n a chemical plant, 24 holding tanks are used for final product storage. Four tanks areselected at random and without replacement. Suppose that six of the tanks contain material inwhich the viscosity exceeds the customer requirements.(a) What is the probability that exactly one tank in the sample contains high-viscosity material

Answer:

Answer

Step-by-step explanation:

(a) B ⊄ A (b) C ⊂ A (c) B ⊄ C (d) ∅ ⊂ B (empty set is an element of any set)

(e) C ⊂ C (reflexitivity).

There are 105 comparisons made with 15 statistically independent scenarios.

According to the statement

we have given value of n is 15.

Then r = 2. so,

we use the formula NcR then

Substitute the values in it then

15c2

we open it according to ncr formula

In this formula we arrange the terms according to the following

NcR formula = n! /r! * (n-r)!

then the terms will arrange in this way.

So,

ncr = 15! / 2! * 13!

After solving the statement some terms will be cancel with each other and remaining terms are

ncr = 15*14/2

ncr = 210/2

ncr = 105

here the value becomes 105.

So, There are 105 comparisons made with 15 statistically independent scenarios.

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Using proportions, it is found that each farmer bought 68,008 kg.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:

6460 x 1000 + 760 = 6,460,760 kg

The amount per farmer is:

6,460,760/95 = 68,008 kg.

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The equation of parabola from graph is y = a(x + 1)² - 4.

According to the statement

we have to determine the parabola equation from the graphical representation.

So,

For this purpose we know that

Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

The general equation of parabola is y = a(x-h)2 + k

And The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

So, The equation of parabola from graph is y = a(x + 1)² - 4.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.

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Answer:

x = 2 ;   x = -8

Step-by-step explanation:

 [tex]\sf \ log_4 \ x +log_4 \ (x +6) = 2\\\\ log_4 \ (x)*(x +6) = 2\\\\[/tex]

    log₄  ( x² + 6x) = 2

                        4² = x² + 6x

         x² + 6x - 16 = 0

   x² - 2x + 8x - 16 = 0  

   x(x - 2) + 8(x - 2) = 0

       (x - 2) (x + 8)   = 0

x - 2 = 0  or x + 8 = 0

    x  = 2  or      x  = - 8

Step-by-step explanation:

To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.

Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0

⇒ 3 + 2√5 = p/ q

⇒ 2√5 = p/ q - 3

⇒ √5 = (p - 3q ) / 2q

⇒ (p - 3q ) / 2 q is a rational number.

However, √5 is an irrational number

This leads to a contradiction that 3 + 2√5 is a rational number.

Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are repeated.

This is an exercise related to Game Theory.

The extended form is typically used to depict repeated games, commonly referred to as supergames, in game theory since they occur repeatedly across time.

The potential of collaborating means that we may choose to compromise in order to continue earning a payout over time, knowing that if we do not fulfill our part of the bargain, our adversary may decide not to either.

As contrast to one-shot games, recurring games provide a new set of incentives.

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Answer:

[tex]69 = 6x - 8[/tex]

Step-by-step explanation:

All 3 numbers must sum to 69, so we can draw out the second option [tex]x = 6x - 8[/tex]

Let the first number be x, adding 5x to the first x would give you 6x for the sum of the first and third numbers, therefore you can remove [tex]69 = 7x - 8[/tex] from your considerations as it includes 7x not 6x.

This leaves you with the one final answer [tex]69 = 6x - 8[/tex]

For the expression to be equal to the original one, we have;

[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]

We are given the algebraic expression;

(5x² + 25x + 20)/(7x)

Now, looking at the numerator, a common factor to all terms is 5. Thus, we will factorize it out to get;

5(x² + 5x + 4) = 5((x + 1)(x + 4))

Now, we see that the expression that simplifies the algebra is given as;

[(x² + 2x + 1) * ( )]/[( ) * (7x² + 7x)]

Now, the numerator and denominator can be factorized to get;

[(x + 1)(x + 1) * ( )]/[( ) * 7x(x + 1)]

Thus, x + 1 will cancel out to get;

[(x + 1) * ( )]/[( ) * 7x]

For the expression to be equal to the original one, we have;

[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]

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The total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.

Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.

We assume the total coins with Balu to be x.

The fraction of coins from Asian countries = 1/2.

Thus, the number of coins from the Asian countries = 1/2 of x = x/2.

The fraction of coins from European countries = 1/3.

Thus, the number of coins from the European countries = 1/3 of x = x/3.

The number of coins from America = 36.

Thus, the total number of coins = x/2 + x/3 + 36.

But, we assumed that the total number of coins is x.

Thus, we get a linear equation in one variable as follows:

x = x/2 + x/3 + 36.

We solve this equation as follows:

x = x/2 + x/3 + 36,

or, x - x/2 - x/3 = 36,

or, (6x - 3x - 2x)/6 = 36,

or, x/6 = 36,

or, x = 36*6 = 216.

Thus, the total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.

Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.

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Based on the amounts that Geraldo Saldana deposited in the month of May, the total simple interest comes to $18.98.

the simple interest earned can be found as:

= (3,600 x 3.5%/360 days x 30 days) + (3,000 x 3.5%/360 days x 20 days) x (5,000 x 3.5%/360 days x 6 days)

= 10.5 + 5.83 + 2.65

= $18.98

rest of the question is:

How much simple interest did his money earn?

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Answer: 9 yards

Step-by-step explanation:

Let's make equations to represent each situation.

The first equation says that the width is 3 less than 4 times the length, so let's put that into an equation:

[tex]w=4l-3[/tex]

Next, we can use the perimeter equation that [tex]P=2l+2w[/tex]. Since we know the perimeter is 24 yards, we can replace it for P.

[tex]24=2l+2w[/tex]

Now that we have two equations with two variables, we can use either elimination or substitution to solve them. Since w is already solved for in the first equation, let's plug it in the second equation.

[tex]24=2l+2(4l-3)\\ 12=l+4l-3\\ 12=5l-3\\ 15=5l\\ l=3[/tex]

Now, let's put l back into the first equation to solve for w.

[tex]w=4(3)-3\\ w=12-3\\ w=9[/tex]

The width is 9 yards

The graph of the line is shown in the attached image.

Given that the equation of the line y=-2/3x+1.

The line equation is an algebraic representation of the set of points, which together form a line in an exceedingly frame of reference.

First, we'll take the intercepts of equation y=-2/3x+1 . find

Find the y-intercept

The y-intercept is that the value of y when the worth of x is adequate zero

For x=0

y=-2/3(0)+1

y=1

The y-intercept is that the point (0.1)

Find the x-intercept

The x-intercept is that the value of x when the worth of y is adequate to zero

For y=0

y=-(2/3)x+1

0=(-2/3)x+1

-1=(-2/3)x

x=3/2 or 1.5

The y-intercept is that the point (1.5,0).

To plot the line on a graph, draw the intercepts and connect the dots as shown within the figure.

Therefore, the graph for the line y=-(2/3)x+1 is attached below.

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Answer:  12.56

Step-by-step explanation:

4 x 3.14

pi = 3.14

The common ratio of the geometric sequence is 1.5

Common ratio can be described as difference between two numbers in a sequence.

The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term

= 15/10

= 1.5

Hence the common ratio of the sequence is 1.5

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Answer:

B

Step-by-step explanation:

The common ratio of the geometric sequence is 1.5

Common ratio can be described as difference between two numbers in a sequence.

The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term

= 15/10

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1.5

Answer:

v=6

Step-by-step explanation:

v²=u²+2as

v²=12²+2(-3)(18)

v²=144-108

v²=30

v=6

Using variable concepts, of dependent and independent variables, it is found that the dependent variable is the amount of sales dollars earned.

In this problem, the manager believes that the amount of sales dollars earned is a function of the number of contacts that the salesperson makes, hence:

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The answer choice which represents the quotient of the expression given is; 1/(t+4)².

