Calculate the pixel size for a fast spin echo sequence with the following parameters: FOV 30cm, TR 600, TE 10, 320 x 320 matrix, 4 NEX, 3 mm slice thickness, 3 ETL.
0.94 mm x 0.94 mm
FOV ÷ Matrix = pixel size
FOV ÷ phase matrix = phase dimension pixel
FOV ÷ frequency matrix = frequency pixel
Convert 30cm to 300 mm before calculating.
300 ÷ 320 = 0.94mm (phase dimension)
300 ÷ 320 = 0.94mm (frequency dimension)

a) The first three terms of Eniki's sequence are 20, 100, and 500.

b) The number 312,500 is the 7th term in Eniki's sequence.

c) The number 94,500 is not a term in Eniki's sequence since it does not correspond to any whole number value of 'n'.

The term 'n' in the formula represents the position of the number in the sequence, starting from the first term.

Enoki's also has a sequence of numbers, which is given by the formula (n) = 4(5ⁿ). Let's break down this formula to understand what it means.

a. To find the first three terms of Eniki's sequence, we substitute the values 1, 2, and 3 for 'n' in the formula. This gives us:

n = 1: 4(5¹) = 20

n = 2: 4(5²) = 100

n = 3: 4(5³) = 500

Therefore, the first three terms of Eniki's s sequence are 20, 100, and 500.

b. Chelita thinks that the number 312,500 is a term in Eniki's sequence. To determine whether she is correct or not, we need to find the value of 'n' that corresponds to this number. We can rearrange the formula to solve for 'n' as follows:

n = log base 5 (312,500/4)

Using a calculator, we find that n is approximately equal to 7. Therefore, the number 312,500 is the 7th term in Eniki's sequence.

c. Elisa thinks that the number 94,500 is a term in Eniki's sequence. To verify this, we can once again solve for 'n' in the formula:

n = log base 5 (94,500/4)

Using a calculator, we find that n is approximately equal to 6. Therefore, the number 94,500 is not a term in Eniki's sequence since it does not correspond to any whole number value of 'n'.

In summary, Eniki's sequence is defined by the formula

=> f(n) = 4(5ⁿ),

where 'n' represents the position of the number in the sequence.

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The expression tan59° = h/17 can be used to determine the height (h), in feet, of the flagpole.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The height of the flagpole is the opposite side of the right triangle formed by the flagpole, its shadow on the ground, and the line from the top of the flagpole to the end of the shadow.

The angle of elevation of the sun is opposite the height of the flagpole, and the length of the shadow is the adjacent side.

Therefore, the tan of the angle of elevation is equal to the height of the flagpole divided by the length of the shadow:

tan59° = h/17

Thus, the correct expression to determine the height of the flagpole is:

B. tan59° = h/17

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The correct statement is the other solution to the quadratic function h is -4-7i.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

Given that, one of the solution to a quadratic function, h, is given, -4 + 7i,

We know that,

The solution of a quadratic function, can be found by using the quadratic formula, which is given by,

x = -b±√b²-4ac / 2a

Here, ± is showing that there are two values of x one in positive and another in negative,

We have one solution = -4 + 7i

Therefore, another solution will be its opposite = -4 - 7i

Hence, the correct statement is the other solution to the quadratic function h is -4-7i.

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The expression that gives the formula of the volume of a cone is interchanged for π, is given by, π = 3V/hr²

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, the formula for the volume of a cone, the expression is,

V = 1/3 πr²h

Where, r and h are radius and height of the cone respectively.

We are asked to interchange the expression to give a formula for, π

Therefore, the given expression,

V = 1/3 πr²h

Multiplying by 3 to each side,

3V = πr²h

Divide by r² to both sides,

3V/r² = πh

Divide by h to both sides,

3V/hr² = π

or,

π = 3V/hr²

Hence, the expression that gives the formula of the volume of a cone is interchanged for π, is given by, π = 3V/hr²

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When comparing the machining techniques for stainless steel sheet material to those for aluminum alloy sheets, it is normally considered good practice to drill the stainless steel at a lower speed with less pressure applied to the drill. Hence, option C is the required accurate answer.

Stainless steel is a much harder and tougher material compared to aluminum, which makes it more difficult to machine.

Drilling at a higher speed with more pressure applied to the drill can cause the drill to overheat and wear out faster, resulting in lower-quality holes and increased production time.

