When will the value of X% of a number be greater than that number itself? Give an example
and explain in words.

we may use BODMAS in answering this question you divide 18 by 6 and your answer will be 3 you then add 5 to the 3 to obtain your answer which is 8

Solution for the question 2 :

It is given that ,

The population after n years is given by exponential function ,

Population after 9 years is calculated as,

Thus the population after 9 years is 956 .

The ratio of liters to gallons in simplest form is 5 : 19.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, 1 gallon is around 3.8 liters.

So, The ratio of liters to gallons in a : b form is 1 : 3.8

Or, 10 : 38,

Or 5 : 19.

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Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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a) au/ax=2xy⁴ and au/ay=4x²y³ ; b) We can differentiate the expression a²u=2ax + c(y) with respect to y to obtain a³u/ax²=0 ; c) f(x,y) has a local maximum at (0,0).

a) To compute the mathematical expressions for al Ək we will have to differentiate the function Q=f(l,k)=(1+1¯ªk¯ß) w.r.t k. Hence, al Ək=0+(-ß)(1+1¯ªk¯ß)-1

=(-ß)/(1+1¯ªk¯ß)

To compute the mathematical expressions for U(x,y) we need to differentiate the function U(x,y)=x²y⁴ w.r.t. x and y. Hence, au/ax=2xy⁴ and au/ay=4x²y³.

b) Let us first differentiate the expression au/ax=x²-a² with respect to x, which gives a². Differentiating the obtained expression with respect to x again gives 2ax,

hence a²u=2ax + c(y), where c(y) is the arbitrary constant of integration that depends on y.

To find c(y), we differentiate the expression au/ax=x²-a² with respect to y, which gives c'(y)=0. Hence, c(y) is a constant, which is determined by the initial condition.

Similarly, we can differentiate the expression au/ay=xy²-b² to obtain a²u=2by + c(x), where c(x) is the arbitrary constant of integration that depends on x.

Hence, c(x) is a constant, which is determined by the initial condition.

Finally, we can differentiate the expression a²u=2ax + c(y) with respect to y to obtain a³u/ax²=0, which means that the second order condition for maximization is satisfied.

c) To find the maxima of the following functions we will have to differentiate each of these functions with respect to x and y and equate them to zero.

f(x)=-x²-x⁴ :

f'(x)=-2x-4x³

=0

=>x=0,

x=±1/√2

f''(x)=-2-12x²

f''(0)=-2<0,

f''(1/√2)=-2+3√2>0,

f''(-1/√2)=-2-3√2<0

=>f(x) has a local maximum at x=-1/√2, a local minimum at x=0, and a local maximum at x=1/√2. Since f(x) is a continuous function, the global maximum and minimum of f(x) must occur at the endpoints of the interval [-1,1], which are x=-1 and x=1.

Hence, f(-1)=f(1)

=-2.

f(x)=-x²+x:

f'(x)=-2x+1

=0

=>x=1/2f''(x)

=-2f''(1/2)

=-2<0

=>f(x) has a local maximum at x=1/2.

Since f(x) is a continuous function, the global maximum and minimum of f(x) must occur at the endpoints of the interval [-1,1], which are x=-1 and x=1.

Hence, f(-1)=0 and f(1)=-2.f

(x,y)=-x²-y²+3:

f'x=-2x

=0

=>x=0,

f'y=-2y

=0

=>y=0

f''xx=-2,

f''xy=0,

f''yy=-2

=>D=(-2)(-2)-0

=4

=>f(x,y) has a local maximum at (0,0).

Since f(x,y) is a continuous function, there is no global maximum or minimum of f(x,y).

f(x,y)=xy-x²-y²+3+9y:

f'x=y-2x

=0

=>y=2x,

f'y=x-2y+9

=0

=>x=2y-9

f''xx=-2,

f''xy=1,

f''yy=-2

=>D=(-2)(-2)-(1)(1)

=3

=>f(x,y) has a saddle point at (2,11/2).

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We want to see which could be the possible score of Kath for the given information. We will find the inequality:

K ≤ 33

The given information is:

First, we need to define the variable K for Kath's points, because of the given information, we can write the inequality:

K + 22 ≤ 55

This means that the sum of the points is smaller than or equal to 55.

Now we just need to solve this for K, to do this, we subtract 22 in both sides:

K ≤ 55 - 22

K ≤ 33

From this, we can conclude that Kath has at most 33 points.

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The height of the cylinder is 4 feet.

The volume of a cylinder can be found as follows;

volume of a cylinder = base area × height

Therefore,

base area = πr²

volume of the cylinder = 48π ft³

base area = 12π ft²

Therefore, let's find the height of the cylinder as follows:

48π = 12π × h

divide both sides of the equation by 12π

h = 48π / 12π

h = 4 ft

Therefore,

height of the cylinder  = 4 feet

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Answer:

C=5+0.25m

Step-by-step explanation:

Truth statement are statements or assertions that is true regardless of whether the constituent premises are true or false. See below for the definition of Euclidean Postulates.

There are five Euclidean Postulates or axioms. They are:

1. Any two points can be joined by a straight line segment.

2. In a straight line, any straight line segment can be stretched indefinitely.

3. A circle can be formed using any straight line segment as the radius and one endpoint as the center.

4. Right angles are all the same.

5. If two lines meet a third in a way that the sum of the inner angles on one side is smaller than two Right Angles, the two lines will inevitably collide on that side if they are stretched far enough.

The right angle in the first page of the book shown and the right angles in the last page of the book shown are all the same. (Axiom 4);

If the string from the Yoyo dangling from hand in the picture is rotated for 360° such that the length of the string remains equal all thought, and the point from where is is attached remains fixed, it will trace a circular trajectory. (Axiom 3)

The swords held by the fighters can be extended into infinity because they are straight lines (Axiom 5)

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Answer:

Step-by-step explanation:

Plants can cause both mechanical and chemical weathering. They cause mechanical weathering by their roots which grow inside rock cracks where soil has collected and eventually crack them. This can also happen in streets or sidewalks.

They cause chemical weathering with their roots, which release acid or other chemicals, onto rocks, which then forms cracks, and breaks apart.

Plants may decrease chemical weathering by binding secondary products and isolating unweathered minerals from meteoric water.

The formation of a forest or a stand of trees in an area where there was previously no tree cover is known as afforestation.

Many government and non-governmental groups are directly involved in afforestation efforts to establish forests and boost carbon sequestration.

Plants can weather both mechanically and chemically. Their roots, which grow inside rock fractures where dirt has accumulated and eventually crack them, produce mechanical weathering. This can also happen on the pavements or on the highways.

Their branches promote melting by releasing acid or other compounds onto rocks, causing fissures and breaking apart.  By binding secondary products and separating uncut diamond minerals from meteoric water, plants can reduce chemical weathering.

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A residual is the difference between "the measured and predicted values of the quantity of interest".

In regression analysis, a residual would be the difference between an observable and anticipated value.

The formula is;

Residual = Observed value – Predicted value

Some key features regarding the residuals are-

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Answer:

1 boy to 15 girls.

Step-by-step explanation:

Since there is only two boys, I divided each number by two and got 1 to 15. Have an amazing day!

The ratio of boys to all children in the group is 1:16.

Given that in a group there are 2 boys and 30 girls.

We need to find the ratio of boys to all children.

To find the ratio of boys to all children in the group, we need to add the number of boys and girls together to get the total number of children.

Then, we can express the number of boys as a fraction of the total number of children.

Number of boys = 2

Number of girls = 30

Total number of children = Number of boys + Number of girls

Total number of children = 2 + 30 = 32

Now, we can express the number of boys as a fraction of the total number of children:

Ratio of boys to all children = Number of boys / Total number of children

Ratio of boys to all children = 2 / 32

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

Ratio of boys to all children = 1 / 16

So, the ratio of boys to all children in the group is 1:16.

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Answer:

(3/4) mile / 6 min = 3/24 = 1/8 mile/min = 0.125 mile/min

(1/2) mile /5 min = 1/10 mile / min = 0.100 mile/min

Step-by-step explanation:

Ron's hourly rate of pay is $24.73. This means that for each hour of work, Ron earns $24.73.

To find his hourly rate of pay, we divide his annual salary by the number of hours worked:

Hourly rate of pay = Annual salary / Total hours worked

Plugging in the values, we have:

Hourly rate of pay = $51,630 / 2,087

Using a calculator, we can determine that Ron's hourly rate of pay is approximately $24.73 (rounded to two decimal places).

Therefore, Ron's hourly rate of pay is $24.73. This means that for each hour of work, Ron earns $24.73.

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(a) The probability that a randomly selected package weighs between 48 and 50 grams is 0.5596.

(b) The probability that a randomly selected package weighs more than 51 grams is 0.1587.

(c) we can solve for k using the formula z = (k - μ) / σ: 1.645 = (k - 49.8) / 1.2

What is probability?

Probability is a measure of the likelihood of an event occurring.

a. To find the probability that a randomly selected package weighs between 48 and 50 grams, we need to calculate the area under the normal curve between these two values.

We can standardize the values using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For x = 48, z = (48 - 49.8) / 1.2 = -1.5

For x = 50, z = (50 - 49.8) / 1.2 = 0.1667

Using a standard normal distribution table or a calculator, we can find the area under the curve between z = -1.5 and z = 0.1667 to be approximately 0.5596.

Therefore, the probability that a randomly selected package weighs between 48 and 50 grams is 0.5596.

b. To find the probability that a randomly selected package weighs more than 51 grams, we need to calculate the area under the normal curve to the right of 51.

Again, we can standardize using z = (x - μ) / σ, where x = 51, μ = 49.8, and σ = 1.2.

z = (51 - 49.8) / 1.2 = 1

Using a standard normal distribution table or a calculator, we can find the area under the curve to the right of z = 1 to be approximately 0.1587.

Therefore, the probability that a randomly selected package weighs more than 51 grams is 0.1587.

c. To find the value of k for which the probability that a randomly selected package weighs more than k grams is 0.05, we need to find the z-score that corresponds to the area to the right of k being 0.05.

Using a standard normal distribution table or a calculator, we can find that the z-score for an area of 0.05 to the right of it is approximately 1.645.

Therefore, we can solve for k using the formula z = (k - μ) / σ:

1.645 = (k - 49.8) / 1.2

Solving for k, we get:

k = 1.645(1.2) + 49.8 ≈ 51.02

So the value of k for which the probability that a randomly selected package weighs more than k grams is 0.05 is approximately 51.02 grams.

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Prime numbers are numbers that can only be divided by itself and 1. The largest possible prime number that fits the scenario is 113

Let the prime numbers be p1 and p2, where p1 > p2; and the odd numbers be x1 and x2

So, we have:

\(p_1 + p_2 + x_1 + x_2 = 128\)

The largest prime number less than 128 is 127.

If \(p_1 = 127\), then

\(p_1 + p_2 + x_1 + x_2 = 128\) becomes

\(127 + p_2 + x_1 + x_2 = 128\)

\(p_2 + x_1 + x_2 = 128-127\)

\(p_2 + x_1 + x_2 = 1\)

This is not possible, because three positive integers cannot add up to 1

The next largest prime number is 113

If \(p_1= 113\), then

\(p_1 + p_2 + x_1 + x_2 = 128\) becomes

\(113 + p_2 + x_1 + x_2 = 128\)

Collect like terms

\(p_2 + x_1 + x_2 = 128-113\)

\(p_2 + x_1 + x_2 = 15\)

Let \(p_2 = 3\)

\(p_2 + x_1 + x_2 = 15\) becomes

\(3 + x_1 + x_2 = 15\)

Collect like terms

\(x_1 + x_2 = 15-3\)

\(x_1 + x_2 = 12\)

\(x_1\) and \(x_2\) are odd numbers.

So, we have:

\(x_1 = 5\\x_2 =7\)

This is true because

\(x_1 + x_2 = 12\)

\(5 + 7 = 12\)

Hence, the largest of the possible primes is 113

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The answers are:
(a) Kn and (b) Cn are regular for every number n ≥ 3.

(a) Kn represents the complete graph with n vertices, where each vertex is connected to every other vertex. In a complete graph, every vertex has degree n-1 since it is connected to all other vertices. Therefore, Kn is regular for every number n ≥ 3.

(b) Cn represents the cycle graph with n vertices, where each vertex is connected to its adjacent vertices forming a closed loop. In a cycle graph, every vertex has degree 2 since it is connected to two adjacent vertices. Therefore, Cn is regular for every number n ≥ 3.

(c) Wn represents the wheel graph with n vertices, where one vertex is connected to all other vertices and the remaining vertices form a cycle. The center vertex in the wheel graph has degree n-1, while the outer vertices have degree 3. Therefore, Wn is not regular for every number n ≥ 3.

In summary, both Kn and Cn are regular graphs for every number n ≥ 3, while Wn is not regular for every number n ≥ 3.

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

\({22p^4qr\sqrt{35q\)

Step-by-step explanation:

I am interpreting what you wrote as  \(\sqrt{11p^4q^3r} \cdot2\sqrt{385p^4r}\), sorry if that's not what you meant!

We rewrite \(385\) as \(5 \cdot 7 \cdot 11\). Since the radicals have the same index, the expression can be written as

\(\sqrt{11p^4q^3r} \cdot2\sqrt{385p^4r}=2\sqrt{11p^4q^3r\cdot5\cdot7\cdot11p^4r}\).

Multiplying like terms, the expression simplifies to

\(2\sqrt{5\cdot7\cdot11^2p^8q^3r^2}\\\).

Taking out the perfect square factors, \(11^2, p^8, q^2,\) and \(r^2,\) we get

\(2\cdot11p^4qr\sqrt{5\cdot7q\), or

\(\boxed{22p^4qr\sqrt{35q}}\).

\(\begin{align*}\\\sqrt{11p^4q^3r} \cdot\sqrt{385p^4r}=\sqrt{11p^4q^3r\cdot5\cdot7\cdot11p^4r}\\=\sqrt{11^2p^8q^3r^2}\\\end{align*}\)\(\begin{align*}\sqrt{5*4}\\\end{align*}\)

There are 95,040 different ways for the first five cars to go through the toll booth.

The first car can be chosen in 12 ways. After the first car has been chosen, the second car can be chosen in 11 ways. This process continues, so the third car can be chosen in 10 ways, the fourth car can be chosen in 9 ways, and the fifth car can be chosen in 8 ways.

So the total number of ways to choose the first five cars is as follows:

12 x 11 x 10 x 9 x 8 = 95,040

Therefore, there are 95,040 different ways for the first five cars to go through the toll booth.

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Answer:

80%

Step-by-step explanation:

We need to find the percent of change from 3,545 pt to 709 pt.

Original value is 3,545

Changed value is 709

Percent change is given by :

\(\%=\dfrac{\text{difference in values}}{\text{original value}}\times 100\\\\\%=\dfrac{3545-709}{3545}\times 100\\\\\%=80\%\)

So, there is 80% of change from 3,545 pt to 709 pt.

Answer:

u ≤ 15

Step-by-step explanation:

=> u/3 ≤ 5

Multiplying both sides by 3

=> 3×u/3 ≤ 5 ×3

=> u ≤ 15

Answer: The truck is 10.0 ft tall.

Step-by-step explanation:

In a particular time ,

Shadow of an item is proportional to its height.

Equation of direct proportion: \(\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}\)

Similarly,

\(\dfrac{\text{height of truck}}{\text{shadow made by truck}}=\dfrac{\text{height of car}}{\text{shadow made by car}}\\\\\Rightarrow\ \dfrac{\text{height of truck}}{51.5}=\dfrac{6.5}{33.2}\\\\\Rightarrow\ \text{height of truck} = \dfrac{6.5}{33.2}\times51.2\approx10.0\text{ ft}\)

Hence, the truck is 10.0 ft tall.

Answer:

C

Step-by-step explanation:

- 8 = z / 3                   Multiply both sides by 3

-8*3 = 3*z/3              

- 24 = x                      The 3s Cancel

Answer:

infinite number of solutions

Step-by-step explanation:

8x + 4 = 8x + 4

Since the expressions on both sides are the same then any value of x will make the equation true.

That is the equation has an infinite number of solutions

Answer:

(x-3) (x-2)

Step-by-step explanation:

\(x^{2}\) - 5x + 6

How to break down the equation and factorise it:

-3 x -2 = 6

-3 + -2 = -5

Final Answer:

(x-3) (x-2)

The value of the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve

C is 0.

To evaluate the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve C:

x = 6cost, y = 12sint (0 ≤ t ≤ 4π), we need to substitute the parametric equations for x and y into the given expression and integrate with respect to t.

Let's calculate the line integral step by step:

∫C (x+5y)dx + (4x-3y)dy

= ∫[0,4π] ((6cost + 5(12sint))(dx/dt) + (4(6cost) - 3(12sint))(dy/dt)) dt

= ∫[0,4π] ((6cost + 60sint)(-6sint) + (24cost - 36sint)(12cost)) dt

= ∫[0,4π] (-36costsint - 360sintsint + 288costcost - 432costsint) dt

= ∫[0,4π] (-360sintsint - 144costsint + 288costcost) dt

= ∫[0,4π] (-144costsint - 360sintsint + 288costcost) dt

Now we can integrate each term separately:

∫[0,4π] (-144costsint) dt = -144 ∫[0,4π] costsint dt

∫[0,4π] (288costcost) dt = 288 ∫[0,4π] costcost dt

∫[0,4π] (-360sintsint) dt = -360 ∫[0,4π] sintsint dt

The integrals of costsint and sintsint over the interval [0,4π] evaluate to zero since they are periodic functions with a period of 2π.

Therefore, the line integral simplifies to:

∫C (x+5y)dx + (4x-3y)dy = -144 ∫[0,4π] costsint dt + 288 ∫[0,4π] costcost dt - 360 ∫[0,4π] sintsint dt

= -144(0) + 288(0) - 360(0)

= 0

Hence, the value of the line integral ∫C (x+5y)dx + (4x-3y)dy along the curve C is 0.

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