Looks like the function on the right hand side is
[tex]f(t)=\begin{cases}1&\text{for }t<4\\-1&\text{for }t\ge4\end{cases}[/tex]
We can write it in terms of the Heaviside function,
[tex]h(t-a)=\begin{cases}1&\text{for }t\ge a\\0&\text{for }t>a\end{cases}[/tex]
as
[tex]f(t)=h(t)-2h(t-4)[/tex]
Now for the ODE: take the Laplace transform of both sides:
[tex]y'(t)+y(t)=f(t)[/tex]
[tex]\implies s Y(s)-y(0)+Y(s)=\dfrac{1-2e^{-4s}}s[/tex]
Solve for Y(s), then take the inverse transform to solve for y(t):
[tex](s+1)Y(s)=\dfrac{1-e^{-4s}}s[/tex]
[tex]Y(s)=\dfrac{1-e^{-4s}}{s(s+1)}[/tex]
[tex]Y(s)=(1-e^{-4s})\left(\dfrac1s-\dfrac1{s+1}\right)[/tex]
[tex]Y(s)=\dfrac1s-\dfrac{e^{-4s}}s-\dfrac1{s+1}+\dfrac{e^{-4s}}{s+1}[/tex]
[tex]\implies y(t)=1-h(t-4)-e^{-t}+e^{-(t-4)}h(t-4)[/tex]
[tex]\boxed{y(t)=1-e^{-t}-h(t-4)(1-e^{-(t-4)})}[/tex]
The following table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament. Pitcher Calvin Thom Shawn Kris Brantley Number of innings pitched 11 1111 12 1212 7 77 3 33 ? ?question mark If the mean of the data set is 8 88 innings, find the number of innings Brantley pitched. innings
Answer:
The number of innings Brantley pitched is 7.
Step-by-step explanation:
We are given that the table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament below;
Pitcher Number of innings pitched
Calvin 11
Thom 12
Shawn 7
Kris 3
Brantley x
Let the number of innings Brantley pitched be 'x'.
The mean of the following data set is given by the following formula;
Mean = [tex]\frac{\text{Sum of all data values}}{\text{Total number of observations}}[/tex]
[tex]8 = \frac{11+12+7+3+x}{5}[/tex]
[tex]8\times 5 =33+x[/tex]
[tex]40 = 33+x[/tex]
x = 40 - 33 = 7
Hence, the number of innings Brantley pitched is 7.
Answer:
7
Step-by-step explanation:
Khan Academy
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. nequals=5353, pequals=0.30.3, and Xequals=20
Answer and Step-by-step explanation: P(X) calculated by the binomial probability formula is:
P(X) = [tex]\left[\begin{array}{ccc}n\\X\end{array}\right][/tex].[tex]p^{x}.(1-p)^{n-x}[/tex]
P(20) = [tex]\left[\begin{array}{ccc}53\\20\end{array}\right] .(0.3)^{20}.(1-0.3)^{33}[/tex]
P(20) = [tex]\frac{53!}{33!.20!}.3.5.10^{-11}.7.7.10^{-6}[/tex]
P(20) = 0.0552
To determine whether the normal distribution can be used to estimate this probability, both n.p and n.(1-p) must be greater than 5:
n . p = 53*0.3 = 15.9
n.(1-p) = 53(1-0.3) = 37.1
Since both ARE greater than 5, normal distribution can be used.
To approximate:
mean = n . p = 15.9
standard deviation = [tex]\sqrt{n.p.(1-p)}[/tex] = 3.34
Find the z-score:
z = [tex]\frac{x - mean}{sd}[/tex] = [tex]\frac{20-15.9}{3.34} = 1.23[/tex]
z-score = 0.8907
Comparing values:
0.8907 - 0.0552 = 0.8355
Solve: 5x=110. (Round to three decimal places.)
Hey there! Welcome to Brainly! I'm happy to help!
In equations, letters like x or y are called variables. They represent a number that we do not know yet, or they can almost be seen as a question mark in an equation. For example, 1+?=2. We know that this ? represents the number 1, and the same would go if you put a variable in there. If you have 1+x=2, you can figure out that x=1!
Our equation is 5x=110. When you see a number next to a variable, that number is called the coefficient. It is a number that multiplies a variable. So, our coefficient is 5. This means that five is multiplied by x to equal 110.
