There are 840 people sitting at tables at a
conference. If each table holds 12 people, there are ____ people at each table.

The random variable x is exponentially distributed, where x represents the waiting time to see a shooting star during a meteor shower. if x has an average value of 53 seconds, what are the parameters of the exponential distribution:  

                    X ~ Exp( μ = 53)

Random Variable:

A random variable is a variable that can take many values. This is because random events can have multiple outcomes. So don't confuse random variables with algebraic variables. Algebraic variables represent the values ​​of unknown quantities in computable algebraic equations. A random variable, on the other hand, can have a range of values ​​that could be the result of a random experiment.

Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X is 2 (1 + 1) and the maximum value is 12 (6 + 6). Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.

According to the Question:

We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:

            X ~ Exp( μ = 53)

But, also we can define the variable in terms of  like this:

            X ~ Exp (λ =1/λ =1/53)

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Josh will cover a total distance of 38 kilometres while trekking in Glacier National Park, having already covered 17 km of the park's trails.

The idea that will be applied in this situation is the usage of models to simplify expression.

Josh was able to hike 17 km, and since this is 2 km short of being halfway done, we can create the equation that models the situation.

The model can be written as  [17 + 2 = (1/2)h ]

h =length of the hike.

then  we can substitute the values so that we can know the value of h,

[17 + 2 = (1/2)h ]

[19 =0.5h]

h = 38 km

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The properly written question:

Josh is hiking Glacier National Park. He has now hiked a total of 17 \text{ km}17 km17, space, k, m and is 2 \text{ km}2 km2, space, k, m short of being \dfrac12 ​2 ​ ​1 ​​ start fraction, 1, divided by, 2, end fraction of the way done with his hike.

The equation that represents the transformation of vertical reflection and shift down by 3 of a cubic function is (a) [tex]g(x) = -x^{3} -3[/tex] .

The Cubic function is represented as ; [tex]y=x^{3}[/tex] ;

we have to apply the given transformations :

(i) The first transformation states that , there is a vertical reflection of the cubic function ,

So , after vertical reflection that equation becomes ⇒ [tex]y=-x^{3}[/tex] ;

(ii) The second transformation is : the graph shifts down by 3 units ,

So ,after shifting down by 3 units the equation becomes ⇒ [tex]y = -x^{3} -3[/tex] ;

let the function y be denoted by g(x) .

Therefore , after applying the transformation the equation becomes [tex]g(x) = -x^{3} -3[/tex] .

The given question is incomplete , the complete question is

Which equation represents these transformations of a cubic function?

(i) vertical reflection

(ii) shift down 3

(a) g(x) = -x³ -3

(b) g(x) = (-x)³ +3

(c) g(x) = (x+3)³

(d) g(x) = -(x-1)³ + 3

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The estimated amount of paint needed for the grain silo is 103.61 m².

The cylinder and the conical lid are the two components that make up the figure. As a result, we solve for the total surface area of the cylinder and the cone and add.

TSA for cylinder = 2πr (h + r), for h = 6.2 m and r = 1.7 m.

= 2π * 1.7 (6.2 + 1.7)

= 84.38

TSA for cone = πr (l + r), for l = slant height = 1.9 m and r = 1.7,

resulting in a value = π * 1.7 (1.9 + 1.7) = 19.23

TSA for the cone plus TSA for the cylinder equals how much paint is needed.

how much paint needed = 84.38 + 19.23

how much paint needed = 103.61 m²

The volume of paint to be used depends on the thickness of the painting.

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Answer: B. [tex]x^{2} - 16x + 64 = -21 + 64[/tex]

Step-by-step explanation:

Step-by-step explanation:

(9-12)×5+13-2

=(-3)×5+13-2, (frist bracket )

=-15+13-2

=-4

Answer:

(9-12)x5+13-2= -4

Step-by-step explanation:

1. Solve the equation in parenthesis. 9-12 is -3. If you use a number line and add 9, then subtract twelve, you'll be three behind zero!

