A sequence is defined by the recursive function f(n + 1) = one-halff(n). If f(3) = 9 , what is f(1) ?
1
3
27
81
Please answer!!!! <3

The values of a and b for the probability density function are a = 56 and b = 216.

According to the given information, the mean daily spending by Americans earning over $90,000 per year was $136 per day, and the probability density function is given by f(x) = 0.00625 for a ≤ x ≤ b.

To find the values of a and b for the probability density function, we can use the formula for the mean of a uniform distribution:

mean = (a + b)/2

Substituting the given mean value of $136 into the formula, we get:

136 = (a + b)/2

Multiplying both sides of the equation by 2, we get:

272 = a + b

Rearranging the equation, we get:

b = 272 - a

Now, we can use the formula for the area under the probability density function, which is equal to 1:

∫_a^b f(x) dx = 1

Substituting the given probability density function and the value of b into the formula, we get:

∫_a^(272-a) 0.00625 dx = 1

Simplifying the integral, we get:

0.00625(272 - 2a) = 1

Dividing both sides of the equation by 0.00625, we get:

272 - 2a = 160

Rearranging the equation, we get:

2a = 112

Dividing both sides of the equation by 2, we get:

a = 56

Substituting the value of a back into the equation for b, we get:

b = 272 - 56 = 216

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The quadratic formula for a polynomial is given by:

Therefore, option (C) is correct.

15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:

Step-by-step explanation:

Sing robbery and ur done

Answer:

$168.15

Step-by-step explanation:

To find 57% of 295 you have to multiply 295 by the decimal form of a percent.

To get the decimal form of a percent you take the decimal point (57.00) and move it twice to the left (57.00 --> .5700)

Now, we can multiply .57 by 295 to get your answer:

(.57)(295) = 168.15

Therefore, 57% of 295 equals $168.15.

Hope this helps!!

- Kay :)

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

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The solution of the system of equation y = 2x - 5 y = -4x + 1 is (1, -3).

The system of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let's solve the system of equation using substitution method.

Therefore,

y = 2x - 5

y = -4x + 1

Hence,

-4x + 1 = 2x - 5

-4x - 2x = -5 - 1

-6x = -6

divide both sides by -6

x = -6 / -6

x = 1

Let's find y.

y = -4x + 1

y = -4(1) + 1

y = -4 + 1

y = -3

Therefore, the solution is (1, -3)

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Answer:

answer  in picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. the question is asking you to multiply the two function expressions together

2. so all we do is (3x - 1)(x² + 4) which gives you 3x³ + 12x - x² - 4

The solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.

What is a quadratic equation?

A quadratic equation is a type of polynomial equation that has the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are coefficients. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants. The solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2-4ac)) / 2a

To solve for x in the equation 2x^2 -19x + 2 = -10x, we need to rearrange it in the standard form of a quadratic equation by isolating the x^2 term and moving the other terms to the other side:

2x^2 -10x -19x +2 = 0

2x^2 -29x +2 = 0

Now we can apply the quadratic formula:

x = (-b ± √(b^2-4ac)) / 2a

x = (-(-29) ± √((-29)^2-422)) / 2*2

x = (29 ± √(841-16)) / 4

x = (29 ± √(825)) / 4

Hence, the solutions of the quadratic equation are given by x = (29 ± √825) / 4 which are two complex numbers.

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Answer:

Maybe try 23-9. Or maybe the answer is 23, hopefully this helped.

Step-by-step explanation:

Answer:

21.2 cm is the right answer.

Step-by-step explanation:

tan(θ)=o/a

tan(23)=17/x

divided by x on both sides to equal

x(letter) x tan(23)=17

and then on the calculator you type in 17/tan(23)

=21.20267129 cm

to 1 s.f= 21.2 cm

the value of F(9) is approximately 23.308.

To find the value of F(9) given that F(x) is an antiderivative of (ln x)^3/x and F(1) = 0, we can use the fundamental theorem of calculus.

According to the fundamental theorem of calculus, if F(x) is an antiderivative of a function f(x), then:

∫[a,b] f(x) dx = F(b) - F(a)

Since F(1) = 0, we can write:

∫[1,9] (ln x)^3/x dx = F(9) - F(1)

To evaluate the integral, we can make a substitution:

Let u = ln x, then du = (1/x) dx

The integral becomes:

∫[ln 1, ln 9] u^3 du

Integrating u^3 with respect to u:

[(1/4)u^4] | [ln 1, ln 9] = (1/4)(ln 9)^4 - (1/4)(ln 1)^4

Since ln 1 = 0, we have:

(1/4)(ln 9)^4 - (1/4)(ln 1)^4 = (1/4)(ln 9)^4

Therefore, F(9) - F(1) = (1/4)(ln 9)^4

Since F(1) = 0, we can conclude that F(9) = (1/4)(ln 9)^4.

Calculating this value:

F(9) = (1/4)(ln 9)^4 ≈ 23.308

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Answer: Total cost of their meal is $78

Step-by-step explanation: 20% of 65 is a 13 dollars tip adding up to a total of $78

65*0.2 = 13

65+13=78

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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the maximum and minimum values of f(x,y) on the ellipse occur at approximately (±0.445, ±0.364) and (±0.364, ±0.445), respectively.

To find the points on the ellipse 3x^2 + 2y^2 = 1 where f(x,y) = xy has its extreme values, we can use the method of Lagrange multipliers.

