What goes in the blank box?

Answer:

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.

Step-by-step explanation:

The given initial value problem y(0)=8, solution is [tex]y=\sqrt{64e^x-3x}[/tex]

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y. An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable is referred to as a differential equation in calculus (variables). The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. If y is a dependent variable, f is an unknown function, and x is an independent variable, then y=f(x) is a function.

The given differential equation is,

[tex]2yy'+3=y^2+3x\\\\2y\frac{dy}{dx}=y^2+3x-3\\\\(3-y^2-3x)dx+2ydy=0\\\\compare, Mdx+Ndy=0\\\\M=3-y^2-3x\\\\N=2y[/tex]

The given equation is not exact but if we multiplied by [tex]e^{-x}[/tex]

[tex]The D.E.\\(3-y^2-3x)e^{-x}dx+2ye^{-x}dy=0\\\\then M_y=-2ye^{-x}=N_x\\The G.S,=y^2e^{-x}+3xe^{-x}=c\\\\y(0)=8\\c=64\\hence,\\y=\sqrt{64e^x-3x}[/tex]

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The temperature of the cup if it is left alone for 20 minutes, can be found to be 97 degrees Fahrenheit

To find the tempertature of the cup, the formula would be:

= Beginning temperature x ( 1 - rate of decrease per minute  ) ^ number of minutes

Beginning temperature = 185 degrees fahrenheit

rate of decrease per minute = 3.2% each minute

number of minutes  = 20 minutes

The temperature is:

= 185 x ( 1 - 3 .2 %) ²⁰

= 97 degrees Fahrenheit

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Answer:

B

Step-by-step explanation:

Trust

Answer:

x = 1, y = - 5

Step-by-step explanation:

2x + 2y = - 8 → (1)

- 13x + 7y = - 48 → (2)

multiplying (1) by 7 and (2) by - 2 and adding will eliminate y

14x + 14y = - 56 → (3)

26x - 14y = 96 → (4)

add (3) and (4) term by term to eliminate y

40x + 0 = 40

40x = 40 ( divide both sides by 40 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

2(1) + 2y = - 8

2 + 2y = - 8 ( subtract 2 from both sides )

2y = - 10 ( divide both sides by 2 )

y = - 5

then solution is x = 1, y = - 5

The amount that you would have to pay in federal income tax if you claim 3 allowances would be:  $65.46

To calculate the amount you will pay in federal income tax using the percentage method of withholding, you will need to know the withholding percentage for your gross pay and the number of allowances you are claiming.

If you claim 3 allowances, each allowance is $80.80, and you gross pay for the week is $710, your taxable income is:

$710 - 3*$80.8 = $710 - $242.4 = $467.6

To find the amount of federal income tax you will pay, you will need to use the withholding percentage for your taxable income. You can find this information by consulting the IRS Circular E (Employer's Tax Guide) or by using an online withholding calculator.

If we use the IRS Circular E, we can find that if you are single and claim 3 allowances, the withholding percentage for a taxable income of $467.6 is 14%.

So the amount you will pay in federal income tax is:

$467.6 * 14% = $65.46

Therefore, you will pay $65.46 in federal income tax if you claim 3 allowances, and your gross pay for the week is $710.

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Average speed is determined by dividing the total distance you traveled by the total time,

In order to calculate average velocity, divide the change in position or displacement (x) by the time intervals (t) during which the displacement takes place. Depending on the displacement's sign, the average velocity can either be positive or negative. The SI unit for average speed is meters per second (m/s or ms-1).

Average speed is determined by dividing the total distance you traveled by the total time, whereas average velocity is determined by dividing your displacement, which is a vector pointing from your initial location to your end position, by the whole time.          

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A symmetric matrix is a square matrix that is equal to transpose of itself. If A is a symmetric matrix, then it satisfies the condition: A = AT. (AT is the inverse of A )

A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

Suppose  λ and  μ are 2 distinct values of matrix  A.

For the matrix to be Symmetric,

                 ( Ax,y)=(x,Ay)

 condition needs to be satisfied.

Here, ( x,y) is dot product between vectors  x and  y

                 λ (u,v) = (λu,v)

 where  u,v are eigen vectors for eigen values  λ and  μ

             λ(u,v) = (Au,v)

             λ(u,v) = (u,Av)

             λ(u,v) = μ(u,v)

             λ(u,v) = μ(u,v)

but  λ≠μ

                             ∴ (u,v) = 0.

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The complete question is :

If a matrix is symmetric then show that any two eigenvectors of that matrix corresponding to different eigenvalues are orthogonal. Assume square matrix.

Slope of regression is 0.8710 and at 4 tons top speed of boat is 111.064 mph.

Linear regression is a data analysis technique that predicts the value of unknown data by using another related and known data value. It mathematically models the unknown or dependent variable and the known or independent variable as a linear equation.

Given, In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded.

Solution(a)

Given in the question

Dependent variable is top speed of a boat (in mph) Independent variable is weight of boat (in tons)

from the coefficient table of Enova summary we can write least square regression line as follows

Top speed = 107.58 +0.8710* Weight of boat

Here intercept of regression line = 107.58

Slope of regression line = 0.8710

Solution(b)

if X = 4 tons

than predictive value of the top speed of a boat can be calculated as

Top speed = 107.58 +0.8710 * 4 = 107.58 +3.484 = 111.064 mph predictive value of the top speed of a boat = 111.064 mph if its weigh It is 4 tons.

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Complete question:

Answer:

= 7n − 3 emde n = 1, 2, 3, ...

Answer:

slope = 1/2

Step-by-step explanation:

rise = 3

run = 6

rise/run

3/6 = 1/2

Answer:

The slope is 1/2

Step-by-step explanation:
The slope is rise over run, from point 1 to point 2 the line rises 3.
The run from point 1 to point 2 is 6.

That means that rise over run is 3/6
Simplify this so that it is in the simplest form to get 1/2.

The image shows the rise and the run.

I hope this helps you out :D

The values of variables a to d are

Polynomial 1

This is given as

x² - 8x + 15 = (ax + b)(cx + d)

The factors of 15 that add up to -8 are

-3 and -5

This means that

b = -3 and d = -5

Because the coefficient of x² is 1, then

a = 1 and c = 1

Polynomial 2

This is given as

2x³ - 8x² - 24x = 2x(ax + b)(cx + d)

Divide through by 2x

x² - 4x - 12 = (ax + b)(cx + d)

The factors of -12 that add up to -4 are

2 and -6

This means that

b = 2 and d = -6

Because the coefficient of x² is 1, then

a = 1 and c = 1

Polynomial 3

This is given as

6x² + 14x + 4 = (ax + b)(cx + d)

Factorize

(x + 2)(6x + 2) = (ax + b)(cx + d)

By comparison, we have

a = 1, b = 2. c = 6 and d = 2

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The number of yards of the automobile of length 'x' meters will be 1.10x yeads.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

A meter is about 1 ¹/₁₀ yards.

Convert the mixed fraction number to a decimal number. Then we have

1 meter = 1 ¹/₁₀ yards

1 meter = 1 + ¹/₁₀ yards

1 meter = 11 / 10 yards

1 meter = 1.10 yards

Let the length of the automobile be 'x' meters. Then the number of yards in 'x' meters is given as,

⇒ x × (1.10)

⇒ 1.10x yards

The number of yards of the automobile of length 'x' meters will be 1.10x yeads.

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Answer:

arrange in ascending order

14,15,16,17,18,20,25

there are odd number of terms so

median = (n+1/2) th observation

here n = 7 which is odd

therefore, 7+1/2 th observation

which is 4th observation

ans) 17

The terms mean median, mode, and range describe properties of statistical distributions.

The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.

The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number of possible values can be represented by a continuous random variable. A term is said to have a probability density function when any value can be assigned to it within an uninterrupted interval or span.

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Answer:

Jade will be farther by 0.6 or .6 miles in 3 hours

Step-by-step explanation:

Jade walks at a speed of 3 miles per hour so 3×3=9 miles per hour

Elena walks at a speed of 2.8 miles per hour so 2.8×3=8.4 miles per hour

Next,the question is how much farther will Jade walk after 3 hours so that means 9-8.4 which is 0.6 or .6 in decimals and we read it as six tenths

hope it helps you

Trapezoid PQRS having vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0),

has the length of the midsegment as 11.07 units.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, PQ and RS.

The points for vertices are given as - P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).

Length of sides PQ and RS is given as -

The line segment PQ = √(x2 - x1)² + (y2 - y1)²

PQ = √(0 - 0)² + (4 - 0)²

PQ = √0² + (4)²

PQ = √0 + 16

PQ = √16

PQ = 4 units

The line segment RS = √(x2 - x1)² + (y2 - y1)²

RS = √(12 - 6)² + (0 - 4)²

RS = √(6)² + (-4)²

RS = √36 + 16

RS = √50

RS = 5√2 units

To find the mid segment add the length of PQ and RS.

So, the equation will be -

Midsegment = PQ + RS

Midsegment = 4 + 5√2

Midsegment = 11.07 units

Therefore, the length of midsegment is 11.07 units.

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Answer: 9

Step-by-step explanation: (6+12) / 2 = 9

The initial deposit was $8000 and after 18 years the simple interest earned is $12960. So, the total amount for Melissa in college account is $20,960.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

The amount that was put in college fund for Melissa, P = $8000

The rate at which interest was earned is, R = 9%

The time period after which the account was checked, T = 18 years

The formula for Simple Interest is -

S.I. = (P R T)/100

Substitute the values into the equation -

S.I. = (P R T)/100

S.I. = (8000 × 9 × 18)/100

S.I. = 1296000/100

S.I. = 12960

The amount of interest earned in 18 years is $12960.

The total amount after 18 years will be -

Total Amount = Initial deposit + Interest earned

Total Amount = $8000 + $12960

Total Amount = $20960

Therefore, the total amount after 18 years is $ 20,960.

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When Melissa was born, her parents put $8,000 into a college fund account that earned 9% simple interest. After 18 years, she had $20,960 in the account. How did this happen?

The ways to represent 3+3+3+3+3 with multiplication are:

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, an expression 3+3+3+3+3

To represent this in multiplication terms,

We need to figure out what the expression tells us. So, there are 5 terms all terms have a value of 3.

Thus,

represent a way to show 3+3+3+3+3 with multiplication is either 3*5 or 5*3.

Therefore, The correct ways of representing the expression 3+3+3+3+3 are:

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Answer:

there's ur answer ...........

By Simplify  expression  -9y-10y -2z  this we get - 19y - 2z.

Examples :

-9y-10y -2z

Simplify

-9y - 10y - 2z : -19y - 2z

-9y - 10y - 2z

= - 19y - 2z.

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The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:

C) Translation (x,y) -> (x + 7, y), and reflection over the x-axis.

The glide reflection is a combination of a reflection with a translation.

The vertices of the original triangle are given as follows:

A(-3,-2), B(-6,-5) and C(-1,-4).

The vertices of the reflected triangle are given as follows:

A'(4,2), B'(1,5) and C'(6,4).

The composite rule for these two transformations is given as follows:

(x,y) -> (x + 7, -y).

The transformation y -> -y is a reflection over the x-axis, hence the correct option is given by option C.

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Average rate of change for the first 10 minutes after the soup was placed in the bowl is 200 .

220 +180/2 = 200

average rate of change for the first 10 minutes after the soup was placed in the bowl 200.

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Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E(X)=xP is the formula's notation (x).

f(x) = 4x³,0 < x < 1

Domain of f(x) = 4x³,0 < x < 1 : Solution : 0 < x < 1

Interval notation : (0,1)

Range of 4x³ ,0 < x < 1;

Solution : 0 < f(x) < 4

Interval Notation : (0,4)

Axis interception points of 4x³,0 <x <1.

Asymptotes of 4x³. 0 < x < 1;

Extreme Points of 4x³ . 0<x < 1:

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The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.

To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:

PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:

PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.

P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12

So the probability that X is one more than Y is 5/12.

It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.

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According to the information, Aaliyah is going to need 8.75 hours to read 50 more pages than Yohance.

To calculate how many hours Aaliyah will beed to read, we have to perform the following mathematical procedure

First, we have to calculate how many pages Yohance is going to read this week, so if she is going to read during 7.5 hours we have to multiply the number of pages she read per hour by time (7.5 hours).

So, Yohance is going to read 300 pages. Now if we want to know how many hours needs Aaliyah to read 50 more pages we have to perform the following operation:

According to the above, Aaliyah needs to read for 8.75 hours to complete 50 more pages than Yohance.

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