Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of four points. How many scores would the professor need so that 99% confidence level would have a margin of error of 0.75 points

Wave interference that results in greater wave amplitude is called Constructive interference.

What is Wave Interference?

Wave interference is a physical phenomena that occurs when two waves collide while traveling through the same medium. Waves interact in two ways.

a) Constructive Interference - In this case, the two waves cancel each other out because their amplitudes are equal and opposite.

b) Destructive Interference - This occurs when two waves add to each other as they travel in the same direction, resulting in a wave with a longer wavelength.

It is Constructive interference.

Therefore, Wave interference that results in greater wave amplitude is called Constructive interference.

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\(\qquad \sf  \dashrightarrow \: 4x + 2 = - 8\)

\(\qquad \sf  \dashrightarrow \: 4x = - 8 - 2\)

\(\qquad \sf  \dashrightarrow \: x = - 10 \div 4\)

\(\qquad \sf  \dashrightarrow \: x = - 2.5\)

The value of x in the equation is 5/2

To solve this question, we have make x the subject of formula.

To solve this problem, we have to make x the subject and we first of all collect like terms and then divide both sides by the coefficient of x

\(4x+2 = -8\)

collect like terms

\(4x+2 = -8\\4x = -8 -2\\4x = -10\)

divide both side by the coefficient of x

\(\frac{4x}{4} =-\frac{10}{4} \\x = \frac{10}{4} \\x = \frac{5}{2}\)

The value of x in the equation is 5/2.

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Answer:

D. Rhombus

Step-by-step explanation:

Rhombus is the quadrilateral that lhas 2 pairs of angle with equal measures and 4 sides of equal length

Attached picture is the shape of Rhombus

Answer: The correct answer is option D; Rhombus

Step-by-step explanation: Basically, all the four options are quadrilaterals, or a plane shape with four sides. However, not all four-sided plane shapes have the same properties, and hence each of them has its own unique name due to its unique features or properties. A rhombus has four sides that are equal in measurement, but not all its four angles are equal in measurement. Two pairs of angles are equal to each other, and these are the pair of opposite angles. Also, the opposite sides/lines are parallel and congruent to each other.

A rectangle has, two opposite sides parallel and congruent, but unlike a rhombus, not all sides measure the same length. Only two opposite sides have equal measurement. In a rectangle, all four angles are congruent and they all measure 90 degrees each.

A trapezoid has only two sides as being parallel, and the other two sides are not parallel. The two parallel sides are referred to as the bases.

A parallelogram also has two equal sides as being parallel to each other and the two opposite sides are also congruent, just like a rhombus. However, unlike a rhombus, a parallelogram does not necessarily have all sides congruent. The two opposite sides may be equal in measure just like in a rectangle, but the angles are not all equal like in a rectangle.

Therefore, only a rhombus satisfies the conditions outlined in the question namely;

Two pairs of angles with equal measures, and four sides of equal length.

The correct statements are:

The mean serves as a metric of central tendency widely known as the arithmetic average. This statistical measure is obtained by aggregating a collection of values and subsequently dividing the sum by the total count of values present within the dataset.

It is a prevalent tool employed in statistical analysis, providing insights into the typical magnitude that can be expected from the dataset's values.

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Answer:

c

Step-by-step explanation:

The statement that best describes this random sample is the five paintings sampled.

The best description for the random sample of five paintings studied in a museum is D which indicates that they represent the five paintings sampled. This sample cannot be generalized to all art in a museum (option A) or all paintings in a museum (option B) because it only includes five specific paintings.

Similarly, it would not be accurate to claim that this sample represents all paintings in the world (option C). The information provided only pertains to the monetary value, type of paint, size of the canvas and weight of the sampled paintings making it limited in scope to the five specific artworks that were examined.

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Answer:

x = 5

Step-by-step explanation:

Since both triangles are similar hence;

m<CAB = m<CDE

Given theta

m<CAB = 50degrees

m<CDE = 10x

Substitute the given angles

50 = 10x

Swap

10x = 50

Divide both sides by 10

10x/10 = 50/10

x = 5

Hence the value of x is 5

There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.

To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:

A vs B

A vs C

A vs D

B vs C

B vs D

C vs D

Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.

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Answer:

12.5 m²

Step-by-step explanation:

The shaded area is a triangle whose area (A) can be calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here b = 8 - 3 = 5 and h = 5 , then

A = \(\frac{1}2}\) × 5 × 5 = 0.5 × 25 = 12.5 m²

Answer:

$7.18

Step-by-step explanation:

$3.59 x 2

The rate of change of the volume of fuel with respect to time is 429.16 / t cubic feet per minute.

To calculate how fast the volume of fuel in the tank increases when filled to a level of 20 feet, we need to find the derivative of the volume function with respect to time.

First, we need to find the height of the fuel in the tank when it is filled to a level of 20 feet.

The total height of the tank is 70 feet, and the level of the fuel is 20 feet, so the height of the air space above the fuel is 50 feet.

The fuel tank is a right circular cone, so we can use similar triangles to find the height of the fuel. The ratio of the height of the fuel to the height of the entire tank is equal to the ratio of the radius of the fuel to the radius of the top of the tank.

That is, h / 70 = 30 / 50, or h = 42 feet.

Now we can plug in the values for h and r into the volume formula:

V = (1/3) * pi * r^2 * h

V = (1/3) * pi * 50^2 * 42

V = 110,907.2 cubic feet

To find the rate of change of the volume of fuel with respect to time, we need to take the derivative of the volume function.

dV/dt = (1/3) * pi * 50^2 * dh/dt

We don't know the value of dh/dt, so we need to find it using similar triangles again.

The rate of change of the height of the fuel with respect to time is equal to the rate of change of the level of the fuel with respect to time, which we'll call dL/dt.

dh/dt = (dL/dt) * (50/70)

We still don't know the value of dL/dt, but we do know that the level of the fuel is increasing at a constant rate, so we can write:

dL/dt = 20 / t

where t is the time it takes to fill the tank to a level of 20 feet.

Now we can plug in the values for h, r, and dh/dt:

dV/dt = (1/3) * pi * 50^2 * (20/t) * (50/70)

dV/dt = 1,500 * pi * (2/7) * (20/t)

dV/dt = 429.16 / t

So the rate of change of the volume of fuel with respect to time is 429.16 / t cubic feet per minute.

Note that this rate of change will decrease as the level of the fuel gets closer to the top of the tank, since the height of the fuel will increase more slowly as the level approaches the top.

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Answer:

The answer to your problem is, 156

First lets find out how many feet or in one yard ?

Well 1 yard = 3 feet.

Now that we know that we can use our knowledge to answer the next question:

If Bill ran 52 yards, how many feet did he ran?

We can do math to solve our answer. :

1 x 52 = 52.

Now we need to multiply 52 x 3.

That is a little bit to much, so lets make the problem easier!

By breaking up the problem \/ to make it more easier.

50 x 3. ( 5 x 3 = 15, just add a zero! ) = 150

3 x 2 = 6.

Next add:

150 + 6 = 156.

Thus the answer to your problem is, 156

A small number of individuals could cause a widespread distribution of the disease.

A researcher applying Watts's mathematical models to study the transmission of an airborne contagious disease can most reasonably assume that:

1. The disease transmission follows a network-based spread pattern.

In Watts's mathematical models, the focus is on network structures and the dynamics of spreading phenomena. Therefore, the researcher can reasonably assume that the transmission of the airborne contagious disease is influenced by the connections and interactions within a network. This implies that individuals are not randomly interacting but are part of a network where the disease can propagate along the links.

The spread of the disease is influenced by the characteristics of the network.

Watts's models highlight the importance of the network structure in determining the spread of contagion. Therefore, the researcher can reasonably assume that factors such as network connectivity, node centrality, clustering, and other network properties significantly influence the transmission dynamics of the airborne contagious disease. These characteristics can affect the speed, reach, and severity of the disease's spread within the network.

By considering these assumptions, the researcher can utilize Watts's mathematical models to gain insights into how an airborne contagious disease might spread through a network and inform strategies for disease control and prevention.

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If we asked people to give their age and you collected it as <5, 6-10, 11-15, 16- 20, 21-25, 26, and older, it is a type of Discrete variable.

Therefore, if we asked people to give their age and you collected it as <5, 6-10, 11-15, 16- 20, 21-25, 26, and older, it is a type of Discrete variable.

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the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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Answer:

the answer I got is 84ft

Substituting the values we get: θ = (96/5) / 12, θ = 8/5 * 1/12 & θ = 2/15.

What is a circle?

A circle is a geometric shape consisting of all the points in a plane that are equidistant from a fixed point called the center. It can also be defined as the locus of all points that are at a fixed distance (called the radius) from a given point in the plane.

The length of an arc in a circle of radius r, subtending an angle of θ radians at the center of the circle, is given by the formula:

arc length = r x θ

We are given the radius of the circle r = 12 feet and the arc length of the arc l = 96/5 feet. We need to find the angle θ in radians.

We can rearrange the formula above to solve for θ:

θ = arc length / r

Therefore, substituting the values we get:

θ = (96/5) / 12

θ = 8/5 * 1/12

θ = 2/15

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Hayden spent a total of 125 minutes working on his social studies project.

What do you mean by equivalent expression?

To find the total amount of time Hayden worked on his social studies project, we need to add the time he spent on Monday and Tuesday.

