Answer:
### What is Algebra?

Don has the **longest **section of pipe because the **fraction **number 11/16 is **greater **than the **fraction **number 2/3.

Algebra is the study of **abstract **symbols, while **logic **is the manipulation of all those **ideas**.

The **decimal **number is the sum of a **whole **number and part of a fraction number. The **fraction **number is greater than zero but **less **than one.

David says he has 2/3 of a line **length **left, while Wear says he **has **11/16 of a **length **left.

Convert the **fraction **numbers 2/3 and 11/16 into the **decimal **number. Then we have

2/3 = 0.6667

11/16 = 0.6875

The **decimal **number 0.6875 is greater than 0.6667. Then the **fraction **number 11/16 is **greater **than the **fraction **number 2/3.

Don has the **longest **section of pipe because the **fraction **number 11/16 is **greater **than the **fraction **number 2/3.

More about the **Algebra **link is given below.

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Answer:

**Answer:**

Don

**Step-by-step explanation:**

1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.

Suppose a regional computer center wants to evaluate the performance of its memory system. One measure of performance is the average time between failures of its disk drive. To estimate the value, the center recorded the time between failures for a random sample of 45 drive failures. The sample mean has been computed to be 1,762 hours and the sample standard deviation is 215. Estimate the true mean time between failures with a 90% confidence interval? Interpret the confidence interval.

In Exercise, expand the logarithmic expression.ln(x + 1)2

Who can answer this(WITH AN EXPLANATION)will mark brainlest

A real estate developer is considering investing in a shopping mall on the outskirts of Atlanta, Georgia. Three parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of four families is selected near each proposed mall. Following are the sample results. At the 0.05 significance level, can the developer conclude there is a difference in the mean income

Please help ASAP in math I have a picture

In Exercise, expand the logarithmic expression.ln(x + 1)2

Who can answer this(WITH AN EXPLANATION)will mark brainlest

A real estate developer is considering investing in a shopping mall on the outskirts of Atlanta, Georgia. Three parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of four families is selected near each proposed mall. Following are the sample results. At the 0.05 significance level, can the developer conclude there is a difference in the mean income

Please help ASAP in math I have a picture

a. $1500.00

b. $150.00

c. $2100.00

d. $210.00

e. $750.00

**Answer:**

0.015 or 1.5% tax

**Step-by-step explanation:**

90000x0.015 = 1350

let’s go to the beach each let’s go get away say say what they gonna say the patron on

**Answer:**

3/8

**Step-by-step explanation:**

add 5+1+3=9

and there is 3 cheese pizza so its 3 over 8.

**Answer:**

3/9

**Step-by-step explanation:**

**Answer:**

5 hours.

**Step-by-step explanation:**

let they meet after t hours.

310t+380t=3450

690t=3450

69t=345

t=345/69=5

Using it's formula, it is found that the **z-scores** are:

- For
**Illinois**, of**Z = -0.625.**

- For
**Florida**, of**Z = -0.75.**

- Due to the
__lower z-score__, the bill is relatively**lower**in Florida.

In a distribution with **mean ** and **standard deviation **, the **z-score** of a** measure X** is given by:

- It
**measures**how many standard deviations the measure is from the mean.

- The
**higher z-score**means that the measure X is relatively higher.

In **Illinois**:

- Bill of $83, mean of $85, standard deviation of $3.2, hence

Then:

In **Florida**:

- Bill of $102, mean of $105, standard deviation of $4, hence

Then:

Due to the __lower z-score__, the bill is relatively **lower **in Florida.

To learn more about **z-scores**, you can take a look at brainly.com/question/21620274

**Answer: **The z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.

**Step-by-step explanation:**

Given: Average monthly electric bill in Illinois = $83

Average monthly electric bill in Florida = $102

**Formula of z **:

In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20.

In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00.

Hence, **the z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.**

**Answer:**

**General Formulas and Concepts:**

__Algebra II__

- Natural logarithms
**ln**and Euler's number**e** - Logarithmic Property [Exponential]:

__Calculus__

Limits

- Right-Side Limit:
- Left-Side Limit:

Limit Rule [Variable Direct Substitution]:

L’Hopital’s Rule:

Differentiation

- Derivatives
- Derivative Notation

Basic Power Rule:

**f(x) = cxⁿ****f’(x) = c·nxⁿ⁻¹**

**Step-by-step explanation:**

We are given the following limit:

Substituting in *x* = 0 using the limit rule, we have an indeterminate form:

We need to rewrite this indeterminate form to another form to use L'Hopital's Rule. Let's set our limit as a function:

Take the ln of both sides:

Rewrite the limit by including the ln in the inside:

Rewrite the limit once more using logarithmic properties:

Rewrite the limit again:

Substitute in *x* = 0 again using the limit rule, we have an indeterminate form in which we can use L'Hopital's Rule:

Apply L'Hopital's Rule:

Simplify:

Redefine the limit:

Substitute in *x* = 0 once more using the limit rule:

Evaluating it, we have:

Substitute in the limit value:

**e** both sides:

Simplify:

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

**Answer:**

**Altitude of the pile will increase by 16.56 cm per second.**

**Step-by-step explanation:**

Sand is poured onto a surface at the rate = 13 cm³ per second

Or

It forms a conical pile with a diameter d cm and height of the pile = h cm

Here d = h

Volume of the pile cm³per sec.

Since h = d = 2r [r is the radius of the circular base]

r =

Since cm³per sec.

13 = [For h = 1 cm]

cm per second.

Therefore, **altitude of the pile will increase by 16.56 cm per second.**

To solve this problem, we first find the **expression **for the volume of the cone in terms of the height. We then differentiate this expression to get the relation between the rates of change of the volume and the height. By substituting the given values, we can find the rate of change of the height when the cone is 1 cm high.

The question is related to the application of calculus in Physics, specifically rates of change in the context of real-world problem involving a three dimensional geometric shape - a cone. The student asks how fast the altitude of a pile of sand is increasing at a given time if sand is being poured onto a surface at a constant rate and the pile forms a cone whose base diameter is always equal to its altitude.

We know that the volume of a cone is given by V = (1/3)πr²h, where r is the radius of the base and h is the altitude. Since in this problem the base diameter is always equal to its altitude, we have d = 2r = h, or r = h/2.

Replace r in the volume formula, yielding V = (1/3)π(h/2)²h = (1/12)πh³. Differentiate this expression with respect to time (t) to find the rate of change of V with respect to t, dV/dt = (1/4)πh² * dh/dt.

Given that sand is poured at a constant rate of 13 cm³/sec (that is, dV/dt = 13), we can solve for dh/dt when h = 1cm. Substituting the given values into the equation, 13 = (1/4)π(1)² * dh/dt, we find dh/dt = 13/(π/4) = 52/π cm/sec. Therefore, when the conical pile is 1 cm high, the altitude is increasing at a rate of 52/π cm/sec.

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