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Unit Test, Part 2: Working with Data
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(Score for Question 1: of 9 points)
1. The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
26 31 40 28 19 23 35 38 43 46 28 30
(a) What is the five-number summary of the data set?
(b) What is the range of the data set? Show your work
(c) What is the interquartile range (IQR) of the data set? Show your work.

Answer:

Step-by-step explanation:

1-    8

3 -    8+2= 10      

Answer: The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x [tex]10^{21}[/tex]

Step-by-step explanation:

Given data,

Two people pair up to create a sequence. Each of them pick five random digits from 1 to 9.

Define Consecutive numbers :

Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers. In a set of consecutive numbers, theme an and the median are Equal. If n is a number, then n, n+1, and n+2 would be consecutive numbers Examples. 1, 2, 3, 4, 5.

The numbers that are given:

Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:

              = (9!) x (8!) x (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

             = 362880 x 40320 x 5040 x 720 x 120 x 24 x 6 x 2 x 1

            [tex]n^{th}[/tex] = 1.834 x [tex]10^{21}[/tex]

Therefore,

The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x [tex]10^{21}[/tex].

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Answer: 2200 yards

Step-by-step explanation:

First find the unit rate, 660/3 = 220

So, Owen can jog 220 yards in one minute.

220 times 10 to find how much Owen can jog in 10 minutes.

220*10 = 2200.

Answer:

2200

Step-by-step explanation:

Answer:

The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a series shown in the picture.

The geometric sequence is shown in the options.

As we know, in the geometric sequence there is a first term and common difference

In the first sequence:

First term a = 2

Common difference = 2(0.1)/2

Common difference d = 0.1

The sum of the infinite series is:

S = a/(1 - r)

S = 2/(1 - 0.1)

S = 2.22

In the second sequence:

First term a = 15

Common difference = 15(0.3)/15

Common difference d = 0.3

The sum of the infinite series is:

S = a/(1 - r)

S = 15/(1 - 0.3)

S = 21.42

In the third sequence:

First term a = 4

Common difference = 4(0.2)/4

Common difference d = 0.2

The sum of the infinite series is:

S = a/(1 - r)

S = 4/(1 - 0.2)

S = 5

Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

Step-by-step explanation:

According to the statement an inequality to describe the possible measures of  ∠Z = 23.

An inequality is a relationship that makes a non-equal comparison of two integers or any other mathematical expressions. It is most commonly used to compare two digits upon that number line based on their size. a statement of an order relationship—greater than, larger than the other or equal thereto, less than, or lesser than or equal to—between two integers or algebraic expressions

the sum of the angles' measurements

triangle is 180 and  ∠ X=157.

∠ X + ∠ Y +∠ Z = 180

∠ Y +∠ Z  = 23

If ∠Y  was 0, then ∠Z would equal 23. But since an angle must have

a measure greater than 0,  ∠Z must be less than

23, so z < 23.

an inequality to describe the possible measures of  ∠Z = 23.

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The machine will take 6.25 minutes to grade 300 multiple choice tests.

Unitary method is a concept in which the value of a single unit is first found out and then multiplied by the necessary value to get the required answer.

Here, we are given that a grading machine can grade 96 multiple choice tests in 2 minutes.

This means that the machine will take 2/96 minutes to grade one multiple choice test

X = number of minutes taken by the machine to grade 300 multiple choice tests

Thus, we can use the proportion 2/96 to predict X in the following manner-

X = 2/96 (300)

X = 600/ 96

X = 100/ 16

X = 6.25

Thus, the machine will take 6.25 minutes to grade 300 multiple choice tests.

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The range of the data set 1 and data set 2 is 4

Data set 1

The maximum value of the data set 1 = 7

The minimum value of the data set 1 = 3

The range is the difference between the maximum value and minimum of the data set

Range = Maximum value - Minimum value

Range of the data set 1 = 7 - 3

= 4

Data set 2

The maximum value of the data set 2 = 7
The minimum value of the data set 2 = 3

The range = Maximum value - Minimum value

The range of the data set 2 = 7 - 3

= 4

Hence, the range of the data set 1 and data set 2 is 4

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23 lies between the two perfect squares 16 and 25 which are the squares of 4 and 5 respectively.

The value of √23 lies between 4 and 5.

What in mathematics is a perfect square?

Informally: A square number, perfect square, or simply "a square" is the result of multiplying an integer (a "whole" number), positive, negative, or zero, times itself. Therefore, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.

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Answer:

a) -18/3 = - 6

b) 18/-3 = - 6

c) - 18/-3 = 6

Hope this helps :)

I bought 2 small notebooks and 4 large notebooks.  

