An oil storage tank ruptures at time t - and oil leaks from the tank at a rate of rt) = 80e-0.05t liters per minute. How much oll leaks out during the first hour? (Round your answer to the nearest lit

Working together, Bill and Maria can finish the same report in 4/3 or 1  1/3 hours.

Work rate:

The job: 1

Bill: 1/2

Maria: 1/4

Working together: 1/x

Equation:

1/2 + 1/4 = 1/x

2/4 + 1/4 = 1/x

3/4 = 1/x

3x = (4)(1)

3x/3 = 4/3

x = 4/3 hours

Working together, Bill and Maria can finish the same report in 4/3 or 1  1/3 hours.

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The answer is 17/20.. sorry for the first answer

Let's define two sequences, one representing the number of ways to order lunch on the "n"th day if Angela ate chicken salad on the (n-1)th day, and another representing the number of ways if she didn't.
If Angela ate chicken salad on the (n-1)th day, then she cannot eat it on the n-th day. Therefore, the number of ways for the "n"th day is equal to the number of ways for the (n-1)th day when Angela didn't eat chicken salad.
If Angela didn't eat chicken salad on the (n-1)th day, then she has two options for the n-th day: either eat chicken salad or not. If she doesn't eat chicken salad, the number of ways for the "n"th day is equal to the number of ways for the (n-1)th day when she didn't eat chicken salad. If she does eat chicken salad, the number of ways for the "n"th day is equal to the number of ways for the (n-2)th day when she didn't eat chicken salad.
Therefore, the recurrence relation is:
f(n) = f(n-1) + g(n-1)
g(n) = f(n-1) if Angela didn't eat chicken salad on the (n-1)th day
g(n) = f(n-2) if Angela ate chicken salad on the (n-1)th day.

To find the recurrence relation for the number of ways for Angela to order lunch for the "n" days, we need to consider two cases: when Angela ate chicken salad on the (n-1)th day and when she didn't.

If Angela ate chicken salad on the (n-1)th day, then she cannot eat it on the n-th day, as she cannot eat chicken salad three days in a row. Therefore, the number of ways for the "n"th day is equal to the number of ways for the (n-1)th day when Angela didn't eat chicken salad.

If Angela didn't eat chicken salad on the (n-1)th day, then she has two options for the n-th day: either eat chicken salad or not. If she doesn't eat chicken salad, the number of ways for the "n"th day is equal to the number of ways for the (n-1)th day when she didn't eat chicken salad. If she does eat chicken salad, the number of ways for the "n"th day is equal to the number of ways for the (n-2)th day when she didn't eat chicken salad.

Therefore, we can define two sequences, f(n) representing the number of ways to order lunch on the "n"th day if Angela didn't eat chicken salad on the (n-1)th day, and g(n) representing the number of ways if she did. Then, the recurrence relation can be written as:

f(n) = f(n-1) + g(n-1)

g(n) = f(n-1) if Angela didn't eat chicken salad on the (n-1)th day

g(n) = f(n-2) if Angela ate chicken salad on the (n-1)th day.

In conclusion, we can use the recurrence relation f(n) = f(n-1) + g(n-1) and g(n) = f(n-1) if Angela didn't eat chicken salad on the (n-1)th day, and g(n) = f(n-2) if she did, to calculate the number of ways for Angela to order lunch for the "n" days if she never orders chicken salad three days in a row.

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Complete Question

At a concert 3 out of 10 people who entered the Alamodome wore Nike shoes based on this information if there are 1200 people at the music concert how many people could be expected to be wearing Nike shoes?

Answer:

360 people

Step-by-step explanation:

The fraction of people wearing Nike shoes = 3/10

The total number of the people at the concert = 1200 people

Therefore, the number of people cthat ould be expected to be wearing Nike shoes is calculated as:

3/10 × 1200 people

= 360 people

The answer is 360 people

Answer:

It is 270, 810 and 2430

Step-by-step explanation:

10 x 3 = 30

30 x 3 = 90

90 x 3 = 270

270 x 3 = 810

810 x 3 = 2430

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\(\heartsuit\) Greetings \(\heartsuit\)

Sincerely: anapaulacbellido

The product of the numbers (−0. 64) and (−2. 5) is

1.6.

To multiply (-0.64)(-2.5), we can accomplish the task using the following steps:

Multiply the absolute values of the numbers:

0.64 x 2.5 = 1.6

Determine the sign of the product: Since we are multiplying two negative numbers, the product is positive.

Add the sign to the product: (-0.64)(-2.5) = 1.6

hence, (-0.64) x (-2.5) = 1.6.

These can also be solved using calculator

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Answer:

Step-by-step explanation:

The best-supported statement by the information in the table is:

C. The fee at Bank K will always be greater than the fee at Bank F.

This is because for any given average daily balance, Bank K has a higher fee than Bank F. For example, for an average daily balance of less than $500, Bank F charges $8 while Bank K charges $12. Similarly, for an average daily balance between $500 and $750, Bank F charges no fee while Bank K charges $12. Therefore, the fee at Bank K will always be greater than the fee at Bank F.

Some random variables that you may want to run a simulation on to find the expected values for your vegetable farm include crop yield, market prices, weather conditions, and pest infestation.

As a vegetable farmer, it is important to understand the expected values of various factors that can impact your farm's success. One important random variable is crop yield, which represents the amount of produce you can expect to harvest.

By simulating different scenarios, you can estimate the average crop yield and plan accordingly. Another variable is market prices, as they determine the revenue you can generate from selling your vegetables. Simulating price fluctuations can help you estimate the expected value of your earnings. Additionally, weather conditions play a crucial role in crop growth, and simulating different weather patterns can help you assess the expected impact on your farm.

Finally, simulating the occurrence of pest infestations can help you anticipate and manage potential losses.

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The length of 175 metres and width of 87.5 metres will maximise the area 15312.5 square metres.

We have been given that Farmer Ed has 350 metres of fencing and wants to enclose a rectangle mat plot that borders on a river. Farmer Ed does not fence the side along the river.  

First of all we will make a relevant figure to represent the perimeter of fencing for 3 sides as shown in the attachment.

Since Ed will not fence the side along the river, fencing is needed for 3 sides and the perimeter of the fencing would be x + x + y = 2x + y.

Now we will equate perimeter with 350 as: 2x + y = 350

y=350-2x

We know that the area of the rectangle is width times length.

A = X•Y

Upon substituting the value of y in area equation, we will get:

A = x•(350-2x)

A(x) = 350x -2x²

Now we will find derivative of area function as:

A'(x) = d(350- 2)/dx

A'(x) = 350-4x

Now we will equate derivative with 0 and solve for x as:

0 = 350-4

4x = 350

x = 350/4 - 87.5

Upon substituting x = 87.5 in equation y = 350-2x, we will get:

y = 350 - 2x

 = 350 - 2(87.5)

 = 350-175

y = 175

Therefore, the length of 175 metres and width of 87.5 metres will maximise the area.

on substituting x = 87.5 in area function, we will get:

A(87.5) = 350(87.5)-2(87.5)²

A(87.5) = 30625-2(7656.25)

A(87.5) = 30625-15312.5

A(87.5)= 15312.5

Therefore, the largest possible area enclosed would be 15312.5 square metres.

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—--------- CORRECT QUESTION FORMAT IS GIVEN BELOW —----------

(Q).

Farmer Ed has 350 meters of fencing and wants to enclose a rectangle mat plot that borders on a river. If farmer Ed does not fence the side along the river find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed ?

Answer:

21.5

Step-by-step explanation:

square is 10x10 = 100

circle is A=πr2=π·5²≈78.54

100-78.54 = 21.46 = 21.5

Answer:

21.5 sq cm

Step-by-step explanation:

Area of Square:

A= LXW= 10x10= 100 sq cm

Area of Circle=

A=πr²

Radius= D/2= 10/2= 5 cm

A=3.14(5²)

A=3.14(25)= 78.5 sq cm

Shaded Region= 100-78.5= 21.5

The area of the shaded region is 21.5 sq cm.

Answer:

$11

Step-by-step explanation:

Let's take 20% and convert it into a decimal, which is .20. Multiply that percentage by $55 (.20 * 55) and you get $11, which is the answer.

John had 4.8 gallons of milk in the first container and 2.4 gallons of milk in the second container

The first container of milk contains twice as much milk as the second container of milk

let the quantity of milk in the first container be x

let the quantity of milk in the second container be y

x = 2y

After John uses 2 gallons of milk from the second container and 3 gallons from the first, the first contains 4.5 times as much milk as the second

x - 3 gallons = 4.5 (y - 2 gallons)

x - 3 = 4.5(y - 2)

x - 3 = 4.5y - 9

x = 4.5y - 6

substituting the value of x

2y = 4.5y - 6

4.5y - 2y = 6

2.5y = 6

y = 2.4 gallons

x = 2y = 4.8 gallons

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Answer:

(4,-1)

Step-by-step explanation:

x is 4 y is -1

Answer:

(2,1)

Step-by-step explanation:

Let's solve your system by elimination.

6x−7y = 5;−4x+7y=−1

6x−7y=5

−4x+7y=−1

Add these equations to eliminate y:

2x = 4

Then solve2x = 4for x:

2x = 4

(Divide both sides by 2)

x = 2

Now let's plug x in to solve for y.

6x - 7y = 5

6(2) - 7y = 5

12 - 7y = 5

subtract 12 on both sides.

-7y = -7

divide both sides by -1

y = 1

Over time, the period becomes the run, and the run becomes the stride.

The given statement seems to be referring to a change or evolution in the terminology or usage of certain terms. However, without further context or clarification, it is difficult to provide an accurate and specific explanation for the intended meaning.

Based on the statement, it can be inferred that the terms "period" and "run" are being used in a specific context or domain. In general, the term "period" is often associated with the time duration or repetition of a cycle, while "run" can refer to a continuous segment or distance covered. However, the specific domain or field where these terms are being used could alter their meanings or interpretations.

Without additional context, it is challenging to provide a more detailed explanation or analysis of the statement's implications.

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10 choose 3 with replacement gives you a mere 220 combinations. A “combination” lock uses permutations, so there would be 1000 possibilities.

What is Combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Mathematically, a combination is a selection of things without regard for order.

The formula for “combination with replacement” is:

   \(C^{R} (n,r)=\frac{(n+r-1)!}{r! (n-r)!}\)

10 choose 3 with replacement gives you a mere 220 combinations.

The toss of three identical 10-sided dice would have 220 possible outcomes.

Hence, A “combination” lock uses permutations, so there would be 1000 possibilities.

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Answer:

(20,280) and (10,300)

Step-by-step explanation:

It was the correct answer on the practice question

Answer:

Edmentum/Plato

Answer:

m∠1=46°

m∠2=44°

m∠3=44°

m∠4=90°

m∠5=73°

m∠6=17°

m∠7=17°

The set of expressions that is NOT an example of the associative property is B. (8 - 2) + 3 and 8 + (-2 + 3).

The associative property states that the way you group numbers when adding or multiplying does not change the result. For example, (8 + 2) + 3 is the same as 8 + (2 + 3). However, the associative property does not apply to subtraction or division. Therefore, (8 - 2) + 3 is not the same as 8 + (-2 + 3).

Besides associative property, there are 3 other mathematical properties that only works on adding and multiplying. They are:

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Given :

To Find :-

Solution :-

As we know that,

Hence the required answer is 10.

Answer:

10 neutrons

Step-by-step explanation:

no.of neutrons = atomic mass - Atomic number

no.of neutrons= 22-12

=10

From the given graph, the interval (0,6)g is not continuous at x=2

A graph is a visual representation of the change of one variable in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or areas. It can also be defined as  a grouping of all locations whose coordinates meet a certain relation (such as a function).

For instance, a function is continuous if the graph can be drawn with a pen without having to remove it from the paper. If a function's graph is a continuous curve without any flaws, gaps, or breaks, it is said to be continuous. However, phrases like "unbroken curve" and "gaps" aren't strictly speaking mathematical words, and at best they only give the reader a description of continuity rather than a definition.

A function may be continuous at a specific location, continuously over a specified time period, or continuously throughout.

In the given graph, we can observe that the line is not a continuous line. Here, the break in the line is being observed at x=2.

Therefore, the given graph, in the interval (0,6)g is not continuous at x=2.

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Answer:

Step-by-step explanation:

p > 9

Hope that helps!

Answer:

Consistent

Step-by-step explanation:

It was a solution.

The steepness of a line is determined by its slope. The value of "k" is 0

First, we need to find the slope of the line passing through the points A (-8, 0) and B (8, 0) as shown:

\(m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{0-0}{8-(-8)}\\m=\frac{0}{16}\\m =0\)

To get the value of k, we will equate the slope of the perpendicular line which is 0 to the slope of the line passing through A (-8, 0)  and (0, k)

\(m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{k-0}{0-8}\\m=\frac{k}{-8}\\0=\frac{k}{-8}\\k = 0\)

Hence the value of "k" is 0

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DOLLARS             CENTS             DOLLARS                         CENTS

The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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The message "UWJUF WJYTR JJYYM DITTR" has been deciphered using a Caesar cipher with a shift constant of 5. The decoded message reveals the original text to be "PETER PAUL MARRY LOU."

A Caesar cipher is a simple substitution cipher where each letter in the plaintext is shifted a certain number of places down the alphabet. In this case, we were given the encoded message "UWJUF WJYTR JJYYM DITTR" and asked to decipher it using a suitable Caesar cipher with a shift constant of k.

To decipher the message, we need to shift each letter in the encoded text back by the value of the shift constant. Since the shift constant is not given, we need to try different values until we find the correct one.

By trying different shift values, we find that a shift of 5 results in the decoded message "PETER PAUL MARRY LOU." The original message was likely a list of names, with "Peter," "Paul," "Marry," and "Lou" being the deciphered names.

In conclusion, by using a Caesar cipher with a shift constant of 5, we successfully deciphered the encoded message "UWJUF WJYTR JJYYM DITTR" to reveal the names "Peter," "Paul," "Marry," and "Lou."

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Answer:

70000

Step-by-step explanation:

you simply just add all the zeros in the equation.

(side note: that wording messed me up so much)

The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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The x-coordinate of the point P is 2 and the y-coordinate is 5. So the coordinates of point P are (2,5).

To find the x-coordinate, we set the derivative of the curve equal to 1/4 and solve for x:

d/dx (1/(x+3)) = 1/4

-1/(x+3)² = 1/4

(x+3)² = -4

x+3 = ±2i

x = -3 ± 2i

Since the curve is defined only for real values of x, we take the real part of the solution and obtain x = -3. Therefore, the y-coordinate is y = 1/(x+3) = 1/(-3) = -1/3.

However, this point is not on the curve because the curve is not defined for x = -3. Instead, we need to look for the point on the curve closest to x = -3. We can do this by finding the limit of the curve as x approaches -3 from the right:

lim (x→-3+) (1/(x+3)) = ∞

Therefore, the point P is at x = 2 (the closest value to -3 on the curve) and y = 1/(2+3) = 1/5. So the coordinates of P are (2,5).

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