Answer:
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
Step-by-step explanation:
To find Autocorrelation function of the following periodic function
Given that:
X(t) = A sin(wt +θ)
with the period T=2π/w , A, θ, and w are constants.
The autocorrelation function of periodic function with period and phase θ can be expressed as:
[tex]R(\tau) = \dfrac{1}{T} \int \limits ^{T/2}_{-T/2} x(t) *x(t - \tau) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{T} \int \limits ^{T/2}_{-T/2} \ A sin ( \omega t + \theta)*A sin [ \omega (t- \tau ) + \theta] \ dt[/tex]
where;
[tex]sinAsin B = \dfrac{1}{2}[cos (A-B) -cos (A+B)][/tex]
Then;
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( \omega t- \omega \tau + \theta - \omega t - \theta) - cos (\omega t - \omega \tau + \theta + \omega t + \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) - cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) \ dt - \dfrac{1}{2T} \int \limits ^{T/2}_{-T/2} cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
The term 2 is the cosine wave of frequency and the phase = [tex]- w \tau + 2 \theta[/tex]
if we integrate that, the second term in the expansion for R(t) = zero
As such,
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits^{T/2}_{-T/2} \ cos ( - \omega \tau ) dt[/tex]
where ;
[tex]cos (-\omega \tau )[/tex]is constant
Then :
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) [t]^{T/2}_{-T/2}[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{T}{2}+ \dfrac{T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{2T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times T[/tex]
[tex]R(\tau) = \dfrac{A^2}{2} cos (-\omega \tau)[/tex]
since [tex]cos (-\omega \tau) = cos (\omega \tau)[/tex]
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
Simplify (x - y + 1) - (x + y - 1).
-2x + 2y
-2y + 2
2y-2
2x - 2y + 2
Answer:
-2y + 2
Step-by-step explanation:
Let's first remove the parentheses. (x - y + 1) becomes x - y + 1 and -(x + y - 1) becomes -x -y + 1. Combine like terms:
x - y + 1 - x - y + 1 = -2y + 2
Answer:
-2y + 2
Step-by-step explanation:
(x - y + 1) - (x + y - 1)
remove ( )
= x - y + 1 - x - y + 1
simplify
= -2y + 2
I need to do 11-117 every other odd. Can someone list the every other odd till i get to 117
Answer:
11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,87,91,95,99,103,107,111,115
Step-by-step explanation:
I think this is what you wanted
Find the difference.
52.74 - 14.6
ao
Answer:
38.14
Step-by-step explanation:
Step 1: Write out equation
52.74 - 14.6
Step 2: Subtract
38.14
Two teaching methods and their effects on science test scores are being reviewed. A random sample of 18 students, taught in traditional lab sessions, had a mean test score of 78.3 with a standard deviation of 6.4 . A random sample of 11 students, taught using interactive simulation software, had a mean test score of 84.3 with a standard deviation of 5.3 . Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ 1 be the mean test score for the students taught in traditional lab sessions and μ 2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
Step 2 of 4 :
Compute the value of the t test statistic. Round your answer to three decimal places.
