11. Simplify the expression.
2x - 5(3x-4)

The total annual salary with a festive bonus is Rs (12r+2000)

In maths, multiply means the repeated addition of groups of equal sizes.

Given that, there is an annual salary at r rupees per month along with a Christmas bonus of, Rs 2000.

Here, a person is getting monthly salary  = Rs r

Therefore, his annual salary = Rs r × 12

= Rs 12r

He is also getting a bonus for Christmas = Rs 2000

So, in total, he will get =  Rs (12r+2000)

Hence, The total annual salary with a festive bonus is Rs (12r+2000)

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The proof principle that you are describing is known as induction. Induction is a method of proof that is used to establish that a property holds for all natural numbers (or, more generally, for all elements of a well-ordered set).

The basic idea behind induction is as follows:

First, you start with a base case, which is a specific natural number (usually 0 or 1) for which you can directly prove that the property holds.

Next, you assume that the property holds for some natural number n. This is known as the induction hypothesis.

Using the induction hypothesis, you then prove that the property also holds for the natural number n+1. This is known as the induction step.

Since you have already established that the property holds for the base case, and you have shown that if it holds for one natural number, it must also hold for the next natural number, it follows that the property holds for all natural numbers.

Induction is a very powerful proof technique and is used extensively in mathematics to prove theorems about the properties of natural numbers and other well-ordered sets.

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43 is equivalent to 64(1/3)

Equivalent is different from equal. Equal means same in all aspects, whereas equivalent means similar but not identical.

For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

Given that, if a=b(1/n) is equivalent to an=b then 43 is equivalent to

If we see the number 43, then converting it according to given pattern

4ⁿ(1/n)

Here, n = 3

So, 43 = 4³(1/3) = 64(1/3)

Hence, 43 is equivalent to 64(1/3)

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Answer: Matthew’s milkshake

Step-by-step explanation: The ratio of ice cream to milk in Philips milkshake is 1:3/8. The ratio of ice cream to milk in Matthew’s milkshake is 1:1/3. 3/8>1/3. Since you want a thicker milkshake, you want less milk in the ratio, Matthew’s milkshake would be thicker.

Answer:

- 4, - 3, - 2, - 1, 0, 1

Step-by-step explanation:

- 15 < 3n < 6 ( divide each interval by 3 )

- 5 < n < 2

then integer value of n are - 4, - 3, - 2, - 1, 0, 1

By combination, Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods =  [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]

The sequence of the selection is irrelevant since a combination in mathematics is a selection of items from a set having various members. Regardless of the sequence in which the items were chosen, a mathematical approach known as a combination may be used to calculate the number of alternative arrangements within a collection of objects. Any order can be chosen by a combination. Combinations and permutations are two alternative strategies to divide up a collection of items into subsets in mathematics. The subset's elements can be listed in any order in a combination. In a permutation, the components of a subset are listed in a certain order.

Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods =  [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]

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Answer:

To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:

S: Write down the given information and identify the problem.

We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".

O: Organize the information and decide on a plan.

To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.

L: Carry out the plan.

For example, let's say we substitute x = 2 into the polynomial. We get:

P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14

= 16 - 24 + 4a - 12 + 14

= -4 + 4a + 2

= 4a - 2

We are given that P(2) = 4a - 2 = 0, so 4a = 2.

Solving for a, we get:

a = 2 / 4

= 0.5

V: Check the solution.

We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.

P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14

Substituting x = 2 and a = 0.5, we get:

P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14

= 16 - 24 + 1 - 12 + 14

= 0

Since P(2) = 0, our solution appears to be correct.

Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.

The equation in the form at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex], the magnitude of the velocity is 7.81 m/s, the direction of the velocity is 50.19°.

Consider the flow field:

u=2+y & v=2 y

Determine the streamline equation by using the following equation:

[tex]& \frac{d x}{u}=\frac{d y}{v} \\ \frac{d x}{2+y}=\frac{d y}{2 y} \\\\& \int d x=\int\left(\frac{2+y}{2 y}\right) d y \\\\& x=\ln y+\frac{y}{2}+C[/tex]

(A)

Since the stream line passes through (3,2).

[tex]$$\begin{aligned}& x=\ln y+\frac{y}{2}+C \\& 3=\ln 2+\frac{2}{2}+C \\& C=2-\ln 2 \\& C=1.31\end{aligned}$$[/tex]

Substitute the value of C in equation (1).

[tex]& x=\ln y+\frac{y}{2}+C \\\\& x=\ln y+\frac{y}{2}+1.31 \\\\& 2 x-1.31 \times 2=2 \ln y+y \\\\& \ln y^2+y=2 x-2.62[/tex]

Therefore, the equation of streamline equation at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex].

(B).

Calculate the magnitude of the velocity of a particle located at point (5m , 3m).

[tex]V & =\sqrt{u^2+v^2} \\\\& =\sqrt{(2+y)^2+(2 y)^2} \\\\& =\sqrt{(2+3)^2+(2 \times 3)^2} \\\\& =\sqrt{5^2+6^2} \\\\& =7.81 \mathrm{~m} / \mathrm{s}[/tex]

Therefore, the magnitude of the velocity of a particle located at point (5m , 3m) is 7.81m/s.

(C).

Calculate the direction of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x-axis is

[tex]\tan \theta & =\frac{v}{u} \\\\& =\frac{2 y}{2+y} \\\\& =\frac{6}{5} \\\\& =50.19^{\circ}[/tex]

Therefore, the direction of the velocity of a particle located at point (5m , 3m) is 50.19°.

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A flow field for a fluid is described by u=(2+y) m/s and v=(2y) m/s, where y is in meters.

      A.) Determine the equation of the streamline that passes through point (3m, 2m). Write the equation in the form

 x={x(y)}, where y is in meters.

      B.) Find the magnitude of the velocity of a particle located at point (5m , 3m).

      C.) Find the direction ? of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x axis.

Answer:

Step-by-step explanation:

Lacey you can do this one  :D

J = H  ( b/c of red marks)

180= 128 + ∠j

52 = ∠j

t = ∠j

t = 52

180 = s + 2*t

180 = s + 2*52

180 = s + 104

180-104 =s

76 = s

Answer:

Below

Step-by-step explanation:

the difference between 51.2 and a number is  :   51.2 - x

 Now multiply this by 6  :   6 x (51.2-x)    

     and this equals 68.3  :      6 x (51.2-x) = 68.3

Answer:

-3<c<11/2

Step-by-step explanation:

-7<2c-1

-7+1<2c

-6<2c

-3<c

and

2c-1<10

2c<10+1

2c<11

c<11/2

Final answer (combine both):

-3<c<11/2

Risk is the potential that a chosen action may lead to an undesirable outcome.

In simple terms, the definition of risk is a condition that is uncertain, but contains an element of danger as a consequence or result of something. Once again, this something is a business, business, activity, or decision that you make.

The risks themselves are divided into several types, complete with different characteristics.

1. Pure Risk 

This pure risk is certain, meaning that when the risk occurs, you will experience a loss. And vice versa, if pure risk does not occur, then you will make a profit.

2. Speculative Risk 

There are three possibilities that will happen, if you experience speculative risk, namely profits, losses, or maybe break even. What is meant by break even is the break even point.

Conditions where there are no profits or losses, so it's normal. The most obvious examples of speculative risk are the lottery, stock exchange, exchange risk, and others.

3. Particular Risk or Special Risk

Specific risks originate from individual activities, so the impact can still be estimated or anticipated at the outset because they are local in nature. For example, a turbine explosion, a shipwreck, or maybe a crash.

How to anticipate it (example for collision risk). You can take out insurance to provide guarantees or protection, both for the vehicle and for yourself.

4. Fundamental Risk 

Fundamental risks come from the surrounding environment or nature which can have quite a big impact, because humans are not able to control them.

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Answer:

Slope: 3

y-intercept: ( 0, −5)

Graph a solid line, then shade the area above the boundary line since

y is greater than 3x −5.

y ≥ 3x −5

The value of the composite function is 2x - 15

A function can be defined as a rule, law ore equation that explicitly shows the relationship between two variables.

These variables are called;

From the information given, we have the functions;

To determine the composite function (fog)(x), we have to substitute the value of g(x) as the variable 'x' in the function, f(x), we have;

(fog)(x) = 2 - (18 -2x) + 1

Now, expand the bracket

(fog)(x) = 2 - 18 + 2x + 1

collect like terms

(fog)(x) = 2x - 15

Hence, the function is 2x - 15

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To determine the number and type of solutions to the quadratic equation x^2 - x = -1/4, we can use the discriminant, which is the part of the quadratic formula that determines the number of solutions. The quadratic formula is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. In this case, the coefficients of the equation are a = 1, b = -1, and c = -1/4. Plugging these values into the formula gives us:

x = (1 +/- sqrt(1^2 - 4(1)(-1/4))) / (2(1))

x = (1 +/- sqrt(1 + 1)) / 2

x = (1 +/- sqrt(2)) / 2

Therefore, the quadratic equation has two solutions: x = (1 + sqrt(2)) / 2 and x = (1 - sqrt(2)) / 2. These solutions are both real numbers.

Answer:

7

Step-by-step explanation:

4+3=7

7-4=3

7-3=4

Simple random sampling is a good way because he will have a more representative sample if he chooses randomly. which is the correct answer would be an option (B).

A sample is randomly chosen from the population in basic random sampling, guaranteeing that each person has an equal chance of being chosen.

Simple random sampling is a good way for a librarian to check a sample of books from the library to get an idea of how many need replacing because it will provide a more representative sample.

In simple random sampling, a sample is selected from the population at random, ensuring that each member of the population has an equal chance of being selected. This means that the sample will accurately represent the characteristics of the population as a whole.

Thus, He will have a more representative sample if he chooses randomly.

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The mean is $67,530 from the reported two average household incomes i.e, $49,445 and $67,530.

Averages can only be computed for numeric variables, regardless of whether the variables are discrete or continuous. This is obtained by simply dividing the sum of all values in the dataset by the number of values.