Let us represent the number of small notebooks with x and number of large notebooks with y.

Forming equation according to bought number of books -

x + y = 6 - equation 1

Rewriting the equation according to x

x = 6 - y  - equation 2

Now, forming equation according to cost of notebooks -

8x + 10y = 56 - equation 3

Keep the value x from equation 2 in equation 3

8 (6 - y) + 10y = 56

Performing multiplication

48 - 8y + 10y = 56

Performing subtraction and shifting values to other side of equation

2y = 56 - 48

2y = 8

Shifting 2 to other side of equation and performing division

y = 8 ÷ 2

y = 4

Keep the value of y in equation 2

x = 6 - 4

x =  2

Hence, I bought 2 small notebooks and 4 large notebooks.

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Step-by-step explanation:

I use a thing call

P-parenthesis

E-exponents

M D-Multiplication and division (Left to right)

A S- Addition and Subtraction (left to right)

We need to wait to use the exponents so 5x2=10, Add the 2 power to ten so 10^2.=100. 100^3.

Answer:

982888428848588828480484883858

Step-by-step explanation:

The constant of variation in  y = (6)x is (6)

y = kx            (Where k is the constant)

Here,

⇒ y = (6)x

So, k = (6)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.

According to the given question.

We have an equation

5/2x -2/3 = 1/x + 5/6

Since, we have to solve the above equation for x.

Thereofore, the solution of the equation 5/2x -2/3 = 1/x + 5/6 is given by

5/2x -2/3 = 1/x + 5/6

⇒ 5/2x -1/x  = 5/6 + 2/3

⇒  (5 -2) /2x  =   5+ 2(3)/6

⇒ 3/2x = 11/6

⇒6(3)  = 11(2x)

⇒ 18 = 22x

⇒ 18/22  = x

⇒ 9/11 = x  or x = 9/11

Hence, the solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.

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Based on the temperature at the beginning of the day, and the change in temperature by the end of the day, the temperature at day's end was -3°C.

The temperature started at 4°C and then dropped during the day by a temperature of 7°C.

The temperature at day's end will therefore be:
= Beginning temperature - Change in temperature

Solving gives:

= 4 - 7

= -3 °C

In conclusion, the change in temperature would lead to an ending temperature of -3°C.

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x=5 that's my final answer because 2(8)=4x-4

According to the question, to check whether the events are mutually exclusive or not for the even integers.

As per question, select random integer numbers from [tex]1[/tex] to [tex]20[/tex] to get either an even number or a number divisible by [tex]3[/tex].

Therefore , the probability can be written as:

[tex]P(e or d) = \frac{P(E)}{n(E)} = P(e)+P(d)-P(e and d)[/tex]  

              [tex]= \frac{10}{20} +\frac{6}{20} -\frac{3}{20} = \frac{13}{20} = 65%[/tex]

The event is not mutually exclusive.

Since, the calculated percentage is [tex]65%[/tex] and it is not nearest to tenth of a percent.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.

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Answer: 2000.18 unit^3

Step-by-step explanation:

radius = 14 / 2 = 7

V of cylinder = π x r^2 x h

= 3.14 x 7^2 x 13

= 3.14 x 49 x 13

= 2000.18 unit^3

There are 5 cups of 3/8 servings in 1 7/8 cups of apple cider

The number of cup servings is 3/8

The number of apple cider cups is 1 7/8

Therefore the number of cup servings can be calculated as follows

15/8 ÷ 3/8

convert to multiplication

= 15/8 × 8/3

= 15/3

= 5

Hence there are 5 cups of 3/8 servings in 1 7/8 cups of apple cider

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The two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.

Steps to find Maximum of a function f(x).

Step 1 : Differentiate the function F(x)

Step 2 : Equate f'(x) to zero to find the critical points .

Step 3 : Substitute the critical points in f''(x) , if

f''(x)< 0 them maximum value will be at the critical point.

in the given function

the sum of two non negative real numbers is 40.

Let the numbers be x and y .

So , x+y=40

y=40-x     ....(1)

We need to maximize the product i.e. x.y

Substituting the value of y from equation (1) we get

[tex]f(x)=x.y\\ \\ f(x)=x.(40-x)\\ \\ f(x)=40x-x^{2}[/tex]

Step (i) differentiating with respect to x we get

[tex]f'(x)=40-2x[/tex]

Step (ii) Equating f'(x) to 0

[tex]40-2x=0\\ \\ x=20[/tex]

x=20 will be the critical point .

Step (iii) Substituting the critical point in f''(x)

again differentiating with respect to x we get

[tex]f''(x)=-2\\ \\ f''(20)=-2[/tex]

Since -2<0. therefore , x=20 is the point where f(x) is maximum.