2. Then multiply -3 by five which is -15. -15+13 is -2, (since the thirteen is positive, it cancels out thirteen negative ones, and leaves us with two negative ones)

3. -2 -2=-4 (Negative two, subtracted by positive two, is negative four) subtracting a positive number, is the same as adding its opposite. Example. 8-5=3 (as we all know). And 8+-5=3. Numbers that have the same absolute value are opposites. AKA Numbers that are the same distance away from zero. -5 and 5 are both 5 spaces from zero!

Answer:

Step-by-step explanation:

15x² - 2x - 1 = 0

15x² - 5x + 3x - 1 = 0

5x(3x - 1) + 3x - 1 = 0

(5x + 1)(3x - 1) = 0

x = -1/5, 1/3

8x² - 10x - 3 = 0

8x² - 12x + 2x - 3 = 0

4x(2x - 3) + 2x - 3 = 0

(4x+1)(2x-3) = 0

x = -1/4 , 3/2

16x² - 8x + 3 = 0

This question has complex answers as the D = 64 - 192 < 0

So, ignore this question. It is wrong or it has complex answers.

Use the quadratic formula for it.

9x² - 6x - 2 = 0

This also needs the quadratic formula as the answer is in roots.

8x² - 2x - 3 = 0

8x² - 6x + 4x - 3 = 0

2x ( 4x - 3) + 4x - 3 = 0

(2x + 1)(4x-3) = 0

x = -1/2 , 3/4

The area, in square inches, of a right triangle with a 24-inch leg and a 25-inch hypotenuse is 84 cm.

The area of a right triangle of base b and height h can be calculated using the formula 1/2 × b × h and its perimeter is obtained by just adding all the sides.

Length of one side of the right triangle (p) = 24-inch

Length of the hypotenuse of the right triangle (h) = 25-inch

Therefore, we can calculate the third side (b) of the triangle by applying the Pythagorean theorem

p² + b² = h²

24² + b² = 25²

b² = 625 - 576

b² = 49

b = 7 inch

Now, the area of the right triangle will be

= 1/2 × b × h

= 1/2 × 7 × 24

= 84 inch²

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The cost of credit, in dollars, for this loan is 299.6107 dollars.

Let's recall the total cost of the computer with tax C. Then,

C = 1999.99 + 0.07 × 1999.99 = 1999.99 + 139.9993 = 2139.9893.

Since the loan allows you to pay for the computer in 12 equal payments of $203.30, the total cost of the loan is 12 × 203.30 = 2439.60.

The cost of credit is then the difference between the total cost of the computer with tax and the total cost of the loan: 2439.60 - 2139.9893 = 299.6107.

So the cost of credit is 299.6103 dollars.

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Answer:

Look, I don't know how to tell the answers by looking at the squares but I can tell you how to do it.

a) Subtract the number on the left with the number on the top, pretty simple, i am sure u can do that.

b) After you have done that, count how many negative scores you got and divide that by 9.

c)Finally, count all the numbers more than 3 again and divide it by 9.

Note: 9 here is the total number of outcomes.

Thanks

The maximum area the rectangle can have, is 2.31 square unit.

In the given question, a rectangle has its base on the x axis and its upper two vertices on the parabola 16 - [tex]x^2[/tex].

We have to find the maximum area the rectangle can have.

Let Length is x and width is y.

So, Area of Rectangle = length × breadth

Area of Rectangle = xy

Since, base is on the x - axis, therefore, length will be 2x.

Now, Area of Rectangle = 2xy

The given parabola y = 16 - [tex]x^2[/tex]

Area of Rectangle = 2x(16 - [tex]x^2[/tex])

Area of Rectangle = 32x - 2[tex]x^3[/tex]

For Largest Area find derivative of Area and set equal to zero.

A'(x) = 32 - 6[tex]x^2[/tex]

Now equating equal to zero

32 - 6[tex]x^2[/tex] = 0

Subtract 32 on both side, we get

- 6[tex]x^2[/tex] = - 32

Divide by -6 on both side, we get

[tex]x^2[/tex] = 5.33

Taking square root on both side, we get

x = 2.31

Hence, the maximum area the rectangle can have, is 2.31 square unit.

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Hope it helps.

If you have any query, feel free to ask.

Answer:

Step-by-step explanation:

TO the center

To find the equivalent expression with the fewest symbols possible for 1/3(3j6),One third of three times the value of six, which is equal to one times the value of two.