Answer:
the value of the t test statistic is - 3.419
Step-by-step explanation:
Given that;
n₁ = 18, u₁ = 78.3, s₁ = 6.4
n₂ = 11, u₂ = 84.3, s₂ = 5.3
α = 0.1
Now The hypothesis are;
H₀ : u₁ = u₂
H₁ : u₁ < u₂
To compute the value of the t test statistic;
t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]
where
s = √ [ ((n₁-1) × s₁² + (n₂ - 1 ) × s₂²) / ( n₁ + n₂ - 2)]
s = √ [ ((18-1) × 6.4² + (11 - 1 ) × 5.3²) / ( 18 + 11 - 2)]
s = √ [ (7 × 40.96 + 10 × 28.09 ) / 27 ]
s = √ [ (286.72 + 280.9) / 27 ]
s = √(567.62/27)
s = √21.0229
s = 4.585
Now t test statistics t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]
t = [(78.3 - 84.3) / 4.585 × √(1/18 + 1/11)]
t = -6 / (4.585 × 0.3827)
t = - 6 / 1.7546795
t = - 3.419
Therefore the value of the t test statistic is - 3.419
as as level of significance α = 0.1
df = 18+11-2 = 27
∴ T(csal) = t(0.1, 27) = -1.313
That is
t(statistics) < t(cal)
{ - 3.419 < -1.313 }
6300m into kilometers
Answer: 6.3 km
Step-by-step explanation:
So we know that to convert meters into km we have to divide the length value by 1000
So:
6300 ÷ 1000 = 6.3
Therefore the answer is 6.3
b) The sum of 9 times a larger number and twice a smaller is 6. The difference of 3 times the larger and the smaller is 7. Compute the numbers. (10marks) Remarks: These questions involved several scenarios 1. Assign the variables -2marks 2. Assumptions of the context of the two numbers -2marks 3. Apply linear systems -2marks 4. Compute using the applicable method of system of linear system -2marks 5. Compute both numbers from above-2marks
Answer:
1) let the larger number be x and the smaller is y
2) 9x + 2y = 6
3x - y = 7
3) 9x+2y=6 and 9x -3y = 21
5y = -15
y= -3
5)
3x=4
x=4/3
Which angle is supplementary to 65 degrees
Answer: 115
Step-by-step explanation: Supplementary angles add to 180, so 180-65 = 115
Answer:
115 degrees
Step-by-step explanation:
A supplementary angle is an angle that add up to 180 degrees
Because of the this we can create an equation that solves for x
65 + x = 180
x = Missing angle measure
All you have to do to solve for x is to subtract 65 from both sides, making x 115
I need help please the question is in the picture.
Answer:
5x+12=42
x=6
Step-by-step explanation:
8+x+x+2+3x+2=42
5x+12=42
5x=42-12
5x=30
x=6
The accompanying data are the shoe sizes and heights (in inches) of 14 men. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not.
(a) x= 11.5
(b) x= 8.0
(c) x = 15.5
(d) x = 10.0
Complete question :
Data of shoe sizes :
X:
8.5
9.0
9.0
9.5
10.0
10.0
10.5
10.5
11.0
11.0
11.0
12.0
12.0
12.5
Height (y) :
66.5
68.5
67.5
70.0
70.0
72.0
71.5
70.0
71.0
71.5
73.0
73.5
74.0
74.0
Answer:
Kindly check explanation
Step-by-step explanation:
Using the online regression calculator :
The regression model obtained in the form:
ŷ = mx + c is ;
ŷ = 1.792X + 52.176
Where ŷ is the predicted or dependent variable
m = 1.792 is the gradient or slope of the regression line
x = the independent variable
c = 52.176 = intercept, where the line of best fit intersects the y axis.
Given the following x values, predict ŷ
(a) x= 11.5
ŷ = 1.792(11.5) + 52.176 = 72.784
(b) x= 8.0
ŷ = 1.792(8.0) + 52.176 = 72.784 = 66.512
(c) x = 15.5
ŷ = 1.792(15.5) + 52.176 = 79.952
(d) x = 10.0
ŷ = 1.792(10.0) + 52.176 = 70.096
The predicted values are meaningful as they show are very close to the actual values of height (y). This could be attributed to the high correlation Coefficient of 0.9299 which exists between both variables
Given: Point K is between points H and J, HK = x − 5, KJ = 5x − 12, and HJ = 25. Find the value o
Answer:
[tex]\huge\boxed{\sf x = 7}[/tex]
Step-by-step explanation:
According to the given statement
HJ = HK + KJ
Given that HJ = 25 , HK = x - 5 and KJ = 5x-12
[tex]\sf 25 = x-5+5x-12[/tex]
Adding like terms
[tex]\sf 25 = 6x-17\\Adding \ 17\ to\ both\ sides\\25 + 17 = 6x\\42 = 6x\\Dividing \ both \ sides \ by \ 6\\7 = x\\OR\\x = 7[/tex]
Please help me out ASAP
Answer:
[tex]26^9[/tex]
Step-by-step explanation:
[tex]26^1 *26 ^8\\=26^{1+8} \\=26^{9}[/tex]
Please Help! I'm stuck
Answer:
D) 11/16
Step-by-step explanation:
Here are the possible combinations she could pull out.
