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vagabundo [1.1K]
2 years ago
12

Caleb is participating in a walk-a-thon. His goal is to walk as far as possible over an 8-hour period.

Mathematics
1 answer:
luda_lava [24]2 years ago
6 0

Caleb is participating in a walk-a-thon. His goal is to walk as far as possible over an 8-hour period.

For the first 3 hours, he keeps a steady pace of 2 miles per hour.

He then stops walking while he takes a 1-hour break for lunch.

It's too short. Write at least 20 characters to explain it well.

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What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio? Negative one-eleventh
Elden [556K]

The location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is \frac{1}{11}.

The given parameters:

  • <em>Partition of the line segment = 5:6</em>

The total segment of the directed line segment from D to E in the given ratio of 5:6 is calculated as follows;

total segment = 5 + 6 = 11

The value of each partition on the directed line segment is calculated as follows;

partition = \frac{1}{11} \times distance

The distance between point D and point E is calculated as follows;

D = 5 - (-4)\\\\D = 5 + 4\\\\D = 9

The partition of the two points (D to E) is calculated as follows;

partition = \frac{1}{11} \times 9 = 0.82

Thus, we can conclude that, the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is \frac{1}{11}.

Learn more about partition of line segments here: brainly.com/question/4429522

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2 years ago
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PLEASE HELP! Points A and B split the circle into two arcs. Measure of minor arc is 150°. Point M splits major arc with the rati
SashulF [63]

Answer:

30 degrees

Step-by-step explanation:

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Step-by-step explanation:

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2 years ago
A photo of a beetle in a science book is increased to 535​% as large as the actual size. If the beetle is 14 ​millimeters, what
AnnZ [28]

Answer: 74.9 millimeters

Step-by-step explanation:

From the question, a photo of a beetle in a science book was.increased to 535​% as large as its actual size and the beetle.has a actual size of 14 ​millimeters,

The size of the beetle on the photo will be 535% of 14 millimeters. This will be:

= 535% of 14

= 535/100 × 14

= 5.35 × 14

= 74.9 millimeters

4 0
3 years ago
In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacem
Damm [24]

Answer:

a) P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) = 0,7120   or 71,2 %

c) P(C) = 0,2055  or P(C) = 20,55 %

Step-by-step explanation:

We will use two concepts in solving this problem.

1.- The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

2.- If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

a) The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )!    ⇒  C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!  

C ( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2    ⇒  C ( 24,4) =  10626

TE = 10626

Splitting the group of tanks in two 6 with h-v  and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3)  = 6 * 18! / 3!*15!  =  18*17*16*15!/15!

FE =  4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) will be the probability of at least 1 tank contains h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

The total number of favorable events for the ocurrence of P is C (18,4)

FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

FE = 18*17*16*15/4*3*2  = 3060

Then P = 3060/10626

P = 0,2879

And the probability we are looking for is

P(B) = 1 - 0,2879

P(B) = 0,7120   or 71,2 %

c) We call P(C) the probability of finding exactly 1 tank with h-v and t-i

having 4 with t-i tanks is:

reasoning the same way but now having 4 with t-i (impurities) number of favorable events is:

FE = 6*4* C(14,2) = 24 * 14!/12!*2!

FE = 24* 14*13*12! / 12!*2

FE = 24*14*13/2    ⇒  FE = 2184

And again as the TE = 10626

P(C) = 2184/ 10626

P(C) = 0,2055  or P(C) = 20,55 %

5 0
3 years ago
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