Classify each sequence as arithmetic, geometric, or neither by dragging it into the correct box.

The domain is [2,6] and the range is  [-2,0].

The Domain is all the possible input values to the function, while the range is all the possible values a function can have as an output.

The parabola has endpoints of (2,-2) and (6,-2).

The vertex is (4,-6)

The domain is [2,6]

The range is [-2,0]

Therefore, the domain is [2,6] and the range is  [-2,0].

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Combine like terms: [tex]6x^{3}[/tex] and [tex]4x^{3}[/tex] make [tex]10x^{3}[/tex]. At that point, disentangle constants: -8 + 6 rise to -2. Result:[tex]10x^{3} - 2x^{2} + 9x - 2[/tex].

To simplify the given expression, take after the arrangement of operations (PEMDAS/BODMAS):

Given expression: [tex]6x^{3} - 2x^{2} + 9x - 8 + 4x^{3} - 2x + 6[/tex]

Step 1: Combine like terms (terms with the same variable and example):

[tex]6x^{3} + 4x^{3} = 10x^{3}[/tex]

Step 2: Combine the steady terms:

-8 + 6 = -2

The expression presently gets to be:

[tex]10x^{3} - 2x^{2} + 9x - 2[/tex]

So, the disentangled expression is [tex]10x^{3} - 2x^[2} + 9x - 2.[/tex]

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The complete question:

Simplify the expression:

6 x 3-2x2+9x-8+4x3-2x+6

The sum of the first five terms of the geometric sequence is -1555

The formula for calculating the sum of geometric sequence is expressed as:

[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]

where

r is the common ratio = 6/1 = 6

a is the first term = -1

n = 5 (number of terms)

Substitute

[tex]S_5=\frac{-1(6^5-1)}{6-1}\\S_5=\frac{-7776+1}{5}\\S_5=-1555[/tex]

Hence the sum of the first five terms of the geometric sequence is -1555

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Rate of change for Function A is: 35

Rate of change for Function B is: 50

Difference is: 15.

Rate of change = change in y / change in x.

The graph for function B is a proportional graph, therefore, rate of change = y/x.

Using a point on the line, (1, 50), rate of change for function B = 50/1 = 50.

Function A is given as y = 35x. Rate of change, is 35.

The difference = 50 - 35 = 15.

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Answer:

300

Step-by-step explanation:

if its 1:1 ratio, then its the same and so if there 300 bean seeds, there has to be 300 groundnut seeds

The vertices of A'B'C' if A(0, 10), B(8, 6), C(4, 2) is dilated by a scale factor of 2 are;

Given that triangle ABC is dilated by a scale factor of 2, we have;

A'B' = 2 × AB

A'C' = 2 × AC

B'C' = 2 × BC

Length of AB = √((8-0)^2 + (6-10)^2) = 4•√5

Length of AC = √((4-0)^2 + (2-10)^2) = 4•√5

Length of BC = √((8-4)^2 + (6-2)^2) = 4•√2

By multiplying the given coordinates by the scale factor, we have;

A' = 2 × (0, 10) = (0, 20)

B' = 2 × (8, 6) = (16, 12)

C' = 2 × (4, 2) = (8, 4)

A'B' = √((16-0)^2 + (12-20)^2) = 8•√5

A'C' = √((8-0)^2 + (4-20)^2) = 8•√5

B'C' = √((16-8)^2 + (12-4)^2) = 8•√2

Therefore when we have;

A'(0, 20), B'(16, 12), C'(8, 4), we get;

The correct option is therefore;

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Answer:

550 square feet

Step-by-step explanation:

There are 4 areas where the pool deck is situated on:

Top, Left, Right, and Bottom of the pool.

So if the deck is 5 feet wide:

Top = (35 feet * 5 feet) = 175

Bottom = (35 feet * 5 feet) = 175

Left = (20 feet * 5 feet) = 100

Right = (20 feet * 5 feet) = 100

175 + 175 + 100 + 100 = 550 square feet

The value of n that satisfies the inequality is 6.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

4n − 12 < 2n + 2

For n= 6

4(6) - 12 = 12

2(6) + 2 = 14

Thus, n=6 satisfies

For n= 7

4(7) - 12 = 16

2(7) + 2 = 16

Thus, n=7 not satisfies

For n=8

4(8) - 12 = 20

2(8) + 2 = 18

Thus, n=8 not satisfies.

For n= 9

4(9) - 12 = 24

2(9) + 2 = 20

Thus, n=9 not satisfies.

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Answer:

the answer to that would be y=3x-9

The median of each of the sixteen​ samples, the sampling distribution of the medians are shown in the table.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have data:

40,40 40,45 40,47 40,53 45,40 45,45 45,47 45,53

47,40 47,45 47,47 47,53 53,40 53,45 53,47 53,53

We can find the sample mean, median, and probability:

sample median   probability   sample median      probability

40                                1/16                         46.5                          2/16

42.5                         2/16                        47                          1/16

43.5                                2/16                       49                          2/16

45                                1/16                          50                             2/16

46                              2/16                         53                             1/16

Thus, the median of each of the sixteen​ samples, the sampling distribution of the medians are shown in the table.

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Answer:

Price of redwood= $3.4

Pine =$1.3

The dimensions of the circular cylinder of maximum volume inscribed in  sphere is r = 20.4 cm , h = 28.86 cm.

A sphere is a three dimensional round shaped figure , It has no vertices and the distance form the centre to any point on the sphere is same.

It is given that

A right circular cylinder is inscribed in a sphere

The circular cylinder has the maximum volume

Radius of the sphere is 25 cm.

Dimensions of the cylinder = ?

As it is a right cylinder.

The Pythagoras theorem can be applied

r² + (h/2)² = 25²

r² = 625 - h²/4

volume of the cylinder

=  πh(625 - h²/4)

= π(625 h - h³/4)

As the volume is maximum ,

so the derivative of the expression = 0

π(625 - 3h²/4) = 0

so h =  50 /√ 3

so r² = 625 - 2500 / (3 *4 )

r = 20.4 cm

h = 28.86 cm

Therefore the dimensions of the circular cylinder of maximum volume inscribed in a sphere is r = 20.4 cm , h = 28.86 cm.

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Answer:

We can now take 2 as the third digit, 3 as the fourth digit, 4 as the fifth digit and finally 5 as the sixth digit. Therefore, the smallest 6-digit number having all different digits is 102345.

The smallest 6-digit multiple of 4 with all different numbers is 102,564. This number is obtained by incrementing from 100,000 until finding a divisible number with distinct digits.

A number that is the result of a given number plus another natural number is said to be a multiple of that number.

Since the smallest 6-digit number, is 100,000.

Check if this number is divisible by 4.

In this case, it is not.

Increment the number by 1 to get 100,001.

Repeat step 2. Not divisible by 4.

Increment the number by 1 to get 100,002.

Repeat step 2. Not divisible by 4.

Increment the number by 1 to get 100,003.

Repeat step 2. Not divisible by 4.

Continue this process until you find a number that is divisible by 4 and has all different digits.

After following these steps, we find that the smallest 6-digit multiple of 4 with all different numbers is 102,564.

Hence,

The required number is 102564.

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The precise equation that represents the situation is as follows:

His cell phone plan provides  300 free minutes each month for a flat rate of $19.

let

x = number of minutes used

Therefore,

$19, x ≤ 300

For any minutes over 300, Andrew is charged 0.39 per minute.

Therefore,

if x > 300

f(x) = 19 + 0.39(x - 300)

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Plane figures are shapes with straight sides. Considering the movement to be lower than the initial path, there are eleven (11) paths from A to B.

A plane figure is given shape with straight sides. And these sides connect each edge of the figure one to another. Examples are triangles, quadrilaterals, polygons, etc.

A path is a connection or link between two reference points. This could be a footpath or a motorable path or other forms of the path.

Considering the given plane figure in the question, it can be observed that the total number of paths from A to B with respect to the given condition is eleven.

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The total revenue for Saturday and Sunday is $1917.50

We know that 815 tickets were sold on Saturday, and on Sunday the number of tickets sold decreased by 96.

Then the total number of tickets sold in the two days is:

(815) + (815 - 96) = 1534

And we know that each ticket costs $1.25

Then the total revenue is:

R = $1.25*1534 = $1917.50

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The regression equation is calculated as: ŷ = -0.99299X + 26.39918

We have these data for the x axis

12 15 20 22 15 8 6 17

These are the values for the y axis

17 15 6 7 6 18 21 7

Sum of X = 115

Sum of Y = 97

Mean X = 14.375

Mean Y = 12.125

Sum of squares (SSX) = 213.875

Sum of products (SP) = -212.375

Regression Equation = ŷ = bX + a

b = SP/SSX = -212.38/213.88 = -0.99299

a = MY - bMX = 12.13 - (-0.99*14.38) = 26.39918

ŷ = -0.99299X + 26.39918

These values where inputted into a regression analysis calculator and the output is ŷ = -0.99299X + 26.39918

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Part A

[tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex]

Part B

Diagonals of a parallelogram bisect each other, so

[tex]BE=ED \implies 2x+3=3y-4 \implies 3y=2x+7 \implies y=\frac{2}{3}x+\frac{7}{3}\\\\AE=EC \implies y+4=4x-6 \implies y=4x-10[/tex]

Solving by substitution,

[tex]\frac{2}{3}x+\frac{7}{3}=4x-10[/tex]

Multiplying both sides by 3,

[tex]2x+7=12x-30\\\\37=10x\\\\x=3.7[/tex]

So, [tex]y=\frac{2}{3}\left(\frac{37}{10} \right)+\frac{7}{3}=\frac{24}{5}[/tex]

Part C

[tex]BE=ED=2(3.7)+3=10.4\\\\AE=EC=4(3.7)-6=8.8[/tex]

[tex]\therefore BD=2(10.4)=20.8, AC=2(8.8)=17.6[/tex]

The Income Statements under Absorption Costing and Variable Costing are as follows:

                                                       Absorption Costing     Variable Costing

Sales (19,500 units)                              $2,145,000               $2,145,000

Cost of goods sold                                $1,491,750               $1,365,000

Gross profit                                            $653,250                 $780,000

Selling and administrative expenses:

Fixed factory overhead                                          $162,500

Variable selling and

 administrative expenses    $296,400                  296,400

Fixed selling and

 administrative expenses       114,800    411,200    114,800   573,700

Net Income                                          $242,050                $206,300

The difference between Absorption Costing and Variable Costing is that the Ending Inventory costs under Variable Costing include only direct materials, direct labor, and variable factory overhead.  Absorption Costing includes all the variable factory costs plus fixed factory overhead (a period cost) in the Ending Inventory costs.

Sales (19,500 units)                              $2,145,000

Production costs (25,000 units):

Direct materials                $1,017,500

Direct labor                          487,500

Variable factory overhead 245,000

Fixed factory overhead       162,500

Total production costs      1,912,500

Cost per unit = $76.50 ($1,912,500/25,000)

Less Ending inventory        420,750               (5,500 x $76.50)

Cost of goods sold                              $1,491,750

Gross profit

Selling and administrative expenses:

Variable selling and administrative expenses $296,400

Fixed selling and administrative expenses 114,800 411,200

Sales (19,500 units)                              $2,145,000

Production costs (25,000 units):

Direct materials                $1,017,500

Direct labor                          487,500

Variable factory overhead 245,000

Total variable production costs  1,750,000

Cost per unit = $70 ($1,750,000/25,000)

Less Ending inventory       385,000               (5,500 x $70)

Cost of goods sold                              $1,365,000

Gross profit

Selling and administrative expenses:

Variable selling and

administrative expenses $296,400

Fixed factory overhead       162,500

Fixed selling and administrative expenses 114,800 411,200

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Answer:

The third answer is correct.

Step-by-step explanation:

1) First find the coordinates of the shape:

G(-1, -2), F(-1, -1), E(2,2), D(2, -2)

2)It asked for dilation of 2 about the origin.

*What is dilation?

Dilation is the expanding/enlarging a transformation by a scale factor

Now we multiply all the coordinates with the factor of 2

G(-1*2, -2*2) = G'(-2, -4)

F(-1*2, -1*2) = F'(-2, -2)

E(2*2, 2*2) = E'(4, 4)

D(2*2, -2*2) = D'(4, -4)

3) Now plot these points and graph the transformation:

A) The number of cards that are in a complete deck of Set is; 81

B) The number of unique sets are; 36

a) We are given;

Number of shapes = 1, 2 or 3

Colour = Red, Purple or Green

Shape = Oval, Diamond or Squiggle

Shading = Hollow, Shaded or Striped

Now, since a set is formed by all 3 cards, then we can say that;

Number of cards in a complete deck of set = 3⁴ = 81 cards

(b) Let us first find all sets = 3² * 4 * 3 = 108.

Thus;

Unique sets = 108/3

= 36 unique sets.

(c) There are 3 ways to choose the number of the cards from the given order.  

For the second one, there 2 choices, and then there is only 1 choice.  Thus; Number of ways to choose the numbers = 3 * 2 * 1 = 6.  

For the other attributes;

Number of ways = 6 * 6 * 24 *6 ways.

Now, since the order of cards doesn't matter in a set, then the number of sets where all three cards are the same for exactly 0 attributes is;

(6 * 6 * 24 *6)/3! = 864 sets

(d) If all the colors are the same, then;

Number of sets = 6 * 24 * 6/3! = 144 sets.  

If all the numbers are the same, then there are 144 sets which is also same for shapes and shading. Thus;

The number of sets where all three cards are the same for exactly 1 attribute is; 4 * 144 = 576

(e) There are C(4, 2) = 6 ways of choosing two attributes.  

For each of the two attributes, there are 3 options.  

For the other two attributes, there are 3 ways of assigning the choices. Thus, number of sets = 6*3*3*3*3 = 486 sets.

(f) There are C(4,3) = 4 ways of choosing which attributes are the same.  There are 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute. Thus;

The number of sets where all three cards are the same for exactly 3 attributes = 4*36*4 = 576 sets.

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Answer:

There are 5 turning points

Step-by-step explanation:

The estimator sample proportion is mathematically unbiased

Generally, the equation for is  mathematically given as

Population sample \mu=1.3

The sample to sample proprotion table will have

first column= 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10

Second coumn= 0,0,0.5,0,0,0.5,05,0.5, total 3

The probability distribution of the distinct variance values table will have

p row=0,0.5,1, Total

probability row= 4/9, 4/9, 1/9, 1

In conclusion, The mean sample

x=3/9

x=1.3

Where

population sample \mu=1.3

\mu= x

Therefore the estimator sample proportion is unbiased for population mean

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Answer:

184cm²

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Divide the figure into two parts,

Part 1 : rectangle with, width = 7 cm and length = 20 cm

Area of part 1 :

[tex] \qquad❖ \: \sf \:20 \times 7[/tex]

[tex] \qquad❖ \: \sf \:140 \: \: {cm}^{2} [/tex]

Part 2 : Trapezoid with parallel sides - 7 cm and 4 cm,and height 8 cm

Area of part 2 :

[tex] \qquad❖ \: \sf \: \cfrac{1}{2} \cdot (7 + 4) \sdot(8)[/tex]

[tex] \qquad❖ \: \sf \:11 \times 4[/tex]

[tex] \qquad❖ \: \sf \:44 \: \: {cm}^{2} [/tex]

Area of whole figure =Area of part 1 + part 2

[tex] \qquad❖ \: \sf \:140 + 44 \: \: {cm}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \qquad❖ \: \sf \:area =184\: \: {cm}^{2} [/tex]

The measure of sin C from the figure is 0.92

These identity is used to determine the measure of sides and angles of a triangle.

From the triangle

Opposite side to m<C = 12

'Hypotenuse = 13

Using the expression

sinC = BC/ACC

sinC = 12/13

sinC = 0.92

Hence the measure of sin C from the figure is 0.92

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The $1 belongs in the box.

s + c = 47 equation 1

5s + 4c = 200 equation 2

Multiply equation 1 by 5

5s + 5c = 235

Subtract equation 2 from equation 3

c = 35

Subtract 35 from 47

c = 47 - 35 = 12

35 couples tickets and 12 individual tickets were sold. This is not possible since the couples tickets were sold in 2.

s + c = 47 equation 1

5s + 4c = 201 equation 2

Multiply equation 1 by 5

5s + 5c = 235

Subtract equation 2 from equation 3

c = 34

34 is divisible by 2 so the $1 belongs in the box.

Here is the complete question:
Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said,

I wonder whether the dollar belongs inside the cash box or not.

The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?

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Using the normal distribution, it is found that there is a 0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 23.8, \sigma = 6, n = 20, s = \frac{6}{\sqrt{20}} = 1.3416[/tex]

The probability that 20 customers will wait an average of less than 21 minutes to be seated is the p-value of Z when X = 21, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{21 - 23.8}{6}[/tex]

Z = -0.47

Z = -0.47 has a p-value of 0.3192.

0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.

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Answer:

given : 0.61 per year

formula poisson probability : p(x=k)=xke-x/k!

(a) The parameter λ is the product of the rate per year and the number of years. The number of years is 1 year in this case.

λ=0.61×1=0.61

Evaluate the formula of the Poisson probability at k=0,1:

P(X=0)= 0!

(0.61)

0

e

−0.61

​

≈0.5434

P(X=1)=

1!

(0.61)

1

e

−0.61

​

≈0.3314

Add the corresponding probabilities:

P(X≤1)=P(X=0)+P(X=1)=0.5434+0.3114=0.8748

Use the complement rule:

P(X>1)=1−P(X≤1)=1−0.8748=0.1252

Note: The solution in the back of the book is the probability of at least one death instead of more than 1 death, thus the solution in the back of the book is not correct.

Step-by-step explanation:

this is prob wrong so im sorry in advance!