Write 2^8 * 8^2 * 4^-4 in the form 2^n

The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

The given sequence is an arithmetic sequence.

First term a1 = [tex]1\frac{1}{2}[/tex] = 3/2

Last term an = [tex]2\frac{1}{2}[/tex] = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

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Disclaimer: The given question in the portal is incorrect. Here is the correct question.

Question: If the first and the last term of an arithmetic progression with a common difference are [tex]1\frac{1}{2}[/tex], [tex]2\frac{1}{2}[/tex] and 1/9 respectively, how many terms has the sequence?

The number of complete packages the store have for sale is  x / 12

The donuts sells packages of 12 donuts. This means the each package has 12 donuts.

The store has made x donuts. This means the store made x number of donut. The donuts are not in packages.

Therefore, the number of complete packages the store have for sale is as follows:

12 donuts = 1 package

x donuts = ?

cross multiply

number of packages for sale = x / 12

Therefore, the number of complete packages the store have for sale is  x / 12

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Answer: 98

Step-by-step explanation:

Area of four walls = Curved surface area

                             = perimeter × height

                              =    28          ×   3.5

                              = 98 m square  

The z-score to the normal distribution table is 1.625

The standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.

The formula for calculating the z-score is expressed as;

z = x-μ/σ

where

μ is the mean of the data

σ is the standard deviation

x is the value

Given the parameters

μ = 25.1

σ = 2.4

x = 29

Substitute the given parameters

z = 29-25.1/2.4

z = 3.9/2.4

z = 1.625

Hence the z-score to the normal distribution table is 1.625

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Missing data:

Viewer's Age Group  Excellent Good Average Poor Marginal Total

16–25                          52                 42       12       7           113

26–35                          33                50         5       9          97

36–45                          58                 12       28      34         132

46–55                          25                17       22       12            76

56 +                               12                 5          3         8             28

Marginal Total             180               126      70      70           446

A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.

A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.

25/446 = 0.05605

0.05605 [tex]*[/tex] 100% = 5.605%

Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.

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Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C

Common ratio, r = second minutes / first minutes

= 95.1 / 97

= 0.98041237113402

Approximately,

r = 0.98

nth term of the sequence, Tn = ar^n -1

Tn = 97 × 0.98^(n-1)

Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)

= 97 × 0.98^(15-1)

= 97 × 0.98^14

= 97 × 0.7536419414749019520643907584

= 73.1032683230654893502459035648

Approximately,

T15 = 73.1°C

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The solutions to the equations are x = 7/3 and y = 24/7

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

4x + 10 = -2x + 4

y - 4(2y - 5) = -4

Considering the first equation

4x + 10 = -2x + 4

Collect the like terms

4x + 2x = 10 + 4

Evaluate the like terms, by adding them

6x = 14

Divide both sides of the equation by 6

x = 7/3

Considering the second equation

y - 4(2y - 5) = -4

Expand the bracket in the above equation

y - 8y + 20 = -4

Collect the like terms

y - 8y = -20 -4

Evaluate the like terms, by adding them

-7y = -24

Divide both sides of the equation by -7

y = 24/7

Hence, the solutions to the equations are x = 7/3 and y = 24/7

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Answer:

time required = 26 min

Step-by-step explanation:

To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):

○ diameter of pipe = 64 mm ⇒ radius = 32 mm

○ water discharge rate = 2.05 mm/s

○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm

○ height of tank = 2.3 m = 2300 mm.

Now, let's calculate the cross-sectional area of the pipe:

Area = πr²

       ⇒ π × (32 mm)²

       ⇒ 1024π mm²

Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:

Volume transferred = 1024π mm² × 2.05 mm/s

                                ⇒ 6594.83 mm³/s

Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h

            ⇒ π × (38)² × 2300

            ⇒ 10433857 mm³

We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,

time required =  [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]  

                     ⇒ 1582.12 s

                     ⇒ 1582.13 ÷ 60

                     ≅ 26 min

Answer:

  26 minutes

Step-by-step explanation:

The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.

For some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...

  V = k·d²·h . . . . d = diameter; h = rate×time

  V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³

For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...

  V = k(0.76 dm)²(23 dm) = k·13.2848 dm³

Then the proportion involving (inverse) rates is ...

  time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)

  fill time = 13.2848/0.503808 min ≈ 26.369

__

Additional comments

1 dm = 100 mm = 10 cm = 0.1 m

1 dm³ = 1 liter, though we don't actually need to know that here.

