If alpha is held constant at .05, what is the relationship between sample size, the critical region, and the risk of a Type I error? (Select one of the following) . 1. As sample size increases, the critical region expands and the risk of a Type I error increases. 2. As sample size increases, the critical region shrinks and the risk of a Type I error increases. 3. As sample size increases, the critical region expands and the risk of a Type I error decreases. 4. There is no relationship between sample size, the critical region, and the risk of a Type I error.

Step-by-step explanation:

b2 =5

.....................

The solution of the quadratic equation is x=5±√35 .

A quadratic equation is given by the equation which can be written in the form ax²+bx +c.

the given quadratic equation is :

x²-10x+25=35

Simplifying the equation we get:

or, x²-10x+25-35=0

or, x²-10x-10=0

Now we will solve the equation by completion squares method:

x²-10x-10=0

or, x²-2×x×5+5²-5²-10=0

or, (x-5)²=35

or, x-5=±√35

or, x= 5±√35

Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .

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The correct equation that is balanced using the given numbers once is;

5(-1 + (-3)) = (7 * -4) + 8

There are different properties of Algebra such as;

Commutative Property of Addition or multiplication

Associative Property of Addition or multiplication

Distributive Property

Now, from the given numbers, it will be best to use only a positive digit outside the bracket on the left hand side to make it easy to balance on the right hand side. Thus, for the left hand side we will try;

5(-1 + (-3))

When that is solved we will get -20

Now, to balance that on the right hand side , we will have;

(7 * -4) + 8

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Therefore, there are number of 120 ways to fill the three roles in the play from the ten students auditioning.

Given that,

Roll can be filled = 3

Here we use concept of combinations:

We know that,

Selections are another name for combinations.

Combinations are the choosing of items from a given collection of items. We do not want to arrange anything here.

We aim to choose them.

The number of distinct r-selections or combinations from a set of n items is denoted by \(^{n}C_{r}\).

The number of ways to choose a group of r items from a larger group of n items is given by the following formula:

\(^{n}C_{r}\) = n! / (r!  (n-r)!)

In this case, we have n = 10 (the number of students auditioning) and r = 3 (the number of roles to be filled).

So, the number of ways to choose 3 roles from 10 students is:

\(^{10}C_{3}\) = 10! / (3! * (10-3)!) = 120

Hence,

There are 120 wats of filling.

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The value to the bakery of one customer prospect would be approximately $40.56  rounding  penny.

To calculate the value to the bakery of one customer prospect, we need to consider the conversion rate and the customer lifetime value.

The conversion rate is given as 24%, which means there is a 24% chance that a booth visitor will become a customer.

The customer lifetime value is given as $169, which represents the average value a customer brings to the bakery over their lifetime.

To calculate the value of one customer prospect, we multiply the conversion rate by the customer lifetime value:

Value of one customer prospect = Conversion rate * Customer lifetime value

Value of one customer prospect = 0.24 * $169

Value of one customer prospect = $40.56

Therefore, the value to the bakery of one customer prospect would be approximately $40.56.

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The total number of students appeared in the examination is 488.

Number of students passed in English = 0.7x

Number of students passed in Mathematics = 0.75x

Number of students failed in both subjects = 0.1x

Number of students passed in at least one subject = 0.9x

Number of students passed in both subjects = 220

We know that the total number of students appeared in the examination is x.

So, the number of students who failed in both subjects will be:

0.1x = (number of students failed in English) + (number of students failed in Mathematics) - 220

0.1x = (0.3x) + (0.25x) - 220

0.1x = 0.55x - 220

0.45x = 220

x = 488

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Given quardratic polynomial is 3x^2+(2k-5)x-7

On Comparing this with the standard quadratic Polynomial ax^2+bx+c

a = 3

b=2k-5

c = -7

Given zeroes α and -α

sum of the zeroes α +(-α) = -b/a

⇛ α +(-α) = -(2k-5)/3

⇛ 0 = -(2k-5)/3

⇛ 0×3 = -(2k-5)

⇛0 = -(2k-5)

⇛-2K+5 = 0

⇛ -2k = -5

⇛ 2k = 5

⇛ k = 5/2

Answer:- The value of k is 5/2.

