1 al - 0 10 1 1 a. Write the linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix. - 5x + 4y + 4z = 3 - 5x - 4y + 4z =

In part A, the problem involves a tank containing water with dissolved salt, where brine is continuously added and removed. By considering the rate of salt entering and leaving the tank, we can determine the amount of salt in the tank after 3 hours.

In part B, the problem asks to solve a second-order linear differential equation using power series. By assuming a power series solution and substituting it into the given equation, we can determine the coefficients of the power series and find the solution.

A. To find the amount of salt in the tank after 3 hours, we consider the rate of salt entering and leaving the tank. Since 5 gallons of brine, each containing 31 pounds of salt, enter the tank per minute, the rate of salt entering the tank is 5 * 31 = 155 pounds per minute. The rate of salt leaving the tank is the same since the mixture is kept uniform by stirring. Therefore, the net rate of salt change in the tank is 155 - 0 = 155 pounds per minute. To find the amount of salt after 3 hours (180 minutes), we multiply the net rate of salt change (155 pounds/minute) by the time in minutes (180 minutes): 155 * 180 = 27900 pounds. Hence, the amount of salt in the tank after 3 hours is 27900 pounds.

B. To solve the differential equation y" - xy' - xy = 0 using power series, we assume a power series solution of the form y(x) = ∑(n=0 to ∞) a_n * x^n. We substitute this series into the differential equation and equate coefficients of like powers of x to obtain a recurrence relation for the coefficients a_n. By differentiating y(x) twice and substituting it into the differential equation, we can collect terms with the same powers of x and solve for the coefficients a_n. The recurrence relation will involve the coefficients a_n, a_(n-1), and a_(n-2).

By solving the recurrence relation, we can find the values of the coefficients a_n in terms of the initial conditions or known coefficients. The power series solution y(x) will be the sum of the terms with the determined coefficients. The power series solution allows us to find the solution to the given differential equation in terms of an infinite series, providing a more general and flexible form of the solution compared to specific analytic functions.

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Answer:

0.59 A

Step-by-step explanation:

The current in a certain resistor is 0.50 A

The potential difference is 110v

The operating potential is 130v

The current in the same resistor can be calculated as follows

= 110/0.50

= 220

= 130/220

= 0.59

Hence the current is 0.59 A

Answer:

n=-12r + 75, r

Step-by-step explanation:

Answer:

N=63

.....................................

Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

In the lighting industry, when selling to commercial clients, I would ask about their current lighting setup, any issues they have faced, the impact on productivity, and the potential benefits of upgrading to modern lighting solutions.



Situation:What kind of lighting setup does your commercial space currently have? Are you satisfied with its performance and energy efficiency?

Problem:Have you noticed any specific issues or challenges with your current lighting system? Are there any areas that lack sufficient illumination or require frequent maintenance?

Implication:How does inadequate lighting impact the productivity and comfort of your employees? Have you considered the potential cost savings and environmental benefits of upgrading to more energy-efficient lighting solutions?

Need-payoff:Can you envision the positive impact of a modern lighting system that offers improved illumination, reduces energy consumption, and requires minimal maintenance? How would your employees and customers benefit from a more well-lit and aesthetically pleasing environment?

Therefore, In the lighting industry, when selling to commercial clients, I would ask about their current lighting setup, any issues they have faced, the impact on productivity, and the potential benefits of upgrading to modern lighting solutions.

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Answer:

31° , 62° , 113° , 154°

Step-by-step explanation:

sum the 4 angles and equate to 360

y + 2y + 3y + 20 + 4y + 30 = 360 , that is

10y + 50 = 360 ( subtract 50 from both sides )

10y = 310 ( divide both sides by 10 )

y = 31

2y = 2(31) = 62

3y + 20 = 3(31) + 20 = 93 + 20 = 113

4y + 30 = 4(31) + 30 = 124 + 30 = 154

the 4 angles are 31° , 62° , 113° , 154°

Answer:

it is 4/3 or 1.333333...

Step-by-step explanation:

make it braintliest please

Answer:

a/4-5/6=-1/2

or, 3a-10 /12 = -1/2. ( putting the factor)

or, 6a-20 =-12 (cross multiplication)

or, 6a= -12+20

or, a=8/6

or, a = 1.33 ( 4/3)

Answer:

565.7 cubic units

Step-by-step explanation:

Volume of cylinder=2πrh

                               =2x(22/7)(10)(9)

                               =180x(22/7)

                               =565.7

1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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The median would be the best representation of the typical value or behavior of the data set for "Ages of college students".

The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The statistical median is the number in the midpoint of a series of numbers. To get the median, sort the numbers by size; the number in the center is the median. The term median is derived from the Latin word medius, which also meaning middle. A number in the center of a list is known as the median in mathematics.