1/3(3j6)

= 1/3(3*6)

= 1/3(18)

= 18/3

= 6

= 1j2

To find the equivalent expression with the fewest symbols possible for 1/3(3j6), we need to start by multiplying 3 and 6 together. This gives us the result of 18. Next, we divide 18 by 3, which gives us the result of 6. Finally, we express the result as 1j2, which is the equivalent of 1/3(3j6) with the fewest possible symbols. By following these steps, we can easily calculate the equivalent expression with the fewest symbols. In this case, it is 1j2. The process of calculating the equivalent expression with the fewest symbols is relatively straightforward, but it is important to remember to use the correct order of operations when performing calculations. To ensure accuracy, it is best to work step by step, multiplying 3 and 6 together first and then dividing 18 by 3 to get the final result of 1j2.

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Answer:

This is an expression. To simplify it, we will combine like terms.

9d - 4p - 6 - 10d + 8 = (-9d - 10d) - 4p - 6 + 8 = -19d - 4p + 2

So the simplified expression is -19d - 4p + 2

The roast needs to sit 116 minutes before it is ready to be eaten.

Let T(t) = temperature after t minutes

By Newton's Law of Cooling, T(t) = 75 + (185-75)e^kt = 75 + 110e^kt

Newton's law of cooling states that the rate of change of temperature of an object is directly proportional to the difference in temperature between the object and its surroundings. Mathematically, it can be expressed as:

dT/dt = k(T - T0)

Where:

dT/dt is the rate of change of temperature (in degrees per time unit, such as degrees per second)

k is the cooling constant (in units of 1/time), which is a measure of how quickly an object cools down and depends on the properties of the object and its surroundings

T is the current temperature of the object (in degrees)

(a). T(30) = 75 + 110e^30k = 150

⇒110e^30k = 75

⇒e^30k = 0.681818

⇒30k = ln(0.681818)

⇒k = -0.0127664

We know, T(t) = 75 + 110e^-0.0127664t

  So, T(45) = 75 + 110e^-0.0127664(45) ≈ 137°

(b).  T(t) = 100 when 75 + 110e^-0.0127664t = 100

⇒ e^-0.0127664t = 0.2272727

⇒-0.0127664t = ln(0.2272727)

 ⇒t ≈ 116 minutes

Therefore, The roast needs to sit 116 minutes before it is ready to be eaten.

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The required proportion of side lengths is JK/LK= JM/LN.

The Side-Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it splits those sides proportionally. In the case of triangle J K L, with line segment M N drawn parallel to side J L and intersecting sides J K and L K, the proportion of the lengths of the sides that are split can be determined by the ratio of the corresponding segments on each side.

Let's call the length of side J K as x, the length of side J L as y, and the length of side L K as z. Let the length of segment J M be a and the length of segment L N be b.

According to the side-splitter theorem, the proportion of the length of side J K to side L K is equal to the proportion of the length of segment J M to segment L N. This means that:

x/z = a/b

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By applying independent and disjoint events theory, it can be concluded that A and B are neither disjoint nor independent (option D).

In probability, based on the occurrences, there are two types of events: independent and disjoint events.

Now we observe the data given:

p(a) = 0.3

p(b) = 0.2

p(a and b) = 0.4.

First, we check the independence. Here p(a and b) = 0.4. Whereas, if a and b are independent events, then:

p(a and b) = p(a) * p(b)

                = 0.3 * 0.2

                = 0.06

Since the value is different, we can conclude that events A and B are not independent.

Second, we check whether these events are disjoint events. Since the value of p(a and b) is not 0, these events are disjoint events.

Therefore, we can conclude that a and b are neither disjoint nor independent (option D)

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Answer:

(1, 1 )

Step-by-step explanation:

choose any value of x to substitute into the equation and solve for y

choosing x = 1 , then

- 1 + 5y = 4 ( add 1 to both sides )

5y = 5 ( divide both sides by 5 )

y = 1

then (1, 1 ) is a solution to the equation

Answer:

- x + 5 y = 4                                     (x = 6)

- ( 6 ) + 5 × 2 = 4                             (y = 2)

- 6 + 10 = 4

 4 = 4

∴ (6, 2) is an ordered pair that is a solution to the given equation .

The curve's approximate length is 33/16, as mentioned throughout the paragraph.

Curved shapes are those composed entirely of curves. A curved form, such as a circle, an ellipse, a parabola, or an arc, can be two-dimensional. Three-dimensional objects like sphere, cones, and cylinders can also have curved forms. A curved line is one that is not straight. A curve results from a point that is not moving in a straight line.

We'll use the following formula to get the angle of a function:

[tex]\begin{aligned}& L=\int d s \\& d s=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y\end{aligned}[/tex]

Let's now calculate x's derivative:

[tex]\begin{aligned}& \frac{d x}{d y}=\frac{4}{8} y^3-\frac{2}{4} \frac{1}{y^3} \\& =\frac{1}{2}\left(y^3-\frac{1}{y^3}\right)\end{aligned}[/tex]

Okay, now enter this into the ds formula to obtain:

[tex]d s=\sqrt{1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2}[/tex]

Observe that:

[tex]\begin{aligned}& 1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2=1+\frac{1}{4} y^6-\frac{1}{2}+\frac{1}{4 y^6} \\& =\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2\end{aligned}[/tex]

The integral will now be easier to understand:

[tex]\begin{aligned}& L=\int_1^2 \sqrt{\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2} d y=\int_1^2 \frac{1}{2} y^3+\frac{1}{2} y^{-3} d y \\& =\left[\frac{1}{8} y^4-\frac{1}{4} y^{-2}\right]_2^1 \\& =\frac{33}{16}\end{aligned}[/tex]

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The complete question is-

Find the exact length of the curve:

[tex]x=\frac{y^4}{8}+\frac{1}{4 y^2}, 1 \leq y \leq 2[/tex]

The number of pencils that he bought will be 21 pencils.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Karani bought 4 pencils and 6 biro pens for $66 and Mary bought 2 pencils and 5 biro pens for $51.

Let 'x' be the cost of pencils and 'y' be the cost of biro pens. Then the equations are given as,

4x + 6y = 66         ...1

2x + 5y = 51

4y + 10y = 102      ...2

From equations 1 and 2, then we have

10y - 6y = 102 - 66

4y = 36

y = 9

Then the value of 'x' is given as,

2x + 5(9) = 51

2x + 45 = 51

2x = 6

x = 3

Ondieki spent $228 to buy the same type of pencils and biro pens. If the number of biro pens he bought was 4 more than the number of pencils.

Let 'm' and 'n' be the number of pencils and biro pens, respectively.

3m + 9n = 288          ...3

n = m + 4                   ...4

From equations 3 and 4, then we have

3m + 9(m + 4) = 288

12m + 36 = 288

12m = 252

m = 21

Then the value of 'n' is given as,

n = 21 + 4

n = 25

The number of pencils that he bought will be 21 pencils.

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Answer:

7) y = [tex]\frac{2}{3}[/tex]x + 13

8) y = 8x - 20

Step-by-step explanation:

Question 7

y - 9 = [tex]\frac{2}{3}[/tex](x + 6)

Step 1: Distribute [tex]\frac{2}{3}[/tex] to (x + 6); y - 9 = [tex]\frac{2}{3}[/tex]x + 4

Step 2: Add 9 to both sides; y = [tex]\frac{2}{3}[/tex]x + 13

Question 8

y + 4 = 8(x - 2)

Step 1: Distribute 8 to (x - 2); y + 4 = 8x - 16

Step 2: Subtract 4 from both sides; y = 8x - 20

Answer: The correct equation that matches the statement "The product of a number, x, and 0.28 is 13.44" is:

0.28x = 13.44

This equation states that when a number x is multiplied by 0.28, the result is 13.44.

Step-by-step explanation:

The factorize expression of 25x²-4x²-9 is 3(7x²-3).

Factorization is a process to simplify the expression by finding the factors of that expression.

And to find the same expression from factors, you have to reverse the process.

We have the quadratic function,

25x²-4x²-9.

To factorize the function:

First, combine similar terms,

25x²-4x²-9,

= 21x²-9.

Now, factor out the common factor.

That means,

3(7x²-3).

Therefore, the required function is 3(7x²-3).

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The measure of angle R, in degrees, is 150°.

A parallelogram is a quadrilateral or four-sided shape, that has opposite sides that are parallel to each other. The opposite sides of a parallelogram are equal in length, and the opposite angles are also equal in measure.

In a parallelogram, opposite angles are equal, so if the measure of angle P is five times the measure of angle Q, then the measure of angle R must also be five times the measure of angle Q.

Let's call the measure of angle Q "x". Then the measure of angle P is 5x, and the measure of angle R is 5x.

Therefore, the measure of angle R in degrees is 5x degrees.

We know,

All of the angles added together = 360°

∠5Q +∠Q+∠5Q+∠Q = 360    Solve for Q

∠12Q = 360  

⇒  ∠Q = 30°

then ∠P = ∠5Q = 5(30) = 150°    

and,

 ∠P = ∠R    

⇒ ∠R = 150°

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The dimensions of the rectangular plot that require the least amount of fencing is :

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

Now, According to the question:

600 [tex]u^2[/tex] of land to be enclosed by fence

Area inside plot should be maximized, amount of fence should be minimized

If we draw a quick sketch, we get something like this:

_____ _____

|        |         |

|        |         |

|        |         |

|        |         |

The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.

Let's put some variables into our picture so we can define our constraints.

       y        y  

  |         |        |

x |      x |      x |

  |         |        |

  |         |        |

Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.

A = x × 2y = area = 600

P = 3x + 4y = perimeter = a minimum

First we solve the area equation for y:

y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]  

and then we substitute that result into our perimeter equation:

P = 3x + 4 (300/x)

P = 3x + 1200/x

Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]

We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.

In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is

P'(x) = 3 - 1200[tex]x^-^2[/tex]

When set equal to zero, we can solve for x:

3 - 1200[tex]x^-^2[/tex]= 0

1 - 400[tex]x^-^2[/tex] = 0

1 = 400/[tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 400

x = ± 20

Our fence length can't be a negative number so our answer must be 20u.

If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.

The y length is 300/(20) = 15

Let's put all of our numbers into our picture to see if it make sense.

      15      15    

    |        |         |

20 |    20 |    20 |

    |        |         |

    |        |         |

       15      15

Sure enough our area is 600.

Here's what we have right now:

A(20, 15) = 600

P(20, 15) = 120

How about we try something a little bigger like 20.5 for x and 14.63 for y?

A(20.5, 14.63) = 600

P(20.5, 14.63) = 120.02

How about we try something a little smaller like 19.5 for x and 15.38 for y?

A(19.5, 15.38) = 600

P(19.5, 15.38) = 120.02

It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.

You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.

Each rectangle is 300 u^2. We want a square so each side would be √(300) = 17.32

              17.32         17.32    

        |                |                 |

17.32 |       17.32 |        17.32 |

        |                |                 |

             17.32          17.32

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

Hence, The dimensions of the rectangular plot that require the least amount of fencing is :

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

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Answer: Side SK

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.The square root function is a mathematical function that returns the positive number that, when multiplied by itself, gives the original number. It can be represented using the symbol √ or using the exponent 1/2. The cube root function is a mathematical function that returns the number that, when multiplied by itself three times, gives the original number. It can be represented using the symbol ∛ or using the exponent 1/3.

2.The ancient civilizations of Babylonia, Greece, and India all independently discovered the square root function. The concept of cube root was first mentioned in the ancient Indian text "Sulbasutras" around 800 BCE. The Greek mathematician Euclid also described the cube root function in his work "Elements" around 300 BCE.

3.The square root function is used in many areas of mathematics and science, including geometry, trigonometry, and physics. In real life, square root functions are used in many areas such as engineering, architecture, and finance. For example, in engineering, square root functions are used to calculate the stress and strain on materials. In architecture, square root functions are used to calculate the area of a building or room. In finance, square root functions are used to calculate the volatility of an asset. Similarly, cube root function is used in mathematics, physics, engineering, economics, and other fields. It is used to find the cube root of a number, to find the volume of a cube, to solve equations, and to calculate the cube root of a complex number.