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The probability that the first person will be seated at a plastic table is 0.8

From the question, we have the following parameters that can be used in our computation:

Plastic tables = 12

Composite tables = 3

Using the above as a guide, we have the following:

Total tables = 12 + 3

Evaluate the sum

Total tables = 15

So, we have the probability to be

P = Plastic tables/Total tables

Substitute the known values in the above equation, so, we have the following representation

P = 12/15

Evaluate

P = 0.8

Hence, the probability that the first person will be seated at a plastic table is 0.8

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By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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The value of x is -1 which makes the model true

The equation from the given model will be 5x+6=1

We have to find the value of x

5x+6=1

Subtract 6 from both sides

5x=-5

Divide both sides by 5

x=-1

Hence, the value of x is -1 which makes the model true

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The zero of f is equal to -12.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (1, -9) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-9) = 3(x - 1)

y = 3x - 12

When x = 0, the y-value is given by;

f(0) = 3(0) - 12

f(0) = -12

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Answer:

  C.  18/48 and 21/56

Step-by-step explanation:

You want to identify pairs of ratios that are proportional.

Ratios are proportional when they have the same value. We can check whether the values are the same by reducing each ratio to lowest terms.

The attached calculator display shows the proportional ratios are ...

  18/48 and 21/56 . . . . choice C

__

Additional comment

Both of these reduce to 3/8. You can remove a factor of 6 from the numbers of the first ratio, and a factor of 7 from the numbers of the second ratio to reduce both of them to 3/8.

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Answer: C.  18/48 and 21/56

Step-by-step explanation:  Hope it helps

The solution of the expression is,

⇒ - 37/14

We have to given that;

Expression to solve is,

⇒ 6 - 5/4 × 6 - 8/7

Now, We can simplify the expression as,

⇒ 6 - 5/4 × 6 - 8/7

⇒ 6 - 5/2 × 3 - 8/7

⇒ 6 - 15/2 - 8/7

⇒ (12 - 15)/2 - 8/7

⇒ - 3/2 - 8/7

⇒ (- 21 - 16) / 14

⇒ - 37/14

Thus, The solution of the expression is,

⇒ - 37/14

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Answer:

[tex]y = (x-1)^2-9[/tex]

Step-by-step explanation:

The form of a quadratic equation is  [tex]y = a(x-h)^2+k[/tex]. Lets identify each change in words before switching to the formula:

Shifted 1 right

Shifted 9 down

No stretch horizontally

No stretch vertically.

Our equation will be [tex]y = (x-1)^2-9[/tex].

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 3, −2+4i, −2−4i

To find the zeros of the polynomial p(x), we need to find the values of x such that p(x) = 0.

One way to do this is to use the rational root theorem, which states that if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors), then p must divide the constant term and q must divide the leading coefficient.

For the polynomial, [tex]p(x) = x^3 + x^2 + 8x - 60,[/tex] the constant term is -60 and the leading coefficient is 1.

Therefore, the possible rational roots are:

±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60

We can then use synthetic division or long division to check which of these roots are actually zeros of the polynomial.

Trying the possible roots, we find that x = 3 is a zero of the polynomial, since p(3) = 0.

Using long division or synthetic division, we can then divide p(x) by (x - 3) to get a quadratic factor:

[tex]x^3 + x^2 + 8x - 60 = (x - 3)(x^2 + 4x + 20)[/tex]

The quadratic factor [tex]x^2 + 4x + 20[/tex] has no real roots since its discriminant [tex](b^2 - 4ac)[/tex] is negative. Therefore, the zeros of the polynomial p(x) are:

x = 3 (with multiplicity 1)

x = -2 ± 4i (with multiplicity 1 each)

Therefore, the zeros of the polynomial p(x) are 3, -2 + 4i, and -2 - 4i.

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The relation is a function because (d) Yes because for each output there is exactly one input.

From the question, we have the following parameters that can be used in our computation:

The graph

The graph can be represented as

x  g(x)

-5  1

-2  0

-1   -1

0  2

1  3

5   1

The above table of values is a function

This is so because each output values have different input values.

i.e. it would pass the vertical line test when represented on a graph

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Answer:

48

Step-by-step explanation:

just add the numbers. 48 is equal to (4+44)

have a great day and thx for your inquiry :)

The sum of their ages if the son’s age is X is 3X.

