if you repeated a hypothesis test 1,900 times (in other words, 1,900 different samples from the same population), how many times would you expect to commit a type i error, assuming the null hypothesis were true, if

The areas and the surface areas of the figures are calculated below

The area of a figure is the amount of space it occupies in a plane, measured in square units.

So, we have

Figure 1

For the first figure, we have

Area = (2a)² - 1/2 * b² * sin(B)

Evaluate

Area = 4a² - b²sin(B)/2

For the second figure, we have

Area = 18 * 10 + 1/2 * 10 * √(4 * 15² + 18²) + 1/2 * 18 * √(4 * 15² + 10²)

Evaluate

Area = 639.53 square units

Figure 2

Here, we have

Area = 2 * 2 * 2.5 + 2 * 1/2 * 3 * √(3² - 2.5²) + 3 * 2

Evaluate

Area = 20.97

Figure 3 (Stairs)

Here, we have

Area = 8 * 4 + 8 * 8 + 8 * 4 + 8 * 8 + 2 * 16 * 4 + 2 * 8 * 4

Evaluate

Area = 384

Figure 3 (Semi-circular)

Here, we have

Area = 4 * 4 * 6 + 6 * 6 + 2 * 1/2 * (22/7 * (6/2)²) + 1/2 * 2 * 22/7 * (6/2) × 6

Evaluate

Area = 216.86

Figure 3 (Cylinder-Hemisphere-Cone)

Here, we have

Area = 2 * 22/7 * (10/2) * 12 + 22/7 * (10/2) * √(8² - 5²) + 2 * 22/7 * (10/2)²

Evaluate

Area = 632.42

Figure 3 (Cylinder-Cylinder)

Here, we have

Area = 2 * 22/7 * 8 * (8 + 3) + 2 * 22/7 * 2 * (2 + 7) - 22/7 * 2²

Evaluate

Area = 653.71

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The point that is not on the same line as the others is E(9, 14).

The point that is not on the same line as the others would not have the same slope as the others.

Slope between A ( 3, 4) and B (2, 2):

= (4 - 2) / (3 - 2) = 2 / 1

= 2

Slope between B (2 , 2) and C (5, 8):

= ( 8 - 2 ) / (5 - 2)

= 6 / 3

= 2

Slope between C ( 5, 8) and D(7, 12):

= (12 - 8) / (7 - 5)

= 4 / 2

= 2

Slope between D ( 7, 12) and E ( 9, 14):

= ( 14 - 12) / (9 - 7)

= 2 / 2

= 1

We can therefore see that E ( 9, 14) is the odd one out and is not on the same line.

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1. $0.5 is 1/2 of a dollar

2. The fraction of her times at a bat that she get a hit is 1/4

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

For example, 0.4 is 0 + 4/10 = 4/10,/. This means the conversion of 0.4 to fraction is 4/10.

1. The fraction of $0.5 to $1 is calculated as;

representing the fraction by x

x of 1 = 0.5

0.5 = 5/10

therefore

x= 5/10 = 1/2

Therefore the fraction of $1 that gives $0.5 is 1/2

2. converting 0.250 to fraction

= 0 + 250/1000

= 250/1000

= 25/100 = 5/20 = 1/4

therefore the fraction of Sue's hit is 1/4.

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The number of 29 year olds who are not expected to be alive in a year would be A. 422 people.

We see that in Apextown, the percentage of people who are expected to be alive in a year, based on their ages, is given.

For those who are 29 years of age, we see that the percentage of people who are expected to be alive in a year would be 99. 868 %. This means that the number of 29 year olds who would not be alive would be:

= Number of 29 years x ( 1 - percentage to be alive)

= 320, 000 x ( 1 - 99. 868 % )

= 320, 000 x 0. 00132

= 422. 4

= 422 people

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according to the given question Anna scored highest in the Afrikaans test.