Whereas, drilling at a lower speed with less pressure applied to the drill helps to reduce the risk of overheating, allows the drill to maintain its sharpness, and helps to produce higher-quality holes.

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Answer:

UM I THINK ITS 1500

Step-by-step explanation:

, $18 will be put into the pile on February 4th.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, 14 friends are saving money for a trip to the movies

On February 3rd, a total of $12 was put into the pile. Let's find out how many friends put money into the pile that day.

The 6 friends who put $1.50 into the pile every day contributed:

6 friends x $1.50/friend/day = $9/day

So, on February 3rd, they would have contributed $9.

Let's assume that there are x friends who put $1.50 into the pile every even day.

Since February 3rd was an odd day, none of these friends would have contributed on that day.

Similarly, let's assume that there are y friends who put $1.50 into the pile every odd day.

Since February 3rd was an odd day,

y friends would have contributed $1.50 each, for a total of $1.50y.

Therefore, we can set up an equation to solve for y:

$9 + $1.50y = $12

Simplifying this equation, we get:

$1.50y = $3

y = 2

So, there are 2 friends who put $1.50 into the pile every odd day.

Thus, friends who contribute on even day are = 14 -6 -2 = 6

So,

on 4th February total money collected = money added by the friends who adds money  every day + money added by the friends who adds money on even days.

Thus,

on 4th February total money collected = 6*1.5 + 6*1.5 = 9 + 9 =18

Therefore, $18 will be put into the pile on February 4th.

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True, for all probability density functions of continuous random variables that the area under the curve is 1.0, but they do not have to be symmetrical or bell-shaped, and they do not have the same height.

A continuous random variable is a random variable that can take any value within a certain range, such as time or distance. Probability density functions (PDFs) describe the probability distribution of continuous random variables, and they have some important properties that hold true for all of them.

The first property of a PDF is that the area under the curve is always equal to 1.0. This means that the total probability of all possible outcomes of the random variable is equal to 1.0.

The second property is that PDFs do not have to be symmetrical or bell-shaped. The shape of the PDF depends on the distribution of the data.

The third property is that PDFs do not have the same height. The height of the PDF depends on the distribution of the data and the range of values that the random variable can take. The height of the PDF represents the density of the probability distribution for a given value.

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Answer:

a. f(0)= -5

b. f(1/2) = -4

c. f(100) = 195

d. x = 7

Step-by-step explanation:

Given that,

f(x) = 2x - 5 .........(1)

a)

Putting x = 0 in equation (1), we have

f(0) = 2(0) -5 = 0 - 5 = -5

b)

Putting x = 1/2 in equation (1), We have

f(1/2) = 2(1/2) -5 = 1 - 5 = -4

c)

Putting x = 100 in equation (1), We have

f(100) = 2(100) -5 = 200 - 5 = 195

d)

Putting f(x) = 9 in equation (1), We have

9 = 2x - 5

⇒ 2x = 9 + 5

⇒ 2x = 14

⇒ x = 14/2

⇒ x = 7

The length of HK is approximately 20.17 units.

what Pythagorean theorem ?

The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is usually written in the form of an equation:

[tex]a^2 + b^2 = c^2[/tex]

According to the questions :

First, we can use the fact that HJ is perpendicular to the base IK to determine the height of triangle HKI. Since J is the midpoint of the hypotenuse IK, we know that HJ is also the median of the hypotenuse, and it divides the hypotenuse into two equal segments of length 16.

Therefore, we can use the Pythagorean theorem to find the height HK of triangle HKI:

[tex]HK^2 = IK^2 - HI^2[/tex]

Since triangle HKI is a right triangle, we know that HI is the height of the triangle, and IK is the hypotenuse. Using the Pythagorean theorem again, we can find the length of IK:

[tex]IK^2 = IJ^2 + JK^2[/tex]

Substituting the given values, we get:

[tex]IK^2 = 16^2 + 16^2[/tex]

[tex]IK^2 = 5123[/tex]

Taking the square root of both sides, we get:

[tex]IK = sqrt(512) ≈ 22.63[/tex]

Now we can use this value to find the height HK:

[tex]HK^2 = IK^2 - HI^2[/tex]

[tex]HK^2 = 22.63^2 - (16/2)^2[/tex]

[tex]HK^2 = 512 - 64[/tex]

[tex]HK^2 = 448[/tex]

Taking the square root of both sides, we get:

[tex]HK = sqrt(448) ≈ 20[/tex]

Therefore, the length of HK is approximately 20 units.

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how many solutions this equation has:

x2 + 3 = 0

answer : no real solution

x = + i√3

x = - i√3

Decide how many solutions this equation has:

x2 - 2x + 1 = 0

answer : has 1 solution

x=1

chatgpt

The tangent line at (x, y) = (3, 33) is y = 25x + 8.Enter as an ordered pair (a,b). The slope of the tangent line comes from f'. For this problem,f'(x) = 8x. And mtan = f'(3) = 24.The equation of the tangent line in slope-intercept form is y = T(x) = 24x - 69.

T(3.05) = 24(3.05) - 69 = -18.2.

f(3.05) = 4(3.05)^2 - 63 = -16.73.

We want to estimate the value of f(x) = 4x^2 - 63 at x = 3.05 using linear approximations. This means we need to find the equation of the tangent line to the graph of f at x = 3, which will give us a good approximation of f(3.05) near x = 3.

To find the tangent line, we first need to find the slope of the tangent line, which is given by the derivative of f at x = 3. We have f(x) = 4x^2 - 63, so f'(x) = 8x. Therefore, f'(3) = 24, which is the slope of the tangent line at x = 3.

Next, we need to find a point on the tangent line. We can use the point (x, y) = (3, 33), which is on the graph of f and also happens to be at x = 3. This means the tangent line at (3, 33) will be very close to the graph of f near x = 3.

Using the point-slope form of a line, we can find the equation of the tangent line at (3, 33):

y - 33 = 24(x - 3)

Simplifying this equation gives us the slope-intercept form of the tangent line:

y = 24x - 69

Now we can use this equation to estimate the value of f(3.05) by plugging in x = 3.05:

T(3.05) = 24(3.05) - 69 = -18.2

This means the tangent line predicts that f(3.05) is approximately -18.2.

To compare this to the actual value of f(3.05), we can plug it into the original function:

f(3.05) = 4(3.05)^2 - 63 = -16.73

So the actual value of f(3.05) is approximately -16.73, which is close to the estimate given by the tangent line.

In summary, using linear approximations, we found that the tangent line at (3, 33) has a slope of 24 and passes through the point (3, 33). The equation of the tangent line is y = 24x - 69. Using this equation, we estimated that f(3.05) is approximately -18.2, which is close to the actual value of -16.73.

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640 measurements are needed to compare the performance of four different tires on dry, damp, and wet roads for decelerations of 1, 3, 5, 7, and 9 m/s², with two measurements per experiment.

The PERIOD method stands for:

P: Performance metric (Deceleration)

E: Environmental condition (Dry, Damp, Wet)

R: Replicates (Two measurements per experiment)

I: Inputs (Four tires)

O: Output (Measurement result)

D: Design (Full factorial)

The number of measurements can be calculated as:

Measurements = R * (number of inputs)^E * P

In this experiment, there are:

R = 2 replicates

E = 3 environmental conditions (Dry, Damp, Wet)

P = 5 different decelerations (1, 3, 5, 7, 9 m/s²)

Inputs = 4 tires

Therefore, the number of measurements can be calculated as:

Measurements = 2 * 4^3 * 5 = 2 * 64 * 5 = 640

So, 640 measurements are needed to compare the performance of four different tires on dry, damp, and wet roads for decelerations of 1, 3, 5, 7, and 9 m/s², with two measurements per experiment.

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The expression 64x^6 can be written as a square of a monomial by taking the square root of both sides of the expression:

√(64x^6) = √(64) * √(x^6) = 8 * x^3

So, the expression 64x^6 can be written as the square of the monomial 8x^3.

Answer: √(64x^6) = √(64) * √(x^6) = 8 * x^3 So, the expression 64x^6 can be written as the square of the monomial 8x^3. The exact thing that legoslucaswang had said but it's just a different way of saying it.

From the given information provided, the first quartile (Q₁) is 4, the median is 8, and the third quartile (Q₃) is 9.

To find the first quartile, median, and third quartile for the given data set, we first need to arrange the data in ascending order:

1 1 4 4 4 4 6 7 7 8 8 8 8 9 9 9 10 10 10

There are 20 data points in the set, so the median is the average of the 10th and 11th values:

Median = (8 + 8) / 2 = 8

To find the first quartile (Q₁), we need to find the median of the lower half of the data set. There are 10 data points in the lower half, so the median is the average of the 5th and 6th values:

Q₁ = (4 + 4) / 2 = 4

To find the third quartile (Q₃), we need to find the median of the upper half of the data set. There are 10 data points in the upper half, so the median is the average of the 15th and 16th values:

Q₃ = (9 + 9) / 2 = 9

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The values of y when the equation is y = 8x + 5 will be -3,5,13,21,29.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Since y = 8x + 5

when x = -1, y will be:

= 8(-1) + 5

= -3

when x = 0, y will be:

= 8(0) + 5

= 5

when x = 1, y will be:

= 8(1) + 5

= 13

when x = 2, y will be:

= 8(2) + 5

= 21

when x = 3, y will be:

= 8(3) + 5

= 29

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The reader can scan 10 sheets in 15 minutes, according to the claim.

One of the four fundamental math processes, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual adding of sets of identical size.

If a scanner can scan 4 pages in 6 minutes, then we can set up the following ratio:

4 pages / 6 minutes = x pages / 15 minutes

where x is the number of pages that the scanner can scan in 15 minutes.

To solve for x, we can cross-multiply and simplify:

4 pages × 15 minutes = 6 minutes × x pages

60 pages = 6x

x = 60 pages / 6

x = 10 pages

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The statement 2π + 5π = 7π is always a proposition.

A proposition is a statement that is either right or wrong. Both results can not be possible for a statement. Only one result occurs at a time.

Clearly, the value of the addition 2π + 5π is 7π. So, the statement 2π + 5π = 7π is always true.

Therefore, the obtained answer is a proposition.

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Answer:

5

Step-by-step explanation:

Answer:

Step 1: The volume of a prism is determined by the area of the cross section multiplied by the height of the prism.

Step 2: The area of an isosceles triangle can be calculated by A = (base x height)/2.

Step 3: Substituting values, we get A = (6 cm * h)/2.

Step 4: Since the volume of the triangular prism is 480 cm3, substituting in the formula V = A * height, we get 480 cm3 = (6 cm * h)/2 * 20 cm.

Step 5: Solving for h, we get h = 16 cm.

Step 6: Since it is an isosceles triangle, the longest side of the cross section is also 16 cm.

Answer: The length of the longest side of the triangular cross section is 16 cm.

The value of of function is  -8x² + 8x - 7.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

The function h(x) = -2x² - 5 and g(x) = 2x - 1

Now,

To find (h•g)(x), we need to first evaluate the composition of functions h(g(x)):

h(g(x)) = -2(2x - 1)² - 5 [substituting g(x) into h(x)]

= -2(4x² - 4x + 1) - 5

= -8x² + 8x - 7

Therefore, the function (h•g)(x) will be equal to -8x² + 8x - 7.

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The probability of getting all vowels when three letters of the alphabet are selected at random with replacement is 1/125.

There are 5 vowels in the English alphabet (a, e, i, o, and u) and 26 letters in total. If we select three letters at random with replacement, we have 5 options for each selection.

The probability of getting a vowel on any one selection is 5/26. Since we are replacing the letter each time, the probability of getting three vowels in a row is:

(5/26) × (5/26) × (5/26) = 1/125

Therefore, the probability of getting all vowels when three letters of the alphabet are selected at random with replacement is 1/125.

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wv

wv equals x because the hypotenuse of rhe quadrilateral is congruent to the pathagoreum theorum

Answer: wv

Step-by-step explanation:

The length of the crane is given as follows:

23.7 feet.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In the context of this problem, the parameters are given as follows:

Hence the length of the crane is obtained as follows:

l² + 8² = 25²

l = sqrt(25² - 8²)

l = 23.7 feet.

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The Greatest Number is -10/11.

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right.

Given:

Rational Number: 10/11,-19/22,-23/33,-39/44

The LCM of 11.22,33,44 is 132

-10/11×12/12=-120/132

-19/22×6/6=-114/132

-23/33×4/4=-92/132

-39/44×3/3=-117/132

In ascending order

-120/132,-117/132,-114/132,-92/132

= -10/11,-39/44,-19/22,-23/33

In descending order

-92/132,-114/132,-117/132,-120/132

= -23/33,-19/22,-39/44,-10/11

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The result of the evaluation of each of the expression are as follows;

Recall that; √a × √a = a.

As evident in the task content; the results of the expressions are as follows;

a). √11 × √11 = 11.

b). √5 × √5 x √2 × √2 = 5 × 2 = 10.

c). √6 × √6 × √6 x = 6√6 x.

Ultimately, the results are as evaluated above.

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The vector is (-3, 4) and its x and y components are -3 and 4.

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.

Given:

Vector v have an initial point at (3, -5) and a terminal point at (0, -1).

It initial point of a vector is (a, b) and terminal point is (c, d), then the vector is

v= (c-a, d-b)

We have (a, b) = (3, -5) and (c, d) = (0, -1)

Then, vector v is defied as

v = (0 - 3, -1 - (-5))

v = (-3, -1+5)

v = (-3, 4)

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If the Garcia family drew a circle graph of their budget I would tell the Garcia family that the circle graph shows the percentage breakdown of their budget.

The largest portion of their budget is going towards rent, followed by taxes and food. Utilities, gas, and miscellaneous expenses make up smaller portions of their budget.

It may be helpful for the family to further analyze their spending in each category to see if any adjustments can be made to better align with their financial goals.

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Answer: A six-person model typically weighs approximately 1,000 pounds empty or 6,000 pounds full.

Using the law of total expectation, the expected circumference of the rectangle is 3/2, and the expected area of the rectangle is 1/6.

Let C and A denote the circumference and area of the rectangle, respectively. Then we have:

E[C] = E[C|X] * P(X) + E[C|X'] * P(X')

where X' is the complement of X, and P(X) and P(X') are the probabilities of X and X' respectively. Since X is a uniform [0, 1] random variable, we have P(X) = 1 and P(X') = 0.

Therefore, we can simplify the above expression to:

E[C] = E[C|X]

To find E[C|X], we can use the formula for the circumference of a rectangle:

C = 2 * (base + height)

Substituting in the values for the base and height of the rectangle, we get:

C = 2 * (X + U[0, X])

where U[0, X] denotes a uniform random variable on [0, X].

Then, we can find the expected value of C given X as follows:

E[C|X] = E[2*(X+U[0,X])|X]

= 2*(X+E[U[0,X]|X])

where we have used the linearity of expectation. Note that E[U[0,X]|X] is simply the expected value of a uniform random variable on [0, X], which is X/2.

Therefore, we have:

E[C|X] = 2*(X+X/2) = 3X

Substituting this back into the expression for E[C], we get:

E[C] = E[3X] = 3E[X]

Since X is a uniform [0, 1] random variable, we have E[X] = 1/2. Therefore, the expected circumference of the rectangle is:

E[C] = 3E[X] = 3/2

Similarly, we can use the Law of Total Expectation to find the expected area of the rectangle by conditioning on X:

E[A] = E[A|X] * P(X) + E[A|X'] * P(X')

where, again, we have P(X) = 1 and P(X') = 0. Therefore, we can simplify the expression to:

E[A] = E[A|X]

To find E[A|X], we can use the formula for the area of a rectangle:

A = base * height

Substituting in the values for the base and height of the rectangle, we get:

A = X * U[0, X]

where U[0, X] denotes a uniform random variable on [0, X].

Then, we can find the expected value of A given X as follows:

E[A|X] = E[XU[0,X]|X]

= XE[U[0,X]|X]

where we have again used the linearity of expectation. Note that E[U[0,X]|X] is X/2, as before.

Therefore, we have:

E[A|X] = X * (X/2) = X^2/2

Substituting this back into the expression for E[A], we get,

E[A] = E[X^2/2] = 1/2 * E[X^2]

To find E[X^2], we can use the formula for the variance of a uniform [0, 1] random variable:

Var(X) = E[X^2] - (E[X])^2 = 1/12

Solving for E[X^2], we get:

E[X^2] = Var(X) + (E[X])^2 = 1/12 + (1/2)^2 = 1/3

Substituting this back into the expression for E[A], we get:

E[A] = 1/2 * E[X^2] = 1/6

Therefore, the expected area of the rectangle is:

E[A] = 1/6

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