1,1 - 1,4 - 1,5 - 1,8 - 4,1 - 4,4 - 4,5 - 4,8 - 5,1 - 5,4 - 5,5 - 5,8 - 8,1 - 8,4 - 8,5 - 8,8
There are 16 possible combinations. 11 would be above 7, so it’s 11/16.
A news report suggested that an adult should drink a minimum of 64 fluid oz of water per day.
Based on this report, determine the minimum amount of water an adult should drink, in pints,
per day. (1 pint= 16 fl oz)
Answer:
4 pints
Step-by-step explanation:
Because 16x4=64
The aircraft A330 flies at an average speed of 600 miles per hour. The expression, 600t gives the distance traveled by the aircraft in t hours. Find the distance traveled by the A330 in 3 hours.
Answer:
1800
Step-by-step explanation:
The equation 600t is multiplication (600 x t). Since t represents hours, and they're asking you to solve for 3 hours, all you have to do is multiply 600 x 3, which will get you your answer of 1800.
Among the seven nominees for two vacancies on a city council are three men and four women. In how many ways can these vacancies be filled
This question is incomplete
Complete Question
Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled
a) with any two of the nominees?
b) with any two of the women?
c) with one of the men and one of the women?
Answer:
a) 21 ways
b) 6 ways
c) 12 ways
Step-by-step explanation:
We solve this question using combination formula
C(n, r) = nCr = n!/r! (n - r)!
a) with any two of the nominees?
Probability (two of the nominees) = 7C2
= 7!/2! ×(7 - 2)!
= 7!/ 2! × 5!
= 7 × 6 × 5 × 4 × 3 × 2 × 1/2 × 1 ×(5 × 4 × 3 × 2 × 1)
= 21
b) with any two of the women?
We have a total of 4 women
Hence, the probability of any two of the four women, filling the vacancies =
P(any two of the women) = 4C2
= 4!/2! ×( 4 - 2)!
= 4!/ 2! × 2!
= 4 × 3 × 2 × 1/ 2 × 1 ×( 2 × 1)
= 6
c) with one of the men and one of the
Total number of men = 3
Total number of women = 4
= 3C1 × 4C1
= [3!/1! ×(3 - 1)! ] × [4!/1! ×(4 - 1)! ]
= [3!/1! × 2!] × [4!/1! ×3!]
= [3 × 2 × 1/ 1 × 2 × 1] × [4 × 3 × 2 × 1/ 1 × 3 × 2 × 1]
= 3 × [24/6]
= 3 × 4
= 12 ways
The probability for any two of the nominees is 21
The probability for two women is 6
This question is incomplete
Complete Question
Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled
a) with any two of the nominees?
b) with any two of the women?
We have given,
Total number of nominees for two vacancy =7
We solve this question using combination formula
What is the formula for combination?
[tex]C(n, r) = nCr = n!/r! (n - r)![/tex]
a) with any two of the nominees?
Total number of nominees(n)=7
We are selecting r nominees r=2
Probability = 7C2
= [tex]\frac{7!}{2! (7 - 2)!}[/tex]
= 7!/ 2! × 5!
= 21
b) with any two of the women?
We have a total number of women=4
Out of 4 we have select 2 women
Hence, the probability of any two of the four women is
4C2
= 4!/2! ×( 4 - 2)!
= 4!/ 2! × 2!
= 6
Therefore,probability for two women is 6
To learn more about the combination visit:
https://brainly.com/question/25821700
MONEY Amanda has $31 in her purse. She pays $6 for lunch. Which expression represents this situation?
plz tell me the answer!
What is the top of the flag pole above ground in inches?
Answer:
13ft 10.2in
Step-by-step explanation:
First let's convert 3ft to in.
3 * 12 = 36 in
Now let's find the angle
We use tangent because we know the opposite and adjacent distances.
tan x = 36/13
tan x = 2.7692
On your calculator, input the value of your tangent. Then press "inv." This should give you the angle associated with that value. The angle associated with tan 2.7692 is 70.14 degrees.
Now that we know the angle we can find the height.