Mathematically, X-bar = Sum of x values/ number of values

We have, the current population survey is conducted by the US Census bureau,

Averages of household income are $49,445 and $67,530. Mean of average incomes is expected to be a right skewed distribution because some individuals belongs to exceptionally high income group which are outliers and which will cause the mean to inflate. Hence, value which is greater will be the mean i.e. $67,530

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The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

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The largest number of stones that could be in the box in the wagon will be 30.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

His wagon can carry 1.2 kg without falling apart.

And, The stones are in a wooden box that weighs 150 grams, and each stone weighs 35 grams.

Now,

Let the number of stones = x

So, We can formulate;

⇒ 150 + 35x = 1200

Solve for x as;

⇒ 35x = 1200 - 150

⇒ 35x = 1050

⇒ x = 1050/ 35

⇒ x = 30

Thus, There are 30 largest number of stones that could be in the box in the wagon.

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Answer:

x² - 3

Step-by-step explanation:

g(f(x))

=> g(x²)

=> x² - 3

Using the fact that all points on a circle are equidistant to its center, we will see that:

a =  -3 ±√21

All the points on a circle are equidistant to its center. Here the center is at (-3, -2), and we know that (0, -6) is on the circle.

The distance between these two is:

d = √( (-3 - 0)^2 + (-2 + 6)^2) = 5

Then the distance between (a, 0) also should be 5 units, so:

5 = √( (-3 - a)^2 + (-2 - 0)^2)

5 = √( (-3 - a)^2 + 4)

5^2 = (-3 - a)^2 + 4

25 - 4 = (-3 - a)^2

21 = (-3 - a)^2

±√21 = -3 - a

a = -3 ±√21

these are the two possible values of a.

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Answer:

11.25

Step-by-step explanation:

If the painter used 2.5 liters of paint every hour, then in 5.5 hours he would have used 2.5 * 5.5 = <<2.5*5.5=13.75>>13.75 liters of paint.

If he had 25 liters of paint to begin with and used 13.75 liters of paint, he would have 25 - 13.75 = <<25-13.75=11.25>>11.25 liters of paint left. Answer: {11.25}.

The painter had 11.25 L paint left.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given here in 1 hour he uses 2.5 L of paint

          then in 5.5 hours he uses 2.5 × 5.5 = 13.5 L

Therefore quantity of paint left is = 25 - 13.5 = 11.5 L

Hence, The painter had left  11.25 L .

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Answer:

y = 2x - 3

Step-by-step explanation:

A (0,-3)

B (2,1)

slope = (-3-1)/(0-2)

-4/-2

2

y intercept = -3

Answer:

D

Step-by-step explanation:

The last one- monetary support that is used to help pay educational costs

:)

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The domain of a radical is the set of all values of the independent variable for which the radical is defined.

For example, consider the radical expression √x. This expression is defined for all nonnegative values of x, since the square root of a nonnegative number is always real. Therefore, the domain of the radical √x is the set of all nonnegative values of x:

{x | x ≥ 0}

This includes all real numbers that are greater than or equal to zero, such as 0, 1, 2, 3, and so on.

On the other hand, if we consider the radical expression √(x-2), this expression is defined for all values of x such that x-2 is nonnegative. This means that the domain of the radical √(x-2) is the set of all values of x such that x ≥ 2:

{x | x ≥ 2}

This includes all real numbers that are greater than or equal to 2, such as 2, 3, 4, 5, and so on.

In general, the domain of a radical is determined by the values of the independent variable that make the expression under the radical nonnegative. If the expression under the radical is always nonnegative, then the domain of the radical is the set of all real numbers. If the expression under the radical is not always nonnegative, then the domain of the radical is the set of all values of the independent variable that make the expression nonnegative.

Answer:

The domain of a radical is the set of all values that can be plugged into the radical without resulting in an undefined or imaginary value.For example, the domain of the square root function sqrt(x) is all non-negative real numbers, since the square root of a non-negative real number is always a real number. This means that the domain of sqrt(x) is the set of all real numbers x such that x >= 0.On the other hand, the domain of the square root function sqrt(x^2 - 4) is all real numbers except for the values x = 2 and x = -2, since the square root of a negative number is an imaginary number. This means that the domain of sqrt(x^2 - 4) is the set of all real numbers x such that x != 2 and x != -2.In general, the domain of a radical is the set of all values for which the expression inside the radical is greater than or equal to 0. This is because the radical of a negative number is an imaginary number, which is not included in the domain of the radical.

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

p+5=-12

p=-12-5

p=-17

Answer:

p+5=-12

p=-12-5

p=-17

so the solution set is -17

Answer: 49/60 mins.

Step-by-step explanation:

First lap time = 5/6 minute

Second lap time = 11/12 minute

Third lap = ?

To find the 3rd lap mins, we need to find 5 x 6, which is 30. Then, we need to find 1 1/12 more than 30. Then, when we get that answer, we need to find 1 1/10 fewer mins to get the 3rd lap time. If you do it all right, you should end up with 49 mins or 49/60 mins as a fraction (The denominator was changed to 60 to make the problem more realistic and easier) I hoped this helped.

Answer:

1/11

Step-by-step explanation:

Add 1/5 + 2 then divide 1/5 by the result