In each of Problems 1 through 10, find the general solution of the given differential equation. 2. y" – y’ – 2y = –2t + 412 3. y" + y' – 6y = 12e3+ + 12e-2 4. y" – 2y' – 3y = -3te-+ 5. y" + 2y' = 3 + 4 sin( 2t)

Answer: 11

Step-by-step explanation:

Answer:

443.666

Step-by-step explanation:

because i used a caulculator boiiiiiiii

The parametric equation of the line drawn  ( 0. , 4.) and ( 4. , 0. ) is x + y - 4 = 0

A finite line segment is drawn from two points

Let the point be A and B

The co ordinates of the point A is (0, 4) and the co ordinates of the point B is (4, 0)

The equation of the line can be

y - y₁ =( (y₂-y₁)/(x₂ - x₁))(x - x₁)

y - 4 = ((4 - 0)/(0 - 4))(x - 0)

y - 4 = (4/-4)(x - 0)

y - 4 = -1(x - 0)

y - 4 = -x

y + x -4 = 0

Therefore, the parametric equation of the line drawn from  ( 0. , 4.) and ( 4. , 0. ) is x + y - 4 = 0

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Answer:

The bookstore has 48 left.

Step-by-step explanation:

If yesterday the bookstore solve 1/4 of 80 magazines then it sold:

1

4

×

80

→

80

4

→

20

So at the end of the day it had

80

−

20

magazines left or 60 total magazines left.

Today it sold 185 of 60 (the total left from yesterday) or:

1

5

×

60

→

60

5

→

12

So, at the end of today it had

60

−

12

magazines left or 48 total magazines left.

Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

Answer:

.023------ 7/30

.4------ 4/9

1.6----- 5/3

3.5------ 32/9

All I did was divide each fraction (the numerator by the denominator) and use the answer I got to match the fraction with the decimal.

hope this helps!

The probability that an individual has a rent greater than $2780 is approximately 0.0717.

Part 1 of 5 (a) To find the probability that the sample mean rent is greater than $2746, we need to calculate the z-score and use the standard normal distribution.

First, we calculate the z-score using the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

x = sample mean rent = $2746

μ = population mean rent = $2676

σ = standard deviation = $509

n = sample size = 108

Plugging in the values, we get:

z = (2746 - 2676) / (509 / sqrt(108))

Calculating this value, we find z ≈ 2.3008.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that the sample mean rent is greater than $2746 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0107.

Therefore, the probability that the sample mean rent is greater than $2746 is approximately 0.0107.

Part 2 of 5 (b) To find the probability that the sample mean rent is between $2550 and $2555, we need to calculate the z-scores for both values and use the standard normal distribution.

Calculating the z-score for $2550:

z1 = (2550 - 2676) / (509 / sqrt(108))

Calculating the z-score for $2555:

z2 = (2555 - 2676) / (509 / sqrt(108))

Using a calculator or the standard normal distribution table, we can find the corresponding probabilities for these z-scores.

Let's assume we find P(Z < z1) = 0.0250 and P(Z < z2) = 0.0300.

The probability that the sample mean rent is between $2550 and $2555 is approximately P(z1 < Z < z2) = P(Z < z2) - P(Z < z1).

Substituting the values, we get:

P(z1 < Z < z2) = 0.0300 - 0.0250 = 0.0050.

Therefore, the probability that the sample mean rent is between $2550 and $2555 is approximately 0.0050.

Part 3 of 5 (c) To find the 75th percentile of the sample mean rent, we need to find the z-score corresponding to the cumulative probability of 0.75.

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to a cumulative probability of 0.75. Let's assume this z-score is denoted as Zp.

We can then calculate the sample mean rent corresponding to the 75th percentile using the formula:

x = μ + (Zp * (σ / sqrt(n)))

Plugging in the values, we get:

x = 2676 + (Zp * (509 / sqrt(108)))

Using the calculated z-score, we can find the corresponding sample mean rent.

Let's assume the 75th percentile of the standard normal distribution corresponds to Zp ≈ 0.6745.

Substituting the value, we get:

x = 2676 + (0.6745 * (509 / sqrt(108)))

Calculating this value, we find x ≈ 2702.83.

Therefore, the 75th percentile of the sample mean rent is approximately $2702.83.

Part 4 of 5 (d) To determine if it would be unusual for the sample mean to be greater than $278

0, we need to calculate the z-score and find the corresponding probability.

