circle o is inscribed in triangle rst such that it is tangent at points m,n, and p. if rp is 7, rt is 17 and sm is 5, then what is the length of side st?

Answers

Answer 1

Answer:

Answer:

The length of side st is 15.

Step-by-step explanation:

A tangent is a straigth line that touches a circle externally at a point on the circumference. Considering one of its properties that tangents from the same point to a fixed point outside a circle are equal.

Then,

/rn/ = /rp/

/tm/ = /tn/

/sm/ = /sp/

But, /rp/ = 7, /rt/ = 17 and /sm/ = 5.

Then,

/rt/ = /rn/ + /tn/

17 = 7 + /tn/ (∵ /rp/ = /rn/ = 7)

⇒ /tn/ = 10

Since /nt/ = 10, then /tm/ = 10 (/tm/ = /nt/)

So that,

/st/ = /sm/ + /tm/

= 5 +10

/st/ = 15

The length of side st is 15.

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Answers

Answer:

This procedure results in a binomial distribution

This procedure would not results in a binomial distribution

This procedure results in a binomial distribution

This procedure would not results in a binomial distribution

Step-by-step explanation:

A procedure must meet the following requirement in order for it to result in a binomial distribution

The procedure trials must be independent
Outcome of individual trials can be classified into two categories
Success probability must remain the same in all trials
The number of trials is fixed

Considering the first procedure we can see that it satisfies the requirement of above especially the requirement that the possible outcome of every trial is two

Considering the second procedure we see that would not results in a binomial distribution because the outcome of it trials cannot be classified into two categories

Considering the third procedure we can see that it satisfies the requirement of above especially the requirement that the trial must be independent

Considering the second procedure we see that would not results in a binomial distribution because there is no defined probability of success or failure

Consider an unreliable communication channel that can successfully send a message with probability 1/2, or otherwise, the message is lost with probability 1/2. How many times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once? Explain your answer. Hint: treat this as a Bernoulli process with a probability of success 1/2. The question is equivalent to: how many times do you have to try until you get at least one success?

Answers

Answer:

6 times we need to transmit the message over this unreliable channel so that with probability 63/64.

Step-by-step explanation:

Consider the provided information.

Let x is the number of times massage received.

It is given that the probability of successfully is 1/2.

Thus p = 1/2 and q = 1/2

We want the number of times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once.

According to the binomial distribution:

$P(X=x)=(n!)/(r!(n-r)!)p^rq^(n-r)$

We want message is received at least once. This can be written as:

$P(X\geq 1)=1-P(x=0)$

The probability of at least once is given as 63/64 we need to find the number of times we need to send the massage.

$(63)/(64)=1-(n!)/(0!(n-0)!)(1)/(2)^0(1)/(2)^(n-0)$

$(63)/(64)=1-(n!)/(n!)(1)/(2)^(n)$

$(63)/(64)=1-(1)/(2)^(n)$

$(1)/(2)^(n)=1-(63)/(64)$

$(1)/(2)^(n)=(1)/(64)$

By comparing the value number we find that the value of n should be 6.

Hence, 6 times we need to transmit the message over this unreliable channel so that with probability 63/64.

1.) Find the first six terms of the sequence.a1 = -6, an = 4 • an-1

A.)0, 4, -24, -20, -16, -12
B.)-24, -96, -384, -1536, -6144, -24,576
C.)-6, -24, -20, -16, -12, -8
D.)-6, -24, -96, -384, -1536, -6144

2. Find an equation for the nth term of the arithmetic sequence.
-15, -6, 3, 12, ...

A.)an = -15 + 9(n + 1)
B.)an = -15 x 9(n - 1)
C.)an = -15 + 9(n + 2)
D.)an = -15 + 9(n - 1)

3. Find an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9

A.)an = -579 + 42(n + 1)
B.)an = -579 + 42(n - 1)
C.)an = -579 - 42(n + 1)
D.)an = -579 - 42(n - 1)

4. Determine whether the sequence converges or diverges. If it converges, give the limit.
48, 8, four divided by three , two divided by nine , ...

A.)Converges; two hundred and eighty eight divided by five
B.)Converges; 0
C.)Diverges
D.)Converges; -12432

5. Find an equation for the nth term of the sequence.
-3, -12, -48, -192, ...

A.)an = 4 • -3n + 1
B.)an = -3 • 4n - 1
C.)an = -3 • 4n
D.)an = 4 • -3n

8. Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 3 + 3 + 9 + ... + 81

A.)summation of the quantity negative nine plus six n from n equals zero to fifteen
B.)summation of negative fifty four times n from n equals zero to fifteen
C.)summation of negative fifty four times n from n equals zero to infinity
D.)summation of the quantity negative nine plus six n from n equals zero to infinity

Answers

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