1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fantom [35]
3 years ago
13

Look at the picture

Mathematics
1 answer:
IRISSAK [1]3 years ago
7 0

Answer:

x = 10

Step-by-step explanation:

In the last step, you can see that the fraction \frac{1}{5} has been multiplied by its reciprocal \frac{5}{1}, making it cancel out. The reciprocal has been multiplied to both sides, so all you need to do is multiply \frac{6}{3} · \frac{5}{1} :

6 · 5 = 30

3 · 1 = 3

<u><em>So now you should have the fraction:</em></u>

x = \frac{30}{3}

<u><em>But, you can still simplify the fraction by dividing 30 by 3:</em></u>

x = 10

You might be interested in
There are 4,389 dogwood trees in the state park. The park workers are going to plant 342 more trees. How many trees will there b
Dmitrij [34]

Answer:

4731

Step-by-step explanation:

4,389+342=4,731

6 0
3 years ago
An urn contains n white balls andm black balls. (m and n are both positive numbers.) (a) If two balls are drawn without replacem
Genrish500 [490]

DISCLAIMER: Please let me rename b and w the number of black and white balls, for the sake of readability. You can switch the variable names at any time and the ideas won't change a bit!

<h2>(a)</h2>

Case 1: both balls are white.

At the beginning we have b+w balls. We want to pick a white one, so we have a probability of \frac{w}{b+w} of picking a white one.

If this happens, we're left with w-1 white balls and still b black balls, for a total of b+w-1 balls. So, now, the probability of picking a white ball is

\dfrac{w-1}{b+w-1}

The probability of the two events happening one after the other is the product of the probabilities, so you pick two whites with probability

\dfrac{w}{b+w}\cdot \dfrac{w-1}{b+w-1}=\dfrac{w(w-1)}{(b+w)(b+w-1)}

Case 2: both balls are black

The exact same logic leads to a probability of

\dfrac{b}{b+w}\cdot \dfrac{b-1}{b+w-1}=\dfrac{b(b-1)}{(b+w)(b+w-1)}

These two events are mutually exclusive (we either pick two whites or two blacks!), so the total probability of picking two balls of the same colour is

\dfrac{w(w-1)}{(b+w)(b+w-1)}+\dfrac{b(b-1)}{(b+w)(b+w-1)}=\dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

<h2>(b)</h2>

Case 1: both balls are white.

In this case, nothing changes between the two picks. So, you have a probability of \frac{w}{b+w} of picking a white ball with the first pick, and the same probability of picking a white ball with the second pick. Similarly, you have a probability \frac{b}{b+w} of picking a black ball with both picks.

This leads to an overall probability of

\left(\dfrac{w}{b+w}\right)^2+\left(\dfrac{b}{b+w}\right)^2 = \dfrac{w^2+b^2}{(b+w)^2}

Of picking two balls of the same colour.

<h2>(c)</h2>

We want to prove that

\dfrac{w^2+b^2}{(b+w)^2}\geq \dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

Expading all squares and products, this translates to

\dfrac{w^2+b^2}{b^2+2bw+w^2}\geq \dfrac{w^2+b^2-b-w}{b^2+2bw+w^2-b-w}

As you can see, this inequality comes in the form

\dfrac{x}{y}\geq \dfrac{x-k}{y-k}

With x and y greater than k. This inequality is true whenever the numerator is smaller than the denominator:

\dfrac{x}{y}\geq \dfrac{x-k}{y-k} \iff xy-kx \geq xy-ky \iff -kx\geq -ky \iff x\leq y

And this is our case, because in our case we have

  1. x=b^2+w^2
  2. y=b^2+w^2+2bw so, y has an extra piece and it is larger
  3. k=b+w which ensures that k<x (and thus k<y), because b and w are integers, and so b<b^2 and w<w^2

4 0
3 years ago
A town's yearly snowfall in inches over a 10-year period is recorded in this table. What is the mean of the snowfall amounts?
lawyer [7]
So to find the mean you add them all together and divide by the number of numbers there is so 11+15+19+17+23+20+17+18+21=174 and there are 10 numbers so it would be 174/10 which is 17.4 so you answer is 17.4
4 0
3 years ago
Hurry plz What is the area of the given circle?
nevsk [136]

Answer:

<em>600π feet</em>

Step-by-step explanation:

<em>If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.</em>

3 0
3 years ago
Read 2 more answers
Which ordered pair is a solution of the system?
kenny6666 [7]
Y = -2x - 4

x + 4y = 19
x + 4(-2x - 4) = 19
x + (-8x) - 16 = 19
-7x - 16 = 19
-7x = 35
-x = 5
x = -5

y = -2x - 4
y = -2(-5) - 4
y = 10 -4
y = 6

Solution set {-5, 6} (C)
3 0
3 years ago
Other questions:
  • What is the area of a regular nonagon with 10 cm sides and an apothem if 6cm?
    15·1 answer
  • Solve the linear equation. X + 5 = -2 ​
    7·2 answers
  • The total number of running yards in a football game was less than 100.The inequality x &lt; 100 represents the situation. Which
    7·2 answers
  • I need help trying to figure this out I think I have and answer but I want to make sure.
    11·1 answer
  • Let H be the set of all points of the form ​(s,sminus​1). Determine whether H is a vector space. If it is not a vector​ space, d
    12·1 answer
  • Steve purchases mushrooms at the grocery
    13·2 answers
  • HELPPP PLEASEEEEEEEEEEEEE
    13·2 answers
  • PLEASE HELP ME GUYS OR I WONT PASS <br>this calculus!!!!​
    13·1 answer
  • For triangle ABC with sides a,b and c the law of cosines states
    13·1 answer
  • PLEASE HELP FAST!!!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!