Answer:
(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Step-by-step explanation:
To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:
a² = 7 cm²
b² = 17 cm²
c² = 10 cm²
We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.
We can rearrange the equations above to solve for a, b, and c:
a = √7 cm ≈ 2.65 cm
b = √17 cm ≈ 4.12 cm
c = √10 cm ≈ 3.16 cm
Now, we can check whether the Pythagorean theorem holds:
c² = a² + b²
(√10 cm)² = (√7 cm)² + (√17 cm)²
10 cm = 7 cm + 17 cm
This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Anna obtained 22 out of 30 for an Afrikaans test and 18 out of 25 for a mathematical literacy test , are these results proportionate? If not , in which subject did she score the highest
according to the given question Anna scored highest in the Afrikaans test.
what is proportionality?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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LOOK AT PHOTO
5x+3> 10
The smallest integer value of x that would be a solution in the inequality would be x = 2.
How to find the smallest integer ?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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PLEASE ANSWER!! WILL GIVE BRAINLIEST
Answer:
the correct answer is option D
Draw a coordinate plane. Plot the points: A(3, 4), B(2, 2), C(5, 8), D(7, 12), and E(9, 14). All but one of the points are on the same line. Which one is not?
The point that is not on the same line as the others is E(9, 14).
How to find the point ?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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In IJK, j=530 cm, i=740 cm and
In the given triangle IJK, the measure of angle J is approximately 32°
Law of Sines: Calculating the measure of angle in a triangleFrom 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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Let r and s be the usual generators for the dihedral group of order 8...
Part a)
list the elements of D8 as 1,r,r^2,r^3,s,sr,sr^2,sr^3 and label these with the integers
1,2,...,8 respectively. Exhibit the image of each element of D8 under the left regular representation of D8 into S8....
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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Hey can anyone solve these questions. Thanks
1. $.50 is what fraction of a dollar? Reduce the fraction to lowest terms.
2. If Sue's batting average is .250, what fraction of her times at bat does she get a hit?
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
What is decimal and fraction?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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Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at negative 5 comma 3, negative 5 comma 6, negative 9 comma 6, negative 9 comma 3, negative 7 comma 1.
50 POINTS ASAP Determine the line of reflection.
Reflection across x = −4
Reflection across y = 1
Reflection across the x-axis
Reflection across the y-axis
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.
The rear windshield wiper blade on a car has a length of 8 inches. The blade is mounted on a 16 inch arm, 8
inches from the pivot point. If the wiper turns through an angle of 130 degrees, how much area is swept
clean?
blade
square inches.
The area swept clean by the wiper blade is approximately 239.3 square inches.
To find the area swept clean by the bladeWe 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
θ is the central angle of the sector (in degrees)r is the radius of the circle π is the constant pi (approximately 3.14)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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Really really need help on this! It’s due tomorrow morning. Thanks if you could help!
The mean number of states will be 6.
The percentage of students who visited more than 7 states will be 20%.
How to calculate the meanThe 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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In Apextown there are 320,000 29-year-olds. Based on the table below, how many are not expected to be alive in a year? • A. 422 • B. 419 • C. 315 • D. 485
The number of 29 year olds who are not expected to be alive in a year would be A. 422 people.
What does the table show about Apextown ?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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The angle of depression from the top of a lighthouse to a boat in the ocean is 44°. If the lighthouse
is 245 feet tall, how far is the boat from the base of the lighthouse? Round to the nearest tenth.
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]
The sum of the interior angles of a regular polygon is 1080°.
a. ) Classify the polygon by the number of sides.
b. ) What is the measure of one interior angle of the
polygon?
c. ) What is the measure of one exterior angle of the
polygon?
a) The polygon has 8 sides and is called an octagon.
b) The measure of each interior angle of the octagon measures 135 degrees.
c) The measure of each exterior angle of the octagon measures 45 degrees.
a. To classify the polygon by the number of sides, we can use the formula for the sum of the interior angles of a polygon:
Sum of interior angles = (n - 2) x 180 degrees
where n is the number of sides of the polygon.
