how to solve the first order linear differential equation

In response to the given problem, we can state that the fraction sum is a rational fraction.  The numerators of true fractions are smaller than the denominators.

To represent a whole, any number of equal parts or fractions can be utilized. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of an entire. In mathematics, numbers are stated as a ratio of the numerator to the denominator.

They can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator.

A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolize half of a full number or object.

And

[tex]-11/4 + 5/9[/tex]

[tex]-99+20 / 36 = -79/36[/tex]

Therefore,  By fraction, sum is fraction as rational.

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The quadratic equation that represents the parabola is y - 2 = - x².

In this problem we find a table representing a quadratic equation, whose definition can be found by using two points and the vertex form of the parabola equation:

Vertex form

y - k = C · (x - h)²

Where:

First, determine the coordinates of the vertex of the parabola by table:

(h, k) = (0, 2)

Second, find the vertex constant:

C = (y - k) / (x - h)²

C = (1 - 2) / (1 - 0)²

C = - 1

Third, write the equation of the parabola:

y - 2 = - x²

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the unit rate is 6/5 inches per hour, or approximately 1.2 inches per hour.

The unit rate in inches per hour can be found by dividing the amount of rain falling per unit of time by the corresponding unit of time. In this case, we have 4/5 inches falling every 2/3 hours, so we can find the unit rate by dividing 4/5 by 2/3:

(4/5) / (2/3) = (4/5) X (3/2) = 6/5 inches per hour

So the unit rate is 6/5 inches per hour, or approximately 1.2 inches per hour.

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Answer:

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

20/5 = 12/3 = x/4

x/4 = 4

x = (4)(4) = 16

Answer:16

Step-by-step explanation:multiply 4 by 4

In equilateral triangles, 7.0 mm is the length of each edge of the diamond.

The equilateral triangle's definition?

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.

                                       A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.

V = 0.4783 S³  = 161

   S³   =  161/0.47

       = ∛ 161/0.47

       ≈ 7.0 mm

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The mean of Y is 103 dollars. The standard deviation of X is 64.8 dollars

The mathematical expression that we would have to use i the representation of Y is Y = 60X - 5.

How to solve for the mean of Y

Y = exp(Y)

= 60 * EXP(X) - 5

the expected value of x is 1.8

= 60 * 1.8 - 5

= 103 dollars

then we have to solve for the standard deviation of Y

standard deviation of x = 1.08

= 60 * 1.08

= 64.8 dollars

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Answer:

ABCD forms a rhombus

Step-by-step explanation:

When you graph it out on a graph, the points make a rhombus

Answer:

70

Step-by-step explanation:

Let x be the number of kangaroos adopted last year.

Twice the number adopted last year is 2x.

So, the number adopted this year is 2x - 24.

Equating this to the given number of kangaroos adopted this year, we have:

2x - 24 = 116

Adding 24 to both sides, we get:

2x = 140

Dividing both sides by 2, we get:

x = 70

So, the number of kangaroos adopted last year was 70.

Answer:

  7 feet

Step-by-step explanation:

You want the height of a 6' by 12' cuboid box that has a total surface area of 396 square feet.

The formula for the surface area of a cuboid is ...

  SA = 2(LW +H(L+W))

For the given box, this is ...

  396 = 2(6·12 +H(6+12))

  198 = 72 +18H . . . . . . . . . . divide by 2

  126 = 18H . . . . . . . . . . . subtract 72

  7 = H . . . . . . . . . . . . divide by 18

The height of the box is 7 feet.

Answer: 1024

Step-by-step explanation:

2 x 2 is 4

4 x 2 is 8

8 x 2 is 16

16 x 2 is 32

32 x 2 is 64

64 x 2 is 128

128 x 2 is 256

256 x 2 is 512

512 x 2 is 1024

The set of parametric equations are

[tex]x=\sqrt{t}[/tex]

[tex]y=\sqrt{3+t[/tex]

A parametric equation uses a parameter, which is an independent variable (often represented by the notation t), and dependent variables, which are expressed as continuous functions of the parameter and are independent of other variables.