We use tangent again.
tan 70.14 = x / 5 We don't know the opposite but we know the adjacent length is 5ft.
2.77 * 5 = x
13.85 ft = x
To get it in ft and inches multiply .85 by 12
.85 * 12 = 10.2
13ft 10.2in
A construction company has eight boxes of shingles with one thousand shingles in each stack. if they need 50000 shingles, do they have enough? Explain how you know
Write: (8 X 100,000) + (4 X 1,000) + (6 X 1) in word form
( eight thousand times one hundred thousand ) plus ( four times one thousand) plus ( six times one )
or if you want the answer to that equation (804,006)
eight hundred four thousand and six
The function D ( p ) D(p) gives the number of items that will be demanded when the price is p. The production cost, C ( x ) C(x) is the cost of producing x items. To determine the cost of production when the price is $5, you would:
A. Solve C(D(p)) = 7 for p
B. Evaluate D(C(7))
C. Evaluate C(D(7))
D. Solve D(C(x)) = 7 for x
Answer:
[tex]C(D(5))[/tex]
Step-by-step explanation:
Given:
D(p): Items demanded when price is P
C(x): Production cost of x items
Required
Cost of producing when price is $5
First, we need to get the number of items demanded;
To do this, we substitute 5 for P in D(p)
This gives;
[tex]D(5)[/tex]
Next, we determine the production cost;
To do this, we substitute D(5) for x in C(x)
This gives;
[tex]C(D(5))[/tex]
None of the listed options answer the question
solve
2 + 2y + z=4
3x-4y- 2z=2
5x+3y+5z=-1
Step-by-step explanation:
ppppppp
ppppppp
pppppp
Now is triangles what’s the awnser to this please
Answer:
32
Step-by-step explanation:
The perimeter of a figure is the sum of all the sides.
So, add up all the sides which equals the perimeter.
And we are given that the perimeter is 66. Thus:
[tex](4z)+(5z-3)+(z-1)=66[/tex]
Combine like terms:
[tex]10z-4=66[/tex]
Add 4 to both sides:
[tex]10z=70[/tex]
Divide both sides by 10:
[tex]z=7[/tex]
So, z is 7.
And VW is 5z-3. Thus:
[tex]VW=5z-3\\VW=5(7)-3=35-3=32[/tex]
Our answer is 32 :)
What number is greater than -8 and less than 0.
will mark BRAINLIEST and give ALL OF MY POINTS!!! Pls help asappp!!!! Tysm!
Answer:
$125$65, $65, $65 -- they are all the sameStep-by-step explanation:
The quantity of food required for the two cats for one day is ...
(3/4 can) + (1/2 can) = (3/4 +2/4) can = 5/4 can
Then the cost per day for cat food is ...
$5/(3 cans) × (5/4 can/day) = $25/12 /day
We note that the cost for some number of days will be the product of this factor and the number of days, rounded up to the next higher $5.
1. The cost for 60 days is ...
(60 days)($25/12 /day) = $25 × 60/12 = $125
A 60-day supply of cat food costs $125.
__
2. A 29-day supply costs ...
(29 day) × $25/12 /day = $60 5/12, rounds up to $65 for 29 days
A 30-day supply costs ...
(30 day) × ($25/12 /day) = $62.50, rounds up to $65 for 30 days
A 31-day supply costs ...
(31 days) × ($25/12 /day) = $64 7/12, rounds up to $65 for 31 days.
These costs are all the same.
_____
3 cans last, on average, 2 2/5 days. That means some purchases of 3 cans will last for 2 days, and some will last for 3 days. It so happens that the purchase made to cover day 29 will also cover day 30 and day 31.
A company makes t-shirts and their research shows that that price and demand are related linearly: p = m x + b . They know that in order to sell 5 shirts they need to set the price at $50, and in order to sell 10 shirts they need to set the price at $40. Find the linear equation relating price to demand.
Answer:
The linear equation relating price to demand is Q=-0.5*P + 30
Step-by-step explanation:
The demand for a good is the quantity of that good that the demanders are willing to purchase at a given price.
Then, the Demand Curve relates the quantity that a consumer would be willing to buy as a function of price.