In this case, we are given that the sum of the interior angles is 1080 degrees. So we can set up an equation as follows:
(n - 2) x 180 = 1080
Simplifying this equation, we get:
n - 2 = 6
n = 8
b. To find the measure of one interior angle of the polygon, we can use the formula for the measure of each interior angle of a regular polygon:
Measure of each interior angle = (n - 2) * 180 degrees / n
Substituting n = 8 into this formula, we get:
Measure of each interior angle = (8 - 2) * 180 degrees / 8
= 135 degrees
c. To find the measure of one exterior angle of the polygon, we can use the fact that the sum of the interior and exterior angles of a polygon is 180 degrees. Therefore, the measure of each exterior angle of a regular polygon is:
Measure of each exterior angle = 360 degrees / n
Substituting n = 8 into this formula, we get:
Measure of each exterior angle = 360 degrees / 8
= 45 degrees
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A cylinder has a height of 20 millimeters and a radius of 6 millimeters. What is its volume?
Use 3.14 and round your answer to the nearest hundredth.
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:
Devaughn is 12 years younger than Sydney. The sun of their ages is 78. What is Sydney’s age?
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
What is the mean of this data set?
Please help ASAP giving Brainlyist (I don’t know how to spell it) it is not 24 cm
The closest option is (b) 23 12/15.
What are mean in statistics?
Mean: The average of a set of values, is calculated by adding up all the values in the set and dividing by the total number of values.
To find the mean (average) of the data set, we need to first find the sum of all the lengths of roses multiplied by their respective frequencies, and then divide by the total number of roses:
(22 x 2) + (23 x 4) + (24 x 5) + (25 x 3) + (26 x 1) = 344
Total number of roses = 2 + 4 + 5 + 3 + 1 = 15
Mean = Sum of all lengths / Total number of roses = 344 / 15 ≈ 22.93 cm
Rounding to the nearest whole number, the mean length of roses in this data set is 23 cm. Therefore, the closest option is (b) 23 12/15.
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Translate the phrase into a variable expression. Use the letter c to name th
variable. If necessary, use the asterisk (*) for multiplication and the slash
(/) for division.
...
the value of the company divided by 96884 shares...
7z + 7> - 2z -4 solve the following for inequality for z simplest form
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]
Please help me with these exercises that uses area and surface area
The areas and the surface areas of the figures are calculated below
Calculating the areas and the surface areasThe 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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Robert models the volume of a popcorn box as a right rectangular prism. Its dimensions are
2
2 in by
2
1
2
2
2
1
in by
7
7 in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.
The popcorn box can hold 35 cubic inches of popcorn when it is full.
How to calculate the volume of the popcorn box?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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Find the slope of the line through the pair of points. D(3, 5), J(8, 7)
20 POINTS
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
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
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
Please help, will give brainliest
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.
given the following scenario, would you use the wilcoxon rank sum or the mann whitney test? determining if there is a difference in ratings in maintenance quality at two tirezone locations. forty customers were randomly selected from the location on 13th street, and forty five customers were randomly selected from the newberry road location. group of answer choices wilcoxon rank sum test mann whitney test
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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What is the value of the expression below?
(31½ - 93) ÷ (-2.5)
A - 2.5
B-2.3
C 2.3
D 2.5
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.
A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the women interviewed, 24% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities.
(a) P(woman asked for a raise) = _____.
(b) P(woman received raise, given she asked for one) = _____.
(c) P(woman asked for raise and received raise) = _____.
Probability
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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The length of a diagonal line in a perfect square measures [tex]4\sqrt{3}[/tex] cm. What is the length of each side?
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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The equation of a circle is x2+y2−12x+6y+20=0.
What is the radius of the circle?
Enter your answer in the box.
r =
units
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!
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
50 POINTS ASAP Triangle NMO is drawn with vertices N(−5, 2), M(−2, 1), O(−3 , 3). Determine the image vertices of N′M′O′ if the preimage is reflected over x = −2.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−2, 2), M′(1, 1), O′(0, 3)
N′(1, 2), M′(−2, 1), O′(−1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
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