Using one or more independent variables known as parameters, a parametric equation defines a set of quantities as functions.

Given the equation:

[tex]x= \sqrt[]{y^{2}-3 }[/tex]

Let's find a set of parametric equation for the given equation given the parameter:

[tex]x = \sqrt{t}[/tex]

From the parameter:

[tex]x = \sqrt{t}[/tex]

Now, substitute [tex]\sqrt{t}[/tex] for x in the given equation:

[tex]x=\sqrt{y^2-3} \\\\\sqrt{t} = \sqrt{y^2 - 3} \\\\t=y^2-3\\\\y^2=3+t\\\\y=\sqrt{3+t}[/tex]

Therefore, the set of parametric equations is:

• [tex]x=\sqrt{t}[/tex]

• [tex]y=\sqrt{3+t}[/tex]

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Answer:

24

Step-by-step explanation:

If we convert this problem into "math language", it's basically asking what is 8 divided by 1/3? So, we set this up: [tex]\frac{8}{\frac{1}{3} }[/tex] = 8 * 3 = 24

A residual plot that shows clear patterns or trends in the residuals suggests that the line of best fit is not a good model.

Here are some characteristics of a residual plot that suggest that the line of best fit is a poor model,

The residuals show a clear pattern or trend, such as a curve or a U-shape.

The residuals are not evenly distributed above and below zero.

There are one or more outliers or extreme values that stand out from the rest of the data.

The variability of the residuals changes across the range of the predictor variable.

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Answer:

12 ways

Step-by-step explanation:

the mother and father can either stand at the front/back or back/front respectively (2 ways)

that leaves 3 children in the middle -- there are 3 choices for the first child to go, 2 for the second, and 1 for the third = 3! = 6

6 ways for the children * 2 ways for the parents = 12 ways

The shapes with the same areas are (c) A and B

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Figures A, B and C

For the figures A, B and C to have the same area, the number of boxes on the shapes must be the same

Using the above as a guide, we have the following:

By comparison, we have

A and B = 16 square units

Hence, the shapes A and B have the same area

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Answer:

3/4 hour-72

1 hour- 92

Step-by-step explanation:

3/4-

24 x 3= 72

1-

24 x 4 =92

The correct answer is C. (1, 5) is the ordered pair which is the solution to the system of equations.

A group of two or more equations with the same variables is referred to as a system of equations. The set of values for the variables that make all of the equations in a system of equations true is known as the solution.

The solution to the systems of equations is x = 1 and y = 5.

To solve this system of equations, we can begin by subtracting the two equations to get y - y = -x + 6 - (x + 4).

Simplifying, we get -2x = 2.

Then, dividing both sides of the equation by -2, we get x = -1.

We can now substitute the value of x into either one of the original equations to find the value of y.

If we substitute x = -1 into the first equation, we get y = -1 + 4, which simplifies to y = 3.

Therefore, the solution for this system of equations is x = -1 and y = 3.

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Answer:

I think a is the right answer

The shipping charge of an item on the purchase $56 is $2.52.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The percentage of a number is the value of the number out of 100.

For example, in a class, there are 26 boys and 24 girls. So, the percentage of boys in the class is 26/(26+24) × 100 = 26/50 × 100 = 52%, which means out of 100, 52 are boys.

A company charges  shipping fee = 4.5% of the purchase price for all items,

Cost of an item =$56

So, shipping fee = 4.5% of 56

= 4.5/100 × 56

= 0.045 × 56

= $2.52

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Yes, providing additional information affect responses to a survey question. The difference in the proportion of shoppers who admitted to texting and driving in the two groups is 0.2.

To calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups, we need to first determine the number of shoppers in each group who admitted to texting and driving.

Let's assume that in Group A, 10 shoppers admitted to texting and driving, while in Group B, 5 shoppers admitted to texting and driving.

