the area of a floor is given as y2+ 4y-5 square feet. if the width of room is (y-1), what is the length?

Using equations, the time for the main engine 14.4 seconds and 21.6 seconds for the auxiliary engine

Let's call the time each engine takes to consume its allotted fuel supply as "t₁" for the main engine and "t₂" for the auxiliary engine.

From the first piece of information, we know:

t₁ = (2/3)t₂

From the second piece of information, we know that the combined fuel consumption time for both engines is 36 seconds:

t₁ + t₂ = 36

Now we can substitute the first equation into the second:

t₁ + (2/3)t₂ = 36

Combining like terms:

t₂ = 21.6

Finally, substituting t₂ back into the first equation:

t₁ = (2/3)(21.6) = 14.4

So the main engine alone could be fired for 14.4 seconds and the auxiliary engine alone could be fired for 21.6 seconds.

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Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.

We have,

The profit function is given by:

P(x,y) = 3x + 2y

The constraints are:

40x + 25y ≤ 360 (time constraint)

x + y ≤ 12 (item constraint)

x, y ≥ 0 (non-negative constraint)

To find the vertices, we need to solve the system of equations for each pair of intersecting lines. The vertices are the points where the lines intersect.

40x + 25y = 360

x + y = 12

Solving this system of equations, we get:

x = 6, y = 6 (vertex 1)

x = 9, y = 3.6 (vertex 2)

x = 0, y = 12 (vertex 3)

Now, we evaluate each vertex in the profit function:

P(6,6) = 3(6) + 2(6) = 24

P(9,3.6) = 3(9) + 2(3.6) = 30.6

P(0,12) = 3(0) + 2(12) = 24

Now,

Vertex 2 yields a maximum profit of $30.60.

Therefore,

Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.

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Answer:

1. (6,3)

2. x = 850, y = 150

Step-by-step explanation:

1. 3x-5y=3

4x-15y=-21

-9x +15y=-3 (multiply by -3)

4x-15y=-21

-5x=-30

x = 6

3(6)-5y=3

18-5y=3

-5y= -15

y= 3

so, x = 6, y = 3

2.

let x be regular

let y be reserved

x+y=1000

x= 5, y= 5+2=7 ("2 dollar more")

5x+7y=5300

x+y=1000

use the elimination method

x=850, y=150

so, the regular tickets were 850 and reserved tickets were 150 sold.

The expressions for the width, W, and area, A, of the rectangle in terms of L are:

The expression for the perimeter of a rectangle is given as:

P = 2(L + W)

where L is its length and W its width

a. Given that the perimeter of the rectangle is 13 feet, then;

13 = 2(L + W)

divide through by 2

\(\frac{13}{2}\) = L + W

So that;

W = \(\frac{13}{2}\) - L

The required formula for the width as a function of L is: W = \(\frac{13}{2}\) - L

b. Area of a rectangle can be expressed as;

A = L * W

substitute the expression for width in that of area to have

A = L * ( \(\frac{13}{2}\) - L)

  = \(\frac{13}{2}\)L - \(L^{2}\)

A = \(\frac{13L - L^{2} }{2}\)

The expression for the area A is: A = \(\frac{13L - L^{2} }{2}\)

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The number of regular cones sold on Wednesday is 60, while the number of deluxe ones sold is 26.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of regular cones sold be x, and the number of Deluxe cones sold be y. Therefore, total number of cones sold can be written as,

x + y = 86

x = 86 - y

Now, the total money collected can be written as,

5x + 9y = 534

5(86 - y) + 9y = 534

430 - 5y + 9y = 534

4y = 104

y = 26

substitute the value of y in the first equation,

x = 86 - 26

x = 60

Hence, the number of regular cones sold on Wednesday is 60, while the number of deluxe ones sold is 26.

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So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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Check the picture below.

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Answer: The awnser is 48

Step-by-step explanation: I took the quiz

6.03 Quiz: Use Theoretical Probability to Predict

It is expected to take 48 spins for a multiple of 5 to be spun 8 times.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since there are 12 sectors, the probability of landing on a multiple of 5 is 2/12 or 1/6.

The probability of not landing on a multiple of 5 is 5/6.

We can use the geometric distribution formula to find the expected number of spins:

E(X) = 1/p, where p is the probability of success.

As per the question, the probability of success is 1/6.

Therefore, E(X) = 1/(1/6) = 6.

We need to spin a multiple of 5 8 times, so we multiply the expected number of spins by 8:

6 x 8 = 48.

Therefore, we can expect to spin a multiple of 5-8 times after 48 spins.

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Answer:

y = -6x + 8

Step-by-step explanation:

\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}

I don't know why it came out like this

Answer:

  2

Step-by-step explanation:

You want to know the mode of a dot plot that could be represented as ...

  1 | x x

  2 | x x x x x

  3 | x x x

  4 | x x x x

  5 | x x

The mode is the data element that appears most often in the data set.

The 5 xs above the 2 is the largest number of xs that appear anywhere, so 2 is the mode.

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

a.)Q' = -kQ + r

b.)Q = \(\frac{r}{k} [ 1 - e^{-kt} ]\)

c.) Limiting long run value of Q = \(\frac{r}{k}\)

Step-by-step explanation:

a.)

The rate of change is directly proportional to the quantity, Q

⇒\(\frac{dQ}{dt}\) ∝ Q

⇒\(\frac{dQ}{dt}\) = -kQ ( because it is decreasing )

Also given, quantity is increasing with a constant rate r

⇒\(\frac{dQ}{dt}\) = -kQ + r

⇒Q' = -kQ + r

b.)

As we have

\(\frac{dQ}{dt}\) = -kQ + r

⇒\(\frac{dQ}{-kQ + r}\) = dt

⇒∫\(\frac{dQ}{-kQ + r}\) = ∫dt

⇒-\(\frac{1}{k}log(-kQ + r) = t + C\)

⇒log(-kQ + r) = -kt -kC

Taking exponential both side, we get

⇒-kQ + r = \(e^{-kt +A}\)

⇒-kQ = -r + \(e^{-kt +A}\)

⇒Q = \(\frac{r}{k}\) - \(\frac{1}{k}\)\(e^{-kt +A}\)

⇒Q = \(\frac{r}{k}\) - \(\frac{1}{k}\)\(e^{-kt}.e^{A}\)

⇒Q = \(\frac{r}{k}\) - \(\frac{1}{k}\)\(Be^{-kt}\)      .......(1)

Now,

At t = 0, Q = 0

0 = \(\frac{r}{k}\) - \(\frac{1}{k}\)B

⇒\(\frac{1}{k}B = \frac{r}{k}\)

⇒B = r

∴ equation (1) becomes

Q = \(\frac{r}{k}\) - \(\frac{r}{k}\)\(e^{-kt}\)

⇒Q = \(\frac{r}{k} [ 1 - e^{-kt} ]\)

c.)

for limiting long run value of Q

\(\lim_{n \to \infty} Q = \lim_{n \to \infty}\)   \(\frac{r}{k} [ 1 - e^{-kt} ]\)

               =  \(\frac{r}{k}\)\(\lim_{n \to \infty} [ 1 - e^{-kt} ]= \frac{r}{k} [ 1 - e^{\infty} ] = \frac{r}{k}[ 1-0]\)

               = \(\frac{r}{k}\)

⇒Limiting long run value of Q = \(\frac{r}{k}\)

Q' = -kQ + r

Q = r/k (1- \(\rm e^{-kt}\))

The limiting long-run value of Q = \(\rm \frac{r}{k}\)

A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with a constant of proportionality k > 0.

The differential equation is an equation that contains the derivative of the unknown function.

a) It is given that the rate of change is directly proportional to the quantity Q

\(\rm \frac{dQ}{dt}\) ∝ Q

\(\rm \frac{dQ}{dt}\) = -kQ

So, Q' = -kQ + r

where quantity Q is increasing with constant rate r and k is unknown constant.

b) Q' = -kQ + r

\(\rm \frac{dQ}{dt}\) = -kQ + r

\(\rm \frac{dQ}{-kQ+r}=dt\\\)

\(\int\limits {\rm \frac{dQ}{-kQ+r} = \int\limits dt\)

log(-kQ + r) = -kt -kC

by taking exponential both side, we get

-kQ + r = \(e^{-kt+A}\)

-kQ = -r + \(e^{-kt+A}\)

-Q /k= -r/k + \(e^{-kt+A}\)/k

Q = -r/k -\(\rm \frac{1}{k}Be^{-kt}\)

At t = 0, Q = 0

\(\rm \frac{1}{k} B=\frac{r}{k}\)

B = r

by substituting the value in the above equation

Q = r/k (1- \(\rm e^{-kt}\))

c) The limiting long-run value of Q

\(\rm \lim_{n \to \infty} Q= \lim_{n \to \infty} \frac{r}{k} [1-e^{-kt} ]\\\rm= \frac{r}{k}\lim_{n \to \infty} [1-e^{-kt} ]\\\rm =\frac{r}{k}[1-0]\\\rm=\frac{r}{k}\)

The value Q =\(\rm \frac{r}{k}\)

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Answer:

Since on July 9, Mifflin Company receives a $ 10,200, 90-day, 6% note from customer Payton Summers as payment on account, to determine what entry should be made on July 9 to record receipt of the note the following calculation must be performed :

90 days = 3 months

6/12 x 3 = 1.5%

10,200 x 1,015 = 10,353

Therefore, a debt cancellation for $ 10,200 must be made in the company's accounting records, plus an interest generation for $ 153, which will be justified by the cash income of $ 10,353.

Answer:

In the picture attached, the question is shown.

a) Applying Pythagorean theorem to triangle ABC, and solving for AC:

CB² + BA² = AC²

5² + 12² = AC²

√169 = AC

13 cm = AC

b) Applying Pythagorean theorem to triangle ACD, and solving for AD:

CD² + AC² = AD²

5² + 13² = AD²

√194 = AD

13.9 cm = AD

Step-by-step explanation:

Answer:

x1 = y1 - a*y2 + (a*c - b)*y3

x2 = y2 - c*y3

x3 = y3

Step-by-step explanation:

Here we have the system:

x1 + a*x2 + b*x3 = y1

x2 + c*x3 = y2

x3 = y3

Where the variables y1, y2, and y3 are known (a, b and c are also known).

The first step is to isolate one of the variables in one of the equations, we can see that in the third equation we have x3 already isolated, so now we can just replace it on the other two equations to get:

x1 + a*x2 + b*(y3) = y1

x2 + c*(y3) = y2

Now we again want to isolate one of the variables in one of the equations, i will isolate x2 in the second equation to get:

x2 = y2 - c*y3

Now we can replace this on the other equation to get:

x1 + a*(y2 - c*y3) + b*y3 = y1

Now we canw write x1 in terms of the known variables:

x1 = y1 - a*y2 + (a*c - b)*y3

And in the process we also found that:

x3 = y3

x2 = y2 - c*y3

Then the solutions are:

x1 = y1 - a*y2 + (a*c - b)*y3

x2 = y2 - c*y3

x3 = y3

Answer:

Slope:  1/4

y-intercept: -6

Step-by-step explanation:

The answer is (0, -6)

Answer:

but i think is 2x

Step-by-step explanation:

hecause 2x

4x divided by 2x=2x

Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

Answer:

The area is 1/2 times the radius times the circumference.

Step-by-step explanation:

got it correct on the test! hope this helps you out!

Answer:

I hope this helps

Step-by-step explanation:

Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

ANSWER= the remaining piece of rope is 48 feet 9 inch long.

Answer:

Step-by-step explanation:

-4x-3=y

Answer:

B. What was the highest temperature this month?

Step-by-step explanation:

Rory is recording the highest temperature for the duration of the day for month's worth of data.

B. is the easiest one to answer, as you simply will have to look for the greatest number within the set, and that will be the answer.

A. is too broad, and does not imply that only the "high temperature" is needed, rather just a leveled temperature within day in that month.

C. is the opposite of what Rory had recorded, and without data, he cannot answer it.

D. is answerable as well, but, again, the only temperature recorded is the high temperature. Temperature can fluctuate depending on the time of the day, and can be in the 50s one hour and the 90s in another.

~

The quotient of 550six and 50six​ is obtained by the calculation to be   11 six

We know that the result that we obtain after we have carried out a division operation is called a quotient. In this case, we have been required to carry out the operation of division in base six.

We could start by converting the both values to base 10 as follows;

(5 * 6^2) + (5 * 6^1) + (0 * 6^0) = 180 + 30 + 0 = 210 ten

(5 * 6^1) + (0 * 6^0) = 30 + 0 = 30 ten

Then we carry out the division in base ten; 210 ten/30 ten = 7 ten

We convert back to base six to obtain 11 six

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So,the value of the 30th percentile of the given data will be =P30=4

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will have a value less than or equal to x in probability theory and statistics.

Using the Cumulative Distribution Function to Calculate Probabilities

F(x) is a cumulative distribution function that calculates the likelihood that the random variable X is smaller than or equal to x:

To get the cumulative probability that X is less than or equal to 1, multiply P(X=0) by P(X = 0) by (P=1):

First, we will determine the value of the cumulative probability P(X<=x):

x         f(x)       P(X<=x)

1       0.02          0.02

2       0.01          0.03

3       0.2          0.23

4       0.17           0.4

5       0.39           0.79

6       0.2           0.99

7 0.01 1

30th percentile will be the x value,

below which less than or equal to 30% of the data falls.

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Answer:

Step-by-step explanation:

\(\frac{9}{15}\)  × 70

\(= \frac{630}{15}\)

= 42

70 - 42 = 28

28 eggs did not hatch.

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