The Z-transform of the given sequence y[n] = 3u[n] - 1.5 8[n-1] is Y[z] = (3z)/(z-1) - (1.5z)/(z-1). To simplify y[n], we need to find the inverse Z-transform of Y[z].
The Z-transform is a useful tool for analyzing discrete-time signals and systems. In this case, we are given the sequence y[n] = 3u[n] - 1.5 8[n-1], where u[n] is the unit step function and 8[n-1] represents the delayed unit impulse function.
To find the Z-transform of y[n], we can use the linearity property of the Z-transform. Since the Z-transform of u[n] is 1/(1-z^(-1)), and the Z-transform of 8[n-1] is z^(-1), we can substitute these values into the expression for y[n] to obtain:
Y[z] = 3(1/(1-z^(-1))) - 1.5(z^(-1))/(1-z^(-1))
To simplify Y[z], we need to combine the terms with a common denominator. By finding a common denominator of (1-z^(-1)), we can rewrite Y[z] as:
Y[z] = (3z - 1.5)/(z-1)
Now, to obtain y[n], we need to find the inverse Z-transform of Y[z]. The inverse Z-transform can be computed using techniques such as partial fraction expansion or by referring to Z-transform tables.
The simplified expression for y[n] would be:
y[n] = 3δ[n] - 1.5δ[n-1]
where δ[n] represents the discrete-time unit impulse function. The graph of y[n] would have an impulse of magnitude 3 at n = 0 and an impulse of magnitude -1.5 at n = 1.
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Which equation is equivalent to 3 = 87 ÷ h? A. 3 = (87 ÷ h) – 9 B. 3 × 9 = (87 ÷ h) ÷ 9 C. 3 + 9 = (87 ÷ h) + 9 D. 3 – 9 = (87 ÷ h)
Answer:
3= (87÷h)
Step-by-step explanation:
The question is to pick among the option the solutions that will be equal to 3= (87÷h)
Therefore the most suitable and correct option is
3×9= (87÷h)÷9
27= (87÷h)÷9
Divide by 9
3= (87÷h)
Hence the answer is 3=(87÷h)
For which the value of f(x) = 2x^2 + 9 will be the same as g(x) = 3^x?
Answer:
For [tex]x = 3[/tex] the value of [tex]f(x) = 2\cdot x^{2}+9[/tex] will be the same of [tex]g(x) = 3^{x}[/tex].
Step-by-step explanation:
To determine for which value of [tex]x[/tex], we need to apply the following identity ([tex]f(x) = g(x)[/tex]) and solve numerically the resulting expression:
[tex]2\cdot x^{2}+9 = 3^{x}[/tex]
[tex]3^{x}-2\cdot x^{2}-9=0[/tex] (1)
A quick approach is using graphic tool and looking for the value of [tex]x[/tex] such that [tex]3^{x}-2\cdot x^{2}-9=0[/tex]. The result of the analysis is included below in the attached image. We find the following result:
[tex]x = 3[/tex]
For [tex]x = 3[/tex] the value of [tex]f(x) = 2\cdot x^{2}+9[/tex] will be the same of [tex]g(x) = 3^{x}[/tex].
Suppose you measured a boiling temperature (in Cº) for a liquid 6 times and observed. the following results:
Sample mean: 101.82, sample variance (biased): 0.81
a. You are given that σ^2 = 1.2 for the population distribution. What is the confidence interval for the mean at 95% confidence level?
b. Assuming σ is unknown, what is the confidence interval for the population mean at 95% confidence level?
Please round your answers to 2 decimal digits.
The confidence interval for the mean at 95% confidence level with the variance known and unknown are (101.17, 102.47), (101.06, 102.58) respectively
A.)
Known VarianceConfidence interval is related by the formula:
CI = μ ± t * s * √(1/n)Where :
μ = population mean
t = critical value for the confidence level
s = sample standard deviation
n = sample size
The critical value for a 95% confidence level is 1.96.
C.I = 101.82 ± 1.96 * 0.81 * √(1/6)
C.I = 101.82 ± 0.648
C.I = (101.172, 102.468)
Hence, the confidence interval is (101.17, 102.47)
B.)
