how to determine if a function is even or odd algebraically

(i) 98³

(100-2)³

100³ + 2³ + 3(100*2)(100+2)

[by using the equation (a-b)3=a3+b3+3ab(a+b)]

1000000+8+(600*102)

The solution is 1000008+61200 1061208.

(ii) 188 × 212 = 39856

Given:

The ratio of 188 to 212

To locate

the importance of adopting a proper identity

Equation: (a + b) = (a2 - b2 ( a - b )

Solution:

Phase 1 of 2:

Note the supplied expression in writing.

The formula is 188 212. Step 2 of 2:

Find the expression's value.

188 × 212\s= ( 200 - 12 ) × ( 200 + 12 )

= ( 200 + 12 ) × ( 200 - 12 ) ( 200 - 12 )

= 200² - 12²

= 40000 - 144

= 39856

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Answer:

10.9%

Step-by-step explanation:

You want to do the number of ways that can happen, which is [tex]_8C_2 = 28[/tex] divided by the total number of possibilities which is [tex]2^8[/tex] to get 10.9%

Answer:  13

Step-by-step explanation:

13+7= 20

Answer:

The number is 13.

Step-by-step explanation:

"A number" is a number we don't know to begin with. It should be represented by a variable. Let's use n. We'll probably be trying to find this number.

"increased by" usually means that there is adding going on here.

So far, we have:

n + 7

that is algebra for "A number increased by 7"

"gives 20" is a little strange wording, but it means yields or equals.

So now we have the whole equation:

n + 7 = 20

To solve, subtract 7 from both sides (of the equal sign)

n = 20 - 7

n = 13

The number is 13.

Check:

13 increased by 7 gives 20?

13 + 7 = 20 ?

20 = 20 ✔Yes! Done!

The distance between  G and H on this number line  is 10

What is number line?

A range of line is a pictorial representation of numbers on a immediately line. It’s a reference for evaluating and ordering numbers. it is able to be used to symbolize any real variety that consists of each whole quantity and herbal quantity. simply to don't forget, the whole wide variety is a set of numbers that encompass all counting numbers (1, 2, three,four,5,6 …….) and zero (0), whereas the herbal number is the set of all counting numbers i.e. 1, 2, three, 4, five, 6……..

Given in the number line,

The number line is from the -12 to 7

And

we have to find the distance between G and H on this number line

GH = -2+12

GH = 10

Hence, The distance between  G and H on this number line  is 10

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Answer:

Step-by-step explanation:

The function y = -2 is a constant function. It means that the output of the function is always equal to -2, regardless of the input value.

Here is a function table that shows the input and output values for y = -2:

x y

1 -2

2 -2

3 -2

4 -2

5 -2

As you can see, for any value of x, the output is always -2, since y = -2 is a constant function

Answer: D

Step-by-step explanation: the amount per cashews (c) is $2.45. Therefore, its 2.45c

The amount per pounds of sugar is $0.61. Therefore, its 0.61s

And, since its "buying" (basically, adding), you gotta add them. So, the answer would be: 2.45c+0.61s

I get to pay a total cost of $89.16 for the meal.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, multiplications and so on). Expressions are made up of terms. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is called a coefficient.

Pretax = 13% of meal cost

Tax = 7% of meal cost

Total = Meal cost + 13% of meal cost + 7% of meal cost

Total = $74.30 + (13/100 x $74.30) + (7/100 x $74.30)

Total = $74.30 + $9.659 + $5.201

Total = $89.16

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Answer:

Independent variable.  cause the sales will be depending upon the weather.

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2y=2-3x-5y=10-5x

-2y=10-5x

2-3x-5y-5x

(SIMPLIFY)

5x-2y=10

2x-5y=8

(MULTIPLY BOTH SIDES)

-25x-10y=-50

4x-10y=16

(ELIMINATE ONE VARIABLE BY ADDING THE EQUATIONS)

-21x=-34

(DIVIDE BOTH SIDES)

X=34/21

(SUBSTITUTE THE VALUE OF X)

2x34/21-5y=8

(SOLVE EQUATION)

Y=-20/21

(A POSSIBLE SOLUTION IS)

(X,Y)=(34/21 , -20/21)

(CHECK THE SOLUTION)

-2x(-20/21)=2-3x 34/21 - 5x (-20/21)=10-5 X 34/21

(SIMPLIFY)

40/21=40/21=40/21

(X,Y)= (34/21 , -20/21)

(SOLUTION)

The value of x would be 7 and perimeter of equilateral triangle would be 75.

What is Equilateral triangle and perimeter of equilateral triangle?

An equilateral triangle is one with the equal length on all three sides. To calculate the perimeter of an equilateral triangle given its area, we must first determine the length of its sides.

An equilateral triangle has three congruent sides, so if AABC is equilateral, we know that AB = BC = AC. We can use this information to write an equation for x, the length of one of the sides.

AB = BC = AC

given equations are,

4x-3 and 2x+11

as we know that, all sides of equilateral triangle are equal then,

4x-3 = 2x+11

2x = 14

x = 7

The perimeter of an equilateral triangle = 3 x side of equilateral triangle

Here, all sides of equilateral triangle are equal then sides = 25

Perimeter of an equilateral triangle = 3 x 25

Perimeter of an equilateral triangle = 75

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The equations with the same y-intercept are y = 9x + 2, y = 8x + 2, y = 3x + 2 and y = (1/4)x + 2.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of  the equation of a line is y = mx+b,

where m is the slope and b is the y-intercept

Let's compare the given equations with y = mx+b:

y = 5x - 2,     y-intercept (b) = -2

y = 9x + 2,    y-intercept (b) = 2

y = 8x + 2,    y-intercept (b) = 2

y = 3x - 7,     y-intercept (b) = -7

y = 3x + 2,     y-intercept (b) = 2

y = 3x + 4,     y-intercept (b) = 4

y = (1/4)x + 2, y-intercept (b) = 2

Therefore, y = 9x + 2, y = 8x + 2, y = 3x + 2 and y = (1/4)x + 2 have the same y-intercept

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The length of the ladder is 22 feet.

Let x = the height the ladder reaches on the wall.

Then 3x = the length of the ladder.

Substituting 15 for the foot of the ladder from the wall, we have:

15 + 3x = the length of the ladder

7 = 3x

x = 7/3

Substituting 7/3 for x in the equation 15 + 3x = the length of the ladder we have:

15 + 3(7/3) = the length of the ladder

15 + 7 = the length of the ladder

22 = the length of the ladder

The length of the ladder can be determined by first figuring out how high the ladder reaches on the wall. Let x equal the height the ladder reaches on the wall. Then, the length of the ladder, 3x, can be determined. Since the foot of the ladder is 15 feet from the wall, the equation 15 + 3x = the length of the ladder can be written. In this equation, 7 is the known value for 3x, since the ladder is 7 feet less than three times longer than the height it reaches on the wall. Therefore, x = 7/3. Substituting 7/3 for x in the equation 15 + 3x = the length of the ladder, the equation 15 + 3(7/3) = the length of the ladder can be written. Simplifying this equation, 15 + 7 = the length of the ladder can be written, which means the length of the ladder is 22 feet.

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[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex] is the result of the operation, Option A is correct.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

The given operations are

[tex]\left[\begin{array}{ccc}13&10&7\\6&8&1\\2&5&0\end{array}\right] -\left[\begin{array}{ccc}3&-2&6\\14&-6&11\\8&-12&9\end{array}\right] +\left[\begin{array}{ccc}6&10&15\\10&0&9\\1&0&7\end{array}\right][/tex]

In the given operation, the operators used are addition and subtraction

[tex]\left[\begin{array}{ccc}13-3+6&10+2+10&7-6+15\\6-14+10&8+6+0&1-11+9\\2-8+1&5+12+0&0-9+7\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex]

Hence, [tex]\left[\begin{array}{ccc}16&22&16\\2&14&-1\\-5&17&-2\end{array}\right][/tex] is the result of the operation, Option A is correct.

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The decimal number and the fraction commonly used as approximations for pi are 3.142 and 22/7

from the question, we have the following parameters that can be used in our computation:

pi

The pi variable is a mathematical constant that has the following fractional value

pi = 22/7

When converted to decimal in 3 decimal places, we have

pi = 3.142

Hence, the representations are 22/7 and 3.142

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The value of x that will give a perimeter of 25 inches is 4 inches

The perimeter of a pentagon is the sum of the lengths of all its sides. The formula to calculate the perimeter of a pentagon is:

P = 5L

where is the side length

Initially, the sides of length, L is 1 inches

Now, we increase L by x and perimeter is 25 inches. Thus, can write:

25 = 5(1 + x)

25 = 5 + 5x

5x = 25 - 5

5x = 20

x = 20/5

x = 4 inches

Therefore, the value of x is 4 inches

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The correct answer is option B : False. Using a stratified sample guarantees that members of each group within a population will be sampled. and true statement is "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled".