When a relationship consistently has the same ratio, it is considered to be proportionate. For instance, the average amount of apples grown on each tree determines the number the trees within a fruit orchard plus the quantity of apples harvested. In mathematics, a linear relationship between two numbers or variables is referred by the term being proportionate. The other amount doubles when the initial amount does. The other variables also decline when one variable is brought down to 1/100th of its prior value.

given,

To determine whether Anna's results are proportionate, we need to compare the percentage scores she received in each test.

For the Afrikaans test, Anna's percentage score is (22/30) x 100% = 73.33%

For the mathematical literacy test, Anna's percentage score is (18/25) x 100% = 72%

Since Anna's percentage score for the Afrikaans test is higher than her percentage score for the mathematical literacy test, her results are not proportionate. Therefore, Anna scored highest in the Afrikaans test.

Note that if we were to compare the raw scores (22 vs. 18), it would seem like Anna performed better in the Afrikaans test. However, since the two tests have different total marks (30 for Afrikaans and 25 for mathematical literacy), comparing the raw scores directly does not give a fair comparison. Instead, we need to compare the percentage scores, which take into account the total marks of each test.

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The best measure of variability for the data is A. The range is the best measure of variability, and it equals 8.

The range is the difference between the highest value and the lowest value in the dataset. In this case, the highest number of rose bouquets is 9, and the lowest is 1. This is the data shown on the line plot.

Range = Highest Value - Lowest Value

Range = 9 - 1

Range = 8

The range is the best measure of variability, and it equals 9. The IQR is used when there are outliers that can affect the data.

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The smallest integer value of x that would be a solution in the inequality would be x = 2.

To find the smallest integer value of x that satisfies the inequality 5x + 3 ≥ 10, first solve the inequality for x:

Subtract 3 from both sides:

5x ≥ 7

Divide by 5:

x ≥ 7/5

The inequality states that x must be greater than or equal to 7/5, which is equal to 1.4. Since we are looking for the smallest integer value, we should round up to the next integer, which is 2. Therefore, the smallest integer value of x that satisfies the inequality is x = 2.

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Answer:

The correct line of reflection that maps the polygon ABCDE to its image polygon A' B' C' D' E' is:

C. Reflection across the x-axis

Explanation:

The given vertices of the original polygon ABCDE are:

A(-3, 3)

B(-3, 6)

C(1, 6)

D(1, 3)

E(-1, 1)

The given vertices of the image polygon A' B' C' D' E' are:

A'(-5, 3)

B'(-5, 6)

C'(-9, 6)

D'(-9, 3)

E'(-7, 1)

Comparing the coordinates of the original polygon ABCDE and its image polygon A' B' C' D' E', we can see that the y-coordinates are negated, while the x-coordinates remain the same. This indicates that the reflection is happening along the x-axis, as it is the line that reverses the y-coordinates while keeping the x-coordinates unchanged.

Therefore, the correct line of reflection is the x-axis, as shown by option C. Reflection across the x-axis.


Double-check this answer i wrote.

Answer:

2/5

Step-by-step explanation:

slope= y2-y1 / x2-x1

in this case:

y2=7                            y1=5                      x2= 8                      x1=3

plug that into the formula above to get the answer

slope= 2/5 or 0.4

Answer:

Sydney’s age is 45 & Devaughn's age is 33

Step-by-step explanation:

D= Devaughn

S= Sydney

D+S= 78

S-12=D

(S-12)+S=78

2S=90

S=45

D=33

Answer:

the correct answer is option D

The mean number of states will be 6.

The percentage of students who visited more than 7 states will be 20%.

The mean number of states will be:

= 120 / 20

= 6.

The percentage of students who visited more than 7 states will be:

= 4/20 × 100

= 20%

The number of students who visited 7 or 8 states compare to the number of students who visited 5 states or less as they're both 7 each. This implies that they're equal.

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Answer:  the value of the expression is 24.6, which corresponds to option C.

Step-by-step explanation: In order to assess the expression, we must adhere to the sequence of operations (PEMDAS) and execute the computations in the subsequent manner:

Begin by calculating the expression in the parentheses as a priority: (31.5 squared minus 93) equals negative 61.5.

