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The result of the operation between two mixed numbers are listed below:

Mixed numbers are real numbers with special notation to transform improper fractions into a combination of integers and fractions. That is:

a b / c = a + b / c

Where a, b, c are integers and c is a non-zero number.

The procedure to simplify the operation is described below:

Case 1

1 3 / 8 ÷ 1 4 / 9

(1 + 3 / 8) ÷ (1 + 4 / 9)

(11 / 8) ÷ (13 / 9)

(11 / 8) / (13 / 9)

99 / 104

Case 2

2 1 / 3 ÷ 1 3 / 4

(2 + 1 / 3) ÷ (1 + 3 / 4)

(7 / 3) ÷ (7 / 4)

(7 / 3) / (7 / 4)

28 / 21

4 / 3

Case 3

4 1 / 5 ÷ 3 1 / 2

(4 + 1 / 5) ÷ (3 + 1 / 2)

(21 / 5) ÷ (7 / 2)

42 / 35

6 / 5

Case 4

5 1 / 5 ÷ 2 1 / 2

(5 + 1 / 5) ÷ (2 + 1 / 2)

(26 / 5) ÷ (5 / 2)

(26 / 5) / (5 / 2)

52 / 25

Case 5

9 1 / 2 ÷ 9 4 / 6

(9 + 1 / 2) ÷ (9 + 4 / 6)

(19 / 2) ÷ (58 / 6)

114 / 106

57 / 53

Case 6

2 2 / 10 ÷ 6 2 / 3

(2 + 2 / 10) ÷ (6 + 2 / 3)

(22 / 10) ÷ (20 / 3)

(22 / 10) / (20 / 3)

(66 / 200)

33 / 100

Case 7

2 1 / 4 ÷ 4 1 / 2

(2 + 1 / 4) ÷ (4 + 1 / 2)

(9 / 4) ÷ (9 / 2)

(9 / 4) / (9 / 2)

18 / 36

1 / 2

Case 8

2 2 / 3 ÷ 1 2 / 3

(2 + 2 / 3) ÷ (1 + 2 / 3)

(8 / 3) ÷ (5 / 3)

(8 / 3) / (5 / 3)

8 / 5

Case 9

5 3 / 5 ÷ 1 2 / 5

(5 + 3 / 5) ÷ (1 + 2 / 5)

(28 / 5) ÷ (7 / 5)

(28 / 5) / (7 / 5)

28 / 7

4

Case 10

4 2 / 3 ÷ 3 1 / 2

(4 + 2 / 3) ÷ (3 + 1 / 2)

(14 / 3) ÷ (7 / 2)

(14 / 3) / (7 / 2)

28 / 21

4 / 3

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Answer:

B

Step-by-step explanation:

The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.

The sum of the first 6 terms of the geometric sequence is calculated as follows:

[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]

[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]

[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]

Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75

The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.

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The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.

It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Consequently, it follows that the greatest possible quotient as required is; 25.

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Answer:

sum up the numbers and divide by the numbers of values.

80+84+79+44+87+73+89+90+82+89+93+97+77+71 / 14

1135/14

= 81•1 is the mean

The 4th interval is called perfect. It is also called consonant.

In mathematics, interval means the gap between two particular numbers in where some numbers can be located.  The numbers that are kept between two particular numbers are all real and their ranges must be maintained between two particular number.

The 4th interval is called perfect. The fourth interval is always consonant because it is maintained by earlier third and next fifth.

Other perfect intervals along with fourth are unison, fifth and octave. The intervals listed above are all consonant. The fourth interval is called perfect because it behaves just like the unison interval.

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Answer:

Length and Width

The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .

The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.

so the height becomes,

√3a/2 = 4√3

The area of the hexagon is calculated using the formula ,

=3√3/2 x a²

=3√3/2 x 64

= 963√3

=332.553 square units.

Volume of a pyramid is calculated as ,

1/3 x base x height

= 1/ 3 x 8 x 8

= 1/3 x 64

=21.33 cubic units answer.

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Answer: 1/36

Step-by-step explanation: 2/9 x 1/8 =2/72 = 1/36

The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached

The values of the constants in the sinusoidal function, h = a + b·(c·t) are;

a = 30

b = -20

c = π/1.5

A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.

The diameter of the Ferris wheel = 40 m

The location of the axle above the ground = 30 m

The time it takes to make a complete a rotation = 3 minutes

The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;

h = a + b·cos(c·t)

The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.

Therefore;

At t = 0, h = 30 - 40/2 = 10

h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b

a + b = 10

Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;

a = 30

a + b = 10, therefore;

b = 10 - a

b = 10 - 30 = -20

b = -20

At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50

50 = a + b·cos(1.5·c)

50 = 30 - 20 × cos(1.5·c)

20 × cos(1.5·c) = 30 - 50 = -20

cos(1.5·c) = -1

cos(π) = -1

Therefore; 1.5·c = π

c = π/1.5

The equation is therefore;

h = 30 - 20·cos((π/1.5)·t)

a = 30, b = -20, c = π/1.5

Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel

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Answer:

Median

Step-by-step explanation:

Mean: Add up all the numbers, then divide by how many numbers there are.

Median: Arrange your numbers in numerical order. Count how many numbers you have. Go to the number in that position and average it with the number in the next higher position to get the median.

Mode: Put the numbers in order from least to greatest and count how many times each number occurs.

Range: The difference between the smallest and highest numbers

Answer:

Mean:

[tex]mean = \frac{(45 + 39 + 49 + 37 + 3 + 51)}{6} \\ = 37.3[/tex]

Median:

[tex]3 \: \: 37 \: \: 39 \: \: 45 \: \: 49 \: \: 51 \\ median = ( \frac{n}{2} + 1) {}^{th} \\ = ( \frac{6}{2} + 1) {}^{th} \\ = 4 {}^{th} \: value \\ median = 45[/tex]

Mode:

[tex]mode = none \\ all \: digits \: are \: repeated \: once[/tex]

Range:

[tex]range = 51 - 3 \\ = 48[/tex]

Answer:

230.86 / 23.8 =9.7 inches-half of the base.

9.7 x 2 =19.4 inches-the length of the base.

Step-by-step explanation:

Function 3x²+24x-6 does not belong with the other three

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the option we have to simplify each function

a. f(x)=3x²+6x-24

b. f(x)=3x²+24x-6

c. f(x)=3(x-2)(x+4)

=3(x²+4x-2x-8)

=3x²+6x-24

d. f(x)=3(x+1)²-27

3(x²+1+2x)-27

3x²+3+6x-27

3x²+6x-24

So function 3x²+24x-6 does not belong with the other three

Hence, function 3x²+24x-6 does not belong with the other three

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Answer:

7

Step-by-step explanation:

So first you substitute A in

15-|-4(2)|

Then you multiply first because of GEMDAS or PEMDAS

15-|-8|

And because absolute value means how far away it is from 0, -8 is 8 away from 0 , thus |-8| is 8. So we simplify the equation

15-8

=7

Answer:

28 cm^2

Step-by-step explanation:

a^+21^2=36^2

a^2+441=1225

a=28

Answer:

your answer is going to be B: Obtuse

Answer:

12.25

Step-by-step explanation:

Solution for What is 35 percent of 35:

35 percent *35 =

( 35:100)*35 =

( 35*35):100 =

1225:100 = 12.25

Now we have: 35 percent of 35 = 12.25

Question: What is 35 percent of 35?

Percentage solution with steps:

Step 1: Our output value is 35.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 35 = 100%

Step 4: Similarly, x = 35%

Step 5: This results in a pair of simple equations:

35 = 100% (2)

x = 35% (2)

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both equations have the same unit (%); we have

[tex]\frac{35}{x} =\frac{100}{35}[/tex] (with % for 100 and 35)

Step 7: Again, the reciprocal of both sides gives

[tex]\frac{x}{35} =\frac{35}{100}[/tex]

⇒ x=12.25

Therefore, 35% of 35  is 12.25

The lower left-hand corner of the graph is the third quadrant.

It contains the negative values of both x and y.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.

Cartesian system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

coordinates

Coordinates are numbers which determine the position of a point or a shape in a particular space.

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Plotting method is the graphical representation of mathematical expression.

A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.

At first, we need to choose the coordinate system by which we plot the point.

suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.

besides, we need to determine the required value that will be plotted on the plan.

if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.

we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.

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Answer:

1. So $7 per hour

For 24 hour =7×24= $168

28-24=4

4×7=28

168+28=$196

or

For 28 hour

7×28

= $196

2. 7×112

=$784

3. To find the difference subtract

784-196=$588

Answer:

196; 784; 588

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

Rate of speed of each cyclist is:

Alisha 10mi/hr

Jose 15mi/hr

Raul 10mi/hr

Ruthie 16mi/hr

Data given of each cyclist;

Formula used: [tex]r=\frac{d}{t}[/tex]

here,

r=rate of speed

d=distance

t=time

Alisha: Distance=40mi; Time=4hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{40}{4} =10mi/hr[/tex]

Jose: Distance=30mi; Time=2hr

applying the formula

[tex]r=\frac{d}{t}\\ r=\frac{30}{2} =15mi/hr[/tex]

Raul: Distance=40mi; Time=4hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{40}{4}=10mi/hr[/tex]

Ruthie: Distance=80mi; Time=5hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{80}{5} =16mi/hr[/tex]

Alisha= 10mi/hr

Jose= 15mi/hr

Raul= 10mi/hr

Ruthie= 16mi/hr

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Answer:

Samples are indicative of the population .

Most values are close to the mean value.

Step-by-step explanation:

The normal distribution is characterized by two parameters mean and standard deviation.

The graph of the normal distribution is symmetrical bell shaped curve called the normal curve. The location and shape of the normal curve are determined by mean and standard deviation.

We see from the figure as the mean and standard deviation increase the spread and curve change.

FALSE:   Standard deviation will be high. This is false because more than 50% of the values lie 1 standard deviation of the mean .When the data is clustered around the mean the standard deviation is low.

FALSE: The smaller the sample, the more the normal distribution takes on a bell curve

The sample size greatly affects the normal curve. The greater the sample size the more likely the distribution is bell shape or normal curve.

TRUE: Samples are indicative of the population .

The normal distribution population with mean and standard deviation has a normal sample with and standard deviation.

Most values are close to the mean value

TRUE: About 68% of values are within 1 standard deviation of the mean and around 95% of values are within 2 standard deviations of the mean in the normal distribution.

Which means more than 50% of the values lie 1 standard deviation of the mean.

Answer:

Nonlinar assosion

Step-by-step explanation:

Answer:

Its B

Step-by-step explanation:

Answer:

2 x 13 x 9 = 234 cm3 is your answer.

Step-by-step explanation:

Whenever given 3 side lengths of a rectangular prism you ALWAYS have to multiply those in order to get the volume..

Answer:y=1.19x

Step-by-step explanation: Since each pound of tomato costs 1.19, you multiple the price by the amount of pounds to get the total cost.