Substituting the value of x=20 in equation (1) we get

y=40-x

y=40-20

y=20.

Therefore , the two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.

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Answer:

50.27

Step-by-step explanation:

The Surface area of a cone is 308.647 sq. inches.

What is the Surface area of cone ?

The area occupied by the surface / boundary of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as curved surface area.

The surface area of the cone can be given by finding the area of the sector by using the formula,

Area of the sector (in terms of length of arc) = (arc length x radius) / 2 = ((2πr) x l) /2 = πrl.

We are given the height and radius

h = 19 inches

r = 5 inches

The formula for Surface Area is:

Surface Area = πrl

We have to find slant height first:

[tex]l=\sqrt{h^{2}+r^{2} }[/tex]

[tex]l=\sqrt{19^{2}+5^{2} }\\ l=\sqrt{361+25}\\l= \sqrt{386}[/tex]

[tex]l=19.467 inches[/tex]

Now, The Surface Area is:

SA = πrl (π = 3.14)

SA = 3.14 x 5 x 19.467

SA = 308.647 [tex]inches^{2}[/tex]

Hence, The Surface area of a cone is 308.647 sq. inches.

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The diameter of the circle is 19.8 inches.

We are given the value of side of square in the question. The diameter of the circle will be equal to the diagonal of square. The diagonal of square can be calculated using Pythagoras theorem. So, finding the diagonal of square, which will be hypotenuse.

Diagonal² = Base² + Perpendicular²

Diagonal² = side² + side²

Keep the values to find the value of diagonal

Diagonal² = 14² + 14²

Take square of values on Right Hand Side of equation

Diagonal² = 392

Diagonal = √392

Taking square root on Right Hand Side of equation

Diagonal = 19.8 inch

So, diagonal of square is diameter of circle which is 19.8 inches.

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The sequence 78,75,72,69,66,63,60, . . . . is arithmetic and the common difference is 3

We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".

To solve this exercise we are going to apply the formula of the arithmetic sequence:

d = aₙ₊₁ - aₙ

Where:

Information about the problem:

Calculating the common difference of the sequence (d), we have:

d = aₙ₊₁ - aₙ

d =78 - 75

d = 3

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

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The simplification of the given complex fraction [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex] is equal to (23)/(28).

As given in the question,

Given complex fraction is [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex]

Simplify the given complex fraction by taking the least common multiple,

[tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }\\\\\\= 1- \frac{1}{\frac{4}{\frac{10-3}{5} }}\\ \\= 1- \frac{(1)(5)}{(4)(7)}\\ \\= \frac{(28-5)}{28}\\ \\= \frac{23}{28}[/tex]

Therefore, the simplification of the given complex fraction [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex] is equal to (23)/(28).

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Applying the triangle midsegment theorem, the length of BC is: 12 units.

The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of a triangle.

According to the triangle midsegment theorem, this midsegment is parallel to the third side of the triangle and also has a length that is half of the length of the third side of the triangle.

That is: length of midsegment = 1/2(length of the third side).

Given the following:

DE is a midsegment and is parallel to BC, a third side.

DE = 6 units

Thus, based on the triangle midsegment theorem, DE = 1/2(BC)

Substitute

6 = 1/2(BC)

2(6) = BC

12 = BC

BC = 12 units.

In conclusion, applying the triangle midsegment theorem, the length of BC is: 12 units.

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Answer:

m = 18

n = 60

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180.

We can write the following equation to find, first value of m, then the value of n:

65 + 42 + 55 + m = 180 add like terms

162 + m = 180 subtract 162 from both sides

m = 18

Now the value of n:

65 + 55 + n = 180 add like terms

120 + n = 180 subtract 120 from both sides

n = 60

hi

Slope is 2 .  

here is how you do the trick :  by reading on the graph

if you go forward of  1 on the X axis , how much did the line goes up or down ?  

Here at  0  on  X- axis, we are at 0 on the Y- axis.

If you go forward of  1 on X axis, you are at 2 on Y axis.  

So the slope is  + 2

Other technique by calculus  between two points.  

Take two diffents  point on the X axis.   Call them A and B  

Slope is  :   (  f(A) -f(B) )     /  A-B

exemple here :   we have two easy points . Take 0  as  A  and  1 as  B

We read on the graph :  

A = 0  and B = 1

f(A)= 0  and f(B) = 2

Now we apply  formula :    

(  f(A) -f(B) )     /  (A-B )

(0 -2 )  / (0-1)  =  -2/-1 =  2

Slope is 2

Easy, dont you think ?