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2 years ago

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Given that angle ABC=65° and angle BCD=105°. Is it possible (consider all cases): that a)Line AB is parallel to line CD. and b)

Line AB is parallel to line CD.

2 answers:

LekaFEV [45]2 years ago

6 0

Answer:

No

Step-by-step explanation:

With the given angle measures, the angle between AB and CD is either 10° or 40°. AB and CD cannot be parallel.

AfilCa [17]2 years ago

6 0

Answer:

No

Step-by-step explanation:

Since BC is common line section, in order to have AB parallel to CD, angles ABC and BCD must be equal.

As ∠ABC ≠ ∠BCD AB and CD can not be parallel

The answer is no

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The flow lines (or streamlines) of a vector field are the paths followed by a particle whose velocity field is the given vector

julia-pushkina [17]

Answer:

Question A and B are already solved for you in the picture attached.

Step-by-step explanation:

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2 years ago

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls invol

bagirrra123 [75]

Answer:

a) 0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b) 0.118 = 11.8% probability that exactly 4 of the calls involve a fax message

c) 0.904 = 90.4% probability that at least 4 of the calls involve a fax message

d) 0.786 = 78.6% probability that more than 4 of the calls involve a fax message

Step-by-step explanation:

For each call, there are only two possible outcomes. Either it involves a fax message, or it does not. The probability of a call involving a fax message is independent of other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

25% of the incoming calls involve fax messages

This means that $p = 0.25$

25 incoming calls.

This means that $n = 25$

a. What is the probability that at most 4 of the calls involve a fax message?

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$ .

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.001 + 0.006 + 0.025 + 0.064 + 0.118 = 0.214$

0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b. What is the probability that exactly 4 of the calls involve a fax message?

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

0.118 = 11.8% probability that exactly 4 of the calls involve a fax message.

c. What is the probability that at least 4 of the calls involve a fax message?

Either less than 4 calls involve fax messages, or at least 4 do. The sum of the probabilities of these events is 1. So

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$ . Then

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.096 = 0.904$

0.904 = 90.4% probability that at least 4 of the calls involve a fax message.

d. What is the probability that more than 4 of the calls involve a fax message?

Very similar to c.

$P(X \leq 4) + P(X > 4) = 1$

From a), $P(X \leq 4) = 0.214)$

Then

$P(X > 4) = 1 - 0.214 = 0.786$

0.786 = 78.6% probability that more than 4 of the calls involve a fax message

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2 years ago

The quotient of the sum of 2t and 2, twice the cube of s

natali 33 [55]

Answer: $\frac{2t+2}{2s^3}$

Step-by-step explanation:

Since you did not indicate what you need to do, I assume that you have to write an expression using the sentence given in the problem.

In order to solve this exercise, it is importat to remember the following information:

1. The quotient is the result of a division.

2. The sum is the result of an addition.

3. The word "twice" indicates a multiplicatio by 2.

4. The word "cube" indicates an exponent 3.

Then, keeping on mind the explained above and the data given in the exercise, you know that:

-The sum of $2t$ and $2$ can be expressed as:

$2t+2$

- Twice the cube of $s$ can be expressed in the following form:

$2s^3$

Therefore, you can dermine that "the quotient of the sum of $2t$ and $2$ and twice the cube of $s$ " is represented with the following expression:

$\frac{2t+2}{2s^3}$

O

8 0

2 years ago

Which sets of numbers contain whole numbers? Check all that apply. Negative 2 and StartFraction 5 Over 6 EndFraction, negative 5

Zigmanuir [339]

Answer:

The whole numbers are 0 and 79.

Step-by-step explanation:

The numbers provided are as follows:

$-2\frac{5}{6},\ -54,\ -4,\ -57,\ -89,\ 79,\ \frac{6}{9},\ \\\\-19\frac{2}{3},\ \frac{2}{4},\ 0,\ \frac{2}{7},\ -3,\ -2, -7,\ -8,\ \\\\\frac{1}{8},\ -\frac{4}{8},\ 1\frac{3}{8},\ -\frac{7}{8}$

Whole numbers are a set of natural positive numbers and 0. This set basically consists of counting discrete numbers.

Such as: 0, 1, 2, 3, 4, 5....

From the provided set of numbers the whole numbers are:

S = {79 and 0}

Thus, the whole numbers are 0 and 79.

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2 years ago

the graph of g(x) is a translation of the function f(x) = x2. the vertex of g(x) is located 5 units above and 7 units to the rig

bulgar [2K]

Translation of 7 units to the right ⇒ subtract 7 units to the argument ⇒ f(x-7)

Translation of 5 units up ⇒ add 5 units to the function ⇒ f(x) + 5

g(x) = f (x-7) + 5 = (x-7)^2 + 5

The subtraction of 7 units to the argument of the function (this is x) translates the function 7 units to the right.

Adding 5 units to the function f, translates the graph 5 units up.

6 0

2 years ago

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