a sample of 36 is used. identify the p-value and state your conclusion for each of the following sample results. use α=.01. x¯=44 and s = 5.2 x¯=43 and s = 4.6 x¯=46 and s = 5.0

A third alternative to the formulas I suggested in a comment is to use the vector cross product. Recast the three given points as points in 3D space with 0 z-coordinate:

A(20, 21, 0), B(8, 29, 0), and C(13, 1, 0)

Now consider two vectors,

u = B - A = 〈8, 29, 0〉 - 〈20, 21, 0〉 = 〈-12, 8, 0〉

v = C - A = 〈13, 1, 0〉 - 〈20, 21, 0〉 = 〈-7, -20, 0〉

Then recall the cross product identity,

||u × v|| = ||u|| ||v|| |sin(θ)|

where θ is the angle between the two vectors. The magnitude of u × v is equal to the area of the parallelogram spanned by u and v, and hence twice the area of the triangle of interest.

So we have

area = ||1/2 〈-12, 8, 0〉 × 〈-7, -20, 0〉||

area = 1/2 ||〈-12, 8, 0〉 × 〈-7, -20, 0〉||

area = 1/2 ||〈0, 0, 296〉||

area = 296/2

area = 148

Answer:

2 mL³

Step-by-step explanation:

Use the density formula, D = m/v, where m is the mass and v is volume.

Plug in the mass and density, then solve for the volume:

D = m/v

6.2 = 12.4/v

6.2v = 12.4

v = 2

So, the volume is 2 mL³

The value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

Let's simplify the addition within the parentheses:

8 1/5 + 4 1/5 = (8 + 4) + (1/5 + 1/5) = 12 + 2/5 = 12 2/5

Next, let's simplify the subtraction within the parentheses:

6 6/8 - 6 2/4 = (6 - 6) + (6/8 - 2/4) = 0 + (3/4 - 1/2) = 0 + 1/4 = 1/4

Now, we can substitute the simplified terms back into the original expression:

(8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) = 12 2/5 - 1/4

To subtract mixed numbers, we need to find a common denominator. The common denominator for 5 and 4 is 20. Converting both terms:

12 2/5 = 12 * 5/5 + 2/5 = 60/5 + 2/5 = 62/5

1/4 = 1 * 5/5 * 5/20 = 5/20

Now we can subtract:

62/5 - 5/20 = (62 * 4)/(5 * 4) - 5/20 = 248/20 - 5/20 = (248 - 5)/20 = 243/20

Therefore, the value of the expression (8 1/5 + 4 1/5) - (6 6/8 - 6 2/4) is 243/20.

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Answer:

x = \(\frac{1}{5}\) , x = 4

Step-by-step explanation:

(x - 4)(- 5x + 1) = 0

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

- 5x + 1 = 0 ( subtract 1 from both sides )

- 5x = - 1 ( divide both sides by - 5 )

x = \(\frac{1}{5}\)

lesser x = \(\frac{1}{5}\)

greater x = 4

Answer:

Megan thinks she can fit all \(539\) boxes into \(24\) trucks, and her estimate incorrect as to fit all \(539\) boxes, \(25\) trucks are needed.

Step-by-step explanation:

It is given that each truck can hold \(22\) boxes, and Megan needs to ship \(539\) boxes total.

The number of trucks that can hold \(539\) boxes will be,

\(\dfrac{539}{22} =24.5\)

So, \(24\) trucks will hold, \(22\times24=528\) boxes.

To hold the remaining \(539-528=11\) boxes, one more truck will be needed.

So, in total, \(25\) trucks are needed to ship \(539\) boxes.

Megan thinks she can fit all \(539\) boxes into \(24\) trucks, so her estimate incorrect.

Answer:

a=2054cm2

b=822cm2

Step-by-step explanation:

a=(26×47) + [(25×16)×2]=2054cm2

b=(26×47)-(25×16)=822cm2

Answer:

no

Step-by-step explanation:

they do not form a proportion because they are not equivalent to each other.

If the probability that interest rates will go up and house sales will decrease is estimated to be 0.15, the probability of an increase in interest rates and not a decrease in house sales is 0.05.

To find the probability of an increase in interest rates and not a decrease in house sales, we can use the formula for conditional probability:

P(Interest rates increase and house sales don't decrease) = P(Interest rates increase) - P(Interest rates increase and house sales decrease)

We are given that the probability of interest rates on housing loans going up in the next 6 months is 0.20, and the probability of house sales decreasing is 0.6. We are also given that the probability of interest rates going up and house sales decreasing is 0.15.

To find the probability of interest rates going up and not house sales decreasing, we subtract the probability of interest rates going up and house sales decreasing from the probability of interest rates going up:

P(Interest rates increase and house sales don't decrease) = 0.20 - 0.15 = 0.05

In summary, we can use conditional probability to calculate the probability of an increase in interest rates and not a decrease in house sales.

Given the probabilities of interest rates going up and house sales decreasing, we can subtract the probability of interest rates going up and house sales decreasing from the probability of interest rates going up to find the probability of interest rates going up and not house sales decreasing.

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According to the given statement The required number of ways the excursion party can be chosen is 1,057,523,766.

The given problem is a permutation problem, where we have to choose 10 students from a class of 25 students. But, there are 3 students who decided to join together or not join together.

Therefore, we need to consider two cases; one where these 3 students will be joining together and another where these 3 students will not join together.

Case 1: If these 3 students will be joining together, then we can select 7 more students from 22 students excluding these 3 students.

Therefore, the required number of ways = 22P7.

Case 2: If these 3 students will not be joining together, then we need to select either all three or none of them. Therefore, the remaining 7 seats can be filled with 22 - 3 = 19 students.

So, the required number of ways = 19P7.

We know that, the total number of ways to select 10 students from 25 students = 25P10.

So, the required number of ways when three students want to join together or not join together = (22P7) + (19P7) (Since the three students either join together or not join together)The value of 22P7 is given by the formula, nPr = n! / (n - r)!.

Therefore, 22P7 = 22! / 15! (22 - 7)! => 1,048,101,600

The value of 19P7 is given by the formula,

nPr = n! / (n - r)!.

Therefore, 19P7 = 19! / 12! (19 - 7)!

=> 9,422,166

Total ways = (22P7) + (19P7) => 1,048,101,600 + 9,422,166

=> 1,057,523,766

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The number of ways to choose the excursion party can be calculated by considering two cases: one where the 3 students who want to join together are chosen, and another where they are not chosen. The excursion party can be chosen in 682,606 ways from a class of 25 students.

Case 1: All 3 students join the excursion party
In this case, we need to choose the remaining 7 students from the remaining 22 students (since 3 students are already chosen). This can be done in C(22,7) ways, where C(n,r) denotes the number of combinations of selecting r items from a group of n items. Therefore, in this case, the number of ways to choose the excursion party is C(22,7).

Case 2: None of the 3 students join the excursion party
In this case, we need to choose all 10 students from the remaining 22 students (since none of the 3 students are chosen). This can be done in C(22,10) ways.

To find the total number of ways to choose the excursion party, we need to sum up the number of ways from both cases: C(22,7) + C(22,10).

Now, let's calculate the values of C(22,7) and C(22,10) using the formula for combinations:

C(n,r) = n! / (r!(n-r)!)

C(22,7) = 22! / (7!(22-7)!)
C(22,7) = 22! / (7!15!)
C(22,7) = (22*21*20*19*18*17*16) / (7*6*5*4*3*2*1)
C(22,7) = 35,960

C(22,10) = 22! / (10!(22-10)!)
C(22,10) = 22! / (10!12!)
C(22,10) = (22*21*20*19*18*17*16*15*14*13) / (10*9*8*7*6*5*4*3*2*1)
C(22,10) = 646,646

Therefore, the total number of ways to choose the excursion party is 35,960 + 646,646 = 682,606.

So, the excursion party can be chosen in 682,606 ways from a class of 25 students.

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The angle ∠AGB and ∠EGD are equal angles / opposite angles / vertical angles.

Given,

∠AGB and ∠EGD

We need to find what types of angles are ∠AGB and ∠EGD.

Vertical angles are angles that are opposite of each other when two lines cross.

Vertical angles are always equal.

We have,

∠AGB and ∠EGD are vertical angles

∠AGB = 30 = ∠EGD

∠CGD and ∠AGF are vertical angles.

∠CGD = 50 = ∠AGF

∠BGC and ∠FGE are vertical angles.

∠BGC = ∠FGE = 2x

We know that,

A straight angle is 180.

∠FGC =180

∠FGC = ∠AGF + ∠AGB + ∠BGC

180 = 50 + 30 + ∠BGC

180 - 50 - 30 = ∠BGC

180 - 80 = ∠BGC

∠BGC = 100

∠FGE = 100

We also see that,

∠FGC = ∠FGE + ∠EGD + ∠CGD

180 =  100 + ∠EGD + 50

180 - 150 = ∠EGD

∠EGD = 30

We see that,

∠EGD = 30°

∠AGB = 30°

Thus, the angle ∠AGB and ∠EGD are equal angles / opposite angles / vertical angles.

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the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

To determine the best estimate of the half-life by combining the two results, we can use the weighted average method. The weights assigned to each measurement are inversely proportional to the squares of their uncertainties. Here's how to calculate the combined result:

Step 1: Calculate the weights for each measurement.

  w1 = 1/σ1^2

  w2 = 1/σ2^2

  Where σ1 and σ2 are the uncertainties associated with each measurement.

Step 2: Calculate the weighted values.

  w1 * t1 = w1 * (15.5 days)

  w2 * t2 = w2 * (16.2 days)

Step 3: Calculate the sum of the weights.

  W = w1 + w2

Step 4: Calculate the weighted average.

  T = (w1 * t1 + w2 * t2) / W

Step 5: Calculate the combined uncertainty.

  σ = √(1 / W)

The best estimate of the half-life is given by the value of T, and the combined uncertainty is given by the value of σ.

Let's calculate the best estimate using the given values:

For the first measurement:

σ1 = 2.3 days

For the second measurement:

σ2 = 1.5 days

Step 1:

w1 = 1/σ1^2 = 1/(2.3^2) ≈ 0.1949

w2 = 1/σ2^2 = 1/(1.5^2) ≈ 0.4444

Step 2:

w1 * t1 ≈ 0.1949 * 15.5 ≈ 3.0195

w2 * t2 ≈ 0.4444 * 16.2 ≈ 7.1993

Step 3:

W = w1 + w2 ≈ 0.1949 + 0.4444 ≈ 0.6393

Step 4:

T = (w1 * t1 + w2 * t2) / W ≈ (3.0195 + 7.1993) / 0.6393 ≈ 13.7421 days

Step 5:

σ = √(1 / W) ≈ √(1 / 0.6393) ≈ 1.3772 days

Therefore, the best estimate of the half-life, combining the two results, is approximately 13.7421 days with an uncertainty of approximately 1.3772 days.

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Vertex: The vertex of the function is at the point (-2, 3).

The domain of a function is the set of all possible input values (often represented as x) for which the function is defined. In other words, it is the set of all values that can be plugged into a function to get a valid output. The domain can be limited by various factors such as the type of function, restrictions on the input values, or limitations of the real-world scenario being modeled.

The range of a function refers to the set of all possible output values (also known as the dependent variable) that the function can produce for each input value (also known as the independent variable) in its domain. In other words, the range is the set of all values that the function can "reach" or "map to" in its output.

In the given question,

Domain: The domain of the function is all real numbers greater than or equal to -2, since the square root of a negative number is not defined in the real number system.

Range: The range of the function is all real numbers less than or equal to 3, since the maximum value of the function occurs at x=-2, where f(x)=3.

Vertex: The vertex of the function is at the point (-2, 3).

Four additional points:When x=-1, f(x)=-(√(-1)+2)+3 = -1, so (-1,-1) is a point on the graph.

When x=0, f(x)=-(√0+2)+3 = 1, so (0,1) is a point on the graph.

When x=1, f(x)=-(√1+2)+3 = 2, so (1,2) is a point on the graph.

When x=4, f(x)=-(√4+2)+3 = -1, so (4,-1) is a point on the graph

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The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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The sample variance formula is: (sum of squared differences between each data point and the sample mean) divided by (sample size minus one).

The sample variance formula is a statistical calculation used to measure the variability of a set of data values in a sample. Variance is a measure of how spread out a set of data is, and it provides a measure of the average deviation of the individual data points from the sample mean.

The sample variance formula is calculated by taking the sum of the squared differences between each data point and the sample mean, and dividing that value by the sample size minus one. The resulting value provides a measure of how much the data points vary from the mean of the sample, and is an important tool for assessing the reliability and validity of statistical results.

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The surface area of the square pyramid with a side length of 6 cm and a slant height of 7 cm is 120 square cm.

To find the surface area of a square pyramid, we need to add up the areas of all its faces. A square pyramid has a square base and four triangular faces. We can use the side length of the square base and the slant height of the triangular faces to calculate the surface area.

First, let's find the area of the square base:

Area of square base = (side length)\(^2\)

Area of square base =\(6^2\)

Area of square base = 36 square cm

Next, let's find the area of one of the triangular faces. Since the pyramid is a square pyramid, all the triangular faces are congruent.

To find the area of a triangular face, we need to use the formula:

Area of one triangular face = (1/2) x base x height

Area of one triangular face = (1/2) x 6 x 7

Area of one triangular face = 21 square cm

Finally, we can calculate the surface area of the pyramid by adding the area of the square base and the total area of the triangular faces:

Surface area of square pyramid = area of square base + total area of triangular faces

Surface area of square pyramid = 36 + 84

Surface area of square pyramid = 120 square cm

Therefore, the surface area of the square pyramid with a side length of 6 cm and a slant height of 7 cm is 120 square cm.

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Answer: The first blank and the second blank both are 7 since you are using distributive property to simplify the equation by multiplying 7 into the numbers in the parenthesis.

1. The solution to the integral is: ∫ x cos 5x dx = (x/5) sin 5x + (1/25) cos 5x + C

2. Therefore, the solution to the differential equation is: \(y = - (4/3) (6 + x^3)^{(1/2)} + Cx^2 + C\)

We have to use integration by parts with the given choices of u and dv to evaluate the integral:

∫ x cos 5x dx

Let u = x and dv = cos 5x dx.

Then we have:

du/dx = 1 and v = (1/5) sin 5x

Using the formula for integration by parts, we have:

∫ x cos 5x dx = uv - ∫ v du/dx dx

= (x/5) sin 5x - ∫ (1/5) sin 5x dx

= (x/5) sin 5x + (1/25) cos 5x + C

where C is the constant of integration.

Therefore, the solution to the integral is:

∫ x cos 5x dx = (x/5) sin 5x + (1/25) cos 5x + C

2. Solving the Differential Equation:

We are given the differential equation:

\(dy/dx = 2x^2/{\sqrt{(6 + x^3)\)

We can rewrite this equation as:

\(dy/(2x^2) = dx/{\sqrt{(6 + x^3)\)

Integrating both sides, we get:

\(\int dy/(2x^2) = ∫ dx/{\sqrt{(6 + x^3)\)

Using substitution, let u = 6 + x^3,

Then du/dx = 3x^2 and dx = du/3x^2, we have:

\(\int dy/(2x^2) = ∫ (1/3) du/u^{(1/2)}\\\int dy/(2x^2) = (2/3) u^{(1/2)} + C\\\int dy/(2x^2) = (2/3) (6 + x^3)^{(1/2)} + C\)

Multiplying both sides by 2x^2, we get:

\(y = - (4/3) (6 + x^3)^{(1/2)} + Cx^2\)

where C is the constant of integration.

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1. (2,-2).  From the origin, go 2 units to the right and two units down

2) (-2,1.5) From the origin, go 2 units to the left and 1.5 units up

3) (-1,\(\frac{2}{4}\)) From the origin, go 1 unit to the left and half a unit up

The area and perimeter of each of the given polygons are a) 12+2√3+√34 units, 32 units² and b) 27 units and 46 units²

A polygon is a two-dimensional geometric figure that has a finite number of sides.

Given that, two polygons, we need to calculate the area and perimeter of each of the following polygons.

1) Calculating the lengths of the side by using Pythagoras theorem,

Sides = 2√3, √34, 5, 5 and 2

Therefore, perimeter = 12+2√3+√34 units

Area =

The polygon is divided into a trapezium and a triangle,

Therefore,

Area = 1/2(8x3)+4/2(8+2) = 12+20 = 32 units²

2) Perimeter = 1+1+2+2+2+3+3+4+4+5 = 27 units

Area = (2x1)+(3x1)+(3x5)+(3x2)+(5x4) = 2+3+15+6+20 = 46 units²

Hence, the area and perimeter of each of the given polygons are a) 12+2√3+√34 units, 32 units² and b) 27 units and 46 units²

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The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

27000

Step-by-step explanation:

I = P×R×T

=2000×25/10×5

=25000

AMOUNT= P+I

=2000+25000

=27000

Compound interest:-

Total:-

When the line of slope of 3 passes through two points, the value of y is -8.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

m=(y2-y1)/(x2-x1)

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of y is -8 when the line of slope of 3 is passing through 2 points as given.

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Answer:

its the second one -1/2

Answer:

I believe Edgar payed $84 for the tickets.

Step-by-step explanation:

12(4)=48

6(6)=36

48+36=84

Answer:

In October, a scarf cost the most.

Answer:

64

Step-by-step explanation:

4×16

64 sorryyy but I think this is it

Answer:

4³ is 64

Step-by-step explanation:

4 × 4 × 4 = 64

hope its correct

else you can report so that someone else can answer the correct one

Answer:

A

Step-by-step explanation: