There are 5 blue pencils and 3 gold pencils in a container. If 2 pencils are drawn randomly without replacement, what is the probability that both pencils drawn are gold? Simplify the fraction into the lowest terms.

13/28

3/28

5/28

1/28

Answers with Explanation:

12. In the picture we saw that there are 3 pears, if one of the factors is \(\frac{1}{2}\)

then we know that the other factor is 6 because \(6 * \frac{1}{2}\) is equal to 3.

So the equation is:

\(6 * \frac{1}{2} = 3\)

13. How you could get the answer for \(45 * \frac{7}{9}\) mentally? Well, you only need to  divide 45 by 9 and then multiply the answer by 7.

So:

45 ÷ 9 = 5

5 × 7 = 35

14. If 2.99 - 1 is equal to 1.99 that means that is less.

Explanation:

\(2.99-1=1.99\) (that means that is less than 3)

Hope this helps :)

Pls brainliest...

The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

We have first three colour Green that is g1 , g2 and g3

And We have next three colour red that is r1 , r2 and r3

The probability that all adjacent points differ in colour = 3! * \(^{4}C_{3}\) 3! / 6!

=> \(\frac{ 3! * 4! *3!}{6!}\)

=> \(\frac{1}{5}\)

The probability that all adjacent points differ in colour is \(\frac{1}{5}\).

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By what would you multiply the top equation by to eliminate x: A. 4.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

x + 3y = 9                .........equation 1.

-4x + y = 3               .........equation 2.

By multiplying the equation 1 by 4, we have:

4(x + 3y = 9) = 4x + 12y = 36

By adding the two equations together, we have:

4x + 12y = 36

-4x + y = 3

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

13y = 39

y = 39/13

y = 3

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Answer:

he bought 2 sodas

Step-by-step explanation:

18 dollars for meal + 2 dollars each soda

well 18+2 =20 so if you get two drinks 1 equals 2 dollars 20+2= 22

2 đô cho 1 lon soda tức là bạn phải lấy 22 :2 =11 và đó là số soda mà anh ta đã uống

a) The equations of the two tangents are:

T₁: y =\((3 - \sqrt(3))(x - 3)\)

T₂: y =\((3 - \sqrt(3))(x - 3)\)

b) The points are (1, -2) and (1, -2).

To find the equations of the tangents to the curve C at the point (3, 0), we need to find the derivative of y with respect to x and evaluate it at x = 3.

(a) Finding the tangents at (3, 0):

To find the derivative of y with respect to x, we use the chain rule:

dy/dx = (dy/dt)/(dx/dt)

dx/dt = 2t  (differentiating x =\(t^2\))

dy/dt = \(3t^2 - 3\)  (differentiating y =\(t^3 - 3t\))

Express t in terms of x

From x = \(t^2\), we can solve for t:

\(t = \sqrt(x)\)

Substitute t into dx/dt and dy/dt

Substituting \(t = \sqrt(x)\) into dx/dt and dy/dt, we get:

dx/dt = \(2\sqrt(x)\)

dy/dt = \(3(x^{(3/2)}) - 3\)

Find dy/dx

Now, we can find dy/dx by dividing dy/dt by dx/dt:

dy/dx = (dy/dt)/(dx/dt)

      =\((3(x^{(3/2)}) - 3) / (2\sqrt(x))\)

Evaluate dy/dx at x = 3

Substituting x = 3 into dy/dx, we get:

dy/dx = \((3(3^{(3/2)}) - 3) / (2\sqrt(3))\)

      = \((9\sqrt(3) - 3) / (2\sqrt(3))\)

      = \((3(3\sqrt(3) - 1)) / (2\sqrt(3))\)

      = \((3\sqrt(3) - 1) / \sqrt(3)\)

      =\((3\sqrt(3) - 1) * \sqrt(3) / 3\)

      =\(3 - \sqrt(3)\)

Find the equations of the tangents

The equation of a tangent at the point (x₀, y₀) with a slope m is given by:

y - y₀ = m(x - x₀)

For the first tangent, let's call it T₁, we have:

Slope m₁ = \(3 - \sqrt(3)\)

Point (x₀, y₀) = (3, 0)

Using the point-slope form, the equation of the first tangent T₁ is:

y - 0 = \((3 - \sqrt(3))(x - 3)\)

y =\((3 - \sqrt(3))(x - 3)\)

For the second tangent, let's call it T₂, we have:

Slope m₂ = \(3 - \sqrt(3)\)

Point (x₀, y₀) = (3, 0)

Using the point-slope form, the equation of the second tangent T₂ is:

y - 0 =\((3 - \sqrt(3))(x - 3)\)

y = \((3 - \sqrt(3))(x - 3)\)

Therefore, the equations of the two tangents to the curve C at the point (3, 0) are:

T₁: y = \((3 - \sqrt(3))(x - 3)\)

