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The given set is (3, 4, 5, ...} is infinite set.

A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.

The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.

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The value of the composite function (f o g)(3) is 1603

The functions are given as

f(x) = 3x² - 7x - 3

g(x) = -4x - 10

Next, calculate (f o g)(x) using

(f o g)(x) = f(g(x))

So, we have

(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3

Substitute 3 for x.

So, we have

(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3

Evaluate

(f o g)(3) = 1603

Hence, the value of the composite function (f o g)(3) is 1603

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The equivalent expression of \(6^\frac 25\) is \((\sqrt[5]{6})^2\)

The expression is given as:

\(6^\frac 25\)

The law of indices states that:

\(a^\frac mn = (\sqrt[n]{a})^m\)

Using the above as a guide, we have:

\(6^\frac 25 = (\sqrt[5]{6})^2\)

Hence, the equivalent expression of \(6^\frac 25\) is \((\sqrt[5]{6})^2\)

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The length of each side of the square is 16 cm, the perimeter is 64 cm, and the area is 256 cm^2.

Let's solve the problem step by step. We have a square ABCD, and we need to find the length of its sides when the diagonal is 16√2 cm long.

In a square, the diagonal forms a right triangle with the sides. The sides of a square are equal in length, so let's assume the length of one side of the square is 'x' cm.

Using the Pythagorean theorem, we can find the relationship between the side length and the diagonal:

x^2 + x^2 = (16√2)^2

2x^2 = 512

Dividing both sides by 2, we have:

x^2 = 256

Taking the square root of both sides:

x = √256

x = 16 cm

So, the length of each side of the square is 16 cm.

To find the perimeter of the square, we simply multiply the length of one side by 4 since all sides are equal:

Perimeter = 4 * 16 cm = 64 cm

To find the area of the square, we square the length of one side:

Area = (16 cm)^2 = 256 cm^2

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Note the complete question is:

Find the length of side of square ABCD when diagonal is 16√2 cm long. Also find the perimeter and area of the square?

The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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The amount of money in Marianna's annuity after 6 years will be approximately $300,516.

To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:

A = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

A = the final amount in the annuity

P = the regular contribution (each quarter) = $10,000

r = annual interest rate = 8% = 0.08

n = number of compounding periods per year = 4 (since it's compounded quarterly)

t = number of years = 6

Plugging in the values:

A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)

Calculating this expression:

A ≈ 10000 * ((1.02)^24 - 1) / 0.02

A ≈ 10000 * (1.601032449136241 - 1) / 0.02

A ≈ 10000 * 0.601032449136241 / 0.02

A ≈ 10000 * 30.05162245681205

A ≈ 300,516.22

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Answer:

304200

Step-by-step explanation:

To find the value of P6, use the savings annuity formula

PN=d((1+r/k)N k−1)r/k.

From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives

P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).

Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.

Rounding as requested, our answer is 304200.

Answer: 200 ways

Step-by-step explanation:

From the given information:

Total number of roads leading from Bluffton to​ Hardeeville = 4

Total number of roads leading from Hardeeville to​ Savannah = 10

Total number of roads leading from Savannah to Macon = 5

We need to find the total number of ways to get from Bluffton to​ Macon.

Total number of ways to get from Bluffton to​ Macon = 4 * 10 * 5

= 200

Therefore, there are 200 required number of ways to get from Bluffton to​ Macon.

Answer:

Step-by-step explanation:

2

the stick number is a knot invariant that intuitively gives the smallest number of straight "sticks" stuck end to end needed to form a knot. Specifically, given any knot K, the stick number of K, denoted by stick (K), is the smallest number of edges of a polygonal path equivalent to K.

The probability that the proportion of students who graduated is greater than 0.750 is 0.4113.

What exactly is probability?

Probability is a measurement of the possibility of an event to be occured. It is a mathematical concept that quantifies the chance of a particular outcome or set of outcomes in a given situation. Probability is expressed as a number between 0 and 1, where 0 represents impossibility (an event that will never occur) and 1 represents certainty (an event that will always occur).

Now,

The given problem involves a binomial distribution with n = 81 and p = 0.74. We are asked to find the probability that the proportion of students who graduated is greater than 0.750, which can be written as:

P(p > 0.750)

To solve this problem, we need to first calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the formulas:

μ = np = 81 × 0.74 = 59.94

σ = √(np(1-p)) = √(81 × 0.74 × (1-0.74)) = 4.487

Next, we need to standardize the proportion value using the formula:

z = (p - μ) / σ

Substituting the values, we get:

z = (0.750 - 0.74) / 4.487 ≈ 0.223

Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.223, which is:

P(z > 0.223) ≈ 0.4113

Therefore,

                 The probability that the proportion of students who graduated is greater than 0.750 is 0.4113.

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Answer:

Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1.

Step-by-step explanation:

Answer:

there's no diagram

Step-by-step explanation:

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:y times 20 p

Step-by-step explanation:

Answer:

it should be 16

Step-by-step explanation:

Given:

• Volume of small containers = 2.5 m³

• Volume of large containers = 4 m³

• Number of containers in the shipment = 140

• Total volume = 440 m³

Let's find the number of the size of each container used.

Let s represent the number of small containers

Let L represent the number of large containers.

• Equation for number of containers:

s + L = 140

• Equation for total volume:

2.5s + 4L = 140

Hence, we have the set of equations:

s + L = 140...........................equation 1

2.5s + 4L = 440...................equation 2

Let's solve the set of equations simultaneously using substitution methos.

Rewrite equation 1 for L:

L = 140 - s...........................equation 3

Substitute (140 -s) for L in equation 2:

2.5s + 4(140 - s) = 440

Apply distributive property:

2.5s + 4(140) + 4(-s) = 440

2.5s + 560 - 4s = 440

Combine like terms:

2.5s - 4s + 560 = 440

-1.5s + 560 = 440

Subtract 560 from both sides:

-1.5s + 560 - 560 = 440 - 560

-1.5s = -120

Divide both sides by -1.5:

Substitute 80 for s in either of the equations.

Take equation 3.

L = 140 - s

L = 140 - 80

L = 60.

Therefore, we have the solutions:

s = 80 and L = 60

Therefore, the company used 80 small containers and 60 large containers

Answer:

To find the distance between the two points.

we know that,

Distance formulas as,

Distance between two points (x1,y1) and (x2,y2) is,

Substitute the given points we get,

Answer is: 2.236 units.

Step-by-step explanation:

To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due ($32,000)

- PMT is the monthly payment we want to find

- r is the annual interest rate (7.9%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**

Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.

p chart from this data are attached below.

Describe about p chart?

P bar = total detective / total sampled

P bar = \(\frac{20}{100}\)

         = \(\frac{1}{5}\)

UCL = P bar + L . \(\sqrt{\frac{p bar q bar}{n} }\)

        = \(\frac{1}{5}\) + 3 * \(\sqrt{\frac{1}{5} *\frac{4}{5} * \frac{1}{100} }\)

        = (\(\frac{1}{5} + \frac{3 * 2}{50}\))

        = (0.20 + 0.12)

UCL = 0.32

CL = P bar = 0.20

LCL = P bar - L . \(\sqrt{\frac{p bar q bar}{n} }\)

       = (\(\frac{1}{5} - \frac{3 * 2}{50}\))

       = (0.20 - 0.12)

LCL  = 0.08

Therefore, UCL = 0.32, CL =  0.20, LCL  = 0.08

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Answer:

Number of cars = 3

Number of trucks = 5

Step-by-step explanation:

Let

Number of cars = x

Number of trucks = y

Total number of cars and trucks = 8

We can write the equation: \(x+y=8\)

For his next birthday, he want to double the cars.

The number of cars will be: 2x

Now, the total number of cars and trucks will be 11

Now equation will be: \(2x+y=11\)

Now, Solving these equations, we can find value of x and y

\(x+y=8--eq(1)2x+y=11--eq(2)\)

Subtracting both equations:

\(x+y=82x+y=11\\-\:\:\:-\:\:\:-\\--------\\-x=-3\\x=3\)

So, we get x =3

Now, for finding value of y, put value of x in equation 1:

\(x+y=8\\3+y=8\\y=8-3\\y=5\)

So, we get y=5

So,

Number of cars = x = 3

Number of trucks = y = 5

Answer:

According to me answer is option C and E

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

1.simply the radical expression.

2.calculate the product.

3.collect like terms

Answer:

a

  \( P(X = 0) =  0.6065 \)

b

\(P(x <  25 ) =   1.18 *10^{-33} \)

c

 \(  P(x \le 5 ) =  0.9994 \)    

Step-by-step explanation:

From the question we are told that

  The rate  is \(\lambda =  \frac{1}{2}\   hr^{-1}\)    =  0.5 / hr

  Generally  Poisson distribution formula is mathematically represented as

       \(P(X = x) =  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}\)

Generally the probability that no error occurred during a day is mathematically represented as  

Here  t =  1  hour according to question a

So

   \(P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}\)

Hence

   \(\(P(X = 0) =  \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}\)

=>  \( P(X = 0) =  0.6065 \)

Generally the probability that  a critical error occurs since the start of a day is mathematically represented as

Here  t =  1  hour according to question a

So

   \(P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}\)

Hence

      \(P(x \ge 25 ) =  1 - P(x <  25 )\)

Here

     \(P(x <  25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}\)

=>   \(P(x <  25 ) =  \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}\)

\(P(x <  25 ) =  0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}\)

\(P(x <  25 ) =  0.6065 + \cdots + 6.0*10^{-32}\)

\(P(x <  25 ) =   1.18 *10^{-33} \)

Considering question c

Here  t =  2  

Gnerally given that the  system just started up and an error occurred  the probability the next reset will occur within 2 hours

\(P(x \le 5 ) =  \sum_{n=0}^{5}  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}\)

=> \(P(x \le 5 ) =   \frac{(0.5 *  2) ^ 0 e^{- 0.5  * 2 }}{0!} + \cdots  +   \frac{(0.5 *  2) ^ 5  e^{- 0.5  * 2 }}{5!}\)

=> \(P(x \le 5 ) =   \frac{1* 2.7183 }{1 } + \cdots  +   \frac{1  *2.7183 }{120}\)

=>  \(P(x \le 5 ) =   2.7183 + \cdots  +   0.0226525\)

 \(  P(x \le 5 ) =  0.9994 \)    

Answer:100,000

Step-by-step explanation:

Answer:

A) 427 × 3 = 400 × 3 + 20 × 3 + 7 × 3

Step-by-step explanation:

\(427*3=(400+20+7)*3=(400*3)+(20*3)+(7*3)\)

Therefore, the first option is correct

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

0.64

Step-by-step explanation:

here is the explanation

Answer:

26 meters

Step-by-step explanation:

To solve the perimeter you need to know the formula which is 6 + 7 x 2 and you get 26 meters