5·x=110
What if we don't know off the top of our heads what we multiply 5 by to get to 110? It was easy with 1+1=2, but this is trickier. Here's how to figure it out.
We want to get the x all by itself on one side of the equation. Then, we will see what x equals.
To do this, we use inverse operations. I will show you below with our 1+x=2 example.
1+x=2
We have a positive one plus an x equals two. We could visualize this like this.
+1+x=2
What we want to do is move the 1 to the other side of the equation so that x is by itself. So, what's the opposite of adding? Subtracting!
However, we don't just subtract the 1 from the left side, but we do it from the right side! You have to do the inverse operation on both sides to find the answer.
So, let's subtract 1 from both sides.
+1+x-1=2-1
x=1
We see that x equals 1, and if we plug this into the equation 1+x=2, we see that it is correct.
Now, with our problem, we need to divide, because that is the opposite of multiplication. We need to divide both sides by 5 to isolate the x. Let's do it!
5x÷5=110÷5
x=22
We see that 5×22 is equal to 110, so this is correct! Now you can solve for variables in equations!
Have a wonderful day!
Determine the margin of error in estimating the population mean, μ . A sample of 74 college students yields a mean annual income of Assuming that , find the margin of error in estimating μ at the 99% level of confidence.
Answer:
$253
Step-by-step explanation:
Margin of error is the critical value times the standard error.
MoE = z × σ/√n
At 99% confidence, z = 2.576.
MoE = 2.576 × 844/√74
MoE = 253
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is$31 . The total cost to rent 6 chairs and 5 tables is $59 . What is the cost to rent each chair and each table?
Answer:
The cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Step-by-step explanation:
Let the:
Cost to rent a chair = x
Cost to rent a table = y
We would form an algebraic equation.
The total cost to rent 2 chairs and 3 tables is $31
2x + 3y = 31 ...... Equation 1
The total cost to rent 6 chairs and 5 tables is $59
6x + 5y = 59 ......... Equation 2
We solve the above equation above using elimination method
Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2
Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1
Hence, we have:
2x + 3y = 31 ...... Equation 1 × 6
6x + 5y = 59 ......... Equation 2 × 2
12x + 18y = 186........ Equation 3
12x + 10y = 118 .…...... Equation 4
Subtracting Equation 4 from Equation 3
= 8y = 68
y = 68/8
y = 8.5
Therefore, the cost to rent a table = $8.50
Substituting 8.5 for y in Equation 1 to get the value of x
2x + 3y = 31 ...... Equation 1
2x + 3(8.5) = 31
2x = 31 - 3(8.5)
2x = 31 - 25.5
2x = 5.5
x = 5.5/2
x = 2.75
The cost to rent a chair = $2.75
Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the trigonometric ratios with their values based on the triangle shown in the diagram.
Answer:
A-2, B-DNE*, C-3, D-DNE, E-4, F-1
---------------------
The first attachment shows the solutions to A and C.
The second attachment shows the solutions to E and F.
There are no real number solutions to systems B and D.
_____
In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.
A.
(3-x) +12 = x^2 +x
15 = x^2 + 2x
16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root
±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A
__
B.
(x -1) -15 = x^2 +4x
-16 = x^2 +3x
-13.75 = x^2 +3x +2.25 = (x +1.5)^2
roots are complex: -1.5 ±i√13.75
__
C.
(1-2x) +5 = x^2 -3x
6 = x^2 -x
6.25 = x^2 -x + .25 = (x -.5)^2
±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C
__
remaining problems are done in a similar way.
_____
* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.
---------------------
Hope this helps!
Brainliest would be great!
---------------------
With all care,
07x12!
you are given the following functions: g(x) = x^2 + 4x + 5 and h(x) = 3x - 4 What is (g+h)(x)
Answer:
g(x) = x² + 4x + 5
h(x) = 3x - 5
To find (g+h)(x) add h(x) to g(x)
That's
(g+h)(x) = x² + 4x + 5 + 3x - 4
Group like terms
(g+h)(x) = x² + 4x + 3x + 5 - 4
Simplify
We have the final answer as
(g+h)(x) = x² + 7x + 1Hope this helps you
The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common
difference between them
Answer:
(a)11
(b)12
Step-by-step explanation:
The first term, a = 1
The last term, l=121
Sum of the series, [tex]S_n=671[/tex]
Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:
[tex]S_n=\dfrac{n}{2}(a+l)[/tex]
Substituting the given values, we have:
[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]
(a)There are 11 terms in the arithmetic progression.
(b)We know that the 11th term is 121
The nth term of an arithmetic progression is derived using the formula:
[tex]a_n=a+(n-1)d[/tex]
[tex]a_{11}=121\\a=1\\n=11[/tex]
Therefore:
121=1+(11-1)d
121-1=10d
120=10d
d=12
The common difference between them is 12.
In the diagram of RST, which term describes point U?
A.
Circumcenter
B.
Centroid
C.
Incenter
D.
Orthocenter
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.
Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.
Learn more about Triangle:
https://brainly.com/question/2773823
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The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? PLEASE COMMENT, I Can't SEE ANSWERS CAUSE OF A GLITCH
Answer:
x + 1 - ( 4 / x³ + 3x² + 8 )
Step-by-step explanation:
If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.
Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Could anyone help me with this? T+S+U=130 T=3(U) S= T+10 U= ?? I need to decipher the value of T,S and U.
Answer:
U = 17 1/7
T = 51 3/7
S = 61 3/7
Step-by-step explanation:
Given
T+S+U=130\
T=3(U)
S= T+10 we have to find value of u
First step:
find S and T in terms of U
T is given
T = 3U
S = T +10 , using T = 3U
S = 3U+10
Using the above value in T+S+U=130
3U + 3U+10 + U = 130
=> 7U = 130-10 = 120
=> U = 120/7 = 17 1/7
T = 3U = 3*120/7 = 360/7 = 51 3/7
S = T+10 = 360/7 + 10 = (360+70)/7 = 430/7 = 61 3/7
Thus,
U = 17 1/7
T = 51 3/7
S = 61 3/7
Good answer fast Find the value of y
Answer: y = 90°
Step-by-step explanation:
55.30786941 = sin-1 (148/180) round to 55.3° angle x
34.69213059 = cos-1 (148/180) . round to 34.7° "angle z" at right
34.7 +55.3 = 90
Sum of All angles of the triangle = 180° 180 -90 = 90
If angle x is 55.7 and angle z is 34.7° Angle y must be 90°
Ratio of inscribed arcs = ratio of chord to diameter
Use the line of best fit to determine the x-value when the y- value is 190
Answer:
A. 9
Step-by-step explanation:
Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.
Thus,
A.9 is the correct answer.
Hope this helps :)
Answer:
A. 9
Step-by-step explanation:
A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.
The graph of f*x)=2^(x+3) shifts 10 units to the right when it is replaced with the graph of f(x)=2^(x-k). What is the value of k?
Answer:
7
Step-by-step explanation:
f(x) = 2^(x + 3)
Shifted 10 units to the right:
f(x) = 2^(x + 3 − 10)
f(x) = 2^(x − 7)
Therefore, k = 7.
Hi Folks, l have this Rearranging difficult formulae exercise, l have the answer but l dont understand at all the procedure, the method applied, if someone can explain it to me please will be appreciatted thanks 1/a = 1/b+1/c the procedure is: 1= a/b + a/c (x a) b= a+ ab/c (x b) bc= ac +ab ( x c) b (c-a) = ac b= ac/c-a OR b= - ac /a - c Def l dont understand the method thanks for your help
Step-by-step explanation:
1/a = 1/b + 1/c
Multiply both sides by a.
1 = a/b + a/c
Multiply both sides by b.
b = a + ab/c
Multiply both sides by c.
bc = ac + ab
Subtract ab from both sides.
bc − ab = ac
Factor b.
b (c − a) = ac
Divide both sides by c − a.
