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Pani-rosa [81]

This problem can be solved using probability, the equation of the probability of an event A is P(A)= favorable outcomes/possible outcomes. The interception of two probable events is P(A∩B)= P(A)P(B).

There are 12 black marbels, 10 red marbles, and 18 white marbels, all the same size. If two marbles are drawn from the jar without being replaced.

The total of the marbles is 40.

If two marbles are drawn from the jar without being replaced, what would the probability be:

1. of drawing two black marbles?

The probability of drawing one black marble is (12/40). Then, the probability of drawing another black marble after that is (11/39) due we drawing one marble before.

P(Black∩Black) = (12/40)(11/39) = 132/1560, simplifying the fraction:

P(Black∩Black) = 11/130

2. of drawing a white, then a black marble?

The probability of drawing one white marble is (18/40). Then, the probability of drawing then a black marble after that is (12/39) due we drawed one marble before.

P(White∩Black) = (18/40)(12/39) = 216/1560, simplifying the fraction:

P(White∩Black) = 9/65

3. of drawing two white marbles?

The probability of drawing one white marble is (18/40). Then, the probability of drawing another white marble after that is (17/39) due we drawed one marble before.

P(White∩White) = (18/40)(17/39) = 306/1560, simplifying the fraction:

P(White∩White) = 51/260

4. of drawing a black marble, then a red marble?

The probability of drawing one black marble is (12/40). Then, the probability of drawing then a red marble after that is (10/39) due we drawed one marble before.

P(Black∩Red) = (12/40)(10/39) = 120/1560, simplifying the fraction:

P(Black∩Red) = 1/13

4 0

3 years ago

What is the product?

Alexxandr [17]

The correct answer is a)

3 0

3 years ago

Skylar owns a trucking company. For every truck that goes out, Skylar must pay the driver $11 per hour of driving and also has a

jeyben [28]

Answer:

The set of needed equations is

h = 30 m

11 m + 3 h = 909 where

the driver drove for m hours.

h : distance covered in m hours

Step-by-step explanation:

Here, according to the question:

The per hour rate of driver = $11

The gas maintenance expense = $3 per mile.

The total distance covered by drives is 30 miles per hour.

The total expenses paid to driver = $909

Now, let us assume the driver drove for m hours.

The average speed of driver was 30 miles / hour

⇒ Driver covers 30 miles in 1 hour

SO, distance covered in m hours = h = m x 30 = 30 m

or, h = 30 m

So,according to the question, the total amount paid :

Charges of m hours driving + maintenance charges for h miles

= 11 m + 3( h)

or, 11 m + 3 h = $909

Hence the set of needed equations is

h = 30 m

11 m + 3 h = 909

4 0

3 years ago

What is the solution to the system of two equations shown?

Nadya [2.5K]

The solution of the given system of equation is x = -3 and y = 4 respectively.

<h3>What is a system of linear equations?</h3>

A system of linear equations can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.

The given system of equations is as,

y = 4x + 16 (1)

y = −2x − 2 (2)

In order to solve them, substitute equation (2) into (1) as follows,

4x + 16 = −2x − 2

=> 4x + 2x = -2 - 16

=> 6x = -18

=> x = -3

Then, y = -2 × -3 - 2 = 4

Hence, the solution of the given system of equation is x = -3 and y = 4.

To know more about system of equations click on,

brainly.com/question/24065247

#SPJ1

6 0

9 months ago

When the expression $-2x^2-20x-53$ is written in the form $a(x+d)^2+e$, where $a$, $d$, and $e$ are constants, then what is the

Sladkaya [172]

We start with $2 x^{2} -20x-53$ and wish to write it as $a(x+d) ^{2} +e$

First, pull 2 out from the first two terms: $2( x^{2} -10x)-53$

Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have $x^{2} -10x$ and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square: $x^{2} -10x+25=(x-5) ^{2}$

The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have $2( x-5) ^{2}-53$ and when we multiply that out it does not give us what we started with. It gives us $2 x^{2} -20x+50-53=2 x^{2} -20x-3$

So you see our expression is not right. It should have a -53 but instead has a -3. So to correct it we need to subtract another 50.

We do this as follows: $2(x-5) ^{2}-53-50$ which gives us the final expression we seek:

$2(x-5) ^{2}-103$

If you multiply this out you will get the exact expression we were given. This means that:
a = 2
d = -5
e = -103

We are asked for the sum of a, d and e which is 2 + (-5) + (-103) = -106

7 0

3 years ago