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xxTIMURxx [149]
2 years ago
13

Which of the following equations represents a line that passes through the points

Mathematics
2 answers:
Ksivusya [100]2 years ago
5 0

Step-by-step explanation:

the slope = (0+15)/(-1-4)=15/(-5)= -3

the Equation :

y+15= -3(x-4)

or

y+15 = -3x+12

y +3x=12-15

3x + y = -3

so, the correct answer is II only

lara [203]2 years ago
4 0

Answer:

y + 15 = -3(x - 4)        II only

Step-by-step explanation:

y2 - y1 / x2 - x1

0 - (-15) / -1 - 4

15 / -5

= -3

- Since the slope is -3, the answer can't be 1.

y + 15 = -3(x - 4)

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A tennis tournament has 2n contestants. We want to pair them up for the first round of singles matches. Show that the number of
ddd [48]

There are

\dbinom{2n}2 = \dfrac{(2n)!}{2! (2n-2)!}

ways of pairing up any 2 members from the pool of 2n contestants. Note that

(2n)! = 1\times2\times3\times4\times\cdots\times(2n-2)\times(2n-1)\times(2n) = (2n-2)! \times(2n-1) \times(2n)

so that

\dbinom{2n}2 = \dfrac{(2n)\times(2n-1)\times(2n-2)!}{2! (2n-2)!} = \boxed{n(2n-1)}

4 0
2 years ago
Mrs. Lewis had $100 to purchase school supplies for her class. She bought 40 glue sticks and 40 boxes of crayons. Each glue stic
ella [17]

Answer:

the answer is she had $4.40 left.

Step-by-step explanation:

1) 40x1.50=<u>60</u> 2) 40x0.89= <u>35.6</u> 3) 60+35.6= <u>95.6</u> 4) 100- 95.6= <u>$4.4</u> I hope this helps if not sorry. :)

4 0
3 years ago
A true-false question is to be posed to a husband and wife team. Both the husband and the wife will give the correct answer with
marysya [2.9K]

Answer:

Choose either strategy both are equally successful

Step-by-step explanation:

Given:-

- The probability of success for both husband (H) and wife (W) are:

                              P ( W ) = 0.8 , P ( H ) = 0.8

Find:-

- Which of the following is a better strategy for the couple?

Solution:-

Strategy 1

- First note that P ( W ) & P ( H ) are independent from one another, i.e the probability of giving correct answer of husband does not influences that of wife's.

- This strategy poses an event such that either wife knows the answer and answer it correctly or the husband knows and answers in correctly.

- We will assume that probability of either the husband or wife knowing the answer is 0.5 and the two events of knowing and answering correctly are independent. So,

                           P ( Wk ) = P (Hk) = 0.5

- The event P(S1) is:

                           P(S1) = P ( Hk & H ) + P ( Wk & W )

                           P(S1) = 0.5*0.8 + 0.5*0.8

                           P(S1) = 0.8

- Hence, the probability of success for strategy 1 is = 0.8

Strategy 2

- Both agree , then the common answer is selected otherwise, one of their answers is chosen at random.

- The success of strategy 2, will occur when both agree and are correct, wife is correct and answers while husband is not or husband is correct and he answers.

- The event P(S2) is:

                   P(S2) = P ( H & W ) + P ( H / W' & Hk ) + P ( H' / W & Wk )

                   P(S2) = P ( H & W ) + P ( H / W') P ( Hk ) + P ( H' / W) P (Wk)

                   P(S2) = P ( H & W ) + P ( H / W')*0.5  + P ( H' / W)*0.5

                   P(S2) = 0.5* [ P ( H & W ) + P ( H / W') ]  + 0.5* [ P ( H' / W) + P ( H & W )]

                   P(S2) = 0.5*P(H) + 0.5*P(W)

                   P(S2) = 0.5*0.8 + 0.5*0.8

                   P(S2) = 0.8

- Hence, the probability of success for strategy 2 is = 0.8

Both strategy give us the same probability of success.

                 

                       

4 0
3 years ago
A car travels 45km in an hour. In each of the next two hours, it travels 78km. What is the average speed of the car.
romanna [79]

Answer:

The average speed of car is 67 kilometers per hour.

Step-by-step explanation:

Given that:

Distance travelled in one hour = 45 km

Distance travelled in next 2 hours = 78*2 = 156 km

Total distance = 45+156 = 201

Total time = 1+2 =  3 hours

Average speed of the car = \frac{Total\ distance}{Total\ time}

Average speed of the car = \frac{201}{3}

Average speed of the car = 67 km/hr

Hence,

The average speed of car is 67 kilometers per hour.

7 0
3 years ago
Jose borrows $200 for 2 years at a rate of 8% simple interest calculated annually. How much will he have to pay back at the end
KatRina [158]
Annually= per year

200 at 8% the first year would be
200 • 0.08 = 16 per year
2 years = 32 dollars in interest at the end of 2 years
6 0
3 years ago
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