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Using the properties of integer exponents, match each expression with its equivalent expression.

Answer:

The limit does not exist

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Constant]:                                                                                             [tex]\displaystyle \lim_{x \to c} b = b[/tex]

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Step-by-step explanation:

*Note:

In order for the limit to exist, the right-hand and left-hand limits must equal each other

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left \{ {{x + 10,\ x < 8} \atop {10 - x,\ x \geq 8}} \right.[/tex]

Step 2: Find Right-Hand Limit

Step 3: Find Left-Hand Limit

∴ since  [tex]\displaystyle \lim_{x \to 8^+} f(x) \neq \lim_{x \to 8^-} f(x)[/tex],  [tex]\displaystyle \lim_{x \to 8} f(x) = DNE[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits

The amount invested by Dylan will be £1200.

Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate.

Given that Dylan invested some money in his bank. He agreed on a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period, the value of his investment increased by £72.

The amount of money invested will be calculated as,

SI = ( P x R x T ) / 100

72 = ( P x 3 x 2 ) / 100

7200 = 6P

P = 7200 / 6

P = £1200

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Answer:

3.9 inches

Step-by-step explanation:

area of a circle = πr²

= π 3²

= 9 π

9π = 28.3 (rounded).

area of a square = length x width

= 6 x 6

= 36 inches

36 - 28.3

= 7.7

÷2 to get the individual value

= 3.9 inches rounded

The area of the yellow region will be  [tex]3.86[/tex] squared inches.

Area is the space occupied by any shape.

Area of the square [tex]=side*side[/tex]

We have,

A square of [tex]6[/tex] inch in side, divided in two semi-circles.

Radius of semi-circle[tex]=3[/tex] inch

Now,

Area of the square [tex]=side*side=6*6=36[/tex] squared inches

Now,

Area of a semi-circle[tex]= \frac{\pi }{2}r^{2}=\frac{22 }{2*7} (3)^2=14.14[/tex] squared inches

So,

Area of two semi-circles[tex]=28.28[/tex] squared inches

Now,

Area of yellow part [tex]= \frac{36-28.28}{2}=3.86[/tex] squared inches

So, Area of yellow part is [tex]3.86[/tex] squared inches find out by dividing by two because other part is equals to yellow part.

Hence, we can say that the area of the yellow region will be  [tex]3.86[/tex] squared inches.

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Answer:

x = 36

Step-by-step explanation:

180 - 126 = 54

90 + 54 + x = 180

144 + x = 180

180 - 144 = x

x = 36

Have a nice day!

You went to the supermarket to buy 10 bananas. Each banana weighed 50 grams. If the price for bananas was $6.50 per kilogram, how much would you have to pay?

You do 10 x 50 = 500                     /                      Your bananas weigh 500g

$6.50 halved is $3.25                     /                       So $3.25 for 500g

So your answer is $3.25

Hope this helps! :)

Check your solution by first checking the end point , in the related equation. Pick a value greater than , such as 2, to check in the inequality. Solve for x. Divide both sides by 3 to isolate the variable.

The probability that all three are female is  0.281

2030⋅1929⋅18282030⋅1929⋅1828 = 0.281

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Answer:

Nancy consumió 12 paquetes de pizzetas y le quedaron 3 paquetes completos.

Step-by-step explanation:

En primer lugar, debemos descomponer el número total de pizzas como una multiplicación de números primos. Al realizar la descomposición factorial tenemos que:

[tex]288 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3[/tex]

Entonces, los familia de divisores de 288 es el siguiente conjunto:

[tex]D_{288} = \{2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144 \}[/tex]

Si tanto la cantidad de paquetes de pizzetas y la cantidad cocinada de pizzetas son números enteros y positivos, siendo la última mucho mayor. Entonces, la cantidad de pizzetas debe ser un número entero y la cantidad de paquetes gastados menor a la cantidad de paquetes comprados y el número entero más cercano a esa cantidad. Entonces, concluimos que Nancy se gastó 12 paquetes de pizzetas, quedándole 3 paquetes completos.

Answer:

7.2 min

Step-by-step explanation:

50.4 / 7 = 7.2 min

The polynomial which has a degree of  7 can be known as a polynomial of class 7.

Polynomials are expressions containing of variables and constants. The variable having the highest power forms the degree of the polynomial.

The degree of a polynomial with one variable is known as the highest exponent power of that variable in the mentioned polynomial.

Finding the degree of a polynomial with more than one variable is a simple task , as adding the exponents of each variable in the supplied terms and then determining which term has the highest degree. That is the polynomial's degree.