False. Using a systematic sample does not guarantee that members of each group within a population will be sampled. A systematic sample is a type of probability sampling in which a random starting point is chosen and then every nth item is selected from the population. This can lead to bias if the population contains patterns or cycles.

A true statement would be: "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled."

The given statement is False

The correct form is given below-

Using a random sample guarantees that members of each group within a population have an equal chance of being sampled.

Thus, The correct answer is option B : False. Using a stratified sample guarantees that members of each group within a population will be sampled. and true statement is "Using a random sample guarantees that members of each group within a population have an equal chance of being sampled".

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1) The lower class limits: 100, 200, 300, 400, 500, 600 .

2) The upper class limits:  199, 299, 399, 499, 599, 699.

3) The class width: 100.

4) Class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5, 649.5.

5) Class boundaries : 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5.

6) The number of individuals included in the summary : 155

The lower class limit in each class: 0,100, 200, 300, 400, 500, 600.

The upper-class limit is the biggest value in each class.

so the upper-class limit is:  99, 199, 299, 399, 499, 599, 699.

As we know the class width is the difference between the lower limit of one class and the lower limit of the previous class.

For example, 300 is the lower limit of one class and the lower limit of the previous class is 200 , so 300 - 200 = 100.

We know that, the class midpoints are the average of the limits of a class.

So, using midpoint formula the class midpoints are:

[tex]\frac{100+199}{2} = 149.5\\\\\frac{200+299}{2} = 249.5\\\\\frac{300+3199}{2} = 349.5\\\\\frac{400+499}{2} = 449.5\\\\\frac{500+599}{2} = 549.5\\\\\frac{600+699}{2} = 649.5\\[/tex]

We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.

So, the class boundaries for the first class = (99.5, 199.5)

the class boundaries for the second class = (199.5, 299.5)

the class boundaries for the third class = (299.5, 399.5)

the class boundaries for the fourth class = (399.5, 499.5)

the class boundaries for the fifth class = (499.5, 599.5)

The total of individuals is equal to the sum of all the frequencies of each class: 3 + 54 + 76 + 21 + 0 + 0 + 1 = 155

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The complete question is:

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Blood Platelet Count of Males ​(1000 ​cells/mu​L) Frequency 0​-99 3 100​-199 54 200​-299 76 300​-399 21 400​-499 0 500​-599 0 600​-699 1 Identify the lower class limits​ (in 1000 ​cells/mu​L).

The equation of the slope is y = -5x + 72.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

Given that:

72 inches is the depth of the liquid level in water tank.

Water drains at a rate of 5 inches per minute.

Let y represent the tank's height, which is given as 72.

Let x be the total number of minutes, here x = 0.

Therefore, the slope's equation is the rate at which the water drains, that is:

m = -5

The equation of the line is given by the formula:

y = mx + c

Substitute the values:

72 = -5(0) + c

c = 72

And the equation is:

y = -5x + 72

Hence, the equation of the slope is y = -5x + 72.

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The following are solutions to the inequalities;

7. c < 7

8. h < -4

9. r ≤ 55

Inequality is a relationship between two expressions or values that are not equal to each other. Lack of balance results in inequality.

In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs.

7. 8c - 21 < 35

8c < 35 +21

8c < 56

c < 7

8. -6h + 17 > 41

-6h > 41 - 17

-6h > 24

h < 24/-6

h < -4

9. r/5 - 2 ≤ 9

Multiplying through by 5

r - 10 ≤ 45

r ≤ 45 + 10

r ≤ 55

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Answer:

Step-by-step explanation:

The selling price of a phone case with a 25% coupon is $56 and the original selling price of the phone case without any discount is $80.

What is the selling price?

The price at which an article is sold is known as the selling price of that article.

Given that you have a 25% off coupon and paid $42.00 for a phone case. The phone case was marked down 30%. So,

Let's consider that you use a 25% off coupon and then paid $42 for the phone case. The price of phone case including coupon is,

75 % of price  = $42.00

100% of price =

Michael wants to place grass on the side of his lap pool, the area of the shaded region that he wants to cover with grass is 204 square yard.

We have to determine the area of the Shaded region that he wants to cover with grass.

By calculating the overall area and taking the area of the lap pool out, the area of the shaded area may be calculated.

We can see that the shape is the trapezium. So;

Area of trapezium = 1/2 × (Sum of parallel sides) × distance between them

Sum of parallel sides = 25 yd + (3 + 12) yd

Sum of parallel sides = 25 yd + 15 yd

Sum of parallel sides = 40 yd

Distance between them = 12 yd

Area of the trapezium = 1/2 × 40 × 12

Area of the trapezium = 40 × 6

Area of the trapezium = 240 square yd

Now finding the area of lap pool.

Area = length × width

Area = 12 × 3

Area = 36 square yd

Now finding the area of shaded region

Area = Area of the trapezium - Area of lap pool

Area = 240 - 36

Area = 204 square yard

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Answer:

C. Mara wished she could visit the stars: she often dreamed of it.

The index form 4 ^–1  as a fraction or whole number without exponents is 1/4

The index form of a number described as the number that is written as an exponential expression

Index forms are also described as a single number that is raised to another number or variable.

The index or exponent of an exponential expression shows how many times to multiply the base by itself in the expression.

From the information given, we have the index form as;

4^-1

This is represented as a fraction;

1/4^1

Note that any number that is raised to 1 is equal to the number

1/4

Hence, the value is 1/4

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Answer:

B

Step-by-step explanation:

The decimal number less than 1.4 and greater than 1.35 is A = 1.39

The decimal numbers can only be expressed as fractions since they contain a fractional component. The accepted method for representing both integer and non-integer numbers is the decimal numeral system. There are 10 single-digit numbers in the decimal system:

0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. After the number 9, comes 10, then comes 11, then 12, and so on. Each time the digit to the right exceeds 9, the number on the left is increased by 1.

Given data ,

Let the decimal number be represented as A

Now , the value of A is

Let the first number be p = 1.4

Let the second number be q = 1.35

Now , q < A < p

The value of A is less than 1.4 and greater than 1.35

So , A = 1.39

Hence , the decimal number is A = 1.39

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The coefficients of the terms on the right side of a binomial equation are the numbers in the triangle.

As the power increases, the expansion becomes more difficult to compute and takes longer. A binomial statement that has been raised to a very high power can be swiftly calculated using the binomial theorem. Find out everything there is to know about the binomial theorem, including its definition, characteristics, and uses.

The binomial theorem can be used to expand an expression that has been raised to any finite power. The binomial theorem is a helpful expansion method having applications in probability, probability theory, and algebra.

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Answer:

The cost of the sneakers after the coupon is applied would be $46.99 - ($46.99 * 15%) = $39.94.

The total cost of the sneakers after 5% sales tax is included would be $39.94 + ($39.94 * 5%) = $41.94

Answer: $41.94

15% off means the sneakers are at 85% of it's original price.

85% = 0.85

$46.99 x 0.85

= $39.94 after 15% coupon

5% sales tax means you are adding 5% to the price.

105% = 1.05

$39.94 x 1.05

$41.94, after the coupon and sales tax.

There are 188 ways to pick one ace and next card as not a queen.

There are 4 aces in a normal 52 card deck, and once one is picked, there are 51 cards left.

If we want to pick two successive cards from a normal 52 card deck so that the first is an ace and the second is not a queen, we can use the following formula:

Number of ways = (number of aces) x (number of cards not a queen)

In this case, the number of aces is 4, and the number of cards not a queen is 47 (52 cards total - 4 queens - 1 ace that has been picked).

So the number of ways to pick two successive cards from a normal 52 card deck so that the first is an ace and the second is not a queen is 4 x 47 = 188.

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No, the equation 2x + 2 = x + 1 has solution which is equal to x = -1.

Mia gave statement for the equation:

Left hand side is double the right hand side implies it has no solution.

2x + 2 = x + 1

Verification for the solution:

Simplify the above equation by subtracting  'x' both the sides we get,

⇒ 2x - x + 2 = x - x + 1

⇒ x + 2 = 1

Now subtract '2' from both the sides of the equations we get,

⇒ x + 2 - 2 = 1 - 2

⇒ x = -1

The above equation has no solution is incorrect statement.

Therefore, the equation 2x + 2 = x + 1 has no solution is wrong statement as the solution is given by x = -1.

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Answer: The explicit formula for a geometric sequence is given by:

an = a1 * r^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

Part A) In this sequence, the first term is 4, and the common ratio is 4/1 = 4.

So the explicit formula for this sequence is:

an = 4 * 4^(n-1)

To find the 8th term of this sequence, we can substitute n = 8 into the formula:

a8 = 4 * 4^(8-1)

a8 = 4 * 4^7

a8 = 4 * 16,384

a8 = 65,536

Therefore, the 8th term of this sequence is 65,536.

Step-by-step explanation: