consider two boxes, one containing 1 black and 1 white marble, and other 2 black and 1 white marble. a box is selected at random, and a marble is drawn from it at random. what is the probability that the marble is black? what is the probability that the first box was the one selected given that the marble is white?

Answer:

Step-by-step explanation:

take length as x,

perimeter= 28cm

Answer:

28cm

Step-by-step explanation:

7+7+7+7

The rationalized form of the surd is;

1) 25/13

2) 144/3

3) 36

We have to note that the term surd would have to refer to an irrational number as we know it.

1) The conjugate of the surd is;

5/4 + √3

Rationalizing we have;

5/4 -  √3 * 5/4 + √3

25/16 + 4√3 - 4√3 -3

25/13

2) The conjugate is √7 - 2

Rationalizing we have;

12/√7 + 2  * 12/√7 - 2

144/7 -2√7 + 2√7 -4

144/3

3) The conjugate of the surd is √2 + √3

Rationalizing we have;

6/ √2 -  √3  * 6/ √2 + √3

36/4 +√6 - √6 - 3

36/1 = 36

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By applying the Pythagorean theorem to the provided question, we can say that in this triangle =>

AC =[tex]\sqrt{115}[/tex]

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Pythagorean theorem applies here, in this triangle

AC = [tex]A^2 + B^2[/tex]

AC  = [tex]\sqrt{14^2 -9^2}[/tex]

AC = [tex]\sqrt{115}[/tex]

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Danielle's sales last week were $. At her job at an electronics store, Danielle receives a  $4,295.16 commission on every sale.

What is an electronics store?

Let's start by first finding out how much commission Danielle earned last week. We know that her total earnings were $1,058.25 and her base salary was $725 per week. Therefore, her commission must have been:

                          $1,058.25 - $725 = $333.25

We also know that Danielle earns a 7.75% commission on everything she sells. Let's use "x" to represent her total sales last week. Then we can set up an equation to solve for x:

                                   0.0775x = $333.25

Solving for x, we get:

x = $333.25 / 0.0775

x = $4,295.16

Therefore, Danielle's sales last week were $4,295.16.

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The answers include the following:

This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.

Sport article or research or record a sports new cast will be able to predict the outcome of this race due to the data being gathered which will provide more information about the race.

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Answer:

Step-by-step explanation:

4 = d

5=1/5

3 the first one is 4x1/12 and 2x3/12

The value of sin (θ/2) in the trigonometry is π/9

Information given in the problem

tan θ = 7/8,

where

0 < θ <  π/2

solving for θ, from tan θ = 7/8

tan θ = 7/8

θ = arc tan (7/8)

θ = 0.7188 radians

soling for sin (θ/2)

= sin (θ/2)

= sin (0.7188/2)

= 0.3517 approximately π / 9

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To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Six triangles are needed for each hexagon.

To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Each hexagon requires six triangles to make it, so two hexagons would need double that amount. Since the pattern blocks come in the shapes of triangles, you can easily construct the hexagons by placing the triangles together. Each triangle has two sides that fit together and two sides that overlap, so the six triangles will create a complete hexagon when they are all put together. Once you have two hexagons constructed, they will fit together to make a larger shape, depending on how you place them. With this method, you can easily make two hexagons out of pattern blocks.

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Answer:

Step-by-step explanation:

is this a bot or girl

Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer: x = 365

Step-by-step explanation:

find the angle bisector and divide and multiply it

Answer:

Step-by-step explanation:

7/x^-8 = 7x^8

Answer:  x=3, y=-1

Step-by-step explanation:

2x+y=5

2y=2x-8

In equation 1, y=5-2x.

Substitute this value in equation 2.

2(5-2x)=2x-8

10-4x=2x-8

Thus,

4x+2x=10+8 (collecting terms)

6x=18

x=3

Now, we said earlier that y=5-2x.

Therefore, y=5-2(3) [because x=3]

y=5-6

y=-1

Hope this helps :]

Total ways can 4 seniors and 2 juniors be chosen to participate in a charity event is 1,91,100.

There are 16 seniors and 15 juniors in a particular social organization and

4 seniors and 2 juniors had to be chosen to participate in a charity event.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by [tex]^nC_r[/tex] and it is given by,                   [tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex] , where 0 ≤ r ≤ n.

Therefore the total ways that 4 seniors and 2 juniors be chosen to participate in a charity event = [tex]^{16}C_{4}.^{15}C_{2}[/tex]

= [tex]\frac{16!}{4!(16-4)!}$\times \frac{15!}{2!(15-2)!}[/tex]

= 1820 × 105

= 1,91,100

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The complete question is:

There are 16 seniors and 15 juniors in a particular social organization. In how many ways can 4 seniors and 2 juniors be chosen to participate in a charity event?

Answer: x is anything from the set {2, 3, 5, 7, 11}

This is the list of primes between 1 and 11. The value 1 is not prime.

We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.

When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.

An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.

Using this property, we can expand the expression as follows:

(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)

Now we can simplify each term separately:

2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110

and

−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165

Therefore, putting the results together, we have:

(2 − 3)(7 2 − + 8) = 110 − 165 = -55

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Step-by-step explanation:

Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.

The surface area of the solid is the sum of all of the areas of its faces.

The area of a right triangle is a well-known formula. You should already know this.

Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.

If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.

Option A: (2, 1)

Substituting x = 2 and y = 1 into the equation, we get:

1 = 4 * 2 - 7

1 = 8 - 7

1 = 1

Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.

Option B: (4, 9)

Substituting x = 4 and y = 9 into the equation, we get:

9 = 4 * 4 - 7

9 = 16 - 7

9 = 9

Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.

Option C: Both (2, 10) and (4, 9)

Substituting x = 2 and y = 10 into the equation, we get:

10 = 4 * 2 - 7

10 = 8 - 7

10 = 3

Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.

So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).

Step-by-step explanation:

The solutions to the equation x³ - x² - 18 = 0 are given as follows:

x = 3, x = -1 ± 2.236i.

The equation for this problem is defined as follows:

x³ - x² - 18 = 0

x - 3 is a factor, hence one solution is given as follows:

x - 3 = 0

x = 3.

Also considering that x - 3 is a factor, and x - 3 is of the first degree while the equation is of the third degree, we have that:

(x - 3)(ax² + bx + c) = x³ - x² - 18

ax³ + (b - 3a)x² + (c - 3b)x - 3c = x³ - x² - 18

Hence the coefficients are given as follows:

Hence the remaining solutions are given as follows:

x² + 2x + 6 = 0.

Using a quadratic function calculator:

x = -1 ± 2.236i.

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25 random students are asked how much they spent on books  is an example of a statistic.

The primary areas of study in statistics include data collection, organization, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model that will be examined when applying statistics to a scientific, industrial, or social problem. There are many different groups of people or things that can be referred to as populations, such as "each person living in a country" or "each atom making up a crystal." Every aspect of data is covered by statistics, including the planning of data collection in terms of survey and experiment design. Statisticians gather data using custom experiment designs and survey samples in the absence of census data.

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The volume of the solid of revolution is equal to 21π cubic units.

In this problem we find the representation of a figure, whose area is also shown and whose solid of revolution is can be defined by following formula:

V = π · A

Where:

First, the area of the representation is found by summing the areas of two compounding rectangles:

A = 5 · 3 + 2 · 3

A = 21

Second, compute the volume of the solid of revolution:

V = 21π

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The only way to completely eliminate the risk of arc flash is to de-energize the equipment before performing any maintenance or testing.

Racking a circuit breaker in energized gear poses a significant arc flash hazard to workers due to the potential for electrical energy to be released and cause an arc flash.

If it is not possible to de-energize the equipment, the following means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker:

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Answer:

y = -2x + 8

When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the number of boys "b" and the number of girls "g". From the ratio, we know that b/g = 11/9.

Also, we know that b = g + 124, so we can substitute the second equation into the first:

b/g = 11/9

b = g + 124

g + 124 / g = 11/9

Cross multiply:

9g + 1112 = 11g

Solve for g:

-2g = -1112

g = 556

So there are 556 girls and 556 + 124 = 680 boys at the school.

The total number of students at the school is 556 + 680 = 1236.

Answer: Approximately 226 miles

Step-by-step explanation:

Km. to Mi.

364 = 226

The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).

In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.

Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).

Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).

Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).

To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:

Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)

Simplifying this expression, we get:

Total number of strings = (n-1) x (n-2)

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