Here,

The median would be the best depiction of the data set's usual value or behavior for "Ages of college students".

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Answer:

3,31

Step-by-step explanation:

i dont got steps for this but i think thats the right answer

Answer: 670

Step-by-step explanation: just subtract

The value of n/p is 8.

What is quadratic equation?

A quadratic equation in algebra is any equation that can be written in standard form as where x is an unknown and where a, b, and c denote known numbers, where a ≠ 0.

Let, for x^2 + mx + n = 0

⇒ x = 2α or 2β

From the given condition,

for x^2 + mx + n = 0 ⇒ x = α or x = β

Then,

2(α + β) = -m           ..(1)

4αβ = n                    ..(2)

and α + β = -p         ..(3)

αβ = m                     ..(4)

From equation (1) and (3),

-m/2 = -p

⇒ p = m/2

and from equation (2) and (4),

n/4 = m

⇒ n = 4m

Therefore,

n/p = 4m / (m/2) = 4 x 2 = 8

Hence, n/p = 8.

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Answer:

-9 and +4 are the factors

Step-by-step explanation:

-9 times +4 is -36 and if you add +4 to -9, you get -5.

After this your function will look like this:

\(x^2-9x+4x-36\)

and then:

\(x(x-9)+4(x-9)\)

so the answer is:

\((x-9)(x+4)\)

If  E and F are two events and that P(E)=0.3 and P(FIE)=0.6 then P(E and F) = 0.18

To find the probability of two events occurring together, we use the formula:

Probability of (E and F) = Probability of (F given E) multiplied by Probability of (E).

We are given P(E) as 0.3 and P(F given E) as 0.6. Substituting these values in the formula, we get the answer as 0.18. Hence, the probability of events E and F occurring together is 0.18.

P(E and F)= P(F|E) * P(E)

Given that P(E)=0.3 and P(F|E)=0.6

Therefore, P(E and F)= 0.6 * 0.3 = 0.18

Thus, the probability of both events E and F occurring is 0.18.

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D. None of these, as neither option B nor option C can be obtained using the Law of Detachment.

The Law of Detachment states that if a conditional statement "if p, then q" is true and p is true, then q must also be true.

Analyzing the given options:

A. The conclusion "There is no school" can be obtained by applying the Law of Detachment to the given information, as it matches the format of the law: "If today is Saturday (p), then there is no school (q)." Since today is Saturday (p), the conclusion that "There is no school" (q) can be derived using the Law of Detachment.

B. The conclusion "He is able to buy a new set of headphones" is not directly obtained by using the Law of Detachment. It involves an additional conditional statement and is not in the form of the given "if p, then q" structure.

C. The conclusion "George lives in both Brick and Ocean County" cannot be derived using the Law of Detachment. It is not in the form of a conditional statement, and there is no given information that connects George's residence to the conditional statement provided. Therefore, D is the right answer. None of them are possible utilizing the Law of Detachment, as neither option B nor option C can be obtained. Therefore, Option D is correct.

The question was incomplete. find the full content below:

Which of the following conclusions is true AND obtained by using the Law of Detachment

A. If today is Saturday, then there is no school.

Today is Saturday.

There is no school.

B. If you work 8 hours, then you'll earn $100.

If you earn $100, you'll be able to buy a new set of headphones.

Jonathan works 8 hours.

He is able to buy a new set of headphones.

C. If a person lives in Long Beach Island, then they live in Ocean County.

Brick is in Ocean County.

George lives in both Brick and Ocean County

D. None of these.

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The statement that is true about what D’Neese said is (d) D’Neese is incorrect because a^-n = a/-n

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation statement is given as

1/10^5 is equivalent to 10^5

The above statement can be rewritten in another way

So, we have the following equation

1/10^5 = 10^5

As a general rule of indices, we have the following exponent rule

So, we have the following equation

1/a^n = a^-n

This means that the equation statement is false

This is so because

1/10^5 is not equivalent to 10^5, instead 1/10^5 is equivalent to 10^-5

Hence, the true option about the statement is (d)

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The size of the monthly payment is $232.32.

To calculate the size of the monthly payment, we can use the formula for the monthly payment of a loan:

Monthly Payment = (Principal × Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

First, let's calculate the principal, which is the remaining balance after the down payment:

Principal = Purchase Price - Down Payment

Principal = $20600 - (16% of $20600)

Principal = $20600 - ($20600 × 0.16)

Principal = $20600 - $3296

Principal = $17304

Next, let's calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

Monthly Interest Rate = 3.1% / 12

Monthly Interest Rate = 0.031 / 12

Monthly Interest Rate = 0.0025833 (rounded to 7 decimal places)

Now, let's calculate the number of payments:

Number of Payments = Number of Years × 12

Number of Payments = 7 years × 12

Number of Payments = 84

Finally, we can substitute the values into the formula to find the monthly payment:

Monthly Payment = ($17304 × 0.0025833) / (1 - (1 + 0.0025833)^(-84))

Monthly Payment = $44.71 / (1 - 0.4913)

Monthly Payment = $44.71 / 0.5087

Monthly Payment = $87.90 (rounded to 2 decimal places)

Therefore, the size of the monthly payment is $87.90.