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Answer:

y= -1/5x+4.4

Step-by-step explanation:

this is written in slop-intercept form

Answer:

y=-1/5x+4.4

Step-by-step explanation:

The answer is the answer above

Answer:

The probability  is  \(P( p  >  0.585) =  0.044565  \)

Step-by-step explanation:

From the question we are told that

   The population proportion is p =  0.50

   The sample size is n = 100

Gnerally the mean of the sampling distribution is  

          \(\mu_x =  0.50\)

Generally the standard deviation of the sampling distribution is  

              \(\sigma  =  \sqrt{\frac{p(1- p)}{n} }\)

=>            \(\sigma  =  \sqrt{\frac{0.5 (1- 0.5)}{100} }\)

=>            \(\sigma  =0.05\)

Generally the approximate probability that the cable company will keep the shopping channel

\(P( p  >  0.585) =  P(\frac{p- \mu_{x}}{\sigma }  > \frac{0.585 - 0.50}{0.05} )\)

Generally  \(\frac{p- \mu_{x}}{\sigma } = Z (The  \  standardized \  value  \  of  p )\)

=>  \(P( p  >  0.585) =  P(Z > 1.7 )\)

From the z-table the probability of  (Z > 1.7 ) is  

       \(P(Z > 1.7 ) = 0.044565\)

So \(P( p  >  0.585) =  0.044565  \)

Explanation:

Recall that y = f(x) since both are outputs of a function.

If k = 2, then f(x) = 2 leads to y = 2 being a horizontal line drawn through 2 on the y axis. This horizontal line only crosses the cubic curve at one spot. The same can be said if k = 0 and k = -2. So we can rule out choices A,B,C.

On the other hand, if k = -3, then f(x) = -3 has three different solutions. This is because the horizontal line through -3 on the y axis crosses the cubic at 3 different intersection points.

Answer:

D) -3

Step-by-step explanation:

we are given that f(x) = k has 3 real solutions.

Recall that graphically, this simply means that if we draw a  horizontal line y = k, the line will intersect the graph as 3 distinct locations.

Looking at the graph below (see attached picture for clarity), we can see that the only place where any horizontal line y = k will intersect the graph at 3 distinct points is between the blue lines pictured. (i.e approximately between y = -4 and y = -2.5)

If we look at all the choices, the only value for k  that falls between the blue lines is -3 (answer D). All the other values for y fall out outside the blue lines and hence do not satisfy the condition of having 3 real solutions

Answer:

\(\frac{155}{21}\)

Step-by-step explanation:

I hope this helps!

Answer:

-4,22

Step-by-step explanation:

x = 8, y = 6, m = 3, p = -1 , n = 1

4x – 2m6. 5y + 8p

4 x 8 - 2 x 3 x 6

32- 2 x 3 x 6

32-36

-4

5 x 6 + 8 x -1

30 + 8 x (-1)

30-8

22

Sothe non-parametric equation of the plane with the given normal vector and passing through the point (5, -6, 0) is: -5x + 6y + 6z + 61 = 0

In order to find the non-parametric equation of the plane, we need the normal vector and a point on the plane. The normal vector is given as (-5, 6, 6), and a point on the plane is (5, -6, 0).

The non-parametric equation of a plane is given by:

Ax + By + Cz = D

where (A, B, C) is the normal vector and (x, y, z) is a point on the plane. We can substitute the values into the equation to find the values of A, B, C, and D.

(-5)(x - 5) + (6)(y + 6) + (6)(z - 0) = 0

Expanding this equation:

-5x + 25 + 6y + 36 + 6z = 0

-5x + 6y + 6z + 61 = 0

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Answer:

278.4 dollars

Step-by-step explanation:

So you know that each month is 29.00 dollars

You mutilpy that by 12 to find out the total cost for paying each month

That would be 348 dollars

So if you pay upfront that takes 20 percent off

So you take the 348 and take 20 percent off

That would be 69.6

So then to find the amount saved you subtract 69.6 from 348

Which would be 278.4 dollars

They saved 278.4 dollars

The answer is D) 5/4.

To find the limit of the given function as x approaches 2, we can plug the value of 2 directly into the function. However, since the denominator of the function becomes 0 when x=2, we need to simplify the function first.

(x^2 + x - 6)/(x^2 - 4) can be factored as [(x+3)(x-2)]/[(x+2)(x-2)].

We can then cancel out the common factor of (x-2) in the numerator and denominator, leaving us with (x+3)/(x+2) as the simplified function.

Now, we can plug in the value of 2 into this simplified function:

limx→2 (x+3)/(x+2)

= (2+3)/(2+2)

= 5/4

Therefore, the answer is D) 5/4.

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The p-value method for testing hypotheses is often preferred by statisticians because it expresses the strength of your evidence against the null hypothesis.

The p-value method for testing hypotheses is often preferred by statisticians because it expresses the strength of your evidence against the null hypothesis. Additionally, it is more flexible than the critical value method, as it does not involve a fixed significance level and allows for adjustments based on the specific context of the analysis. While it does not completely eliminate the possibility of type II errors, it does provide a more nuanced understanding of the uncertainty surrounding your results. Finally, it is worth noting that the p-value method does involve a test statistic, as the p-value is calculated based on the distribution of the test statistic under the null hypothesis.

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We will have the following:

From the problem we will have the following expressions:

Now, from this we determine the value for the bill on september:

Now, since there are 3 people, the payment for each one is:

So, the payment for each one is $26.87 in September.

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

I think the constraint of proportionality is 25 because each dot it increases buy 25.

I also believe that at 10 the total should be at 225.

Answer:

width =  32 cm

Length = 46 cm

Step-by-step explanation:

Let width =  w

Length = w + 14

Perimeter = 156 cm

2*(length + width) = 156

2* (w +14 + w) = 156         {combine like terms}

2 *(2w + 14) = 156            {Divide both sides by 2}

      2w + 14  = 156/2

     2w + 14 = 78          {Subtract 14 from both sides}

2w + 14 - 14 = 78 -14

             2w = 64         {Divide both sides by 2}

          2w/2 = 64/2

w = 32 cm

length = w + 14 = 32 + 14

          = 46

Answer:

x= 7

Step-by-step explanation:

add (12x+1) and (5x-3) which becomes 17x-2 and then set that equal to 117 and solve. move the 2 to the right side of the equation which becomes 17x=119 and then divide 119 by 17 which x equals 7.

plug in 7 for x to make sure you get 117

The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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The coin will reach the stream in 5.61 seconds.

Since the height of the coin, after t seconds, is given by the equation:

h = -16t² + 72t + 100

The stream is the ground level. Thus, the coin reaches the stream when h(t) = 0.

So we can equate the equation to zero and solve for t:

-16t² + 72t + 100 = 0

Using the quadratic formula:

t = −b ± √(b² − 4ac) 2a

where a = -16, b = 72 and c = 100

t = −72 ± [√(72² − 4(-16)(100))] /2(-16)

t =  −72 ± [√11584]/(-32)

t = (-72 ± 107.63)/(-32)

t =  (-72 + 107.63)/(-32) or  (-72 - 107.63)/(-32)

t = -1.11 or  5.61

Since t cannot be negative. Thus, t = 5.61 seconds

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Complete Question

Travis tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t² + 72t + 100. How long will it take the coin to reach the stream?

A racecar driver goes around in circles on a racetrack.

The driver that goes around in circles is a racecar driver on a circular racetrack.

In motorsport events like stock car racing or Formula 1, drivers often compete on oval or circular tracks where they make continuous laps around the circuit.

These tracks are specifically designed to allow drivers to navigate the curves and maintain a circular path throughout the race.

The nature of circular tracks requires drivers to master the art of maintaining speed and control while making consistent and precise turns.

They need to find the optimal racing line, which is the most efficient path around the track, to maximize their speed and minimize the time taken to complete each lap.

The driver's skill and strategy play a crucial role in their success on circular tracks.

In addition to professional racing, drivers in amusement park rides such as go-karts or bumper cars also go around in circles as they maneuver the vehicles on circular tracks.

These attractions provide a fun and thrilling experience for participants as they navigate the circular path, often competing with others to reach the finish line or engage in friendly collisions.

Overall, drivers who go around in circles are typically found in racing events or amusement park attractions that involve circular tracks. Their ability to handle the curves and maintain control is essential for their performance and enjoyment of the activity.

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The probability of selecting a red disk, given that an odd-numbered disk is selected, is 1/5.

If an odd-numbered disk is selected, it can only be one of the following: 1, 3, 5, 7, 9. Out of these, only one is a red disk, which is numbered 1.

Therefore, if we know that an odd-numbered disk is selected, the probability of selecting a red disk is simply the probability of selecting the red disk numbered 1, which is:

P(Red disk | Odd-numbered disk) = P(Red disk and Odd-numbered disk) / P(Odd-numbered disk)

We can calculate the denominator of this expression by noting that there are 5 odd-numbered disks in total, out of a total of 10 disks:

P(Odd-numbered disk) = 5/10 = 1/2

To calculate the numerator, we note that there is only one odd-numbered red disk, which is disk number 1:

P(Red disk and Odd-numbered disk) = 1/10

Therefore, we can substitute these values into the expression for conditional probability:

P(Red disk | Odd-numbered disk) = (1/10) / (1/2) = 1/5

Therefore, the probability of selecting a red disk, given that an odd-numbered disk is selected, is 1/5.

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Answer:

1. False

2. True

3. False

4. True

A total of \(10 + 4 + 4 = \boxed{18}\) three-digit numbers that satisfy the given property.

Let the three-digit number be written as abc, where a, b, and c are the hundreds, tens, and ones digits, respectively. We want b to be the absolute value of half the difference between a and c. In other words, we want b = \(\left|\frac{a-c}{2}\right|.\)

Since a, b, and c are digits, we know that \(0 \leq a, b, c \leq 9.\) Since b is the absolute value of a number, we know that b is non-negative.

Case 1: \(a \geq c\)

If \(a \geq c\), then\(b = \frac{a-c}{2}\). Since b must be non-negative, we have two

subcases to consider:

Subcase 1: a=c

In this subcase, b=0, which means that the number abc is of the form a00, where \(0 \leq a \leq 9\). There are 10 such numbers.

Subcase 2: a>c

In this subcase, \(b = \frac{a-c}{2}\) is a positive integer. Since a and c must have the same parity (i.e., they are either both even or both odd), we have two

sub-subcases to consider:

Sub-subcase 1: a and c are both even

In this sub-subcase, a and c are both integers between 0 and 8 inclusive (since they are even and cannot be equal to 0 or 9). There are 4 such pairs of values for a and c: (2,0), (4,2), (6,4), and (8,6). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.

Sub-subcase 2: a and c are both odd

In this sub-subcase, a and c are both integers between 1 and 9 inclusive (since they are odd and cannot be equal to 0 or 8). There are 4 such pairs of values for a and c: (9,7), (7,5) , (5,3), and (3,1). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.

Case 2: a < c

If a < c, then\(b = \frac{c-a}{2}\). Since b must be non-negative, we have only one

subcase to consider:

Subcase: c- a is even

In this subcase, c-a is an even integer between 2 and 8 inclusive (since it cannot be equal to 0 or 9). There are 4 such even integers: 2, 4, 6, and 8. For each even integer, the values of a and c that satisfy c-a are uniquely determined, and the value of b is then uniquely determined. So there are 4 corresponding numbers abc.

Putting everything together, we have a total of \(10 + 4 + 4 = \boxed{18}\) three-digit numbers that satisfy the given property.

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Data set: Factor A: Brand of Car Factor B: Type of Fuel Response Variable: Fuel Efficiency Levels of Factor A: 4 (Toyota, Honda, Ford, Chevrolet) Levels of Factor B: 2 (Gasoline, Diesel) Value of n: 3 (3 replicates per combination or treatment)

The data set has two factors: Brand of Car and Type of Fuel. The response variable is Fuel Efficiency, which is the value that is being measured in response to the two factors. There are four levels of Factor A (Toyota, Honda, Ford, Chevrolet) and two levels of Factor B (Gasoline, Diesel). Finally, the value of n is 3, meaning there are 3 replicates or treatments per combination of the two factors.

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