For the data set below, calculate the variance to the nearest hundredth decimal place. 27 38 47 42 33 56 37 57 38 52

Answer: (40+10π) mm.

Step-by-step explanation: Given diameter of the circle = 10mm.

Radius of the circle = 10/2 = 5 mm.

From the figure, we can see that each or the four corners makes a quarter of the circle.

And four corners would make the complete circle with radius 5mm.

Therefore, circumference of the four quarters of a circle = 2 π r

= 2 π  (5) = 10 π.

Now, we can see that each side 10 mm of band also there.

So, the length of straight band on all four sides = 4 × 10 = 40 mm.

Total length of the band = (40+10π) mm

The length of the band is the number of units it covers

The actual length of the band is: [tex]\mathbf{40 + 10\pi}[/tex]

The diameter of 1 pencil is given as:

[tex]\mathbf{d = 10}[/tex]

The circumference of 1 pencil is:

[tex]\mathbf{C = \pi d}[/tex]

So, we have:

[tex]\mathbf{C = 10\pi }[/tex]

Multiply by 4, to calculate the circumference of all pencils

[tex]\mathbf{4C =4 \times 10\pi }[/tex]

[tex]\mathbf{4C =40\pi }[/tex]

The rubber band covers a quarter of the 4 pencils.

So, we divide by 4

[tex]\mathbf{C = 10\pi }[/tex]

The length of the band on one pencil is:

[tex]\mathbf{L = 10}[/tex]

Multiply by 4, for the 4 pencils

[tex]\mathbf{L = 40}[/tex]

So, the actual length of the band is:

[tex]\mathbf{Length = 40 + 10\pi}[/tex]

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The above answer will be calculated as -

We are given -

600 ( 1 + 0.03)^12

We will first add - 1 + 0.03 = 1.03

Now, we will multiply 1.03 into 12 times, in order to find the value of ( 1.03)^12

The answer for ( 1.03)^12 = 1.4268

Now, we will multiply 1.4268 with 600

600 × 1.4268 = 856.08 approximately.

Thus, the value of 600*(1.03)^12 has been calculated.

Hello There!

Median: The middle number when all the numbers are listed in oder from least to greatest.

To find the median, place the numbers in order from least to greatest.

In this case, the numbers would be 4, 5, 8, 9, 10

The middle number would be 8 so the median for this set of numbers is 8.

The simplification of ( n + 8) + ( n -12 ) is 2(n -2)

algebraic expression are expression with unknown.

This unknown is represented by letters and in linear algebraic equations , the highest power of the unknown is 1.

Simplifying (n + 8) + (n-12)

n + 8 + n -12

collecting like terms

n + n + 8 -12

2n -4

we can further Factorize

2( n -2)

Therefore, the simplification of ( n + 8) + ( n -12 ) is 2(n -2)

To find (f o g)(2), substitute the value of g(2) into f. To find (f+g)(2), find f(2) and g(2) separately, then add them together.

To find (f o g)(2), we need to first find g(2), and then substitute that value into f. To find g(2), we substitute 2 into the expression for g(x). g(2) = 4(2) + 9 = 8 + 9 = 17. Now, we substitute 17 into the expression for f(x), which is 1/x. (f o g)(2) = f(g(2)) = f(17) = 1/17.

To find (f+g)(2), we first need to find f(2) and g(2) separately. f(2) = 1/2, and g(2) = 17. Now, we add them together. (f+g)(2) = f(2) + g(2) = 1/2 + 17 = 1/2 + 34/2 = 35/2 = 17.5.

Answer:

step three is the incorrect one making step three the answer

Step-by-step explanation:

In the following steps student made the error in the third step.

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

The error occurred in Step 3.

Step 3 should be:

-2(m) = -2(6 + n)

-2m = -12 - 2n

The mistake was that the student distributed the negative sign only to the 6 and not to the n.

The correct next step is to simplify equation 2:

2m = 8 + 8n

So the student made an error in Step 3.

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Final answer:

To solve the expression 2 + 3 × 16 − 2 × 21 − 3, we use the order of operations rule, starting with multiplication to get 48 and 42, followed by addition and subtraction to arrive at the final answer of 5.

Explanation:

The student's question requires us to solve a mathematical expression using the correct order of operations. In the expression 2 + 3 × 16 − 2 × 21 − 3, we need to follow the BIDMAS/BODMAS/PEMDAS rule (Brackets, Indices/Orders, Division and Multiplication, Addition and Subtraction). This rule ensures that we perform multiplication and division before addition and subtraction.

First, we calculate the multiplication parts: 3 × 16 and 2 × 21.
3 × 16 = 48
2 × 21 = 42

Substituting these into the original expression gives us:
2 + 48 − 42 − 3

Next, we perform the addition and subtraction in order from left to right:
2 + 48 = 50
50 − 42 = 8
8 − 3 = 5

So, the expression simplifies to the number 5.

Final answer:

The expression cosx (tanx+cotx) simplifies to sinx+cosx by using trigonometric identities and recognizing that tanx and cotx can be expressed in terms of sinx and cosx, allowing terms to cancel out.

Explanation:

To simplify the expression cosx (tanx+cotx), we need to use trigonometric identities. Recall that tanx = sinx/cosx, and cotx = cosx/sinx. Therefore, when we multiply cosx by tanx, the cosx in the numerator and denominator will cancel out, leaving us with sinx. Similarly, when we multiply cosx by cotx, sinx in the numerator and denominator will cancel out, leaving us with cosx.

So the simplification process will look like this:

cosx * tanx = sinx

cosx * cotx = cosx

Thus, cosx (tanx+cotx) = sinx+cosx.

This is the simplified form of the expression given. It's important to remember that trigonometric identities are a powerful tool in simplifying expressions involving trigonometric functions.

a + b = 43 (the sum of two numbers is 43)
(a +11) = b (he larger number is 11 more than the smaller number)

so:
a + b = 43
a + (a + 11) = 43
a + a + 11 = 43
2a = 43 - 11
2a = 32
a = 16

now:
a + b = 43
16 + b = 43
b = 43 - 16
b = 27

that is:
a = 16
b = 27

 --------------------------

 checking:

b - a = 11 
27 - 16 = 11 (TRUE)

We have that for the Question "identify the two rational numbers. " it can be said that

Option B,C,D is rational

From the question we are told

identify the two rational numbers.

A)√2

B) 1.01

C) 1.010010001...

D) -2/5

Generally

Rational number are real number that exist is a form where the denominators are not zero

Therefore

A)√2 this is an irratioanl number as its \pm 1

B) 1.01  Rational

C) 1.010010001... rational

D) -2/5 rational

Hence

Option B,C,D is rational

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Answer:

x(x+1)²

Step-by-step explanation:

x is a common factor to all terms so the first step is to factor it out:

... x(x² +2x +1)

The quadratic factor is recognizable as the square (x+1)², so the factoring is ...

... x(x +1)²

Answer:

Step-by-step explanation:x(x+1)2

The cost of the automobile, excluding the impact of the interest, is $26,500.

For this question, we need to determine the total cost of the automobile purchased by Dave Krug. We know that Dave made an upfront payment of $6,500, and also agreed to make 40 monthly payments of $500 each. The total amount paid through monthly payments is $500 * 40 = $20,000.

Here, it is also stated that the loan bears an annual interest rate of 12%. However, no additional data are given for us to calculate the impact of the interest on the overall cost of the car. So, we'll proceed without including the interest.

So, to find the total cost of the car, we combine the upfront payment with the total monthly payments. That is, $6,500 (upfront payment) + $20,000 (total monthly payments) = $26,500. Therefore, the cost of the automobile without taking into account the interest is $26,500.

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For every mole of carbon dioxide used, one mole of methane is produced. Therefore, 71.1 moles of carbon dioxide would produce 71.1 moles of methane, assuming hydrogen is in excess.

According to the given reaction, we can infer that the stoichiometric ratio between methane (CH4) and carbon dioxide (CO2) is 1:1. This means for each mole of methane produced, one mole of carbon dioxide is consumed. Therefore, if you are starting with 71.1 moles of carbon dioxide and assuming there is excess hydrogen, you would produce 71.1 moles of methane because of this 1:1 mole ratio.

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