We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).

__

The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.

When followers' needs for security and certainty, belonging, and feeling chosen or special are strong, it makes them vulnerable to the dictates of abusive leaders.

The epistemic attribute of beliefs that one cannot rationally reject is certainty, often known as epistemic certainty or objective certainty. Epistemic certainty is commonly defined as a belief being certain if and only if the person holding it could not be wrong in holding it.

In both public and private markets, securities are fungible, tradeable financial instruments used to raise capital.

The three main categories of securities are: equity, which gives holders ownership rights; debt, which is effectively a loan returned with recurring payments; and hybrids, which include features of both debt and equity.

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Answer:

i think this may help you

The diagram to show that the square root of 121 is 11 attached below

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

Assume that x-a be the closest perfect square less than x,let x+b be the closest perfect square more than x, then we get: x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).

Then, we get:

[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]

Thus, [tex]\sqrt{x-a} and \sqrt{x+b}[/tex] are the closest integers, less than and more than the value of {x}. (assuming x is non-negative value).

Herewe are given the number as 121

It is perfect root then ;

√121 = 11

The solution that show that the square root of 121 is 11 attached below

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Answer:

Exact Form:

61/12

Decimal Form:

5.083 with 3 repeating

Mixed Number Form:

5   1/12

Step-by-Step Explanation:

-5/3×3/8 = -5/8

-5/8+3/8= -1/4

-1/4+6/9=5/12

5/12+14/3=61/12

Based on the given task content; the product of StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction is (4n² - 8n) / (4n²x - 5nx - x)

Product of numbers refers to the multiplication of two or more values to arrive at a single result.

4n / (4n - 1) × (n - 1) / (n + 1) 2/x

= 4n / (4n - 1) × 2(n - 1) / x(n + 1)

= 4n / (4n - 1) × (2n - 2) / (nx + x)

= 4n(2n - 2) / (4n - 1) (nx + x)

= 4n² - 8n / (4n²x - 4nx - nx - x)

= (4n² - 8n) / (4n²x - 5nx - x)

Therefore, the product of 4n / (4n - 1) × (n - 1) / (n + 1) 2/x is (4n² - 8n) / (4n²x - 5nx - x)

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Answer:

(2, - 1 )

Step-by-step explanation:

3x - y = 7 → (1)

2x + 3y -= 1 → (2)

multiplying ( 1) by 3 and adding to (2) will eliminate y

9x - 3y = 21 → (30

add (2) and (3) to eliminate y

11x = 22 (divide both sides by 2 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

2(2) + 3y = 1

4 + 3y = 1 (subtract 4 from both sides )

3y = - 3 ( divide both sides by 3 )

y = - 1

solution = (2, - 1 )

The the biggest 5 digit number based on the computation will be 87,978.

The difference between the sum of the odd-numbered digits (1st, 3rd, 5th...) and the sum of the even-numbered digits (2nd, 4th...) is divisible by 11.

An example is that 34871903 is divisible by 11

3+8+1+0=12

4+7+9+3=23

23-12=11

Here, we want (b + b) - (a + c + a) to be divisible by 11.

2b - (2a + c) to be divisible by 11

ab,cba (using 7 and 8 and 9 since they biggest)

78 987 --> 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO

87 978 --> 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES

79 897 --> 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO

97 879 --> 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO

89 798 --> 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO

98 789 --> 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO

Therefore, the biggest 5 digit number is 87,978.

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The total cost of electricity when the business operates for 4 hours is correct.

The slope of a line is also known as rate of change, The formula for calculating the slope of a line is expressed as:

Slope = y2-y1/x2-x1

If the proportional relationship between the number of hours a business operates and its total cost of electricity is shown in the following graph.

Using the coordinate points (1, 20) and (2, 40)

Slope = 40-20/2-1
Slope = 20/1

Slope = 20

This shows that the total cost of electricity is $20 when operating business for 1 hour.

According to the coordinate point A (4, 120), this shows that the y-coordinate of point A is represents the total cost of electricity when the business operates for 4 hours.

