PLEASE HELP

Part A:
List the three different types of visuals we use to organize all the possible outcomes in a sample space
1
2
3.

Part B:
Leena is arranging 3 different books in a row on a shelf. A detective story (D), a mystery story (M), and a comic book (C)
1. Pick one of the three types of visuals you listed in Part A to create a sample space for the arrangement of all possible outcomes for arranging the 3 books on a shelf. (1 point)
Fill in the Blank I will choose to create a
for this scenario
2. Create your visual either by hand or using technology

Since the waiting times are uniformly distributed between 0 and 7 minutes, the probability density function (PDF) of the waiting time is:

f(x) = 1/7 for 0 ≤ x ≤ 7

0 otherwise

To find the probability that the waiting time is less than 0.75 minutes, we need to integrate the PDF from 0 to 0.75:

P(X < 0.75) = ∫[0,0.75] f(x) dx

P(X < 0.75) = ∫[0,0.75] 1/7 dx

P(X < 0.75) = [1/7 * x] [0,0.75]

P(X < 0.75) = 1/7 * 0.75

P(X < 0.75) = 0.1071

Therefore, the probability that the waiting time is less than 0.75 minutes is 0.1071 (rounded to three decimal places).

The missing lengths of the following two triangles:

Case 1: x = 50 km

Case 2: x = 40 km

Case 3: Obtuse

Case 4: Acute

Case 5: Right

Case 6: m = 16, n = 8√3

Case 7: x = 3√2, y = 3

In this problem we must determine all missing lenghts in a triangle, this can be done by law of cosine:

x² = a² + b² - 2 · a · b · cos X

Where X is the angle opposite to side x.

Now we proceed to determine the missing lengths of the following two triangles:

Case 1

x = √[(14 km)² + (48 km)² - 2 · (14 km) · (48 km) · cos 90°]

x = 50 km

Case 2

x = √[(24 km)² + (32 km)² - 2 · (24 km) · (32 km) · cos 90°]

x = 40 km

In addition, we can determine if any triangle is acute, obtuse and right also by law of cosine:

cos X = - (x² - a² - b²) / (2 · a · b)

Case 3

cos X = - [(18 in)² - (12 in)² - (9 in)²] / [2 · (12 in) · (9 in)]

cos X = - 0.458 (Obtuse)

Case 4

cos X = - [(15 ft)² - (12 in)² - (14 in)²] / [2 · (12 in) · (14 in)]

cos X = 0.342 (Acute)

Case 5

cos X = - [(5 ft)² - (3 in)² - (4 in)²] / [2 · (3 in) · (4 in)]

cos X = 0 (Right)

Finaly, we determine the missing lengths of two right triangles by trigonometric functions:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Now we find the missing lengths:

Case 6

m = 8 / cos 60°

m = 16

n = 8 · tan 60°

n = 8√3

Case 7

x = 3 / sin 45°

x = 3√2

y = 3 / tan 45°

y = 3

To learn more on law of cosine: https://brainly.com/question/30766161

#SPJ1

Answer: 7.35 km = 7350000 mm

Step-by-step explanation:

Multiply km by 1000000

7.35 * 1000000 = 7350000 mm

Answer:

  x = (1 +i√83)/6  or  x = (1 -i√83)/6

Step-by-step explanation:

You want the solutions to the quadratic equation 3x² -x +7 = 0.

The solutions to the equation ax² +bx +c = 0 are given by the formula ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The given equation has a=3, b=-1, c=7, so the solutions are ...

  [tex]x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(7)}}{2(3)}=\dfrac{1\pm\sqrt{-83}}{6}\\\\\\\boxed{x=\dfrac{1+i\sqrt{83}}{6}\quad\text{or}\quad x=\dfrac{1-i\sqrt{83}}{6}}[/tex]

<95141404393>

Answer:

-6x - 2y = 12

Step-by-step explanation:

The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).

The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.

Given the equation: 3x - 2y = 5

Setting y = 0, we get;

3x - 2(0) = 5

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0).

The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.

Setting x = 0, we get;

3(0) - 2y = 5

-2y = 5

y = -5/2

So, the y-intercept is (0, -5/2).

To know more about intercept here

https://brainly.com/question/14180189

#SPJ1

Answer:

A stem-and-leaf plot is a graphical representation of a dataset where the numbers are separated into two parts: the stem (the leftmost digit or digits) and the leaf (the rightmost digit). The stem values are listed vertically and the corresponding leaf values are listed to the right of the stem in a row. This type of plot allows for quick and easy data analysis, as it shows the distribution of the data and provides information about the frequency and range of the values. It is particularly useful for smaller datasets and can be easily constructed by hand or with software.

Answer:

144π = (1/2)(4/3)π(r^3)

144 = (2/3)(r^3)

r^3 = 216, so r = 6 mm, meaning the diameter is 2 × 6 mm = 12 mm.

The linear regression equation is y = 22.6x + 52.33

The profit would reach 234 thousand dollars during the calendar year of 2020.

Replacing the means, the intercept a is given by:

108.8 = 22.6(2.5) + a.

a = 108.8 - 22.6(2.5)

a = 52.33

Therefore, the linear regression equation is y = 22.6x + 52.33

The profit would reach 234 thousand dollars during the calendar year of 2020.

Learn more about regression on

https://brainly.com/question/21826199

#SPJ1

Answer:

Step-by-step explanation:

No, the pairs of vectors 3i - 8j, 8i - 3j are not orthogonal.

The dot product will help us to determine if the pair of vectors are orthogonal or not.

If the dot product is equal to zero, then the pair of vectors are orthogonal.

The dot product of the vectors is calculated as follows;

(3i - 8j).(8i - 3j)

= (3i x 8i) - (3i x 3j) - (8j x 8i) + (8j x 3j)

= (24) - (0) - (0) + (24)

= 24 + 24

= 48

So the pairs of vectors are not orthogonal.

Learn more about orthogonal vectors here: https://brainly.com/question/17278431

#SPJ1

Answer:

Step-by-step explanation:

Blue line: 0 + -4<x

Black line: 8 - 7<7

Orange: 0=0>y

Green: 1-9<y

Starting points and ending

Answer:

Step-by-step explanation:

considering that it is not an equation but an algebraic expression we solve it like this

10 + 6k6k =

10 + 36k²

length LD = 6 units

length DF = 9 units

length HF = 6 units

length LH = 9 units

length L'D' = 2 units

length D'F' = 3 units

length H'F' = 2 units

length L'H' = 3 units

Dilation is the scaling of an object, where it gets bigger or smaller.

Scale factor = new dimension/old dimension

length LD = 15-9 = 6units

length DF = 6-(-3) = 9units

length HF = 15-9 = 6 units

length LH = 6-(-3) = 9 units

Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.

learn more about dilation from

https://brainly.com/question/10253650

#SPJ1

Answer:7

Step-by-step explanation:

use the Pythagoras theorem to find su (40^2-32^2) take the square root =24 use this to solve for ru. (25^2-24^2=49) square root of 49 is

m² × m² is equal to m⁴.

w³ × w² is equal to w⁵.

5k³ × 4k⁴ × k is equal to 20k⁸.

The length of each side of the square is 9x.

A simplification of the expression 28x³ ÷ 4x is 7x².

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangle = (27x) × (3x)

Area of rectangle = 81x²

Note: Area of square = Area of rectangle

Area of square = (side length)²

81x² = (side length)²

Side length = √(81x²)

Side length = 9x

Read more on area of a rectangle here: https://brainly.com/question/18159221

#SPJ1

Answer:

X can be any number greater than -2 and less than or equal to 1/4.

Step-by-step explanation:

To solve for x in the inequality 3x + 1 ≤ 2 - x < 18 + 7x, we will first isolate the variable x on one side of the inequality.

3x + 1 ≤ 2 - x

Adding x to both sides, we get:

4x + 1 ≤ 2

Subtracting 1 from both sides, we get:

4x ≤ 1

Dividing both sides by 4, we get:

x ≤ 1/4

Next, we solve the second inequality:

2 - x < 18 + 7x

Adding x to both sides, we get:

2 < 18 + 8x

Subtracting 18 from both sides, we get:

-16 < 8x

Dividing both sides by 8, we get:

-2 < x

Therefore, the solution to the inequality 3x + 1 ≤ 2 - x < 18 + 7x is:

-2 < x ≤ 1/4

This means that x can be any number greater than -2 and less than or equal to 1/4.

Note that the upper bound for v is 2.356.

To find the upper bound for v, divide te upper bound for s by the lower bound for t,    because dividing by a   smaller integer give a bigger quotient.

Adding 0.5 x 0.1 t to the value of s yields the upper bound for s with t decimal places.

As a result, the upper bound for s with two decimal places is......

8.24 + 0.5 x 0.1² = 8.245

The lower bound for t with 1   decimal place is simply the given value of 3.5.

So, the upper bound for v is  ..

v = s/t = 8.245/3.5 = 2.355714...

Rounding this to 3 decimal places, we get:

v ≈ 2.356

Learn more about upper bound:
https://brainly.com/question/22965427

#SPJ1

The perimeter of the rectangle is P = 18 units

Given data ,

Let the rectangle be represented as ΔWXYZ

Now , the coordinates of the triangle are

W ( 3 , 3 ) , X ( 8 , 3 ) , Y ( 8 , 7 ) and Z ( 3 , 7 )

The perimeter of the rectangle = 2 ( length + width )

The width of the rectangle W = ( 7 - 3 ) = 4 units

The length of the rectangle L = ( ( 8 - 3 ) = 5 units

So , P = 2 ( 4 + 5 )

P = 2 x 9

P = 18 units

Hence , the perimeter is 18 units

To learn more about perimeter of rectangle click :

https://brainly.com/question/15725265

#SPJ1

The angle BFC is the angle that is complementary to AFB

Whenever the sum of two angles adds up to 90 degrees, they are defined as complementary angles. Take 30 and 60 degrees, for instance; they are complementary angles.

From the definition we have to find the angle when if added to AFB would give us the sum of 90 degrees

AFC is a 90 degree angles

We have AFC = AFB + BFC

90 = 78 + BFC

BFC  = 90 - 78

= 12

Hence the angle BFC is the complementary angle

Read more on angles here:https://brainly.com/question/25716982

#SPJ1

Answer:

There are 13 diamonds in a deck of cards, including one king and one ace.

The probability of drawing a king on the first draw is 1/13, since there is one king among 13 diamonds.

Assuming that the king is not replaced, there are now 12 diamonds left, including one ace. The probability of drawing an ace on the second draw is 1/12, since there is one ace among 12 diamonds.

The probability of drawing a king on the first draw and an ace on the second draw is the product of these probabilities:

P(king first, ace second) = P(king first) * P(ace second|king first not replaced)

P(king first, ace second) = (1/13) * (1/12)

P(king first, ace second) = 1/156

Therefore, the chances of drawing a king on your first draw and an ace on your second draw, when drawing 2 cards from only the diamonds, is 1/156.

Step-by-step explanation:

Branliest please

The two inequalities of the graph are:

y ≥ 3x - 1

y < -¹/₂x + 4

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

The first inequality with a solid line has a y-intercept of -1 and since it is shaded above the line, we will use ≥.

Two coordinates on the line are: (0, -1) and (1, 2)

The slope = (2 + 1)/(1 - 0) = 3

Thus, inequality is:

y ≥ 3x - 1

The second inequality with a dashed line has a y-intercept of 4 and since it is shaded below the line, we will use <.

Two coordinates on the line are: (4, 0) and (0, 2)

The slope = (2 - 0)/(0 - 4) = -1/2

Thus, inequality is:

y < -¹/₂x + 4

Read more about Inequality Graph at: https://brainly.com/question/11234618

#SPJ1

The area of the composite figure in this problem is given as follows:

A = 87 ft².

When we want to obtain the area of a composite figure, we must add the areas of all the components of the figure.

The figure in this problem is composed as follows:

The areas are calculated as follows:

Hence the area of the composite figure is given as follows:

A = 10 x 6 + 6 x 3 + 0.5 x 6 x 3

A = 87 ft².

More can be learned about the area of a composite figure at https://brainly.com/question/10254615

#SPJ1

The ratio of sec θ is determined as 5/3.

option A.

The ratio is sec θ is calculated by applying the following method;

sec θ =  1/cosθ

Given that tanθ = -4/3 = oppo/adjacent

The hypotenuse side is calculated by applying Pythagoras theorem as shown below;

h = √ 4² + 3²

h = 5

The ratio of sec θ is calculated as follows;

sec θ =  1/cosθ

1/cosθ = 1/(3/5)

1/cosθ = 5/3

Learn more about trig ratios here: https://brainly.com/question/10417664

#SPJ1

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

The circumference of the circle is 75.4 cm.

The circumference of the circle is calculated from the radius of the circle.

Considering the equilateral triangle, each of the interior angle is 60⁰, a line passing the center of any of this angle, divides it into two with each angle 30⁰.

Considering the right triangle inside the equilateral triangle, the hypothenuse is equal to the radius of the circle.

The radius of the circle is calculated as follows;

sin (30) = opp/hypo

sin (30) = 6 cm/r

r = 6 cm / sin (30)

r = 12 cm

The circumference of the circle is calculated as follows;

C = 2πr

C = 2π x (12 cm)

C = 75.4 cm

Learn more about circumference here: https://brainly.com/question/20489969

#SPJ1

There are 5 sheets of paper will she need to complete 10 problems.

We have to given that;'

Kendra is doing her math homework. For each problem, she uses 1/2 of a sheet of paper.

Hence, For complete 10 problems, number of sheets are,

⇒ 1/2 of 10

⇒ 1/2 x 10

⇒ 5

Thus, There are 5 sheets of paper will she need to complete 10 problems.

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

Based on these factors, the polynomial that graph crosses the x-axis at only one point is A. f ⁡ ( x ) = x ³ − 7 ⁢x² + 3 ⁢x − 21

A polynomial in mathematics is a mathematical statement made up of variables (also known as indeterminates) and coefficients that only include the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Polynomials are a fundamental algebra topic that is used in many areas of mathematics. A polynomial's degree is the largest exponent of the variable x in the expression. The correct option is A.

Learn more about polynomial on

https://brainly.com/question/2833285

#SPJ1

The Function is linear with a common first difference of 2.

We have,

x     y

-3   -2

-2   0

0    4

4    12

For the first set of points

m=(0-(-2))/(-2--3)

m = (0+2)/(-2+3)

m= 2/1 = 2

For the second set of points

m = (4-0)/(0-(-2))

m = 4/(0+2)

m = 4/2 = 2

For the third set of points

m = (12-4)/(4-0)

m = 8/4

m = 2

Thus, the function is linear with a common first difference of 2.

Learn more about Linear Function here:

https://brainly.com/question/20286983

#SPJ1

Answer:

The correct function is y = 4(.25^x).