T₂: y = \((3 - \sqrt(3))(x - 3)\)

(b) Finding the points on C where the tangent is horizontal:

For the tangent to be horizontal, dy/dx must be equal to zero.

dy/dx = 0

\((3(x^(3/2)) - 3) / (2\sqrt(x))=0\)

Setting the numerator equal to zero, we have:

\(3(x^{(3/2)}) - 3 = 0\\x^{(3/2)} - 1 = 0\\x^{(3/2)} = 1\\x = 1^{(2/3)}\\x = 1\)

Substituting x = 1 back into the parametric equations for C, we get:

\(x = t^21 \\\\= t^2t \\= \pm 1\)

\(y = t^3 - 3t\\y = (\pm1)^3 - 3(\pm1)\\y = \pm1 - 3\\y = -2, -2\\\)

Therefore, the points on C where the tangent is horizontal are (1, -2) and (1, -2).

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Answer:

6/21

Step-by-step explanation:

bc thats the answer

Answer:

Simplified: 6/15 = 2/5

Step by-step explanation:

Answer:

46 (23%)

Step-by-step explanation:

If 10% of x is 20, we can assume that 100% of x is 200. This is because since 10% is such a nice number to work with, we can simply add a zero to the end of it and the number. Now, we can see that 50% is 100 and 25% is 50. 20% is 40 and 10% is 20. 5% is 10 and 1% is 2. That being said, we need to do 50% + 3%. Which leaves us with 50 (25%) - 4 (2%). That being said, the answer is 46 (23%).

The triangle with maximum area has a height of 11 cm and a base of 11 cm.

To find the dimensions for which the area of the triangle is a maximum, we can use the formula for the area of a triangle, which is A = 1/2 * b * h, where A is the area, b is the base, and h is the height.

Since we know that the sum of the base and height is 22 cm, we can express the base in terms of the height as b = 22 - h.

Substituting this expression for b into the formula for the area, we get A = 1/2 * (22 - h) * h.

To find the maximum value of A, we need to find the value of h that maximizes the expression 1/2 * (22 - h) * h. We can do this by taking the derivative of the expression with respect to h, setting it equal to zero, and solving for h.

Differentiating the expression with respect to h, we get dA/dh = 11 - h. Setting this equal to zero, we get 11 - h = 0, which implies h = 11.

Therefore, the maximum area of the triangle is achieved when the height is 11 cm and the base is also 11 cm (since the sum of the height and base is 22 cm).

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Answer:

114

Step-by-step explanation:

,

Answer:

686 crystals.

Step-by-step explanation:

You can set up an algebraic equation to find the answer.

Let x represent the number of crystals Lily uses.

The question is asking how many crystals it will take to raise 6,174 zombies, when each crystal raises 9.

9x = 6174

x = 6174 / 9

x = 686

That means it will take Lily 686 dark power crystals to raise 6,174. That's a lot of dark power!

Hope this helps!

Answer:7

Step-by-step explanation:

3(2)+1

6+1=7

Answer: 7

Step-by-step explanation:

if n=2 then

3*2+1

3*2=6

6+1=7

Answer:

Step-by-step explanation:

4x is in a multiplication form

4x=36

meaning a number when multiplied with 4 gives the answer 36

hence in order to find the answer

36 divided by 4 which is equivalent to 9

answer is 9

Answer:  \(x = 9\)

Step-by-step explanation:

We must isolate \(x\) on one side of the equation in order to solve the equation \(4x = 36\) for \(x\).

Step 1: Divide both sides of equation by 4:

\(\frac{4x}{4} = \frac{36}{4}\)

Step 2: Simplify

\(x = 9\)

Therefore, the solution to the equation is \(x = 9\).

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

Rearranging an algebraic equation so that \(x\) is on one side and all other terms are on the other side of the equal sign is known as isolating \(x\).

Answer:

Step-by-step explanation:

Given is 30 x 60 x 90 triangle.

The ratio of sides is:

According to the ratio:

Answer:

x = +4 , -4

Step-by-step explanation:

    x² - 16 = 0

           x² = 16

           \(\sf x = \sqrt{16}\\\\x = \sqrt{4*4}\\\\\)

          x = ±4

Answer:

  B. slope -5, y-intercept (0, 7)

Step-by-step explanation:

The y-intercept is the first (x, y) pair shown in the table: (0, 7). (This eliminates choices C and D.)

The slope is ...

  change in y / change in x

  (-13 -7) / (4 -0) = -20/4 = -5 . . . slope

This matches choice B.

The surface described by the equation z = sin(y) is a sinusoidal cylinder.

To visualize the surface, we can consider the equation in terms of the variables x, y, and z. However, since the equation only involves the variable y and the trigonometric function sin(y), we can infer that the surface will vary in the y-direction while remaining constant in the x and z directions.

