MATHEMATICS COLLEGE

Leo dug up 6 4/5 pounds oftreasure on his first dig. Anne dug
up 4 1/2 pounds of treasure. How
much more treasure did Leo dig
up than Anne?

Answers

Answer 1
Answer: 6 4/5 = 6.8
4 1/2 = 4.5

6.8-4.5= 2.3

Answer: 2 3/10 more pounds of treasure

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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.

Which two numbers on the number line have an absolute value of 1.75?Select the location of both numbers on the number line.

Answers

Answer:

The absolute value of a number is the distance of the number from zero on the line. The line has always values increasing from left to right. Right side is greater than the left side.

Every absolute value has two numbers on the line like absolute value of 1 has two points, one is 1 and the other is -1. Hence the absolute value of 1.75 also has two numbers on the line one is 1.75 and other is -1.75.

So the point 1.75 can be found on the right side of zero at a distance of 1.75 and in the middle of point 1.5 and 2. Again -1.75 point can be found at the left side of zero at a distance of 1.75 and in the middle of -1.5 and -2.

Note: Refer the image attached. The Red colour marks in the image attached shows the location of both numbers on the number line.

Answer:

-1.75 and 1.75

Step-by-step explanation:

The absolute value is the distance that certain number has from it's position to the number 0.

There are only two numbers that have a distance of 1.75 to the number 0: -1.75 and 1.75.

The location on the graph must be marked on the line that is between -1.5 and -2, and between 1.5 and 2.

X² - 6x + 21 = 0 answer and solution?
please help me ​

Answers

there is no solution

Is line / parallel to line m? Explain.
Note: Not drawn to scale

Answers

Parallel lines are defined to be two lines that will never intersect even when they go on infinitely. Think of it like railroad tracks. The rails must always be parallel, or the train will gets stuck. By observing lines L and M, you'll notice both lines make perfect railroad tracks, and they will never intersect. These lines are parallel.

For which product or quotient is this expression the simplest form? (image attached)! please help :((

Answers

Answer:

D

Step-by-step explanation:

For simplify the work we can start to factorise all the possibles expressions:

2x + 8.

8 is multiple of 2, so it can became

2(x+4)

x^2 - 16 this is a difference of two squares, so it can be rewritten as:

(x+4)(x-4)

x^2 + 8x + 16

we have to find two numbers whose sum is 8 and whose product is 16

the two number are 4 and 4

it becames:

(x+4)(x+4)

x+ 4 can‘t be simplified

if we look at the expression, we can find that x-4 appears at the numerator so

x^2 - 16 must be at numerator

but the second factor (x+4) doesn’t appear, so has been simplified. This situation can be possible only in the D option

in fact

(x+4)(x-4)/2(x+4) * (x+4)/(x+4)(x+4)

it became

(x+4)(x-4)/2 * 1/(x+4)(x+4)

(x-4)/2(x+4)

Answer:

Step-by-step explanation:

I got 100% on the test

19) Solve the system,
*****
x + 3y - 5
-2x + 2y = 14

Answers

Answer:

y = 3

x = -4

Step-by-step explanation:

Hopefully the first equation is x + 3y = 5

x = 5 - 3y

Plug in:

-2(5 - 3y) + 2y = 14

-10 + 6y + 2y = 14

8y = 24

y = 3

x = -4
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