a) The number of ways in which the dogs can be lined up in a row is = 15! / 5!
b) The number of ways in which the dogs can be distinguished by their sweater colours is 15! / (3! × 4! × 3! ×5!)
c) The probability that the instructor sees all of the dogs with the same sweater colour sitting next to each other is
(a) The total number of dogs is 15, of which 5 dogs are Dalmatians and others are different.
So, by using permutation the number of dogs can be arranged in 15! / 5! ways.
(b) There are 3 dogs wearing yellow sweater, 4 dogs wearing red sweater, 3 dogs wearing blue sweater, and 5 dogs wearing green sweater.
Thus, the number of dogs can be arranged in 15! / (3! × 4! × 3! ×5!) ways.
(c) The 15 dogs can be arranged in 15! ways.
There are sweaters of 4 different colours, so the 4 colours can be arranged in 4! ways.
There are 3 dogs wearing yellow sweater, so they can be arranged in 3! ways.
There are 4 dogs wearing red sweater, so they can be arranged in 4! ways.
There are 3 dogs wearing blue sweater, so they can be arranged in 3! ways.
There are 5 dogs wearing red sweater, so they can be arranged in 5! ways.
Therefore, the probability that the instructor sees all of the dogs with the same sweater colour sitting next to each other is
4! (3! × 4! × 3! ×5!) / 15!
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find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 1 + 10. Vt, y+t^5 -t, and z + t^5 + t; (11, 0, 2)?
Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.
What is the formula for parametric equations?The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.
The given x=1+12+ dx=dt 0+12(1) =12
Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12
(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).
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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)
x(t), y(t), z(t) =
The pattern in this table continues. Which equation below relates the number of squares to the figure number?
a) s=4 f+1
b) s=2 f+3
c) s=f+2
d) f=2 s+3
A
B
C
D
The final equation that represent the given table is s=f+2. So the option c is correct.
In the given question, the pattern in this table continues.
We have to check which equation below relates the number of squares to the figure number.
a) s=4f+1
b) s=2f+3
c) s=f+2
d) f=2s+3
From the given table;
f(1) = 5, f(2) = 7, f(3) = 9, f(4) = 11, f(5) = 13
If we check closely the value of f(x), we can see that the difference between each number is of 2.
So if we want to write the function as
f(1) = 5,
f(2) = f(1)+2 = 7,
f(3) = f(2)+2 = 9,
f(4) = f(3)+2 = 11,
f(5) = f(4)+2 = 13
So the final equation that represent the given table is;
s=f+2
So the option c is correct.
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HELP IM IN K12 PLEASE HELP
Step-by-step explanation:
p = a + 3
Three more a than p
5 + 2a = a - 9 what does a equal
a= -14.
Step-by-step explanation:1. Write the expression.[tex]5 + 2a = a - 9[/tex]
2. Subtract 5 from both sides of the equation.[tex]5 + 2a -5= a - 9-5\\ \\2a=a-14[/tex]
3. Subtract "a" from both sides of the equation.[tex]2a-a=a-14-a\\\\a=-14[/tex]
4. Verify.[tex]5 + 2(-14) = (-14) - 9\\ \\5-28=-23\\ \\-23=-23[/tex]
Both sides are equal to each other, hence a= -14 is the correct solution.
5. Conclude.a= -14.
-------------------------------------------------------------------------------------------------------
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Triangle TVW is dilated according to the rule
(x,y)(three-fourths x, three-fourths y) to create the image triangle T'V'W', which is not shown.
On a coordinate plane, triangle T V W has points (negative 4, 8), (0, 4), and (4, 4).
What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
T'(-3, 6) and V'(0, 1)
T'(-1, 2) and V'(0, 3)
T'(-1, 2) and V'(0, 1)
The coordinates of the endpoints of the segment T'V' are equal to: A. T'(-3, 6) and V'(0, 3).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of triangle TVW by using the following transformation rule with a scale factor of 3/4: (x, y) → (3x/4, 3y/4)
For coordinate T, we have;
Coordinate T = (-4, 8) → (3/4(-4), 3/4(8)) = Coordinate T' = (-3, 6).
For coordinate V, we have;
Coordinate V = (0, 4) → (3/4(0), 3/4(4)) = Coordinate V' = (0, 3).
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Answer:
A. T'(-3, 6) and V'(0, 3)
Step-by-step explanation:
a church window is bounded above by a parabola and below by the arc of a circle (see figure). find the surface area of the window. (round your answer to three decimal places.)
The surface area of a church window bounded above by a parabola and below by the arc of a circle is 2.750x^2, rounded to three decimal places.
Let x be the length of the window. The radius of the arc of a circle is x/2.
Surface area = [Area of parabola] + [Area of arc of a circle]
= (1/2)x^2 + (π/2)*(x/2)^2
= (1/2)x^2 + (π/4)x^2
= (π/4 + 1/2)x^2
= (1 + π/4)x^2
= 2.75x^2
Answer: 2.750
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Darren kept track of the number of e-mails he received from one of his customers each day for 14 days on the dot plot. A number line goes from 1 to 12. 1 dot is above 2. 2 dots are above 7. 3 dots are above 8. 1 dot is above 9. 3 dots are above 11. 4 dots are above 12. Which statement must be true according to the dot plot?
The customer sent Darren more than 12 e-mails over the 14-day period. The maximum number of emails represented in the dot plot is 12 + 4 = 16
The dot plot provides information about the number of emails he received from one customer over a 14-day period.
The number line goes from 1 to 12, but there are 4 dots above 12 which means that the customer sent him more than 12 emails over the 14-day period.
Therefore, the statement "The customer sent Darren more than 12 e-mails over the 14-day period" must be true according to the dot plot.The maximum number of emails represented in the dot plot is 12 + 4 = 16. Therefore, the customer sent Darren more than 12 emails over the 14-day period.
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UX ≅ UY, YZ ≅ WX, TZ ≅ VW, and UV ≅ TU. Complete the proof that ∠W≅∠Z.
This is the first question I have seen with this type of two column proof, and i do not want to get it wrong as a large portion of my score will be taken from me.
(There may have to be another row(s) added, which can be done with the "Add line" button)
Geometry, Proofs involving SSS(and CPCTC)
https://www.ixl.com/math/geometry/proofs-involving-sss
You are just couple of steps away from completing the proof.
So far you have concluded that two sides of triangles ZTX and WVY are congruent. You need to complete it for the third side and prove the triangles are congruent. Then use it to complete the proof.
Missing statement and reasons given below.
Statement Reason
12. WY = XZ Transitive property13. ΔZTX ≅ ΔWVY SSS congruency14. ∠W ≅ ∠Z CPCTCselect all that apply identify the steps involved in the six sigma approach. (check all that apply.)
the steps involved in the six sigma approach. -Define-Measure-Analyze-Improve-Control
-Define: Identify the problem and set objectives and goals
-Measure: Collect and analyze data related to the problem
-Analyze: Identify the root cause of the problem
-Improve: Develop and implement solutions to the problem
-Control: Monitor and maintain the improvements to ensure the problem does not recurrence are the steps involved in six sigma.
1. Define: Identify the problem, set objectives and goals, and develop a project plan.
2. Measure: Collect and analyze data related to the problem and determine the current process performance.
3. Analyze: Examine the data to identify the root cause of the problem.
4. Improve: Develop and implement solutions to improve the process.
5. Control: Monitor and maintain the improvements to ensure the problem does not recur.
6. Optimize: Continuously look for ways to make the process more efficient and effective.
the complete question is:
Select all that apply identify the steps involved in the six sigma approach. (check all that apply.)
-Define
-Measure
-Analyze
-Improve
-Control
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in a certain quadrilateral, the three shortest sides are congruent and both diagonals are as long as the longest side. what is the degree measure of the largest angle of tihs quadrilateral
The measurement of the largest angle of the quadrilateral is 108°
Given,
Quadrilateral;
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Here,
Three shortest sides of the quadrilateral are congruent.
Both diagonals are as long as the longest side.
That is,
Side 1 ≅ Side 2 ≅ Side 3
Side 4 = Diagonal 1 = Diagonal 2
Then,
The largest angles of the quadrilateral will be 108°
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4. *
This pattern of squares continues. Which equation below relates the number of squares, n, in a picture to the size number, s ?
Size 1
Size 2
a) n=s+4
b) n=4 s
c) n=4 s+1
d) s=4 n
A
B
c
D
The required equation that following the pattern is n = 4s+1. So the option c is correct.
In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.
The given options are:
a) n = s+4
b) n = 4s
c) n = 4s+1
d) s = 4n
We find the pattern we firstly observe the given diagram closely.
As we can see that in first diagram have 5 blocks.
In second diagram have 9 blocks.
In third diagram have 13 blocks.
So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.
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Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are:
a) an = 3an-1 + 4an-2 +5an-3
b) an = 2nan-1 + an-2
c) an = an-1 + an-4
A linear recurrence relation is homogeneous if f(n) = 0. The order of the recurrence relation is determined by k. We say a recurrence relation is of order k if an = f(an−1,...,an−k).
Given: a) an = 3an-1 + 4an-2 +5an-3
We note that the given recurrence relation is linear, because the right-hand side is a linear combination of previous terms. We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms. The degree of the recurrence relation is the largest value k for which are occurs in the recurrence relation.
k=3
Given: b) an = 2nan-1 + an-2
We note that the given recurrence relation is not linear, because the right-hand side is not a linear combination of previous terms (due to the
fact that 2n is not a constant). We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms.
Given: c) an = an-1 + an-4
Because the right-hand side is a linear combination of the prior terms, we observe that the provided recurrence relation is linear. Given that there are no constant terms in the recurrence relation, it is important to observe that it is homogenous. The biggest value k for which are k appears in the recurrence relation is the recurrence relation's degree.
Degree of linear homogeneous recurrence are k=3 .
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find the critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom
The critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom are roughly 21.02 and 32.36.
The critical value for the 95% confidence interval using the 15 degrees of freedom chi-square distribution is the value that divides the distribution into two;
lower tail and upper tail. These values are calculated such that the area under the curve of the chi-square distribution between the critical values represents 95% of the total area under the curve.
To find critical values, you can use a chi-square table or a computer program that calculates critical values for a given confidence level and degree of freedom.
In this case, the critical value for the 95% confidence interval with 15 degrees of freedom can be determined as follows:
Lower critical value:
The lower critical value is the value corresponding to the area under the chi-square distribution curve to the left of the value, equal to 2.5% (half of 5% not included in the confidence interval). Using a chi-square table or computer program, we can find that the lower critical value for the 95% confidence interval with 15 degrees of freedom is approximately 21.02. Upper critical value:
The upper critical value is the value corresponding to the area under the chi-square distribution curve to the right of the value, equal to 2.5% (half of 5% is not included in the confidence interval).
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Which of the following points would fall on the line produced by the point-slope form equation y + 12 = 3(x - 4) when graphed
Answer:
where r the points??
Step-by-step explanation:
give them atleast to find the ans.
10:35 AM Sat Dec 10
Homework 6.2
:
ด
1.) Mr. Keith is paid semimonthly. His annual salary is $64,733. What is his semimonthly
salary rounded to the nearest cent?
3%
Sa
Mr. Keith's semimonthly salary is $16183.25.
What is rounded to the nearest cent?
If the number is five or higher and is to the right of the full cents, increase the cents by one. The cents should remain the same if the number is four or less.
For instance: $143.864. Consider the last digit, 4, since it is less than 5 and the cents should remain the same. Rounding up from $143.864 to $143.86.
Given that the annual salary of Mr. Keith is $64,733.
Semiannual means 4 times in yearly.
Thus divide whole salary by 4 to get semimonthly salary.
Therefore the semimonthly income is $64,733/4 = $16183.25 (rounded to the nearest cent)
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Find the area of the parallelogram with vertices P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
The area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
Given that,
The vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
We have to find the area of parallelogram with the vertices.
We know that,
PQ=Q-P=(3,3,3) -(1,0,2)=(2,3,1)
PR=R-P=(7,5,8) -(1,0,2)=(6,5,6)
Find area using cross product as
Area= |PQ x PR|
=|i (3(6)-1(5)) - j (2(6)-1(6)) + k (2(5)-3(6)) |
= |i (18 - 5) - j (12 -6) + k (10 -18) |
= |{13; 6; -8}|
=√(13²+6²+(-8)²)
=√269
Therefore, the area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
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Which is true?
A. 0.0093>0.01
B. 0.2673>0.2562
C. 0.5330>0.533
D. 0.6409>0.641
Answer: B; B. 0.2673>0.2562
Step-by-step explanation: So, let's focus on the decimals, we already know that 0.26 IS GREATER than 0.25. All the other expressions are showing the smaller number as greater, or equal to, I hoped this helped!
Find the value of the variable. The sum of angle measures is 180°. Then find the angle measures of the polygon
Answer:
28° + 112° + 40° = 180°
Step-by-step explanation:
A Triangle has 3 angles that adds up to 180°
You are given 3 angles already so they must add up to 180°
Equation: n + 4n + 40° = 180°
Simple the equation.
Add the variable n together.
5n + 40° = 180°
Subtract 40 to both sides.
5n = 140°
Divide 5 to both side to solve for n.
n = 28°
Now plug n into our angles to have our angles in degree.
n = 28°
4n = 4×28° = 112°
40°
28° + 112° + 40° = 180°
Answer:
Step-by-step explanation:
The internal angles of a triangle sum 180°
n + 4n + 40 = 180
5n = 180 - 40
5n = 140
n = 140/5
n = 28
Check:
28 + 4*28 + 40 = 180
28 + 112 + 40 = 180
Answer:
variable n = 28°
∡n = 28°
∡4n = 4*28 = 112°
a company's sales in year 1 were $330,000 and in year 2 were $367,500. using year 1 as the base year, the percent change for year 2 compared to the base year is:
Percentage change in company's sales is 11%
What is percentage?
In arithmetic, a proportion may be a range or magnitude relation expressed as a fraction of a hundred. it's usually denoted victimisation the percentage sign, "%", d. A proportion may be a dimensionless number; it's no unit of measuring.
Main body:
According to the question:
company's sales in year 1 = $330,000
company's sales in year 2 =$367,500
Change = $ 367500 – 330000 = $ 37,500
Percentage change = $ 37500 / $ 330000 = 0.11
Percentage change = 11%
Hence ,Percentage change in company's sales is 11%.
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Determine the number and type of solutions for the equation x^2+8x+15=0
Two different irrational-number solutions
One repeated irrational-number solution
One repeated rational-number solution
Two different rational-number solutions
Two imaginary-number solutions
Answer:
Step-by-step explanation:
disc=8²-4×1×15=64-60=4=2²>0
it is a perfect square and >0
so it has one repeated rational number solution.
the following are midterm scores of an algebra class of 20 students in a high school: 69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77 find the interquartile range using r.
13.3 is the interquartile range of the data set.
Given,
The midterm scores of an algebra class of 20 students;
69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77
We have to find the interquartile range using r.
Interquartile Range;-
The second and third quartiles, or the centre half of your data set, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data set.
Interquartile range = Q3 - Q1
Q1 is the lower quarter
Q3 is the upper quarter
Q2 is the median
Here,
Q2 = 63 + 87 / 2 = 150 / 2 = 75
Q1 = 81 + 74 / 2 = 77.5
Q3 = 74 + 55 / 2 = 64.5
Then,
Interquartile range = Q3 - Q1 = - (64 . 5 - 77.5) = 13.3
That is,
The interquartile range for the given data set is 13.3
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TRUE OR FALSE the difference between timing diagrams and state diagrams is that timing diagrams show changes along the flow of time, whereas state diagrams show changes based on triggers received from other objects in or outside the system.
Therefore, the answer to this problem is that the statement is true.
What is state diagram?A state diagram is a particular kind of diagram used in computer science and related subjects to represent system behavior. A system must have a finite number of states in order to be represented by a state diagram; sometimes this is the case, and other times it is a valid abstraction.
Here,
Since,
Timing diagrams depict changes during the passage of time, whereas state diagrams depict changes as a result of triggers from other system objects or from external sources.
So ,the above statement is true
Therefore the answer to this problem is that the statement is true.
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For a standard normal distribution, find: P(Z > -1.56) Express the probability as a decimal rounded to 4 decimal places. For a standard normal distribution, find: P(Z < 0.26) Express the probability as a decimal rounded to 4 decimal places.
the value of P(Z>-1.56) is 0.9406
The value of P(Z<0.26) is 0.6026
For a standard normal distribution,
the standard normal distribution is also known as the Z - distribution
it is a very special type of distribution in which the value of mean is zero and the value of standard deviation is one.
the formula of standard normal distribution is
[tex]f(x)=\frac{1}{\sigma\sqrt{2\pi } } e^{\frac{-1}{2}(\frac{x-\mu}{\sigma})^2 }[/tex]
(OR)
Z=[tex]\frac{x-\mu}{\sigma}[/tex]
where
[tex]\mu[/tex] is the value of mean
[tex]\sigma[/tex] is the value of standard deviation
f(x) is the probability density function
now,
the value of P(Z>-1.56) is
P(Z> -1.56) = 1 - P(Z< -1.56)
=> 1 - 0.05938
=> 0.94062 (By rounding to 4 decimal places we get)
=> 0.9406
P(Z<0.26) = 1 - P(Z<0.26)
=> 0.60257 (By rounding to 4 decimal places we get )
=> 0.6026
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PLS HELP QUICK! 20 POINTS
Can a triangle be formed with side lengths 5, 6, 12? Explain.
No, because 5 + 6 < 12
Yes, because 5 + 6 > 12
No, because 12 − 6 < 6
Yes, because 12 − 6 < 5
Answer:
No, because [tex]5+6<12[/tex]
Step-by-step explanation:
The side lengths do not satisfy the triangle inequality.