It follows from the task content that the quotient which is to be evaluated is;

(t+3)/t+4) ÷ (t²+7t +12)

The quotient can therefore be evaluated as follows;

= (t+3)/t+4) ÷ (t+3)(t+4)

= (t+3)/t+4) × 1/(t+3)(t+4)

= 1/(t+4) × 1/(t+4)

= 1/(t+4)².

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Answer:

c

Step-by-step explanation:

c

The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

            After 1 hour, the population is 3*10

            After 2 hours, -> 3*3*10

            After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

              number of the  insects per hour

              This can be generalized as a function of t, the time in hours:

              f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                             P = (3^t) * 10

             Since 20 minutes is equal to (1/3) hours, t can be substituted for

             (1/3) in order to calculate the population size after 20 minutes:

                  P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

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Answer:The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

           After 1 hour, the population is 3*10

           After 2 hours, -> 3*3*10

           After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

             number of the  insects per hour

             This can be generalized as a function of t, the time in hours:

             f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                            P = (3^t) * 10

            Since 20 minutes is equal to (1/3) hours, t can be substituted for

            (1/3) in order to calculate the population size after 20 minutes:

                 P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

F=ma

10=5m

4m=10*4/5

4m=8

So the answer is 8

Answer:

[tex]\frac{\sqrt{731}}{30}[/tex]

Step-by-step explanation:

We first observe that the angle is located in quadrant III

This allows us to draw a triangle as attached in the attachments.

Using this triangle, we can find sin([tex]\theta_1[/tex]).

Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].

So our final answer is the answer shown above.

You may be wondering how did the side lengths appear on the triangle.

From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.

Answer:

Meena age = 5 yrs Meenas father = 30

Step-by-step explanation:

let,

meena's age = x

meena's father's age = 6x

Five years from now

meena's age will be 1/3(6x)

meena's father's age will be 6x+5

A/Q

x+5+6x+5=2x+6x+5

=x+6x-2x-6x=5-5-5

= -x =-5

= x =5

meena's age = 5

meena's father's age = 6x

= 6×5

= 30

Answer:

A:(1/3x)+(x-2/4x^2+9)

Step-by-step explanation:

Edg2022

[tex]a(n) = 3 + 5n[/tex]

[tex]b(n) = - 2 + 6n[/tex]

[tex]a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)[/tex]

[tex]a(5) \: or \: b(5) = 3 + 5(5) = 28[/tex]

The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.

From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.

The new length will be:

= 2 × 3 2/3

= 7 1/3

Therefore, the new length is 7 1/3 feet.

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The total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape

The two cubes are stacked upon one another, so they form a composite figure.

The side lengths of the cubes are given as

Cube 1 = 4p

Cube 2 = 2q^2

The volume of each cube is calculated as:

Volume = Side length^3

So, the total volume is

Total = (4p)^3 + (2q^2)^3

Evaluate the exponents

Total = 64p^3 + 8q^6

Using the sum of cubes, we have the factored form to be

Total = (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

Hence, the total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

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Complete question

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?

Answer:

No, L and S are parallel.

Step-by-step explanation:

Perpendicular lines go directly opposite from each other, making a + looking arrangement. While parallel lines go in the exact same direction, making a = looking arrangement. The only way both S and L can both be perpendicular to R is if they are both parallel to each other. An illustration by yours truly is placed below to represent it visually.

                    L                                              |

_______________________________|_____

                                                                    |

                                                                    |

                                                                    |   R

                                                                    |

_______________________________|_____

                     S                                             |  

                                                                    |

Now, if this were on the outside of a sphere, then it would be totally possible to have three lines all be parallel, because they can curve with the sides of the sphere and create a triangle with all right angles.

The width of the rectangular backyard is 9 yards.

The width of the yard is three less than four times the length.

Therefore,

w = 4l - 3

Perimeter of a rectangle = 2l + 2w

where

l = length

w = width

Hence,

24 = 2l + 2(4l - 3)

24 = 2l + 8l - 6

24 = 10l - 6

24 + 6 = 10l

30 = 10l

l = 30 / 10

l = 3 yards

Hence,

w = 4(3) - 3

w = 12 - 3

w = 9 yards

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