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Answer:

189

Step-by-step explanation:

0.54*350=189

(can I get brainliest please)

The value of z if the area to the left of z is 0.9082 will be 1.2816.

The area to the left of a standard normal random variable Z is given by the cumulative distribution function (CDF) of the standard normal distribution. If the area to the left of Z is 0.9082, this means that P(Z <= z) = 0.9082. To find the value of z, we can use a standard normal table or a calculator that can compute the inverse cumulative distribution function (ICDF) of the standard normal distribution, often denoted as "norminv" or "z^-1". In this case, we would find that z = 1.2816, as P(Z <= 1.2816) = 0.9082.

The value of z in this case is 1.2816, as we found that the area to the left of z is 0.9082, which means P(Z <= z) = 0.9082. This value can be found by using a standard normal table or a calculator that can compute the inverse cumulative distribution function (ICDF) of the standard normal distribution.

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this is not a fair method, as we found at least two different probabilities.

We will say that this is a fair method if and only if the probability for each of the 7 friends is exactly the same.

So, each friend selects a number from 1 through 7 and then it repeats, so, this means that the person who selects the number 1 has the possible outcomes:

{1, 8, 15, 22, 29, 36, 43, 50}

While the person who gets the number 7, has the possible outcomes:

{7, 14, 21, 28, 35, 42, 49}

Now, notice that the person who got the number 1 has 8 outcomes in which he sits out.

While the person who got the number 7 has 7 outcomes in which he sits out.

So, the person with the number 1 has a larger probability of sitting out than the person with the number 7, thus, this is not a fair method, as we found at least two different probabilities.

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Answer:

-8,-6,-3,7,9,10

The true statements for a concession sale at a sporting event are:

The following statements are true based on the given data:

7/11 of the people who ordered a hamburger ordered French fries. (252 hamburger orders x 7/11 = 162 orders of French fries with hamburger)

4/11 of the people who ordered French fries ordered a hamburger. (468 French fry orders x 4/11 = 168 orders of hamburgers with French fries)

6/7 of the people who ordered a hot dog ordered French fries. (216 hot dog orders x 6/7 = 186 orders of French fries with hot dog)

2/3 of the people who ordered French fries ordered a hot dog. (468 French fry orders x 2/3 = 312 orders of hot dogs with French fries)

3/7 of the people who ordered a hamburger ordered onion rings. (252 hamburger orders x 3/7 = 108 orders of onion rings with hamburger)

1/3 of the people who ordered a hot dog ordered onion rings. (324 hot dog orders x 1/3 = 108 orders of onion rings with hot dog)

4/7 of the people who ordered onion rings ordered a hamburger. (252 onion ring orders x 4/7 = 144 orders of hamburger with onion rings)

1/2 of the people who ordered onion rings ordered a hot dog. (252 onion ring orders x 1/2 = 126 orders of hot dog with onion rings)

The total number of orders for each item can be calculated by adding up the corresponding row or column totals.

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Image transcribed:

Concession sales at a sporting event are monitored, and the data is recorded in the two-way table below. Which of the following statements are true?

| French fries | Onion rings | Total

Hamburger | 252 | 144 | 396

Hot dog | 216 | 108 | 324

Total | 468 | 252 | 720

7/11 of the people who ordered a hamburger ordered French fries.

4/11 of the people who ordered French fries ordered a hamburger.

6/7 of the people who ordered a hot dog ordered French fries.

2/3 of the people who ordered French fries ordered a hot dog.

3/7 of the people who ordered a hamburger ordered onion rings.

1/3 of the people who ordered a hot dog ordered onion rings.

4/7 of the people who ordered onion rings ordered a hamburger.

1/2 of the people who ordered onion rings ordered a hot dog.

Answer: (i) Interval for proportion of underpaid nurses: 0.15 ± 0.0415.

(ii) Interval for difference in proportion: 0.03 ± 0.0641

Step-by-step explanation: Confidence Interval for a representation of the proportion is calculated by:

\(p_{hat}\) ± z.\(\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }\)

(i) \(p_{hat}\) is the proportion, in this case, of underpaid nurses: \(p_{hat}\) = 0.15

Confidence Interval is 90%, so z = 1.645

The interval is:

0.15 ± 1.645.\(\sqrt{\frac{0.15(0.85)}{200} }\)

0.15 ± 1.645*0.0252

0.15 ± 0.0415

Which means that, in 90% of times, the proportion of underpaid nurses wil be between 0.1085 and 0.1915.

