Two days later, Kelly surveyed the same 13 classmates and found that none of them had been given math homework since she last surveyed them.



By how much does the mean of Kelly’s second data set change in comparison with the mean of the data set in her original survey? Explain how to determine the change in the means without calculating the mean of either data set

The correct answer is A. The null hypothesis is rejected in error.

In statistical hypothesis testing, a Type II error occurs when the null hypothesis is incorrectly retained or failed to be rejected when it is actually false.

In other words, a Type II error happens when the researcher concludes that there is no significant difference or relationship between variables when, in reality, there is.

It is a false negative result, as the researcher fails to detect a true effect or relationship.

Option A accurately describes Type II error, while the other options are not related to Type II error.

Option B refers to rejecting the research hypothesis, which is not a Type II error but rather a Type I error.

Option C refers to the study being underpowered, which may increase the likelihood of both Type I and Type II errors but is not a direct description of Type II error.

Option D mentions double-blinding, which is a methodological consideration and not directly related to Type II error.

Option E refers to accepting the research hypothesis in error, which is not a Type II error but rather a correct decision or Type I error.

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The cubic feet of a box that is 1/2ft x 1/4ft x 3/4ft will be 3/32 cubic feet.

Volume is the measure of the capacity that an object holds. For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains.

Volume of the box will be = l x b x h

Volume = 1/2ft x 1/4ft x 3/4ft

Volume = 3/32 cubic feet.

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A direct relationship between two variables is reflected in a "POSITIVE" correlation coefficient.

Correlation is a statistical technique for measuring and describing the relationship between two variables.

The variables move in the same direction when they have a positive correlation. In other words, as one variable increases, so does the other, and conversely, as one variable decreases, so does the other.

Typically, the two variables are simply observed rather than manipulated. Two scores from the same individuals are required for the correlation.

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The speed of the motorboat without the current is 9 mph, and the speed of the current is 3 mph.

To solve this problem, let's denote the speed of the motorboat as "b" (in miles per hour) and the speed of the current as "c" (in miles per hour). We'll use the following formula to calculate the boat's speed without the current:

Speed without current = (Speed downstream + Speed upstream) / 2

Given that Paul can motorboard downstream a distance of 24 miles in two hours, we can write the equation:

24 miles = (b + c) * 2 hours

We also know that it takes him four hours to motorboat the same distance upstream, which gives us:

24 miles = (b - c) * 4 hours

Now, let's solve these two equations simultaneously to find the values of b (boat's speed without current) and c (speed of the current).

Solving the first equation:

24 = 2(b + c)

12 = b + c   (Dividing both sides by 2)

Solving the second equation:

24 = 4(b - c)

6 = b - c     (Dividing both sides by 4)

Adding the two equations together:

12 + 6 = b + c + b - c

18 = 2b

b = 9 mph

Substituting the value of b into one of the equations to find the value of c:

6 = 9 - c

c = 9 - 6

c = 3 mph

So, the speed of the motorboat without the current is 9 mph, and the speed of the current is 3 mph.

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Answer:

64

Step-by-step explanation:

Let x represent the number.

x + 23 represents 23 added to the number.

2x - 41 represents 41 less than twice the number.

Set these expressions equal to each other and solve for x to find the number:

x + 23 = 2x - 41

23 = x - 41

64 = x

So, the number is 64

Based on the given information, it is not considered unusual for Susan to take 12 minutes to drive to school.

To determine if it is unusual for Susan to take 12 minutes to drive to school, we can use the rare event rule based on the given data. The rare event rule states that if an event has a probability of less than 5% of occurring, then it can be considered unusual.

Since we don't have the complete set of data or information about the distribution, we cannot directly calculate the probability. However, we can compare the given times and use them as a reference point to assess the likelihood of Susan's travel time being unusual.

Given the options:

15. x = 5 minutes

16. x = 13 minutes

17. x = 6 minutes

18. x = 12 minutes

From these options, we can observe that the times range from 5 minutes to 13 minutes, with Susan's travel time of 12 minutes falling within this range. Since her travel time is within the range of the given times, it is not unusually long or short compared to the provided data points.

Therefore, based on the given information, it is not considered unusual for Susan to take 12 minutes to drive to school.

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Answer:

I think 3 is the median.....