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Answer:

$329.00

Step-by-step explanation:

Let the original price be $x, then

x - 0.30x - 0.10(x - 0.30x) =  207.27

x - 0.30x - 0.10x + 0.03x = 207.27

0.63x = 207.27

x = 329.00.

we conclude that the linear equation represented by the given table is:

y = (1/2)*x + 2

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂), then the slope is given by:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we can use just the first two points on the given line:

(-8, -2) and (-4, 0)

Then the slope will be:

[tex]a = \frac{0 - (-2)}{-4 -(-8)} = \frac{2}{4} = \frac{1}{2}[/tex]

Then the linear equation is something like:

y = (1/2)*x + b

To find the value of b, we can use one of the two given points, I will use (-4, 0), then:

0 = (1/2)*(-4) + b

0 = -2 + b

2 = b

Then we conclude that the linear equation represented by the given table is:

y = (1/2)*x + 2

Then the correct option is the first one.

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the parallel linear equation is:

y = (2/5)*x - 3

Two lines are parallel if the lines have the same slope but different y-intercept.

Here we know the line equation:

y = (2/5)*x + 4

Then a parallel line is of the form:

y = (2/5)*x + c

Where c is different than 4.

We want this line to pass through (5, -1), then:

-1 = (2/5)*5 + c

-1 = 2 + c

-1 - 2 = -3 = c

Then the parallel linear equation is:

y = (2/5)*x - 3

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The value of x for the given equation is 0.632 and -0.632.

According to the statement

We have given that the equation and we have to a find the value of the x.

So, The given quadratic equation are:

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation

The given terms are

[tex]6x^2 + 4(x^2 - 1) = 0[/tex]

Solving the equation the the outcome equation is

[tex]6x^2 + 4x^2 - 4 = 0\\10x^2 - 4 = 0\\10x^2 = 4\\x^2 = 4/10[/tex]

The value of x is 0.632 and -0.632.

So, The value of x for the given equation is 0.632 and -0.632.

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The answers to the questions are:

This defined as the total number of points that a person has been able to cover at a given period. It is calculated by taking the time and the speed of takeoff into consideration. The speed that a person used and the time it took them to get to their destination is what is used to calculate distance

The time it takes for sunlight to reach is given as

distance/speed

778000000000/300000000

=2593.33 * 60

= 43.22 minutes

The formula for distance is given as speed * time

speed = 15km/hr

time = 1 hour

The distance = 15 * 1

= 15 km/hr

If the time is 2*1/2

the distance = 15 / 2.5

= 6 km

Expressed as a fraction we have the following

0.37 = 37/100

0.086 = 86/1000

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The true statements about the functions are:

The function is given as:

f(x) = 25000 * 0.96^x

Set x = 0 to determine the initial value of the function

f(0) = 25000 * 0.96^0

Evaluate

f(0) = 25000

This means that the population of the city in 2010 is 25000 i.e. option (B) is correct

Also, we have:

f(x) = 25000 * 0.96^x

The rate at which the population decreases every year is calculated as:

r = 1 - 0.96

Evaluate the difference

r = 0.04

Express as percentage

r = 4%

This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct

The population after 5 and 10 years are:

f(5) = 25000 * 0.96^5

f(5) = 20384

f(10) = 25000 * 0.96^10

f(10) = 16621

Divide these populations by the initial population in 2010

20384/25000 = 82%

16621/25000 = 66%

This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.

So, options (d) and (e) are false

Lastly, because the population function is an exponential decay function;

The function value would approach 0 as it decreases

This means that option (f) is correct

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The value of (f - g)(x) is as follows:

(f - g)(x)  =  4x³ + 6x² - 7x - 1

f(x) = 4x³ + 6x² - 3x - 4

g(x) = 4x - 3

Let's find the function:

(f - g)(x)

Therefore,

(f - g)(x)  = 4x³ + 6x² - 3x - 4 - ( 4x - 3)

Hence, let's open the bracket

(f - g)(x)  = 4x³ + 6x² - 3x - 4 - 4x + 3

Let's combine like terms

(f - g)(x)  =  4x³ + 6x²  - 3x - 4x - 4 + 3

Therefore,

(f - g)(x)  =  4x³ + 6x² - 7x - 1

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The mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

A cylinder is a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

larger-sized candle = 2(smaller-sized candle)

= 2(240 cubic centimeters)

= 480 cubic centimeters

Therefore, the mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

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Answer:

A cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.

Hope this helps!

Step-by-step explanation:

[tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

We can find the A as shown below:

Given A^2=I

We know that A^2=A×A

And [tex]I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

So, [tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

Let [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

[tex]A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

[tex]A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right][/tex]

[tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

Hence, [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]

Hence, option C is correct

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Disclaimer: Given question is incomplete. Complete question is attached.

It looks like you have

[tex]f(x) = \begin{cases} 3 & \text{if } -4 \le x \le 0 \\ 4 - x^2 & \text{if } 0 < x \le 3\end{cases}[/tex]

and the integral you want to compute is

[tex]\displaystyle \int_{-4}^3 f(x) \, dx[/tex]

Split the integral up at [tex]x=0[/tex]. Then

[tex]\displaystyle \int_{-4}^3 f(x) \, dx = \int_{-4}^0 f(x)\,dx + \int_0^3 f(x)\,dx \\\\ ~~~~~~~~~~~~ = \int_{-4}^0 3 \, dx + \int_0^3 (4 - x^2) \, dx \\\\ ~~~~~~~~~~~~ = 3(0 - (-4)) + \left(4\cdot3 - \frac{3^3}3\right) = \boxed{15}[/tex]

After evaluating the integral we get 15

Integral is the representation of the area of a region under a curve. We approximate the actual value of an integral by drawing rectangles. A definite integral of a function can be represented as the area of the region bounded by its graph of the given function between two points in the line.

Given,

f(x) = 3         if   - 4 ≤ x ≤ 0

f(x) = 4 - [tex]x^{2}[/tex]  if   0 < x ≤ 3

Then,

[tex]f(x) = \left \{ {{3} \atop {4-x^{2} }}[/tex]

We need to solve the integral -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]

Elaborate the integral with x = 0

                                             -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]

                                          = -[tex]\int\limits^0_4 {f(x)} \, dx + \int\limits^3_0 {f(x)} \, dx[/tex]

                                          = -[tex]\int\limits^0_4 {3} \, dx + \int\limits^3_0 {4-x^{2} } \, dx[/tex]

                                          = 3 ( 0 - (-4)) + (4.3 - [tex]\frac{3^{3} }{3}[/tex])

                                          = 15

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the correct inequality is"any rational number less than 9"

x < 9

Remember that when we have a number line, an open circle means that we can use the symbols > or <.

While a closed circle uses the symbols ≤ or ≥.

Here we know that we have an open circle at 9, ant everything to the left of the circle is shaded.

To the left of 9 there are the numbers smaller than 9, then the inequality would be:

x < 9

Then the correct option is "any rational number less than 9"

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Answer: x<9

any rational number less than 9"

Step-by-step explanation:

The expression 25p+18(p+4) represents the total amount spent on shirts and pants

The given parameters are:

Shirts = 4 more than pants (p)

Cost of shirt = $18

Cost of pant = $25

The above means that:

p + 4 represents the number of shirts Chris buys, while p represents the number of pants

The terms of the expression 25p + 18(p+4) are

25p and 18(p+4)

This means that:

25p = The total cost of pants

18(p+4) = The total cost of shirts

Hence, the expression 25p+18(p+4) represents the total amount spent on shirts and pants

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Answer:

x = -1

y = 1

Step-by-step explanation:

Given expressions

1) 2x + 3y - 1 = 0

2) 5x + 2y + 3 = 0

Add 1 on both sides of the 1) equation:

2x + 3y - 1 + 1 = 0 + 1

2x + 3y = 1

Subtract 3 on both sides of the 2) equation:

5x + 2y + 3 - 3 = 0 - 3

5x + 2y = -3

Current System

1) 2x + 3y = 1

2) 5x + 2y = -3

Multiply 2.5 on both sides of the 1) equation

(2.5) 2x + (2.5) 3y = (2.5) 1

5x + 7.5y = 2.5

Current System

1) 5x + 7.5y = 2.5

2) 5x + 2y = -3

Subtract 2) equation from 1) equation

(5x + 7.5y) - (5x + 2y) = 2.5 - (-3)

Get rid of the parenthesis

5x + 7.5y - 5x - 2y = 2.5 + 3

Combine like terms

5x - 5x + 7.5y - 2y = 5.5

0 + 5.5y = 5.5

5.5y = 5.5

Divide 5.5 on both sides

5.5y / 5.5 = 5.5 / 5.5

[tex]\boxed{y=1}[/tex]

Substitute the y-value back to one of the equations to find the x-value

2x + 3y - 1 = 0

2x + 3(1) - 1 = 0

Combine like terms

2x + 3 - 1 = 0

2x + 2 = 0

Subtract 2 on both sides

2x + 2 - 2 = 0 - 2

2x = -2

Divide 2 on both sides

2x / 2 = -2 / 2

[tex]\boxed{x=-1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions