A bag contains n white tiles and 5 black tiles. The tiles are all equal in shape and size. A tile is drawn at random and not replaced. A second tile is drawn. Find:
a.The probability that the first tile is white.
b.The probability that both the first and second tiles are white.

The equation of the line is y = (2/3)x + 2, having a y intercept of 2 and slope of 2

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

The equation of a line with slope m passing through (x₁, y₁) is:

y - y₁ = m(x - x₁)

The line that passes through (0, 2) and has a slope of 2/3, hence:

y - 2 = (2/3)(x - 0)

y = (2/3)x + 2

The equation of the line is y = (2/3)x + 2

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

3.37

Step-by-step explanation:

Answer:

x= r/s+t

Step-by-step explanation:

Answer:

x=larger no

y= smaller no

Step-by-step explanation:

x+y=7--------(1)

x=16 + 2y------(2)

(2)--->(1)

16+2y+y = 7

3y + 16 = 7

3y = -9

y = -3//

so x=10

Answer:

x=larger no

y= smaller no

Step-by-step explanation:

x+y=7--------(1)

x=16 + 2y------(2)

(2)--->(1)

16+2y+y = 7

3y + 16 = 7

3y = -9

y = -3//

so x=10

A discrete probability distribution is a probability distribution that lists each possible value a random variable can assume, together with its probability. The two conditions that determine a probability distribution are:

The probability of each value must be between 0 and 1, inclusive.

The sum of the probabilities of all values must be equal to 1.

A random variable is a variable that can take on a finite or countable number of values. For example, the number of heads that come up when you flip a coin is a random variable. The possible values of the random variable are 0 and 1, and the probability of each value is 0.5.

A probability distribution is a function that describes the probability of each possible value of a random variable. For example, the probability distribution for the number of heads that come up when you flip a coin is:

P(0 heads) = 0.5

P(1 head) = 0.5

The two conditions that determine a probability distribution ensure that the probabilities are consistent and that they add up to 1. This means that the probabilities represent all of the possible outcomes and that they are all equally likely.

The correct answer is B. A discrete probability distribution lists each possible value a random variable can assume, together with its probability.

Here are some examples of discrete probability distributions:

The probability of rolling a 1, 2, 3, 4, 5, or 6 on a standard die.

The probability of getting heads or tails when you flip a coin.

The probability of getting a multiple of 3 when you roll a standard die.

Discrete probability distributions are used in a wide variety of applications, such as gambling, statistics, and finance.

Learn more about random variable here:

brainly.com/question/30789758

#SPJ11

Answer:

1 foot 6 inches

Step-by-step explanation:

divide the length value by 12. Hope this helps.

Answer:

√13

Hope that helps! :)

Step-by-step explanation:

An irrational number is a number that is non-terminating and non-recurring.

√13 is an irrational number because it cannot be expressed as either a terminating or a repeating decimal.

Option C is the correct answer.

An irrational number is a number that is non-terminating and non-recurring.

We have,

3

This is an integer so it is not an irrational number.

17

This is also an integer so it is not an irrational number.

6

This is also an integer so it is not an irrational number.

√13  = 3.6-55512755..

It is a non-terminating and non-recurring number so it is an irrational number.

0.2971

It is a terminating number so it is not an irrational number.

Thus,

√13 is an irrational number because it cannot be expressed as either a terminating or a repeating decimal.

Option C is the correct answer.

Learn more about irrational numbers here:

https://brainly.com/question/4031928

#SPJ5

Answer:

\(\dfrac{7}{9}\)

Step-by-step explanation:

\(\dfrac{2}{3}=\dfrac{2\cdot 3}{3\cdot 3}=\dfrac{6}{9} \\\\\\\dfrac{6}{9}+\dfrac{1}{9}=\dfrac{7}{9}\)

Hope this helps!

Answer:

Step-by-step explanation:

\(\frac{2x3}{3x3} \\\)

multiplying by three because you want the denominator same as the other.

  \(\frac{6}{9}\)

+ \(\frac{1}{9}\)

Add the numerators and keep the denominator the same - the denominator never gets added by the way. You only multiply them to get the denominators to equal

\(\frac{7}{9}\)

The function 2y = -4x is linear and the graph is given below.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Here the given function is 2y = -4x.

The function is linear since the exponent of the two variables x and y are 1.

This can be written as,

y = -4x / 2

y = -2x

This is a proportional function with slope -2.

Graph will be a decreasing function.

The points on the graph includes (-2, 4), (-1, 2), (0, 0), (1, -2) and (2, -4).

Hence the graph of the function is given below.

Learn more about Linear Functions here :

https://brainly.com/question/21107621

#SPJ9

Answer:

13x^8 + 4x^5 - 16x^2

Step-by-step explanation:

Standard form is just rearranging each group of numbers so that the group with the most exponents on the variables is at the beginning. So it's basically least to greatest but with exponents. Hope this helped!

To shade 3/8 of a rectangle, divide the rectangle in 8 parts and shade 3 parts

Draw a rectangle that represents the whole shape.

We need 4 lines to divide the rectangle into 8 equal parts. Two of these lines will be horizontal, and two will be vertical.

The vertical line will divide the rectangle into two equal parts, from left to right.

The three horizontal lines will divide the top half of the rectangle into three equal parts, from top to bottom.

This gives us a total of 8 equal parts in the top half of the rectangle.

To shade in 3/8 of the rectangle, we need to shade in 3 of these 8 parts, which means shading in the top left, top middle, and top right parts of the rectangle.

Learn more about rectangle here

brainly.com/question/23247148

#SPJ4

Answer:

See Explanation

Step-by-step explanation:

\(

\because \sin\bigg(\frac{\pi}{2} + x\bigg)= \cos x\\

\&\: \sin (\pi - x) = \sin x\\\\

Now,

\frac{\sin\bigg(\frac{\pi}{2} + x\bigg)}{\sin (\pi - x)} = \cot x\\\\

LHS

= \frac{\sin\bigg(\frac{\pi}{2} + x\bigg)}{\sin (\pi - x)} \\\\

=\frac{\cos x}{sinx} \\\\

= \cot x\\\\

= RHS\\\\

Hence\: Proved

\)

Answer:

Step-by-step explanation:

3

Step-by-step explanation:

a+3=−3

a=-6

!!!!!!!!!!!!!

Answer:

A= -6

Step-by-step explanation:

A+3=-3

A= -3 -3

A= -6

Answer:

346.88 meters

Step-by-step explanation:

Given that the area of the square-shaped terrain is 470 square meters.

Let a be the side of the terrain, so

Area of the square-shaped terrain, \(a^2=470\) square meters.

Therefore, the length of one side, \(a=\sqrt {470}=21.68\) meters.

The length of single thread wire required in circulating the square-shaped terrain = the perimeter of the square-shaped terrain

As the perimeter of a square having side a = 4a

So, the length of single thread wire required in circulating the square-shaped terrain= 4 x 21.68 =86.72 meters

Therefore, the length of 4 thread wire required in circulating the square-shaped terrain= 4 x 86.72=346.88 meters.

Answer:

y= 4x + 9

Step-by-step explanation:

y= 4x+5

y= 4(x+ 5/4)

m, gradient= 4

rule if parallel: their gradients are equal

rule if perpendicular : m1*m2=-1

parallel gradient, m1=4

passes through (-2, 1) so x= -2,  y= 1

y - 1= 4(x -- 2)

y= 4x + 9

The line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

The given equation is:

y = 4x + 5

Compare y = 4x + 5 with the equation y = mx + c

m = 4, c = 5

The equation parallel to y = 4x + 5 will also have a slope, m = 4

The point-slope form of the equation of a line is given as:

y - y₁ = m(x - x₁)

substitute m = 4, x₁ = -2 and y = 1 into the equation above

y - 1 = 4(x - (-2)

y - 1 = 4(x + 2)

y - 1 = 4x + 8

y = 4x + 8 + 1

y = 4x + 9

Therefore the line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

Learn more on equation of a line here: https://brainly.com/question/13763238

Answer:

The answer the the above question is 31

Step-by-step explanation:

f(x)=5x-3

so, f(8) = 5×8-3 = 37

Also,

g(x)= 3x

So, g(2)= 3×2 = 6

Now,

f(8)-g(2)= 37-6 = 31

9514 1404 393

Answer:

Step-by-step explanation:

A ray is named by naming its end point and one other point on the ray. Here, the ray can be named IL or IR, using end point I and either of points L or R to complete the name.

The range of possible lengths for the third side be

0 ft < x < 76 ft

0 ft < x < 33 ft

Given, two sides of a triangle

we have to find the range of possible length for the third side of the triangle.

a) 24 ft and 52 ft

given first side of the triangle be, 24 ft

and second side of the triangle be, 52 ft

as we know that the third side should be less than the sum of the remaining two sides of any triangle.

So, let the third side be x

x < 24 + 52

x < 76

Therefore, the third side should be less than 76 ft and obviously greater than 0 ft.

Range of the third side be, 0 ft < x < 76 ft

b) 16 ft and 17 ft

given first side of the triangle be, 16 ft

and second side of the triangle be, 17 ft

as we know that the third side should be less than the sum of the remaining two sides of any triangle.

So, let the third side be x

x < 16 + 17

x < 33

Therefore, the third side should be less than 33 ft and obviously greater than 0 ft.

Range of the third side be, 0 ft < x < 33 ft

Hence, the range of possible lengths for the third side be

0 ft < x < 76 ft

0 ft < x < 33 ft

Learn more about Sides of Triangles here https://brainly.com/question/22407545

#SPJ4

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

<95141404393>

Answer:

false FALSE FALSE FALSE

Answer:

(a) E - certain

The number of bacteria in the culture after 4 hours is 903.

Given data:

Since the bacteria triple every 10 hours, the growth rate constant k can be determined using the exponential formula:

\(P(t)=P_0e^{kt}\)

Where:

\(P(t)\\\) is the number of bacteria at time t.

\(P_0\) is the initial number of bacteria (800 in this case)

k is the growth constant.

t is the time in hours.

Given that the bacteria triple every 10 hours, we know that after 10 hours, the number of bacteria becomes three times the initial count. Therefore, we can set up the equation:

\(3P_0=P_0e^{(10k)}\)

On simplifying the equation:

\(k = \frac{ln3}{10}\)

Now, we can use the value of k to find the number of bacteria after 4 hours:

\(P(4)=800(e^{\frac{ln3}{10}*4})\)

On simplifying the equation:

P(4) = 903

Hence, the number of bacteria is 903.

To learn more about exponential form, refer:

https://brainly.com/question/29337692

#SPJ12

The equation of the straight line is y = -1/6(x - 10) + 4

The equation is given as:

y = 2x + 6

Linear equations are represented as:

y = mx + c

Where:

Slope = m

So, we have:

m = 6

The slopes of perpendicular lines are represented as:

n = -1/m

So, we have:

n = -1/6

The equation is then represented as:

y = n(x - x1) + y1

This gives

y = -1/6(x - 10) + 4

Hence, the equation of the straight line is y = -1/6(x - 10) + 4

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Answer:

Nijah has 6 stickers left.

Step-by-step explanation:

Starting stickers:

45

2/5 are given away:

\(\frac{2}{5}\) * 45

\(\frac{2}{5}\) * \(\frac{45}{1}\)

\(\frac{90}{5}\)

18

1/3 of the remaining are given away:

\(\frac{1}{3}\) * 18

\(\frac{1}{3}\) * \(\frac{18}{1}\)

\(\frac{18}{3}\)

6

Nijah has 6 stickers left.

Answer:

18

Step-by-step explanation:

Find the part she gave to her sister

45 *2/5 = 18

The part remaining is

45 - 18 = 27

She gives 1/3 to Brett

27 * 1/3 = 9

She has 27 - 9 = 18

She has 18 remaining

Answer:

a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population

Step-by-step explanation:

a. The first female had 4 pups.

If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.

b. 1st generation                        =     1 pup

2nd generation = 4 ×  1 pup      =    4 pups

3rd generation  = 4 ×  4 pups    =  16 pups

4th generation  = 4 × 16 pups    = 64 pups

5th generation  = 4 × 64 pups = 256 pups

The sequence is           1,   4, 16, 64, 256, …

We can also write it as 4⁰, 4¹, 4²,  4³,   4⁴, …

Note that the exponent is one less than the number of the generation.

Thus, the general formula for the nth term, aₙ, is

aₙ = 4ⁿ⁻¹, where

n = the number of the generation

a = the number of pups in that generation.

c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion

The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.

There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,