2√5 is this rational or irrational?

Answer:

f(x) = 2(x - 2)² - 1

Step-by-step explanation:

Given the vertex, (2, -1) and the point, (0, 7), we can plug these values into the vertex form of the quadratic function:

f(x) = a(x - h)² + h

where:

vertex = (h, k)

a = determines whether the graph opens up or down, and the wideness or narrowness of the parabola.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

We could substitute the given values into the vertex form, and solve for the value of "a":

f(x) = a(x - h)² + h

7 = a(0 - 2)² - 1

7 = a(-2)² - 1

7 = a(4) - 1

Add 1 to both sides:

7 + 1 = a(4) - 1 + 1

8 = 4a

Divide both sides by 4 to solve for a:

8/4 = 4a/4

2 = a

Since a = 2, and the vertex = (2, -1) then we could plug this value into the given function:

f(x) = 2(x - 2)² -1

Attached is a screenshot of the graph where it contains the given points.

Please mark my answers as the Brainliest, if you find my explanations helpful :)

The given probability of having six girls in a six-child family is 0.015625. To determine the method used to compute this probability, we need to analyze the information provided.

The Classical method is based on theoretical assumptions and probabilities calculated using mathematical principles. It assumes equally likely outcomes and relies on counting favorable outcomes over the total number of possible outcomes.

The Empirical method involves gathering data from observations or experiments to estimate probabilities. It relies on observed frequencies and relative frequencies to compute probabilities. However, the given probability does not suggest a sample or data collection, making it unlikely that the Empirical method was used.

The Subjective method involves assigning probabilities based on personal judgment or opinions. Individuals subjectively evaluate the likelihood of an event based on their own beliefs or knowledge.

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Position vs. time graph is a graph that shows the position of an object over time. It can be a straight line or a curved line depending on the motion of the object.

What is graph ?

A graph is a mathematical structure used to represent relationships between objects. In a graph, objects are represented by vertices (or nodes) and relationships are represented by edges (or arcs). Graphs can be used to model a wide variety of real-world systems, including networks of roads, social networks, and the internet.

The position vs. time graph is a visual representation of an object's motion, where the position of the object is plotted on the y-axis and the time it took to reach that position is plotted on the x-axis. The graph helps to show the relationship between the position and time of an object in motion. The line on the graph can be either straight or curved, depending on the type of motion the object is undergoing. If the object is moving at a constant speed, the line will be straight. If the object is accelerating or decelerating, the line will be curved.

Position vs. time graph is a graph that shows the position of an object over time. It can be a straight line or a curved line depending on the motion of the object.

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Answer:

5,006 :)

Step-by-step explanation:

The whole statement says that "for all people x and y who are not Ralph, x trusts y".

Let F(x, y) be the statement x trusts y, where the domain of discourse for both x and y is all people, nobody trusts Ralph.

The logic symbolization of the given statement is:

∀x ∀y [(x ≠ Ralph ∧ y ≠ Ralph ∧ x ≠ y) → F(x, y)]

Here, the universal quantifier ∀ means "for all".

So, ∀x means "for all people x" and ∀y means "for all people y".

The symbol → means "implies" or "if-then".

The statement (x ≠ Ralph ∧ y ≠ Ralph ∧ x ≠ y) means "x is not Ralph, y is not Ralph, and x is not equal to y".

So, the whole statement says that "for all people x and y who are not Ralph, x trusts y".

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Answer:

A. 10

B. 10 then -10

C. 10 for both

Step-by-step explanation:

I hope that this helps!!!!

Answer:

- 16.2

Step-by-step explanation:

You can just divide it XD

-8.1 ÷ 0.5

= - 16.2

We know that y varies directly with x.

First we need to find the constant of variation

7=14k

k= 7/14

k=1/2

the equation that relates x and y is

The trigonometric ratios for each triangles are:

Please note that all angles B are the right angle, then:

cos B = 1; sin B = 0; tan B = -

The trigonometric ratio of sin, cos, tan, can be formulated as:

(please refer to the attached triangle below for reference)

cos A = side adjacent to A / Hypotenuse

Cos A = b/c

Sin A = side opposite to A / Hypotenuse

Sin A = a/b

Tan A = Side opposite to A / Side adjacent to A

Tan A = a/b

From these formulas, we can find that:

Triangle 1

Cos A = 40/50 = 4/5

Sin A = 30/50 = 3/5

Tan A = 30/40 = 3/4

Cos C = 30/50 = 3/5

Sin C = 40/50 = 4/5

Tan C = 40/30 = 4/3

Triangle 2

Cos A = 27/45 = 3/5

Sin A = 36/45 = 4/5

Tan A = 36/27 = 4/3

Cos C = 36/45 = 4/5

Sin C = 27/45 = 3/5

Tan C= 27/36 = 3/4

Triangle 3

Cos A = 15/17

Sin A = 8/15

Tan A = 8/15

Cos C = 8/17

Sin C = 15/17

Tan C = 15/8

Please note that all angle B on the three triangles are all a right angle, then:

Cos B = 1

Sin B = 0

Tan B = -

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Therefore, according to the unitary data provided, we can conclude that there are a greater number of trout than perch in the pond and that trout make up the majority of the fish community there.

After finding the size of a tiny slice, multiply the number by two to complete a task using unitary variable procedure. Simply stated, the unit technique is used to separate a designed object from a particular set or set of sets. For example, the price of 40 pencils is 400 pounds ($1.01) or Rs. It's possible that one country will have total authority over the method employed to accomplish this. Almost every living creature has a distinctive quality.

Here,

One conclusion that can be drawn is that the majority of the pond's fish are trout.

This is due to the fact that the quantity of trout captured (109) is now almost twice that of bluegill caught (81) and much more and over four times that of largemouth caught (25).

Another conclusion is the existence of 28 so much trout in the water than perch.

Calculate this by dividing the quantity of perch captured by the quantity of fish captured:

=>  109 - 81 = 28.

Therefore, according to the data provided, we can conclude that there are a greater number of trout than perch in the pond and that trout make up the majority of the fish community there.

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Answer:

(m+10)(m-9)

Step-by-step explanation:

To factor this equation we want to find two numbers that multiply to -90 but also add/subtract to 1.

Those two numbers are 10 and -9 (10×-9=-90, 10-9=1)

Answer:

\((m-9)(m+10)\)

Step-by-step explanation:

When you are given an expression in this format

\(ax^2+bx+c\)

You must find two numbers that add up to b while the product is c.

You do trial and error to figure it out for your equation.

\(m^2+m-90\)

Hmm... what two numbers add up to 1 and multiplied together equal -90.

Start off with pairs that can equal 90.

45 2

18 5

9 10

Ok, well 45 * 2 does equal 90 but 45 + 2 = 47and 45 + -2 = 43 but there's no way I can make it equal to 1. Next!

18 * 5 equals 90 but 18 + -5 = 13 and 18 + 5 = 23, I can just tell that there's no way I can make this equal to 1.

9 * 10 equals 90, 9 + 10 = 19 but 9 + -10 = -1. Now, that's interesting, We have -1 but we need 1. All we have to do is flip the order. 10 + -9 = 1. And -9 * 10 = -90, PERFECT!

Now use the two numbers and put it in factored form.

\((m-9)(m+10)\)

John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

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Percentage =  1% = 0.01, 10% = 0.1 and 100% = 1

Increase in percentage = 1 + percentage eg. (1  + 0.08 = 1.08)

Decrease in percentage = 1 - percentage eg. (1 - 0.08

Answer:  69. 24  

Step-by-step explanation:

To round the number  69.238  to the nearest hundreths, you will  check if the number on the right side of the hundredths  place value is greater, equal to, or less than 5.

If it's equal to five there that means the hundredths place value will go up by one

If it's less than five then  it will stay the same and all the numbers to the right of it will be zero.

if it's greater than 5 then you will also round up the hundredths place value by one.  

In the number 3 is  in the hundredths  place and the number right to it is greater than 5 so 3 will become 4.  

Answer:

8 is the maximum he can get.

Step-by-step explanation:

Good luck!

Answer:

(4,-2)

Step-by-step explanation:

The health club has 2 employees who work on lead generation. Each employee contacts leads for 20 hours a week and is paid $20 per hour. Approximately 8% of the leads become members and pay a one-time fee of $100. Material costs are $190 per week, and overhead costs are $1,100 per week. To analyze the productivity of the operation, we need to calculate the multifactor productivity in fees generated per dollar of input. The owner is also considering purchasing a new software program that would allow each employee to contact 20 more leads per week, but it would increase material costs by $260 per week. We need to calculate the new multifactor productivity if the software is purchased and determine how it would affect productivity.

a. To calculate the multifactor productivity, we need to determine the total fees generated and the total input costs. The total fees generated per week can be calculated as 8% of the total number of leads contacted multiplied by the one-time fee of $100, which is (0.08 * 200) * $100 = $1,600. The total input costs per week are the sum of employee wages, material costs, and overhead costs, which is (2 employees * 20 hours/week * $20/hour) + $190 + $1,100 = $2,490. Therefore, the multifactor productivity is $1,600 / $2,490 = 0.64.

b. If the owner purchases the software program and each employee can contact 20 more leads per week, the total number of leads contacted per week by both employees will be 2 * (200 + 20) = 440. The new material costs per week will be $190 + $260 = $450. The overhead costs remain the same at $1,100. The total input costs per week become (2 employees * 20 hours/week * $20/hour) + $450 + $1,100 = $1,650. The new multifactor productivity is $1,600 / $1,650 = 0.97.

c. The new multifactor productivity after purchasing the software program has increased to 0.97 from the previous value of 0.64. The change in productivity can be calculated as ((0.97 - 0.64) / 0.64) * 100 = 51.6%. Therefore, purchasing the software program would increase productivity by approximately 51.6%.