The smallest measurement used in the apothecary system for volume is the minim.

The apothecary system is an outdated system of measurements primarily used in pharmacy and medicine. It includes various units for measuring volume, weight, and other quantities.

In the apothecary system, the minim is the smallest unit of measurement for volume. It is equivalent to approximately 0.0616 milliliters.

The minim is a small unit of measurement and is typically used for precise dosing of liquids in the apothecary system. It is commonly used in pharmaceutical compounding and in the preparation of medications.

However, it's important to note that the apothecary system is no longer widely used in modern healthcare practices. The metric system, with units such as milliliters and liters, has become the standard for measuring volume in most countries.

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The measure of angle ∠S in triangle RST is approximately 103.1 degrees.

To find the measure of angle ∠S in triangle RST, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and opposite angles A, B, and C respectively, the following equation holds true:

\(c^2 = a^2 + b^2 - 2abcos(C)\)

In our case, we know the side lengths r = 23 cm, s = 99 cm, and t = 94 cm. We want to find the measure of angle ∠S. Let's substitute the known values into the Law of Cosines equation:

s^2 = r^2 + t^2 - 2rtcos(S)

99^2 = 23^2 + 94^2 - 2(23)(94)cos(S)

9801 = 529 + 8836 - 4348cos(S)

9801 = 9365 - 4348cos(S)

4348cos(S) = 9365 - 9801

4348cos(S) = -436cos(S) = -436 / 4348

cos(S) ≈ -0.1

To find the measure of angle S, we can take the inverse cosine (cos^-1) of -0.1:

S ≈ cos^-1(-0.1)

Using a calculator, we find that S ≈ 103.13 degrees (rounded to the nearest 10th of a degree). Therefore, the measure of angle ∠S in triangle RST is approximately 103.1 degrees.

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Answer:

9/30

Step-by-step explanation:

To minimize your losses while gambling at a casino and playing slot machines, you need to minimize your regret R in the experts problem. R is defined as the difference between your total cost and the best expert's cost.

To minimize R, follow these steps:

1. Begin by assigning equal weight to each expert (slot machine).
2. After each day t, observe the cost c_ti for each expert i.
3. Update the weights by multiplying them by (1 - c_ti), making sure they remain non-negative.
4. Normalize the weights so they sum up to 1.
5. On day t+1, choose the expert with the highest weight to take advice from.

By following this adaptive strategy, you will minimize your regret R, allowing you to reduce your losses while gambling at the slot machines.

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Answer:

7

Step-by-step explanation:

4(x + 1)+3x + 7

Distribute

4x+4 +3x+7

Combine like terms

4x+3x   +4+11

7x+15

The coefficient is the term in front of the x

7

Answer: 12

Step-by-step explanation:

8/2=4

4x1=4

8+4=12

Answer:

12

Step-by-step explanation:

following the 2:1 ratio, or 2 kids meals for every adult meals sold, so if 8 kids meals are sold, 4 adult meals must have been sold.

8/2 = 4

Answer:

8.5m

Step-by-step explanation:

Using the volume x³ + 10x² + 19x  - 30, the missing side of the rectangular prism is (x + 6)

Two sides of a rectangular prism are x + 5 and x - 1. The volume of the rectangular prism is given as x³ + 10x² + 19x  - 30.

Let's find the missing side of the rectangular prism.

Therefore,

volume of a rectangular prism = lwh

where

Therefore,

volume of the prism = x³ + 10x² + 19x  - 30

Let's factorise it to find the missing side length

x³ + 10x² + 19x  - 30  = 0

(x - 1)(x² + 11x + 30)

let's factorise x² + 11x + 30

x² + 11x + 30

x² + 5x + 6x + 30

x(x + 5) + 6(x + 5)

(x + 6)(x + 5) = 0

Therefore, the side length of the rectangular prism are (x - 1), (x + 5) and (x + 6)

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35, ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.

What is alternate interior angles?

Given

           m∠4=35

From the image given, angle 2 and angle 4 lie on opposite side of the line that intercepts the two parallel lines, AB and CD. Angle 2 and angle 4 both lie within the parallel lines.

Therefore, ∠2 and ∠4  are alternate interior angles.

Thus,

m ∠2 = m∠4 (alternate interior angles theorem)

since m∠4 = 35°

therefore m∠2 = 35°

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Answer:

D'E' be parallel to the original line

Step-by-step explanation:

Given

\(\triangle ABC\)

Line \(DE\)

\(k = 3\) -- scale factor

Required

The relationship between \(DE\) and \(D'E'\)

When \(\triangle ABC\) is dilated by a scale factor of 3, \(\triangle A'B'C'\) will be three times as big as \(\triangle ABC\).

Also:

Line \(D'E'\) will be three times as long as \(DE\)

Since no further transformation is done on \(\triangle ABC\) and line \(DE\), then \(D'E'\) will be parallel to \(DE\)

Answer:

B. 720 ways

Step-by-step explanation:

To solve you would multiple 6x5x4x3x2x1 .

The required number of ways can 6 players be assigned to 6 positions on a baseball team is 720ways.

Given that,

Number of players = 6

Assigned position on a baseball = 6

We have to determine,

In how many ways can 6 players be assigned to 6 positions on a baseball team.

According to the question,

To solve this problem assuming that any player can play any position.

The formula to find \(^nP_r\) is given by:

\(^np_r\) is the permutation of arrangement of 'r' objects from a set of 'n' objects, into an order or sequence.

The formula to find permutation is:

\(^np_r = \frac{n!}{(n-r)!}\)

Where, n = 6 and r = 6

Therefore,

\(^6p_6 = \frac{6!}{(6-6)!} \\\)

     \(= \frac{6\times5\times 4 \times 3 \times 2 \times 1}{0!} \\\\= \frac{720}{1} \\\\= 720 \ ways\)

Hence, The required number of ways can 6 players be assigned to 6 positions on a baseball team is 720ways.

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Answer:

13/25

Step-by-step explanation:

52% is 52/100, and 52/100 is the same as 26/50, which can be reduced to 13/25

We can find the number of distinct numbers that Virginia writes down by finding the number of unique values of the product a*b for all possible combinations of integers a and b between 0 and 9, inclusive.

What in math is an integer?

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

When a = 0 or b = 0, the product ab is equal to 0. So, we have 2 values of ab that are equal to 0.

When a = 1 or b = 1, the product ab is equal to a or b, respectively. So we have 20 values of ab that are equal to a or b.

When a = 2 or b = 2, the product ab is equal to 2 * a or 2 * b, respectively. So we have 20 values of ab that are equal to 2 * a or 2 * b.

We can see that for a = 3, b = 3, a = 4, b = 4, and so on, ab will be equal to 3a, 3b, 4a, 4*b, respectively.

So, we have 20 distinct values for each a and b between 2 and 9.

So, we have 2 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = 182 distinct values that Virginia writes down.
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There were 31875 papers involved.

Given that a piece of paper is 0.0032 inches thick and a stack of paper in a warehouse measures 102 inches high.

We need to find the number of papers involved.

Let the number of papers be x,

So,

0.0032x = 102

x = 102 / 0.0032

x = 31875

Hence there were 31875 papers involved.

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Answer:

13°

Step-by-step explanation:

Since these are complementary angles, we can add them together, set it equal to 90, and solve for x:

[Equation] (-6x + 53)° + (-9x + 22)° = 90°

[Distribute] -6x° + 53° + -9x° + 22° = 90°

[Combine like terms] 15x° + 75 = 90°

[Subtract 75 from both sides] 15x° = 15

[Divide both sides by 15] x = 1°

Then, plug-in our x for angle ADC:

[Given] (-9x + 22)°

[Distribute] -9x° + 22°

[Subsititue / plug-in] -9(1)° + 22°

[Multiply] -9° + 22°

[Combine like terms] 13°

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

The original amount of nuts, x, in the recipe is 103

The equation for the original amount is 2x + 2x = 412

An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.

These expressions are also known to be made up of mathematical operations such as;

From the information given, we have that;

Beverly doubles the amount of nuts and peanut butter chips

Total number = 412

This is represented as;

2x + 2x = 412

collect like terms

4x = 412

Make 'x' the subject of formula

x = 412/ 4

x = 103

Hence, the value is 103

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Answer:

The correct option is (D).

Step-by-step explanation:

A one-to-one function can be defined such the every value of x corresponds to exactly one value of y.

That is:

x₁ → y₁

x₂ → y₂

x₃ → y₃

.

.

.

and so on.

Consider the graph.

From the graph it can be seen that for y = 0 and y = 2 there are multiple x coordinates.

So, the graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

According to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.

Given :

Draw the graph of the three lines in order to determine the function is one-one function or not.

The equation of the line passing through (-5,6) and (-2,0) is given by:

\(\dfrac{y-6}{x+5}=\dfrac{0-6}{-2+5}\)

\(\dfrac{y-6}{x+5}=\dfrac{-6}{3}\)

\(y-6=-2(x+5)\)

y + 2x + 4 = 0    --- (1)

The equation of the line passing through (-2,0) and (2,2) is given by:

\(\dfrac{y-0}{x+2}=\dfrac{2-0}{2+2}\)

2y = x + 2   ---- (2)

The equation of the line passing through (2,2) and (4,-2) is given by:

\(\dfrac{y-2}{x-2}=\dfrac{-2-2}{4-2}\)

y - 2 = -2(x - 2)

y + 2x = 6   ---- (3)

Now, with the help of these three equations, the graph of the three lines can be plotted. The Graph is attached below.

So, according to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.

Therefore, the correct option is D).

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Answer:

31

Step-by-step explanation:

25/0.80=31.25

(You cant have a quarter of a parking space.)

The correct answer is: III only. Variance investigation is typically based on a cost-benefit analysis.

Statement I is incorrect because the relative size of a variance, in comparison to other variances, can be important in understanding its significance.

Statement II is incorrect because variance investigation does not focus solely on unfavorable variances. Both favorable and unfavorable variances are considered during the investigation.

Statement III is true. Variance investigation is typically based on a cost-benefit analysis, where the potential benefits of investigating and addressing variances are weighed against the associated costs.

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The perimeter and area of each polygons are

Polygon A

From the figure, we have the vertices to be

A = (-10, 7),

B = (8, 4),

C = (-8, -8)

The area is calculated as

Area = 1/2 * |x1 * (y2 - y3) + x2 * (y1 - y3) + x3 * (y1 - y2)|

So, we have

Area = 1/2 * |-10 * (4 + 8) + 8 * (7 + 8) - 8 * (7 - 4)|

Evaluate

Area = 12 square units

The perimeter is the sum of the side lengths, where the side lengths are calculated using

Length= √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(-10 - 8)² + (7 - 4)²] = 18.2

AC = √[(-10 + 8)² + (7 + 8)²] = 15.1

BC = √[(8 + 8)² + (4 + 8)²] = 20

So, we have

Perimeter, P = 18.2 + 15.1 + 20

P = 53.3 units

Polygon B

From the figure, we have the vertices to be

A = (-5, 6),

B = (1, 8),

C = (8, -9),

D = (-10, -6)

Using the area formula in (a), we have

Area = 1/2 * |-5 * (-6 - 8) + 1 * (6 + 9) + 8 * (8 + 6) - 10 * (-9 - 6)|

Evaluate

Area = 173.5 square units

Using the side lengths formula in (a), we have

Length= √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(-5 - 1)² + (6 - 8)²] = 6.3

BC = √[(1 - 8)² + (8 + 9)²] = 18.4

CD = √[(8 + 10)² + (-9 + 6)²] = 18.2

DA = √[(-5 + 10)² + (6 + 6)²] = 13

So, we have

Perimeter, P = 6.3 + 18.4 + 18.2 + 13

P = 55.9 units

Hence, the perimeter is 55.9 units

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Answer:

x ≤ - \(\frac{1}{3}\)

Step-by-step explanation:

Given

3x + 14 ≤ 13 ( subtract 14 from both sides )

3x ≤ - 1 ( divide both sides by 3 )

x ≤ - \(\frac{1}{3}\)

Answer:

Step-by-step explanation:

3x+14≤13

x

\(step - 1 \colon \: define\)

\(3x + 14 \leqslant 13\)

\(step - 2 \colon \: subtract\)

\(3x + 14 - 14 \leqslant 13 - 14\)

\(3x \leqslant - 1\)

\(step - 3 \colon \: divide\)

\( \frac{3}{3} x \leqslant - \frac{1}{3} \)

\(x \leqslant - \frac{1}{ 3} \)