Megan has $25 to spend at the movies. If her ticket cost $8.75 and she already
purchased a drink for $3.50, how much does she have left to spend on snacks?

The value of 4 to the 3rd power =64

According to the power rule of exponents,

am = m times a x a x a

Thus, 43 can be written as 4 × 4 × 4 = 64.

Thus, the value of 4 to the 3rd power i.e., 4^3 is 64

Exponent is the process of representing huge numbers as powers, according to the definition. Exponent, then, is the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

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A linear equation, with five variables, has an infinite number of solutions.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Let linear equation:

5 =  x + a + b + c + y

In this equation,

there are five variables, x, a, b, c and y.

And the number of equation is one.

That means,

the number of unknowns > the number of equation

5>1.

Substitute the value of 4 variables to find the value of one variable.

Let, we have to find solutions as subject to y.

We so obtain varied values of y when preserving distinct values of x, a, b, c.

Therefore, infinitely many solutions are possible.

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The solution of the given system of equations 6x + 2y = 4 , 9x -3 y = 12 is equal to x =1 and y = -1.

As given in the question,

Given system of equations are :

6x + 2y = 4     ____(1)

 9x -3 y = 12   _____(2)

Multiply (1) by 3 and (2) by 2 and add equation (1) and  (2) to eliminate y variable and get the value of variable x ,

18x + 6y = 12

18x - 6y = 24

36x      = 36

⇒x = 36 / 36

⇒ x = 1

Substitute value of x = 1 in the given equation (1) to get the value of variable y,

6(1) + 2y = 4

⇒ 6 + 2y = 4

⇒ 2y = 4 - 6

⇒ y = -1

Therefore, given system of equations 6x + 2y = 4 , 9x -3 y = 12 solution is equal to x = 1 and y = - 1.

The above question is incomplete, the complete question is:

What is the solution of the system of equations 6x + 2y = 4 , 9x -3 y = 12?

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The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms. Hence, we can say;

Mean = Sum of the Given Data/Total number of Data

Mean= 6 +7+ 10+ 12+ 13+ 4+ 8 +12 /  8 = 72/8 = 9

Hence, The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.

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Answer:

x-intercept: (-21/2,0)

y-intercept : (0,-21)

The complete question should be: What is the per capita personal income for a given state in 2004, represented by the value [?] on the vertical axis of the state table?

The missing value on the vertical axis represented by [?] must be $21,200.

In order to determine the missing value on the vertical axis represented by [?], we need to consider the per capita personal income for each of the states listed in the table. The states are listed in order from highest income to lowest income. The highest-earning state is listed first with a per capita personal income of $52,000. The next-highest-earning state has a per capita personal income of $21,200. Therefore, the missing value on the vertical axis represented by [?] must be $21,200.

To enter this answer, first identify the numerical keypad on the calculator. Then, enter the numerical value of $21,200 (21200) using the keypad. Finally, press the “enter” or “equals” key to submit the answer. This will cause the missing value on the vertical axis to be displayed on the calculator screen.

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Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

Answer:

  (A)  $26

Step-by-step explanation:

You want to know the amount Byron received from the distribution to Alyah, Byron, and Cecil, given Cecil received $40.

Let x represent the amount being distributed, and a, b, c represent the amounts received by Alyah, Byron, and Cecil, respectively.

The given relations tell us ...

  a = 1 + 1/3(x -1)

  b = 6 + 1/3(x -a -6)

  c = x -a -b = 40

Substituting for b gives us ...

  40 = x - a - (6 +1/3(x -a -6)) = x -a -6 -1/3x +1/3a +2 = 2/3x -2/3a -4

  44 = 2/3(x -a) . . . . . . . add 4, factor out 2/3

  66 = x -a . . . . . . . . . multiply by 3/2

Substituting for a gives us ...

  66 = x -(1 +1/3(x -1)) = x -1 -1/3x +1/3 = 2/3x -2/3 = 2/3(x -1)

  99 = x -1 . . . . . . . multiply by 3/2

  100 = x . . . . . . add 1

Then ...

  a = 1 + 1/3(100 -1) = 1 + 99/3 = 34

  b = 6 + 1/3(100 -34 -6) = 6 + 1/3(60) = 26

Byron received $26.

__

Additional comment

Based on results, the "what is left" is the amount after the $1 or $6 distributions are made.