b = ac / (c − a)
Answer:
see below
Step-by-step explanation:
1/a = 1/b+1/c
Multiply each side of the equation by a
a( 1/a) =a( 1/b+1/c)
1 = a/b + a/c
Then multiply each side of the equation by b
b*1 =b( a/b + a/c)
b = a + ab/c
Then multiply each side of the equation by c
cb = c( a+ ab/c)
bc = ac + ab
We have gotten rid of the fractions
Now we can solve for a
Factor out a on the right side
bc = a( c+b)
Then divide by c+b on each side
bc / ( c+b) = a ( c+b) / ( c+b)
bc / ( c+b) = a
Now we can solve for b
bc = ac + ab
Subtract ab from each side
bc -ab = ac + ab-ab
bc -ab = ac
Factor out b on the left side side
b( c-a) = ac
Then divide by c-a on each side
b( c-a) / ( c-a) = ac / ( c-a)
b = ac/ ( c-a)
We can factor out -1
b = -ac/( a-c)
Translate into a variable expression the product of p and the sum of p and 12
They're making me write something here so I can post the answer:
p(p + 12)
Create a circle such that its center is point a and b is a point on the circle
Step-by-step explanation:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
Answer:
i think that this question is wrong
Step-by-step explanation:
The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time. When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year. By how much does the machine depreciate during the fifth year
Answer: The machine depreciates during the fifth year by $4000.
Step-by-step explanation:
Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.
When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.
Then, the machine depreciates A(x) during the fifth year as
[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]
Hence, the machine depreciates during the fifth year by $4000.
Probability can never be equal to 154Probability can never be equal to 154
Answer: True
Step-by-step explanation:
The probability of an event occurring lies between zero and one. A probability of 0 means that the event has no chance of happening for example, rolling a die once and getting a number greater than 6 while a probability of 1 means the event will definitely happen for example, getting a number less than 7 when you roll a die once.
Every other probability falls in-between this range so probability can never be 154.
Someone help me please
Answer:
3
Step-by-step explanation:
If the cube has 54 stickers across its six faces, and each face has the same number of stickers, first we can find the number of stickers in each face by dividing the number of stickers by the number of faces:
[tex]stickers\ per\ face = number\ of\ stickers / number\ of\ faces[/tex]
[tex]stickers\ per\ face = 54/6 = 9[/tex]
Each face has 9 stickers.
If each row and column has the same number of stickers, we can find the numbers of rows and columns by finding the square root of the number of stickers in the face:
[tex]\ number\ of\ rows = \sqrt{9} = 3[/tex]
If we have 3 rows, and each roll has the same number of stickers, the number of stickers per row or column is:
[tex]stickers\ per\ row = stickers\ per\ face / number\ of\ rows[/tex]
[tex]stickers\ per\ row = 9/3 = 3[/tex]
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 11 students, he found the average time was 4.52 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.1 level of significance. Assume normality. (can you please show how to do this without a calculator or excel i just dont want answer but want to know how to do it).
a) What are the appropriate null and alternative hypotheses?
A) H0: μ = 5 versus Ha: μ < 5
B) H0: μ = 5 versus Ha: μ ≠ 5
C) H0: x = 5 versus Ha: x ≠ 5
D) H0: μ = 5 versus Ha: μ > 5
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
A) Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
B) Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
C) Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
D) Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
Answer:
A) Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) test statistic = -2.1226
C) p-value = 0.0598
D) Option A is correct
Step-by-step explanation:
We are given;
x = 4.52 minutes
s = 0.75 minutes
μ = 5 minutes
n = 11
degree of freedom = n - 1 = 11 - 1 = 10
A) The hypotheses are;
Null Hypothesis;H0: μ = 5
Alternative Hypothesis;Ha: μ ≠ 5
B) t-statistic = (x - μ)/(s/√n)
(4.52 - 5)/(0.75/√11) = -2.1226
C) From the t-score calculator results attached, the p-value is approximately 0.0598.
D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.
Help ASAP!!!
Find sin(c). Round to the nearest hundredth if necessary.
A: 0.38
B: 0.92
C:0.42
D:1.08
Answer:
The answer is option A
0.38Step-by-step explanation:
sin ∅ = opposite / hypotenuse
Since we are finding sin (c)
From the question
The opposite is BA
The hypotenuse is AC
So we have
sin c = BA/ AC
BA = 5
AC = 13
sin c = 5/13
sin c = 0.384615
sin (c) = 0.38 to the nearest hundredth
Hope this helps you
Answer:
[tex]\boxed{Sin C = 0.38}[/tex]
Step-by-step explanation:
Sin C = opposite/hypotenuse
Where opposite = 5, hypotenuse = 13
Sin C = 5/13
Sin C = 0.38
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation
Answer:
15
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
30 hcchxfifififififfud7dd7d
i need these THREE questions ANSWERED please!!!! please i really need these done!!!
