Since computers were invented, computational speed has multiplied by a factor of 4 about every three years. If a typical computer operates with a computational speed s today, write an expression for the speed at which you can expect an equivalent computer to operate after x three-year periods.

Answer:

x = 155º

Step-by-step explanation:

y = 25°    {Vertically opposite angles}

x + y = 180    {Co-interior angles are supplementary}

x + 25 = 180

Subtract 25 from both sides

x = 180 - 25

x = 155°

The total number of seats in the theatre are 1287.

Given that:-

Number of rows in the theatre = 22

Seats in 1st row = 27

Seats in 2nd row = 30

Seats in 3rd row = 33

and so on.

This is a question of Arithmetic Progression (AP).

Here,

First element = 27

Common difference = 3

Number of terms = 22

First we will find the number of seats in 22nd row.

Number of seats in 22nd row = 27 + (22-1)*3 = 27 + 21*3 = 27 + 63 = 90.

Now, we have to find,

27 + 30 + 33 + 36 + .... + 90

Hence, sum of the number of seats in all the rows = (22/2)(2*27 + (22-1)*3) = 11(54 + 21*3) = 11(54+63) = 11(117) = 1287.

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(a) The expected value of the height obtained using the instrument once is 200 feet and the variance is 400 square feet.

Let X be the height obtained using the instrument once.

Then X can take on the values of 198, 199, 200, 201, or 202 with equal probabilities of 1/5 each.

The expected value of X is given by:

E(X) = ΣxP(X=x) = (198)(1/5) + (199)(1/5) + (200)(1/5) + (201)(1/5) + (202)(1/5) = 200

The variance of X is given by:

Var(X) = E(X^2) - [E(X)]^2

To find E(X^2), we have:

E(X^2) = Σx^2P(X=x) = (198^2)(1/5) + (199^2)(1/5) + (200^2)(1/5) + (201^2)(1/5) + (202^2)(1/5) = 40000/5 = 8000

Thus, the variance of X is:

Var(X) = 8000 - (200)^2 = 400

Therefore, the expected value of the height obtained using the instrument once is 200 feet and the variance is 400 square feet.

(b) The estimated probability that in 18 independent measurements of the tower, the average of the measurements is between 199 and 201, inclusive, is approximately 0.8664.

Let X1, X2, ..., X18 be the heights obtained in 18 independent measurements of the tower. Then, the sample mean of these measurements, denoted by X-bar, is given by:

X-bar = (X1 + X2 + ... + X18)/18

The expected value of X-bar is the same as the expected value of a single measurement, which is 200 feet. The variance of X-bar is given by:

Var(X-bar) = Var(X1 + X2 + ... + X18)/18^2

Since the measurements are independent, we have:

Var(X1 + X2 + ... + X18) = Var(X1) + Var(X2) + ... + Var(X18)

                                    = 18(400) = 7200

Therefore, the variance of X-bar is:

Var(X-bar) = 7200/18^2 = 20/9

To estimate the probability that X-bar is between 199 and 201, we standardize X-bar by subtracting its mean and dividing by its standard deviation:

Z = (X-bar - 200)/(2/3) = 3(X-bar - 200)/2

Then, we have:

P(199 ≤ X-bar ≤ 201) = P(-1.5 ≤ Z ≤ 1.5) ≈ 0.8664

Therefore, the estimated probability that in 18 independent measurements of the tower, the average of the measurements is between 199 and 201, inclusive, is approximately 0.8664.

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The given expression is,

distributive property is,

thus,

the answer is -12x-24.

The equation is 6c - 55 = 455 and the regular cost of each chair is $85

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let c stands for the usual price for x chairs.

So c = mx + b

When a customer purchases a set of dining chairs, a one-time discount of $55 is applied to the total.

Given that a discount of $55 is applied to the total,

Therefore b = -55.

During the sale, Rhianna buys a set of 6 chairs and pays 455,

So 6c - 55 = 455

⇒ 6c = 510

⇒ c = 510/6

⇒ c = 85

Hence, the equation is 6c - 55 = 455 and the regular cost of each chair is $85

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Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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f(-3) ≠ f(3) and f(-3) ≠ -f(3), which means that the function f does not satisfy the properties required for it to be even or odd.

To determine whether the function f is even, odd, or neither, we need to evaluate the symmetry of the function with respect to the y-axis and the origin.

For a function to be even, it must satisfy the property f(x) = f(-x) for all values of x in the function's domain. This means that if we substitute -x for x in the function, we should obtain the same output as when we evaluate the function at x.

For a function to be odd, it must satisfy the property f(x) = -f(-x) for all values of x in the function's domain. This means that if we substitute -x for x in the function, we should obtain the negative of the output we obtain when we evaluate the function at x.

Let's evaluate the function f using the given points (-3,5) and (3,-5):

For the point (-3,5):

f(-3) = 5

For the point (3,-5):

f(3) = -5

We can see that f(-3) ≠ f(3) and f(-3) ≠ -f(3), which means that the function f does not satisfy the properties required for it to be even or odd.

We can conclude that the function f is neither even nor odd.

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The domain on which the graph described as in the image is increasing is to be determined; (-4, ∞).

It follows from the task content that the domain for which the function described by the graph is increasing is to be determined.

Since the graph is a quadratic function which opens upward and whose minimum point is at; x = -4.

Also, since a graph of a function, f(x) is increasing when f'(x) > 0.

Therefore, by observation the graph is increasing on the domain defined by; (-4, ∞).

Put simply, the function is increasing in the Domain; x > -4.

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Answer:

200 kg

Step-by-step explanation:

To satisfy the ratio 1:2:3, Mark must use 100 kg cement, 200 kg sand, and 300 kg gravel

Answer:

6 kg

Step-by-step explanation:

The bacterial population after 80 minutes is 19047

and,  the size of the bacterial population after 10 hours 196,608,000.

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

Given:

A bacteria culture initially contains 3000 bacteria and doubles every half hour.

So, The exponential growth law for this is

p(t) = 3000 \((2)^{t/30\)

where t is the time in minutes.  

Now, To find the population after 80 minutes put in t=20

P(80) =3000 \((2)^{80/30\)

         = 3000 x  6.349

         = 19047.

and, For t= 8 hours put= 480 min

P(80) =3000 \((2)^{480/30\)

         = 3000 x  65536

         = 19,66,08,000.

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The first term, a1, in the geometric series is -3.

What is Geometric Series?

A geometric series is a series for which the ratio of two consecutive terms is a constant function of the summation index. The more general case of a ratio and a rational sum-index function produces a series called a hypergeometric series. For the simplest case of a ratio equal to a constant, the terms have the form

To find the first term, a1, in a geometric series given the sum, Sn = 93, the common ratio, r = 2, and the number of terms, n = 5, we can use the formula for the sum of a geometric series:

Sn = a1 * (1 - r^n) / (1 - r)

Plugging in the given values, we have:

93 = a1 * (1 - 2^5) / (1 - 2)

Simplifying the expression:

93 = a1 * (1 - 32) / (-1)

93 = a1 * (-31)

Now we can solve for a1 by dividing both sides of the equation by -31:

a1 = 93 / -31

a1 = -3

Therefore, the first term, a1, in the geometric series is -3.

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Answer:

2m3n3

 —————

   3  

Step-by-step explanation:

I Think that the answer i tried

L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

x=5   x=3

Step-by-step explanation:

f(x) = x^2 - 8x+ 15

Factor

What two numbers multiply to 15 and add to -8

-5*-3 = 15

-5+-3 = -8

f(x) = (x-5) (x-3)

Setting equal to 0

0= (x-5) (x-3)

Using the zero product property

x-5 =0     x-3=0

x=5   x=3

Answer:

hope this helps................................u

Step-by-step explanation:

208

Answer:

y = 3x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (- 1, - 6 )

m = \(\frac{-6-6}{-1-3}\) = \(\frac{-12}{-4}\) = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 6 )

6 = 3(3) + c = 9 + c ( subtract 9 from both sides )

- 3 = c

y = 3x - 3 ← equation of line

0.29 km is equal to 290,000 mm when rounded to two significant figures.

Convert kilometers to millimeters, you need to multiply the given value by a conversion factor. In this case, since there are 1,000 meters in a kilometer and 1,000 millimeters in a meter, the conversion factor is 1,000,000 (1,000 x 1,000).

Step 1: Multiply 0.29 km by the conversion factor:

0.29 km x 1,000,000 = 290,000,000 mm

Step 2: Round the result to two significant figures:

Since the original value, 0.29 km, has two significant figures, we round the result to match.

290,000,000 mm becomes 290,000 mm.

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the statement is true

this is

The amount of work required to stretch the spring from 30.0 cm to 36.0 cm is 1.411 joules, which can be rounded to three decimal places.

According to Hooke's Law, the amount of work required to stretch or compress a spring by a certain amount is given by the formula:

W = (1/2) k (x2 - x1)²

where W is the work done (in joules), k is the spring constant (in newtons per meter), x1 is the initial displacement (in meters), and x2 is the final displacement (in meters).

In this case, the spring has a natural length of 30.0 cm, which is equivalent to 0.3 meters. To find the spring constant, we can use the fact that a 20.0-N force is required to keep it stretched to a length of 42.0 cm, which is equivalent to 0.42 meters.

Using Hooke's Law, we have

F = k (x2 - x1)20.0 N

= k (0.42 - 0.3) m

=> k = 80.0 N/m

Now we can use Hooke's Law again to find the amount of work required to stretch the spring from 30.0 cm to 36.0 cm, which is equivalent to 0.36 meters.

Using Hooke's Law, we have:

F = k (x2 - x1)W

= (1/2) k (x2 - x1)²W

= (1/2) (80.0 N/m) (0.36 - 0.3) m²W

= 1.411 J

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The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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The percentage of students at the college have a gpa below 2.4 is 15.87%.

Given,

The gpa's are normally distributed with given mean and SD.

mean \(\bar{x}\)= 2.8

SD σ=0.4

raw score=2.4

The z score can be calculated by using the formula

z=\(\frac{x-\bar{x}}{\sigma}\)

z=\(\frac{2.4-2.8}{0.4}\)

\(z=\frac{-0.4}{0.4}\)

z=-1

Using the z table we get the value P(z<-1), it is 0.8413, as it is less than we subtract it from 1 and we get 0.1587. As the value we got is negative, we used left tail z table to get the value of the z.

To get the percentage, we have to multiply by 100,

0.1587 x100

=15.87%

Therefore, the percentage of students at the college with gpa below 2.4 is 15.87%.

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The given statement, "smoothing parameter (alpha) close to 1 gives more weight or influence to recent observations over the forecast" is true.

The smoothing parameter (alpha) defines the weight or impact given to the most recent observation in the forecast when we apply a smoothing approach such as Simple Exponential Smoothing. If alpha is near to one, we are assigning greater weight or influence to the most recent observation, which makes the forecast more sensitive to changes in the data. In other words, an alpha value near one indicates that we are depending on current data to estimate future values.

If alpha is near zero, the forecast will be less sensitive to changes in the data and will depend more largely on previous observations. This is because we are giving equal weight or influence to all observations, regardless of when they occurred.

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Answer:

f(4)>g(4)

Step-by-step explanation:

f(x)=3x^5 ,  f(4)= 3072

g(x)=11*4^x when x=4 then g(4)=2816

Answer:

48 (my sis did this)

correct option: 137

mark me brainleast:)

Step-by-step explanation:

Answer: 86,676,480 Visitors!

Step-by-step explanation:

There are 1,440 minutes per day and if there are 60,192 visitors per day, by multiplying 1,440 by 60,192 you would get 86,676,480.

For a non-constant member function of class test, the this pointer has type D. const Test * const. The this pointer is a special pointer in C++ that points to the object whose member function is being executed.

It is a hidden parameter that is passed to all non-static member functions. The type of the this pointer depends on the const-ness of the member function and the const-ness of the object on which the member function is being called.
In this case, the member function is non-constant, which means it can modify the object on which it is being called. Therefore, the this pointer is a pointer to a constant object of type Test. This is because the object on which the member function is being called is being treated as constant inside the member function, even though it may not actually be constant.
The const keyword before Test indicates that the object pointed to by the this pointer is constant, and the const keyword after Test indicates that the this pointer itself is constant and cannot be modified. Therefore, the correct answer is D. const Test * const.
In summary, the type of the this pointer for a non-constant member function of class test is a pointer to a constant object of type Test, which is itself a constant pointer that cannot be modified.

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