Evaluate 8/9 power of 2 as a fraction in simplest form

Answer:

Product: 96

GCF: 4

LCM: 24

Product of the GCF and LCM: 96

Step-by-step explanation:

Now that we know what definitions are, we can solve this word problem.

12 × 8 = 96.

96 is the product.

To find the greatest common factor, we can list all of the factors for each number.

12: 1, 2, 3, 4, 6, 12

8: 1, 2, 4, 8

The largest factor both numbers have in common is 4.

Therefore, 4 is the greatest common factor.

To find the least common multiple, we can list the multiples of both numbers.

12: 12, 24, 36, 48, 60, 72, 84, 96

8: 8, 16, 24, 32, 40, 48, 56, 64

The smallest multiple both numbers have in common is 24.

Therefore, 24 is the least common multiple.

Lastly, we have to find the product of the GCF and the LCM.

The GCF is 4 and the LCM is 24.

4 × 24 = 96.

96 is the product.

Therefore, 96 is the product of the greatest common factor and the least common factor of 12 and 8.

Gracie poured out 3/10 gallons of the original mixture.

In mathematics →

Given is that Gracie has made 2 gallons o punch that contains 50% juice. After Gracie pours out some of her mixture and replaced with an equal amount of pure 100% juice, she has 2 gallons of punch that contains 65% juice.

Assume that she pour out {x} gallons of original mixture. We can write -

{50% of 2} - {x} = {(100 - 65)% of 2}

{50/100 x 2} - {x} = {35/100 x 2}

{1/2 x 2} - {x} = {35/100 x 2}

1 - x = 7/10

1 - 0.7 = x

x = 0.3

x = 3/10

Therefore, Gracie poured out 3/10 gallons of the original mixture.

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Answer:

Los jugadores dan 36 palmadas en total.

Step-by-step explanation:

Dado que 9 jugadores de un equipo de baloncesto chocan palmadas unos con otros, para determinar cuántas palmadas dan en total, sabiendo que 2 jugadores dan una palmada, 3 jugadores, tres palmadas, 4 jugadores, seis palmadas, y 5 jugadores, diez palmadas, se debe realizar el siguiente cálculo:

Cada jugador da un número de palmadas igual al número de jugadores en el campo, menos 1. A su vez, esa palmada es recíproca con el otro jugador que la recibe, con lo cual el número de jugadores a contar va disminuyendo.

8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = X

15 + 6 + 5 + 4 + 3 + 2 + 1 = X

21 + 5 + 4 + 3 + 2 + 1 = X

26 + 4 + 3 + 2 + 1 = X

30 + 3 + 2 + 1 = X

33 + 2 + 1 = X

35 + 1 = X

36 = X

Por lo tanto, dan 36 palmadas en total.

Answer:

The height of the triangle = 6 inches

The base of the triangle = 10 inches

Step-by-step explanation:

The formula for the Area of a Triangle = 1/2 × Base × Height

Area = 30 in²

h = b - 4

Hence

30 = 1/2 × b × b - 4

Cross Multiply

30 × 2 = b² - 4b

60. = b² - 4b

b² - 4b - 60

We factorise the Algebraic expression to find b

b² - 4b - 60 = 0

b² - 10b + 6b - 60 = 0

b(b - 10) + 6(b - 10) = 0

(b - 10) + (b + 6 ) = 0

b - 10 = 0 , b = 10

b + 6 = 0, b = -6

We are going to take the positive answer of b as the value of b

b = 10 inches

Solving for h

h = b - 4

h = 10 - 4

h = 6 inches

Therefore, the height of the triangle = 6 inches

base of the triangle = 10 inches

A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to (X - ц0) / (s / √n), where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to [tex](X - ц0) / (s / √n)[/tex], where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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Answer:42.875 feet3

Step-by-step explanation:

Answer:

Step-by-step explanation:

V=a³

=[tex](3\frac{1}{2})^3=42\frac{7}{8}[/tex]in³

Using the formula for the volume of cuboid that is the product of length, breadth and height, The answer is 7cm.

A cuboid is a three-dimensional shape with six rectangular faces, three of which are pairs of congruent squares and the other three are rectangles. It is also known as a rectangular prism. The opposite sides of a cuboid are parallel and equal in area. The length, width, and height of a cuboid are three of its measures of size.