Assuming variance is Unknown
We use the t-distribition; The critical value at 95% confidence and (6-1) degree of freedom = 2.306
CI = μ ± t * s * √(1/n)
C.I = 101.82 ± 2.306 * 0.81 * √(1/6)
C.I = 101.82 ± 0.763
C.I = 101.057, 102.583
Hence, the confidence interval is (101.06, 102.58)
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the perimeter of the triangle is ___ units.
Answer:
29 units
Step-by-step explanation:
12 + 12 + 5
29
How do I solve this problem. I have to find the missing side lengths and lease my sender as radicals in simplest form
Answer:
x = y = 2√2
Step-by-step explanation:
Find the diagram attached
To get the unknown side x and y, we need to use the SOH CAH TOA identity
Opposite side = x
Adjacent = y
Hypotenuse = 4
Sin theta = opposite/hypotenuse
sin 45 = x/4
x = 4 sin 45
x = 4 * 1/√2
x = 4 * 1/√2 * √2/√2
x = 4 * √2/√4
x = 4 * √2/2
x = 2√2
Similarly;
cos theta = adjacent/hypotenuse
cos 45 = y/4
y = 4cos45
y = 4 * 1/√2
y = 4 * 1/√2 * √2/√2
y = 4 * √2/√4
y = 4 * √2/2
y = 2√2
HELP ASAP PLZ!!! Question in picture!
Answer:YOUR ANSWER IS C
Step-by-step explanation:
Answer:
y=11/2x-10
20 character minimum
Q10.
Prove algebraically that the recurring decimal 0.178 can be written as the fraction 59/330
Answer:
bbv
Step-by-step explanation:
Recurring decimal is decimal representation of a number whose digits are periodic and infinite. Proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330 below.
Given information;Given number in the decimal form is [tex]0. 1 \overline 7 \overline 8[/tex]
Suppose the number is equal to the x,
[tex]x=0. 1 \overline 7 \overline 8[/tex]
Recurring decimalRecurring decimal is decimal representation of a number whose digits are periodic and infinite.
As the number 78 is the recurring number. Thus the recurring number can be written as,
[tex]x=0.1787878.....[/tex] .......equation 1.
Suppose this is equation number 1.
Multiply the above equation with 100 both the sides,
[tex]100\times x=100\times0. 1 787878....[/tex]
[tex]100x=100\times0.1787878...[/tex]
[tex]100x=17.87878...[/tex]
Subtract the above equation from equation number 1. Thus,
[tex]\begin{aligned}\ 100x-x&=17.87878-0.1787878\\ 99x&=17.7\\ \end[/tex]
Solve for x ,
[tex]x=\dfrac{17.7}{99} [/tex]
Multiply with 10 in both numerator and denominator,
[tex]x=\dfrac{177}{990} \\ x=\dfrac{59}{330} \\[/tex]
Hence proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330
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Which of the numbers listed below are solutions to the equation?
Check all that apply.
x2 = 49
A. -7
B. 14
C. 24.5
D. 7
E. -14
F. 2401
Find all the missing sides and angles of this triangle.
A
7
B
70°
C
The approximation of 1 = integral cos(x3 + 10) dx using composite Simpson's rule with n= 3 is: When approximating Sof(x)dx using Romberg integration, R3,3 gives an approximation of order:
The approximation of the integral ∫cos(x³ + 10) dx using composite Simpson's rule with n = 3 is 0.126. When approximating the integral using Romberg integration, R₃,₃ gives an approximation of order h⁶.
To calculate the approximation using composite Simpson's rule, we divide the interval of integration into subintervals and apply Simpson's rule to each subinterval. The formula for Simpson's rule is:
S = h/3 * (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 2f(x_{n-2}) + 4f(x_{n-1}) + f(xₙ))
where h is the step size and n is the number of subintervals. In this case, we have n = 3, so we divide the interval into three equal subintervals, and the step size is h = (b - a) / n = (π - 0) / 3 = π/3.
Evaluating the function cos(x³ + 10) at the points x₀ = 0, x₁ = π/3, x₂ = 2π/3, and x₃ = π, we get:
f(x₀) = cos((0)³ + 10) = cos(10) ≈ -0.8391
f(x₁) = cos((π/3)³ + 10) = cos(π³/27 + 10) ≈ -0.4586
f(x₂) = cos((2π/3)³ + 10) = cos(8π³/27 + 10) ≈ -0.8391
f(x₃) = cos((π)³ + 10) = cos(π³ + 10) ≈ -0.3473
Using the Simpson's rule formula, we can now calculate the approximation:
S ≈ π/3 * (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃))
≈ π/3 * (-0.8391 + 4(-0.4586) + 2(-0.8391) + 4(-0.3473))
≈ 0.126
To calculate the order of approximation using Romberg integration, we use the formula:
Rₙ,ₖ = Rₙ₋₁,ₖ₋₁ + (Rₙ₋₁,ₖ₋₁ - Rₙ,ₖ₋₁) / (4ₖ - 1)
where Rₙ,ₖ represents the Romberg approximation at level n and column k. The order of approximation is determined by the highest power of h in the error term. In this case, we have R₃,₃, so the order is h⁶.
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Find the area of the following
triangle:
5 cm
10 cm
A= [?] cm?
Answer:
25
Step-by-step explanation:
A=1/2×b×h
A=1/2×5cm×10cm
A=25cm
please help easy math!! 8th grade math Storypromblem answer number 9
Answer: Chris's Gym pays $2.75
Step-by-step explanation:
So i was glancing at this question wondering how I was gonna figure it out then flipped it upside down in my head and figred out what I was missing
So basically we know that Tyrell pays $2.00 for court reservations
Chris on the other hand according to the table pays $52.75 for court reservation in addition to his monthly fee. Now we have to find out how much is just the court fee. So if we look at the next box I realized that a second court recomendation costs $55.5 and I realized that to find the court reservation costs I needed to subtract so 55.5-52.755= 2.75 which means Chis has a monthly costs of 50 and pays $2.75 for a court holding
 what would be the equation of a line that passes through (3,-4) with slope 2/3
Answer:
y = 2/3x - 6
Step-by-step explanation:
Use the slope intercept equation, y = mx + b
Plug in the slope and given point, then solve for b
y = mx + b
-4 = 2/3(3) + b
-4 = 2 + b
-6 = b
Plug in the slope and b into the equation
y = 2/3x - 6
So, the equation of the line is y = 2/3x - 6
plzz hurryyyy its for my mathhhh classss
Answer:
A
Step-by-step explanation:
4x+2 = 10
=> 2x+2 = 10-2x
Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
i think the answer is c but im not sure sorry if im wrong
Step-by-step explanation:
18,8. Assuming the tree shown below is perpendicular to the base distance, use trigonometry
to calculate its height to 1 decimal place. Dimensions are in feet.
I
32°
150
Answer:
x = 93.7ft or x = 94ft
Step-by-step explanation:
Hope that helps :)
jada says she can write an equivalent fraction with a denominator of 100 by multiplying 5 by 5, then writing the number of hundredths as a decimal
what is the ratio for 0.875?
The simplified ratio for 0.875 is 7:8 .
To express the ratio for 0.875, we need to convert the decimal value to a ratio form.
0.875 can be written as 875 / 1000 because the decimal value is equivalent to the fraction obtained by dividing the numerator by the denominator.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 125 in this case.
Dividing 875 and 1000 by 125, we get:
875 / 125 = 7
1000 / 125 = 8
So, the simplified ratio for 0.875 is 7:8 .
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Test the claim that the proportion of people who own cats is significantly different than 90% at the 0.02 significance level.
The null and alternative hypothesis would be:
H0:μ≥0.9H0:μ≥0.9
H1:μ<0.9H1:μ<0.9
H0:p=0.9H0:p=0.9
H1:p≠0.9H1:p≠0.9
H0:μ=0.9H0:μ=0.9
H1:μ≠0.9H1:μ≠0.9
H0:p≥0.9H0:p≥0.9
H1:p<0.9H1:p<0.9
H0:μ≤0.9H0:μ≤0.9
H1:μ>0.9H1:μ>0.9
H0:p≤0.9H0:p≤0.9
H1:p>0.9H1:p>0.9
The test is:
left-tailed
right-tailed
two-tailed
Based on a sample of 500 people, 82% owned cats
The p-value is:__________ (to 2 decimals)
Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis
The null and alternative hypotheses for testing the claim that the proportion of people who own cats is significantly different from 90% at the 0.02 significance level are:
H0: p = 0.9 (proportion of cat owners is 90%)
H1: p ≠ 0.9 (proportion of cat owners is not equal to 90%)
Based on a sample of 500 people, where 82% owned cats, we can conduct a hypothesis test to determine the p-value at the 0.02 significance level. The p-value is the probability of obtaining a sample proportion as extreme as the observed proportion (82%) assuming the null hypothesis is true.
The p-value for this test is the probability of observing a sample proportion as different from 90% as 82%. Since the p-value is not provided in the question, it needs to be calculated based on the sample data and the assumed null distribution.
If the p-value is less than 0.02, we would reject the null hypothesis and conclude that the proportion of cat owners is significantly different from 90%. However, if the p-value is greater than or equal to 0.02, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the proportion of cat owners from 90%.
Without the calculated p-value, we cannot make a definitive conclusion about rejecting or failing to reject the null hypothesis.
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Please show me step by step how to do this
Answer:
You know that the beginning salary is $32,000, and it is raised by $1,000 per year.
a) We want to find a recursive relation, let's try to find a pattern:
S₁ = salary on the first year = $32,000
S₂ = salary on the second year = $32,000 + $1,000 = $33,000
S₃ = salary on the third year = $33,000 + $1,000 = $34,000
and so on.
We already can see that the recursive relation is: "the salary of the previous year plus $1,000", this can be written as:
Sₙ = Sₙ₋₁ + $1,000
Such that S₁ = $32,000
b) Your salary in the fifth year is S₅
Let's construct it:
S₃ = $34,000
S₄ = $34,000 + $1,000 = $35,000
S₅ = $35,000 + $1,000 = $36,000
Your salary on the fifth year is $36,000
c) When we have a recursive relation like:
Aₙ = Aₙ₋₁ + d
The sum of the first N elements is given by:
Sum(N) = N*(2*A₁ + (N - 1)*d)/2
Then the sum of your salary for the first 20 years is:
S(20) = 20*(2*$32,000 + (20 - 1)*$1,000)/2
S(20) = $830,000
A woman bought a bag of rice for 5,700 naira and in three weeks later,she could only buy 3/4 of a bag for 5,700 find the percentage increase
I need help with math.
Step-by-step explanation:
Circumference of a circle= 2πr
where r=6
and π=22/7
C=2πr
=2×22/7×6
=44/7×6
=264/7
=37.71cm
Consider the function f(x)=6x+5
(A) find it’s average rate of change by changing x=1 to x=5
Answer: I really don’t know
Step-by-step explanation: I need help with this as well. I’m really sorry if you were looking for a real answer
Compare the probability that a student will pass the test in the morning with
the probability that a student will pass the test in the afternoon. Draw a
conclusion based on your results.
A. P(pass morning) = 0.24
P(pass afternoon) = 0.41
Conclusion: A student taking the test in the morning has a greater
chance of passing it than a student taking it in the afternoon
O B. P(pass morning) = 0.24
P(pass | afternoon) = 0.41
Conclusion: A student taking the test in the afternoon has a
greater chance of passing it than a student taking it in the
morning.
O c. P(pass morning) = 0.48
P(pass | afternoon) = 0.82
Conclusion: A student taking the test in the afternoon has a
greater chance of passing it than a student taking it in the
morning.
D. P(pass morning) = 0.48
P(pass afternoon) = 0.82
Conclusion: A student taking the test in the morning has a greater
chance of passing it than a student taking it in the afternoon.
Answer: C
Step-by-step explanation:
just took the quiz
The conclusion based on the statement would be option C. Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We need to Compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon.
The conclusion based on the statement would be;
C. P(pass morning) = 0.48
P(pass | afternoon) = 0.82
Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.
Therefore, the correct option is C.
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Determine whether true or false
(i) Let X be a random variable, then Cov (X,X) = VAR(X).
(ii) The mean and standard deviation of an exponential random
variable are equal.
(iii) The joint PDF fXY(x,y)
(i) True.
(ii) False.
The first statement is true.
It is a well-known fact that for any random variable X, the covariance of X with itself is equal to the variance of X. This can be easily shown by applying the definition of covariance and variance and using the fact that the correlation between X and X is always 1.
The second statement is false. The mean of an exponential random variable is equal to 1/λ, where λ is the rate parameter. On the other hand, the standard deviation of an exponential random variable is equal to 1/λ as well. These two values are not equal, unless λ=1. Therefore, the statement is false.