Hayden worked for 1 hour and 15 minutes on Monday, which is equivalent to 60 + 15 = 75 minutes.

He worked for 50 minutes on Tuesday.

Therefore, the total time he spent working on his project is:

75 + 50 = 125 minutes.

So, Hayden spent a total of 125 minutes working on his social studies project.

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Answer:

I do belive your answer should be B and C if it's multiple choice but of its single the answer is B

Answer:

63/5

Step-by-step explanation:

I have no explanation

First is $677.5

Second is 2.8%

Third is  increase, decrease, and increase i believe

Answer:

v = - 31

Step-by-step explanation:

v - 5 = 6 x (-6) multiply 6 by - 6

v - 5 = -36 Add 5 to both sides of the =

+5 +5

v = -31

The span of {u, v} represents a plane in three-dimensional space. w is not in the span of {u, v}. the span of {u, v, w} is the entire three-dimensional space.

(a) The span of {u, v} represents a plane in three-dimensional space. Geometrically, this plane can be visualized as a flat surface extending infinitely in all directions. It includes all possible vectors that can be obtained by scaling and adding u and v. Any vector lying on this plane can be expressed as a linear combination of u and v.

(b) To determine if w is in the span of {u, v}, we need to check if w can be expressed as a linear combination of u and v. We can write w as follows:

w = a*u + b*v

Solving the system of equations formed by equating corresponding components, we have:

-2 = 3a - 2b

2 = -a + 2b

6 = -2a - 6b

Solving this system, we find that there are no values of a and b that satisfy all three equations simultaneously. Therefore, w is not in the span of {u, v}.

(c) The span of {u, v, w} is the entire three-dimensional space. To justify this, we consider the matrix A whose columns are u, v, and w:

A = [u v w] = [1 3 -2; -1 1 2; -2 -6 6]

We can row-reduce matrix A to its echelon form:

[1 3 -2; -1 1 2; -2 -6 6] -> [1 3 -2; 0 4 0; 0 0 0]

The echelon form shows that the columns of A are linearly independent, and they span the entire three-dimensional space. Therefore, any vector in three-dimensional space can be expressed as a linear combination of u, v, and w, indicating that the span of {u, v, w} is the entire three-dimensional space.

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Benji made par or better on 7 holes in his round so far.

the ratio of holes with par or better to total holes played is equal to 0.4. We need to determine on how many of the holes Benji has made par or better. Table that shows the number of holes Benji has played during his round so far is shown below: Number of holes played in round so far Holes played 6 12 18Number of holes with par or better Number of holes played

2x 6 0.4

The ratio of the number of holes with par or better to the total number of holes played is 0.4.So, (Number of holes with par or better) /

(Number of holes played) = 0.4

Number of holes with par or better

/ (6 + 12 + 18) = 0.42x / 36 = 0.4

Cross-multiplying the above equation, we get,

2x = 0.4 x 36 = 14.4Dividing by 2 on both sides, we get x = 7.2

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Answer:

>

>

>

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

apply the slope formula: rise/run or y2-y1 / x2-x1

if you choose (2,-5) as your x1, y1

choose (7,1) as your x2, y2

(1-(-5)) / (7-2) = 6/5

Answer:

y2-y1/x2-x1

=1-(-5)/7-2

=1+5/7-2

=6/5

Step-by-step explanation:

First write down the formula.

Indicate your coordinates(x1, y1) (x2, y2)

Find the gradient /slope

The abore solution will help you

The sample size that should be used in this study is approximately 93.

To determine the sample size for the study, we can use the formula:

n = (Z * σ / E)^2,

where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the maximum allowable error or margin of error.

In this case, the researchers want the average time to fix a rivet to be off by at most 3.5 seconds, which can be considered as the margin of error (E).

Given that the confidence level is 95%, the corresponding z-score (Z) is 1.96. The population variance (σ^2) is known to be 55 seconds^2.

Plugging these values into the formula, we can calculate the sample size:

n = (1.96 * sqrt(55) / 3.5)^2,

where sqrt denotes the square root.

Evaluating the expression:

n ≈ 92.607.

Sine the sample size should be a whole number, we can round up the value to obtain the final sample size.

Therefore, the recommended sample size for the study is approximately 93.

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Answer:

the given expression is equivalent to

Step-by-step explanation:

\(2(x - 3) {}^{2} \\ 2( {x}^{2} - 2.x.3 + {3}^{2} ) \\ using \: formula \: (x - y) {}^{2} = x {}^{2} - 2.x.y + y {}^{2} \\ 2(x {}^{2} - 6x + 3) \\ 2 {x}^{2} - 12x + 6\)

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

Answer:

It's A.

Step-by-step explanation:

Answer:

y = 9 (x + one-half) squared minus thirteen-fourths

Step-by-step explanation:

i hope