A 14-in. diameter pizza is cut into 6 equal
slices. About how many square inches of
pizza are in each slice? Round to the
nearest square inch.

The pattern suggests that the sequence is the reciprocals of the squares of positive integers. Therefore, the nth term of the sequence {an} is given by, And the answer: a) The nth term of the sequence {an} is 1/n^2. b) The dot product v ∙ w is sqrt(3) + 5.

an = 1/n^2
To find the dot product v ∙ w, we need to multiply the corresponding components of the two vectors and then add them up. So,
v ∙ w = (sqrt3i) ∙ (i) + (-5j) ∙ (-j)
     = sqrt3 + 5
     = 5 + sqrt3
Therefore, the dot product of v and w is 5 + sqrt3.

a) The given pattern continues, and you want to find the nth term of the sequence {an} suggested by the pattern 1/1, 1/4, 1/9, 1/16, 1/25. Notice that each term of the sequence can be written as the reciprocal of a perfect square (1^2, 2^2, 3^2, etc.). The nth term can be represented as 1/n^2. So, the nth term of the sequence {an} is 1/n^2.
b) To find the dot product v ∙ w, where v = sqrt(3)i - 5j and w = i - j, follow these steps:
Step 1: Identify the components of vectors v and w.
For v, the components are (sqrt(3), -5).
For w, the components are (1, -1).
Step 2: Multiply the corresponding components of the vectors.
(sqrt(3) * 1) + (-5 * -1) = sqrt(3) + 5
Your answer:
a) The nth term of the sequence {an} is 1/n^2.
b) The dot product v ∙ w is sqrt(3) + 5.

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Answer:

The answer is "1:2"

Step-by-step explanation:

Let 96 car sales are X and 96 truck sales are Y  And income from 97 cars is 0.89X, income from 97 trucks is 1.07Y

\(\to \frac{(0.89X+1.07Y)}{(X+Y)}=1.01\\\\\frac{X}{Y}=?\\\\\to \frac{(0.89X+1.07Y)}{(X+Y)}\ \ \text{Divide by Y and get}\ \ \frac{( \frac{0.89X}{Y}+1.07)}{(\frac{X}{Y}+1)} =1.01\\\\\)

Then

\(\to \frac{X}{Y}=1:2\)

The equation that matches the number of bacteria in the population after 3 hours is y = 100(2)³.

What is an exponential function?

A mathematical function with the form f (x) = aˣ is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Here, we have

Given: In a lab experiment, a population of 100 bacteria is able to double every hour.

We have to find the equation that matches the number of bacteria in the population after 3 years.

The equation for the number of bacteria after 2 hours is y = 100(2)³, where y is the number of bacteria and 300 is the initial number of bacteria.

This equation calculates the number of bacteria in the population after 2 hours by multiplying the initial number of bacteria by 2 raised to the power of the number of hours the bacteria has been doubling, or 2³ in this case.

Hence, The equation that matches the number of bacteria in the population after 3 hours is y = 100(2)³.

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Using Green's theorem, we can evaluate the line integral of the vector field F = (2y³, -4x³y²) along the positively oriented circle of radius 2 centered at the origin. The result is 0.

Green's theorem states that the line integral of a vector field F = (P, Q) around a simple closed curve C is equal to the double integral of the curl of F over the region R enclosed by C. Mathematically, it can be expressed as ∮C F · dr = ∬R curl(F) · dA.

To evaluate the given line integral, we first need to find the curl of the vector field F. The curl of F is given by ∇ × F = (∂Q/∂x - ∂P/∂y). Computing the partial derivatives, we have ∂Q/∂x = -12x²y² and ∂P/∂y = 6y². Therefore, the curl of F is -12x²y² - 6y². Next, we calculate the double integral of the curl of F over the region R enclosed by the circle. Since the circle is centered at the origin and has a radius of 2, we can describe it parametrically as x = 2cosθ and y = 2sinθ, where θ ranges from 0 to 2π.

Substituting these parametric equations into the curl of F, we get -12(2cosθ)²(2sinθ)² - 6(2sinθ)². Simplifying further, we have -96cos²θsin²θ - 24sin²θ.

To evaluate the double integral, we convert it to polar coordinates, where dA = r dr dθ. The limits of integration for r are from 0 to 2 (radius of the circle) and for θ are from 0 to 2π (a full revolution).

Integrating the expression -96cos²θsin²θ - 24sin²θ over the given limits, we find that the double integral evaluates to 0. Therefore, according to Green's theorem, the line integral of F along the circle C is also 0.

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The 3 pounds of tomato cost will cost £4.5.

Pound and lbs. are practically synonyms for one another. The popular shorthand used to denote pounds is "lbs," which stands for libra. The pound is the real unit of measurement.

The cost of 7 lbs of tomatoes is £10.50.

then, the cost of 1 lbs of tomatoes is,

10.50/7 = 1.5

The cost of 1 lbs of tomatoes is 1.5 lbs.

Since, 1 lbs = 1 pound

Thus, the total cost of 3 pounds of tomatoes is,

3×1.5 = 4.5

Therefore, the  3 pounds of tomatoes will cost £4.5.

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The distance between two vertical white gridlines on a graph typically represents a specific interval or scale.

Based on the options you provided, the correct answer would depend on the context of the graph.

If the graph is displaying population data over time, the distance between two vertical white gridlines could either represent:

- A time span of 20 years
- A time span of 50 years

If the graph is displaying population increase directly, the distance could represent:

- A population increase of 20 million
- A population increase of 2 billion

To determine the correct answer, please examine the labels and context of the graph you are analyzing.

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Answer:

n = -29

Step-by-step explanation:

6n = -174

n = - 29

If four students enter a classroom that has 10 vacant seats, they can be seated in 5,040 ways.

How can be four students seated at 10 seats in 5040 ways?                                                                                                To come to this conclusion, you can use the formula for permutations:                                                                                              P(n, r) = n! / (n-r)!,                                                                                                                                                                           where n is the total number of seats (10) and r is the number of students (4).    

It follows three steps which are given below:
Step 1: Calculate the factorial of n (n!):                                                                                                                                       10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
Step 2: Calculate the factorial of (n-r):                                                                                                                                       (10-4)! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
Step 3: Divide the factorial of n by the factorial of (n-r):                                                                                                                    3,628,800 / 720 = 5,040
So, the four students can be seated in 5,040 different ways in the classroom with 10 vacant seats.

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Answer:

\(\tt x= 62.5\)

Step-by-step explanation:

\(\tt x+5+x+7+(180-137)=180\)

\(\tt x= 62.5\)

~

Answer:

Step-by-step explanation:

The easiest way about this is to give a certain arbitrary value as the area of the yard.

now let’s say the area of the yard is 60 ft^2

Cody mowed 1/4 of this = 1/4 * 60 = 15 ft^2

Now Sam mowed 1/3 of remainder. What remains will be 60-15 = 45 ft^2

so what Sam mowed would be 1/3 * 45 = 15 ft^2

Seeing that they mowed same area, they deserved to be paid equal amount of money and Sam need not complain at all

(a) To prove that if V=U⊕W, then U∩W={0} and dim(V)=dim(U)+dim(W), we can start by assuming that V is the direct sum of U and W. This means that every vector v∈V can be uniquely written as v=u+w, where u∈U and w∈W.

To show that U∩W={0}, suppose there exists a non-zero vector x∈U∩W. This would mean that x can be expressed as x=u_1=w_1, where u_1∈U and w_1∈W. However, since the representation of vectors in the direct sum is unique, this would imply that x has two different representations, which contradicts the assumption that V is the direct sum of U and W. Therefore, U∩W must be {0}.

Next, we can consider the dimensions of U, W, and V. Since U and W are subspaces of V, their dimensions must be less than or equal to the dimension of V. We can show that dim(V)=dim(U)+dim(W) by proving that V=U⊕W implies that dim(V)≥dim(U)+dim(W) and dim(V)≤dim(U)+dim(W).

The fact that every vector v∈V can be uniquely written as v=u+w implies that the span of U and W together spans the entire space V. Hence, dim(V)≥dim(U)+dim(W).

On the other hand, since the representation of vectors in the direct sum is unique, any linearly independent set of vectors in U combined with a linearly independent set of vectors in W will form a linearly independent set in V. Therefore, dim(U)+dim(W)≥dim(V).

Combining both inequalities, we conclude that dim(V)=dim(U)+dim(W).

(b) In an inner product space V, suppose W is a subspace of V. We want to show that V=W⊕W⊥, where W⊥ represents the orthogonal complement of W.

To prove this, we need to show two things: (1) every vector v∈V can be written as a sum of a vector in W and a vector in W⊥, and (2) the representation of vectors in V as the sum of a vector in W and a vector in W⊥ is unique.

For (1), let v∈V. We can decompose v as v=w+w', where w∈W and w'∈W⊥ (orthogonal complement of W). This is possible because in an inner product space, any vector v can be written as the sum of its orthogonal projections onto a subspace and its orthogonal complement.

For (2), suppose v=w+w' and v=w"+w"', where w, w'∈W and w", w'∈W⊥. Then, we have w+w'=w"+w"'. Subtracting w" and w' from both sides gives w-w"=w'-w"'. Since w-w"∈W and w'-w"'∈W⊥, this implies that their difference lies in both W and W⊥, which is only possible if w-w"=w'-w"'=0. Therefore, the representation of vectors in V as the sum of a vector in W and a vector in W⊥ is unique.

Hence, we have shown that V=W⊕W⊥.

(c) The statement "If V is a finite-dimensional inner product space, if U and W are subspaces of V, and if V=U⊕W, then W=U⊥" is not necessarily true.

To disprove this statement, consider a counterexample where V is a finite-dimensional inner product space, and U and W are subspaces of V such that V=U⊕W. Let's assume that U and W are not orthogonal complements of each other, meaning U⊥≠W.

In this case, if we take the orthogonal complement of both sides of the equation V=U⊕W, we would have V⊥=(U⊕W)⊥. Since the orthogonal complement distributes over the direct sum, this can be further simplified to V⊥=U⊥⊕W⊥.

Now, if we compare this result with the original statement, we can see that W=U⊥ does not hold because U⊥ and W⊥ are not necessarily equal. Hence, the statement is disproved.

Therefore, in general, V=U⊕W does not imply W=U⊥

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Both? or just the westbound?

Answer:

Step-by-step explanation:

A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. The fixed point is called the center of rotation. The amount of rotation is called the angle of rotation and it is measured in degrees.

Therefore, the fixed point is called the center of rotation.

What are the angles?

Angles are formed when two lines intersect at a point. The measure of the 'opening' between these two rays is called an 'angle'.

A rotation means that the transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point.

So,the fixed point is called the center of rotation. The amount of rotation is called the angle of rotation and it is measured in degrees.

Hence, the fixed point is called the center of rotation. The amount of rotation is called the angle of rotation and it is measured in degrees.

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Considering the slopes of the lines, we have that:

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

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Answer:

12,20

Step-by-step explanation:

That's the answer

Answer:

y + 32 = 3( x + 8 )

Step-by-step explanation:

point slope form: y-y1 = m(x-x1)

first we need to find the rate of change or the slop. We find that by dividing the difference in the y values from the cordinates by the x values from the cordinates (y2-y1/x2-x1)

so, 1 -- 32 / 3 -- 8 = 1 + 32 / 3 + 8 = 33/11 = 3

m = 3

With this information we can plug the cordinate (-8,-32) into the point slope equation.

y -- 32 = 3( x -- 8)

=

y + 32 = 3( x + 8 ) <---- Answer

and if you ever want to turn this into standard slope form all you have to do is distribue three to 'x' and '8' then subtract 32 from both sides.

y = 3x - 8

Answer:

Step-by-step explanation:

3/6, 1/4, 1/8

Step-by-step explanation:

All three fractions have a common denominator of 24.

1/4=6/24

3/6=12/34

1/8=3/24

Lastly, order them from greatest to least, hence 3/6, 1/4, and 1/8

Yes , the confidence interval still valid because the sample size is large ( n = 100 is greater than 30 ).

Given :

Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .

if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid .

Here

sample size n = 100

The sample size is a term used in market research for defining the number of subjects included in a sample size.

here

n > 30

Hence the confidence interval is still valid .

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Full question:

Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .

if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?

The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.

A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).

The area of a rectangle = (length of rectangle)(width of rectangle).

Given the following parameters for the patio and the bench:

Area to be painted = area of rectangular patio - area of rectangular bench

Area of rectangular patio = (x + 20)(x + 10)

Area of rectangular bench = (6)(2) = 12

Area to be painted = (x + 20)(x + 10) - 12

The answer is: B. A = (x + 20)(x + 10) - 12.

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Answer:

x=  5

Step-by-step explanation:

Your teacher should have explained it but give me points please

Answer:

the answer  is c. just finished the assignment on brainly

Step-by-step explanation:

Answer:

no u cnt

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expression is not factorable with rational numbers.

x^4 − 8x + 16

Step-by-step explanation:

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

Answer:

(-2,0)

Step-by-step explanation:

Herr you go, I hope this helps you.

The coordinates of the vector after rotation is (-2,0)

The given parameters are:

Vector = (0,2)

Rotation = 270°clockwise about the origin

The rule of 270° rotation clockwise about the origin is:

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

So, we have:

(0,2) = (-2,0)

Hence, the coordinates of the vector after rotation is (-2,0)

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1  1/4

Step-by-step explanation:

Using induction, it can be proven that a Turing machine with 'k' tapes is equivalent to a single tape Turing machine.

Let's consider the base case when k = 2, i.e., a two-tape Turing machine. We know from class that a two-tape Turing machine is equivalent to a one-tape Turing machine. Therefore, the statement holds true for k = 2.

Now, let's assume that a Turing machine with 'k' tapes is equivalent to a single tape Turing machine. We need to prove that it also holds for k + 1 tapes.

Suppose we have a Turing machine with k + 1 tapes. We can simulate this machine using a single tape Turing machine as follows:

1. We can combine the first two tapes into a single tape, simulating the behavior of a two-tape Turing machine.

2. We can then combine the resulting tape with the third tape, simulating the behavior of a three-tape Turing machine.

3. We can continue this process until we have combined all k + 1 tapes into a single tape.

By induction, we have shown that a Turing machine with k + 1 tapes can be simulated by a single tape Turing machine, assuming that a Turing machine with k tapes can be simulated by a single tape Turing machine.

Using induction, we have proven that a Turing machine with any number of tapes 'k' is equivalent to a single tape Turing machine. This result holds true for any positive integer value of 'k'. Therefore, a Turing machine with 'k' tapes can always be converted into a single tape Turing machine without loss of computational power.

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The distance from the point (2, 1) is double it's distance from (1, 2)​ is 2.8

The distance between two points in a 2D Cartesian coordinate system is the length of the path connecting them. The shortest path distance is a straight line. The Pythagorean theorem states that the distance between points (X1, Y1) and (X2, Y2) is given by the formula [(x2 x1)2 + (y2 y1)2], where (x1, y1) and (x2, y2) are two points on the coordinate plane.

Distance = √(y₁-y₂)² + (x₁-x₂)²

distance = √(2-1)² + (1-2)²

the distance = √1+1

The distance = √2 = 1.4 = 2*1.4 = 2.8

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Answer:

You can have it as a decimal (0.6 repeatings), or you can have it as a fraction. It would be easier to keep it as a fraction.