The volume of a three-dimensional object is a measure of the amount of space it occupies. It is typically measured in units of cubic units, such as cubic centimeters (cm^3) or cubic meters (m^3). The formula for the volume of a cuboid is length x width x height. For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, its volume would be 5 x 3 x 2 = 30 cubic centimeters. In general, the volume of a three-dimensional object can be found by multiplying the area of its base by its height.

length = 2cm

breadth =3cm

volume = 42 cm³

volume = l*b*h

42 = 2*3*h

h= 42/6 =7cm

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yes it  is the same as that of all students at Faber GPAs as 2.32 and lower will mean that a track team athlete will be recommended for extra tutoring and population is 2.3* student number

What is the definition of a population?

In ordinary usage, a population is a distinct group of individuals with shared citizenship, identity, or characteristics. In statistics, a population is a representative sample of a larger group of people (or even things) with one or more characteristics in common.

When the distribution is normal, we use the z-score formula.

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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Answer:

$21,200

Step-by-step explanation:

Given the best fit equation:

y= 34,000 - 1,600x

Where ;

y = value of vehicle in $

x = Age of vehicle in years

The predicted value of vehicle aged 8 years ;x = 8

y = 34000 - 1600(8)

y = 34000 - 12800

y = 21,200

Hence, the predicted value of car aged 8 years is $21,200

Answer: o.7619

Step-by-step explanation: i used the standard algorithm i am sorry i cant do a more in depth just hard to do with words ;)

Answer: 0.7619

:)

Step-by-step explanation:

If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)

Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.

F = P(1+rt), formula for simple rate of interest

Here,

=> Future value is F

Present value is P

=> Rate is R

=> Time is t

Substituting x for r

And, n for t

Also, 10,000 in for P

F = 10,000(1+xn)

The formula tells us principal + interest,

F = 10,000(xn)

Now, to get the x into terms of a percentage,

F = 10,000(n * x/100)

F = 10,000n(x/100)

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Answer:

A, y = x

Step-by-step explanation:

Slope is equal to one

Y-intercept is origin

Answer:

A.) Y=X

Step-by-step explanation:

It intercepts with origin

Answer:

B: weather occurs because the climate is constantly changing

Step-by-step explanation:

See comment for complete question

Answer:

81 games

Step-by-step explanation:

Given

[tex]P(Red) = 0.45[/tex]

[tex]P(Blue) = 0.40[/tex]

[tex]n = 180[/tex]

Required

Expected game the red team will win

Expected number is calculated as:

[tex]E(x) = n * P(x)[/tex]

In this case, the number of winnings for the red team is:

[tex]Expected = 180 * P(Red)[/tex]

[tex]Expected = 180 * 0.45[/tex]

[tex]Expected = 81[/tex]

A three-variable system is a system of equations or inequalities involving three variables.

The three variables could refer to any three related quantities, such as a person's age, height, and weight. In a three-variable system, the number of equations is equal to the number of variables, so three equations are needed to solve the system. Each equation in the system will involve all three variables and will be solved through a combination of algebraic manipulation, substitution, and elimination techniques. Once all three equations have been solved, the values of the variables can be found.

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Answer:

10 walnuts..

Step-by-step explanation:

12 - 2 = 10

Answer:

10?

Step-by-step explanation:

12-2=10

Answer:

Step-by-step explanation:

Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.

Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

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Answer:

g= 92°

h= 88°

k= 91°

m= 89°

Step-by-step explanation:

Answer:

g = 92°

h = 88°

k = 91°

m = 89°

Step-by-step explanation:

Have a nice day!

In the given graph the domain and range of function y=f(x) is

Domain: (-2,2]

Range : [-4, 5)

A function's domain is the set of all possible inputs to the function. This means it can be any number that can be entered into a function. For the majority of functions, this will be any number that can be substituted for the letter x. Except for a few exceptions such as square root functions and rational numbers, your domain will almost always be all real numbers.

The set of all possible outputs of a function is referred to as its range. This is usually represented by the letters y or f(x). The range is any number obtained by substituting any number for x.

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The duckweed increases by a percentage each day which is calculated by the equation

(1230.25t/16)/a - 1.

This equation can be further simplified to 1230.25t/16a - 1 and then multiplied by 100 to get a percentage.

So the percentage increase of duckweed each day is calculated by multiplying 1230.25t/16a - 1 by 100.

1230.25t/16a×100

This will give us the percentage of increase each day, rounded to the nearest whole number.

