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3 years ago

Identify the segments that are parallel, if any, if ∠DCB and ∠CDA are supplementary.

Mathematics

1 answer:

Triss [41]3 years ago

8 0

Answer:

Step-by-step explanation:

We are given that

$\angle$ DCB and $\angle$ CDA are supplementary.

We have to identify the parallel segments if $\angle$ DCB and $\angle$ CDA are supplementary.

Supplementary angles: If the angles are supplementary then the sum of two angles is 180 degrees.

Therefore,

$\angle DCB+\angle CDA=180^{\circ}$

Therefore, angle DCB and angle CDA are interior angles .

Because CA is a transversal line and sum of interior angles is 180 degrees.

When the sum of interior angles formed between two lines and on same side of transversal line is 180 degrees. Then the lines are parallel.

Therefore, angle DCB and angle CDA are formed between line AD and BC.

Hence, AD is parallel to BC.

Option C is correct.

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Travelers who fail to cancel their hotel reservations when they have no intention of showing up are commonly referred to as no-s

notsponge [240]

Answer:

a) 0.0523 = 5.23% probability that at least two of the four selected will turn to be no-shows.

b) 0 is the most likely value for X.

Step-by-step explanation:

For each traveler who made a reservation, there are only two possible outcomes. Either they show up, or they do not. The probability of a traveler showing up is independent of other travelers. This means that the binomial probability distribution is used 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.

No-show rate of 10%.

This means that $p = 0.1$

Four travelers who have made hotel reservations in this study.

This means that $n = 4$

a) What is the probability that at least two of the four selected will turn to be no-shows?

This is $P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)$

In which

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

$P(X = 2) = C_{4,2}.(0.1)^{2}.(0.9)^{2} = 0.0486$

$P(X = 3) = C_{4,3}.(0.1)^{3}.(0.9)^{1} = 0.0036$

$P(X = 4) = C_{4,4}.(0.1)^{4}.(0.9)^{0} = 0.0001$

$P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.0486 + 0.0036 + 0.0001 = 0.0523$

0.0523 = 5.23% probability that at least two of the four selected will turn to be no-shows.

b) What is the most likely value for X?

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

$P(X = 0) = C_{4,0}.(0.1)^{0}.(0.9)^{4} = 0.6561$

$P(X = 1) = C_{4,1}.(0.1)^{1}.(0.9)^{3} = 0.2916$

$P(X = 2) = C_{4,2}.(0.1)^{2}.(0.9)^{2} = 0.0486$

$P(X = 3) = C_{4,3}.(0.1)^{3}.(0.9)^{1} = 0.0036$

$P(X = 4) = C_{4,4}.(0.1)^{4}.(0.9)^{0} = 0.0001$

X = 0 has the highest probability, which means that 0 is the most likely value for X.

7 0

2 years ago

I think of a number, add 8 to it and the result is 14. Find the number

Leya [2.2K]

Answer:

Step-by-step explanation:

The equation for this would be:

n+8=14, since we are adding 8 to a number and getting 14

To solve, isolate the variable n, by subtracting 8 from both sides

n+8=14

n+8-8=14-8

n=6

The number is 6

3 0

2 years ago

Read 2 more answers

Slope intercept form that passes though the point (-2,-3) and has a slope of 5/2

olganol [36]

$\text{Given that,}\\\\(x_1,y_1) = (-2,-3), ~~\text{and slope,}~~m = \dfrac 52\\\\\\\text{Now,}\\\\y -y_1 =m(x-x_1)\\\\\implies y +3 = \dfrac52 (x+2)\\\\\implies y = \dfrac 52(x+2) -3\\\\\\\implies y = \dfrac{5}2 x + 5 -3 \\\\\\\implies y = \dfrac 52 x + 2\\\\\\\text{This is the slope-intercept form(y =mx+b)}.$

8 0

2 years ago

Read 2 more answers

Please answer this :))))

Anton [14]

Answer:

Answer is E hope this helps :)

Step-by-step explanation:

8 0

2 years ago

A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterl

dusya [7]

There is a missing content in the question.

After the statements and before the the options given; there is an omitted content which says:

Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?

Answer:

C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).

Step-by-step explanation:

From the given question:

The resulting regression equation can be represented as:

$\hat Y = 3.37 + 0.117 X - 0.083 Q_1 + 1.28 Q_2 + 0.617Q_3$

where;

the estimated number of contracts in a quarter X is the coded quarterly value with X = 0

the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise

Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise

Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise

Our null and alternative hypothesis can be stated as;

Null hypothesis :

$H_0 :$ The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05)

$H_a:$ The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From the missing omitted part we added above; we can see that the t-statistics value = 9.08 and the p-value = 0.000 .

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

4 0

3 years ago