We are given that;

x=A father is twice as old as his son

Now,

If the son’s age is X,

Then the father’s age = 2X.

The sum of their ages

= X + 2X

= 3X.

Therefore, by algebra the answer will be 3X.

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right isosceles triangle.

Right Scalene Triangle

Angles

Acute angle:  An angle whose measure is less than 90 degrees.

Right angle:  An angle whose measure IS 90 degrees.  As a consequence, the two rays that form the angle are perpendicular.

Obtuse angle:  An angle whose measure is greater than 90 degrees.

Triangles (defined by side lengths)

Equilateral Triangle:  A triangle with all three sides congruent (all three sides have the same length)

Isosceles Triangle:  A triangle that contains two congruent sides (two sides with the same length).

Scalene Triangle: A triangle with three different length sides.

Triangles (defined by angle measures)

Acute Triangle:  A triangle whose angles are all acute angles

Right Triangle:  A triangle that contains one right angle.

Obtuse Triangle:  A triangle that contains one obtuse angle.

By angle

Our triangle has an angle that appears to be a right angle (the two sides look perpendicular).  This would be a Right Triangle (when classified by angles).

By side length

All three sides of this triangle are different in length.  This would be a Scalene Triangle (when classified by side length).

Combining the attributes:

This is both a Right Triangle and a Scalene Triangle.  Together, it is a Right Scalene Triangle.

Right Isosceles

To be a Right Isosceles Triangle, the triangle needs to be both a Right Triangle, and an Isosceles Triangle.

A Right triangle contains one right angle, and an Isosceles Triangle contains a pair of sides that are the same length.

While this triangle does contain a right angle, all three sides appear to be different length (scalene).

This is not a Right Isosceles Triangle.

Acute Isosceles

To be an Acute Isosceles Triangle, the triangle needs to be both an Acute Triangle, and an Isosceles Triangle.

An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and an Isosceles Triangle contains a pair of sides that are the same length.

However, this triangle contains a right angle (equal to 90 degrees, not less than), so it cannot be an Acute Triangle, and this triangle does not contain a pair of sides that are the same length, so it cannot be an Isosceles Triangle.

This is not an Acute Isosceles Triangle.

Acute Scalene

To be an Acute Scalene Triangle, the triangle needs to be both an Acute Triangle, and a Scalene Triangle.

An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and a Scalene Triangle has sides that are all different length.

While this triangle does have sides that are all different length, it contains a right angle, whose measure IS 90 degrees (not less than 90 degrees).  So it cannot be an Acute Triangle

This is not an Acute Scalene Triangle.

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]

The unlabeled side length for this problem has the measure given as follows:

13.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The sides for this problem are given as follows:

5 and 12.

Hence the measure of the hypotenuse is obtained as follows:

h² = 5² + 12²

h² = 169

h = 13.

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The value of sin Ф is 72/97.

We have,

Since cos Ф = -65/97 and Ф terminates in quadrant III, we know that cos Ф is negative (since cosine is negative in quadrants II and III).

We can use the Pythagorean identity to find sin Ф:

sin² Ф + cos² Ф = 1

Substituting cos Ф = -65/97, we get:

sin² Ф + (-65/97)² = 1

Simplifying, we get:

sin² Ф = 1 - (-65/97)²

Taking the square root of both sides (since sin Ф is positive in quadrant III), we get:

sin Ф = √(1 - (-65/97)²)

sin Ф = √(1 - 4225/9409)

sin Ф = √(5184/9409)

sin Ф = 72/97

Therefore,

The value of sin Ф is 72/97.

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Answer:

2553(base 7) = 969(base 10)

Step-by-step explanation:

3 in units place means 3.

5 in the 7's place means 5 × 7 = 35

5 in the 7²'s place means 5 × 7² = 5 × 49 = 245

2 in the 7³'s place means 2 × 7³ = 2 × 343 = 686

3 + 35 + 245 + 686 = 969

The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR.

To calculate the MIRR, we need to find the future value of the positive cash flows at the end of year 4, using the reinvestment rate equal to the WACC. We can then find the discount rate that equates the present value of the initial investment with the future value of the negative cash flows and the positive future value of the positive cash flows.

Using the financial calculator or spreadsheet software, we can find that the future value of the positive cash flows is $698,711.27, and the MIRR is 27.46%.

Therefore, the MIRR is 27.46%, and based on the MIRR criterion, the project should be accepted if the required rate of return is less than 27.46%.

The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR. This is because the IRR assumes that positive cash flows are reinvested at the IRR, which may not be realistic, while the MIRR assumes that positive cash flows are reinvested at the WACC, which is usually more realistic.

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Find three additional polar representations of the point, using −2π<θ<2π. (Enter your answers in order from smallest to largest first by r-value, then by θ-value.) (r,θ)= ( (r,θ)r= ( (r,θ)= ( Question: That's it! Find three additional polar representations of the point, using −2π<θ<2π.

The number that belongs on the green box is given as follows:

g = 11.08.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the internal angles of a triangle is of 180º, hence the missing angle is given as follows:

120 + 37 + x = 180

157 + x = 180

x = 23º.

Then the relation to obtain the number in the green box is given as follows:

sin(23º)/5 = sin(120º)/g

g = 5 x sine of 120 degrees/sine of 23 degrees

g = 11.08.

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Answer:

18. The probability of rolling a number less than five or an odd number

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The value of the product of expression is,

⇒ m⁶n² + 3m³n - 40

We have to given that;

Expression is,

⇒ (m³n + 8) (m³n - 5)

Now, We can product the expression is,

⇒ (m³n + 8) (m³n - 5)

⇒ m⁶n² - 5m³n + 8m³n - 40

⇒ m⁶n² + 3m³n - 40

Thus, The value of the product of expression is,

⇒ m⁶n² + 3m³n - 40

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The value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

arc TV = 2(m∠TUV)

54x - 2 = 2(80)

54x - 2 = 160

54x = 160 + 2 {collect like terms}

54x = 162

x = 162/54 {divide through by 3}

x = 3

Therefore, the value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3.

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Answer:

Perimeter is 20.57 yards.

Step-by-step explanation:

Perimeter is the distance around the outside of a shape. This shape is a semicircle, that is, half of a circle.

We can calculate the circumference of the circle (that's the distance around the whole circle) and then cut it in half. Then add on the flat, straight side.

Circumference is:

C = pi•d

C = pi•8

C = 25.1327

This is the distance around the whole circle. For the curved part of our shape, we only need half of that.

25.1327/2

= 12.56637

Lastly, we add on the straight side, which was given as 8 yds.

12.56637 + 8

= 20.56637

Round to two decimal places.

20.57

The perimeter is 20.57yds.

Answer:

your answer is B

Step-by-step explanation:

because if you look at the c coordinator plane 1 is on y=1 and x=1 so if you just decrease but yet add you'll get y=2 and x+2 and you'll get B

The solution of the equation using Cramer's rule is x = -3, and y = 2.

The solution of the equation using Cramer's rule is calculated as follows;

x + 2y = 1

-3x - 2y = 5

Find the determinant of the matrix;

[1     2]

[-3   -2]

Δ = -2 - (-6) = 4

Find the x determinant;

[1      2]

[5     -2]

Δx = -2 - 10 = -12

Find the y determinant;

[1      1]

[-3   5]

Δy = 5 - (-3) = 8

The value of x = Δx/Δ  = -12/4 = -3

The value of y = Δy/Δ  = 8/4 = 2

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Answer:

The median is the best measure of center, and it equals 19.

Step-by-step explanation:

The line for the median is exactly on 19

The line in the box of a box plot represents the median of the data. For this particular data set shown in the box plot, the median is 19.

In the described box plot, the line in the box that is at the number 19 represents the median of the data. This is because a box plot illustrates the five number summary of a data set: the minimum, the first quartile, the median (second quartile), the third quartile, and the maximum. The line inside the box always represents the median. Therefore, the correct choice is: The median is the best measure of center, and it equals 19.

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