute value function stretches the graph vertically by a factor of 1/3. This means that the graph is narrower and closer to the x-axis than the parent function. However, because the absolute value function is symmetrical, the graph is still centered at (0, 0).
- The function f(x) = -2|x - 1| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-1" inside the absolute value function shifts the graph 1 unit to the right. The "2" in front of the absolute value function stretches the graph vertically by a factor of 2. This means that the graph is narrower and closer to the x-axis than the parent function, and it is also reflected across the x-axis. The vertex of the graph is at (1, 0).
Using Trig to Find a Side
Using trigonometric ratio, the value of x in the figure is 2.61 units
What is the trigonometric ratiosThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In this problem, we have the adjacent side and we need to find the opposite side.
The ratio that gives us room to find this is the tangent to the angle
tanθ = opposite / adjacent
tan 43 = x / 2.8
x = 2.8 * tan 43
x = 2.61
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Please answer a) b) and c)
I’ll give 65 points
a
1.5/4
b
0.5/4
c
0.5/4
because half of 3 is 1.5
Answer:
I'm pretty sure the answer is B(
Consider the following. Circle: x = h + r cos(theta), y = k + r sin(theta) Use the above to find a set of parametric equations for the conic. Circle: center: (−2, −3); radius: 6
Answer:
Step-by-step explanation:
The standard parametric equations for a circle with center (h, k) and radius r are:
x = h + r cos(theta)
y = k + r sin(theta)
Here, center is (−2, −3) and the radius is 6. Therefore, we have:
h = -2
k = -3
r = 6
Substituting these values into the standard equations, we get:
x = -2 + 6 cos(theta)
y = -3 + 6 sin(theta)
So the set of parametric equations for the circle is:
x(t) = -2 + 6 cos(t)
y(t) = -3 + 6 sin(t)
where t = theta.
I really need help I will give you points
A.
x = 60; m∠ROS = 28°
B.
x = 62; m∠ROS = 31°
C.
x = 28; m∠ROS = 60°
D.
x = 31; m∠ROS = 62°
Answer:
D.
x = 31; m∠ROS = 62°
Step-by-step explanation:
we know that a right angle is always 90 degrees, so we subtract 90° by ∠QOR:
[tex]90 - 28 = 62[/tex]
Then we insert the 62 with the (2x)
[tex]62 = 2x[/tex]
we divide both sides by 2 and we get:
[tex]31 = x[/tex]
so the answer is D
x is equal to 31 and we can multiply 31 by 2 and we can get 62°
Lines MN and GH are parallel. If m
S is 38°, then what is m
Y?
The calculated measure of the angle Y is 38°
From the question, we have the following parameters that can be used in our computation:
Lines MN and GH are parallel. Angle S = 38°The angle S and angle Y are corresponding angles
This means that the angles are congruent
So, we have
Y = S
Substitute the known values in the above equation, so, we have the following representation
Y = 38°
Hence, the measure of the angle Y is 38°
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Complete question
Lines MN and GH are parallel. If mS is 38°, then what is mY?
See attachment for figure
will mark as brainlist is answer correct. which meauser of center is the most appropriate answer for table two. pls give a reason. 25 points.
The meauser of center is the most appropriate answer for table two is the mean.
How to explain the meanMean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.
Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set. Pythagorean means consist of arithmetic mean, geometric mean, and harmonic mean
It is the mean because all of the data points are fairly close and there aren't any outliers (extreme values).
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fill in "blanks"
blank g = blank kg = 3/10 kg
The amount of grams that is equivalent to 3/10 of a kg is given as follows:
300 grams.
How to obtain the amount of grams?The amount of grams that is equivalent to 3/10 of a kg is obtained applying the proportions in the context of the problem.
The amount of kg is 3/10 of a kilogram is given as follows:
3/10 = 0.3kg.
(conversion of a fraction to decimal, divide the numerator by the denominator).
Each kg is composed by 1000 grams, hence the amount of grams in 0.3 kg is given as follows:
0.3 x 1000 = 300 grams.
(proportion applied to obtain the conversion).
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how many miles is 60,000 inches
Answer:
it is 0.94 miles
Step-by-step explanation:
that is because to make a mile you need 63,360 but since you have 60,000 it is not technically a mile
solve all four parts
The rocket will hit the ground after 19.09 seconds.
How to calculate projectilea) The height of the rocket can be describe as:
h(t) = -16t² + 210t + 75
where
t = time in seconds
h(t) = height of the rocket in feet
b) To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The vertex is given by the formula:
t = -b/(2a)
where
a = -16
b = 210
Substituting these values, we get:
t = -210/(2(-16)) = 6.5625 seconds
To find the maximum height, we substitute this value of t back into the equation for h(t):
h(6.5625) = -16(6.5625)² + 210(6.5625) + 75 = 690.625 feet
This means that the rocket reaches its maximum height of 690.625 feet after 6.5625 seconds.
c) We need to find the time interval during which the height of the rocket is greater than 721 feet. We set the height function h(t) greater than 721 and solve for t:
-16t² + 210t + 75 > 721
-16t² + 210t - 646 > 0
Solving for t using the quadratic formula, we get:
t < 2.975 or t > 14.038
Therefore, the rocket will be more than 721 feet above ground level between 0 and 2.975 seconds, and between 14.038 and infinity seconds.
d) To find the time at which the rocket hits the ground, we set h(t) equal to 0 and solve for t:
-16t² + 210t + 75 = 0
Solving for t using the quadratic formula, we get:
t = [tex]\frac{-b \± \sqrt{b^{2} - 4ac } }{2a}[/tex]
a = -16, b = 210, c = 75
t = [tex]\frac{-210 \± \sqrt{210^{2} - 4(16)(75) } }{2(-16)}[/tex]
t = [tex]\frac{-210 \± \sqrt{22225} }{-32}[/tex]
t = [tex]\frac{-210 \± 149}{-32}[/tex]
t = 2.53125 or t = 13.53125
Since the rocket was launched from the top of a 75-foot building, it will hit the ground after an additional time of:
t + 2.53125 = 5.09375 seconds or t + 13.53125 = 19.09375 seconds
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Help please!!!!
Whoever answers right gets brainliest!
4w+6.
Step-by-step explanation:1. Formula of perimeter.The perimeter is just the summation of the length of all sides of a shape. In the case of a circle, the perimeters is its circumference length. So for this case, all we need to do is add up all the sides in a single expression that will represent the perimeter.
2. Calculating the perimeter formula.So perimeter for this triangle should be:
Side 1 + Side 2 + Side 3.
Where:
Side 1= w+4;
Side 2= 2w+2;
Side 3= w.
Then, perimeter is:
(w+4)+(2w+2)+(w)
Adding up all the like terms:
(w+2w+w)+(4+2)
(4w)+(6)
4w+6.
What’s the answer? Will give brainliest if correct
Explain reasoning
The statement that is not true is: C. The translation of a line is a pair of parallel lines.
What is transformation?In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.
Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.
In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.
The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.
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50 Points! Multiple choice algebra question. Write the expression x^4+5x^2-8 in quadratic form, if possible. Photo attached. Thank you!
Answer:
A!!!!!!!!!!!!!!!!!!!!!!!!!
A sixth-grade class collected data on the number of letters in the first names (name lengths) of all the students in class. Here is the dot plot of the data they collected:
How many students are in the class?
Based on the data displayed in the dot plot, it can be concluded there are 25 students in this class.
How to know the number of students based on the dot plot?Dot plots represent data and trends but using dots. In these types of graphs, each individual is represented with a dot. For example, in the number 3, we can see there are 3 dots, which means three students have a first name made of three letters.
Therefore, you can get the total of students by counting all the dots. Based on this, there are 25 students in this class.
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Please help me with this
a)There is higher variability of Y with larger values of X.
b) There is non linear relation between X and Y.
a) Based on the given figure, we can make the following observations:
The scatterplot shows an upward trend, indicating a positive relationship between X and Y.The points appear to be spread out in a fan-like shape, suggesting increasing variability of Y with larger values of X. This means that as X increases, the values of Y become more spread out.The scatterplot does not provide clear information about the variability of X with larger values of Y.Therefore, the correct statement is There is higher variability of Y with larger values of X.
b) Based on the features, it is likely that a linear model may not be suitable for these data, and a non-linear model or other regression techniques may be more appropriate to capture the relationship between X and Y accurately.