In summary, the first statement is true, while the second statement is false. The covariance of a random variable with itself is equal to its variance, but the mean and standard deviation of an exponential random variable are not equal unless λ=1.
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Which expression is equivalent to the following expression? -4 (5x - 6)
1.) -20x - 24
2.) -20x + 24
3.) -20x + 6
4.) -20x - 6
Step-by-step explanation:
2.) -20× + 24
maaf kalo salah
Look at the triangle: A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as x degrees What is the value of cos x°? (1 point) 8 ÷ 17 17 ÷ 8 15 ÷ 17 8 ÷ 15 I can't put in the photo. So, description. h- 17cm o- 8cm a- 15cm. This is a right triangle btw. (this is 9th grade work)
Answer:
15 ÷ 17
Step-by-step explanation:
Since our hypotenuse side is 17 cm, our opposite side is 8 cm and our adjacent side is 15 cm. Since the acute angle is x degrees,
From trigonometric ratios, cosx° = adjacent/hypotenuse
= 15 cm/17 cm
= 15/17
= 15 ÷ 17
Questions (a,b), 1 (a,b)
a )
First of all we need to find the value of x ,
because the angles are written in terms of the variable x .
______________________________________
Let's find the value of x :STV angle & SUV angle have same measure because both of them are the front angle of SV arc .
[tex]STV angle \: = SUV angle \: \: = \frac{SV \: arc}{2} \\ [/tex]
So :
[tex]3x - 5 = 2x + 15[/tex]
Add sides 5
[tex]3x - 5 + 5 = 2x + 15 + 5[/tex]
[tex]3x = 2x + 20[/tex]
Subtract sides minus 2x
[tex]3x - 2x = 2x + 20 - 2x[/tex]
Collect like terms
[tex]x = 2x - 2x + 20[/tex]
[tex]x = 20[/tex]
Thus the measure of angle T equals :
[tex]measure \: of \: angle \: T = 3x - 5 \\ [/tex]
Now just need to put the value of x which we found :
[tex]measure \: of \: angle \: T \: = 3 \times (20) - 5 \\ [/tex]
[tex]measure \: of \: angle \: T \: = 60 - 5[/tex]
[tex]measure \: of \: angle \: T \: = 55°[/tex]
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b )
angle S & angle V are also have same measure because they both are the front angles to the TU arc .
And we need to find the value of x again in this part exactly like we did for a .
[tex]angle \: \: S = angle \: \: V[/tex]
As the question told :
[tex]angle \: \: S = 3x[/tex]
and ,
[tex]angle \: \: V = x + 16[/tex]
Thus :
[tex]3x = x + 16[/tex]
Subtract sides minus x
[tex]3x - x = x + 16 - x[/tex]
Collect like terms
[tex]2x = x - x + 16[/tex]
[tex]2x = 16[/tex]
Divide sides by 2
[tex] \frac{2x}{2} = \frac{16}{2} \\ [/tex]
Simplification
[tex]x = 8[/tex]
So ;
[tex]measure \: \: of \: \: angle \: \: S = 3x[/tex]
[tex]measure \: \: of \: \: angle \: \: S = 3(8)[/tex]
[tex]measure \: \: of \: \: angle \: \: S = 24°[/tex]
And we're done.
The amount of carbon-14 in an object is given by y = ae– 0.00012t where a is the initial amount of carbon and t is the age in years. A fossil bone contains 25% of its original carbon-14. What is the approximate age of the bone?
Answer:
The approximate age of the bone is approximately 11552 years.
Step-by-step explanation:
The current proportion of carbon-14 with respect to its original amount is defined by following formula:
[tex]\frac{y}{a} = e^{-0.00012\cdot t}[/tex] (1)
Where:
[tex]y[/tex] - Current amount of carbon-14, no unit.
[tex]a[/tex] - Initial amount of carbon-14, no unit.
[tex]t[/tex] - Time, in years.
If we know that [tex]\frac{y}{a} = 0.25[/tex], then the approximate age of the bone is:
[tex]t = -8333.333\cdot \ln \frac{y}{a}[/tex]
[tex]t\approx 11552.453\,yr[/tex]
The approximate age of the bone is approximately 11552 years.
y=-3x + 4
y = 3x - 2
What solution does this system have? How do you
know? Justify(explain).