Perform the indicated operations,the simplify

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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First, multiply \(18*5 = 90\)

Then, divide \(90 / 6 = 15\)

Therefore, each group has 15 students.

The research explores the various factors that may influence the learning choices of first-year undergraduates, such as the family and educational background of the student, their socioeconomic status and the availability of resources, among others.

Factor is a mathematical quantity which is multiplied with another quantity to give a product. Factors can also be defined as the numbers that divide a given number exactly. Factors are used in everyday life to calculate many different types of problems, such as compound interest, speed, distance and time, and more. Factors are also used in statistics and probability to determine the likelihood of certain events occurring.

The paper will also examine the various types of postgraduate courses that are available to undergraduates, including those offered by universities and other institutions, such as professional courses or distance learning programmes.

The research adopts a qualitative approach, and will use semi-structured interviews with first-year undergraduates to gain an understanding of their learning choices, and the factors that influence them. Interviews will be conducted with students in different disciplines, in order to gain an insight into how the different disciplines shape students' learning preferences. The research will also use questionnaires to obtain data on the socioeconomic background, family background and educational background of students.

In addition, the research will use documentary analysis of university prospectuses and websites, and information from other sources, such as employers and professional bodies, to gain an understanding of the various postgraduate courses that are available to undergraduates. This data will be used to compare and contrast the learning choices of undergraduates from different disciplines and economic backgrounds.

Finally, the research will use an interpretive approach to analyse the data collected and develop a theory of the factors that influence the learning choices of first-year undergraduates. The theory will be used to inform the design of initiatives to help undergraduates make informed decisions about their learning choices.

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Answer:

You will add!

Step-by-step explanation:

Words words words

Answer:

Step-by-step explanation:

Answer:

y = -5x + 21

Step-by-step explanation:

Step 1: Find the slope

Take the negative reciprocal of the original equation

y = -5x + b

Step 2: Find b using given coordinate

-4 = -5(5) + b

-4 = -25 + b

b = 21

Step 3: Write equation

y = -5x + 21

And we have your equation!

Answer:

Equation of a line is y = mx + c

m = slope

c = intercept on y axis

y=1/5×+4

Comparing with the above equation

Slope = 1/5

Since the lines are perpendicular to each other the slope of the line we are to find is the negative inverse of the original equation.

Slope = -5

Equation of the line using point

(5 , -4)

y + 4 = -5( x - 5)

y + 4 = -5x + 25

y = -5x + 21

Hope this helps

The solution to the inequality \(w - 0.9 >-2.1\) is \(w >-1.2\)

Inequalities are used to represent expressions of unequal values

The inequality is given as:

\(w - 0.9 >-2.1\)

Add 0.9 to both sides of the inequality

\(w - 0.9+ 0.9 >-2.1 + 0.9\)

Simplify the inequality

\(w >-1.2\)

The above inequality means that:

See attachment for the inequality that represents \(w >-1.2\)

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A = 144 square inches

Step-by-step explanation:

surface area of rectangular prism :

A = 2(hℓ + ℓw + hw)

A = 2(7 · 4 + 4 · 4 + 7 · 4)

A = 2(28 + 16 + 28)

A = 2(72)

A = 144 square inches

Answer: 100

Step-by-step explanation: 5+5+10+30-50+100

The vector field F = 1i + 1j + 3k has a flux of 2 across the surface S. We use Green's Theorem to determine the vector-flux field.

φ = ∫ F.n ds

φ = ∫∫ F. divG.dA

In which, G is equivalent to a part of given plane = 2x + 1y + z = 2.

And,  F = 1i + 1j + 2k

Thus,

div G = div(2x + 1y + z = 2) = 2i + 4j + k

Flux = ∫(1i + 1j + 3k) (2x + 1y + z).dA

φ = ∫ (2 + 4 + 2).dA

φ = 8∫dA

A = 1/2 XY (on this given x-y plane)

2x+4y =2

For, x = 0, y = 1/2

y = 0, x = 1

1/2 (1*1/2) = 1/4

Thus,  flux = 8*1/4 = 2

φ = 2.

There are several uses for Green's theorem. Solving two-dimensional flow integrals, whose assert that its sum of fluid outflows from just a volume equals the sum of outflows around an enclosed area, is one way to accomplish this.

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The complete question is-

Let S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward. Find the flux of the vector field F = 1i + 1j + 3k across the surface S. F = 1i + 1j + 3k across the surface s2x + 1y + z = 2 which lies in the first octant, oriented upward. Find the flux of the vector field.

Answer:

Lion area: 60

Lion Perimeter: 34

Tiger Area: 60

Tiger perimeter: 64

Step-by-step explanation:

9514 1404 393

Answer:

  111.46 units

Step-by-step explanation:

The right triangle has side lengths that are 1/√2 times the hypotenuse length, so each is (18√2)/(√2) = 18 units. The top is this length shorter than the bottom, so the total of all side lengths (CW from left) is ...

  18 + (43 -18) +18√2 +43 = 86 +18√2 ≈ 111.46 units

Answer:

Each classmate received 1/16

Step-by-step explanation:

5/8= 0.625

0.625 ÷ 10 = 0.0625

= 1/16

\(\tt{Hey~There!\)

\(\tt{6x-9=33\)

\(\tt{Add~9~to~both~sides:\)

\(\tt{6x-9+9=33+9\)

\(\tt{6x=42\)

\(\tt{Divide~both~sides~by~6:\)

\(\tt{\frac{6x}{6}=\frac{42}{6}\)

\(\tt{Simplify~42/6:\)

\(\tt{\frac{42}{6}=7\)

\(\boxed{\tt{x=7}}\)

\(\tt{Hope~this~helps!\)

\(\boxed{\tt{-TestedHyperr}}\)

The length of the third side is 13 units

It is important to note that from the Pythagorean theorem, we have that the square of the longest side, that is, the hypotenuse is equivalent to the square of the other two sides.

From the information given, we have that;

x² = 12² + 5²

Now, find the square values of the numbers, we have;

x² = 144 + 25

Add the values

x² = 169

Take the square root of both the sides, we have;

x= √169

Find the square root of the value

x =1 3 units

Hence, the value is 13 units

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The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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Domain: 8, 9, 10, 11.Range: -7, 7 This relation does not represent a function because the same x-value (8, 10, 11) is associated with more than one y-value (-7, 7).

Domain: 8, 9, 10, 11

Range: -7, 7

A function is a relation between a set of inputs and a set of outputs such that each input is associated with exactly one output. This particular relation fails to meet this condition because the domain value 8 is associated with two different range values (-7 and 7). In other words, the same input (8) is associated with two different outputs, which means the relation does not represent a function. The domain of the relation is 8, 9, 10, 11 and the range is -7 and 7. Therefore, this relation does not represent a function because it violates the condition that each input must have one and only one associated output.

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Answer:

\({19}C_1=19\)

Step-by-step explanation:

We need to find the value of \({19}C_1\).

C stands for combination.

The formula of combination is as follows :

\(nC_r=\dfrac{n!}{r!(n-r)!}\)

Here,

n = 19 and r = 1

So,

\(nC_r=\dfrac{19!}{1!(19-1)!}\\\\nC_r=\dfrac{19!}{1!\times 18!}\\\\nC_r=\dfrac{19\times 18!}{1!\times 18!}\\\\nC_r=19\)

So, the value of \({19}C_1\) is 19.

Answer:

Your answer will be 19C1 =19

using techniques such as anonymity or confidentiality to encourage honest and open responses.

There are several potential sources of bias that could be present in the sample selected for this study. One possible source of bias is selection bias, which occurs when the sample is not representative of the population from which it was drawn. This can happen if certain groups of people are more likely to be included in the sample than others, or if some individuals are more likely to participate in the study than others.

Another potential source of bias is response bias, which occurs when participants provide inaccurate or incomplete information in their responses. This can happen if participants feel uncomfortable sharing certain information, or if they have a particular agenda or bias that influences their responses.

To avoid sample bias, researchers should aim to select a sample that is as representative as possible of the population they are interested in studying. One way to do this is to use random sampling techniques, such as simple random sampling or stratified random sampling, to ensure that every member of the population has an equal chance of being included in the sample. Additionally, researchers can take steps to minimize response bias by using clear and unbiased survey questions, providing a comfortable and non-judgmental environment for participants to provide their responses.

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Answer:

The answer is 135

Step-by-step explanation:

all angles in a triangle equal to 180.

so, 25+22= 45

then, 180-45= 135

the missing angles measure is 135 degrees

hope this helps!

Answer:

the first one is (23)

number 7 is ( 34.069)

Step-by-step explanation:

The margin of error for the 90% confidence interval is 3.

To find the margin of error for a 90% confidence interval, we can use the formula:

Margin of Error = (Upper Limit - Lower Limit) / 2

Given the confidence interval (72, 78), where 72 is the lower limit and 78 is the upper limit, we can substitute these values into the formula to calculate the margin of error.

Margin of Error = (78 - 72) / 2

Margin of Error = 6 / 2

Margin of Error = 3

Consequently, the 90% confidence interval's margin of error is 3.

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Answer:

D

Step-by-step explanation:

It's asking  would not be a solution soo

(-10, -9) as you can see

You're welcome thank me later

Answer:

The pink one

Step-by-step explanation:

3^-5 x 3^2 = 3^(-5+2) = 3^-3

Answer:

B

Step-by-step explanation:

We can either use sine or cosine, I choose cosine but sine works the same. cos(angle) = adj/hyp. adj = cos(angle) x hyp. adj = cos(30)8, cos(30) = √3/2. √3/2 x 8 = 4√3

The number of years it will take the investment to amount to $6,000 is 8 years.

Simple interest is when the return on an investment grows at a linear rate. This means that the investment would grow at a constant value with the passage of time.

Time = Interest earned / (principal x interest rate)

Interest rate = value of the investment - amount deposited

$6,000 = $4,000 = $2,000

Time = $2,000 / ($4,000 x 0.0625)

Time = 8 years

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Linear Equation: y = mx + b

They tend to have same common differences. They increase linearly. They always have a straight line while making a graph. For every x-value there is only one y-value.

Quadratic Equation: y = ax² + bx + c

They have constant second differences. For every y value there are two x values. They always make a smile [ ∪ ] when the coefficient of x² is positive and sad [ ∩ ] curve on the graph when coefficient of x² is negative.

Exponential Equation: y = a(b)ˣ

Here the values of y changes more rapidly than the value of x. The values shifts too quickly in a exponential graph. For every y value there is only one x value. Has constant ratio.

Exponential equation

Exponential equations have a rate of change and a exponent with respect to the rate of change

The general form is

where c is any real no .

Quadratic equation

The general form is

Linear equation

The equation whose graph is a straight line is called linear equation

The general form is