joe is using his allowance money to download songs from the internet. he can download them at a rate of eight songs every 10 minutes. Jasmine, who is downloading songs with the money she made from her part time job, can download at a rate of 12 songs every 15 minutes. Who is downloading songs faster?

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

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)

Step 1

Find the slope of the given line

Let

[tex]A(-4,4)\ B(4,-2)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-2-4}{4+4}[/tex]

[tex]m=\frac{-6}{8}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Step 2

Find the slope of the line perpendicular to the given line

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

we have

[tex]m1=-\frac{3}{4}[/tex] ------> slope of the given line

Find the value of m2

[tex]m2=-1/m1[/tex]

substitute

[tex]m2=-1/(-3/4)[/tex]

[tex]m2=\frac{4}{3}[/tex]

Step 3

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{4}{3}[/tex]

x-intercept is equal to [tex]6[/tex] --------> is the point [tex](6,0)[/tex]

substitute in the formula

[tex]y-0=\frac{4}{3}(x-6)[/tex]

[tex]y=\frac{4}{3}x-8[/tex]

therefore

the answer is the option

[tex]y=\frac{4}{3}x-8[/tex]

The equation of a line containing the point (3, –2) and having a slope of 2, is y = 2x-8

The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers. When we represent the equation geometrically, we always get a straight line.

Given that a line containing the point (3, –2) and having a slope of 2, we need to find the equation of the line,

So, the general equation of a line is y = mx+c

Where, m is the slope and c is the y-intercept.

Therefore,

y = 2x+c

Now, put x = 3 and y = -2 in the equation to find the value of c,

-2 = 3(2)+c

-2 = 6+c

c = -8

Put the value of c in the equation,

y = 2x-8

Hence, the equation of a line containing the point (3, –2) and having a slope of 2, is y = 2x-8

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Jase's chickens laid more eggs.

From the information given, Jase farm has 9 chickens and each laid 3 eggs, therefore the total eggs laid will be:

= 9 × 3

= 27 eggs.

On the other hand, Ednas farm has chickens which lay a total of 23 eggs. Therefore, since 27 eggs are more than 23 eggs, Jase's chickens laid more eggs.

In conclusion, Jase's chickens laid more eggs.

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Answer:

C

Step-by-step explanation:

k is the slope of the line

The equation of the line is y = kx. Therefore, the special thing about k is that it is the slope of the line.

Using a slope intercept equation,

y = kx + b

where

Therefore, the y-intercept of the line y = kx is zero.

What is special about k is that it is the slope of the line y = kx.

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We know that William paid his deductible that amount is the $150. 

Then William paid 20 percent of everything else. That's 20 percent of (750 minus 150), it is equal to 150.

Then the insurance company paid 80 percent of (750 minus 250), it is equal to 480.

Answer:

its is he payed 270 and insurance payed 480

Step-by-step explanation:

just simply add up the numbers to 750 and the only ones that go together are 270 + 480 = 750 hope it helps :)

To express the number of miles driven, y, in terms of the number of hours driven, t, we first find the speed and then use it to formulate the equation of the line as y = 60t. However, to accurately represent the entire trip, we must include the initial 100 miles driven in 2 hours, leading to y = 60t - 20 as the final equation.

To write an equation that gives the number of miles driven, y, in terms of the number of hours driven, t, we can use the relationship between distance and travel time. Given that after two hours you had gone 100 miles and after 8 hours, you reached your destination, which is 460 miles away, we establish two points on our distance-time graph: (2, 100) and (8, 460).

Using the two points, we can find the slope of the line, which represents the speed:
Slope (speed) = (change in distance) / (change in time) = (460 - 100) miles / (8 - 2) hours = 360 miles / 6 hours = 60 miles/hour.

We can now express the equation of the line as y = mx + b, where m is the slope and b is the y-intercept. The y-intercept represents the distance at time zero, which for most driving scenarios we assume to be 0 miles. Thus, the equation becomes y = 60t. However, this equation would not accurately represent the entire trip since it doesn't account for the initial 100 miles driven in the first 2 hours.

To adjust for that, we'll introduce an offset for the initial 100 miles traveled in the first 2 hours. The y-intercept would be 100 miles less than if we had started from 0 miles at 0 hours. The corrected equation for the entire trip would be of the form y = 60t + b, where b = y - 60t and y are the miles covered in the initial 2 hours, which is 100 miles. Substituting the values, we get b = 100 - 60 x 2 which equals -20.

The final equation, accounting for the first 2 hours of travel, would therefore be: y = 60t - 20.

Final answer:

There is a family of normal probability distributions, each representing different populations or sets of data with varying mean and standard deviation values.

Explanation:

Yes, there is a family of normal probability distributions. The normal distribution is a continuous probability distribution that can take on different forms depending on the mean and standard deviation. The family of normal distributions is characterized by different mean and standard deviation values, which result in different shapes of the distribution curve.

For example, the standard normal distribution has a mean of 0 and a standard deviation of 1, and its curve is symmetrical around the mean. Other normal distributions may have different means and standard deviations, resulting in curves that are shifted or stretched.

Each normal distribution in the family represents a different population or set of data, and knowing the specific mean and standard deviation allows us to calculate probabilities and make statistical inferences.

Answer:

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

Given : Graph of slope [tex]\frac{-3}{4}[/tex] and passes through the point (–5, 4).

To find : Which is the equation of the line.

Solution : we have given that point ( -5 ,4)

By equation of line ([tex]y-y_{1}) = m (x -x_{1})[/tex]

y - 4 =  [tex]\frac{-3}{4}[/tex]( x +5).

y - 4 =  [tex]\frac{-3x}{4}[/tex] +[tex]\frac{-15}{4}[/tex].

On adding 4  both sides we get,

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15}{4}+4[/tex].

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15 +16}{4}[/tex].

y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

Therefore, y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].

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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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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Answer:

Option: B is the correct answer.

The equation of the new function g(x) on flipping the function f(x) over the x-axis is:

[tex]g(x)=-2^x[/tex]

Step-by-step explanation:

We are given a graph of the exponential function f(x) which is represented by:

[tex]f(x)=2^x[/tex]

We know that when a graph of a function is reflected or flipped over the x-axis then the the change that take place to the function is that f(x) is transformed to -f(x).

( Since on flipping the function over the x-axis the positive value of the function get changed to negative and the negative value of the function is changed to positive)

Hence, the equation for the new function is:

[tex]g(x)=-f(x)\\\\g(x)=-2^x[/tex]

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.