(ii) For the difference in proportions:

\(p_{hat_1}-p_{hat_2}\) ± z.\(\sqrt{\frac{p_{hat_1}(1-p_{hat_1})}{n_{1}}+\frac{p_{hat_2}(1-p_{hat_2})}{n_{2}} }\)

The proportion for the second hospital is \(p_{hat_2}\) = 0.12 and, since it is the same confidence interval, z = 1.645.

Calculating:

(0.15-0.12) ± 1.645.\(\sqrt{\frac{0.15(0.85)}{200} + \frac{0.12(0.88)}{120} }\)

0.03 ± 1.645*0.0389

0.03 ± 0.0641

The 90% confidence interval for the difference in proportions of nurses being underpaid is between 0.0341 and 0.0941

a) Binomial probability distribution is the type of probability distribution which used in this case

b) Probability that there will be no red flowered plants in the five offspring is 0.2373.

c) The value of the cumulative probability that there will be less than two red flowered plants is 0.4473.

,Number of trials = 5

Number of success (red flowered plants) =1

a) Type of probability distribution : Binomial probability distribution

b) Probability that there will be no red flowered plants in the five offspring

P(red flower) = 25% = 0.25

Probability of white flower = 1 - P(red flower) = 1 - 0.25 = 0.7

Using binomial probability distribution formula:

P(X=k) = nCk * p^k * q^(n-k)

Where,P(X=k) is the probability of getting k successes in n trials

nCk is the binomial coefficient = n!/ (n-k)!

k!p is the probability of success

q = 1 - p is the probability of failure

In this case, k = 0, n = 5, p = 0.25, q = 0.75P(X=0) = 5C0 * 0.25^0 * 0.75^(5-0)= 1 * 1 * 0.2373= 0.2373

Probability that there will be no red flowered plants in the five offspring is 0.2373.

c) . Cumulative Probability:

There will be less than two red flowered plants

Using binomial probability distribution formula: P(X < 2) = P(X=0) + P(X=1)P(X=0) is already calculated in the part a.

P(X=1) = 5C1 * 0.25^1 * 0.75^(5-1)= 5 * 0.25 * 0.168 = 0.21

P(X < 2) = P(X=0) + P(X=1)= 0.2373 + 0.21= 0.4473

Therefore, cumulative probability that there will be less than two red flowered plants is 0.4473.

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Answer:

9 miles per one half of an hour

Step-by-step explanation:

Step 1:

36 miles ÷ 2 hours

Step 2:

18 miles ÷ 2

Answer:

9 miles

Hope This Helps :)

The statements that are TRUE regarding the box plots are:

A, D, and E.

The box plots are given in the image attached below.

The values displayed by a box plot for a given data are:

Interquartile range = Third Quartile - First Quartile.

Thus, shelter's A median is 21, shelter B's 18.

Interquartile range for shelter A = 28 - 8 = 20

Interquartile range for shelter B = 28 - 10 = 18

Therefore, the statements that are TRUE regarding the box plots are:

A, D, and E.

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By the principle of mathematical induction, the statement is true for all positive integers n.

To prove that n^p−n is always divisible by p, we can use the principle of mathematical induction.

When n = 1, we have 1^p - 1 = 0, which is divisible by p.

Assume that the statement is true for n = k, i.e., k^p - k is divisible by p. Now, we need to prove that the statement is also true for n = k+1, i.e., (k+1)^p - (k+1) is divisible by p.

Expanding (k+1)^p using the binomial theorem, we get:

(k+1)^p = k^p + pk^(p-1) + ... + p(k^2) + p(k) + 1

Subtracting (k+1) from both sides gives:

(k+1)^p - (k+1) = k^p - k + pk^(p-1) + ... + p(k^2) + p(k)

Since k^p - k is divisible by p by the induction hypothesis, and all the other terms on the right-hand side are multiples of p, we can conclude that (k+1)^p - (k+1) is also divisible by p.

Therefore, by the principle of mathematical induction, the statement is true for all positive integers n.

We have proved that n^p−n is always divisible by p for any prime p using induction on n.

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Answer:

D. 27.5

Step-by-step explanation:

The 3rd quartile is the rightmost line on the box which appears between points 25 and 30. This leaves us with 27.5 being the best choice.

It's Linear Equation!!!

A linear equation is an equation whose graph is a straight line.

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The graph of equation is a straight line.

Now,

Since, The graph of equation is a straight line.

We know that;

The graph of a linear equation is always a straight line.

Thus, A linear equation is an equation whose graph is a straight line.

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