Show that cos(x) >1 – x²

Q: Example Let Y. < Ya <.. < Yo denote the arder statistics of a random sample of size n from a…

A: It is an important part of statistics. It is widely used.

Q: Q.47 Consider a discrete time Markov chain on the state space {1,2,3} with one-step transition 1 2 3…

A: Step 1 Given a tradition probability matrix. And by using this matrix make a transition probability…

Q: 3. Approximate integration formula | f(x)dx = aof (0) + a¡f (1/2) + azf(1) is exact functions f (x)…

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Q: Concentrations of nitrogen oxides and of hydrocarbons (recorded in ug/m3) were determined in 11…

A: Here the data are not Normally distributed and the sample is collected twice (one for nitrogen oxide…

Q: . The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

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Q: 3, 5x 60(x 2 + x;), 3 b) Y = In 7.

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Q: FromSassamplesof n = 15 readingsSon X = TrafficSVolume$(carsSpershours) Sand Y = Carbon Monoxide…

A: The strength of relationship between the two numerical variable is calculated using the correlation.…

Q: Bivariate data for the quantitative variables x and y are given in the table below. These data are…

A: Bivariate data for the quantitative variables x and y:- x y 5.5 6.8 6.5 6.4 6.1 4.5 7.1…

Q: The compressive strength of samples of cement can be modeled by a normal distribution with a mean of…

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Q: (III) If f'(x) > 0 for every x, then f(z) is an increasing function (in fact, f(z) is strictly…

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Q: Let F be a field and f (x) e F[x] be a polynomial of degree > 1. If f(a) =0 for some a e F, then f…

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Q: Below is a table of valucs for a continuous function f . X -1 -0.5 (),5 f(x) | 2.0 | 1.5 -1.0 0.5…

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Q: 1. Find , if y = x² sin 3x dx

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Q: Use optimization techniques to answer the question. Find the two real numbers x and y whose sum is…

A: Given that: Sum of two numbers x and y is 90.

Q: If f is derivable in [a, b} and f' (a) #f' (b), then for each number k lying between f' (a) and f'…

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Q: Suppose denotes an equivalence relation on a set A and a, b E A. Then a b if and only if anb=0.

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Q: 5 - x2 + 2x – 3 = 0

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Q: In a random sample of size n = 600 people in a city it is found that 340 of them like to watch TV…

A: Given,n=600x=340p^=xnp^=340600=0.5671-p^=1-0.567=0.433α=1-0.90=0.1α2=0.05Z0.05=1.645   (from…

Q: dy Find , if y = e-3x tan 5x dx

A: Giveny=e−3xtan5x

Q: Σ (-3)" 3.5.7... (2n + 1) n=1 8.

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Q: In this exercise will derive Simpson's rule using Taylor's theorem. Suppose ƒ € C¹([a, b]) and…

A: As per the question, we explore the derivation and properties of Simpson's rule for numerical…

Q: Find , if y = x² cot x dy dx

A: Given Data, y=x2cotx

Q: 3. Using the Mean Value Theorem, show that there is a c E (0,1), such that f'(c) = 2. fx) =4x

A: Given, fx=4x1+x2  To show there exist c=0,1 such that f'c=2

Q: How can the Mean Value Theorem be used?

A: The Mean Value Theorem states that if a function f is continuous on a closed interval [a,b] and…

Q: What is the level of significance?

A: It is given that the sample size n is 15.

Q: Compute the area of the unit circle by computing the following double integral 1dædy. z² +y?<1

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