MATHEMATICS COLLEGE

Describe how to simplify the expression 3^-6/3^-4a. Divide the bases and then add the exponents.
b. Keep the base the same and then add the exponents.
c. Multiply the bases and then subtract the exponents.
d. Keep the base the same and then subtract the exponents.

Answers

Answer 1
Answer:

Answer:

The correct option is d. To simplify the given expression we should keep the base the same and then subtract the exponents.

Step-by-step explanation:

The given expression is

(3^(-6))/(3^(-4))

In the above expression we have common base 3 but the exponents are different.

According to the rule of exponent, if the numerator and denominator have same base and different exponent, then the base remains the same and the exponent of denominator subtracted from exponent of numerator.

(a^m)/(a^n) =a^(m-n)

Use this rule in the given expression.

(3^(-6))/(3^(-4))=3^(-6-(-4))

(3^(-6))/(3^(-4))=3^(-2)

Therefore the correct option is d.
Answer 2
Answer:

Answer:

d or Keep the base the same and then subtract the exponents.

Step-by-step explanation:

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100pts: Convert the following expression into postfix notation: 4*(5/2^3-4)+4*(9-2)

Answers

Answer:

  4 5 2 3 ^ / 4 - × 4 9 2 - × +

Step-by-step explanation:

Start by putting a left parenthesis "(" on the operator stack, and adding a right parenthesis ")" to the end of the input expression.

Conversion algorithm

Copy any operands to the output string until an operator is encountered. Pop operators from the operator stack to the output string if they have equal or higher precedence, then put the operator encountered onto the operator stack. When a right parenthesis is encountered, pop operators from the operator stack to the output string until a left parenthesis is found. Drop that left parenthesis.

__

Given example

For the given expression, we copy 4 and 5 to the output, push / to the operator stack, copy 2 to the output, push ^ to the operator stack, and copy 3 to the output. At this point, the output is ...

  4 5 2 3

and the operator stack is

  ( * ( / ^ . . . . . top item is on the right

When we encounter the - sign, we write the ^ and / operators to the output string and push - to the operator stack. At this point, the state is ...

  output: 4 5 2 3 ^ /   operator stack: ( * ( -

Next, we copy 4 to the output. When we encounter the right parenthesis, we copy - to the output and pop the ( from the operator stack.

The next input symbol, +, is lower precedence than the remaining * on the operator stack, so we output the * and push the +. Now we have ...

  output: 4 5 2 3 ^ / 4 - *   operator stack: ( +

The output string so far completes the evaluation of the first term of the input expression.

Now, we copy out 4, push * and (, copy out 9, push -, copy out 2. The right parenthesis triggers the popping of the - to the output, and the final right parenthesis that we added at the start pops the * and + from the operator stack. Our final output is ...

  4 5 2 3 ^ / 4 - × 4 9 2 - × +

_____

The result is 14.5.

Hope This Helps!!!

Have a great day!!!

What is the greatest common factor of 18, 36 , and 54

Answers

Answer:

18

Step-by-step explanation:
Answer:
GCF = 18
Explanation:

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54

Then the greatest common factor is 18.

Which relation is a function?

Answers

Answer:

the third one cause of it's inputs

Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix of 480 * 500 picture elements (pixels), where each pixel can take on one of 32 intensity values. Assume that 30 pictures are sent per second. (This digital source is roughly equivalent to broadcast TV standards that have been adopted.) Find the source rate R (bps).

Answers

Answer:

36,000,000 bps

Step-by-step explanation:

Matrix of 480 by 500 = 480 X 500 = 240,000 pixels

Intensity values per pixel = 32. This simply means the color variations in this TV.

The bit per pixel for an intensity value of 32 is 5 (That's 2 raised to the power of 5)

Pictures sent per second = 30

Source rate R (bps) = Total number of pixels in the matrix X bit per pixel X Number of pictures sent per second.

Source rate R (bps) = 240,000 X 5 X 30 = 36,000,000 bps

Final answer:

The source rate for the digitized TV picture is 230,400,000 bps.

Explanation:

The source rate can be calculated by multiplying the number of pixels per picture element by the number of intensity values per pixel and by the number of pictures sent per second.

So, the source rate R (bps) is given by:

R = (480 * 500) * 32 * 30

Calculating this, we find that the source rate is 230,400,000 bps.

Learn more about Calculating the source rate for a digitized TV picture transmission here:

brainly.com/question/33582527

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a home has a triangular backyard. The second angle of the triangle is 6 more than the first angle. The third angle is 14 more than three times the first angle. Find the angles of the triangular yard

Answers

Answer: The first angle is 32 degrees

The second angle is 38 degrees

The third angle is 110 degrees.

Step-by-step explanation:

Let x represent the size of the first angle.

Let y represent the size of the second angle.

Let z represent the size of the third angle.

The second angle of the triangle is 6 more than the first angle. This means that

y = x + 6

The third angle is 14 more than three times the first angle. This means that.

z = 3x + 14

The sum of the angles in a triangle is 180 degrees. It means that

x + y + z = 180 - - - - - - - - - - - -2

Substituting y = x + 6 and z = 3x + 14 into equation 2, it becomes

x + x + 6 + 3x + 14 = 180

x + x + 3x = 180 - 14 - 6

5x = 160

x = 160/5 = 32

y = x + 6

y = 32 + 6 = 38

z = 3x + 14

z = 3×32 + 14 = 96 + 14

z = 110

Based on the data, select the most reasonable prediction about the height ofsecond-grade students.A. The typical second-grade student is less than 45 inches tall.B. The typical second-grade student is about 45 inches tall.C. The typical second-grade student is more than 50 inches tall.D. The typical second-grade student is about 48 inches tall.

Answers

second-gradeWe are given the following data set:

44,45,47,49,48,48,49,50,48,52

We can calculate the mean of this data set, by adding all the terms and dividing by the number of terms, that is 10:

\text{mean}=(44+45+47+49+48+48+49+50+48+52)/(10)=(480)/(10)=48

Since the mean is 48 this means that the typical second grade student is 48 inches tall. the right answer would be D.

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