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3 years ago

AB and CD are straight line segments.

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

5 0

Answer:

<h3>i) Angle AOC is 95° </h3><h3>Reason:- Angle AOC is equal to Angle DOB since they are Vertically Opposite Angles. </h3>

<h3> ii) Angle BOC is 85° </h3><h3>Reason:- Angle AOC + Angle BOC - 180° (they lie in a straight line so they are a linear pair. Sum of the angles will be 180°) </h3><h3> Angle AOC is 95°, So:- </h3><h3> 95° + Angle BOC = 180° </h3><h3> Angle BOC= 180° - 95° </h3><h3> Angle BOC = 85° </h3><h3> </h3><h3>iii) Angle DOE is 17° </h3><h3>Reason:- Angle AOE+ Angle DOE+ Angle DOB = 180° (they lie in a straight line so they're a linear pair. Sum of the angles will be 180°) </h3><h3> So, </h3><h3> 68° + Angle DOE+ 95° = 180° </h3><h3> 163° + Angle DOE = 180° </h3><h3> Angle DOE= 180° - 163° </h3><h3> Angle DOE is 17°</h3>

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How many 1/4 cup servings are in 4 cups of oatmeal ?

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3 years ago

Read 2 more answers

Every day your friend commutes to school on the subway at 9 AM. If the subway is on time, she will stop for a $3 coffee on the w

Shtirlitz [24]

Answer:

1.02% probability of spending 0 dollars on coffee over the course of a five day week

7.68% probability of spending 3 dollars on coffee over the course of a five day week

23.04% probability of spending 6 dollars on coffee over the course of a five day week

34.56% probability of spending 9 dollars on coffee over the course of a five day week

25.92% probability of spending 12 dollars on coffee over the course of a five day week

7.78% probability of spending 12 dollars on coffee over the course of a five day week

Step-by-step explanation:

For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so $p = 0.6$

The week has 5 days, so $n = 5$

She spends 3 dollars on coffee each day the train is on time.

Probabability that she spends 0 dollars on coffee:

This is the probability of the train being late all 5 days, so it is P(X = 0).

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

$P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102$

1.02% probability of spending 0 dollars on coffee over the course of a five day week

Probabability that she spends 3 dollars on coffee:

This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).

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

$P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768$

7.68% probability of spending 3 dollars on coffee over the course of a five day week

Probabability that she spends 6 dollars on coffee:

This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).

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

$P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304$

23.04% probability of spending 6 dollars on coffee over the course of a five day week

Probabability that she spends 9 dollars on coffee:

This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).

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

$P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456$

34.56% probability of spending 9 dollars on coffee over the course of a five day week

Probabability that she spends 12 dollars on coffee:

This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).

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

$P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592$

25.92% probability of spending 12 dollars on coffee over the course of a five day week

Probabability that she spends 15 dollars on coffee:

Probability that the subway is on time all days of the week, so $P(X = 5)$ .

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

$P(X = 5) = C_{5,5}.(0.6)^{5}.(0.4)^{0} = 0.0778$

7.78% probability of spending 12 dollars on coffee over the course of a five day week

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3 years ago

Which technique for gathering data (observational study or experiment) do you think was used in the following studies?(a) The Co

miv72 [106K]

Answer:

For question a, the correct option is: This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

For question b, the correct option is: This is an experiment because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

For question c, the correct option is: This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured.

For question d, the correct option is: This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

Step-by-step explanation: To give us a background on why the options above were chosen, let us see the difference between Observational study and Experimental study.

In an observational study, the researcher draws inferences from an independent variable that is not under his/her control. While in an experimental study, there in an intervention and the effects of the intervention are studied.

Therefore, in the questions a to d above, all we need to do is identity which variables were influenced and which were merely observed.

For question a, the variables were only observed.

For question b, the variables were influenced.

For question c, the variables were also influenced.

For question d, the variables were merely observed.

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3 years ago

9dx10=240 pls hurry

vaieri [72.5K]

Answer:

2.6 or $\frac{8}{3}$

Step-by-step explanation:

9d×10=240

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2.6 or $\frac{8}{3}$

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2 years ago

Kaylee drove her scooter at an average speed of 15 miles per hour. Sophia drove her scooter at an average speed of 10 miles per

maksim [4K]

Answer:

Kaylee drove her scooter for 2h and Sophia drove her scooter for 3h.

Step-by-step explanation:

From the graph shown below, we can see that the intersection point is (2,3). When using the graphing method to solve a system of equations, the intersection point is the answer. In this case, x = 2 and y = 3.

Thus, Kaylee drove her scooter for 2h and Sophia drove her scooter for 3h.

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3 years ago