when you are designing a research study and considering what hypothesis test you might use, a common rule of thumb is to select the most powerful test. why is this a good idea? the most powerful test is the test most likely to reject the null hypothesis when it is false the most powerful test is the test least likely to result in a type i error. the most powerful test is the test least likely to reject the null hypothesis. the most powerful test is the test most likely to get the right answer.

The probability that the artist chosen will be a painter or a photographer is 3/4

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

To solve this exercise the formula and the procedure that we have to use for probability is:

probability= (achieving success / possible outcomes)

Achieving success = 7 painters + 5 photographer = 12

Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16

Applying the formula to calculate the probability we get:

probability= (achieving success / possible outcomes)

probability= 12/16

Simplifying:

probability= 3/4

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Answer:

Step-by-step explanation:

We are being asked for times, so we can express the rate in terms of seconds per meter.

  (15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter

__

1) It will take Robot A 1 1/14 seconds to go 1 meter.

2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)

Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: \((7x+4)\)  and \((x-1)\)

If the given quadratic expression is of the form \(ax^2 + bx + c\),

then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

\(b = \alpha + \beta \\ ac =\alpha - \beta\)

The given expression is \(7x^2 - 3x - 4\)

Comparing it with the standard form of quadratic expression \(ax^2 + bx + c\), we get: a = 7, b = -3, c = -4

ac = -28

-28 = -2 times 14

-28 = -7 times 4 (-7 + 4 = -3 = b)

Thus, \(\alpha = -7, \beta = 4\)

Thus, we get:

\(7x^2 - 3x - 4 = 7x^2 - 7x + 4x - 4 = 7x(x-1) + 4(x-1) = (7x+4)(x-1)\\7x^2 - 3x - 4 = (7x+4)(x-1)\)

Thus, The factors of given expression are: \((7x+4)\)  and \((x-1)\)

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Answer:

Step-by-step explanation:

Answer:

b. x² + 8x + 12 =

1. use the factoring X (see attachment)

2. 6 x 2 = 12; 6 + 2 = 12

3. (x + 6)(x + 2) = 0

4. x = -6, -2

c. x² + 13x + 12 =

1. 12 x 1 = 12; 12 + 1 = 13

2. (x + 12)(x + 1) = 0

3. x = -12, -1

c. x² + x - 12 =

1. 4 · (-3) = -12; 4 - 3 = 1

2. (x +4)(x - 3) = 0

3. x = -4, 3

f. x² + 15x + 36 =

1. 12 x 3 = 36; 12 + 3 = 15

2. (x + 12)(x + 3) = 0

3. x = -12, -3

hope this helps :)

Answer:

b) - (x + 2)(x + 6)

c) - (x + 12)(x + 1)

c) - (x - 3)(x + 4)

f) - (x + 12)(x + 3)

Step-by-step explanation:

Well to factor the given info we need to find the factors.

b)

\(x^2 + 8x + 12\)

So 6*2 = 12

6x + 2x = 8x

x*x = x^2

Factored - (x + 2)(x + 6)

c)

\(x^2 + 13x + 12\)

Well x*x = x^2

and 12*1 = 12

12x + x = 13x

Factored - (x + 12)(x + 1)

The second c)

\(x^2 + x - 12\)

Well x*x = x^2

-3*4 = -12

-3x + 4x = x

Factored - (x - 3)(x + 4)

f)

\(x^2 + 15x + 36\)

So x*x = x^2

12*3 = 36

12x + 3x = 15x

Factored - (x + 12)(x + 3)

Thus,

everything factored is (x + 2)(x + 6) , (x + 12)(x + 1) , (x - 3)(x + 4) ,

(x + 12)(x + 3).

Hope this helps :)

Answer:

Subtract from both sides:
10x+25 = 43

10x+25-25 =43 -25

Simplify

10x = 18

Divide both sides by the same factor

10x/10 = 18/10

Simplify once more

x = 9/5

Step-by-step explanation:

Answer:

answer C!!

Step-by-step explanation:

Given  : sphere with radius 15.To find : Which expression gives the volume.Solution : We have given that radius of sphere = 15 units.Volume of sphere =  .Plugging the value of radius Volume of sphere =  .

Answer:

2 1/2

Step-by-step explanation:

Answer:

2 1/2

Step-by-step explanation:

Since P is at -4 and you want a number that is 6 1/2 units away from it. You are either adding 6 1/2 to it or subtracting 6 1/2 to that number.

-4 + 6 1/2 = 2 1/2

-4 - 6 1/2 = -10 1/2

Also if you count 6 and 1/2 notches in either directions from -4, you will also get both of those answers.

The multiple choice only gives you the 2 1/2 option so that is the one they are looking for.

Answer:

Isosceles

Step-by-step explanation:

Two sides are equal to each other and not the same length as the other side, so it'd be an isosceles triangle.

The elementary matrix E = [1 0 0; 0 1 0; 5/3 -2 1] such that EC = A.

To find an elementary matrix E such that EC = A, we need to perform row operations on the matrix C such that it becomes A.

We can achieve this by performing the following row operations on C:

R3 ← R3 + R1

R1 ← R1/3

R2 ← R2 - 3R1

R3 ← R3 + 5R2

The resulting matrix after these row operations is:

1 0 0

0 1 0

5/3 -2 1

Therefore, the elementary matrix E that corresponds to these row operations is:

1 0 0

0 1 0

5/3 -2 1

We can verify that EC = A by multiplying EC:

[0 3 -5 0 1 2-1 2 0 0 0 0-1 2 0 0 0 0] x [0 3 -5 0 1 2                      

0 1 2 0 0 0                      -1 2 0 0 0 0]

= [0 3 -5 1 -1 2   -1 2 0 0 0 0   0 3 -5 0 1 2]

= A

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Answer:

Concept: Algebraic Manipulation

Answer:

130.26

Step-by-step explanation:

257.40-21.82-150.32=45=130.26

Answer:

D. IT shows it is Exponential function i believe

Step-by-step explanation:

Without more information about the methodology and context of Lindsay's study or survey, it's difficult to determine the validity of her inference with certainty.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

If Lindsay has conducted a survey or study and found that out of 400 people, 300 would prefer to watch movies in a theater, her inference would be valid based on the data she collected. However, it's important to note that her inference would only be valid within the context of her study or survey.

If Lindsay's study or survey was conducted in a specific geographic location or demographic group, her results may not be generalizable to other populations or locations. Additionally, if her study or survey had any methodological flaws, such as a biased sample or leading questions, her results may not be reliable.

Therefore, without more information about the methodology and context of Lindsay's study or survey, it's difficult to determine the validity of her inference with certainty.

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If event a be being chosen for the first round, and event b being chosen for this second round events A and B are mutually exclusive, but not independent.

Based on the given information, the probability of being chosen for the first round on the show is P(A) = 1/30, and the probability of being chosen for the second round on the show is P(B) = 2/15. The probability of being chosen for both rounds on the show is P(A and B) = 0.

If P(A and B) = 0, then events A and B are mutually exclusive, meaning that they cannot happen at the same time. If a person is chosen for the first round, they cannot be chosen for the second round.

Since A and B are mutually exclusive, they cannot be independent. Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event.

However, in this case, the occurrence of A affects the probability of B, because if a person is not chosen for the first round, they cannot be chosen for the second round. Therefore, events A and B are mutually exclusive, but not independent.

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Answer:

60

Step-by-step explanation:

70% of x = 42

.7x = 42

x = 42 ÷ .7

x = 60

Answer:

60

Step-by-step explanation:

We have, 70% × x = 42

or,

\(\frac{70}{100}\) × x = 42

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 42 × \(\frac{100}{70}\)

x = 60

If you are using a calculator, simply enter 42×100÷70, which will give you the answer of 60

Answer:

34

Step-by-step explanation:

Step-by-step explanation:

5x+4y

5×45+4×75

225+300

525

When a confidence interval for the difference of two population means contains 0 (D) the population means may be the same.

