make x the subject of m=n + x/p

The slope of the linear function described in this problem is:

m = -3.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the line goes through points (5,3) and (8,-6). Considering that the slope is given by change in y divided by change in x, for this function, it is given by:

m = (-6 - 3)/(8 - 5) = -9/3 = -3

The slope of the linear function described in this problem is:

m = -3.

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The multiplication of the given equation i.e. \((5x + 4)^2\) should be considered as the \(25x^2 + 40x + 16\).

Since the given equation is \((5x + 4)^2\)

We have to break this equation

So, it can be like

\((5x)^2 + 2 \times 5x \times 4 + 4^2\)

\(25x^2 + 40x + 16\)

Hence, we can conclude that The multiplication of the given equation i.e. \((5x + 4)^2\) should be considered as the \(25x^2 + 40x + 16\).

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No. Since the limit as x approaches 3 from both sides of f(x) equals 6, f(x) will have a hole at x equals 3 and not a vertical asymptote.

A vertical asymptote is a vertical line on a graph that the function approaches but never touches as the input values approach a certain value. In other words, it is a value of the independent variable for which the function approaches infinity or negative infinity as the independent variable approaches that value.

It is often found in rational functions, where the denominator becomes zero at some value, causing the function to become undefined at that point.

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Answer:

\( \frac{7.90 \times {10}^{ - 2} }{1.0 \times {10}^{ - 5} } \\ = 7.9 \times {10}^{5 - 2} \\ = 7.9 \times {10}^{3} \)

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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The number formed by the digits 16, 06, and 68 is 160668, which is determined by concatenating them in the given order.

To determine the number formed by the given digits, we concatenate them in the given order. Starting with the first digit, we have 16. The next digit is 06, and finally, we have 68. By combining these three digits in order, we get the number 160668.

When concatenating the digits, the position of each digit is crucial. The placement of the digits determines the resulting number. In this case, the digits are arranged as 16, 06, and 68, and when they are concatenated, we obtain the number 160668. It's important to note that the leading zero in the digit 06 does not affect the value of the resulting number. When combining the digits, the leading zero is preserved as part of the number.

Therefore, the number formed by the digits 16, 06, and 68 is 160668.

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The sample standard deviation is 0.89

In the given statement is:

A sample n = 5 scores which means that there are 5 sample having m = 20 which is the arithmetic mean (A.M.)of these samples, and \(s^{2}\) = 4 is the variance of these samples.

Let us know the :

What is meant by Sample Standard deviation?

The sample standard deviation (s) is the square root of the sample variance and is also measure of the spread from the expected values.

Standard deviation is the square root of the variance.

Therefore, \(s^{2}\) =4 => s = 2

(Where, s denotes sample standard deviation ,σ)

Also, Standard error of the sample S(E) = Sample standard variance / \(\sqrt{number of samples}\)

= σ /\(\sqrt{n}\) = 2/\(\sqrt{5}\)

and, root 5 = 2.24

put the value of root 5

=2 / 2.24

= 0.89

Hence, The sample standard deviation is 0.89

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a. Optimal solution: X1 = 140, X2 = 0, X3 = 80, Objective Function Value = 4700.000.

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding.

c. The dual price for the second constraint is 2.333, indicating that for each unit increase in its right-hand side value, the objective function value increases by 2.333.

d. The objective function coefficient of X2 can vary between 30 and 40 without changing the optimal solution

a. The complete optimal solution is:

X1 = 140

X2 = 0

X3 = 80

Objective Function Value = 4700.000

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding because it has a slack/surplus value of 0.

c. The dual price for the second constraint (9X1 + 15X2 + 3X3 < 1500) is 2.333. This means that for each unit increase in the right-hand side value of the second constraint, the objective function value will increase by 2.333 units, assuming all other variables and constraints remain constant.

d. The objective function coefficient of X2 can vary between 30 and 40 before a new solution point becomes optimal. This means that as long as the coefficient remains within this range, the current solution will still be optimal. However, if the coefficient of X2 goes below 30 or above 40, a new optimal solution may be obtained.

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The Jacobian matrix represents the partial derivatives of one set of variables with respect to another set of variables. In this case, we need to find the Jacobian matrix for the transformation from (x, y, z) to (s, t, u) using the given equations:

The jacobian matrix J is given by:

J = ∂(x, y, z) / ∂(s, t, u)

To find the elements of the Jacobian matrix, we calculate the partial derivatives of each component of (x, y, z) with respect to (s, t, u).

∂x/∂s = -\(4s^3tu\)

∂x/∂t = -\(5s^4u\)

∂x/∂u = -\(s^4t\)

∂y/∂s = \(6s^2tu\)

∂y/∂t =\(4st^2u\)

∂y/∂u = 2stu

∂z/∂s = -3u

∂z/∂t = 1

∂z/∂u = -3s

Therefore, the Jacobian matrix J is:

J = \([-4s^3tu, -5s^4u, -s^4t]\)

\([6s^2tu, 4st^2u, 2stu]\)

[-3u, 1, -3s]

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Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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Answer:

3/4

Step-by-step explanation:

8x = 6

x = other number = 6/8 = 3/4

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.

Direct Materials: It includes the cost of raw materials used in manufacturing a product.

Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.

Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process

Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.

To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.

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Answer:

To convert the degrees to radians

we know that,

Radian is equivalent to the angle subtended at the centre of a circle by an arc equal in length to the radius.

we get that,

That is,

we get that,

Answer is: 0.8

Answer: 60,004.41 kilograms

Step-by-step explanation:

Given: Weight of Blue whales = \(1.362 \times 10^5\) kilograms

= \(1.3621\times 100000=136210\)

Weight of blue whale = 2.27 x (weight of largest dinosaur )

\(136210=2.27\times \text{(weight of largest dinosaur)}\\\\\Rightarrow\ \text{(weight of largest dinosaur)} =\dfrac{136210}{2.27}\\\\\Rightarrow\ \text{(weight of largest dinosaur)}=60004.41\)

Hence, The weight of largest dinosaur = 60,004.41 kilograms

The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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Given :

The price of a sandwich is $5.50 more than the price of a smoothie, which is d dollars

so, the expression :

d + 5.5 represents : The price of of a sandwich

Answer:

Step 4 is incorrect ⇒ C

Step-by-step explanation:

Let us check step by step

∵ sin(x + y)

∵ sin(z) = cos(\(\frac{\pi}{2}\) - z)

→ Replace z by (x + y)

∴ sin(x + y) = cos(\(\frac{\pi }{2}\) - [x + y])

∴ Step 2 is correct

∵ cos(\(\frac{\pi }{2}\) - [x + y]) = cos(\(\frac{\pi }{2}\) - x - y])

∵ take [\(\frac{\pi }{2}\) - x] as the 1st angle and y as the 2nd angle

∴ cos(\(\frac{\pi }{2}\) - x - y]) = cos([\(\frac{\pi }{2}\) - x] - y)

∴ Step 3 is correct

∵ cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

→ Replace a by ([\(\frac{\pi }{2}\) - x] and b by y

∴ cos([\(\frac{\pi }{2}\) - x] - y) = cos(\(\frac{\pi }{2}\) - x)cos(y) + sin(\(\frac{\pi }{2}\) - x)sin(y)

∴ Step 4 is incorrect, the second angle is y not (-y)

∵ cos(\(\frac{\pi }{2}\) - x) = sin(x)

∵ sin(\(\frac{\pi }{2}\) - x) = cos(x)

∴ cos(\(\frac{\pi }{2}\) - x)cos(y) + sin(\(\frac{\pi }{2}\) - x)sin(y) = sin(x)cos(y) + cos(x)sin(y)

∴ Step 5 is correct

Answer:

C. Step 4

Step-by-step explanation:

got it right on edge :)

This question is about family functions.

If we want to know which family this sequence represents we must see if there's a pattern among the values for x and the values for f(x).

First I see that on the left column of the table x increases by 1 every time:

-1 , if I add +1 , we get

0 , if I add +1, we get

1 and so on

2

3

Now I can also see on the right column that f(x) increases by 2 every time.

-3 , if I add +2, we get

-1 , if I add +2, we get

0 , and this goes on and on

3

5

What have we found out? As x increases by 1 , f(x) increases by 2 as well.

A function that has this behavior must be a linear function.

A linear function has the following form: y = f(x) = a + bx

And that's how we know if the sequence is linear.

So, the idea is always see the how x behaves from one roll to the other as well as how f(x) behaves.

---------------------------------------------------------------------------------------------------------------

A function is linear if both x and f(x) are increasing or decreasing constant:

* If x increases, f(x) must increase as well

* If x decreases, f(x) must decrease too

----------------------------------------------------------------------------------------------------------------

Tim owns 74 socks, the colours of which are unknown.

He does, however, have an additional pair that is white rather than black.

Therefore, it suggests that we are working with the two hues white and black.

The result of dividing the total number of socks by two is:

= 74/2

= 37 socks, two pairs each for black and white.

But let's not forget that Tim has a pair of white socks in addition to his black pair.

The total number of white socks is equal to= 37+1= 38 socks.

Total black sock pairs= 37-1=36 socks.

Last but not least, the question asks us to count the number of single socks rather than pairs.

For white then:

There will be = (38x 2) socks per pair.

= 76 socks

For Black

The individual socks will be = (36 × 2)socks

= 72 socks

We can then deduce that there are 76 individual socks for white and 72 individual socks for black.

