Find the interquartile range (IQR) for the data. 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22

Answer: 4th option (the one already selected)

Step-by-step explanation: as the X variable changes by 7 the Y variable changes by 1

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The probability that the two smartest people will be in the same group is approximately 0.023 or 2.3%.

The probability of the two smartest people being in the same group can be calculated by considering the total number of possible ways the groups can be formed and the number of ways the two smartest people can be in the same group.

To find the total number of ways the groups can be formed, we can use the concept of combinations. In this case, we have 36 people in the class and we want to split them into 12 groups of 3. We can calculate the total number of ways the groups can be formed using the formula for combinations:

C(n, r) = n! / (r! * (n-r)!)

where n is the total number of people and r is the number of people in each group.

In our case, n = 36 and r = 3. Plugging these values into the formula, we get:

C(36, 3) = 36! / (3! * (36-3)!)

Simplifying this expression, we find that there are 7140 different ways to form the groups.

Now, let's calculate the number of ways the two smartest people can be in the same group. Since there are 12 groups and we want the two smartest people to be in the same group, we can treat them as a single unit. So, we need to calculate the number of ways to distribute the remaining 34 people into 11 groups of 3.

Using the same combination formula, we have:

C(34, 3) * C(11, 1) = (34! / (3! * (34-3)!) * (11! / (1! * (11-1)!))

Simplifying this expression, we find that there are 163,800 different ways to distribute the remaining people.

Now, to calculate the probability, we divide the number of ways the two smartest people can be in the same group by the total number of possible ways the groups can be formed:

Probability = (Number of ways the two smartest people in the same group) / (Total number of possible ways to form groups)

Probability = 163,800 / 7,140

Simplifying this expression, we find that the probability is approximately 0.023 or 2.3%.

Therefore, the probability that the two smartest people will be in the same group is approximately 0.023 or 2.3%.

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Answer:

in 13 years it will be at 432,480

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

1) Comparing the two equations, we see that the multiplier 'x' is missing from both sides in equation B. That is, it has been divided out:

  (5x)/x = (3x)/x   ⇒   5 = 3

Both sides have been divided by x.

__

2) The equations are equivalent if and only if x ≠ 0. Unfortunately, in equation A, the only solution is x = 0. For equations like the one in A, it is better to subtract one side from both:

  5x -3x = 3x -3x   ⇒   2x = 0

Now, dividing by 2, it is clear that the solution is x = 0.

Equations A and B are not equivalent, because the condition on the division property of equality was violated (you cannot divide by 0).

Answer: 80% of 20 is 16. 100% of 20 is 20, therefore 80 percent of 20 equals 16. To learn how to solve 16 is 80 percent of what Number, see the step by step instructions below.

Step-by-step explanation: Hope this help :D

The number is 20. Thus 16 is 80% of 20.

To find the number that 16 is 80% of, set up the following equation:

80% of x = 16

To solve for x, to convert the percentage to a decimal. 80% is equivalent to 0.8. Now, rewrite the equation as:

0.8x = 16

To isolate x, divide both sides of the equation by 0.8:

x = 16 / 0.8

Evaluating the division:

x = 20

Therefore, the number 16 is 80% of the number 20.

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The lengths of the sides of the translated triangle that are equal are sides ST' and SU.

To determine the side lengths of the translated triangle, we need to find the new coordinates of the vertices after the translation.

The translation involves moving all points down 8 units, so we subtract 8 from the y-coordinate of each vertex.

Given: The initial vertices:

S(4, 3)

T(2, 6)

U(6, 6)

After the translation, the vertices become:

S'(4, 3 - 8) = S'(4, -5)

T'(2, 6 - 8) = T'(2, -2)

U'(6, 6 - 8) = U'(6, -2)

Next, we calculate the lengths of the sides of the translated triangle.

Length of side ST:

√((x2 - x1)² + (y2 - y1)²)

ST' = √((2 - 4)² + (-2 - (-5))²)

= √((-2)² + 3²)

= √(4 + 9)

= √13

Length of side SU:

SU' = √((6 - 4)² + (-2 - (-5))²)

= √(2² + 3²)

= √(4 + 9)

= √13

Length of side TU:

TU' = √((2 - 6)² + (-2 - (-2))²)

= √((-4)² + 0²)

= √(16 + 0)

= √16

= 4

Therefore, the side lengths of the translated triangle are as follows:

ST' = SU' = √13

TU' = 4

Thus, we can see that the lengths of the sides ST' and SU' are equal, while the length of side TU' is different.

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The composition R2(R1(x)) is a rotation about the center C with angle of rotation given by the angle between the vectors P-Q and R2(R1(P))-C.

Lemma 10.3.3 states that any rigid motion of the plane is either a translation a rotation about a fixed point or a reflection across a line.

