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2 years ago

Find the following angle measures. mEAD = ° mCAB = °

Mathematics

2 answers:

Dimas [21]2 years ago

8 0

29 and 119
Just did it :(

sergejj [24]2 years ago

6 0

Part 1) Find m∠EAD

we know that

m∠EAD+m∠DAF+m∠BAF= $180\°$ ----> by supplementary angles

solve for m∠EAD

m∠EAD= $180\°$ -(m∠DAF+m∠BAF)

in this problem we have

m∠DAF= $90\°$

m∠BAF= $61\°$

substitute in the formula above

m∠EAD= $180\°-90\°-61\°=29\°$

therefore

the answer part 1) is

m∠EAD= $29\°$

Part 2) Find m∠CAB

we know that

m∠CAB+m∠BAF= $180\°$ --------> by supplementary angles

solve for m∠CAB

m∠CAB= $180\°$ -m∠BAF

in this problem we have

m∠BAF= $61\°$

substitute in the formula above

m∠CAB= $180\°-61\°=119\°$

therefore

the answer part 2) is

m∠CAB= $119\°$

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Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the proba

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Answer:

(a) Probability mass function

P(X=0) = 0.0602

P(X=1) = 0.0908

P(X=2) = 0.1704

P(X=3) = 0.2055

P(X=4) = 0.1285

P(X=5) = 0.1550

P(X=6) = 0.1427

P(X=7) = 0.0390

P(X=8) = 0.0147

NOTE: the sum of the probabilities gives 1.0068 for rounding errors. It can be divided by 1.0068 to get the adjusted values.

(b) Cumulative distribution function of X

F(X=0) = 0.0602

F(X=1) = 0.1510

F(X=2) = 0.3214

F(X=3) = 0.5269

F(X=4) = 0.6554

F(X=5) = 0.8104

F(X=6) = 0.9531

F(X=7) = 0.9921

F(X=8) = 1.0068

Step-by-step explanation:

Let X be the number of people who arrive late to the seminar, we can assess that X can take values from 0 (everybody on time) to 8 (everybody late).

For X=0

This happens when every couple and the singles are on time (ot).

$P(X=0)=P(\#1=ot)*P(\#2=ot)*P(\#3=ot)*P(\#4=ot)*P(\#5=ot)\\\\P(X=0)=(1-0.43)^{5}=0.57^5= 0.0602$

For X=1

This happens when only one single arrives late. It can be #4 or #5. As the probabilities are the same (P(#4=late)=P(#5=late)), we can multiply by 2 the former probability:

$P(X=1) = P(\#4=late)+P(\#5=late)=2*P(\#4=late)\\\\P(X=1) = 2*P(\#1=ot)*P(\#2=ot)*P(\#3=ot)*P(\#4=late)*P(\#5=ot)\\\\P(X=1) = 2*0.57*0.57*0.57*0.43*0.57\\\\P(X=1) = 2*0.57^4*0.43=2*0.0454=0.0908$

For X=2

This happens when

1) Only one of the three couples is late, and the others cooples and singles are on time.

2) When both singles are late , and the couples are on time.

$P(X=2)=3*(P(\#1=l)*P(\#2=ot)*P(\#3=ot)*P(\#4=ot)*P(\#5=ot))+P(\#1=ot)*P(\#2=ot)*P(\#3=ot)*P(\#4=l)*P(\#5=l)\\\\P(X=2)=3*(0.43*0.57^4)+(0.43^2*0.57^3)=0.1362+0.0342=0.1704$

For X=3

This happens when

1) Only one couple (3 posibilities) and one single are late (2 posibilities). This means there are 3*2=6 combinations of this.

$P(X=3)=6*(P(\#1=l)*P(\#2=ot)*P(\#3=ot)*P(\#4=l)*P(\#5=ot))\\\\P(X=3)=6*(0.43^2*0.57^3)=6*0.342=0.2055$

For X=4

This happens when

1) Only two couples are late. There are 3 combinations of these.

2) Only one couple and both singles are late. Only one combination of these situation.

$P(X=4)=3*(P(\#1=l)*P(\#2=l)*P(\#3=ot)*P(\#4=ot)*P(\#5=ot))+P(\#1=l)*P(\#2=ot)*P(\#3=ot)*P(\#4=l)*P(\#5=l)\\\\P(X=4)=3*(0.43^2*0.57^3)+(0.43^3*0.57^2)\\\\P(X=4)=3*0.0342+ 0.0258=0.1027+0.0258=0.1285$

For X=5

This happens when

1) Only two couples (3 combinations) and one single are late (2 combinations). There are 6 combinations.