We want to find the points (x, y) on the ellipse where the gradient of f(x,y) is parallel to the gradient of the constraint function g(x,y) = 3x^2 + 2y^2 - 1. The gradient of f(x,y) is <y, x>, and the gradient of g(x,y) is <6x, 4y>. Thus, we need to solve the system of equations:

y = λ(6x)

x = λ(4y)

3x^2 + 2y^2 = 1

From the second equation, we get λ = x/(4y). Substituting into the first equation, we get y = (3/8)x^2. Substituting into the third equation, we get:

3x^2 + 2[(3/8)x^2]^2 = 1

3x^2 + (27/32)x^4 = 1

Multiplying both sides by 32, we get:

96x^2 + 27x^4 - 32 = 0

This is a quartic equation in x^2, which can be solved using standard methods. We can also note that the function f(x,y) = xy is symmetric with respect to the line y = x, so any extreme values on one side of this line will have a corresponding extreme value on the other side.

Therefore, the maximum and minimum values of f(x,y) on the ellipse occur at approximately (±0.445, ±0.364) and (±0.364, ±0.445), respectively.

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Answer: 25°

Step-by-step explanation:

From the question, Toothy the crocodile wants to eat a delicious chicken and his mouth is open to an angle of 30 degrees but he needs to open his mouth to the angle of 55 degrees for the chicken to fit.

The additional angle that Toothy's mouth needs to be open so he can eat the chicken will be:

= 55° - 30°

= 25°

Answer:

25

Step-by-step explanation:

did it on khan academy

We are given that 2 people, John and Bob, travel a distance of 4 miles and 2 miles respectively. To determine which of the two went faster, we need to find the ratio of distance per time for each individual.

For Jhon we have:

For bob we have:

Therefore, John and Bob had the same speed.

A discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.

The main difference between a discrete function and a continuous function lies in the nature of their domains and ranges. A discrete function is defined on a set of distinct, separate values, while a continuous function is defined on a continuous interval or range of values.

A discrete function can be thought of as a function that consists of isolated points. For example, let's consider a function that represents the number of students in a classroom over the years. The domain of this function would be the set of discrete values representing each year, such as {2010, 2011, 2012, ...}. The range would be the set of corresponding numbers representing the number of students in the classroom each year.

On the other hand, a continuous function is one that can take on any value within a given interval. For instance, consider a function that represents the temperature in a room over time. The domain of this function would be a continuous interval, such as [0, 24] representing the 24-hour day. The range would be the set of possible temperature values within that interval.

To summarize, a discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.
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Answer:

4/5

Step-by-step explanation:

From the above question, we are given the number of people who like a particular flavor.

The number of people who like:

Vanilla = 36

Strawberry = 45

Therefore, the ratio of the people who prefer vanilla to the people who prefer strawberry is written as

Vanilla : Strawberry

= 36:45

= 4:5

= 4/5

Therefore, option B = 4/5 is the correct option

Answer:

3.5 hours

Step-by-step explanation:

74-32=42

42/12=3.5

Answer:

Step-by-step explanation:

What are the main categories of electors in India?

Ans.- There are 3 categories of electors in India: –

(i)    General electors,

(ii)    Oversees   (NRI)   electors    -    (   Kindly   refer   to   ‘Frequently   Asked Questions – Overseas Electors’),

(iii)    Service Electors - (Kindly refer to ‘Frequently Asked Questions – Service Electors’).

Q2. Who is eligible to be registered as a general elector?

Ans. Every Indian citizen who has attained the age of 18 years on the qualifying date i.e. first day of January of the year of revision of...

faqs

resident electors

The median is the value in the middle of a data set, meaning that 50% of data points. The y intercept of the median line for the dataset 2 3 4 5 7 8 10 12 is 1.65.

To find the y-intercept of the median-median line for the given dataset, we first need to find the median of the x-values and the median of the y-values.

The median of the x-values can be found by first arranging the dataset in ascending order:

2, 3, 4, 5, 7, 8, 10, 12

The median of this dataset is the middle value, which is 5.

The median of the y-values can be found in a similar way:

2, 3, 4, 5, 7, 8, 10, 12

The median of this dataset is also 5.

Now that we have the medians of the x- and y-values, we can use them to find the slope of the median-median line. The slope is given by:

slope = (median of y-values for points above median of x-values - median of y-values for points below median of x-values) / (median of x-values for points above median of y-values - median of x-values for points below median of y-values)

To apply this formula, we need to split the dataset into two parts: the points above the median of x-values (5) and the points below the median of x-values.

Points above median of x-values:

7, 8, 10, 12

Points below median of x-values:

2, 3, 4, 5

The median of the y-values for the points above the median of x-values is 9, and the median of the y-values for the points below the median of x-values is 3.

Plugging these values into the slope formula, we get:

slope = (9 - 3) / (10 - 2) = 0.67

Now we can use the point-slope form of a line to find the equation of the median-median line:

y - median of y-values = slope × (x - median of x-values)

y - 5 = 0.67 × (x - 5)

Simplifying this equation, we get:

y = 0.67x + 1.65

Therefore, the y-intercept of the median-median line for the given dataset is 1.65.

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55/63 is already in its simplified form.

To simplify 55/63, we can divide both the numerator and denominator by their greatest common factor (GCF). To find the GCF of 55 and 63, we can use prime factorization:

55 = 5 × 11

63 = 3 × 3 × 7

The common factors of 55 and 63 are 1, so the GCF is 1. We can divide both the numerator and denominator by 1:

55/1/63/1

Therefore, 55/63 in simplest form is 55/63.

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Answer:

Step-by-step explanation:

f(x) = -4x - 4

f(x - 2) = -4 (x - 2) - 4

f(x - 2) = -4x + 8 - 4

f(x - 2) = -4x + 4

Answer: Cumulative frequency distribution

Step-by-step explanation: Not entirely sure but I believe you are looking for this definition based on the question. Hope this helps :)