For example, if the initial number of fronds is 1000 and the number of days is 2, the percentage increase of duckweed will be (1230.25(2)/16(1000)) - 1 = 24.6%, rounded to the nearest whole number which is 25%.

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Answer:

-4

Step-by-step explanation:

Answer:

y = -1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 0, and the y-intercept is located at (0,-1), so the equation is

y = -1

Answer:

y = -1

Step-by-step explanation:

Answer:

[tex]-\sqrt{7/4}[/tex]

Step-by-step explanation:

[tex] \sin( \theta) = \frac{ \sqrt{3} }{2} [/tex]

Answer:

I don't really know but I will help you if I can

Answer:

e/f

Step-by-step explanation:

sin =opposite/ hypothenuse

e is opposite

f is hypothenuse

With respect to the reference angle E, sinE = e/f.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

We know, sin is opposite over hypotenuse.

From the given figure, With respect to the reference angle E,

opposite is FG and hypotenuse is EG.

Therefore, sinE = FG/EG.

sinE = e/f.

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Line segment theorem states that if a line segment is bisected by another line, then the two parts of the line segment are equal.

This theorem is also known as the Midpoint Theorem. The formula for the Line Segment Theorem is A/B = C/D, where A and C are the two halves of the line segment, and B and D are the distances from the midpoint to the two endpoints of the line segment.

For example, consider a line segment AB with endpoints at A(-3, 2) and B(3, 2). The midpoint of the line segment is at (0,2). To calculate the length of each half of the line segment, we would use the distance formula and plug in the coordinates of the two endpoints and the midpoint.

For half A, the distance is d(A, M) = sqrt[(-3 - 0)^2 + (2 -2)^2] = 3.

For half C, the distance is d(M, B) = sqrt[(3 - 0)^2 + (2 -2)^2] = 3.

Therefore, A/B = 3/3 = 1 and C/D = 3/3 = 1. This confirms that the two halves of the line segment are equal in length.

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The greatest number of classrooms is 4, Joanne can distribute materials

5 flyers and 4 buttons.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor or GCF.

Given:

Joanne is campaigning for class president and plans to distribute some campaign materials.

20 flyers and 16 buttons.

She wants each classroom to receive an identical set of campaign materials, without having any materials left over.

In order to find the greatest number of classrooms, Joanne can distribute materials:

We have,

the number of flyers = 20.

Number of buttons = 16

We need to find the GCF.

GCF of 16 - 1,2,4,8,16

GCF of 20-1,2,4,5,10,20

Clearly, 4 is the GCF.

Therefore, total number of classrooms = 4

Number of flyers distributed to each classroom

= Total number of flyers / Total number of classroom

= 20/4

= 5

Number of buttons distributed to each classroom

= Total number of buttons/ Total number of classrooms

= 16/4

= 4

Therefore, the Joanne can distribute 5 flyers and 4 buttons to each classroom.

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1. The quotients of the following division operations are as follows:

a) 126 ÷ 12 is 10.5.

b) 217 ÷ 4 is 54.25.

c) 75 ÷ 6 is 12.5.

d) 11 ÷ 9 is 1.2222.

e) 200 ÷ 35 is 5.7143.

2a) The quotient of 7 ÷ 2.2 is a nonterminating or repeating decimal.

2b) The quotient of 0.5 ÷ 0.12 is a nonterminating or repeating decimal.

2c) The division operation with a quotient that is nonterminating or repeating decimal is 2 ÷ 2.7.

3) The identification of each resulting quotient as a terminating or nonterminating, repeating decimal is as follows:

4) The quantity of meat in one piece of hamburger, if they are evenly shared or divided, is 41.67 g.

The quotient is the result of the division operation.

Every division operation involves the dividend (the numerator), the divisor (the denominator), the division operand (÷), and the equal sign (=).

2)

a) 7 ÷ 2.2 = 3.181818

b) 0.5 ÷ 0.12 = 4.16667

c) 3 ÷ 0.8 = 3.75

9 ÷ 0.16 = 56.25

2 ÷ 2.7 = 0.740740

3)

a. 2 ÷ 3 = 0.6667

b. 5 ÷ 1.2 = 4.16667

c. 0.3 ÷ 0.9 = 0.3333

d. 2.4 ÷ 1.8 = 1.3333

4) Total weight of ground pork = 1.25 kilograms

1 kg = 1,000 g

1.25 kg = 1,250 g

The pieces of patties = 30

The weight of each piece = 41.67 g (1,250/30)

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