help with this problem

Answer:

0,7. 0,7. should be the right answer from what ive looked at

By applying Pascal's triangle concept for the f(n) as per given condition the value f(2) is 1.

To find f(2),  calculate the sum of the elements in the second row of Pascal's triangle

and subtract the sum of all the elements from the previous rows.

Pascal's triangle is formed by starting with a row containing only 1

and then each subsequent row is constructed by adding the two numbers above it.

The first row of Pascal's triangle is simply 1.

The second row of Pascal's triangle is 1 1.

To calculate f(2),  sum the elements in the second row and subtract the sum of the elements in the previous rows.

Sum of elements in the second row = 1 + 1 = 2

Sum of elements in the first row = 1

This implies, f(2) = 2 - 1 = 1.

Therefore, using Pascal's triangle the value f(2) is equal to 1.

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Answer:

45 degrees

Step-by-step explanation:

Hi there!

We're given that one of the triangle's exterior angles is 90 degrees. Using that, we can solve for the corresponding interior angle by subtracting 90 from 180 degrees:

180-90 = 90

Given that the two legs of this right triangle are of equal length, we know that the remaining two angles both measure x. Knowing that the sum of the interior angles in a triangle is 180 degrees, we can set up an equation:

x+x+90=180

2x=90

x=45

Therefore, x is 45 degrees.

In fact, any right triangle with legs of equal length will be a 45-45-90 triangle, meaning the other two angles measure 45 degrees.

I hope this helps!

The line which has an undefined slope among the answer choices given in the task content as described is; the line R which is a vertical line.

It follows from the task content that the line which has an undefined slope is to.be determined among the answer choices.

Since, the slope of a graph is the rate of change in the vertical axis to that in the horizontal axis; it follows that the slope of vertical lines is undefined.

The statement above is true because, no change is recorded in the X axis of vertical lines. Hence, the denominator in the slope formula is; 0 and ultimately, the slope is undefined.

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Answer:

Step-by-step explanation:

The answer is R

Answer:

14/x+3

Step-by-step explanation:

The actual distance between the two cities is 96 miles.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that the map shows that 16 miles are represented by 0.5 inches.

Let x miles would be the actual distance between the two cities

When they are 3 inches apart on the map

According to the given situation, we can write the ratio would be as:

16 miles : 0.5 inches = x miles : 3 inches

⇒ 16/0.5 = x/3

Apply the cross-multiplication operation,

⇒ 0.5x = 48

⇒ x = 48/0.5

⇒ x = 96

Therefore, the actual distance between the two cities is 96 miles.

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Answer:

592 Square inches

Step-by-step explanation:

We solve the above question by calculating the surface area of the rectangular box

A =2(wl + hl + hw)

w = Width = 8 inches

l = Length = 12 inches

h = Height = 10 inches

The square inches of wood would Mitchel need to build the box is calculated as:

Surface Area = 2 × (8 × 12 + 10 × 12 + 10 × 8) = 592 Square inches

Answer:

the ratio is 2:11

Step-by-step explanation:

I already wrote this in a comment, but I'm writing it here because the other person's answer was deleted.

when all the measurements of the ingredients are added together, that makes 11.

according to the recipe, there's 2 cups of mixed nuts.

so the ratio is 2 cups of mixed nuts to 11 cups of granola.

The actual length of the bus is 35 feet

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

Scale drawing:

The scale is given as

7 inches : 2 inches = x : 10 feet

Express the ratio as a fraction

So, we have

7/2 = x/10

Make x the subject

This gives

x = 10 * 7/2

Evaluate

x = 35

Hence, the actual length is 35 feet

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Answer:

6

Step-by-step explanation:

We can look that AB=BC=CD=18/3=6

So, AB = 6

Answer:

Step-by-step explanation:

6....

Answer:

4

Step-by-step explanation:

1/2 goes into 1/8 4 times.

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 20

Step-by-step explanation:

0.5x+8=-7.2

0.5x=-7.2-8

0.5x=-15.2

×=-15.2÷0.5

x=30.4

Required value of f(g(x)), g(f(x)), f(f(x)) are 2x²- 4x + 2 , 2x² -1 and 8x⁴ respectively.

the range of f(g(x)) is [0, ∞), the range of g(f(x)) = = 2x²-1 is [-1,∞) and the range of f(f(x)) is [0, ∞).

What is composition of functions?

Suppose we are given two functions f(x), g(x). We construct a new function h(x) as follows. plug 'x' into g(x) and find its value. then plugin this value into f(x), that is find f(g(x)). Now set h(x) = f(g(x)). This new function h(x) is called the composition of functions f(x) and g(x).

a. f(g(x)) = 2 * (x - 1)² = 2(x² - 2x + 1) = 2x²- 4x + 2 Since fg(x)) is a polynomial its domain is all real numbers. to find the range note that f(g(x)) = 2 * (x - 1) ² . and the range of the square is all non-negative real numbers. So the range of f(g(x)) is [0, ∞).

b. g(f(x)) = (2x²) - 1 =2x² -1.g(f(x)) is a polynomial function, so the domain of g(f(x)) is (-∞, ∞). Note that the range of 2x² is [0, ∞). So the range of g(f(x)) = 2x²-1 is [-1,∞)

c. f(f(x)) = 2 * (2x²)² = 2(4x⁴) = 8x⁴ . Since this is a polynomial function, the domain is (-∞, ∞), and clearly the range is [0, ∞).

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The standard deviation of the sampling distribution of the sample mean would be approximately 2.8284

To determine the standard deviation of the sampling distribution of the sample mean, we will use the formula;

σ_mean = σ / √n

where σ is the standard deviation of the population that is 20 and n is the sample size (n = 50).

So,

σ_mean = 20 / √50 = 20 / 7.07

σ_mean  = 2.8284

The standard deviation of the sampling distribution of the sample mean is approximately 2.8284 it refers to that the sample mean would typically deviate from the population mean by about 2.8284, assuming that the sample is selected randomly from the population.

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The complete question is;

Another application of the sampling distribution of the sample mean Suppose that, out of a total of 559 full-service restaurants in Delaware, the number of seats per restaurant is normally distributed with mean mu = 99.2 and standard deviation sigma = 20. The Delaware tourism board selects a simple random sample of 50 full-service restaurants located within the state and determines the mean number of seats per restaurant for the sample. The standard deviation of the sampling distribution of the sample mean is Use the tool below to answer the question that follows. There is a.25 probability that the sample mean is less than

1. The function f(x) = x³ - x² - 6x has two stationary points.

2. The derivative of y = sin⁻¹(2 - √(1 - x²)) with respect to x is not provided.

3. The rate at which the radius of a circular region is increasing when its area is 64 square meters is 4√3 meters per second.

1. To determine the number of stationary points of the function f(x) = x³ - x² - 6x, we need to find the values of x where the derivative of f(x) is equal to zero. Taking the derivative of f(x), we have f'(x) = 3x² - 2x - 6. Solving the equation 3x² - 2x - 6 = 0, we find two real solutions for x, indicating that the function has two stationary points.

2. The derivative of y = sin⁻¹(2 - √(1 - x²)) with respect to x is not provided in the given information. Therefore, we cannot determine the value of dy/dx.

3. When the area of the circular region is 64 square meters, the rate at which the area is increasing is given as 96 t square meters per second. Since the area of a circle is given by A = πr², where r is the radius, we can differentiate both sides with respect to time to find the rate at which the radius is increasing. Using dA/dt = 96 and A = 64, we can solve for dr/dt to find that the radius is increasing at a rate of 4√3 meters per second.

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The derivative of f(x) = cos³(2^csc(x)) is found using the Chain Rule. The final result is 3cos²(2^csc(x)) * ln(2) * 2^(csc(x)) * -csc(x)cot(x).



(a) To compute the derivative of f(x) = cos³(2^csc(x)), we can visualize it as a 4-layer "onion" of functions. Each layer represents a function in the composition:Layer 1: f(x) = cos³(u)

Layer 2: u = 2^v

Layer 3: v = csc(x)

Layer 4: x

(b) Now let's compute the derivative using the Chain Rule. Starting from the innermost layer and working our way out:

Layer 4: Take the derivative of x, which is 1.

Layer 3: Derivative of v = d(csc(x))/dx = -csc(x)cot(x).

Layer 2: Derivative of u = d(2^v)/dv * dv/dx = ln(2) * 2^v * -csc(x)cot(x).

Layer 1: Derivative of f(x) = d(cos³(u))/du * du/dv * dv/dx = 3cos²(u) * ln(2) * 2^v * -csc(x)cot(x).

Combining the derivatives from each layer, we have:

f'(x) = 3cos²(2^csc(x)) * ln(2) * 2^(csc(x)) * -csc(x)cot(x).

The derivative of f(x) is given by this expression.

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Answer:

4+(-11)

Step-by-step explanation:

you need to put the negative 11 in ()

We have shown that for any given positive real number ɛ, there exists an index N such that if n > N, then |xiyi - xy| < ɛ. Hence, the sequence (xiyi) converges to xy.

What is sequence?

In mathematics, a sequence is an ordered list of elements. The elements can be any type of object, such as numbers, functions, or other mathematical entities. Sequences are typically denoted by listing the elements with commas between them or by using a notation that indicates the general term of the sequence.

To show that the sequence (xiyi) converges to xy, we need to show that for any given positive real number ɛ, there exists an index N such that if n > N, then |xiyi - xy| < ɛ.

Since (xi) and (yi) are convergent sequences, we know that for any given positive real number ɛ/2, there exist indices N1 and N2 such that if n > N1, then |xi - x| < ɛ/2 and if n > N2, then |yi - y| < ɛ/2.

Now, let N = max{N1, N2}. Then, for n > N, we have:

|xiyi - xy| = |xiyi - xiy + xiy - xy|

= |xi(yi - y) + y(xi - x)|

<= |xi||yi - y| + |y||xi - x|

< ɛ/2 * ɛ/2 + ɛ/2 * ɛ/2 = ɛ,

where we used the triangle inequality and the fact that |xi| and |y| are bounded by some constant M (since (xi) and (yi) are convergent sequences, they are both bounded).

