find an explicit formula for , if 0, 1, 2, … is a sequence satisfying the given recurrence relation and initial conditions

Answer:

c

Step-by-step explanation:

We have the following functions

Let's determine the domain of the following:

1. domain of g(x)/f(x):

Let's simplify the above

The above it's like having to functions, hence two domains:

Therefore, the domain of g/f (x) is:

2. domain of g(f(x)):

Since, x^2-4 > 0, therefore domain of g(f(x)) is the following:

3. domain of f(g(x)):​

Since, x>0, Therefore, the domain of f(g(x)) is:

Answer:

y = 2x2

y + 3x = 2x2 – 8

Step-by-step explanation:

The equations that are quadratic in nature are -

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c.

Given are the set of equations.

A quadratic equation is a equation of degree 2. The equation with degree 2 are -

Therefore, the equations that are quadratic in nature are -

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Answer:

b = 48 °, c = 46°

Step-by-step explanation:

c = 46 ° as between parallel lines, alternate opposite angles are equal.

since opposite angles are equal 94 ° = 46 ° + additional angel

therefore b = 94° - 46 ° = 48 ° , as sum of 2 internal angles of a triangle is equal to opposite exterior angle.

Answer:

Step-by-step explanation:

13

We can solve the Inequalities by Isolating the variables that are present in the given Inequality.

In mathematics, an inequality is a connection between two values or mathematical equations that results in an unequal comparison.

The signs that we use in Inequalities are less than( < ), less than or equal to ( ≤ ), greater than ( > ), greater than or equal to ( ≥ ), and not equal to (≠) sign.

Lets us consider we have inequality 3x + 2 + x ≥ 10

We can solve the above inequality as given below

Here we will solve the inequality by Isolating the variable  

Step - 1

Add x term and constant terms

=> 4x + 2 ≥ 10   [ here 3x + x = 4x ]

Step - 2  

Bring out x terms at one side, and constant terms at another side by doing required operations like adding

=> 4x + 2 ≥ 10    [ here we will subtract 2 from both sides ]

=> 4x + 2 - 2  ≥ 10 - 2

=> 4x  ≥ 8  

Step - 3

Now isolate the variable to get the solution

=>  4x/4  ≥ 8/4         [ here divided by 4 ]

=> x  ≥ 2  

Therefore, the required solution is x ≥ 2    

Therefore,

We can solve the Inequalities by Isolating the variables that are present in the given Inequality.

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The first, second and third number is -4, 11 and 5.

An equation is formed from two or more numbers and variables, forming an expression through the use of mathematical operations of addition, subtraction, multiplication and division.

Let x represent the first number, y represent the second number and z represent the third number.

The sum of three numbers is 12. Hence:

x + y + z = 12      (1)

The sum of the first number and the second number is 2 more than the third number. Hence:

x + y = 2 + z     (2)

The second number minus the sum of the first number and third number is twice the third number. Hence:

y - (x + z) = 2z     (3)

From the 3 equations:

x = -4, y = 11 and z = 5

The numbers are -4, 11 and 5.

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Step-by-step explanation:

Create your own puzzle problem similar to the problem at the beginning of the lesson. Post your original puzzle on the discussion board.

Original problem: The sum of three numbers is 12. The sum of the first number and the second number is 2 more than the third number. The second number minus the sum of the first number and third number is twice the third number

Answer:

$36.97  

The cost of the meal was $32.57 and he used a 10% off coupon. You can make 10% equal to 0.1 because . Now do . This is the discount, so you want to subtract this from the original to get the actual price of the meal, .

The tax was 8% so this means he is adding

Answer:

The expression x(2.15)= 4.73

Answer:

\(Goat = 2080IU\)

Step-by-step explanation:

Given

Ratio = 3 : 4

Litre of cow = 1560IU

Required

IU of a litre of goat

The ratio represents ratio of cow milk to goat milk

In other words;

\(Cow:Goat = 3 : 4\)

To calculate the number of IU in a litre of goat milk; we substitute Cow with 1650 in the above expression

\(Cow:Goat = 3 : 4\)

\(1560:Goat = 3 : 4\)

Convert  to fraction

\(\frac{1560}{Goat} = \frac{3}{4}\)

Multiply both sides by 4

\(4 * \frac{1560}{Goat} = \frac{3}{4} * 4\)

\(\frac{4 * 1560}{Goat} = \frac{ 4 * 3}{4}\)

\(\frac{6240}{Goat} = 3\)

Multiply both sides by Goat

\(Goat * \frac{6240}{Goat} = 3 * Goat\)

\(6240 = 3 * Goat\)

Divide both sides by 3

\(\frac{6240}{3} = \frac{3 * Goat}{3}\)

\(\frac{6240}{3} = \frac{3 * Goat}{3}\)

\(2080 = Goat\)

\(Goat = 2080\)

The value of ( g o f ) (x) is x^2 + 2

A function is a rule or an expression that shows relationship between a variable known as the independent variable and another variable known as the dependent variable.

From the information given, we have;

( g o f ) (x) can be determined by substituting the value for x in g(x) as the function f(x) = x + 1

( g o f ) (x) = (x+ 1) ^ 2 + 1

( g o f ) (x) = x^2 + 1^ 2 + 1

Find the square

( g o f ) (x) = x^2 + 1 + 1

( g o f ) (x) = x^2 + 2

The value of ( g o f ) (x) is x^2 + 2

Thus, the value of ( g o f ) (x) is x^2 + 2

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Answer: 40320 ways

Step-by-step explanation:

From the question, we are informed that we should the number of arrangements that are in the letters in the word: CHAPTERS.

First, we should note that there are 8 letters in the word CHAPTERS, therefore the number of ways that the word can be arranged is 8! which simply means:

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40320 ways

Answer: 6.2

Step-by-step explanation:

Geometric Mean = √( 2 x 19 ) = 2√38 = 6.1644

Hand-grip strength is a sign of general toughness and a good indicator of significant consequences.

For grip strength measurements, current, population-specific reference values are required to interpret the results appropriately.

Objectives

To offer grip-strength reference values and formulae based on population for US citizens ages 18 to 85.

Methods

In this cross-sectional study, hand-grip data from 1232 participants, aged 18 to 85, were taken from the database of the 2011 normative phase of the US National Institutes of Health Toolbox project. Equations and descriptive reference values were derived from the data.

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The question is incomplete
the standard deviation for hand grip strength. what Objectives and Methods of the distribution

Answer:

D. 240

Step-by-step explanation:

6 types of backpacks = 6

4 types of binders = 4

5 types of pencils = 5

2 types of notebook paper= 2

6×4×5×2=

24×10=

240

The number of possible outcomes will be 240. The correct option is D.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that there are 6 types of backpacks, 4 types of binders, 5 types of pencils, and 2 types of notebook paper.

6 types of backpacks = 6

4 types of binders = 4

5 types of pencils = 5

2 types of notebook paper= 2

The number of possible outcomes will be calculated as:-

N = 6×4×5×2

N = 24×10

N = 240

Therefore, there will be 240 possible outcomes. The correct answer is D.

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Answer:

5+2+2(5)+3=4(5)

simplify

5+2+10+3=20 and  4(5)=20  

20=20

Answer: 20

Step-by-step explanation:

Simplify:

5+2+2x5+3

Remove parentheses:

5+2+2(5)+3=4(5)

Multiply the numbers 2x5=10:

5+2+10+3

Add the Numbers:

=20

Simplify (4)5 :

Remove Parentheses:

4 x 5

Multiply:

=20

20=20

Answer:

|x| = x if x >= 0, -x if x < 0

Step-by-step explanation:

Answer:  £6.50

Step-by-step explanation:

Let the cost of one jumper be x, and since Kara buys 5 jumpers, she pays for 4 and gets 1 free.

Therefore, she effectively pays for 4 jumpers. Now we can form the equation to find the value of x: (4x / 5) = (5.20)

Now solving the equation, we get; x = £6.50

Hence, the regular cost of one jumper when not in this offer is £6.50.

The smallest number that can be subtracted from each number to obtain a perfect square of 996058 is 998.

To find the smallest number that can be subtracted from each number so that the difference is a perfect square of 996058, we need to find the square root of 996058 and round it down to the nearest whole number.

The square root of 996058 is approximately 998.027. Rounding it down gives us 998.

Therefore, the smallest number that can be subtracted from each number to obtain a perfect square of 996058 is 998.

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The correct question is given thus:

what smallest number could be subtracted from each number so that the difference is a perfect square number of 996058?

To determine μx and σx, we can use the formula:

μx = μ
σx = σ / √n

Plugging in the values we get:

μx = 68
σx = 20 / √29 ≈ 3.71

Therefore, the sample mean is 68 and the sample standard deviation is approximately 3.71.


μx represents the mean of the sample and σx represents the standard deviation of the sample. We can calculate these values using the formula provided above, which involves the population mean (μ), population standard deviation (σ), and sample size (n).

In this case, the population mean is 68, the population standard deviation is 20, and the sample size is 29. By plugging in these values into the formula, we can calculate the sample mean and sample standard deviation.


By calculating the sample mean and sample standard deviation, we have a better understanding of the distribution of the sample data. These values can be used to make inferences about the population, such as estimating population parameters or testing hypotheses.
 Let's determine μx (the mean of the sample) and σx (the standard deviation of the sample) using the given population parameters and sample size.


μx = μ = 68
σx = σ / √n = 20 / √29

Explanation:
1. The mean of the sample (μx) is equal to the mean of the population (μ), so μx = 68.
2. To find the standard deviation of the sample (σx), you need to divide the population standard deviation (σ) by the square root of the sample size (n). In this case, σ = 20 and n = 29, so σx = 20 / √29.


For the given population parameters and sample size, the mean of the sample (μx) is 68, and the standard deviation of the sample (σx) is approximately 3.71 (20 / √29 ≈ 3.71).

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Answer:

64 feet squared

Step-by-step explanation:

Since it's a square, all sides have a length of 8 ft. Area is length x width, so simply multiply 8 by itself. 64 feet squared is therefore the answer.

The total surplus at the equilibrium point is: $200,000

This is the maximum total surplus that can be achieved in the market for the digital camera.

To compute the maximum total surplus, we need to find the equilibrium quantity and price in the market for the digital camera, and then calculate the consumer and producer surplus at that point.

First, we need to set the demand and supply functions equal to each other to find the equilibrium quantity:

50 - 2P = 2P - 10

4P = 60

P = 15

Substituting this equilibrium price into either the demand or supply function, we can find the equilibrium quantity:

Q = 50 - 2(15) = 20

So the equilibrium price is $15, and the equilibrium quantity is 20,000 digital cameras.

Next, we can calculate the consumer and producer surplus at the equilibrium point. Consumer surplus is the difference between the maximum price a consumer is willing to pay for a good and the market price, summed over all consumers in the market. Producer surplus is the difference between the market price and the minimum price a producer is willing to accept for a good, summed over all producers in the market.

The demand function gives us the maximum price consumers are willing to pay for each quantity of digital cameras:

P = 25 - 0.5Q

So at the equilibrium quantity of 20,000 digital cameras, the maximum price consumers are willing to pay is:

P = 25 - 0.5(20) = 15

This is exactly the same as the market price, so there is no consumer surplus at the equilibrium point.

The supply function gives us the minimum price producers are willing to accept for each quantity of digital cameras:

P = 0.5Q - 5

So at the equilibrium quantity of 20,000 digital cameras, the minimum price producers are willing to accept is:

P = 0.5(20) - 5 = 5

The market price is $15, so the producer surplus is:

(15 - 5) * 20 = $200,000

Therefore, the total surplus at the equilibrium point is:

$200,000

This is the maximum total surplus that can be achieved in the market for the digital camera.

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Answer: How many distinct license plates can be formed if the first number cannot be zero and the three letters cannot form "DOG"?

Step-by-step explanation:

Since the first digit cannot be 0, there are 9 choices for the first digit.

For the three letters, there are 26 choices for the first letter, 26 choices for the second letter, and 25 choices for the third letter (since we cannot use "D", "O", or "G").

For the last three digits, there are 10 choices for each digit.

Therefore, the total number of distinct license plates can be formed is:

9 x 26 x 26 x 25 x 10 x 10 x 10 = 16,290,000

So there are 16,290,000 distinct license plates that can be formed if the first number cannot be zero and the three letters cannot form "DOG".

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Answer:

Perimeter = 6s + 9 units

Step-by-step explanation:

Perimeter = 2s + 4 + 4s + 2 + 3

                = 2s + 4s + 4 +  2 + 3

                = 6s + 9 units

The equation of the transformed function is g(x) = -x² - 2

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

f(x) = x² -- parent root function

When the graph is examined (see attachment), we have the transformation to be

g(x) = reflect f(x) across the x-axis and a downward shift of 2 units.

Mathematically, this can be represented as

g(x) = -f(x) - 2

Substitute the known values in the above equation, so, we have the following representation

g(x) = -x² - 2

Hence, the transformed function is g(x) = -x² - 2

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Answer:

Try ABECFDGHI

Step-by-step explanation:

Im going FROM left to right

Answer:

1 2 3 ways for it to function

Step-by-step explanation:

Answer:

height = 14.2 m , base = 7.1 m

Step-by-step explanation:

let the base be b then height h = 2b

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh

Here A = 50 , then

\(\frac{1}{2}\) × b × 2b = 50

b² = 50 ( take square root of both sides )

b = \(\sqrt{50}\) ≈ 7.1 ( to the nearest tenth )

Then base = 7.1 m and height = 2 × 7.1 = 14.2 m

The number of incorrect answers is 8.

linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Let,

number correct of answer = x

number of incorrect answer = y

Given that,

Total number of answer  x+y = 30 ......(1)

Total score = x-\(\frac{1}{4}\)y = 20  .......(2)

In equation (2) multiply by -1 on both side.

-x+\(\frac{1}{4}\)y = -20   .......(3)

Now,

Adding both the equation (1) and (3)

x+y-x+\(\frac{1}{4}\)y = 30-20

\(\frac{5}{4} y\) = 10

y = 8

Hence, The number of incorrect answers is 8.

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