Step-by-step explanation:
8. As the name implies, a box-and-whisker plot looks like a box with two whiskers. The box is the middle 50%. The whiskers are the bottom 25% and the top 25%.
First, we need to sort the numbers from smallest to largest. Starting with Set A:
Set A = {56, 57, 62, 68, 71, 82, 84, 92, 97, 101, 103, 106}
Now we find the median of the set, or the middle number. Set A has 12 data points. Since 12 is an even number, the median will be the average of the 6th and 7th numbers.
M = (82 + 84) / 2 = 83
Next, we find the median of the lower half. There are 6 numbers in the lower half, so the median is the average of the 3rd and 4th numbers.
Ml = (62 + 68) / 2 = 65
Now we find the median of the upper half. Again, there are 6 numbers in the upper half, so the median will be the average of the 3rd and 4th numbers.
Mu = (97 + 101) / 2 = 99
So the left whisker is from 56 to 65.
The box is from 65 to 99.
The right whisker is from 99 to 106.
Don't forget to mark the median, 83.
Repeat for Set B.
Set B = {36, 37, 42, 46, 48, 56, 58, 63, 69, 72, 75, 78}
M = (56 + 58) / 2 = 57
Ml = (42 + 46) / 2 = 44
Mu = (69 + 72) / 2 = 70.5
So the left whisker is from 36 to 44.
The box is from 44 to 70.5.
The right whisker is from 70.5 to 78.
The median is 57.
By graphing both on the same number line, we can easily compare them.
9. To make a dot plot, draw a number line starting from the smallest number and ending at the largest number. For each number, draw a dot every time the number appears in the set. For example, the number 3 appears twice in Set A, so draw two dots on 3. You may find it helpful to sort the data first.
10. Draw a dot plot of the set to determine the shape.
Which table represents the inverse of the function defined above?
Hello!
Answer:
Table B.
Step-by-step explanation:
An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:
We can use points on the table:
[tex]f(x)[/tex] = (7, 21)
The inverse of this function would 7 as its y value, and 21 as its x value:
[tex]f^{-1} (x)[/tex] = (21, 7)
The only table shown that correctly shows this relationship is table B.
A set of raw paired sample data is given below. Convert this raw data into paired ranks, and calculate the value of the rs test statistic for this data. a. 0.647 b. 0.652 c. 0.955 d. 0.921
here is the data set for the complete question
x: 18 21 19 21 20 21
y; 2 14 5 6 18 18
Answer:
B. 0.652
Step-by-step explanation:
x y rank of x rank of y d d²
18 2 1 1 0 0
21 14 4 4 0 0
19 5 2 2 0 0
21 6 4 3 1 1
20 18 3 5.5 -2.5 6.25
21 18 4 5.5 -1.5 2.25
∑d² = 8.5
rs = 1 - 6[∑di² + ∑m(m²-1)]/n(n²-1)
= 1 - 6[8.5 +{3(3²-10/12 + 2(2² - 1)/12}]/6(6²-1)
= 1 - 0.348
= 0.652
therefore option b is the right answer.
Verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power x2n + 1 let k = n + 1.] y = (-1) nx2n, (1 + x2)y' + 2xy = 0
Answer:
The given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
Step-by-step explanation:
This is a very trivial exercise, follow the steps below for the solution:
Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.
[tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex].....................(1)
[tex]y = 1 - x^2 + x^4 - x^6 + x^8.........[/tex]
Step 2: Find the derivative of y, i.e. y'
[tex]y' = -2x + 4x^3 - 6x^5 + 8x^7 .............[/tex]
Step 3: Substitute y and y' into equation (2) below:
[tex](1+x^2)y' + 2xy = 0\\\\(1+x^2)(-2x + 4x^3 - 6x^5 + 8x^7......) + 2x(1 - x^2 + x^4 - x^6 + x^8.......) = 0\\\\-2x+ 4x^3 - 6x^5 + 8x^7........ - 2x^3 +4x^5 - 6x^7 + 8x^9 ......+ 2x - 2x^3 + 2x^5 - 2x^7 + 2x^9...... = 0\\\\0 = 0[/tex]
(Verified)
Since the LHS = RHS = 0, the given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced?
Answer:
The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.
need some help thxx ;)
Answer:
DEA
Step-by-step explanation: