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Nataly_w [17]
3 years ago
14

Sanjay, Colby, and Arpitha are training to run a marathon. On Saturday, Sanjay ran StartRoot 125 EndRoot miles, Colby ran 13 mil

es, and Arpitha ran the shortest route from the library to her house, as shown in the diagram.
A right triangle. The distance from the angle with measure 90 degrees to Arpitha's Home is 9 miles, and the distance to the Library is 6 miles.

Which list shows the names in order from the person who ran the shortest distance to the one who ran the greatest distance?
Colby, Sanjay, Arpitha
Sanjay, Arpitha, Colby
Sanjay, Colby, Arpitha
Arpitha, Sanjay, Colby
Mathematics
1 answer:
bija089 [108]3 years ago
7 0
Sanjay arpitha Colby
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Can someone help me with this!
Doss [256]

Answer:

<u>Please read the answers below.</u>

Step-by-step explanation:

Let's recall that in a square all its sides are equal length and all the four internal angles measure 90 °

5. If LN = 46, then we have:

OM = <u>46</u> (Same length than LN)

PN = LN/2 = 46/2 = <u>23</u>

ON = √LN²/2 = √ 46²/2 = √ 2,116/2 = √ 1,058 = <u>32.53 (Rounding to two decimal places)</u>

MN = ON = <u>32.53</u>

6. m ∠EFG = <u>90°</u>

m ∠GDH = ∠GDH/2 = 90/2 =<u> 45°</u>

m ∠FEG = ∠DEF/2 = 90/2 =<u> 45°</u>

m ∠DHG = 180 - (∠GDH + ∠DGH) = 180 - (45 + 45)= 180 - 90 = <u>90</u>°

7. Solve for x

6x - 21 = ∠PQR/2

6x - 21 = 90/2

6x - 21 = 45

6x = 45 +21

6x = 66

<u>x = 11</u>

3 0
3 years ago
The difference of the square of a number and 40 is equal to 3 times that number. Find the positive solution.
Wewaii [24]

Answer: The answer is 8.

Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;

Y^2 - 40.

Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,

Y^2 - 40 = 3Y

If we move all expressions to one side of the equation, what we would have is,

Y^2 - 3Y -40 = 0

(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)

We now have a quadratic equation

Y^2 -3Y - 40 = 0

By factorizing we now have

(Y -8) (Y + 5) = 0

Therefore Y - 8 = 0 or

Y + 5 = 0

Hence, Y = 8 or Y = -5

Since we are asked to calculate the positive solution, Y = 8

5 0
3 years ago
can someone help? I'm getting ready to slit someone's throat, I'm so irritated. I have 7 of these to do. ​
Brums [2.3K]
97.8ft^2 but if you round it to the nearest 10 it will be 100ft^2
8 0
3 years ago
1,459,327 rounded to the nearest hundred
Ratling [72]

Answer:

1,459,000

Step-by-step explanation:

8 0
3 years ago
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not
Lorico [155]

Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

  • C_x^n=n!/(n-x)!x!   (i.e. combination)
  • x= total number of successes
  • p=probability of success (p=1-q)  
  • q=probability of failure (q=1-p)
  • n=number of trials
  • P(X)= probability of total number of successes

Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155  

P(X)=0.165465  

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

P(X)=48620×0.00000689×0.0610  

P(X)=0.020  

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.

3 0
3 years ago
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