How many ways can two names be chosen from 76 in a raffle if only one entry per person is allowed

2 cars are 700 miles apart. They travel toward each other. One of the cars travels at 75mph, the other travels at 100 mph. How l

olga2289 [7]

Answer: C 4

Step-by-step explanation:

Use the formula: distance = rate x time

We can say that train 1 travels a distance of x, and train 2 travels a distance of 700 - x

The rate of train 1 is 75 mph, and the rate of train 2 is 100 mph

The time traveled for the two trains will be the same. We can represent that with the variable t.

We have the following equation for train 1:

x = 75t

For train 2, we have this equation:

700 - x = 100t

Use the Substitution Method by replacing x in the equation for train 2 with the value 75t.

700 - 75t = 100t

700 = 175t

700/175 = 4 hours.

It will take 4 hours for the two trains to meet.

6 0

3 years ago

A group of three undergraduate and five graduate students are available to fill certain student government posts. If four studen

creativ13 [48]

Answer:

$Pr = 0.4286$

Step-by-step explanation:

Given

Let

$U \to\\$ Undergraduates

$G \to$ Graduates

So, we have:

$U = 3; G =5$ -- Total students

$r = 4$ --- students to select

Required

$P(U =2)$

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.

First, we calculate the total possible selection (using combination)

$^nC_r = \frac{n!}{(n-r)!r!}$

So, we have:

$Total = ^{U + G}C_r$

$Total = ^{3 + 5}C_4$

$Total = ^8C_4$

$Total = \frac{8!}{(8-4)!4!}$

$Total = \frac{8!}{4!4!}$

Using a calculator, we have:

$Total = 70$

The number of ways of selecting 2 from 3 undergraduates is:

$U = ^3C_2$

$U = \frac{3!}{(3-2)!2!}$

$U = \frac{3!}{1!2!}$

$U = 3$

The number of ways of selecting 2 from 5 graduates is:

$G = ^5C_2$

$G = \frac{5!}{(5-2)!2!}$

$G = \frac{5!}{3!2!}$

$G =10$

So, the probability is:

$Pr = \frac{G * U}{Total}$

$Pr = \frac{10*3}{70}$

$Pr = \frac{30}{70}$

$Pr = 0.4286$

5 0

2 years ago

Give an example of how people have used igneous rock. PLSS GIVE ME EXAMPLE PLSSSs

bogdanovich [222]

Answer:

Granite is a one of the most common igneous rock. Its used in building materials and making statues.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 150 li

Anika [276]

Answer:

N(AUC∩B') = 121

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121

Step-by-step explanation:

Let A represent snickers, B represent Twix and C represent Reese's Peanut Butter Cups.

Given;

N(A) = 150

N(B) = 204

N(C) = 206

N(A∩B) = 75

N(A∩C) = 100

N(B∩C) = 98

N(A∩B∩C) = 38

N(Total) = 500

How many students like Reese's Peanut Butter Cups or Snickers, but not Twix;

N(AUC∩B')

This can be derived by first finding;

N(AUC) = N(A) + N(C) - N(A∩C)

N(AUC) = 150+206-100 = 256

Also,

N(A∩B U B∩C) = N(A∩B) + N(B∩C) - N(A∩B∩C) = 75 + 98 - 38 = 135

N(AUC∩B') = N(AUC) - N(A∩B U B∩C) = 256-135 = 121

N(AUC∩B') = 121

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121

See attached venn diagram for clarity.

The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is the shaded part

6 0

3 years ago

Help please, my brains is empty :o(

den301095 [7]

Answer:

I think 5 and 5 are equal so the angles are equal which are 70,70

Step-by-step explanation:

70+70+x=180

140+x=180

x=40

6 0

3 years ago