a box contains 7 green marbles, 4 blue marbles, and 8 red marbles. three marbles are selected at random from the box, one at a time, without replacement. find the probability that the first two marbles selected are not red, and the last marble is red.

Consecutive terms in the α sequence have a common difference of

8 - 10 = 6 - 8 = 4 - 6 = … = -2

so they are given recursively by

[tex]\begin{cases} \alpha_1 = 10 \\ \alpha_n = \alpha_{n-1} - 2 & \text{for } n\ge2 \end{cases}[/tex]

By substitution, we have

[tex]\alpha_n = \alpha_{n-1} - 2 \\\\ \alpha_n = \alpha_{n-2} - 2\cdot2 \\\\ \alpha_n = \alpha_{n-3} - 3\cdot2 \\\\ \vdots \\\\ \alpha_n = \alpha_{n-(n-1)} - (n-1)\cdot 2 = \alpha_1 - 2(n-1) = 12-2n[/tex]

Consecutive terms in the β sequence have a common ratio of

6/9 = 4/6 = (8/3)/4 = … = 2/3

so the recurrence for these terms is

[tex]\begin{cases} \beta_1 = 9 \\\\ \beta_n = \frac23 \beta_{n-1} & \text{for } n\ge2 \end{cases}[/tex]

We can solve for [tex]\beta_n[/tex] similarly:

[tex]\beta_n = \dfrac23 \beta_{n-1} \\\\ \beta_n = \left(\dfrac23\right)^2 \beta_{n-2} \\\\ \beta_n = \left(\dfrac23\right)^3 \beta_{n-3} \\\\ \vdots \\\\ \beta_n = \left(\dfrac23\right)^{n-1} \beta_{n-(n-1)} = \left(\dfrac23\right)^{n-1} \beta_1 = \dfrac{2^{n-1}}{3^{n-1}} \cdot 3^2 = \dfrac{2^{n-1}}{3^{n-3}}[/tex]

The γ sequence has [tex]n[/tex]-th term

[tex]\gamma_n = \alpha_n \beta_n = (12-2n) \dfrac{2^{n-1}}{3^{n-3}} = (108-18n) \left(\dfrac23\right)^{n-1}[/tex]

and we want to compute

[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \sum_{n=1}^\infty \left(\frac23\right)^{n-1} - 18 \sum_{n=1}^\infty n \left(\frac23\right)^{n-1}[/tex]

Recall the sum of an infinite geometric series with common ratio [tex]|r|<1[/tex] converges to

[tex]\displaystyle \sum_{n=1}^\infty r^{n-1} = \frac1{1-r}[/tex]

so that

[tex]\displaystyle \sum_{n=1}^\infty \left(\frac23\right)^{n-1} = \frac1{1-\frac23} = 3[/tex]

For the remaining sum, we can use the method shown in question [24494877] to compute

[tex]\displaystyle \sum_{n=1}^\infty nr^{n-1} = \frac1{(1-r)^2}[/tex]

which gives

[tex]\displaystyle \sum_{n=1}^\infty n \left(\frac23\right)^{n-1} = \frac1{\left(1-\frac23\right)^2} = 9[/tex]

Then the infinite sum of the terms of γ converges to

[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \cdot 3 - 18 \cdot 9 = \boxed{162}[/tex]

Answer:106.81

Step-by-step explanation:

To find the Circumference of a circle you have to do is 2×[tex]\pi[/tex]×17 which would give you 106.81.

The circumference is the outline of the circle, it is the edge; in other words it is the perimeter of the circle.

To calculate the circumference of the circle, we apply the following formula:

We have that the radius is 17 meters, and the value of pi is 3.14, we substitute these data in the formula and solve:

Using the greatest common factor, it is found that the greatest number of cards that she can place in a row is of 14.

The number of cards for each family is given as follows:

We want to find a way to distribute them having the same number of cards in each row, hence this is possible finding the greatest common factor (GCF) of the numbers of 154 and 140.

The GCF is found factoring both numbers 154 and 140 simultaneously by prime factors, as follows:

154 - 140|2 (both 154 and 140 are divisible by 2).

77 - 70|7 (both 77 and 70 are divisible by 11).

11 - 7

There are no numbers for which both 11 and 7 are divisible by, hence the greatest number of cards that she can place in a row is:

gcf(154, 140) = 2 x 7 = 14.

The complete problem is:

April is arranging place cards for a wedding reception on a table. The bride's family has 154 cards and the groom's family has 140 cards. She wants the arrangements for the two families to have the same number of cards in each row. What is the greatest number of cards that she can place in a row?

