In this problem, you will investigate expected value.

b. Use the random number generator on a calculator to generate, 20 pairs of integers between 1 and 6 . Record the sum of each pair.

Answer:

The Answer is y=-6

The function is neither an even function nor an odd function

The function is given as

g(x) = x + x^2

Calculate g(-x)

So, we have

g(-x) = -x + (-x)^2

Evaluate

g(-x) = -x + x^2

Calculate -g(x)

So, we have

-g(x) = -x - x^2

In the above computations;

g(x) does not equal g(-x) and -g(x)

Hence, the function is neither an even function nor an odd function

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The ratio of pencils to all the item on the desk is 1 : 10

According to Gary,

    Number of pencils on the desk = 4

    Number of markers on the desk = 12

   Number of crayons on the desk = 24

Total number of item son the desk = 4 + 12+ 24

                                                             = 40

The ratio of pencils to all the item is given as = (number of pencils)/(total number of items)

                                                                                = 4/40

                                                                                = 1/10

                       Which in ratio can be written as 1 : 10

Thus the ratio of pencils to all the item is 1 : 10  

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Part (a)

The horizontal part of the rectangle goes from m = -1 to n = 4. This is a distance of 5 units because |m-n| = |-1-4| = 5

The height is some unknown variable h

It must multiply with the base (5) to get an area of 1

base*height = area

5h = 1

h = 1/5

h = 0.2

========================================================

Part (b)

x = dismissal time minutes after class

Something like x = 2 means he dismisses class 2 minutes after the bell, while x = -1 is him dismissing class 1 minute early before the bell.

The phrasing "within 1 minute" means that x is between p = -1 and q = 1. So we can say [tex]-1 \le x \le 1[/tex]

This is a span of 2 units because |p-q| = |-1-1| = 2. Divide this over the entire horizontal span: 2/5 = 0.4

Exactly 40% of the time the teacher lets his class out within one minute of the scheduled end time.

    The Volume of the requested pyramid is 68.5 in³.

  The scale factor is a dimensionless number that allows us to relate dimensions in figures, it is also known as numerical ratio or proportion.

   We must determine the scale factor with the data of the inclined heights of each of the pyramids:

  If the scale factor is a/b, the reason of the volume will be:;

(a/b)³ = 1/8

1/8 = V/540

V = 1/8 x 540

V = 68.5

V = 68.5in³

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The required value of constant of variation, k does not exist for which x and y vary directly..

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Given relation is  y + 3 = -3 x

y = -3 x - 3

y = -3(x + 1)

Comparing with equation 1, we get that y does not vary directly for any value of k.

Hence, the required value of constant of variation is does not exist.

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Answer:

1) 140°

2) 40°

3) 140°

4) 40°

5) 140°

6) 40°

7) 140°

Step-by-step explanation:

1) Angles on a straight line = 180°

180° - 40° = 140°

2) Angle 3 is Vertically opposite to Angle 1

So they are the same Angle

3) Angle 4 is Vertically opposite to Angle 2

So they are the same Angle

4) Angle 5 is corresponding to Angle 1

So they are the same angle

5) Angle 6 is corresponding to Angle 2

So they are the same angle

6) Angle 7 is corresponding to Angle 3

So they are the same angle

7) Angle 7 is corresponding to Angle 4

So they are the same angle

The numerical length of BD is 20.

We have a Line Segment BD and a point C on it.

We have to determine the numerical length of BD.

A line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.

According to question, we have -

BD = 5x

BC = 4x

CD = 4

Now,

BD = BC + CD

5x = 4x + 4

x = 4

Therefore - BD = 5x = 5 x 4 = 20

Hence, the numerical length of BD is 40.

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Sn = a(1 - rⁿ)/(1 - r) is the formula for the sum of a finite number of terms in a geometric series, where is the number of terms, is the first term, and is the common ratio.

The sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ be 2.407.

The equation be Sn = a(1 - rⁿ)/(1 - r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an finite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Let the series be Σ⁴ n=1 (2/3)ⁿ⁻¹

Σ⁴ n=1 (2/3)ⁿ⁻¹ = (2/3)¹⁻¹ + (2/3)²⁻¹ + (2/3)³⁻¹ + (2/3)⁴⁻¹

= 1 + (2/3) + (2/3)² + (2/3)³

= 1 + (2/3) +(4/9) +(8/27)

Where, the first term is a = 1

common ratio be r = 2/3

n th term be n = 4

Let the equation be Sn = a(1 - rⁿ)/(1 - r)

substitute the values in the above equation, we get

S4 = 1(1 - (2/3)⁴)/(1 - (2/3))

S4 = 1(1 - (16/81)⁴)/(1/3)

S4 = (65/81) × 3

S4 = (65/27) = 2.407

Therefore, the sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ is 2.407.

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The statement "∠1 and ∠7 are alternate exterior angles" is true

Given,

The statement "∠1 and ∠7 are alternate exterior angles"
Here,

∠1 and ∠7 are lie on opposite sides of the transversal and both are nonadjacent exterior angles

So, ∠1 and ∠7 are alternate exterior angles.

Hence, the statement  "∠1 and ∠7 are alternate exterior angles" is true

The complete question is:

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

Angles 1 and 7 are alternate exterior angles.

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Step-by-step explanation:

least value is q

greatest value is n-q

close to zero is q-n

Answer:

In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them.

Step-by-step explanation:

in easy language it's Transformations. Transformation means to change. Hence, a geometric transformation would mean to make some changes in any given geometric shape.

The compound inequality in this problem is represented by:

y > -(x + 2)² + 6.

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.

For this problem, the vertex is at (-2,6), hence:

h = -2, k = 6.

y = a(x + 2)² + 6.

When x = 0, y = 2, hence we use it to find a as follows:

2 = 4a + 6

a = -1.

Hence:

y = -(x + 2)² + 6.

The inequality is the interior of the parabola, hence values greater, and the parabola is dashed, hence it is an open interval and the inequality is given by:

y > -(x + 2)² + 6.

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The fraction converted to an improper fraction is 11/3

An improper fraction can be defined as a type of fraction whose numerator is equal to or is greater than its denominator.

Examples of improper fractions are;

5/ 3, 8/2 , 11/ 7, 20/ 5, 4/ 1, 2/ 2, 5/ 3

Given the fraction;

3 2/3; this is a mixed fraction

To convert to improper fraction, we take the steps

Multiply the whole number by the denominator;

= 3 × 3 = 9

Add the value to the numerator

= 9 + 2 = 11

Divide by the denominator

= 11/ 3

Thus, the fraction 3 2/3 converted to an improper fraction is 11/3

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[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-16} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(-1)}~~~~ ,~~~~ -16-\cfrac{ (-6)^2}{4(-1)}\right) \implies \left( - \cfrac{ -6 }{ -2 }~~,~~-16 - \cfrac{ 36 }{ -4 } \right) \\\\\\ (-3~~,~~-16+9)\implies (-3~~,~~-7)[/tex]

Answer:

x = 7

Step-by-step explanation:

➟ x² = 49

in order to find the value of x will have to take square root of both side

➟ [tex] \sf \sqrt{x} = \sqrt{49} [/tex]

Calculate

➟ [tex] \sf \: x = 7[/tex]

Answer:

k = -10

Step-by-step explanation:

1) Because of the division of the left side of the equation by 2, multiply both sides of the equation by 2, which means you now have :

-8 - 3k = 22

2) Now, add eight to both sides. Your equation now looks like this:

-8 + 8 - 3k = 22 + 8

3) Simplify.

-3k = 30

4) You now have k = -10

an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

See the pattern

-32-(-20) = -12

-20-(-8) = -12

-8-4 = -12

By this the explicit and a recursive formula for each sequence is  an=a1+d(n−1).

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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We can conclude that triangle ΔPQR ≇ ΔXYZ.

So,

Given: P(-3,-3), Q(-5,1), R(-2,6), X(2,-6), Y(3,3), Z(5,-1)

To find if ΔPQR ≅ ΔXYZ

So, ΔPQR ≇ ΔXYZ.

Therefore, ΔPQR ≇ ΔXYZ.

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13 litres of 0.8-liter glasses of waters does it take to fill up a 10.4-liters pitcher.

Concept: In simple words, division can be defined as the splitting of a large group into smaller groups such that every group will have an equal number of items. It is an operation used for equal grouping and equal sharing in math.

Quantity of 1 glass of water= 0.8 liters

Quantity to be filled completely = 10.4 liters

No . of 0.8-liter glasses of waters does it take to fill up a 10.4-liters pitcher = 10.8/0.4 = 13

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Answer: 1.6,1.8,2.5,6.7,6.9,7.5

Step-by-step explanation:

Step-by-step explanation:

1.6 1.8 2.5 6.7 6.9 7.5

was that really all ? I don't see any trap in these numbers, so this is straight forward.

Evaluating the expression 3(a - b) for a = 3 and b = -5 is equal to 24.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the expression 3(a - b), substitute the value of the variable a and the value of variable b.

3(a - b)

3[3 - (-5)]

Performing the arithmetic operations, we can have the value of the expression.

3[3 - (-5)]

= 3(3 + 5)

= 3(8)

= 24

Hence, the expression 3(a - b) when a = 3 and b = -5 is equal to 24.

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The value of 5•10⁷ µs​ quantity in second is 50 .

We know that 10⁶μs is equal to 1 second .

Using unitary method , we get

 1 μs have = 10⁻⁶ second

 5•10⁷ µs​ have = 5 × 10⁷ × 10⁻⁶

                        = 50 second

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Answer:

Distance: 4√41

Midpoint: (2, 3)

Step-by-step explanation:

A: (-6, 13) B: (10, -7)

    (x₁, y₁)       (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(10 - (-6))² + (-7 - 13)²

d = √(16)² + (-20)²

d = √256 + 400

d = √656

d = √16 × 41

d = 4√41

midpoint:

(x₁ + x₂)    (y₁ + y₂)

---------- , ------------

    2            2

(-6 + 10)   (13 + (-7))

---------- , ------------

    2            2

   4             6

---------- , ------------

    2            2

Midpoint = (2, 3)

I hope this helps!

Answer:

Step-by-step explanation:

80¢ is your answer because Derek paid $3.20 for a pack of 4 Gatorade so you would have to divide $3.20 by 4 which will be 80¢

So your answer would be 80¢ per bottle.

The least common multiple of the given polynomial 9(x+2)(2 x-1) and 3(x+2) is 3(x + 2).

According to the given question.

We have two polynomials 9(x + 2)(2x - 1) and 3(x + 2).

Since, we have to find the least common multiple of 9(x + 2)(2x -1) and 3(x+2).

As we know that, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.

From the definition of least common multiple, we can say that the least common multiple of 9 and 3 is 3 and (x +2)(2x -1) and (x + 2) is (x + 2).

Thereofrore, the least common multiple of the given polynomial 9(x+2)(2 x-1) and 3(x+2) is 3(x + 2).

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Answer:69999

Step-by-step explanation:your gay

The given equations are neither parallel nor perpendicular with each other.

According to the question, to calculate the slope of the given equations.

y = x - 3 and Y = 4x + 3

Now, equate the given equations with the standard slope equation that is: y = mx + c

Using above equation, the slope for first equation is: m1 = 1

And the slope for the second equation is: m2 = 4

When the value of the slopes are equal, means lines are parallel. Similarly, when the value is negative one, then the lines are perpendicular to each other otherwise neither parallel nor perpendicular.

Hence, the given equations are neither parallel nor perpendicular with each other.

What is the slope of a line?

The slope of a line is the ratio of the y-axis coordinates and the x-axis coordinates. It is also called as gradient which tells the steepness of a straight line. Depending upon the values, it is categorized as parallel, perpendicular or no line.

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