What is the mean absolute deviation for 1.25 3.50 2.55 8.20 4.80 0.30 0.75 2.25

Answer:

D

Step-by-step explanation:

You know the slope has to be -5, because in the equation it says -5x. You know the y intercept has to be a number on the y axis, and since it says the y intercept is 4 in the equation, you would know its (0,4).

Answer:

The gecko's function would be Y = 19x + 6

Step-by-step explanation:

Traveled for 6 minutes flat, so that is not moving
19 meters per minute, this rule is moving so it gets a variable
19 * 6 = 114 btw

Answer: 1.45 is a growth factor.

Step-by-step explanation:

Exponential growth function: \(y=Ab^x\), where A = initial value , b = growth factor (if b>1)

Here, The expression \(6.7\cdot(1.45)^t\) models the number of billions of genetic sequence bases available in the public database of the Whole Genome Shotgun project t years since 2002.

Here, b=1.45 >1

Thus,1.45 is a growth factor.

What Jerry can do if he is testing for normality of the residuals in the regression analysis is to; construct a normal quantile plot of the residuals and see if the result is an approximately upward sloping straight line.

Regression Analysis creates an equation that is the best fit of the given data of both the dependent and the independent variables. Now, it should be noted that the residuals are the error in the regression equation predicted values as well as the actual sample values.

The quantile plot is basically a standard way to tell us whether the data is distributed. Now, If the data points stay quite close to an upward sloping line in the quantile plot, then it can be assumed that the residuals are normally distributed. Then, values of the coefficients are tested to check that they are not statistically equal to zero via a t-test. The t-test is required to know whether the results of the regression are seen to be significant. Finally, results of a t-test usually possess a requirement that the residuals, is normally distributed.

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The Z scores a way to standardize and compare data, as well as to identify outliers.

In simple terms, Z bases give information about how far a data point is from the means of the data set in standard deviation units. The original non-standardized heights, on the other hand, did not guarantee this information.

Z scores are used to standardize data and are useful when comparing two or more different data sets. By converting the original data to Z scores, we can compare data that is on different scales or has different units.

For example, suppose we have two data sets: one with heights measured in inches and the other with weights measured in pounds. We cannot compare these data sets directly as they are at different scales. However, by converting them to Z scores, we can compare them on the same scale.

In addition, the obtained Z's provided a way to identify outliers in the data set. Outliers are data points that are unusually far from the means of the data set. Z scores greater than 3 or less than -3 are generally considered outliers.

In general, the obtained bases are a way to standardize and compare data, as well as to identify outliers.

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The equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.

To find the equation of the tangent to the curve at the point corresponding to t=1:

We first need to find the corresponding values of x and y. Substituting t=1 into the given equations, we get:

\(x = 1^4 + 3 = 4\)
\(y = 1^3 + 1(1) = 2\)

So the point on the curve corresponding to t=1 is (4,2).

To find the equation of the tangent at this point,

we need to find the slope of the curve at this point. We can do this by taking the derivative of y(x) with respect to x:

\(dy/dx = (dy/dt)/(dx/dt) = (3t^2+t)/(4t^3)\)

Substituting t=1, we get:

dy/dx = (3+1)/(4) = 1

So the slope of the curve at the point (4,2) is 1.

Now we can use the point-slope form of the equation of a line to find the equation of the tangent:

y - 2 = 1(x - 4)

Simplifying, we get:

y = x - 2

So the equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.

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Answer:

\(r(x) = 0.05 (x^{2}+1 )x-6\)

Step-by-step explanation:

Function r has two complex zeros and one real zero. Based on the instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.

The failure of beta cells to function can result in a condition called diabetes mellitus.

Beta cells are specialized cells located in the pancreas that produce and release insulin. A hormone responsible for regulating blood sugar levels. When beta cells fail to function properly, it can lead to two main types of diabetes:

1. Type 1 Diabetes: In this autoimmune disease, the immune system mistakenly attacks and destroys the beta cells in the pancreas, resulting in little to no insulin production.

Without sufficient insulin, glucose (sugar) cannot enter the body's cells for energy, leading to high blood sugar levels.

2. Type 2 Diabetes: This form of diabetes is characterized by insulin resistance, where the body's cells become less responsive to the effects of insulin.

Over time, the beta cells may also fail to produce enough insulin to compensate for the increased demand. Type 2 diabetes is often associated with factors such as obesity, sedentary lifestyle, and genetic predisposition.

The failure of beta cells to function properly disrupts the normal regulation of blood sugar, leading to elevated glucose levels and potential complications associated with diabetes.

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Answer:

12 hours

Step-by-step explanation:

1 pair per hour ?

Answer:

you would get around 1.07 or 5.35

Step-by-step explanation:

The correct system of inequalities with a solution point represented by the graph is:

y > 2x – 2 and y < Negative one-half x + 1; (–3, 1)

To see why, we can plot the points given in each of the answer choices and see which one matches the graph:

Choice 1: (3, 1) is not on the shaded region of the graph, so this is not the correct answer.
Choice 2: (–3, 1) is on the shaded region of the graph, so this is a possible solution.

Let's check the other inequality to make sure it's also true: -1 < (-1/2)(-3) - 1. Simplifying, we get -1 < 2.

This is true, so we have a detailed solution.
Choice 3: (3, 1) is not on the shaded region of the graph, so this is not the correct answer.
Choice 4: (–3, 1) is on the shaded region of the graph, but the other inequality y > 2x + 2 is not true at that point. 1 is not greater than 2(-3) + 2 = -4, so this is not the correct answer.

Therefore, the detailed solution is: y > 2x – 2 and y < Negative one-half x + 1; (–3, 1)

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Answer: Number of water bottles a team can fill  from a single watercooler = 48

Step-by-step explanation:

Given: A watercooler contains 160 cups of water.

Each person on a team fills a water bottle with \(3\dfrac13\) cups of water from the cooler.

Here, \(3\dfrac13=\dfrac{10}{3}\)

Now , Number of water bottles a team can fill  from a single watercooler = \(160\div \dfrac {10}3\)

\(=160\times\dfrac3{10}\\\\=16\times3=48\)

Hence, Number of water bottles a team can fill  from a single watercooler = 48

Number of water bottle IT team can feel a single watercooler =48

Answer:

final cost of 42" TV after deducting 15% discount and adding 6.5% sales tax will be $1163.56

Step-by-step explanation:

final cost of 42" TV after deducting 15% discount and adding 6.5% sales tax will be $1163.56

The final cost of the TV would be $1,063.50.

To calculate this:

First, calculate the discount by multiplying the original price of the TV ($1,250) by 15% (0.15). This equals $187.50.

Subtract the discount from the original price of the TV ($1,250 - $187.50 = $1,062.50)

Next, calculate the sales tax by multiplying the price after the discount ($1,062.50) by 6% (0.06). This equals $63.75

Finally, add the sales tax to the price after the discount ($1,062.50 + $63.75 = $1,063.50)

speed at t = 2.10 s is 2.08 m/s.

Given, the position vector for a particle is given as a function of time by z(t) = x(t)i + y(t)j,

where x(t) = at + b and y(t) = ct² + d, where a = 2.00 m/s, b = 1.15 m, c = 0.120 m/s², and d = 1.12 m.

(a) Average velocity during the time interval from t = 2.10 s to t = 3.80 s

Average velocity is given as the displacement divided by time.

Average velocity = (displacement) / (time interval)

Displacement is given by z(3.80) - z(2.10), where z(t) = x(t)i + y(t)j

Average velocity = [z(3.80) - z(2.10)] / (3.80 - 2.10) = [x(3.80) - x(2.10)] / (3.80 - 2.10)i + [y(3.80) - y(2.10)] / (3.80 - 2.10)j

= [a(3.80) + b - a(2.10) - b] / (3.80 - 2.10)i + [c(3.80)² + d - c(2.10)² - d] / (3.80 - 2.10)j = (2.00 m/s) i + (0.1416 m/s²) j

Hence, the average velocity is (2.00 m/s) i + (0.1416 m/s²) j. b) Velocity at t = 2.10 s

Velocity is the rate of change of position with respect to time.

Velocity = dr/dt = dx/dt i + dy/dt

jdx/dt = a = 2.00 m/s

(given)dy/dt = 2ct = 0.504 m/s (at t = 2.10 s)

[Using y(t) = ct² + d, where c = 0.120 m/s², d = 1.12 m]

Therefore, velocity at t = 2.10 s is 2.00i + 0.504j m/s.

c) Speed at t = 2.10 s

Speed is the magnitude of the velocity vector. Speed = |velocity| = √(dx/dt)² + (dy/dt)²

= √(2.00)² + (0.504)² = 2.08 m/s

Therefore, speed at t = 2.10 s is 2.08 m/s.

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Step-by-step explanation:

The Missing side using Pythagorean theorem

=√(19)²+(38)²

=√361+1444

=√1805=19√5

=42.485≈42.49( to the nearest hundredth)

Missing angle

=let the angle be x

tan(x)=19/38

x=tan^-1(½)=26.565

x=26.57(to the nearest hundredth)

If the length,breadth, height of cuboid are 16 m, 5 m,4 m , slant height of pyramid is 10m,  height be 6 m then the surface area of composite figure be 444 \(m^{2}\).

Given that the length,breadth,height of cuboid are 16m,5 m, 4m and slant height be 10 m and height be 6 m.

Surface area is basically sum of area of all the sides of a figure.

Surface area of composite figure =  area of cuboid less area of common side + area of 2 slant sides of pyramid+area of two triangles.

=2(lb+bh+hl)-(lb)+2(slant height*breadth of cuboid)+2[1/2* length of cuboid* height of triangle)

=2(16*5+5*4+4*16)-16*5+2(10*5)+2[1/2*16*6]

=2(80+20+64)-80+2*50+2(48)

=2(164)-80+100+96

=328-80+196

=248+196

=444\(m^{2}\)

Hence the surface area of composite figure having a cuboid and pyramid on top is 444\(m^{2}\).

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Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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The equations should be matched with the correct transformation rule as follows;

In Mathematics and Geometry, the translation of a graph to the left means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

y = |x + 1|

In Mathematics and Geometry, the translation of a graph downward means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

y = x² - 1

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y);

y = -|x|

In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y);

y = (-x)²

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The rate of change of capital in terms of units of labor is -2.0 As more labor is used, available capital decreases As more capital is used, available labor decreases.

\(100x^{0.75} y^{0.25} = 135540\)

x = 1500 units and y = 1000 units

A) \(\frac{d}{dx}(100x^{0.75}y^{0.25} = \frac{d}{dx}(135540)\)

\(100[{\frac{d}{dx}(x^{0.75})y^{0.25} + x^{0.75}\frac{d}{dx}(y^{0.25})] = 0\)

\(0.75 x^{-0.25} y^{0.25} + x^{0.75} (0.25y^{-0.75\frac{dy}{dx} }) = 0\)   ______(1)

X & Y values in equation 1

\(0.75(1500^{-0.25}(1000)^{0.25}+(1500)^{0.75}(0.25)(1000)^{-0.75}\frac{dy}{dx} = 0\)

(0.75) (0.16) (5.62) + (0.41) (0.25) (0.0056) \(\frac{dy}{dx}\) = 0

0.6744 + 0.3374 \(\frac{dy}{dx}\) = 0

0.3374 \(\frac{dy}{dx}\) = -0.6744

\(\frac{dy}{dx}\) = -1.9988

\(\frac{dy}{dx}\) ≈ -2.0

B) If the labor x is increased then the capital invested in manufacturing process decreased

C) As more capital is used then the available labor is reduced

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Answer:

The value of the coin tosses per time in the air

Step-by-step explanation:

The value of n for which the experimental probability of tossing tails can equal the theoretical probability is any even number.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The theoretical probability of tossing tails in a fair coin is 0.5 or 1/2.