  Alyah: $34, Byron: $26, Cecil: $40, for a total of $100.

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Counting numbers are another name for natural numbers. These are 1, 2, 3, and so forth.

Natural numbers plus zero are whole numbers.

Natural numbers, whole numbers, and the opposites of whole numbers are all considered integers. These numbers range from -3 through -2, -1, 0, 1, 2, 3, etc.

Integers, whole numbers, rational numbers, and numbers that may be expressed as fractions are all considered rational numbers. In this case, fraction [tex]\frac{a}{b}[/tex], where; a and b must both be integers.

All non-rational numbers are categorized as being irrational. These figures cannot be expressed as fractions. This includes decimals like [tex]\pi[/tex], [tex]\sqrt{2}[/tex], and 3.2576352417942 that doesn't end or repeat.

The collection of all rational and irrational numbers, as well as their subsets, is known as the Real Number System.

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Answer:

Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer: Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer:

C. Subtraction Property of Equality

Step-by-step explanation:

The equation is

m<1 + m<2 = m<2 + m<4

m<1 = m<4

We see that is subtraction property, so the answer is C

The probability to get tails is 0.50.

What is rounding 2decimal place?

The second place to the right of the decimal point, or the hundredths place, is used to round a decimal value to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

The probability of an event is the ratio of the number of outcomes of the required event to the number of total outcome.

In a coin, there are two parts in coins that are tails and heads.

The total number of possible outcomes is 2.

The number of tails of a coin is 1.

The probability to get tails is = 1/2

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Answer:

6138

Step-by-step explanation:

First, we have to find the population of the city in 2015

6% = 0.06

193,000 times 0.06 = 11580 people increase

We know it is increasing, so we have to add them

193,000 + 11580 = 204580 people in 2015

Now let's find the 3% decrease

3% = 0.03

204580 times 0.03 = 6137.4

So, about 6138 people decrease from 2015 to 2020

A triangle's area is 1/2(b*h), where b is the base and h is the height. A triangle's base can be any of its sides, and its height is the length of the altitude from the opposite vertex to that base.

The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

The area of a triangle is 1/2(b*h), where b is the base and h is the height. A triangle's base is any one of its sides, and its height is the length of the altitude from the opposite vertex to that base.

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We are aware that a discrete function is one that satisfies the criteria for a function and has a countable domain (represented as a collection of disconnected points) (each input has at most one output). Many inputs in discrete functions won't have any outputs.

According to the inquiry,

All three of the functions have a y-intercept and, given the facts in the question, f(x) is the highest maximum.

The largest maximum of the three functions—g(x), f(x), and f(y)—has an x-intercept.

Three distinct discrete functions are displayed in the table.

f(x)minimum: 1 g(x)minimum; -4 12 h(x)minimum-5; as a result, f(x)maximum: 10 g(x)maximum; 3 12 h(x)maximum; 12 f(x)domain; (0, 2) g(x)domain; (-2, 2) h(x)domain; (0, 1) g(x)y-inter (0, -5)

Using the procedures above, we may conclude that f(x) has no x.

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5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.

What equation contains an expression?

The equal to sign (=) is the best indicator of whether a given problem is an equation or an expression because it indicates that the problem is an equation.

                It is only an expression if there isn't an equal to (=) sign present. It contains data that is used to demonstrate value, such as numbers, variables, and operators.

5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.

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The Median for the following data 3 445 712 767 will be 578.5.

One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.

When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:

sorting of the sample data in ascending or descending order.

If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.

The average of the top two observations is the same as the median of the data given (as determined in step 2).

Here n = 4, So [4/2 + (4/2)+1}/2, So the median will be 578.5.

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The cartesian equation for x = t² and y = 2 + 3t is x = (1/9)y² - (4/9)y + (4/9).

Where the value of A, B, and C are 1/9, - 4/9, and 4/9.

The parameter t that we have

The cartesian equation x = (1/9)y² - (4/9)y + (4/9)

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If you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned.

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

Consequently, if you have three side lengths, you should discover the lowest angle by finding the angle that is opposite the smallest side, the medium-sized angle by finding the angle that is opposite the medium-sized side, and the greatest angle by finding the angle that is opposite the largest side.

Therefore, if you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

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The two important first steps in data analysis are data cleaning and exploring it, so, option A is correct.