The solution would have to be four. Despite the large number of socks in the drawer, there are only three different colours, so if you take four socks, you will undoubtedly find at least one pair that matches.

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The money that will remain after he pays back the loan amount and interest is $320.

The cost a company pays a lender (creditor) for a loan is called interest. Although many other arrangements are available, interest payments are typically based on the remaining balance of a loan and paid on a monthly basis.

With he use of basic interest formula supplied.

A= P( 1+r)

A= (3000) + (1+ (00.6))

A= 3000* 1.06

A= 3180

hence $3180 will be due at the end of the year.

Amount remaining =(amount reserved- amount owed).

3500-3180

= $320

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complete question;

At the beginning of the year, Mr. Simms took

out a $3,000 loan from a bank that charges a

simple interest rate of 6%. He plans to save

$3,500, which he will use to pay back the entire

amount of the loan plus interest at the end of

the year.

Exactly how much money will remain after he

pays back the loan amount and interest?

Use: A = P(1 + r)

Answer:

She has 3 $10 bills, 5 $5 bills and 8 $1

3 times 10= $30

5 times 5 = $25

8 times 1 = $8

$30 + $25 + $8 = $63

A system of equations is a group of equations that can be solved simultaneously. Here we can find one that allows us to solve the given question.

We will see that: Jemila has 8 $1 bills, 5 $5 bills, and 3 $10 bills.

First, let's define the variables:

Then the total amount of money in the piggy bank is:

$1*x + $5*y + $10*z

And we know that the total value is $63, then one equation is:

$1*x + $5*y + $10*z = $63

We also know that she has two more $5 bills than $10 bills, then:

y = z + 2

We also know that she has three more $1 bills than $5 bills, then:

x = y + 3

So  our system of equations is:

$1*x + $5*y + $10*z = $63

y = z + 2

x = y + 3

To solve this, we need to isolate one of the variables in one of the equations. We can see that some variables are already isolated, like on the second or third equations.

For example, we can replace the second equation into the first and third ones:

$1*x + $5*y + $10*z = $63

x = y + 3

$1*x + $5*(z + 2) + $10*z = $63

x = (z + 2) + 3

Now we can simplify these to get:

$1*x + $15*z + $10 = $63

x = z + 5

Now we can replace the second equation on the first one:

$1*x + $15*z + $10 = $63

$1*(z + 5) + $15*z + $10 = $63

Finally, we can solve this for z.

$16*z + $5 + $10 = $63

$16*z = $63 - $15

$16*z = $48

z = $48/$16 = 3

z = 3

Now that we know the value of z, we can use it in the equations:

x = z + 5 = 3 + 5 = 8

y = z + 2 = 3 + 2 =5

Then the solution is:

Then Jemila has 8 $1 bills, 5 $5 bills, and 3 $10 bills.

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For the differential equation dy/dx=y^2+cos(x), the applicable ones are: Autonomous, Separable, Nonhomogeneous, Homogeneous.

The given differential equation is dy/dx=y²+cos(x). Let's check which one of these apply to this equation:

Autonomous equation: An autonomous equation is one in which the independent variable x does not appear explicitly. The given equation does have independent variable x appearing in it. So, this equation is not an autonomous equation.

Separable equation: A separable equation is one in which the variables can be separated on opposite sides of the equality symbol, with only functions of x on one side and functions of y on the other. This differential equation can be written as dy/(y² + cos x) = dx This equation is a separable equation. So, this differential equation is a separable equation.

Logistic equation: The logistic equation is of the form: dy/dt = ky(M-y) This differential equation is not in the form of the logistic equation. So, this differential equation is not a logistic equation.

Nonhomogeneous equation: If a differential equation is not a homogeneous equation, then it is called a nonhomogeneous equation. Nonhomogeneous differential equations have terms that do not contain the dependent variable y or its derivatives and are called the nonhomogeneous part of the equation. The given differential equation contains a term cos(x) which is not homogeneous. So, this differential equation is a nonhomogeneous equation.

Homogeneous equation: If a differential equation is such that replacing y by ky, where k is a constant, produces an equivalent equation, then it is called a homogeneous equation. This differential equation is not a homogeneous equation. So, this differential equation is not a homogeneous equation.

Linear equation: An equation that can be written in the form y'+p(x)y = f(x), where p(x) and f(x) are continuous functions of x is a linear differential equation. This differential equation can be written asdy/dx - y² = cos(x)Here, y² is a non-linear term. So, this differential equation is not a linear differential equation.

So, the applicable ones are: Autonomous, Separable, Nonhomogeneous, Homogeneous.

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The calculated value of x in the circle is 18 degrees

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

The circle

The angle at a semicircle is 90 degrees

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

5x = 90

Divide by 5

So, we have

x = 18

Hence, the solution for x is 18 degrees

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