8x + 9y = 3 and x + y = 0
Answer:
x is 3 and y is -3
Step-by-step explanation:
[tex]x + y = 0 \\ x + y - y = 0 - y \\ x = - y \\ \\ 8x + 9y = 3 \\ (8 \times - y) + 9y = 3 \\ - 8y + 9y = 3 \\ y = 3[/tex]
X = -3
X is the midpoint of UV. Y is the midpoint of UW. If mZUYX= 46, find mZW.
mZW=
U
Y
W
Answer:
46°
Step-by-step explanation:
As m<UYX and m<W is corresponding angle because X is the midpoint of UV and Y is the midpoint of UW, therefore
m<W = 46°
I hope my answer helps you.
Answer:
m<W = 46 degrees
Step-by-step explanation:
UX = UV/2 ==> This is because X is the mid-point of UV, dividing UV by 2
to make UX
UY = UW/2 ==> Y is the mid-point of UW, dividing UW by 2 to make UY
XY = VW/2 ==> Since X is the midpoint of UV and Y is the midpoint of UW,
segment XY is exactly in the middle of point U and
segment VW, so segment XY is half of segment VW.
Since all sides of the small triangle(ΔUXY) are exactly half of all sides in the big triangle(ΔUVW), The corresponding angles in each triangle are equal to each other:
Hence, m<UYX = m<UWV
m<UWV ==> m<W = 46 degrees ==> since m<UYX=46, m<W = 46 as well
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A population of squirrels lives in a forest with a carrying capacity of 1800 Assume logistic growth with growth constant k = 0.8 yr-1 . (a) Find a formula for the squirrel population P(t) , assuming an initial population of 450 squirrels_ P(t) 1800/(1+3e^(-0.8t)) (b) How long will it take for the squirrel population to double? doubling time ~ 83 years
By applying formulas of logistic growth we can find the answers as part (a) P(t) = 1800 / (1+3e^(-0.8t)) and part(b) 1.37 years
What is logistic growth?In a logistic growth the growth rate decreases with the passage of time until the growth reaches the maximum capacity at infinite time.
What is formula for logistic growth?The formula is f(t) = L / (1+ ye^(-kt))
where L is the maximum value, k is the growth rate, y is a constant and t is time.
Part(a)
In this case, L = 1800, k = 0.8 yr-1
f(t) = 1800 / (1 + ye^(-0.8)t)
at t = 0 , f = 450,
450 = 1800/ (1+y)
solving this gives, y = 3
Thus the final answer is f(t) = 1800/ (1+ 3e^(-0.8t))
Part(b)
we need to find the time when f(t) = 900
900 = 1800/(1+3e^(-0.8t))
t = 1.37 years
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How many pounds are in 2,600 ounces? Enter only a number. Do not enter units.
Answer: 162.5 Pounds
refer to the work hrs.rds dataset. in this problem, we want to examine the effect of an hourly wage (wage), education (educ), and the number of children (nchild) on the hours worked per week by married women (hrswork).
The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).
To examine this, we would use a regression analysis to look at the relationship between each of these variables and the hours worked per week. We would create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable. We can then analyze the coefficient of each of these variables to measure the effect they have on the hours worked per week. The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).
1. Load the work hrs.rds dataset.
2. Examine the data to identify the independent and dependent variables. In this case, the independent variables are wage, educ, and nchild, and the dependent variable is hrswork.
3. Use a regression analysis to examine the relationship between the independent and dependent variables.
4. Create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable.
5. Analyze the coefficient of each of the independent variables to measure the effect they have on the dependent variable (hrswork).
6. Interpret the results to determine the effect of the independent variables on the dependent variable.
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As part of a study on the selection of grand juries in Alameda county, an educational level of grand jurors was compared with the county distribution:
Educational Level County # of Jurors
Elementary 28.4% 1
Seconday 48.5% 10
Some College 11.9% 16
College Degree 11.2% 35
Total 100% 62
Could a simple random sample of 62 people from the county show a distribution of educational level so different from the county-wide one? Chose one option and explain.
1) this is absolutley possible
2)this is possible, but fantastically unlikely
3)this is possible but unlikely-the chance is around 10% or so
4)this is nearly certain
This is possible but fantastically unlikely. A simple random sample of 62 people from the county would be unlikely to produce a distribution of educational levels so different from the county-wide one. The chances of this happening are extremely small.
A simple random sample is a sample drawn from a population in such a way that each member of the population has an equal chance of being selected. In this case, the population is the county, and the sample is the group of 62 grand jurors. When a simple random sample is drawn, it is possible for the sample to be different from the population in various ways.
For example, the sample may have a different distribution of educational levels than the population. However, the larger the sample size is, the more likely it is that the sample will be representative of the population. In this case, the sample size of 62 is relatively small, so it is possible that the sample will be different from the population in terms of educational level. However, the chance of this happening is not very high, since the sample size is not very large.
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