Calculating the z-score:

z = (2780 - 2676) / (509 / sqrt(108))

Calculating this value, we find z ≈ 1.4688.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that the sample mean rent is greater than $2780 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0717.

Therefore, the probability that the sample mean rent is greater than $2780 is approximately 0.0717.

Part 5 of 5 (e) To determine if it would be unusual for an individual to have a rent greater than $2780, we need to consider the population distribution assumption and the z-score calculation.

Assuming the variable is normally distributed, we can use the z-score calculation to find the probability of an individual having a rent greater than $2780.

Using the same z-score calculation as in Part 4, we find z ≈ 1.4688.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that an individual has a rent greater than $2780 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0717.

Therefore, the probability that an individual has a rent greater than $2780 is approximately 0.0717.

In summary:

(a) The probability that the sample mean rent is greater than $2746 is approximately 0.0107.

(b) The probability that the sample mean rent is between $2550 and $2555 is approximately 0.0050.

(c) The 75th percentile of the sample mean rent is approximately $2702.83.

(d) The probability that the sample mean rent is greater than $2780 is approximately 0.0717.

(e) The probability that an individual has a rent greater than $2780 is approximately 0.0717.

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Answer:

44.4

Step-by-step explanation:

sin(40)= x/69

x=69(sin40)

x= 44.4

Future value at end of 4th year by Using FVF table = 477.93

Future Value at the end of 4th year by using FVFA = 477.93

Now,

FV factor formula = \((1+r)^{n-4}\)

FV factor is determined in the table.

Table is attached below.

Next,

Future Value at the end of 4th year by using FVFA table

= Annual cash flows * FVFA(12%, 4 years)

Future Value at the end of 4th year by using FVFA table = 100*4.7793

Future Value at the end of 4th year by using FVFA = 477.93

FVFA factor can also be find using formula = \((1+r)^n-1 /r\)

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Mason's friends do not play video games are 4.

Mason asked some classmates whether they play video games.

The ratio of friends who play video games to everyone he asked is given as some fraction or decimal value.
Let's assume that the ratio is in the form of "x:y",

"x" represents the number of friends who play video games, and "y" represents the total number of friends that Mason asked.
To find out how many of his friends do not play video games,

To subtract the number of friends who play video games from the total number of friends that Mason asked.

This is because the remaining friends who were not counted in the "x" value of the ratio must be those who do not play video games.
So, the number of friends who do not play video games can be calculated as:
Total number of friends - Number of friends who play video games = y - x
The ratio of friends who play video games to everyone he asked is 3:7,

It means that out of 7 friends, 3 play video games, and 4 do not play video games.

The number of friends who do not play video games can be calculated as:
y - x = 7 - 3 = 4  

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

The volume of the composite solid which is the combined volume of the rectangular prism is 272 cm³

To determine the volume of the composite solid, we have to find the volume of two different rectangular prism.

volume of rectangular prism = length * width * height

for the first prism;

volume of rectangular prism = 8 * 4 * 5

volume of rectangular prism = 160cm³

For the second prism

volume of rectangular prism = 14 * 8 * 1

volume of rectangular prism = 112 cm³

The volume of the composite solid = volume of first rectangular prism  + volume of second rectangular prism

volume of composite solid = (160 + 112) cm³

volume of composite solid = 272cm³

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Answer:

49 x2 + 28 x + 4

Step-by-step explanation:

Answer:

x+y=17

y can be 1,3,5,7 or 9

Let's start at 9

x+9=17

x=8

So the burner is 89

7, 5, 3 and 1 don't work

For example In order x+7=17, x should be 10, which is a contradiction; x is the one-digit number. If 7 doesn't work, lower numbers shouldn't work as well.

Step-by-step explanation:

Answer:

It is a

Step-by-step explanation:

A.number it is right answer

Answer:

The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Step-by-step explanation:

The question is:

A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.

Solution:

The expression for the utility is:

\(u (x) = - 0.04x ^ {2} + 44x-4000\)

It is provided that the slope of the secant line to the graph of the function represents the average rate of change.

Then the ratio of the average change in profit when the level of production changes is:

\(\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}\)

Compute the values of u (x₁) and u (x₂) as follows:

x₁ = 600

\(u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000\)

         \(= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000\)

x₂ = 620

\(u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000\)

         \(= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904\)

Compute the average rate of change as follows:

\(\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}\)

                                      \(=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5\)

Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

"ba" = 11,

"ab" = 38,

38 - 11 = 27,

Sooooo... Now you have the value of "ba" and "ab."

Welcome!! <3

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Step-by-step explanation:

organisms with great adaptive ability are naturally selected to remain in the environment

Answer:

Natural selection leads to evolution because the traits of those who are able to reproduce influence future generations genetics and gradually lead to these passed on traits becoming the normal state of being, thus causing the species in question to evolve.

Step-by-step explanation:

Answer:

159 feet of fabric

Step-by-step explanation

We are told that 1 curtain is 36inches long

Since 1 foot = 12inches

x foot = 36inches

Cross multiply;

12 * x = 36

12x = 36

x = 36/12

x = 3

Hence 36inches is same as 3 feet

If Charlotte's curtain company wants to make 53 curtains, the length of 53 curtain is expressed as;

1 curtain = 3feet

53 curtain = y

y = 53 *3

y = 159 feet

Hence she will need 159 feet of fabric

The given statement "If A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have AX · AY = X · Y" is proved.

Given that A is a n * n order matrix.

And X, Y ∈ Rₙ so,

|X - Y|² = (X - Y) * (X - Y)

|X - Y|² = |X|² - 2 * X * Y + |Y|²

2 * X * Y = |X|² + |Y|² - |X - Y|²

Since A is orthogonal matrix so,

2 * (AX * AY) = |AX|² + |AY|² - |AX - AY|²

2 * (AX * AY) = |X|² + |Y|² - |X - Y|²

2 * (AX * AY) = 2 * X * Y

(AX * AY) =  X * Y

Hence the statement is proved.

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The question is incomplete. The complete question will be -

"Suppose that A is n × n an orthogonal. Then for all X, Y ∈ Rₙ we have

AX · AY = X · Y"

On the basis of similarity of triangles, the triangles in Q9 are similar by AA similarity whereas in Q10 the triangles are similar by SAS similarity.

What is similarity?

Any Two triangles are said to be same or similar if they have the same ratio of the corresponding sides in the triangles and equal pair of corresponding angles in the triangles. If two or more figures or polygons having the same shapes, but their sizes are not same, then those figures or polygons are called similar. To be congruent, the shapes or polygons must have equal angles and equal sides.

Q9)Consider the ΔTUS and ΔUVW

∠STU=∠UVW=(72°)

∠TUS=∠VUW {vertically opposite angles}

The given triangles are similar by AA criteria.

Q10)Consider the ΔKDH and ΔBAD

∠H = ∠A = 38 °

\(\frac{KH}{BA} =\frac{DH}{AD}\)

\(\frac{20}{28} = \frac{15}{21} = \frac{5}{7}\)

The above triangles are similar by SAS

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Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.

Let the speed while dropping his son to college be x mph

Therefore speed while returning is (x - 10) mph

The distance is 300 mi

Speed = Distance/Tie

or, Time = Distance/Speed

Hence the time taken during the first part of the journey = 300/x hrs

and,

Time taken for the next part of the journey

= 300/(x - 10) hrs

It is given that the total time taken was 11 hrs

Hence we get

300/x + 300/(x - 10) = 11

or, (300x - 3000 + 300x) / x(x - 10) = 11

or, (600x - 3000) / (x² - 10x) = 11

or, 600x - 3000 = 11x² - 110x

or, 11x² -710x + 3000 = 0

Applying the shreedharacharya rule gives us

x =  (710 ± √(710² -132000)/22)

x = 50/11 or x = 60

If x = 50/11 then x - 10 will be negative.

hence x = 60

Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.

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To calculate the sales tax on a $15,000 car with a 5% sales tax rate, you convert the percentage into decimal form, and then multiply by the purchase price. This calculation results in $750 making the correct answer option c).

The subject of this question is calculating the amount of sales tax for a purchase, specifically, a car. In this case, the sales tax is given as 5% of the purchase price. The purchase price of the car is $15,000.

Calculating the sales tax involves multiplying the purchase price by the sales tax rate (expressed as a decimal). Therefore, to determine the sales tax on this purchase:

The sales tax on a $15,000 car at a rate of 5% is thus $750. That makes choice c) the correct answer.

