What is the rate of change of y with respect to x for this function?
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The rules of the order of operations tells you to multiply and divide in order from left to right.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The order of operations can be remembered by the acronym PEMDAS, which stands for: parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right. There are no parentheses in this problem, so start with exponents. Then, multiply and divide from left to right.

Hence, the rules of the order of operations tells you to multiply and divide in order from left to right.

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The limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) is DNE

To take the limit of the function lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6), we proceed as follows

Since we have the function  lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) and we want to take the limit, we proceed thus,.

First, we divide both the numerator and denominator by x⁴. So,

lim x → ∞(x⁴ - 9x² + x)/(x³ - x + 6) = lim x → ∞(x⁴ - 9x² + x)/x⁴ ÷ (x³ - x + 6)/x⁴

= lim x → ∞(x⁴/x⁴ - 9x²/x⁴ + x/x⁴ ÷ (x³/x⁴ - x/x⁴ + 6/x⁴)

= lim x → ∞(1 - 9/x² + 1/x³ ÷ (1/x - 1/x³ + 6/x⁴)

Now, taking the limit as x tends to infinity, we have that

= lim x → ∞1 - lim x → ∞9/x² + lim x → ∞1/x³ ÷ lim x → ∞1/x - lim x → ∞1/x³ + lim x → ∞6/x⁴

= (0 - 9/∞² + 1/∞³)/(1/∞ - 1/∞³ + 6/∞⁴)

= (0 - 9/∞ + 1/∞)/(1/∞ - 1/∞ + 6/∞)

= (∞ - 0 + 0)/(0 - 0 + 0)

= (∞)/(0)

= DNE

Answer:

10 customers were spoken to in every 30 minutes

Step-by-step explanation:

First, we convert 40 hours into minutes by multiplying it with 60 [as 1 hour = 60 minutes]

So, 40 hours =  40*60 minutes

                      = 2400 minutes

In 2400 minutes, number of customers served = 800

In 1 minute, number of customers served = [tex]\frac{800}{2400}[/tex]

In 30 minutes, number of customers served = [tex]\frac{800}{2400}*30[/tex]

                                                                         = [tex]\frac{800}{2400} * \frac{30}{1}[/tex]

                                                                         = [tex]\frac{800*30}{2400*1}[/tex]

                                                                         = [tex]\frac{24000}{2400}[/tex]

                                                                         = 10

So,

10 customers were spoken to in every 30 minutes

Final answer:

You spoke with 10 customers every 30 minutes.

Explanation:

To find out how many customers you spoke to every 30 minutes, we can set up a proportion. We know that you spoke with 800 customers in 40 hours, which is equivalent to 2400 minutes. So, the proportion is:

800 customers / 2400 minutes = x customers / 30 minutes

Now, we can cross-multiply and solve for x:

800 * 30 = 2400 * x

x = 800 * 30 / 2400

x = 10

Therefore, you spoke with 10 customers every 30 minutes.

To find the value of x in a system of equations, you can use the substitution or elimination method. In this case, x = 2 is the solution.

To find the value of x in the system of equations x − 2y = 2 and 3x + y = 6, we can use the method of substitution or elimination.

Substitution method:

Therefore, the value of x in the solution to the system of equations is x = 2.

by adding the numbers in a different order would be a way to check so the answer is:

C. 877 + 228 + 34 + 104

1 foot = 12 inches

1/4 foot = 12/4 = 3 inches

61 +3 = 64 inches tall ( 5 ft 4 inches)

Answer:

The required equation of line is y=-6x-57.

Step-by-step explanation:

The point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

Where m is slope of the line.

It is given that a line that passes through (–9, –3) and has a slope of –6.

Substitute m=-6, x₁=-9 and y₁=-3 in the above equation.

[tex]y-(-3)=-6(x-(-9))[/tex]

[tex]y+3=-6x-54[/tex]

Subtract 3 from both the sides.

[tex]y=-6x-54-3[/tex]

[tex]y=-6x-57[/tex]

Therefore the required equation of line is y=-6x-57.

Answer:

D).y+3=-6(x+9)

Step-by-step explanation:

took it on edge

f(x) = 4x − 12

f−1(x) =1/4 x + 3

The inverse of the function f(x) = 4x - 12 is f^-1(x) = (x + 12)/4.

To find the inverse of the function f(x) = 4x - 12, we need to switch the roles of x and y and solve for y.  

Step 1: Replace f(x) with y: y = 4x - 12.

Step 2: Swap x and y: x = 4y - 12.

Step 3: Solve for y: x + 12 = 4y.  

Step 4: Divide both sides by 4: (x + 12)/4 = y.

Therefore, the inverse function is f-1(x) = (x + 12)/4.

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a. The 50 independent network servers would be needed if each has 98% reliability.

b. Approximately 9 independent network servers would be needed if each has 89% reliability.

To calculate the number of independent network servers needed for a given level of reliability, we can use the following formula:

[tex][ \text{Number of servers} = \frac{1}{1 - \text{Reliability}} ][/tex]

a) For servers with 98% reliability:

[tex][ \text{Number of servers} = \frac{1}{1 - 0.98} = \frac{1}{0.02} = 50 ][/tex]

Therefore, 50 independent network servers would be needed if each has 98% reliability.

b) For servers with 89% reliability:

[tex][ \text{Number of servers} = \frac{1}{1 - 0.89} = \frac{1}{0.11} \approx 9 ][/tex]

Therefore, approximately 9 independent network servers would be needed if each has 89% reliability.

The program is an illustration of functions

Functions are collections of defined program statements, that are executed when evoked

The program in Python, where comments are used to explain each line is as follows:

#This imports the math module

import math

#This defines the function

def calculateDistance(x1,y1,x2,y2):

      #This calculates the distance between the points

      dist = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)

      #This returns the calculated distance

      return dist distance

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It's C if you're taking the test

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{The formula of a distance between two points on a number line:}\\\\d=|a-b|\\\\\text{for}\ a\geq b:\ d=a-b\\=========================\\\\\text{We have}\ 4.7\ \text{and}\ -11.2.\ \text{Substitute:}\\\\d=4.7-(-11.2)=4.7+11.2=15.9[/tex]

The distance between 4.7 and -11.2 on the number line is 15.9.

The distance between two points on a number line can be found by taking the positive difference between their coordinates. In this case, the distance between 4.7 and -11.2 is found by subtracting the smaller number from the larger number and taking the absolute value.

Distance = |-11.2 - 4.7| = |-15.9| = 15.9

Therefore, the correct expression is Distance = 15.9.

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Answer:

The circumference of the given circle = 182.12 meters

Step-by-step explanation:

The circle P is given to us in which length of PB = 29 meter

Now, Since P is the center of the circle so PB will be the radius of the circle

So, Radius of the circle = 29 meter

We need to find the circumference of this circle with radius 29 meter

So, Circumference of the circle = 2π × radius of the circle

⇒ Circumference of the circle = 2 × 3.14 × 29

                                                  = 182.12 meter

Hence, The circumference of the given circle = 182.12 meters

Final answer:

The 8 in the number 8.4 has a value that is 100 times greater than the 8 in the number 0.084. The first 8 represents 8 ones, while the second represents 8 hundredths.

Explanation:

The value of the 8 in 8.4 is 100 times greater than the 8 in 0.084. To understand why, let's remember that each position in a decimal number has a place value that is 10 times less than the place value to its left. For instance, in the number 8.4, the 8 is in the ones place, meaning its value is 8 ones or '8'. However, in the number 0.084, the 8 is in the hundredths place, so its value is 8 hundredths or '0.08'.

Therefore, when comparing the two eights, we see that:

The 8 in 8.4 equals 8 ones (8 × 1 = 8).

The 8 in 0.084 equals 8 hundredths (8 × 0.01 = 0.08).

To find a number whose 8 is worth 100 times less than the 8 in 8.4, we need the 8 to be two places to the right of the decimal point, which is the hundredths place. The number 0.084 satisfies this because 8 ones (the value of the 8 in 8.4) are 100 times greater than 8 hundredths (the value of the 8 in 0.084).

The probability of rolling a sum of 8 on a pair of standard six-sided dice is 5 out of 36, or 0.139 rounded to three decimal places.

The subject of your question is

probability

, a topic in Mathematics. To solve this, we want to know the total number of outcomes when two dice are rolled; which is 6*6 = 36. Then we determine how many of these outcomes result in a sum of 8. Upon careful examination, we find that there are 5 (2,6), (3,5), (4,4), (5,3), and (6,2). Therefore, the

probability of rolling a sum of 8

on a standard pair of six-sided dice is 5 out of 36, which can be expressed as

5/36 or 0.139

rounded to three decimal places.

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