You seek to determine the linear equation that relates the price to the demand Q = m * P + b where Q is the quantity demanded at a price P, and compared with the equation of the straight line y = mx + b, m is the slope and b is the ordinate to the origin.
On a line of the form y = m * x + b, the value of m, having two points, is calculated by:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
And the ordinate to the origin b is calculated, taking the value of m, replacing any of the two points (replacing any of the two because it must give the same value of b) in the expression y = m * x + b and solving its value.
In the case of Q=m*P+b, the value of m, having two points, is calculated by:
[tex]m=\frac{Q2-Q1}{P2-P1}[/tex]
Being:
Q1= 5P1= $50Q2= 10P2= $40and replacing:
[tex]m=\frac{10-5}{40-50}[/tex]
you get:
m= -0.5
So, being Q=-0.5*P+b, b is calculated by:
Replacing the point Q1= 5 and P1= 505= -0.5*50 + b → 5= -25 + b → 5+25= b → b= 30
Replacing the point Q1= 10 and P1= 4010= -0.5*40 + b → 10= -20 + b → 10+20= b → b= 30
Then, the linear equation relating price to demand is Q=-0.5*P + 30
find the area of the given triangle a = 19, c= 14, B=60°. Round your answer to the nearest tenth.
Answer: 115.2 units²
Step-by-step explanation:
Since you know the length of two sides and the measure of the included angle, you can use the following trig formula:
[tex]Area=\dfrac{1}{2}ac \sin B[/tex]
Given: a = 19, c = 14, B = 60°
[tex]A=\dfrac{1}{2}(19)(14) \sin 60^o\\\\.\quad =133\sin 60^o\\\\.\quad =115.2[/tex]
Answer:
[tex]\huge \boxed{\mathrm{115.2 \ units^2 }}[/tex]
Step-by-step explanation:
We can solve for the area of the triangle when two sides are given and the angle in between the two sides.
[tex]\displaystyle A=\mathrm{\frac{1}{2}ac \cdot sinB }[/tex]
[tex]\displaystyle A=\mathrm{\frac{1}{2} \cdot 19 \cdot 14 \cdot sin60 }[/tex]
[tex]\displaystyle A=\mathrm{\frac{133\sqrt{3} }{2} }[/tex]
[tex]\displaystyle A=\mathrm{115.18137870...}[/tex]
The area of the triangle is 115.2 units².
Help with the below image… Thank you!
Answer: third one
Step-by-step explanation:
Answer:
alternate ext angles are <4 <5
if you are dealt 4 cards from a shuffled deck of 52 cards find the probability that all 4 are hearts
Answer:
Probability of getting 4 hearts = 11/833
Step-by-step explanation:
Find:
Probability of getting 4 hearts
Computation:
Probability of getting 1st heart = 13 / 52
Probability of getting 2nd heart = 12 / 51
Probability of getting 3rd heart = 11 / 50
Probability of getting 4th heart = 10 / 49
Probability of getting 4 hearts = [(13 / 52)(12 / 51)(11 / 50)(10 / 49)]
Probability of getting 4 hearts = 11/833
if any two ordered pair (2x-3,6)=(x+1,2y/3) find the value of x and y
Answer:
2x-3= x+1
or, 2x- x = 1+3
or, x = 4
so, x = 4
NOW,
6= 2y/3
or, 6×3 =2y
or, 18/2 = y
so, y = 9
X = 4 and Y = 9
ANS
Can someone please help me
Answer: B
Step-by-step explanation:
To find the factors, you know that they are known as the zeros. The zeros are located on the x-axis, where the graph crosses. On the graph, we see that the parabola crosses the x-axis at x=-5 and x=-1. Unfortunately, those are not displayed in our answer choices.
We know that each factor is set equal to 0 to get x=?. With this knowledge, let's make it so that we can get factors.
x=-5 [add both sides by 5]
x+5=0
Now, we see that it is a factor, (x+5).
x=-1 [add both sides by 1]
x+1=0
Now, we see that it is a factor, (x+1).
Our final answer is (x+5) and (x+1) or (x+1) and (x+5).