Then, we can calculate the proportion of shoppers who admitted to texting and driving in each group by dividing the number of shoppers who admitted to texting and driving by the total number of shoppers in each group:

Proportion in Group A = 10/25 = 0.4

Proportion in Group B = 5/25 = 0.2

The difference in proportions is then:

Difference = Proportion in Group A - Proportion in Group B

Difference = 0.4 - 0.2

Difference = 0.2

Therefore, the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B) is 0.2 or 20%.

This suggests that providing additional information about the potential consequences of texting and driving may reduce the proportion of people who admit to engaging in this behavior. However, it's important to note that this study has a small sample size and there may be other factors that influence people's responses to survey questions about texting and driving.

Correct Question :

Does providing additional information affect responses to a survey question? Two statistics students decided to investigate by asking different versions of a question about texting and driving. Fifty mall shoppers were divided into two groups of 25 at random. The first group was asked Version A and the other half were asked Version B. Version A: A lot of people text and drive. Are you one of them? Version B: About 6000 deaths occur per year due to texting and driving. Knowing the potential consequences, do you text and drive? Calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B).

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The area and circumference of each circle are 78.5cm², 31.4cm, 113.04cm², 37.68cm, 28.26cm², 18.84cm and 153.86cm², 43.96cm respectively

Using the formula of area of a circle and circumference of a circle, we can solve for each circle as

a.

The area is given as;

A = πr²

A = 3.14 * 5²

A = 78.5cm²

The circumference = 2πr

C = 2 * 3.14 * 5 = 31.4cm

b

A = πr²

A = 3.14 * 6²

A = 113.04cm²

C = 2πr

C = 2 * 3.14 * 6

C = 37.68cm

c.

A = πr²

A = 3.14 * 3²

A = 28.26cm²

C = 2 * 3.14 * 3

C = 18.84cm

d.

A = πr²

A = 3.14 * 7²

A = 153.86cm²

C = 2πr

C = 2 * 3.14 * 7

C = 43.96cm

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The volume of the rectangular prism will be (4x - 3)(x + 1)( x+2) cubic feet.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

Given that the length, width, and height of the rectangular prism are,

The volume of the rectangular prism will be calculated as,

Volume = Length x width x Height

Volume = (4x - 3)(x + 1)( x+2) cubic feet

Therefore, the polynomial for the volume will be (4x - 3)(x + 1)( x+2) cubic feet.

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The following measures of typical value in a data set would be affected by the error:

Mean: The mean is the sum of all the values divided by the number of values. If one value is significantly different from the rest, it can significantly affect the mean. In this case, the mean would be affected because the value of 5 is much lower than the other values in the data set, which would cause the mean to be lower than it should be.

Median: The median is the middle value in a data set. If the error is low enough, it may not affect the median, but if it is low enough to move the value of 5 to the middle of the data set, the median would be affected.

In conclusion, the mean and median of this data set would be affected by the error of recording the value of 75 as 5.

The mode, mean and median of this data set would be affected by the error of recording the value of 75 as 5.

Given that, a data set represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 suppose that the last value, 75, was mistakenly recorded as 5.

so, here, due to mistake the mode, mean and the median will be affected.

Adding a data point to the set, or taking one away, can affect the mean, median, and mode.

If we add a data point that's above the mean, or take away a data point that's below the mean, then the mean will increase.

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Note that the lenght of segment LN = 55.14 (Option D)

This is arrived at using the Chord Bisector Theorem and the  lengths of the sides of a right-angled triangle.

According to the theorem, the line that goes through the circle's center and is perpendicular to the chord also bisects it.

This means that LK (as per the attached image) is the same as MK.

The Right Angle Postulate also means that:

LX = √[KX² - LK²]

LX = √[29² - 9²]

LX = √(841  81)

LX = √760

LX = 27.57

Since LN = LX *2
LN = 27.57 * 2

LN = 55.14

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The unshaded area is 11.5 times bigger than the shaded area.

The area of the circle is given by:

A_circle = πr^2

where;

n this case, r = 10 cm, so:

A_circle = π(10 cm)^2 = 100π cm^2

The area of the semicircle is given by:

A_semicircle = (1/2)πr^2

where;

In this case, the diameter of the semicircle is 8 cm, so the radius is 4 cm:

A_semicircle = (1/2)π(4 cm)^2 = 8π cm^2

To find the area of the shaded region, we need to subtract the area of the semicircle from the area of the circle:

A_shaded = A_circle - A_semicircle

= 100π cm^2 - 8π cm^2

= 92π cm^2

The unshaded area is the area of the circle minus the area of the shaded region:

A_unshaded = A_circle - A_shaded

= 100π cm^2 - 92π cm^2

= 8π cm^2

So the unshaded area is 8π cm^2 and the shaded area is 92π cm^2.

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Answer:

1

Step-by-step explanation:

1 cubed is 1 so it only makes sense for t=1

The cube root of 1 is 1. So, t = 1.

Part (a)

The LCM of 2 and 3 is 2*3 = 6.

Lars and Rita's schedule aligns every 6 days.

These two went swimming together on June 1st.

6 days later would be June 7th, which is when they swim together again. See the chart in part (d) below.

======================================================

Part (b)

LCM = 3*5 = 15

Add 15 days to the first of June to get 1+15 = 16. See the chart in part (d) below.

======================================================

Part (c)

The LCM of 2, 3, and 5 is 2*3*5 = 30

The trio will swim together every 30 days.

Since there are 7 days in a week, divide 30 over 7 and find the remainder.

30/7 = 4 remainder 2

We don't care about the quotient. All we focus on is the remainder.

A remainder of 2 means that we move 2 days ahead of Friday to land on Sunday. You can use a calendar to confirm that adding 30 days to the starting Friday will get you to Sunday. It doesn't matter what month you are in, so it could be June or any month really.

======================================================

Part (d)

Here's a chart when all three go swimming:

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Lars} & \text{Rita} & \text{Alan}\\\cline{1-3}1 & 1 & 1\\\cline{1-3}3 & 4 & 6\\\cline{1-3}5 & 7 & 11\\\cline{1-3}7 & 10 & 16\\\cline{1-3}9 & 13 & 21\\\cline{1-3}11 & 16 & 26\\\cline{1-3}13 & 19 & 31\\\cline{1-3}15 & 22 & 36\\\cline{1-3}\end{array}[/tex]

Each number refers to a day number in June, with exception to the 36 for Alan. Treat that "36" as 36-30 = 6 days beyond the end of June (aka July 6th).

Each person starts at 1. Lars will involve adding 2 to each item. Rita has +3 to each item. Alan has +5 to each item. That chart shows "15" only in the Lars column.

Answer:

change the 2w value

Step-by-step explanation:

first, check the equation:

14w + 21 = 14w + 20

when subtracting the 14w from both sides you can see that

21 is NOT EQUAL to 20, making the answer NS.

now, reread the question... create a new equation with ONE solution.

to fix this, we need to change the amount of W's, NOT the amount of constant.

let's try out another number in place of 2w

7 ( 3w + 3 ) = 14w + 20

21 w + 21 = 14w + 20

7 w = -1

w = -1/7

so now it is clear. to change the outcome of the equation, try out another value instead of 2w. Maybe try 3w, 3.5w, or maybe even 1w, or 1.5w .

Answer:

change the 2w

Step-by-step explanation:

=> 7 ( 3w + 3 ) = 14w + 20

=> 21 w + 21 = 14w + 20

=> 7 w = -1

=> w = -1/7

So everything is now evident. Change the value of 2w to anything else to alter the equation's result. Try 3w, 3.5w, or even 1w or 1.5w if you can.

Hope it have been helpful.

Answer:

-94.94

Step-by-step explanation:

f(x)=23.2x+2.5

Let x = -4.2

f(4)=23.2(-4.2)+2.5

    =-97.44+2.5

    =-94.94

Answer:

Since x = -4.2, just fill it in the equation and solve:

23.2 * -4.2 + 2.5 =

23.2 * -4.2 = -97.44

-97.44 + 2.5 = -94.94

f(x) = -94.94

Step-by-step explanation:

Hope it helps! =D

Hope it ain't wrong either. If so, I'm sorry.