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Emilio puts $4,000.00 into an account to use for school expenses. The account earns 15% interest, compounded annually. How much will be in the account after 6 years?
Round your answer to the nearest cent.
Answer:
$10,359.73.
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money after the specified time
P = the principal amount (the initial amount of money)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, we have:
P = $4,000.00
r = 15% = 0.15
n = 1 (compounded annually)
t = 6 years
Substituting into the formula, we get:
A = 4000(1 + 0.15/1)^(1*6)
A = 4000(1.15)^6
A ≈ $10,359.73
Therefore, the amount in the account after 6 years, rounded to the nearest cent, is $10,359.73.
Math question sb please do ts giving branliest
Answer:
All lines are parallel
Step-by-step explanation:
Get each equation in Slope-Intercept form:
1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]
2. No change
3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]
Notice:
a. All slopes are -4/3, AND
b. All y-intercepts are different
Find the distance between the two points (3,−2) and (2,6) .
Simplify your answer, and write the exact answer in simplest radical form for an irrational answer. For example, 2–√= sqrt(2) .
Answer:
[tex] \sqrt{( {3 - 2)}^{2} + {( - 2 - 6)}^{2} } [/tex]
[tex] \sqrt{ {1}^{2} + {( - 8)}^{2} } [/tex]
[tex] \sqrt{1 + 64} = \sqrt{65} [/tex]
. A and B completed a work together in 5 days. Had A worked at twice the speed and B at half the
speed, it would have taken them four days to complete the job. How much time would it take for
A alone to do the work
So it would take A 10 days to do the whole job alone.
What is equation?An equation is a statement that asserts the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in a variety of mathematical contexts, including algebra, calculus, and geometry, as well as in physics, engineering, and many other fields.
Here,
Let's denote A's speed as "a" and B's speed as "b" (in units of work per day). Then, we know that:
In 5 days, A and B together completed the job, so we can write: 5(a + b) = 1 (where 1 represents the whole job).
If A worked at twice the speed (2a) and B worked at half the speed (0.5b), then they would complete the job in 4 days, so we can write: 4(2a + 0.5b) = 1.
We can simplify the second equation by multiplying out the brackets and collecting like terms:
8a + 2b = 1
Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other, and substitute the result into the other equation to find the value of the remaining variable. Let's solve for "b" in terms of "a" from the first equation:
5(a + b) = 1
5b = 1 - 5a
b = (1/5) - a
Now we can substitute this expression for "b" into the second equation:
8a + 2b = 1
8a + 2((1/5) - a) = 1
8a + (2/5) - 2a = 1
6a = (3/5)
a = (1/10)
So A can do 1/10 of the job in one day. To find out how long it would take A to do the whole job alone, we can use the formula:
time = amount of work / rate
Since A can do the whole job alone, the amount of work is 1, and A's rate is 1/10. Therefore:
time = 1 / (1/10)
= 10 days
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What expression represents a x 5
A: Product
B: Sum
C: Difference
D:Quotient
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 32 weeks. Assume that for the population of all unemployed individuals is normally distributed and the population mean length of unemployment is 32 weeks and that the population standard deviation is 3.9 weeks. Suppose you would like to select a random sample of 66 unemployed individuals for a follow-up study.
Answer the following, rounding all answers to three decimal places.
Find the probability that a single randomly selected value is greater than 31.9.
P(X > 31.9) = ???
Find the probability that a sample of size
is randomly selected with a mean greater than 31.9.
P(M > 31.9) = ???
The probability that a single randomly selected value is greater than 31.9 is 0.511.
The probability that a sample of size 66 is randomly selected with a mean greater than 31.9 is 0.641.
How to calculate the probabilityProbability that a single randomly selected value is greater than 31.9:
z = (31.9 - 32) / 3.9 = -0.026
We can find the probability:
P(X > 31.9) = P(Z > -0.026) = 0.511
Also, μ = 32, σ = 3.9, n = 66
z = (31.9 - 32) / (3.9 / √66) = -0.363
Using a standard normal distribution table or calculator, we can find the probability:
P(M > 31.9) = P(Z > -0.363) = 0.641
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