Below are the final exam scores of twenty introductory statistics students.
57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94
Create a box plot of the distribution of these scores. The five number summary provided below may be useful.
Min Q1 Q2 (Median) Q3 Max
57 72.5 78.5 82.5 94
This assignment is to be done in R only.
1. For each of the datasets (i and ii) listed below, find:
a. Mean
b. Median
c. Variance
d. Standard Deviation
i. {0,1,1,4,5,5,6}
ii. {-2,-10,5,4,-1,-9,3}

The true statement about a ladder is; the ladder has parallel line segments and perpendicular line segments.

Parallel lines are lines that never meet on the same plane which have equal distance apart from each other.

They are lines that intersect each other to form a right angle.

Therefore, the ladder has parallel line segments and perpendicular line segments.

Learn more about parallel line:

https://brainly.com/question/26961508

#SPJ1

The quadrants in which the tangent is positive are I and III.

Option B is the correct answer.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

Tangent is defined as the ratio of the opposite side to the adjacent side of a right triangle.

It is positive when the opposite side and the adjacent side are both positive or both negative.

In the first quadrant (I), both the opposite and adjacent sides are positive, so the tangent is positive.

In the second quadrant (II), the opposite side is positive and the adjacent side is negative, so the tangent is negative.

In the third quadrant (III), both the opposite and adjacent sides are negative, so the tangent is positive.

In the fourth quadrant (IV), the opposite side is negative and the adjacent side is positive, so the tangent is negative.

Therefore,

The quadrants in which the tangent is positive are I and III.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ7

56 sweets can be shared in the ratio 2 : 5 as 16 sweets and 40 sweets.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, Share 56 sweets in the ratio 2 : 5.

First share is = (2/2+ 5)×56.

= (2/7)×56.

= 16.

And the second share is (5/2 + 5)×56.

= (5/7)×56.

= 40.

learn more about proportion here :

https://brainly.com/question/7096655

#SPJ2

The probability that at least 20 out of 30 spark plugs will last more than 10 years is approximately 0.964, or 96.4%.

Using the binomial probability formula.

The formula for the probability of getting exactly k successes in n independent trials is:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

In this case, the probability of a spark plug lasting more than 10 years is 0.65, and we want to find the probability of getting at least 20 successes out of 30 trials.

P(X = k) = (30Ck) * (0.65)^k * (1-0.65)^(30-k)

Calculating the probabilities and summing them up:

P(X ≥ 20) ≈ 0.964

Therefore, the probability that at least 20 out of 30 spark plugs will last more than 10 years is approximately 0.964, or 96.4%.

Learn more about probability at https://brainly.com/question/13604758

#SPJ1

Answer:

1. y= x- 15

2. 20

Step-by-step explanation:

Answer:

68°

Step-by-step explanation:

The angles are equal to each other.  Set them equal and solve for x

5x + 18 = 8x - 12  Subtract 5x from both sides of the equation

18 = 3x - 12  Add 12 to both sides of the equation

30 = 3x  Divide both sides by 3

10 = x

Now that you have found x plug is back into  5x + 18

5(10) + 18

50 + 18 = 68

Answer:

∠ FLJ = 68°

Step-by-step explanation:

∠ EKG and ∠ FLJ are alternate exterior angles and are congruent , then

8x - 12 = 5x + 18 ( subtract 5x from both sides )

3x - 12 = 18 ( add 12 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Then

∠ FLJ = 5x + 18 = 5(10) + 18 = 50 + 18 = 68°

Answer:

1/4 i think

Step-by-step explanation:

hope this helps

if i was right pls mark brainliest

Answer:

4/7

there is 3 blue and 4 red so in total you would get 7(our denominator), and since there are 4 gallons of red that would be our numerator.

The value of the variable is 1. 40

we need to know that algebraic expressions are described as expressions that are made up of term, variables, constants, factors and coefficients.

these algebraic expressions are also made up of arithmetic operations.

These arithmetic operations are listed as;

From the information given, we have that;

7.5x/11=4.8/5

cross multiply the values, we get;

7.5x(5) = 4.8(11)

multiply the values

37. 5x = 52. 8

Divide both sides by the coefficient of x, we get;

x = 1. 40

Learn about algebraic expressions at: https://brainly.com/question/4541471

#SPJ1

Answer:

It is 2/3 or 0.666666667

Answer:

the answer is is 2/3

Step-by-step explanation:

hope this helped

Answer:

\(3.126666666666...=3.12\overline{6}\)

Step-by-step explanation:

If the decimal number is repeating, then bar notation is used. A symbol called "bar" is used to express that type of numbers. it is placed at the top of the number that is repeating.

We have a number i.e. 3.126666666666...

We need express it in bar notation.

In this problem, 6 is repeating. It means "bar" is placed over 6.

So,

\(3.126666666666...=3.12\overline{6}\)

It is the bar notation of 3.126666666666...

Answer:

0.777777778

Step-by-step explanation:

it is a terminating digit

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

The calculated value of x in the circle is 5

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

The circle

Using the intersection of secant and tangent equation, we have

4 * (4 + x) = 6 * 6

This gives

x * (4 + x) = 36

When solved for x, we have

x = 5

Hence, the value of x is 5

Read more about circle at

https://brainly.com/question/32192505

#SPJ1

Answer:

D. 3x(x-5)

Step-by-step explanation:

3x^2 - 15x

factor out 3 x from the expression

3x x (x-5)

therefore, ur answer is 3x(x-5) or D

Given : x³+y³+z³=k , k from 1 to 100

To Find : x, y, and z

Solution:

This Question can have lot of solutions as constraints are very less

there is no information whether x , y & z are integer

+ ve , Real numbers

k = 1

x= 1 , y = 0 , z = 0

x =0 , y = 1 , z = 0

x = 0 , y = 0 , = 1

k=2

x= 1 , y = 1 , z = 0

x =0 , y = 1 , z = 1

x = 1 , y = 0 , = 1

k = 3

x= 1 , y = 1 , z = 3

x = 1 , y = 1 , z = 1

x = 1 , y = 0 , = 1

k = 4

x=∛3 , y = 1 , z = 0

This way we can have so many solution

Easiest :

x³+y³+z³=k,

x = ∛k , y = 0 , z = 0 will satisfy

The possible values of k are 1, 2, 3, 8, 9, 10, 17, 24, 43, 62 and 81

The equation is given as:

\(x^3 + y^3 + z^3 = k\)

To determine the values of k for the equation \(x^3 + y^3 + z^3 = k\), we simply set the values of x, y and z to 1,2,3....... while \(1 \le k \le 100\) is true.

Some possible scenarios are:

When k = 1, we have the following possible values

When k = 2, we have the following possible values

When k = 3, we have the following possible value

Hence, the possible values of k are 1, 2, 3, 8, 9, 10, 17, 24, 43, 62 and 81

Read more about equations at:

https://brainly.com/question/2972832

Answer:

C

Step-by-step explanation:

You can divide the hexagon into a rectangle and two triangles. Using the area formulas for all shapes, the area of each can be calculated and added together.

Answer:

b

Step-by-step explanation:

edmentum

Step-by-step explanation:

LHS= csc^2 θ . tan^2 θ - 1

= (1/Sin^2 θ). (Sin^2 θ / cos^2 θ) - 1

= 1/cos^2 θ - 1

= (1 - cos^2 θ) / cos^2 θ

= sin^2 θ / cos^2 θ

= tan^2 θ

= RHS

Hence proved

Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.

Step-by-step explanation:

First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.

73 + 90 + x = 180

163 + x = 180

x = 17

So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).

17 + x = 180

x = 163

So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.

Therefore, angle r is 163 degrees. The correct answer is option C.

Hope this helps!

B. Lin can make 2 batches of blueberry muffins.

C. Lin needs to make 2/3 of a batch of blueberry muffins to use all of the blueberries.

What is mixed fraction?

A mixed number is one that contains both a whole number and a fraction. The fraction is written after the whole number, with a space or plus sign placed between them. The mixed number 2 1/4 serves as an explanation for how the numbers 2 and 1/4 were added. Objects that aren't whole numbers but are close to them, such length or time measurements, are typically represented by mixed numbers.

a) Diagram

   4 cups of blueberries

    __ __ __ __

    |    |     |    |    |

    |__|__|__|__|

Each batch uses 3/2 cups of blueberries

B) To find the number of batches Lin can make, we need to divide the total amount of blueberries by the amount of blueberries per batch:

4 cups of blueberries ÷ (3/2 cups of blueberries per batch)

= (4 cups of blueberries) × (2/3 batches per cup of blueberries)

= 8/3 batches

Therefore, Lin can make 8/3 or approximately 2.67 batches of blueberry muffins using all of the blueberries.

C) To find the fraction of a batch Lin will need to make in order to use all of the blueberries, we need to subtract the number of whole batches from the total number of batches:

8/3 batches - 2 batches = 2/3 of a batch

Therefore, Lin will need to make 2/3 of a batch in order to use all of the blueberries.

Learn more about mixed fraction here:

https://brainly.com/question/29264210

#SPJ1

The total number of points scored is given by the equation A = 23 points

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total points scored be represented as A

Now , the equation will be

Substituting the values in the equation , we get

A = 3x + 2y + z   be equation (1)

where x = red team = 3 points

y = yellow team = 5 points

z = blue team = 2 points

So , A = 3 ( 3 ) + 2 ( 5 ) + 2

A = 9 + 10 + 2

A = 21 points

Hence , the equation is A = 21 points

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.

A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.

The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.

Given that John paid $485 to build a deck.

And he will pay $25 per hour to his brother for building the deck.

one hour of work costs John $25 + $485 .

Total cost of building deck = $25 × h number of hours + $485

3 hour of work costs $25 × 3 = $75 + $485 = $560

8 hour of work costs = $25 × 8 = $200 + $485 = $685

12 hour of work costs = $25 × 12 = $300 + $485 = $785

To know more about work and time visit:

https://brainly.com/question/16734978

#SPJ1

The complete question is-

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?

h c

0 485

3 510

8 535

12 560

h c

0 510

3 535

8 560

12 585

h c

0 485

3 560

8 685

12 785

h c

0 510

3 585

8 710

12 810

Answer:

We have the three angles of a triangle as an equation, so we can add them together, and they equal 180.

So:

4x+10+12x-6+3x+5= 19x+9=180

19x=171 ... so: x= 171/19 = 9.

So ABC = 102 .. Obtuse angle

BAC = 46 .. Acute angle

BCA = 32 .. Acute Angle

Edit:

Angle 1 = 180 - BAC = 180 - 46 = 134

Angle 2= 180 - ABC = 180 - 102 = 78

The type of angle in which angle 3 and angle 6 are, is that they are alternate interior angles ( option C)

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Since line c and line b are parallel to each other and line a is the transversal that cut through both of them the angle on line a and line b will have the following characteristics;

They can be;

supplementary

alternate exterior

alternate interior

vertically opposite

and corresponding

The property between angle 3 and angle 6 is that they are alternate interior to each other.

Therefore angle 3 and angle 6 are alternate interior angles.

learn more about angle on parallel lines from

https://brainly.com/question/24607467

#SPJ1

Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Answer:

28

Step-by-step explanation:

the amount of sheets u would need is 3 and a 1/2 because they each contain 10 tickets so then u multiply 8 dollars by 3 and 1/2 which leads u to 28

a) The initial height of the football at t = 0 is 2 feet.

b) The ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball is approximately 23.9 feet.

d) It takes approximately 4.579 seconds for the ball to hit the ground.

a) The initial height of the football at time t = 0 can be found by substituting t = 0 into the equation \(5t^2 + 20.5t + 2:h = -5(0)^2 + 20.5(0) + 2 = 0 + 0 + 2 = 2\)

Therefore, the initial height of the football is 2 feet.

b) To find the time at which the ball reaches its maximum height, we can observe the graph of the equation h = \(-5t^2 + 20.5t + 2.\) The maximum height corresponds to the vertex of the parabolic graph. The t-coordinate of the vertex can be calculated using the formula t = -b/2a, where a and b are the coefficients of the quadratic equation.

In this case, a = -5 and b = 20.5. Plugging these values into the formula, we get:

\(t = -20.5 / (2\times (-5)) = -20.5 / -10 = 2.05\)

Therefore, the ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball can be found by substituting the time t = 2.05 into the equation \(h = -5t^2 + 20.5t + 2:\)

h = -5(2.05)^2 + 20.5(2.05) + 2 ≈ -20.125 + 42.025 + 2 ≈ 23.9

Therefore, the maximum height of the ball is approximately 23.9 feet.

d) To find the time it takes for the ball to hit the ground, we need to determine when the height h becomes zero. We can set the equation \(-5t^2 + 20.5t + 2 = 0\) and solve for t.

This quadratic equation can be solved using factoring, the quadratic formula, or by graphing. The solutions are t ≈ -0.179 and t ≈ 4.579. Since time cannot be negative in this context, the ball takes approximately 4.579 seconds to hit the ground.

For more such questions on maximum height

https://brainly.com/question/26746473

#SPJ8