To prove that the composition of two rotations with the same center is a rotation can use the following argument:

Let R1 and R2 be two rotations with the same center C and let theta1 and theta2 be their respective angles of rotation.

Without loss of generality can assume that R1 is applied before R2.

By Lemma 10.3.3 know that any rotation about a fixed point is a rigid motion of the plane.

R1 and R2 are both rigid motions of the plane and their composition R2(R1(x)) is also a rigid motion of the plane.

The effect of R1 followed by R2 on a point P in the plane. Let P' be the image of P under R1 and let P'' be the image of P' under R2.

Then, we have:

P'' = R2(R1(P))

= R2(P')

Let theta be the angle of rotation of the composition R2(R1(x)).

We want to show that theta is also a rotation about the center C.

To find a point Q in the plane that is fixed by the composition R2(R1(x)).

The angle of rotation theta must be the angle between the line segment CQ and its image under the composition R2(R1(x)).

Let Q be the image of C under R1, i.e., Q = R1(C).

Then, we have:

R2(Q) = R2(R1(C)) = C

This means that the center C is fixed by the composition R2(R1(x)). Moreover, for any point P in the plane, we have:

R2(R1(P)) - C = R2(R1(P) - Q)

The right-hand side of this equation is the image of the vector P-Q under the composition R2(R1(x)).

The composition R2(R1(x)) is a rotation about the center C angle of rotation given by the angle between the vectors P-Q and R2(R1(P))-C.

The composition of two rotations with the same center is a rotation about that center.

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Answer:

0

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

Answer:

correct

Step-by-step explanation:

The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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Answer:

Step-by-step explanation:

i)14π/9

ii)91π/18

iii)77π/9

iv)140⁰

The Laplace transform F(s) = L(f)(s) is defined for all real values of s except s = 0.

To evaluate the Laplace transform F(s) = L(f)(s) for the given function, we need to split the function into three parts based on the given intervals:

For 0 ≤ t ≤ 2, f(t) = 6 - 2t.

For 2 ≤ t ≤ 3, f(t) = 0.

For t ≥ 3, f(t) = 3.

Let's calculate the Laplace transform of each part separately:

Laplace transform for 0 ≤ t ≤ 2:

Using the standard Laplace transform formula for f(t) = 6 - 2t, we have:

L{6 - 2t}(s) = 6 * L{1}(s) - 2 * L{t}(s)

The Laplace transform of the constant function 1 is given by:

L{1}(s) = 1/s

t's Laplace transform is determined by:

L{t}(s) = \(1/s^2\)

When we plug these figures into the formula, we get:

L{6 - 2t}(s) = 6 * (1/s) - 2 * \((1/s^2)\)

= 6/s - \(2/s^2\)

Laplace transform for 2 ≤ t ≤ 3:

For this interval, f(t) = 0, which means it has no impact on the Laplace transform. Therefore:

L{0}(s) = 0

Laplace transform for t ≥ 3:

For this interval, f(t) = 3. Using the standard Laplace transform formula, we have:

L{3}(s) = 3 * L{1}(s)

= 3/s

Now, let's combine all the Laplace transforms:

F(s) = L{f}(s) = L{6 - 2t}(s) + L{0}(s) + L{3}(s)

= 6/s - \(2/s^2\) + 0 + 3/s

= (6 - 2/s + 3)/s

To determine for what real values of s the Laplace transform F(s) is defined, we need to find the values that make the denominator nonzero. In this case, the denominator is s. Therefore, F(s) is defined for all real values of s except when s = 0.

In conclusion, the Laplace transform F(s) = L(f)(s) is defined for all real values of s except s = 0.

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Cost of each Hamburger = $3

Cost of 90 Hamburgers = 3×90

= $270

Therefore cost of 90 hamburgers is $270

Must click thanks and mark brainliest

Answer:

G: 7/5

Step-by-step explanation:

12x - 15 = 6 - 3x

12x + 3x = 6 + 15

15x = 21

x = 21/15

x = 7/5

The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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Answer:

Question 19: 4(x+5)+3 = 4·x+4·5+3 (second option).

Question 20: (117.50-83.50)+6(22.50+3) = 34+6(25.50) --> (last option).

Third question:

375=x-28

x= 375+28

x= 403

Fourth question:

0.57, 0.66, 0.75, 0.84,...

0.66-0.57= 0.09 and 0.75-0.66= 0.09 and 0.84-0.75= 0.09

So, the next three terms are: 0.93, 1.02, 1.11

Answer:

The correct answer is 5b²-b-2

Answer:

Mr. Brown was speeding at around 59 miles per hour.

Explanation:

If 1 kilometer = 0.62 mile, then:

95 km/h = 59.03 mph

55 < 59

Mr. Brown was going 4 mph over the speed limit.

Answer:

6:

x=  6(y−2)/5

8:a=−(b+c+4)

b=−(a+c+4)

Step-by-step explanation:

Answer:

(1) y = - 2x - 2

(2) y = 1/3x + 6

Step-by-step explanation:

(Picture 1)

y = mx + b

The line cuts the y axis at -2, meaning b = -2

When y increase s by 1, x decreases by 2, meaning mx = -2x

That makes y = - 2x - 2

(Picture 2)

The line cuts the y axis at 6, meaning b = 6

When y increases by 1, x increases by 3, meaning mx = x/3 or 1/3x

That makes y = 1/3x + 6

Answer:

-0.7

Step-by-step explanation:

You are subtracting 0.7 from 8. The pattern keeps going

Answer:

It would take 14 months for the center to reach its goal, and the line should be discrete because there cannot be partial members.

Step-by-step explanation:

At x = 14 months, the members will become 500 in number.

The general equation of a straight line is -

Other possible equations of line are -

We have the fitness center already has 150 members and adds an average of 25 members per month. The function f(x) = 150 + 25x represents the membership after [x] months.

We have the function as -

f(x) = 150 + 25x

Now, it can be seen from the graph that at x = 14 months, the members will become 500 in number.

Therefore, at x = 14 months, the members will become 500 in number.

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Answer:

m = 0

Step-by-step explanation:

Answer:

m = 0

Step-by-step explanation:

Use the slope formula m = y2 - y1/x2 - x1

(5-5)/(-1-3) = 0/-4

= 0

Answer:

19 miles

Step-by-step explanation:

If they had to ride 342 split by 18 horses, divide 342 by 18 to get 19

Answer:

They rode 19 miles before replacing each horse.

Step-by-step explanation:

This problem can be represented as:

\(\frac{342 miles}{18 horses}\)

To find the number of miles per horse simply divide 342 by 18. You will get your answer of:

\(\frac{19 miles}{1 horse}\)

A good method for evaluating the integral ∫2 to -√27 involves using the fundamental theorem of calculus and applying techniques of integral calculus.

Here's an explanation of the steps involved:

1. Start by determining the antiderivative of the integrand. In this case, the integrand is not specified, so let's assume it as f(x).

2. Apply the fundamental theorem of calculus, which states that if F(x) is the antiderivative of f(x), then ∫[a, b] f(x) dx = F(b) - F(a).

3. Find the antiderivative F(x) of f(x). This step can be challenging depending on the specific integrand. If the integrand has a known antiderivative, such as a polynomial or trigonometric function, then you can use the appropriate integration techniques.

4. Evaluate F(x) at the upper and lower limits of integration, which are 2 and -√27, respectively. Plug in these values into F(x) and subtract F(2) from F(-√27).

5. Simplify the expression obtained in step 4 to obtain the final result.

It's important to note that without the specific form of the integrand, it's not possible to provide an exact solution or determine the integral's numerical value. The above steps outline a general approach to evaluating integrals using the fundamental theorem of calculus and integration techniques. However, the specific method for evaluating the integral will depend on the nature of the integrand.

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The area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

Suppose that the two adjacent sides of a rectangle be of 'a' units and 'b' unit lengths.

Then, we get the area of that rectangle as:

\(S = a \times b \: \rm unit^2\)

For this case, we're specfied that:

Let the other side (adjacent) be of 'b' units length

Then, as perimeter of a rectangle = 2(sum of lengths of one pair of adjacent sides of the rectangle)

Therefore, we get:

\(24 = 2(a+b)\\\text{Dividing both the sides by 2}\\12 = a + b\\b = 12 - a\)

We expressed 'b' in terms of 'a' so that we can represent the area of the considered rectangle in terms of 'a' alone.

The area of the rectangle is:

\(S =a \times b = a \times (12 - a) \: \rm unit^2\)

Thus, the area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

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The local maximum and minimum values of the function are as follows: maximum at (smaller x value), minimum at (larger x value), and there are no saddle points.

To find the local maximum and minimum values of the function, we need to analyze its critical points, which occur where the partial derivatives are equal to zero or do not exist.

Let's denote the function as f(x, y) = -8 - 2x + 4y - x^2 - 4y^2. Taking the partial derivatives with respect to x and y, we have:

∂f/∂x = -2 - 2x

∂f/∂y = 4 - 8y

To find critical points, we set both partial derivatives to zero and solve the resulting system of equations. From ∂f/∂x = -2 - 2x = 0, we obtain x = -1. From ∂f/∂y = 4 - 8y = 0, we find y = 1/2.

Substituting these values back into the function, we get f(-1, 1/2) = -9/2. Thus, we have a local minimum at (x, y) = (-1, 1/2).

There are no other critical points, which means there are no local maximums or saddle points. Therefore, the function has a local minimum at (x, y) = (-1, 1/2) but does not have any local maximums or saddle points.

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