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Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.

The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")

Using math operations one can relate x values with y values via an equation of the type:

y = 2 x - 5

where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.

For example, try the number x = 0

and see which y number connects with it:

y = 2 (0) - 5 = 0 - 5 = -5

Then you say that the number 0 in the Domain connects with the number -5 in the Range.

This relationship can also be given with coordinate pairs of the form:

(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.

The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.

I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.

Given:

a.) The admission fee at a small fair is $2.50 for children and $4.00 for adults.

b.) On a certain day, 2400 people enter the fair and $7140 is collected.

Let,

x = total number of children

y = total number of adults

Let's generate two equations based on the given scenario:

EQUATION 1: Total number of children and adults entered the fair.

EQUATION 2: Total money collected from the admission.

We will be using the substitution method. We get,

Substitute to Equation 2:

Therefore, 1,640 children went to the fair.

For the adults,

x + y = 2400

1,640 + y = 2400

y = 2400 - 1,640

y = 760 adults

In summary: 1,640 children and 760 adults went to the fair.

90 letters out of the inspected sample of 900 letters will be found to be open

Inspection is done by mail carrier for every 20th letter

Inspection rate = 1/20*100 = 5%

It is a form of inspection where a sample of the same unit's manufactured goods, produced using the same procedures, is taken and examined, as opposed to the entire unit being examined. In general, the unit relates to the lot, and the lot determines whether the things are acceptable or rejectable.

Number of letters found open in 600 letters = 3 letters

Rate of letter found open = 3/600*100 = 0.5%

The sample being mailed = 18000 letters

Number of letters that were inspected for being open = 5% of 18000 = 900

letters

The number of letters found open = 0.5% of 18000 = 90

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The recursive formula is f(n - 1) . 3

The correct option is (c)

What are Recursive Formula ?

A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:

Given,

The sequence is:

3, 6 , 12 ....

To find the recursive formula of above sequence :

Now, The first term is 3.

Recursive formula is :

f(n - 1) . 3

Hence, The recursive formula is f(n - 1) . 3

The correct option is (c)

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Answer: 15

Step-by-step explanation:

This is the answer because 22 divided by 11 equals 2 kilometer each trip to work so 30 kilometer divided by 2 is 15.

Flight attendants for one carrier must be between 63 and 73 inches tall. The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.

Given that,

Flight attendants for one carrier must be between 63 and 73 inches tall.

We have to find what absolute value equations from the list below can be used to express these minimum and maximum heights.

In algebra, an absolute value function is a function where the variable is inside the bars denoting absolute values. The absolute value function is also known as the modulus function, and its most popular representation is function of x = |x|, where x is a real number. The absolute value function is typically written as function of x = a |x - h| + k, where a denotes the vertical stretch of the graph, h denotes the horizontal shift, and k denotes the vertical shift from the graph of function of x = |x|.

Therefore, The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.

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The given function is:

The theorem states that the factors are p/q where p is the factors of the last term (constant term) and q is the factors of the leading coefficient.

Here the leading coefficient is -25 and the constant term is -1.

The factors are listed below:

So the value of p/q can be the values shown below:

Hence the possible zeroes of the given function are:

Answer: Slope intercept from is y= 4/13x-5/13

Step-by-step explanation:

Answer:

8x17.50

Step-by-step explanation:

Identify that the shape created is a Triangle.

For this exercise it is important to remember that, given a point P (x , y), "x" is the the x-coordinate of the point and "y" is the y-coordinate of the point.

In this case, Ms. Juhal has the following points:

1) Point A (-5 , 5)

x = -5 and y = 5

2) Point B (-5 , 3)

Where:

x = -5 band y = 3

3) Point C (-5 , 1)

x = -5 and y = 1

4) Point D (2,1)

Where:

x = 2 and y = 1

Therefore, knowing the coordinates of each point, you can plot them and connect them in order (Observe the picture attached).

Finally, you can identify that the shape created is a Triangle.

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Erica worked 4 hours  to prepare 26 flower arrangements.

Erica prepared 13 flower arrangements after working 2 hours.

Time Erica took to prepare 1 flower arrangement = 2 / 13 hours.

Therefore time Erica took to prepare 26 flower arrangement = 2/13 x 26 hours.

=4 hours.

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Answer:

No, it doesn't satisfy.

Step-by-step explanation:

2x - 6y = -3

let us post the ordered pair in the equation and solve it

2(3) - 6(7/2) = -3

6 - 21 = -3

-15 = -3  ......  which isn't equal

so we conclude that the given ordered pair doesn't satisfy the equation.

The proportional relationship modeled by Table A is graphed on the image given at the end of the answer.

A direct proportional relationship is defined when the output variable y is calculated with the multiplication of the input variable x and the constant of proportionality r as follows:

y = rx.

The meaning of this is that a proportional relationship is only represented when the division of y by x for all pairs of points (x,y) are the same.

Hence, the proportional relationship in this problem is represented by table A, as:

r = 10/5 = 8/4 = 6/3 = 2/1.

Hence the equation is:

y = 2x.

For table B, a proportional relationship is not shown, as:

3/1 is different of 4/2.

The graph containing the points listed on table A are given at the end of the answer.

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As a fraction 3.83 (3 repeating )is 3x 83/99

what is repeating decimals ?

Repeating decimal values are created by fraction that  do not divide evenly. when converting a repeating decimal to a fraction we can ignore the units in the start as the units remain unchanged ,which allows us to  convert our decimal values and then the units back in afterward.

so ,

To convert the 3.83 to a fraction , we ignore the units as they will remain units.

we then set up one equation of our unknown x being equal to 0.83333......and another that is 100 times greater , 100x = 83.33333....

by subtracting these two equation from each other we can then divide by the coefficient of x to create our fraction .

10x=83.3333...

    x= 0.83333...

  99x = 82.5

we now divide both sides by 99 to isolate x:

99x=82.5

99x/99=82.5/99

x= 82.5/99

x = 82.5 x10/99x10

x = 825/990

x = 165/198

we cannot simplify this fraction any more

finally we add back the 3 units we set aside at the beginning ,making our fraction 3x165/198

so , the fraction 3.83 is 3x 83/99

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The solution of the given equation in quadratic form will be; (x^{2} -6x - 8)/(x^{2} -4 )

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

WE have been given an algebric equation as;

x/x+2 - 4/x-2

Solving it;

[tex]\dfrac{x}{x+2 }- \dfrac{4}{x-2}\\\\\\\dfrac{x(x-2)}{x+2 }- \dfrac{4(x+2 )}{x-2}\\\\\\\dfrac{x(x-2)- 4(x+2 )}{(x+2 )(x-2)}\\\\\\\dfrac{x^{2} -2x- 4x - 8}{x^{2} -2^{2} }\\\\\\\dfrac{x^{2} -6x - 8}{x^{2} -4 }[/tex]

Hence, the solution of the given equation in quadratic form will be;

(x^{2} -6x - 8)/(x^{2} -4 )

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Circumference of the circle = 17.8 units

Area of the circle = 25.1 square unit

An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle."

Formula to get the circumference of a circle = 2πr

Where r = radius of the circle

Radius of the given circle = Distance between the points A(2, 3) and B(4, 1)

r = [tex]\sqrt{(2-4)^{2} +(3-1)^{2} }[/tex]

r = 2√2units

Therefore, circumference = 2π(2√2)

= 17.77

≈ 17.8 units

Area of the circle = πr²

= π(2√2)²

= 8π

= 25.13

≈ 25.1 square unit

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The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

√9x^3/25y^2

Evaluate the square root of 9

So, we have the following equation

√9x^3/25y^2 = 3x^3/25y^2

The above expression cannot be further simplified

Hence, the solution to the expression is 3x^3/25y^2

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Answer:

9.38%

Step-by-step explanation:

First this is the solution I used:

Percentage change = actual change/original amount x 100

Hope this helps.

Two parallel lines have the same slope. Given the equation of one of the lines, you can determine the slope of the other line:

The slope of the line is the coefficient of the x-term, in this case, that coefficient is -5. Then the slope of both parallel lines is m= -5.

The line you have to find must cross through the point (9,-42). Using the point-slope form you can determine the equation of the parallel line:

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point of the line:

To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:

Subtract 42 to both sides of the expression to pass the term to the right side of the equal sign:

The equation of the line is y= -5x + 3

It would cost him $ 5 to cover a distance of 2 miles.

Amount charged by the taxi driver which is mandatory to be paid is $ 2.50

Additional amount charged by the driver is $1.25

Since Ian is driving 2 miles thus we can write it as follows :

2.50  + (1.25 × 2) = 2.50 + 2.5

= $5

The additional charges are basically the amount which is charged by the driver to cover a particular distance and thus this distance changes as the distance changes.

However the mandatory fees is constant and it never changes.

It would cost him $ 5 to cover a distance of 2 miles.

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The most appropriate choice for volume of cuboid and cylinder will be given by-

Total mass of sculpture is 10.0464 tonnes

What is volume of cuboid and cylinder?

Cuboid is a three dimensional figure that has 6 faces, 12 edges and 8 vertices.

Volume of cuboid is given by the formula length [tex]\times[/tex] breadth [tex]\times[/tex] height

Cylinder is a three dimensional round figure that has two circular bases at the end

If r is the radius of the cylinder and h is the height of the cylinder, volume of the cylinder is given by the formula

V = [tex]\pi \times r^2 \times h[/tex]

Here,

Radius of cylinder = 40 cm

Height of cylinder = 70 cm

Volume of cylinder = [tex]\pi \times r^2 \times h[/tex]

                                = [tex]\frac{22}{7} \times (40)^2 \times 70\\[/tex]

                                = 352000 [tex]cm^3[/tex]

Length of cuboid = 80 cm

Breadth of cuboid = 80 cm

Height of cuboid = 140 m

Volume of cuboid = [tex]80 \times 80 \times 140[/tex]

                              = 896000 [tex]cm^3[/tex]

Total volume of sculpture = (352000 + 896000) [tex]cm^3[/tex]

                                           = 1248000 [tex]cm^3[/tex]

Density of sculpture = 8.05 [tex]g / cm^3[/tex]

Mass of sculpture  = [tex]1248000 \times 8.05[/tex]

                               = 10046400 g

                               = 10046.4 kg

                                = 10.0464 tonnes

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The equation whose graph is parallel to that of line 2x - y = - 1 is →

y = - 2x - 1

The general equation of straight line is -

y = mx + c

Given is an equation of line as → 2x - y = - 1

The equation of the line whose graph will be parallel to that of the graph of line 2x - y = -1, will have same slope as that of given line itself.

2x - y = - 1

y = -2x - 1

m = -2

The equation whose graph is parallel to that of 2x - y = -1 is -

y = - 2x - 1

Therefore, the equation whose graph is parallel to that of line 2x - y = - 1 is → y = - 2x - 1

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The equation of a line that passes through the point ( -5, 6) and has a slope equal to 3 is  y = 3x + 21

The equation of the line passes through the point (-5, 6) and has a slope equal to 3.

Therefore, the equation of a line can be represented as follows;

y = mx + b

where

Therefore,

y = 3x + b

slope = 3

using (-5, 6), let's find the y-intercept

6 = 3(-5) + b

6 = - 15 + b

b = 6 + 15

b = 21

Therefore, the equation of the line is y = 3x + 21

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The relative error exists multiplied by 100 to estimate the percent error. The percent error in Yvonne's calculation exists 11% error.

The difference between the estimated value and the actual value in relation to the actual value is known as the percent error. To calculate the percent error, the relative error is multiplied by 100.

Percent error calculates the difference between an estimate and a correct value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual value. It is also referred to as % error and percentage error.

%error = (calculated value - experimental value) / calculated × 100%

%error = (10 - 9)/9 × 100%

= 1/9 × 100%

= 11.11111 ≈ 11% error

Therefore, the percent error in Yvonne's calculation exists 11% error.

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cos2x = (1+cos(2x))/2

The cosine power is odd (n odd): u = sin x and du = cos x dx should be used. d u = cos ⁡ To create an even number of cosine powers, replace dx with (a), canceling one power of cos x by substituting du. The Power Factor is the sine of the angle formed by Current and Voltage.

The ratio of the length of the side next to the angle to the length of the hypotenuse is known as the cosine, sometimes abbreviated as "cos." The ratio of the length of the side across from the angle to the length of the side next to it is called the tangent, which is frequently abbreviated as "tan."

cos2(2x) = (1+cos(4x))/2

cos4(2x)= [(1+cos(4x))/2]²

[tex]cos^{4}[/tex](2x) = [(1+cos(4x))/2]²

[tex]cos^{4}[/tex] (2x) = (1/4) × [1 + cos(4x)]²

[tex]cos^{4}[/tex](2x) = (1/4) × (1 + 2cos(4x) + cos²(4x))

[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1 + cos(2x))/2]

[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1/2)*(1 + cos(2x))]

[tex]cos^{4}[/tex](2x) = (1/8)*[2 + 4cos(4x) + 1 + cos(2x)]  

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