David says he has 2/3 of a pipe length​ left, while Don says he has 11/16 of a length left. Which person has the longest section​ left?

Answers

Answer 1
Answer:

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

What is Algebra?

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.

brainly.com/question/953809

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Answer 2
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.


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The tax on a property with an assessed value of $90,000 is $1,350. Find the tax on a property with anassessed value of $140,000.
a. $1500.00
b. $150.00
c. $2100.00
d. $210.00
e. $750.00

Answers

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

There are 5 slices of pepperoni pizza, 1 slice of sausage pizzá, and 3 slices of cheese pizza left at the pizza party. Without looking, Amy took a slice of pizza, ate it, and then took another slice. What is the probability of Amy eating two slices of cheese pizza?

Answers

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:

Two cities are 3450 miles apart. A plane leaves one of​ them, traveling towards the other at an average speed of 310 miles per hour. At the same time a plane leaves the​ other, traveling towards the​ first, at an average speed of 380 miles per hour. How long will it take them to​ meet?

Answers

Answer:

5 hours.

Step-by-step explanation:

let they meet after t hours.

310t+380t=3450

690t=3450

69t=345

t=345/69=5

When Stephan moved from Illinois to Florida, his average monthly electric bill increased from $83 to $102. He is curious to know whether his IL or FL electric bill is relatively more or less expensive, when compared to the distribution of electric bills for each state. 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. Compute the z-scores for Stephan's IL and FL electric bills. Round to three decimal places if necessary.

Answers

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.

Z-score:

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

Z = (X - \mu)/(\sigma)

  • 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 X = 83, \mu = 85, \sigma = 3.2

Then:

Z = (X - \mu)/(\sigma)

Z = (83 - 85)/(3.2)

Z = -0.625

In Florida:

  • Bill of $102, mean of $105, standard deviation of $4, hence X = 102, \mu = 105, \sigma = 4

Then:

Z = (X - \mu)/(\sigma)

Z = (102 - 105)/(4)

Z = -0.75

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 : z=(X-mean)/(standard\ deviaton)

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

z=(83-85)/(3.20)= -0.625

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

z=(105-102)/(4)=(3)/(4)=0.75

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

Find the limit of the formula given​

Answers

Answer:

\displaystyle  \lim_(x \to 0^+) x^\big{√(x)} = 1

General Formulas and Concepts:

Algebra II

  • Natural logarithms ln and Euler's number e
  • Logarithmic Property [Exponential]:                                                             \displaystyle log(a^b) = b \cdot log(a)

Calculus

Limits

  • Right-Side Limit:                                                                                             \displaystyle  \lim_(x \to c^+) f(x)
  • Left-Side Limit:                                                                                               \displaystyle  \lim_(x \to c^-) f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_(x \to c) x = c

L’Hopital’s Rule:                                                                                                     \displaystyle \lim_(x \to c) (f(x))/(g(x)) = \lim_(x \to c) (f'(x))/(g'(x))

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹  

Step-by-step explanation:

We are given the following limit:

\displaystyle  \lim_(x \to 0^+) x^\big{√(x)}

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

\displaystyle  \lim_(x \to 0^+) x^\big{√(x)} = 0^0

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

\displaystyle y = \lim_(x \to 0^+) x^\big{√(x)}

Take the ln of both sides:

\displaystyle lny = ln \Big( \lim_(x \to 0^+) x^\big{√(x)} \Big)

Rewrite the limit by including the ln in the inside:

\displaystyle lny = \lim_(x \to 0^+) ln \big( x^\big{√(x)} \big)

Rewrite the limit once more using logarithmic properties:

\displaystyle lny = \lim_(x \to 0^+) √(x)ln(x)

Rewrite the limit again:

\displaystyle lny = \lim_(x \to 0^+) (ln(x))/((1)/(√(x)))

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

\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = (\infty)/(\infty)

Apply L'Hopital's Rule:

\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}}

Simplify:

\displaystyle \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}} = \lim_(x \to 0^+) -2√(x)

Redefine the limit:

\displaystyle lny = \lim_(x \to 0^+) -2√(x)

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

\displaystyle \lim_(x \to 0^+) -2√(x) = -2√(0)

Evaluating it, we have:

\displaystyle \lim_(x \to 0^+) -2√(x) = 0

Substitute in the limit value:

\displaystyle lny = 0

e both sides:

\displaystyle e^\big{lny} = e^\big{0}

Simplify:

\displaystyle y = 1

And we have our final answer.

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

Unit:  Limits

Sand is poured onto a surface at 13 cm3/sec, forming a conical pile whose base diameter is always equal to its altitude. How fast is the altitude of the pile increasing when the pile is 1 cm high? Note that the volume of a cone is 13πr2h where r is the radius of the base and h is the height of the cone.

Answers

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 (dV)/(dt)=13

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

Here d = h

Volume of the pile V=(1)/(3)* \pi  r^(2)hcm³per sec.

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

r = (h)/(2)

V=(1)/(3)\pi  ((h)/(2))^(2)h

V=(1)/(3)\pi ((h^(2)))/(4)(h)

V=(1)/(12)\pi  h^(3)

(dV)/(dt)=(1)/(12)\pi * 3(h)^(2)(dh)/(dt)

(dV)/(dt)=(1)/(4)\pi * h^(2)* (dh)/(dt)

Since (dV)/(dt)=13 cm³per sec.

13 = (1)/(4)\pi  (1)^(2)(dh)/(dt) [For h = 1 cm]

(dh)/(dt)=(13*4)/(\pi )

(dh)/(dt)=(52)/(3.14)

(dh)/(dt)=16.56cm per second.

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

Final answer:

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.

Explanation:

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.

Learn more about Calculus in Physics here:

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