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3 years ago

Question #4

Mathematics

1 answer:

Vitek1552 [10]3 years ago

7 0

Answer:

80.11 inches

Step-by-step explanation:

The formula to finding the circumference of a circle is:

C = 2πr (C = circumference, π = pi, r = radius)

Replace r with the radius:

C = 2π(12.75)

Now, multiply 2 times pi, then multiply that by 12.75, and the answer rounded

to the nearest hundredth is 80.11

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Two friends argue about the calculated probability of flipping a coin to show heads three times in a row. steve mentions that ea

den301095 [7]

Solution:

A coin is flipped three times,resulting three heads in a row.

Since Steve has mentioned that , each flip of a coin is unconnected to the previous flip.

Two or more events are said to be independent if occurrence of one of them is not affected by the Occurrence of other.

This is an example of independent events.

In terms of probability, P (A∩B∩C)= P(A)×P(B)×P(C)

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3 years ago

6) (after 2.3) Consider the infinite system of linear equations in two variables given by ax + by = 0 where (a, b) moves along t

Paraphin [41]

Answer:

Step-by-step explanation:

Given infinite system of linear equations is ax + by = 0

when (a,b) moves along unit circle in plane.

a) system having unique system (0, 0)

Since two of equation in thus system will be

$1.x+0.y=0\\x=0$

and

$0.x+1.y=0\\y=0$

It is clear that x = 0, y= 0 is the only solution

b) Linear independent solution in this system gives some set of solutions

$1.x+0.y=0\\\x=0$

and

$0.x+1.y=0\\y=0$

Vector form is

$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =I$

c) for this equation if add 0x +0y = 0 to system , Nothing will change

Because [0,0] satisfies that equation

d) If one of the equation is ax + by = 0.00001

where 0.00001 is small positive number

so, the system will be inconsistent

Therefore, the system will have no solution.

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3 years ago

A food manufacturer uses an extruder (a machine that makes bite size cookies)that yields revenue for the firm at a rate of $200

julsineya [31]

Answer:

$1300

Step-by-step explanation:

The extruder yields a revenue of $200per hour

Y denotes the number of breakdown per day.

The daily revenue generated is given as

R = 1600 - 50Y^2

We have an average of 2 breakdown per day

Lamda = 2

Represent lamda as β

E(Y) = β

E(Y(Y-1)) = β^2

E(Y^2) = E[Y(Y-1)] + E(Y)

= β^2 + β

E(R) = E(1600 - 50Y^2)

= 1600 - 50E(Y^2)

= 1600 - 50(β^2 +β)

Recall that β = lamda = 2

= 1600 - 50(2^2 + 2)

= 1600 - 50(4+2)

= 1600 - 50(6)

= 1600 - 300

= 1300

$1300

The expected daily revenue of the extruder is $1300

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3 years ago

The pressure of a gas p(v) varies inversely with the volume of the gas v. The pressure of a gas measures 25 kg/cm^2 when its vol

Mashcka [7]

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{\underline{p(v)} varies inversely with \underline{v}}}{p(v)=\cfrac{k}{v}}\qquad \textit{we also know that } \begin{cases} p(v)=25\\ v=200 \end{cases} \\\\\\ 25=\cfrac{k}{200}\implies 5000=k\qquad therefore\qquad \boxed{p(v)=\cfrac{5000}{v}}$

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3 years ago

How do you do this question?

dezoksy [38]

Answer:

∫₂⁵ ln(x) dx

Step-by-step explanation:

lim(n→∞) ∑ᵢ₌₁ⁿ (3/n) ln((2n + 3i) / n)

lim(n→∞) ∑ᵢ₌₁ⁿ (3/n) ln(2 + (3/n) i)

The width of the interval is b−a = 3, and there are n rectangles. So the width of each rectangle is 3/n, and the height of each rectangle is ln(2 + (3/n) i).

The ith term is 2 + (3/n) i, so a = x₀ = 2. Therefore, b = 2+3 = 5.

So the region is the area under f(x) = ln(x) between x=2 and x=5.

∫₂⁵ ln(x) dx

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3 years ago