When we plot the surface, we will have a cylinder shape where the height (z-coordinate) at any given point on the surface is determined by the sine of the y-coordinate. As the value of y changes, the height of the surface will oscillate according to the sine function.

Since the equation does not involve x or z, the surface will have an infinite extent in those directions. It will form a circular cylinder shape with the radius determined by the amplitude of the sine function.

The sketch of the surface will show a cylindrical shape with wavy or sinusoidal variations along the y-axis.

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Answer:93

Step-by-step explanation:75+105+127=307

307-250=57

150-57=93

The answer is;

62.83

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The first 6 prime numbers are  2, 3, 5, 7, 11 ,13

The square of 6 prime number

4, 9 ,25, 49 , 121 , 169

The mean difference of these number is

⇒ (4 + 9 + 25 + 49 + 121 + 169) / 6

⇒ 62.83

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Volume is a three-dimensional scalar quantity. The volume of the empty space is 20.602 units³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the volume of the prism, the box is 96 units³ and the diameter of the cylindrical container is 4 units(Radius=2 units), while the height of the cylinder is 6 units. Therefore, The volume of the empty space is,

The volume of the empty space

= Volume of prism - Volume of the cylindrical container

= 96 units³ - (π×2²×6) units³

= 96 units³ - 75.398 units³

= 20.602 units³

Hence, the volume of the empty space is 20.602 units³.

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Work Shown:

A = pi*r^2

A = 3.14 * 10^2

A = 3.14 * 100

A = 314 square inches

This value is approximate since pi = 3.14 is approximate.

The area of the circle is :

Work:

To calculate the circle's area, I will use the formula

\(\sf{C=\pi r^2}\)

Diagram:

\(\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 10\ inches}\end{picture}\)

Plug in the values :

      \(\begin{gathered}\sf{A=3.14\times10^2}\\\\\sf{A=3.14\times100}\\\\\boxed{\boxed{\bf{A=314\:in^2}}}\end{gathered}\)

Answer:

4 quarters

Step-by-step explanation:

4 quarters = $1

14 nickels = $0.70

Answer:

Step-by-step explanation:

6.5 + w = 20

13.5 km

Answer:

C first then for second one is b

Step-by-step explanation:

I just did the assignment

Answer: i choose c because the line is going right so the > means that it is going that way and the line under the> means that the circle under the graph is closed but the answer is c

Step-by-step explanation:

Ok, we need find the price of each dvd unit, then for this we are going to take the total price of the dvd's and divide it by the quantity that was compared.

So we have this:

Total dvd price: 76.57

Number of dvd: 13

Dividing we get:

76.57/13=5.89

The long division is:

76/13 equals 5 and we have a remainder of 11 that goes down, we went down on the 5th of ten, 115 divided by 13 equals 8 and there are 11 remainders left, we lower the 7 of the hundredths, and 117 divided 13 equals 9.

So finally we get that the unitary price of dvd is $5.89.

The equation is d = 3m + 5

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.

The cost function is given by the equation d = 3m + 5

where, d = dollars, m = movies

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The distance between them when the force is 36 pounds is 5.06 feet.

According to the statement

We have to find that the distance between two bodies.

So, For this purpose, we know that the

A force is a push or pull upon an object resulting from the object's interaction with another object.

From the given information:

If the force of attraction is 64 pounds when the distance between the bodies is 9 feet

Then

F1 =64 pounds, r1 = 9 ft

F2 = 36 , r2 = ?

The gravitational force of attraction is inversely proportional to the square of distance between the two bodies.

So, F2 / F1 = r1^2 / r2^2

36 / 64 = 9 / r2

r2 = 0.56*9

r2 = 5.06.

So, The distance between them when the force is 36 pounds is 5.06 feet.

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Answer:

12 ft

Step-by-step explanation:

there is less force so the distance is greater

A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.

To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.

First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4

So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)

Integrating this expression with respect to t over the interval [0,3], we get:

\(\int\limits^3_0\) M(t) dt = \(\int\limits^3_0\) (4 - 0.75sin(t) + 0.25sin(3t)) dt

= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]

= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))

= 11.544

Therefore, the answer is (C) 11.544.

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The numerator of the fraction is 2.

The fraction can be written as 2/7, and since the numerator is nine less than the denominator, when the fraction reduces to (1/7) it means that the numerator must be 2.

To solve this problem, first determine what is given in the question: a fraction with a numerator that is nine less than the denominator, and that reduces to (1/7).

Using this information, the goal is to determine the numerator of the fraction.

To do this, simply subtract nine from the denominator and the result will be the numerator. In this case, the denominator is 7, so subtracting 9 from 7 gives us 2, which is the numerator of the fraction.

Therefore, the numerator of the fraction is 2.

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Answer: 115°

Step-by-step explanation:

The angles in a triangle add up to 180

Z+35+30=180

Z+65=180

Z=115

Answer:

36

Step-by-step explanation: