log tan 0 = log sin 0 - log cos 0

Q: Find the exact value of the expression 321/ln 2

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Q: 1. Use the properties of logarithms to simplify the expressions: a) In sin 0 sin 0 In 5 b) In (4r*)…

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Q: Show that : log (1+ x) 1+x? dx = log 2 8

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Q: If a, b > 0, find the number a that satisfies (ax)loga = (br)logb, where log is the logarithm of any…

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Q: Use the properties of logarithms to write the expressions in as a single term. ln sec θ + ln cos θ

A: Given                 ln secθ + ln cosθ  So,    as           ln x + ln y =ln xy

Q: Find the inverse 2-Transforrm of log(z f log 241 by Power senies method and by division method

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Q: log10 (1000100) 100 + 100 ANT sin(n) + (-1) n 1000 II 1 cos(™M)²

A: Given expression as log101000100100+∑n=1100sinπn+1-1n·∏m=110001cosπm2

Q: Determine the numerical value of the following expression without the use of a calculator: TT + log,…

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Q: |

A: We will show it using log property

Q: Determine the numerical value of the following expression without the use of a calculator: + log,…

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Q: Show that 3x2 + log2x2 is Theta(x2). log2x is log base 2 of x.

A: Consider 3x2+log2x2 . It is known that  log2x2<x2, for all x>0. Then, log2x2<3x2 for all…

Q: Use the properties of the natural logarithms to simplify the following expressions sin 0 a) In sin e…

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Q: Using properties of logarithms, we can rewrite the equation as In(y) - In(x7 cos(x)), which is…

A: Consider the equation  ln(y)=ln(x7cos(x))

Q: Then use your work to calculate the discre Show that 6 is a primitive root of 13 logarithm of 11…

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Q: Evaluate the expression, ln (1/e2)  without using a calculator. If evaluation is not possible, state…

A: Evaluate: ln1e2

Q: Using the complex exponential function, Find integral e^(3x)*sin(2x)*x^7

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Q: Determine the numerical value of the following expression without the use of a calculator: TT + log,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find a formula for the inverse of f(x) = -1+ log2 x.

A: Given function is : fx=-1+log2x To find the formula of the inverse.

Q: Determine the numerical value of the following expression without the use of a calculator: 100 log10…

A: We have to find the numerical value of the following expression: log101000100100+∑n=1100…

Q: Determine y′(x) if y(x)=(4x^3+6)^sinx.  Enter an exact answer in terms of a natural logarithm.

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Q: Simplify the expression (62)4. (1) |0| sin cos tan sin- cos %3D tan csc sec cot log log, In Reset…

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Q: Use the properties of logarithms to simplify the following functions before computing f 1x2.

A: Given expression: fx=lnsec4x tan2x

Q: Evaluate : |(log x)sin' x dx

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Q: Differentiate log sin x by first principles.

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Q: In LRT reject H, when Ais small, so we reject Ho when the value -2 log A is small Select one: True…

A: Answer : False

Q: 1 log(e)= In(10) %3D Use the change of base property to show

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Q: Which of the following expressions is equivalent to 6*? 6 In x 6x xIn 6 log 6X

A: Solution: We know that

Q: Condense the expression to a single logarithm using the properties of logarithms. log (x) – 5 log…

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Q: Condense the expression to a single logarithm using the properties of logarithms. log (x) – log (y)…

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Q: Differentiate the following with respect to x (i) (a)log (cosx)

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Q: Use definition of hyperbolic function to show that 5e2z 1 2 cosh a + 3 sinhr Hence, solve the…

A: We need to prove: 2 cosh x + 3 sinh x =125e2x-1ex and then solve: 4 cosh x + 6 sinh x =ex This can…

Q: Determine the numerical value of the following expression without the use of a calculator:√√√√sin(π+…

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Q: Use the properties of the natural logarithms to simplify the following expressions: (sin 0 a) In sin…

A: Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to…

Q: The principal value of tan-' (2i) is :Select one 1 +i-log, 3.a 2 1 loge 3+ i .b c. None of these 1…

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Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Given expression: logcosecθ=-logsinθ The objective is to verify the left hand side equal to right…

Q: If p(x)=(x3+2x)^sinx, find p′(x).  Enter an exact answer in terms of a natural logarithm.

A: As the given function :- P(X) = ( X3 + 2X )sinx  P'(X) = ?

Q: According to the properties of logarithms In sec x= - In cos x O True O False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Show that loga ( 1/N) = - loga N, where a and N are positive real numbers and a ≠ 1.

A: To Show: loga1N=-logaN, where a and N are positive real number and a≠1. Concept: i.…

Q: In arcsin x (V1-x²)arcsin x

A: Given:     ∫lnarcsinx1-x2arcsinxdx    =∫lnarcsinx1-x2arcsinxdx substitute…

Q: If p(x)=(2x+4)^tanx, find p′(x).  Enter an exact answer in terms of a natural logarithm.

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Q: b. y= tan(7x-3)•log 4(5 + 2x) use the Product rule (3)

A: We use product rule of derivative :d/dx(uv)=ud/dx(v)+vd/dx(u). See 2nd step.

Q: Given that h(x) = log(x + 1) and f(x) = 2+ 10², find and simplify foh(æ)).

A: Composition of two function f(x) and g(x) is the process of making a new function h(x) such that the…

Q: Use the properties of logarithms to write the expressions in as a single term.

A: Given: ln sin θ - ln sin θ5 To write: Using the logarithmic properties to write the given…

Q: f(x) = 3x + log(9x − 8), find f(2). f(2) = ?

A: Given a function f(x) , need to find f(2).

Q: Use these formulas to express the numbers in terms of natural logarithms. 61. sinh-' (-5/12) 63.…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: The principal value of tan- (2i) is :Select one 1 +i-log, 3 .a 1 log, 3+ i- .b 2 2 c. None of these…

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.