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The amount of money should you deposit now to have $10,000 5 years from now is $7407.

Theoretically, continuously compounded interest means that interest is continuously earned on an account balance as well as reinvested into the balance to increase future interest earnings.

Given that If an investment company pays 6% compounded continuously and $10,000 for 5 years.

The amount of money invested will be calculated by the formula below,

[tex]P = P_o(e)^{rt}\\10000 = P_o ( e)^{0.06\times5}\\[/tex]

P₀ = 10000 / 1.35

P₀ = 7407

The amount of money invested would be 7407.

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Coordinate (-a , b ) belongs to second quadrant.

The axes (x-axis and y-axis) of a two-dimensional Cartesian plane system divide the plane into four infinite regions called quadrants. The horizontal line or x-axis and vertical line or y-axis intersect each other at the right angle.  The intersection of two lines is known to be the reference point. All the measurement is done by taking this point as the reference (or starting point) in the coordinate system.

"A quadrant is simply defined as the region of a cartesian plane formed when the x-axis and y-axis intersect each other."

Given, Coordinate ≡ (-a , b)

1st Quadrant: The upper right-hand corner of the graph is the first quadrant. In this quadrant the values of x and y both are positive.

2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant, the value of x is negative whereas the value of y is positive.

3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains the negative values of both x and y.

4th Quadrant: Finally, the fourth quarter is at the lower right-hand corner, which has a positive value of x and a negative value of y.

Hence, by the above observation, given coordinate (-a, b) belongs to the 2nd quadrant.

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The length of the wood altogether is 340 inches

Robert is building a deck

Each piece of the wood measures 42.5 inches

Robert has 8 boards

The length of the wood altogether is

= 42.5 × 8

= 340

Hence the length of the wood is 340 inches

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Step-by-step explanation:

hope this helps. n=6 or n=9 work is in the attached pic

Answer:

Perimeter = 18 units

Step-by-step explanation:

one side = 4

other side²  = 3² + 4² + 25

other side = √25 = 5

Perimeter = (2 x 4) + (2 x 5) = 18 units

Answer:

d

Step-by-step explanation:

Answer:

y ≈±6.8556546

Step-by-step explanation:

y^2 = 47

Take the square root of each side

sqrt(y^2) = ±sqrt(47)

y ≈±6.8556546

Answer: y≈6.85565

Step-by-step explanation:

[tex]\sqrt{y}[/tex] =[tex]\sqrt{47}[/tex]

y≈6.85565

The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.

Table C: Ending Inventory

Product Store A Store B Store C

X 441 278 546

Y 266 389 360

Z 322 814 330

The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.

The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A.

The value of the entry represented by c22 in the matrix C that shows the inventory at the end of July is 389, and the maximum possible value that a31 can have is 903.

The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B. The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A. This value indicates that the maximum number of units of Product Z that can be stored in Store C is 903. In summary, the value of c22 in the matrix C is 389, and the maximum value of a31 is 903.

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Answer: The answer would be C

Step-by-step explanation:

You want to divide. 15/3= 5 and then a^3 is basically being divided by 1 so your completed answer would be 5a^3

Answer

rotation around point b

Step-by-step explanation:

The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.

Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.

Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?

1. Describe one way to estimate the solution to this problem.

By dividing the amount of milliliters of water in the baker by 16.5 ml

2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?

No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.

Therefore, the correct answer should be 36 test tubes.

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Answer:

135

Step-by-step explanation:

540-75-120-120-90=135

Answer:

x = 135

Step-by-step explanation:

Total sum of interior angles of a pentagon = 540

75 + 120 + 120 + 90 + x = 540

405 + x = 540

=> Subtract 405 on both sides of "="

x = 135

Hope this helps!

The given expression is equivalent to 22 for x = 17 and y = 12.

Given is the expression as follows -

2x - y

For x = 17 and y = 12, we can evaluate the expression as -

2 x 17 - 12

34 - 12

22

Therefore, the given expression is equivalent to 22 for x = 17 and y = 12.

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Answer:

3x^2 - 19x - 14

Step-by-step explanation:

Answer:8748

Step-by-step explanation:

The pattern is multiplying the number by 3, 3x12=36. 36x3=108.

4, 12, 36, 108, 324, 972, 2916, 8748

Answer:

C. Connor is correct because it is likely that the increased income and better benefits he will earn throughout his career will outweigh the $80,000 and four years he invests in his college education.

Step-by-step explanation:

I did 100% on edge 2021

good luck! :)