A measure of the relationship between two variables is a correlation. Variables can be related in a number of ways, including linearly, non-linearly, and in other ways. Variables can also have varying degrees of association with one another. The most popular linear coefficient used to determine how closely two variables correlate is called Pearson's correlation coefficient, or PCC.

The steps of data analysis are shown below,

First, define the question. Identifying your purpose is the first stage in any data analysis procedure.

Gathering the data is the second step.

Third step: data cleaning.

The fourth step is data analysis.

Five: Present your findings.

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The parent function of a parabola is y = x².

A function is said to be a parent function if it is expressed in the simplest form and satisfies the definition of a particular type of function.

The simplest function that satisfies the definition of a parabola is given by y = x². It is also called quadratic function.

Its graph passes through the origin (0,0) and lies in first and second quadrant.

One or more parabolas can be easily obtained by transforming the parent function of the parabola.

Therefore, the parent function of parabola is given by y = x².

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Answer:

Step-by-step explanation:

The number of events is 5 (since there are 5 red marbles), and the number of outcomes is 20. The probability is 5 ÷ 20 = 1/4. You could also express this as 0.25 or 25%.

The true inequality is 4π > 12.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. Therefore, let's solve the inequalities that is true.

Hence,

[tex]\frac{2\pi }{2} < 3[/tex]

π < 3 (This is false because 3.14 is greater than 3)

4π > 12

divide both sides by 4

π > 3 (This is true.)

π + 6 < 9

subtract 6 form both sides

π < 3 (This is false)

3π - 1 < 8

3π < 9

π < 3 (This is false)

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Answer:

x=4

y= 5

Step-by-step explanation:

6x+y=29

3x-y=7

Let's add them together

9x = 36

x= 4

Then put 4 back in the equation for x

6(4) + y =29

24 + y = 29

y= 5

(well i'll give it my best shot)

14:17

 ⬇️

let's add 14 and 17 together.

***************

14 + 17 = 31

14 = 14/31 (*fraction*)

17 = 17/31 (*fraction*)

I hope this helps in any way possible.

Merry Christmas (Eve), Happy New Year, and Happy Holidays!

All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.

We have the given polynomial:

f(x) = 20x4 + x3 + 8x2 + x - 12

All potential polynomial roots are represented by rational numbers, according to the Rational Root Theorem:

x = a/b

Where a is a factor of a constant term

b is the factor of coefficient of leading term

From the given polynomial:

-12 is the constant term and 20 is the coefficient of leading term

The possible factors of -12 are ±1, ±2, ±3, ±4, ±6, ±12

The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20

So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)

Solve for x when the given function is equal to zero

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

So we get:

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x =1, x = -1

Hence, the rational roots are x = 3/4, x = -4/5.

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We have the given polynomial:

f(x) = 20x4 + x3 + 8x2 + x - 12

x = a/b

b is the factor of coefficient of leading term

-12 is the constant term and 20 is the coefficient of leading term

The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20

So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)

Solve for x when the given function is equal to zero

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x =1, x = -1

The range of the function f(x) = x² - 6x with domain of (-7, -2, 1) is calculated to be (91, 16, -5)

The domain is controlled by the input values. considering the points (-7, -2, 1)

The range is solved using the given function

f(x) = x^2 - 6x

substituting for x in the function

for x = 7

= 7² - 6 * -7 = 91

for x = -2

= -2² - 6 * -2 = 16

for x = 1

= 1² - 6 * 1 = -5

The range is (91, 16, -5)

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The third step in sketching the graph of a rational function is "Finding the function's zeros and vertical asymptotes and plotting them on a number line".

What is vertical asymptotes?

A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as the inputs get closer to the value of a. A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph approaches the line as the inputs go closer to ∞ or –∞.

The steps to sketch a graph of rational function:

1. Ensure that the function's denominator and numerator are listed in decreasing order of power.

2. Discover the domain

3. Completely factor the numerator and denominator. Any shared factors between the numerator and denominator should be eliminated. (Once factors have been cancelled, the reduced function is what remains. For all subsequent actions, employ the reduced function.) Skip Step 4 if there are no common factors.

4. Look for any holes

5. Search for any vertical asymptotes.

6. Find the Horizontal Asymptote.

7. Look for any x- and y-intercepts.

8. Locate test points

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