Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statistically fair and morally fair.
Situation #1 A high school student is deciding whether to first clean his room or do his homework. He decides by picking a tile at random from a bag of lettered tiles. If he picks a consonant he will clean his room, and if he picks a vowel he will do his homework.
Situation #2 There are four candidates eligible for a vacancy at a company. Ignoring qualifications and experience, the recruitment manager decides which candidate to hire by writing their names on pieces of paper, shuffling the papers, and drawing one at random.
Situation #3 Five cousins are deciding which board game to play. They each write their preferred game on a different section of a spinner that has five equally-sized sections. They spin the spinner and will play the game written on the section where the spinner lands.
Situation #4 To determine who can choose the spot for a picnic, Kate picks a tile at random from a collection of five tiles, numbered 2 through 6. Kate chooses the spot if she picks a prime number, and Charles chooses if Kate picks a composite number.
Situation #5 Five roommates all want to attend an event, but they only have four invites. To decide who will attend, they shuffle a set of five cards consisting of four aces and a king. Each roommate is randomly dealt a card. The ones dealt an ace will attend the event.
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Answer:

goto gauth maths and ask again

Answer:

2/3(cx+1/2)-1/4=5/2. CX=29/8

Answer:

v = √(LT/m)

Step-by-step explanation:

Given :

Multiply both sides with L :

Divide both sides by m :

Take the square root on each side :

Answer:

[tex]v = \sqrt{ \frac{tl}{m} } [/tex]

Step-by-step explanation:

[tex]t = \frac{mv {}^{2} }{l} \\ making \: v \: the \: subject \\ t \times l = mv {}^{2} \\ dividing \: bothsides \: by \: m \\ \frac{tl}{m} = \frac{mv {}^{2} }{m} \\ v {}^{2} = \frac{tl}{m} \\ finally \\ v = \sqrt{ \frac{tl}{m} } [/tex]

Answer:

A- 17/24 sugar all together

B- yes the bowl would be big enough because when you add all the ingredients together it equals 3 5/24 and it's less than 3 1/2.

Based on the table, a conclusion which can be drawn about f(x) and g(x) is that: B. the functions f(x) and g(x) are reflections over the y-axis.

In Mathematics, two functions are considered to be reflections over the y-axis under the following condition:

If, f(-x) = g(x).

Evaluating the given functions, we have:

f(x) = 2ˣ

f(-x) = 2⁻ˣ = ½ˣ = g(x).

Similarly, two functions are considered to be reflections over the x-axis under the following condition:

If, -f(x) = g(x).

Evaluating the given functions, we have:

f(x) = 2ˣ

-f(x) = -2ˣ ≠ g(x).

Therefore, we can logically conclude that the two functions f(x) and g(x) are considered to be reflections over the y-axis but not the x-axis.

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Answer:

b

Step-by-step explanation:

The statements true about the slopes and lines are

a) Line TV has a slope of 0.

b) Lines RS and TV are parallel.

c) Line SW has an undefined slope.

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be S ( 2 , 6 )

Let the second point be R ( -8 , 6 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 6 - 6 ) / ( -8 - 2 ) = 0

So , the slope of line RS = 0

Let the point T = T ( -6 , -4 )

Let the point V = V ( 8 , -4 )

Slope m = ( -4 - (-4) ) / ( 8 - (-6) ) = 0

So , the slope of line TV = 0

And , the lines RS and TV are parallel as they have the same slope

Now , the x coordinate of the point S and W does not change

So , it has an undefined slope

Hence , the equation of line is solved

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The complete question is attached below :

Lines RS, TV, and SW are shown.

Which statements are true about these lines? Select

three options.

Line RS has a slope of 6.

Line SW has an undefined slope.

Line TV has a slope of 0.

Lines RS and TV are parallel.

Line SW is perpendicular to line RS, but not to line TV.

Step-by-step explanation:

The height of the wall would be x - 1 and the perimeter of the wall is 32 feet

The area of the window is given as:

A = x^2 - 4x + 3

Expand

A = x^2 - 3x - x + 3

Factorize

A = x(x - 3) - 1(x - 3)

Factor out x - 3

A = (x - 1)(x - 3)

The width of the wall is given as: x - 3

So, the height of the wall would be x - 1

How to determine the perimeter?

The perimeter is calculated using:

P = 2 *(Width + Height)

This gives

P = 2 * (x - 1 + x - 3)

When x = 10, we have:

P = 2 * (10 - 1 + 10 - 3)

Evaluate

P = 32

Hence, the perimeter of the wall is 32 feet

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Equation of the function: f(x) = 4 sin (x/2) + 6.

The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).

Given: max value= 6, min value= -2, y-intercept= 6.

As, standard form f(x) = A sin (ωx +φ) + k,

where A is the amplitude, ω is the angular velocity with ω=2πf.

Now,

A = |6- (-2)/2|

A = |6 +2/2| = 8/2

A = 4

Also, ω:

The period of a sinusoidal is T = 1/f

so, f = 1 / T

ω = 2πf

ω = 2π ( 1/T) with T = 4π

ω = 2π (1/(4π) = 2π (2)

ω = 1/2

The y-intercept k = 6

So, equation with values A =4, ω = 1/2, k = 6, φ = 0.

f(x) = A f(x)

f(x) = A sin (ωx +φ) + k

f(x) = 4 sin (x/2) + 6.

Hence, equation of the function f(x) = 4 sin (x/2) + 6.

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Answer:

Step-by-step explanation:

NOTE : we have 6×6=36 possible outcome.

we can resume the set of outcomes in the table below :

Then

the probability that the sum is not divisible

by 2 and not divisible by 4 :

= 18/36

= 1/2

Answer:

B

Step-by-step explanation:

Total money spent = 25 + 30 + 10 + 8 = 73

Per week = 73 / 4 = 18.25

Answer:

The answers are in the picture. Remember that first is x and then y when you see those coordinated again. (10,11) X=10 and Y=11.

Step-by-step explanation:

Answer:

???

Step-by-step explanation:

Answer:

perpendicular

Step-by-step explanation:

x = -2    is a vertical line at   x   =  -2

y is a horizontal line          the two lines are perpindicular

the lines  x=−2, y=10 are perpendicular to each other.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Here, The given equations are :

x=−2 and y=10

First, consider x = -2 equation :

equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.

Consider second line y = 10 :

line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.

Therefore, the lines  x=−2, y=10 are perpendicular to each other.

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Answer:

-204kk+3+32k/4k

Hope this helps!!

Answer:

Nominal wages, prices, and perceptions adjust upward to this new price level

Step-by-step explanation:

The rule for construction of Inscribed equilateral triangle

Means if marks are from 1 to 6 then

Or

Now

Here the rest two segments are

Answer:

FB and DB

Step-by-step explanation:

got it right on the test

The interval notation that defines this set is: (-∞, -5]

And the graph can be seen below.

Here we want to graph the inequality:

x ≤ -5

This refers to all the values of x equal or smaller than -5.

To graph this, we need to graph a closed circle at -5, and we need to draw an arrow that points to the left (values smaller than -5). The graph is the one that you can see below.

The interval notation that defines this set is: (-∞, -5]

The first end is open, and the second is closed (because of the symbol ≤).

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The most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.

In mathematics, parenthesis is used to arrange numbers in the sequence of operations, clarify numbers, and denote multiplication.

Suppose you have an expression as:-

E = { ( 5-2 )8} 6

In this case, you would calculate 5 minus 2 first (parentheses), then multiply by 8 (brackets), then complete the part inside the curly braces, and finally multiply by 6.

Therefore the most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.

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Answer:

215

Step-by-step explanation:

1/6 chance to roll a 6

1/6 * 1290

Answer:

a=2

Step-by-step explanation:

[tex]area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2[/tex]

[tex]\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)[/tex]

the curve is a right parabola.

here b=0,and a=4a for x

we are finding the area between x-axis and x from 0 t0 4a.

curve is symmetrical about x-axis so we multiply by 2.

If the area of the region bounded by the curve [tex]y^2 =4ax[/tex]  and the line [tex]x= 4a[/tex]  is [tex]\frac{256}{3}[/tex] Sq units, then the value of  [tex]a[/tex] will be [tex]2[/tex] .

An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.

Area bounded by the curve  [tex]=\int\limits^a_b {x} \, dx[/tex]

We have,

[tex]y^2 =4ax[/tex]  

⇒ [tex]y=\sqrt{4ax}[/tex]

[tex]x= 4a[/tex],

Area of the region  [tex]=\frac{256}{3}[/tex]  Sq units

Now comparing both given equation to get the intersection between points;

[tex]y^2=16a^2[/tex]

[tex]y=4a[/tex]

So,

Area bounded by the curve  [tex]= \[ \int_{0}^{4a} y \,dx \][/tex] ​

 [tex]\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \][/tex]

[tex]\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \][/tex]

 [tex]\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \][/tex]                                            

[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}[/tex]

[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}[/tex]

[tex]\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}[/tex]

On applying the limits we get;

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right][/tex]

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }[/tex]

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}[/tex]

[tex]\frac{256}{3}= \frac{4}{3} * 8 *a^{3}[/tex]

⇒ [tex]a^{3} =8[/tex]

[tex]a=2[/tex]

Hence, we can say that if the area of the region bounded by the curve [tex]y^2 =4ax[/tex]  and the line [tex]x= 4a[/tex]  is [tex]\frac{256}{3}[/tex] Sq units, then the value of  [tex]a[/tex] will be [tex]2[/tex] .

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Answer:

See below

Step-by-step explanation:

You will just need to use your protractor to measure the given angles..

  Here is some gross guesses  starting with top row

      45     120   100  25   90   80  135  120 °

Answer:

B) 52

Bodmas rule:

Solving Steps:

⇒ 2 × (3 - 1)⁴ + 5 × 4

⇒ 2 × (2)⁴ + 5 × 4

⇒ 2 × 16 + 5 × 4

⇒ 32 + 20

⇒ 52

Option B

Answer:

0.03 second time the flight

Answer:

162.5

Step-by-step explanation:

25=height

13=base

to find the area of a triangle you do (h(b)b)/2

In the diagram, the area of the given shape is 102 cm²

From the question question, we are to determine the area of the given shape

The given shape is a kite

The area of a kite is given by the formula,

[tex]A =\frac{pq}{2}[/tex]

Where A is the area

p and q are the diagonals

In the given diagram,

p = 6cm + 6 cm = 12 cm

q = 3 cm + 14 cm = 17 cm

Thus,

Area of the kite = [tex]\frac{12 \times 17}{2}[/tex]

Area of the kite = 6 × 17

Area of the kite = 102 cm²

Hence, the area of the given shape is 102 cm²

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The option first is correct because  y= 2√x and y= √2x have same domain which is x ≥ 0.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

y= 2√x

From the above function the domain should be:

x ≥ 0 (because square root of negative values does not exist)

The function:

y = √(2x)

2x ≥ 0

x ≥ 0

Thus, the option first is correct because  y= 2√x and y= √2x have same domain which is x ≥ 0.

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