Next, perform the operation of dividing -61.5 by -2.5 which results in 24.6.

To find the radius of the circle, we need to rewrite the equation of the circle in standard form, which is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is its radius.

To rewrite the given equation in standard form, we need to complete the square for both x and y terms:

x^2 - 12x + y^2 + 6y + 20 = 0

(x^2 - 12x + 36) + (y^2 + 6y + 9) = -20 + 36 + 9 (adding and subtracting appropriate terms to complete the square)

(x - 6)^2 + (y + 3)^2 = 25

Comparing this equation with the standard form, we see that the center of the circle is (6, -3) and the radius is sqrt(25) = 5.

Therefore, the radius of the circle is 5 units.

HOPE THIS HELPS!

Answer:

1. Mean : 85.6

2. Median : 90

3. Mode : 95

4. Range : 35

Step-by-step explanation:

1. For Mean, you add up all the terms and divide the resulting sum by the number of terms. In this case there were 9 terms that added up to 770, and when you divided that result by 9, the answer was 85.555 repeating. Since the question asks to round to the nearest tenth 85.6 represents the correct mean or average of the class.

2. To find the median, line up all the numbers in order from least to greatest. Like so :

60,75,75,90,90,95,95,95,95

In order to find the median, find the middle term. Since there are 9 terms, the middle term will be the fifth one. In this case, the answer was 90.

3. Mode represents the number that appears the most in a data set. Look at the 9 terms and find the one that appears the most. In this case it is 90.

4. Lastly, to find the range, subtract the lowest value in the data set from the highest one. 95 is the highest and 60 is the lowest. Do [tex]95-60[/tex] and you will get an answer of 35.

Hope this helps!

Answer:

Mean: 85.6

Median: 90

Mode: 95

Range: 35

Step-by-step explanation:

Mean: Add up all the value and divide by the number of values you have.

75 + 95 + 90 + 95 + 60 + 95 + 75 + 95 + 90 = 770

770 / 9 = 85.6

Median: Rearrange in increasing order + look at middle number

60, 75, 75, 90, 90, 95, 95, 95, 95

Mode: Number that shows up the most.

95 shows up 4 times.

Range: Maximum - Minimum.

95 - 60 = 35.

The area swept clean by the wiper blade is approximately 239.3 square inches.

We need to find the area of the circular sector that is swept out by the blade as it rotates through an angle of 130 degrees. The radius of the circular sector is the length of the wiper arm, which is 16 inches.

The formula for the area of a circular sector is

A = (θ/360) × πr^2

Where

In this case, θ = 130 degrees and r = 16 inches, so we can plug these values into the formula to get:

A = (130/360) × 3.14 × (16)^2

Simplifying this expression, we get:

A ≈ 239.3 square inches

Therefore, the area swept clean by the wiper blade is approximately 239.3 square inches.

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The following probabilities are found under the condition that  a certain national survey of heads of households P(woman asked for a promotion) = 24%, P(woman received promotion, given she asked for one) = 45%, P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Now,
Regarding  a national survey concerning the head od households,  only 24% of women interviewed had requested for a promotion and of those women who had asked for a promotion, 45% received the raise.

Therefore,

(a) P(woman asked for a promotion) = 24%
(b) P(woman received promotion, given she asked for one) = 45%
(c) P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Probability refers to the percentage of an event taking place in a required time frame, in a specified place. It is considered a great aid in the fields of science and mathematics.

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Step-by-step explanation:

'3'  is greater than 0     so we use the second portion of f(x)

f(3) =   x+1

     =   3 + 1   = 4  

Each element of D8 is mapped to a permutation of {1, 2, 3, 4, 5, 6, 7, 8} by considering its action on the labeled generators 1, 2, ..., 8 under composition.

The elements of D8 are 1, r,[tex]r^2, r^3, s, sr, sr^2, sr^3,[/tex] which we can label with the integers 1, 2, 3, 4, 5, 6, 7, 8 respectively. The left regular representation of D8 into S8 is given by:

1 → (1)(2)(3)(4)(5)(6)(7)(8)

r → (1 2 3 4)(5 6 7 8)

[tex]r^2[/tex] → (1 3)(2 4)(5 7)(6 8)

[tex]r^3[/tex]→ (1 4 3 2)(5 8 7 6)

s → (1 2)(3 4)(5 6)(7 8)

sr → (1 8 3 6)(2 7 4 5)

[tex]sr^2[/tex]→ (1 4)(2 3)(5 8)(6 7)

[tex]sr^3[/tex] → (1 6 3 8)(2 5 4 7)

Here, each element of D8 is mapped to a permutation of {1, 2, 3, 4, 5, 6, 7, 8} by considering its action on the labeled generators 1, 2, ..., 8 under composition.

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We have exhibited the image of each element of D8 under the left regular representation into S8, represented as a product of disjoint cycles.

The left regular representation of D8 is a homomorphism from D8 to the symmetric group S8, where each element of D8 is represented as a permutation of the set {1, 2, ..., 8}.

Using the generators r and s, we can construct the elements of D8 as follows:

[tex]r^0[/tex] = 1

[tex]r^1[/tex]= r

[tex]r^2[/tex] = rr

[tex]r^3[/tex] = rrr

[tex]s^0[/tex]= 1

[tex]s^1[/tex] = s

[tex]s^2[/tex] = 1

[tex]s^3[/tex] = ss

Now, let's apply the left regular representation to each element of D8:

1 → (1 2 3 4 5 6 7 8)

r → (1 2 3 4 5 6 7 8)(1 2)

[tex]r^2[/tex] → (1 2 3 4 5 6 7 8)(1 3)(2 4)

[tex]r^3[/tex]→ (1 2 3 4 5 6 7 8)(1 4 3 2)

s → (1 8)(2 7)(3 6)(4 5)

sr → (1 7 3 5)(2 8 4 6)

[tex]sr^2[/tex] → (1 6 3 2)(4 7 5 8)

[tex]sr^3[/tex] → (1 5)(2 6)(3 7)(4 8)

Note that we can represent each permutation as a product of disjoint cycles, where each cycle corresponds to an orbit under the action of the permutation. For example, the permutation corresponding to r is a product of two cycles: (1 2) and (3 4 5 6 7 8). This means that r fixes the elements 1 and 2, and permutes the elements 3, 4, 5, 6, 7, and 8 cyclically. Similarly, the permutation corresponding to s is a product of four cycles: (1 8), (2 7), (3 6), and (4 5), which means that s fixes the pairs (1, 8), (2, 7), (3, 6), and (4, 5), and transposes each pair.

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The appropriate statistical test for comparing the difference in maintenance quality ratings at two tirezone locations, where there are two independent groups of customers, would be the Mann-Whitney test or Wilcoxon rank-sum test.

The Mann-Whitney test would be appropriate for this scenario because it is used to compare the difference between two independent groups. In this case, we have two independent groups of customers from different locations, and we want to determine if there is a significant difference in their ratings of maintenance quality.

The test compares the ranks of the observations in the two groups and uses that information to determine if there is a significant difference between them. The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is another name for the same test.

Therefore, the Mann-Whitney test or Wilcoxon rank-sum test is the appropriate statistical test to use in this scenario.

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The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:

[tex]90^\circ-27^\circ=63^\circ[/tex]

The distance to the boat is the side opposite the angle of 63° while the height of the lighthouse is the adjacent side.

[tex]\dfrac{\text{opposite}}{\text{adjacent}} =\text{tan 63}^\circ[/tex]

[tex]\dfrac{\text{distance}}{245} =\text{tan 63}^\circ[/tex]

[tex]\text{distance}=245\times \text{tan 63}^\circ[/tex]

[tex]=480.83=480.84\thickapprox\boxed{\bold{480.8}}[/tex]

Answer:

To reflect a point over a vertical line x = c, where c is a constant, we can use the formula (2c - x, y).

Given the line of reflection x = -2, and the original points N(-5, 2), M(-2, 1), O(-3, 3), we can apply the formula as follows:

For N(-5, 2):

N' = (2(-2) - (-5), 2) = (1, 2)

For M(-2, 1):

M' = (2(-2) - (-2), 1) = (2, 1)

For O(-3, 3):

O' = (2(-2) - (-3), 3) = (1, 3)

So, the correct image vertices of N'M'O' after reflecting over x = -2 are N'(1, 2), M'(2, 1), O'(1, 3), which corresponds to the option:

N′(1, 2), M′(2, 1), O′(1, 3)

Please double-check to make sure if its right ;D

Answer:

z > - [tex]\frac{11}{9}[/tex]

Step-by-step explanation:

7z + 7 > - 2z - 4

9z + 7 > -4

9z > - 11

z > - [tex]\frac{11}{9}[/tex]

The length of each side is 2√6 cm.

We have,

Length of diagonal of square = 4√3 cm

Now, To compute the length of a side of a square Divide d by √2.

So, length of each side

= 4√3 / √2

= 4√6/ 2

= 2√6

Thus, the length of each side is 2√6 cm.

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In the given triangle IJK, the measure of angle J is approximately 32°

From the question, we are to determine the measure of angle J in the given triangle

From the Law of Sines,

We can write that

sin (I) / i = sin (J) / j

From the given information,

j = 530 cm

i = 740 cm

∠I = 133°

Substituting the parameters into the formula,

sin (I) / i = sin (J) / j

sin (133°) / 740 = sin (J) / 530

sin (J) = (530 × sin (133°)) / 740

sin (J) = 0.5238

J = sin⁻¹ (0.5238)

J = 31.59°

J ≈ 32° (to the nearest degree)

Hence,

The measure of angle J is approximately 32°

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The popcorn box can hold 35 cubic inches of popcorn when it is full.

To find the volume of the popcorn box modeled as a right rectangular prism with dimensions 2 inches by 2.5 inches by 7 inches, you need to multiply the three dimensions together:

Volume = Length × Width × Height

In this case, the dimensions are:

Length = 2 inches; Width = 2.5 inches ; Height = 7 inches

Now, multiply the dimensions:

Volume = 2 × 2.5 × 7

Volume = 5 × 7

Volume = 35 cubic inches

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The interpretation of the slope is On average, for every additional year of age, bone density loss increases by approximately 0.41. (option a)

To calculate the least squares regression line, the data points are first plotted on a scatter plot. The line of best fit is then drawn through the data points such that the sum of the squared distances between the line and the data points is minimized. The slope of this line can be calculated using the following formula:

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

where n is the number of data points, Σ represents the sum of the values, x represents age, y represents bone density loss, and xy represents the product of x and y.

Using this formula, the slope for this data set can be calculated to be approximately 0.41. This means that, on average, for every additional year of age, bone density loss increases by approximately 0.41. In other words, the slope indicates a positive relationship between age and bone density loss, with bone density loss increasing as age increases.

Therefore, the correct answer is (a) On average, for every additional year of age, bone density loss increases by approximately 0.41.

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Complete Question:

Osteoporosis is a condition in which bone density decreases, often resulting in broken bones. Bone density usually peaks at age 30 and decreases thereafter. To understand more about the condition, a random sample of women aged 50 and over were recruited. Each woman's bone loss was recorded and the date is shown in this file. Create a scatter plot of these two variables, with age as the x variable and bone density loss as the y variable. Calculate the least squares regression line. What is your interpretation of the slope?

a. On average, for every additional year of age, bone density loss increases by approx 0.41.

b. On average, for every additional one point of bone density loss, age increases by approx 0.41.

c. On average, for every additional year of age, bone density loss increases by approx 6.9.

d. none of the above

Answer:

V = hpi(r)^2

 =  20(3.14)(17)^2 = 18,149.20 cubic mm

More accurately,

V = 20(3.14159)(17)^2 = 18158.39 mm^3

Step-by-step explanation: