Multiply. Write your answer as a fraction in simplest form.
8
X
9

1) 1

When x = 2, y = 1.

2) 1

As x approaches 2 from the left, y approaches 1.

3) 3

As x approaches 2 from the right, y approaches 3.

4) Does not exist

Since the two one-sided limits are not equal, the overall limit doesn't exist.

The population of Australia in 2018 was 24.909 million.

Given: The population of Sydney in 2018 = 5.48 million

           This population of Sydney is equal to 22 % of the total population of Australia.

To find: Total population of Australia

Solution:

According to the Question,

Total population of Australia * 22% = total population of Sydney

Total population of Australia * 22/100  = 5.48 million

                                                                = 5.48 million * 100/22

                                                                = 24.909 million (approx.)

Hence, the population of Australia in 2018 was 24.909 million.

The total population of Australia in 2018 was 24.90 million.

A percent is a dimensionless number, meaning that it has no units of measurement, since it represents a part of whatever whole is being measured.

Given that, the population of Sydney was 5.48 million, which was 22% of the total population of Australia.

We need to find the total population of Australia.

Let the total population of Australia be y.

Therefore,

y × 22% = 5.48

y = 5.48 × 100/22

y = 24.90

Hence, the total population of Australia in 2018 was 24.90 million.

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The angles that we have in the image here are:

When two angles are measured, they sum up to 180. They are said to be supplementary angles.

On the question, we have two angles that are 90 degrees on a straight line. Hence they are supplementary.

This is an angle that is at 90 degrees. We have to two right angles on the diagram that we have here.

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Part A : The domain of this function is [3, ∞) as (x - 3) ≥ 0.

Part B : The range of this function is (- 17, ∞).

Part C : The vertical and horizontal asymptotes of this function are 3 and 2 respectively.

The interval at which the graph is positive is (3, 28)

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function g(x) is defined by g(x) = - log4(x - 3) + 2.

The domain of this function is [3, ∞) as (x - 3) ≥ 0.

The range of this function is (- 17, ∞).

The vertical and horizontal asymptotes of this function are 3 and 2 respectively.

The interval at which the graph is positive is (3, 28)

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Complete Question

Evaluate the Fermi function for an energy kT above the Fermi energy. Find the temperature at which there is a 1% probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron.

Answer:

a

The Fermi function for the energy KT is  \(F(E_o) = 0.2689\)

b

The temperature is  \(T_k = 1261 \ K\)

Step-by-step explanation:

From the question we are told that

   The energy considered is  \(E = 0.5 eV\)

Generally the Fermi  function is mathematically represented as

       \(F(E_o) = \frac{1}{e^{\frac{[E_o - E_F]}{KT} } + 1 }\)

    Here K is the Boltzmann constant with value \(k = 1.380649 *10^{-23} J/K\)

            \(E_F\)  is the Fermi energy

            \(E_o\)  is the initial energy level which is mathematically represented as

     \(E_o = E_F + KT\)

So

     \(F(E_o) = \frac{1}{e^{\frac{[[E_F + KT] - E_F]}{KT} } + 1}\)

=>   \(F(E_o) = \frac{1}{e^{\frac{KT}{KT} } + 1}\)

=>   \(F(E_o) = \frac{1}{e^{ 1 } + 1}\)

=>   \(F(E_o) = 0.2689\)

Generally the probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron is mathematically represented by the  Fermi  function as

     \(F(E_k) = \frac{1}{e^{\frac{[E_k - E_F]}{KT_k} } + 1 } = 0.01\)

Here\(E_k\) is that energy level that is  0.5 ev above the Fermi energy  \(E_k = 0.5 eV + E_F\)

=>   \(F(E_k) = \frac{1}{e^{\frac{[[0.50 eV + E_F] - E_F]}{KT_k} } + 1 } = 0.01\)

=>   \(\frac{1}{e^{\frac{0.50 eV ]}{KT_k} } + 1 } = 0.01\)

=>   \(1 = 0.01 * e^{\frac{0.50 eV ]}{KT_k} } + 0.01\)

=>   \(0.99 = 0.01 * e^{\frac{0.50 eV ]}{KT_k} }\)

=>   \(e^{\frac{0.50 eV ]}{KT_k} } = 99\)

Taking natural  log of both sides

=>   \(\frac{0.50 eV }{KT_k} } =4.5951\)

=>    \(0.50 eV =4.5951 * K * T_k\)

Note eV is electron volt and the equivalence in Joule is     \(eV = 1.60 *10^{-19} \ J\)

So

     \(0.50 * 1.60 *10^{-19 } =4.5951 * 1.380649 *10^{-23} * T_k\)

=>   \(T_k = 1261 \ K\)

Answer:

30+8[6^2- (2^2+5)]

30+8(36-(4+5))

30+8(36-9)

30+8 x 27

20+216

246

Step-by-step explanation:

evaluate 2^2 and 6^2 first

add (4+5)

then calculate (36-9)

then multiply (8 x 27)

then add (30+216)

solved

:)

hope this helped

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

Total of 7 + 18 = 25 employees, which means that \(N = 25\)

7 over 50, which means that \(k = 7\)

10 were dismissed, which means that \(n = 10\)

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055\)

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

632

Step-by-step explanation:

Answer:

528

Step-by-step explanation:

Surface area of bottom block + Surface area of top block - 2(Shared surface area)

Bottom block: 2(10*12) + 2(5*12) + 2(5*10) = 240 + 120 + 100 = 460 square inches

Top block: 2(2*2) + 4(2*8) = 8 + 64 = 72 square inches

Shared surface area = 2*2 = 4 square inches

Plugging into our formula:

460 + 72 - 4 = 528 square inches

9514 1404 393

Answer:

  -2

Step-by-step explanation:

The average rate of change on the interval [3, 9] is ...

  (f(9) -f(3))/(9 -3) = (41 -53)/(9 -3) = -12/6 = -2

Answer:

Step-by-step explanation:

The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.

Step 1: Evaluate the expression inside the parentheses.

7.4 - 3.6 = 3.8

After evaluating the expression inside the parentheses, the expression becomes:

12 ÷ 3.8 + 8 - 2

Step 2: Perform the division.

12 ÷ 3.8 = 3.158

After performing the division, the expression becomes:

3.158 + 8 - 2

Step 3: Perform the addition and subtraction from left to right.

3.158 + 8 = 11.158

11.158 - 2 = 9.158

Therefore, the value of the given expression is approximately 9.158.

The first step is:

Work/explanation:

The expression is:

12 ÷ (7.4 − 3.6) + 8 − 2

Let's recall the order of operations first:

So we evaluate

\(\sf{12\div(7.4-3.6)+8-2}\)

\(\sf{12\div3.8+8-2}\)

Next, division:

\(\sf{3.158+8-2}\)

Next, addition & subtraction:

\(\sf{9.158}\)

Answer:

0.63

Step-by-step explanation:

3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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The equivalent expressions of the percentages are 0.08 * 94 and 8/100 * 94

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

8% of 94

To start with, we express 8% as decimal

So, we have the following representation

0.08 of 94

Express as product

0.08 * 94

Next, we express it as fraction

8/100 * 94

Hence, the expressions are 0.08 * 94 and 8/100 * 94

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The spider needs 15 hours to climb up the top of the wall.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

A spider is trying to climb a wall of height = 15 meters

In each hour, it climbs up 3 meters but falls back 2 meters,

⇒ \(+3-2=1\)

Thus spider climbs 1 meter per hour.

For 15 meter wall, the spider needs 15 hours to climb up the wall.

Hence we can conclude that the spider needs 15 hours to climb up the top of the wall.

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The equation that results if Kiran squares both sides as his first step is gotten as; x + 2 - 10√(x + 2) + 25 = 121

We want to simplify the expression;

[√(x + 2)] - 5 = 11

Squaring both sides is;

([√(x + 2)] - 5) * ([√(x + 2)] - 5) = 11 * 11

⇒ x + 2 - 10√(x + 2) + 25 = 121

Thus, the correct answer is;

x + 2 - 10√(x + 2) + 25 = 121

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Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

Answer:

x = 11/c

Step-by-step explanation:

Solve for x:

c x - 4 = 7

Hint: | Isolate terms with x to the left-hand side.

Add 4 to both sides:

c x = 11

Hint: | Solve for x.

Divide both sides by c:

Answer: x = 11/c

Answer:

c(x)=2x+300 and $312

Step-by-step explanation:

c(6)=2(6)+300

c(6)=12+300=312

Answer:

part A: 12x=30

part b: 12x+15y=30

part c: 510=12x+15x

Step-by-step explanation:

Answer:

A={3,4,5,...,}

Step-by-step explanation:

Roster form means that we list each element of the set within curly braces

A relation may or may not represent a function.

The costs are given as:

(a) The mapping diagram

To do this, we simply point the number of movies, to the corresponding costs, using arrows

See attachment for the mapping diagram.

(b) Is the relation a function

From the attached mapping, we can see that:

The costs of each movie are different.

This means that: the relation is a function.

(c) Describe the pattern

Notice that as the number of movies increases, the cost also increases;

However, the unit cost decreases.

Hence, the unit cost of each movie decreases as the number of movies increases.

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The number of words Gillan can read in 1 minute is,  165

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Gillan read 3,135 words in 19 minutes

The number of words read each minute = w

Now, it has given,

Total words = 3135

Time taken = 19 minutes

For words per minute,

we need to take ratio of total words and total time taken,

Ratio =  Total words/Time taken

         =   3135/19

         =   165

Hence, the number of words in 1 minute is 165

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First we have the given function, so y = 6 - x/2

Then, the first step to find the inverse is switching places of x and y, so x = 6 - y/2

Then, we need to isolate y, so first we have y/2 = 6 - x

Now, multiplying the equation by 2, we have y = 12 - 2x

And finally, switching y by f^-1(x), we have f^-1(x) = 12 - 2x

Answer:

can u explain this a little bit more i think ik the answer but im not sure #3 is well i think it is 120#4 is 164.85 #5 is 40 yea hope this helps :)

Step-by-step explanation:

Answer:

#3 = 120

#4 = 164.85

#5 = 40

#6= 240

Step-by-step explanation:

hope i helped!

Answer:

1

0.8

0.4

Step-by-step explanation:

y = 5x

Substituting '5':

5 = 5x

x = 5/5

x = 1

Substituting 4:

4 = 5x

x = 4/5

x = 0.8

Substituting 2:

2 = 5x

x = 2/5

x = 0.4

Answer:

1) x = 1

2) x = 4/5

3) x = 2/5

Step-by-step explanation:

1) 5= 5x

x = 1

2) 4 = 5x

x = 4/5

3) 2 = 5x

x = 2/5

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​