Therefore, we have shown that for any given positive real number ɛ, there exists an index N such that if n > N, then |xiyi - xy| < ɛ. Hence, the sequence (xiyi) converges to xy.

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Answer:

4

Step-by-step explanation:

You can rewrite 1 1/2  as 1.5. This just makes it easier if you use a calculator.

6/1.5 = 4

Let's just think of a different way to think about it:

If you add up two 1 1/2 ft sandwiches, (1.5 + 1.5), that equals 3. Two 3's equal 6. Again, the answer is 4.

Answer:

Step-by-step explanation:

The equation for an arithmetic sequence is

\(a_n=a_1+d(n-1)\)  where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.

Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:

\(a_n=2+3(n-1)\) which simplifies to

\(a_n=2+3n-3\) and a bit more to

\(a_n=3n-1\) (which should tell you that arithmetic sequences are lines!)

Finding the 13th number simply requires that we replace n with 13 and solve:

\(a_{13}=3(13)-1\) so

\(a_{13}=38\)

Answer:

38

Step-by-step explanation:

This isn't the most efficient way but it's the best I can do.

2, 5, 8, 11....

The pattern is that we add 3 every time.

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38,

1 , 2, 3, 4, 5,  6,   7,    8,    9,   10,  11,   12,  13

We can see that 38 is the 13th term of the sequence.

Answer:

because of the metric system

for centimeters you use it to measure length of something or someone

for kilometers you use it to measure distance for something

for each object or what you need you have its own metric unit

Answer:

75lbs

Step-by-step explanation:

if the mean of the packages was 15 then all the items averaged to 5 pounds each meaning they had a total of 15*5 or 75lbs

Answer:

(2/5, 9/5)

Step-by-step explanation:

To find the solutions, we are given the value of y in terms of x: y = 2x + 1. We can plug this into the circle equation to get:

(x - 1)^2 + (2x + 1 - 1)^2 = 1

Now, we can expand and simplify:

x^2 - 2x + 1 + (2x)^2 = 1

x^2 - 2x + 1 + 4x^2 = 1

5x^2 - 2x = 0

Now, we can factor:

x(5x - 2) = 0

And, using the zero product property, we get two equations which we can solve:

x = 0

5x - 2 = 0

5x = 2

x = 2/5

Since x is 0 in the first solution, we use the other solution and plug it into the equation y = 2x + 1 to find y:

y = 2(2/5) + 1

y = 4/5 + 1

y = 9/5

This means the coordinates of the point is (2/5, 9/5)

Shor's Algorithm Efficiency of Shor’s algorithm in the general case, when r does not divide 2, is calculated as follows:

Shor's algorithm is an effective quantum computing algorithm for factoring large integers. The algorithm calculates the prime factors of a large number, using the modular exponentiation, and quantum Fourier transform in a quantum computer.In this algorithm, the calculation of the quantum Fourier transform takes O(N2) quantum gates, where N is the number of qubits required to represent the number whose factors are being determined.

To calculate the Fourier transform efficiently, the number of qubits should be set to log2 r. The general form of Shor's algorithm is given by the following pseudocode:

1. Choose a number at random from 1 to N-1.

2. Find the greatest common divisor (GCD) of a and N. If GCD is not 1, then it is a nontrivial factor of N.

3. Use quantum Fourier transform to determine the period r of f(x) = a^x mod N. If r is odd, repeat step 2 with a different value of a.

4. If r is even and a^(r/2) mod N is not -1, then the factors of N are given by GCD(a^(r/2) + 1, N) and GCD(a^(r/2) - 1, N).

The efficiency of the algorithm is determined by the number of gates needed to execute it. Shor's algorithm has an exponential speedup over classical factoring algorithms, but the number of qubits required to represent the number whose factors are being determined is also exponentially large in the number of digits in the number.

In the general case when r does not divide 2, the efficiency of Shor's algorithm is reduced. However, the overall performance of the algorithm is still better than classical factoring algorithms.

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Answer:

3.9

Step-by-step explanation:

8.2-4.3=3.9

3.9+4.3=8.2

To obtain the ordered pair that is not on the solution set, we obtain the numeric value of each condition at the x-coordinate of the numeric pair.

For the ordered pair (2,-3), we have that:

For the ordered pair (3,-2), we have that:

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Answer:

Median score = 82.5

Step-by-step explanation:

First, arrange the given data in an ordered manner. Thus:

55, 68, 72, 73, 75, 77, 78, 79, 82, 82, 83, 85, 85, 85, 86, 86, 87, 91, 92, 95

The median = the average of the 10th and 11th data

Median = (82 + 83) ÷ 2

Median = 165 ÷ 2

Medina = 82.5

Answer:

1/6

Step-by-step explanation:

rise=1

run=6

therefore run over run is 1/6

Answer:

B) y = 4/3x - 2

Step-by-step explanation:

In pic below.

Answer:

The correct answer is B

Step-by-step explanation:

hope it will help you