The experimental probability of tossing tails in n trials is the number of times tails appear divided by n.

So, we want to find a value of n such that:

number of times tails appear / n = 0.5

Solving for n:

number of times tails appear = 0.5n

Since the number of times tails appear must be a whole number, n must be even.

This is because if n is odd, then it is not possible to have exactly half the trials result in tails.

For example,

If n=3, the possible numbers of tails that can appear are 0, 1, 2, or 3. Half of 3 is 1.5, which is not a whole number, so it is impossible to have exactly half the trials result in tails.

On the other hand,

If n=4, the possible numbers of tails that can appear are 0, 1, 2, 3, or 4.

Half of 4 is 2, which is a whole number, so it is possible to have exactly half the trials result in tails.

Therefore,

The value of n for which the experimental probability of tossing tails can equal the theoretical probability is any even number.

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Yes, an angle in a right-angled triangle is always present.  Without any additional information about the triangle, it is impossible to determine the value of the angle in question.

In a right-angled triangle, one of the angles is a right angle, which measures 90 degrees. The other two angles in the triangle are acute angles and their measures always add up to 90 degrees.

To find the value of the angle in question, we need to know some additional information about the triangle. If we have the lengths of two sides of the triangle, we can use trigonometric ratios to find the measure of the angle.

For example, if we know the length of the side opposite the angle and the length of the hypotenuse (the longest side of the triangle), we can use the sine ratio to find the measure of the angle.

If we know the length of the side adjacent to the angle and the length of the hypotenuse, we can use the cosine ratio.

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The mean greater than median when skewed right, because the median is not affected by having much larger values.

We know that the skewness is nothing but the measure of the asymmetry of a distribution.  A distribution can have right skewness (also called positive skewness), left skewness (or negative), or zero skewness. A distribution is said to be asymmetrical when its left and right side are not mirror images.

As we know, in a perfectly symmetrical distribution, the mean and the median are the same.

In case of right skewness, the mode is often less than the median, which is less than the mean. It's because the median is not affected by having much larger values but there would be increase in the mean.

For example {1, 2, 3, 4, 5} both the mean and the median equal 3  

But in case of {1, 2, 3, 4, 50} the median is still 3 and the mean is 12

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The probabilities are as follows:-

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability will be calculated as follows:-

Total combinations are = 10⁴ = 10000

A) if none of the digits are repeated:-The combinations will be 10 x 9 x 8 x 7 = 5040

Probability =  5040 /  10000

Probaility = 0.504

B) If any of the digits can be repeated:- The combinations will be 10 x 10 x 10 x 10 = 10000

Probabilityy = 10000 / 10000 = 1

C )If any of the digits can be repeated but the 3 and 8 are not in the combination the combinations will be 7 x 7 x 7 x 7 = 2401

Probability = 2401 / 10000 = 0.24

Therefore if none of the digits is repeated 0.50.If any of the digits can be repeated 1.If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.

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Answer:

b) Use the distributive property to get 4c-12=8

c) Divide both sides by 4 to get c-3=2

Step-by-step explanation:

Solve the equation 4(c-3)=8

What are two ways to start solving this equation?

We are given the Equation

4(c - 3) = 8

The two ways to start solving this Equation is given as:

1. 4(c - 3) = 8

We expand the brackets, using Distributive property

4c - 12 = 8

Or

2. 4(c - 3) = 8

Divide both sides by 4

4(c - 3)/4 = 8/4

c - 3 = 2

Therefore, options b and c is correct

The measure of angle Q is equal to 40°.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. In Geοmetry, triangles are the type οf pοlygοns, which have three sides and three vertices.

This is a twο-dimensiοnal figure with three straight sides. A triangle is cοnsidered a 3-sided pοlygοn. The sum οf all the three angles οf a triangle is equal tο 180°. The triangle is cοntained in a single plane. Based οn its sides and angle measurement, the triangle has six types.

Using Cos θ = adjacent/ Hypotenuse

Cos Q = 720/ 940

Cos Q = 36/47

Q = arccos 36/47

Q = 40.007793734°

Thus, The measure of angle Q is equal to 40°.

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To describe this dependency, we require non-dimensional groups. To find out how many non-dimensional groups are needed to describe this dependency, we'll use the Buckingham Pi Theorem.

When it comes to a wind turbine, the power (P) produced depends on the wind speed (U), the diameter of the turbine (d), the turbine angular velocity (w), and the air density (p) and viscosity (u).

This theorem states that, for any physical situation involving n variables, m non-dimensional groups can be formed, where

m = n - k, and k is the minimum number of reference dimensions required to specify all the variables.

The reference dimensions are the dimensions of the seven SI base units.    We know that there are 5 variables in this situation: U, d, w, p, and u.

Each of these has a reference dimension. As a result,

k = 5. m

= n - k

= 5 - 5

= 0.

Therefore, there are no non-dimensional groups required to describe this dependency because the number of non-dimensional groups is zero. So, this means that all the variables are dependent on one another directly or indirectly.

The power (P) generated by a wind turbine is directly proportional to the cube of the wind speed (U) and the square of the turbine radius (d).

We can see that all the variables in the equation have units of time, mass, and length. As a result, we can describe them in terms of three fundamental dimensions: L (length), M (mass), and T (time).

Therefore, we require a minimum of three reference dimensions to specify all the variables.

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The Complete Question :

The power, P, produced by a wind turbine depends on the diameter of the turbine, d, the wind speed, U, the turbine angular velocity ω and the air density and viscosity, ρ and μ respectively. a) Find the maximum number of non- dimensional groups required to describe this dependency. [Total 4 Marks]

b) Explain why P and μ are not suitable choices for the repeating variables. [5 Marks]

c) Using ρ, ω and d as the repeating variables, rewrite this relation in dimensionless form. [7 Marks]

d) An engineer wishes to test the performance of a wind turbine with a diameter of 4m whose operational angular velocity is 200 rad/s with a wind speed of 15 m/s. She builds a small-scale model which she wishes to test in water at a speed of 5m/ s. Calculate the diameter and angular velocity required for the model turbine to reproduce the operating conditions of the full-scale wind turbine. [6 Marks]

e) The measured power produced by the scale model is 400 kW, determine the power produced by the full-scale wind turbine? [3 Marks]

f) The rotational speed of the wind turbine, ω, is found to be proportional to the wind speed U. If the effects of viscosity are negligible, comment on how the power of a specific wind turbine changes with wind speed.

Answer:

x = 4

Step-by-step explanation:

35/60 = (5x+1+35)/96

3,360 = 60(5x+36)

56 = 5x+36

20 = 5x

x = 4

Answer:

16.67 I THINK

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

Answer:

25 and 55

Step-by-step explanation:

Let's call the larger number L and the smaller S

L = 5 + 2×S

And the sum is:

L + S = 80 Subtract S in both sides:

L = 80 - S

Now, substitute this value of L in the first equation:

80 - S = 5 + 2×S Add S in both sides:

80 = 5 + 2×S + S

80 = 5 + 3S Subtract 5 in both sides

75 = 3S Divide both sides by 3

25 = S

We find the value of S, and now we substitute it in the second equation to find the value of L:

L = 80 - 25

L = 55

Answer:

3.26

Step-by-step explanation:

33.5/3.14 = 10.66 ( when rounded to the nearest tenth).

10.66 square rooted is 3.26

The required radius of the sphere is 2 inch.

Volume of sphere = 33.5 cubic inches . Radius of sphere to be determine.

Volume, is defined as mass gained per unit cube of density.

Here, area of sphere = \(4/3\pi r^3\)

                         33.5 = 4/3 πr³
                              r³ = 33.5 * 3/4π
                              r  = 2

Thus, the required radius of the sphere is 2 inch.

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