By analyzing the multifactor productivity and the impact of purchasing the software program, the owner can make an informed decision about whether the investment is worthwhile considering the potential increase in productivity.

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A positive integer y is a whole number by definition, so we are essentially being asked how many positive integers there are. There are infinitely many positive integers, so the answer to the question is also infinity.

A positive integer y is a whole number if it isn't a bit or a numeric. In other words, it's a number that can be expressed without using  fragments or numbers, and can be written as a finite sum of positive integers. For  illustration, 2, 5, and 10 are whole  figures, but3/4,1.5, and √ 2 are not.   To determine how  numerous different values of y are whole  figures, we need to understand the  parcels of whole  figures.

Whole  figures have two main  parcels they're closed under addition and  addition. This means that when you add or multiply two whole  figures, the result is always a whole number. For  illustration, 2 3 =  5 and 2 × 3 =  6, both of which are whole  figures.   To find how  numerous different values of y are whole  figures, we can start with the  lowest possible value of y, which is 1.

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This value is approximate.

=========================================================

Work Shown:

area = 0.5*side1*side2*sin(included angle)

area = 0.5*AB*AC*sin(A)

area = 0.5*11*18*sin(55)

area = 81.0960523846101

area = 81.1 cm^2

The cm^2 refers to "square cm".

Notice that the angle must be between the two sides, hence the "included".

The pool will have approximately 12,555 gallons of water left in it after 12 days.

To find out how many gallons of water will be left in the pool after 12 days, given that it evaporates at a rate of 2% per day and has 16,000 gallons today, follow these steps:

1. Determine the rate of water remaining in the pool each day:

Since the pool loses 2% of water daily, the remaining percentage is 100% - 2% = 98%.

In decimal form, this is 0.98.

2. Calculate the amount of water after 12 days:

To do this, raise the daily remaining water rate (0.98) to the power of the number of days (12):

0.98¹² ≈ 0.7847.

This represents the percentage of water remaining in the pool after 12 days.

3. Multiply the initial water amount (16,000 gallons) by the percentage of water remaining after 12 days (0.7847):

16,000 * 0.7847 ≈ 12,555 gallons.

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Answer:

Step-by-step explanation:

90+35=exterior angle(sum of two interior opposite angle is equal to the exterior angle formed)

125=exterior angle

Answer:

125

Step-by-step explanation:

all the angles inside the triangle should add to 180:

so 180 - 35 - 90 = 55

then since it asked for exterior it should be:

180 - 55 = 125

because it on a straight line and a straight line is 180 it becomes:

125

I can help with more too

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer: C

A

B

D

Step-by-step explanation:

Answer:

(x+y)+2

hope this helps

Answer:

n = 11

Step-by-step explanation:

let first odd number be n(as stated in question)

to have the next consecutive odd number, add 2 to the n:

1st odd number = n

2nd odd number = n + 2

3rd odd number = n + 4

following the qn, sum of n, twice of n + 2 and thrice of n + 4 is 82

thus n + 2(n+2) + 3(n+4) = 82

n + 2n + 4 + 3n + 12 = 82

6n = 66

therefore n = 11

Answer:

r is usually the radius but can also be a variable, in this case r = -189

Step-by-step explanation:

Solve for r:

-13 = r/9 + 8

Put each term in r/9 + 8 over the common denominator 9: r/9 + 8 = r/9 + 72/9:

-13 = r/9 + 72/9

r/9 + 72/9 = (r + 72)/9:

-13 = (r + 72)/9

-13 = (r + 72)/9 is equivalent to (r + 72)/9 = -13:

(r + 72)/9 = -13

Multiply both sides of (r + 72)/9 = -13 by 9:

(9 (r + 72))/9 = -13×9

(9 (r + 72))/9 = 9/9×(r + 72) = r + 72:

r + 72 = -13×9

9 (-13) = -117:

r + 72 = -117

Subtract 72 from both sides:

r + (72 - 72) = -72 - 117

72 - 72 = 0:

r = -72 - 117

-72 - 117 = -189:

Answer: r = -189

Answer:

60cm and 100cm

Step-by-step explanation:

12 parts in total

240/12 is 20

each part is 20

3x20 is 60 and 5x20 is 100

The volume of the cone is 64π

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

Height, h = 12 m

Radius, r = 4 m

The volume is calculated s

V = 1/3πr²h

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

V = 1/3π * 4² * 12

Evaluate

V = 64π

Hence, the volume is 64π

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Answer:

Step-by-step explanation:

think we hve to use trigonometry here

sin 30⁰

see the pic

sorry I am from India and we solve this type of sum with this method