$P(X=6)=6*(P(\#1=l)*P(\#2=l)*P(\#3=ot)*P(\#4=l)*P(\#5=ot))\\\\P(X=6)=6*(0.43^3*0.57^2)=6*0.0258=0.1550$

For X=6

This happens when

1) Only the three couples are late (1 combination)

2) Only two couples (3 combinations) and one single (2 combinations) are late

$P(X=6)=P(\#1=l)*P(\#2=l)*P(\#3=l)*P(\#4=ot)*P(\#5=ot)+6*(P(\#1=l)*P(\#2=l)*P(\#3=ot)*P(\#4=l)*P(\#5=ot))\\\\P(X=6)=(0.43^3*0.57^2)+6*(0.43^4*0.57)\\\\P(X=6)=0.0258+6*0.0195=0.0258+0.1169=0.1427$

For X=7

This happens when

1) Only one of the singles is on time (2 combinations)

$P(X=7)=2*P(\#1=l)*P(\#2=l)*P(\#3=l)*P(\#4=l)*P(\#5=ot)\\\\P(X=7)=2*0.43^4*0.57=0.0390$

For X=8

This happens when everybody is late

$P(X=8)=P(\#1=l)*P(\#2=l)*P(\#3=l)*P(\#4=l)*P(\#5=l)\\\\P(X=8) = 0.43^5=0.0147$

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1 year ago

Jeremiah and Tristan work at a dry cleaners ironing shirts. Jeremiah can iron 35 shirts per hour, and Tristan can iron 20 shirts

laiz [17]

The number of hours Jeremiah ironed = 10 hours

The number of hours Tristan ironed = 7 hours

Step-by-step explanation:

Jeremiah can iron = 35 shirts per hour
Tristan can iron = 20 shirts per hour
Total work done by both = 490 shirts

Let 'x' be the number of hours Jeremiah ironed.

Let 'y' be the number of hours Tristan ironed.

x+y = 17 ------(1)

35x + 20y = 490 -------(2)

Multiply (1) by 20 and subtract (2) from (1),

20x + 20y = 340

-(35x + 20y = 490)

-15x = -150

x = 150/15

x = 10

Substitute x=10 in (1)

10+y = 17

y = 7

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1 year ago

The Godari family is planning to build a new patio in their backyard. They haven’t decided how big it will be, but they know the

ioda

Let the letter $l$ represent the length of the patio. From the question we already know that the relationship between the length and the width ( $w$ ) of the patio are:

$l=2w-5$

1. The relationship between the width and the length is linear because it involves only the power/exponent of 1. In other words, $l$ is raised to the power 1 and $w$ too is raised to the power of 1 in the equation $l=2w-5$ .

2. Because both the width and the length are in feet, when graphing this relationship, the appropriate units would be feet.

We may take 1 cm to be 1 ft in both the x and the y axes.

3. For this part a table has been attached.

As can be seen from the table, width of 2 ft gives us length to be -1 ft and that is an absurdity.

Width of 10 ft gives a length of 15 ft which does make sense and that is acceptable because we do not want a square patio and means width and length should not be the same. Same is the analysis for width of 50 feet. We get the length to be 95 feet. Again, the patio will not be a square but a rectangle as is the requirement.

Thus, for widths of 10 and 50 only is the Godari Family's patio possible from the given data and the given relationship between the length and the width.

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1 year ago

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sasho [114]

Answer:

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(2) a parameter, because it is a numerical summary for a population.

(3) a statistic, because it is a numerical summary for a sample.

Step-by-step explanation:

We are given that it has been reported that 5% of all undergraduate students in the U.S. who take an introductory statistics course will continue their education in statistics.

A random sample of 400 students from this list was selected. Of the 400 undergraduate students, 80 (or 20%) did continue their education in statistics.

(1) In this study, the population of interest is;

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(2) In this study, the 5% value could be considered a parameter, because it is a numerical summary for a population which states that this value represents all undergraduate students in the U.S. who take an introductory statistics course will continue their education in statistics.

(3) In this study, the 20% value can be considered a statistic, because it is a numerical summary for a sample which represents the % of students who did continue their education in statistics out of the 400 selected undergraduate students.

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