When a confidence interval for the difference between the two population means contains 0, it means that there is no significant difference between the two population means.

However, it does not rule out the possibility that the population means are different.

This is because the confidence interval provides a range of values that are likely to contain the true difference between the population means, but it is possible that the true difference falls within this range and is not equal to 0.

Therefore, the conclusion that can be drawn is that the population means may be the same.

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Answer:

The coordinates are (15,-55).

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer:

12/13

Step-by-step explanation:

48/52 simplified in the lowest terms is 12/13

You do this by finding common numbers in the fraction

Answer:

12/13

Step-by-step explanation:

48/52     we can find an identical multiple for each 48 = 4*12  and 52 =4 *13 Turn into new fractions instead of 4*12 we show 4/12 and 4/13  - Then it is strike out the 4's and we are left with = 12 / 13   This is the recommended working out method.  

The proportion of time that none of the rats are eating is approximately 0.0416% or 0.000416. To solve this problem, we need to consider the transition rates between the eating and non-eating periods for each of the four rats, taking into account that they act independently.

1. First, calculate the transition rates for each rat.
  - Eating period: Mean duration is 0.5 hours, so the rate is λ1 = 1/0.5 = 2 per hour.
  - Non-eating period: Mean duration is 3 hours, so the rate is λ2 = 1/3 ≈ 0.33 per hour.

2. Next, determine the transition probabilities for each rat.
  - The probability of a rat eating (P_eating) = λ1 / (λ1 + λ2) = 2 / (2 + 0.33) ≈ 0.857.
  - The probability of a rat not eating (P_not_eating) = λ2 / (λ1 + λ2) = 0.33 / (2 + 0.33) ≈ 0.143.

3. Since the rats act independently, calculate the probability of all four rats not eating simultaneously.
  - P_all_not_eating = P_not_eating ^ 4 ≈ (0.143) ^ 4 ≈ 0.000416.

So, the proportion of time that none of the rats are eating is approximately 0.0416% or 0.000416.

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The value of the quotient when 30.94 is divided by 0.7 will be 44.2

Dividing two numbers involves obtaining the number of times the denominator value can be obtained from the numerator.

Here, the numerator is 30.94 and the denominator is 0.7

To make things easier, we can convert the values to whole numbers by multiplying the values by 100

30.94 × 100 = 3094

0.7 × 100 = 70

Hence, Using a calculator ;

3094 / 70 = 44.2

The quotient value would be 44.2

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The sum of number is 270, after adding 5 to each number , sum of numbers is 320 and mean is 32.

What is mean ?

The mean is the set of two or more numbers' mathematical average. It is possible to calculate two different sorts of means: the arithmetic mean and the geometric mean. Add the numbers in a set together and divide by the total number of numbers in the set to find the arithmetic mean.

Here the mean of 10 number is 27. We know that ,

Mean = Sum of numbers / Total numbers.

=> 27= sum of numbers/10

=> sum of numbers = 27*10=270.

Now 5 added to each number, we need to add 5 in 10 times( because 10 total number), Then 5*10=50.

Sum of numbers after adding 5 to each number = 270+50=320.

Now mean = 320/10 = 32.

Hence the sum of number is 270, after adding 5 to each number , sum of numbers is 320 and mean is 32.

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Answer:

\(0 \: = 80 \\ 1 = 95 \\ 2 = 110 \\ 3 = 125\)

Step-by-step explanation:

\(p(x) = 15x + 80\)

Step-by-step explanation:

Whole numbers less than 5 may be termed as Rational numbers.

To find the derivative using the fundamental theorem of calculus, we need to apply the second part of the theorem, which states that if F(x) is an antiderivative of f(x), then the definite integral of f(x) from a to x is equal to F(x) - F(a).  The derivative of ∫(1/t^3) dt with the limits of integration from 1 to x is -(1/2x^2).

In this case, we have the integral ∫(1/t^3) dt with the limits of integration from 1 to x. We need to find the antiderivative of 1/t^3. The antiderivative of 1/t^3 is -(1/2t^2).

Applying the fundamental theorem of calculus, the derivative of the integral is equal to the derivative of F(x) - F(a), which is F'(x). Therefore, the derivative of the given integral is -(1/2x^2).

In summary, the derivative of ∫(1/t^3) dt with the limits of integration from 1 to x is -(1/2x^2).

To explain the solution in more detail, let's go step by step. We want to find the derivative of the integral ∫(1/t^3) dt with the limits of integration from 1 to x. According to the fundamental theorem of calculus, the derivative of the integral is equal to the derivative of the antiderivative evaluated at x.

First, we need to find the antiderivative of 1/t^3. To do this, we use the power rule for integration, which states that the antiderivative of t^n is (1/(n+1)) * t^(n+1), as long as n ≠ -1. Applying this rule, the antiderivative of 1/t^3 is -(1/2t^2).

Next, we differentiate the antiderivative -(1/2t^2) with respect to t. Using the power rule for differentiation, the derivative of t^-2 is -2t^(-2-1), which simplifies to -2/t^3. Multiplying this result by -(1/2) gives us the derivative of -(1/2t^2) as (1/t^3).

Finally, we evaluate the derivative at x, and our final answer is -(1/2x^2).

In summary, the derivative of ∫(1/t^3) dt with the limits of integration from 1 to x is -(1/2x^2).

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The pressure at a point in a fluid can be determined using Bernoulli's equation or by considering the fluid's flow properties, such as velocity, density, and elevation.

When analyzing the structural load of a structure that is suddenly flooded by moving water, the following forces should be considered:

Buoyancy Force: The upward force exerted on the structure due to the displacement of water.

Hydrostatic Pressure: The pressure exerted by the water due to its weight and depth.

Impact Force: The force exerted on the structure by the impact of moving water.

Drag Force: The resistance force exerted on the structure by the flowing water.

b. In the fluid boundary layer around the structure under flood, several physical processes may occur that can affect the structure's dynamic response:

Turbulence: The flow of water around the structure can create turbulence in the boundary layer, leading to fluctuations in pressure and forces acting on the structure.

Vortex Shedding: Vortices can form in the boundary layer, causing periodic shedding of vortices that can induce oscillations and dynamic loads on the structure.

Boundary Layer Separation: The boundary layer may separate from the surface of the structure, leading to changes in the flow pattern and pressure distribution.

Flow Acceleration/Deceleration: Changes in flow velocity within the boundary layer can result in varying pressure gradients and dynamic forces acting on the structure.

c. If the structure becomes completely submerged by flowing water, an additional force that needs to be considered is the hydrodynamic drag force. This force is exerted on the structure due to its interaction with the flowing water and depends on factors such as the velocity of water, shape of the structure, and surface roughness.

d. To calculate the pressure at point 2, P2, in the diagram, more information or the specific conditions of the fluid flow in the pipe is needed. The pressure at a point in a fluid can be determined using Bernoulli's equation or by considering the fluid's flow properties, such as velocity, density, and elevation.

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The right-hand side of an ODE dy/dt=f(y,t) can be rewritten as the product of a function of y alone and a function of t alone.

False.

The method of separable ODEs can be applied when the right-hand side of an ODE dy/dt = f(y,t) can be written as a product of a function of y alone and a function of t alone, not necessarily as the sum of such functions. Specifically, the ODE can be written in the form:

g(y) dy/dt = h(t)

where g(y) is a function of y only and h(t) is a function of t only.

We can then integrate both sides with respect to their respective variables to obtain:

∫ g(y) dy = ∫ h(t) dt + C

where C is the constant of integration. We can then solve for y in terms of t, if possible, to obtain the general solution of the ODE.

Therefore, the correct statement is: The method of separable ODEs can be applied only when the right-hand side of an ODE dy/dt=f(y,t) can be rewritten as the product of a function of y alone and a function of t alone.

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39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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