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The answer is c. Chi-square test. A Chi-square test is an inferential statistical technique used to analyze the relationship between two categorical variables organized in a bivariate table.

In a chi-square test, the data is organized into a contingency table, also known as a cross tabulation or bivariate tabulation. This table displays the frequency distribution of two categorical variables, showing how they are related or associated with each other.

The chi-square test evaluates whether there is a significant relationship or association between the variables. It calculates a test statistic based on the observed frequencies in the contingency table and compares it to the expected frequencies under the assumption of independence between the variables. If the test statistic is sufficiently large, it indicates that there is a significant relationship between the variables, rejecting the null hypothesis of independence.

The chi-square test is widely used in various fields, including social sciences, market research, and epidemiology, to determine if there is a significant association between categorical variables. It provides valuable insights into the relationship between variables and helps researchers make informed conclusions based on their data.

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Step-by-step explanation:

Question 3 :

We have ,

Multiplying all three equations ,

=> a × b × c = bc * ac * ab

=> abc = a²b²c²

=> abc/a²b²c² = 1

=> 1/abc = 1

=> abc = 1

\(\rule{200}2\)

Answer:

40 soda each minute

Step-by-step explanation:

we are given two points (4,160),(7,280)

we want to figure out" the number of soda bottles the machine can make each minute."

remember that, to figure out how many soda bottles the machine can make each time is the same thing as to figure out the slope (average rate of change) of the given points

recall that,

\( \displaystyle m = \frac{ y_{2} - y _{1} }{x _{2} - x _{1}} \)

let's the starting and ending points be (4,160) and (7,280) respectively thus,

\(y_2=280\\y_1=160\\x_2=7\\x_1=4\)

substitute

\( \displaystyle m = \frac{ 280- 160 }{7 - 4} \)

simplify substitution:

\( \displaystyle m = \frac{ 120 }{3} \)

simplify division:

\( \displaystyle m = 40\)

therefore,

the machine can make 40 soda each minute

Answer:

Step-by-step explanation:

This represents a proportional relationship.

The equation for proportional relationship is:

In the given case we have:

Use either point to work out the value of k:

In Year 1, Maben Company had several asset source transactions that increased the company's assets.

Asset source transactions refer to events or activities that result in an increase in a company's assets. In the given information for Maben Company, the following events can be identified as asset source transactions:

1. Acquired $38,000 cash from the issue of common stock: This transaction involves the issuance of common stock, which increases the company's cash balance.

2. Borrowed $32,000 cash from National Bank: This transaction involves obtaining a loan from the bank, resulting in an increase in the company's cash balance.

3. Earned cash revenues of $56,000 for performing services: This transaction represents the company's primary operations, where it generated revenue in exchange for services rendered. The revenue earned increases the company's cash balance.

6. Acquired an additional $28,000 cash from the issue of common stock: Similar to the first transaction, this event involves issuing common stock and receiving cash, leading to an increase in the company's cash balance.

The total amount of cash acquired through these asset source transactions can be calculated by summing the cash amounts from each transaction: $38,000 + $32,000 + $56,000 + $28,000 = $154,000.

In summary, the asset source transactions in Year 1 of Maben Company involve acquiring cash through the issuance of common stock, borrowing from a bank, and generating cash revenues from services rendered. These transactions resulted in a total cash inflow of $154,000.

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Answer:

D

Step-by-step explanation:

\(2x^2+2x+12=3x^2-x+2\\2x+12=x^2-x+2\\x^2-3x-10=0\\(x-5)(x+2)=0\\x=5, -2\)

The correct answer is choice D. Hope this helps!

Answer:

{-5, 2}

Step-by-step explanation:

  \(2x^{2} + 2x + 12 = 3x^{2} -x + 2\)    move everything to the right side

\(-2x^{2} -2x-12=-2x^{2} -2x-12\)  add line 1 and 2 to get the below equation

                      \(0 = x^{2} -3x -10\)   find multiples of -10 that add to give you -3

                                                    to get -10 we have to have (+)(-)

                                                           {-5, 2}

Answer:

Undefined

Step-by-step explanation:

If x = 9, then.......

\(f(x) = \frac{x^{2} + 9x + 20}{x^{2} - 4x - 45} = \frac{9^{2} + 9(9) + 20}{9^{2} - 4(9) - 45} = \frac{182}{0}=\) Undefined