Ask question

Ask question

All categories

3 years ago

5

A university is building a new student center that is two- thirds the distance from the arts center to the residential complex.

What are the coordinates of the new center? Explain.
The points are (1, 9) and (9, 3)

1 answer:

Natasha2012 [34]3 years ago

7 0

Answer:

$C = (\frac{21}{5},\frac{33}{5})$

Step-by-step explanation:

Given

Points: (1, 9) and (9, 3)

Ratio = 2/3

Required

Determine the coordinate of the center

Represent the ratio as ratio

$Ratio = 2:3$

The new coordinate can be calculated using

$C = (\frac{mx_2 + nx_1}{n + m},\frac{my_2 + ny_1}{n + m})$

Where

$(x_1,y_1) = (1, 9)$

$(x_2, y_2) = (9, 3)$

$m:n = 2:3$

Substitute these values in the equation above

$C = (\frac{2 * 9 + 3 * 1}{3 + 2},\frac{2 * 3 + 3 * 9}{2 + 3})$

$C = (\frac{18 + 3}{5},\frac{6 + 27}{5})$

$C = (\frac{21}{5},\frac{33}{5})$

Hence;

<em>The coordinates of the new center is </em> $C = (\frac{21}{5},\frac{33}{5})$ <em></em>

You might be interested in

From a group of six people, two individuals are to be selected at random. how many possible selections are there

Murrr4er [49]

You can do C(6,2) which gives $6*5/2$ which is 15!

6 0

3 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

So

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

For the following right triangle find the side length x

sertanlavr [38]

Since there is a right angle, you can use Pythagoras' Theorem:

So x = √(24² + 7²) = 25

---------------------------------------------------------

Answer:

25

6 0

3 years ago

Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. U

babunello [35]

Answer:

Step-by-step explanation:

We can solve this question using proportion

Perimeter of the square/Time is takes to unlock

We are told in the question that:

The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds.

Hence, the perimeter of the square after 1.5 seconds is:.x = unknown

32/2.5 = x/1.5

Cross Multiply

2.5x = 32 × 1.5

x = 32 × 1.5/2.5

x = 19.2 centimeters

4 0

2 years ago

A circle had a sector with area 33pi and central angle of 11/6pi radians

MissTica

Answer:

The area of the circle is $36\pi\ units^{2}$

Step-by-step explanation:

we know that

The area of a circle subtends a central angle of $2\pi$ radians

so

By proportion find the area of the circle

$\frac{33\pi }{(11\pi /6)}=\frac{x}{2\pi}\\ \\ x=2\pi*( 33*6)/11\\ \\x=36\pi\ units^{2}$

3 0

3 years ago

Read 2 more answers