We have successfully drawn the given planes when working on a body centered cubic structure.
When working with a body centered cubic structure, it's important to understand that the unit cell consists of a cube with one additional atom at the center of the cube. This gives rise to unique properties and symmetry within the crystal structure.
To draw the planes (100), (010), and (101) within this structure, we can use the Miller indices notation. In this notation, each plane is represented by three integers that correspond to the intercepts of the plane with the three axes of the unit cell.
For example, the (100) plane intersects the x-axis at a point where x=1, and intersects the y- and z-axes at points where y=0 and z=0, respectively. Using the Miller indices notation, we can write this plane as (100).
Similarly, the (010) plane intersects the y-axis at a point where y=1, and intersects the x- and z-axes at points where x=0 and z=0. Therefore, this plane can be written as (010).
Finally, the (101) plane intersects the x-axis at a point where x=1, the y-axis at a point where y=0, and the z-axis at a point where z=1. Using Miller indices notation, we can represent this plane as (101).
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Discuss how statistics led to the development of computer systems and how computer systems led to the development of statistics.
Statistics and computer systems have a mutually beneficial relationship that has contributed to significant advancements in both fields. The use of statistics has played a crucial role in the development of computer systems, while computer systems have greatly impacted the field of statistics.
Statistics has been instrumental in the development of computer systems by providing a framework for data analysis and interpretation. Without statistics, computers would not be able to process and analyze large amounts of data efficiently. For example, statistical models and algorithms are used in machine learning and artificial intelligence to enable computers to learn and make decisions based on data. Additionally, statistics is used to test and validate the effectiveness of computer systems, ensuring that they are reliable and accurate.
On the other hand, computer systems have revolutionized the field of statistics by making data analysis faster and more accurate. With the availability of powerful computers, statisticians can analyze and interpret large datasets more quickly and accurately, leading to new insights and discoveries. Computer systems have also enabled the development of sophisticated statistical software and tools, making statistical analysis more accessible to a wider audience.
In conclusion, the relationship between statistics and computer systems has been symbiotic, with each field contributing to the growth and advancement of the other. The use of statistics has led to the development of sophisticated computer systems, while computer systems have greatly impacted the field of statistics, making data analysis faster and more accurate.
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use law of sines to solve triangle with B=52 C=15 b=43
Using the Law of Sines, we can solve the given triangle with B = 52, C = 15, and b = 43. The three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all sides and their opposite angles. Therefore, we can use the Law of Sines to solve the given triangle as follows
sin(A)/a = sin(B)/b = sin(C)/c
We are given B = 52, C = 15, and b = 43, so we can use the Law of Sines to find a
sin(A)/a = sin(B)/b
sin(A)/a = sin(52)/43
sin(A) = a sin(52)/43
a = 43 sin(A)/sin(52)
Similarly, we can use the Law of Sines to find c
sin(A)/a = sin(C)/c
sin(A)/a = sin(15)/c
sin(15)c = a sin(A)
c = a sin(A)/sin(15)
Now, we can substitute the expressions for a and c into the equation sin(A)/a = sin(B)/b and solve for sin(A)
sin(A)/(43 sin(A)/sin(52)) = sin(52)/43
sin(A) = (43 sin(52) sin(15))/c
Substituting the expression for c, we get
sin(A) = (43 sin(52) sin(15))/(a sin(A)/sin(15))
Simplifying, we get
sin²(A) = (43²sin²(52) sin²(15))/(a²sin²(A))
Multiplying both sides by a^2 sin^2(A), we get
a²sin⁴(A) = 43^2 sin²(52) sin²(15)
Taking the square root of both sides and solving for a, we get
a = √((43² sin₂(52) sin²(15))/(sin⁴A)))
Substituting the given values and solving for A, we get
a = 28.29 (approx)
A = 112.94° (approx)
c = 8.11 (approx)
Therefore, the three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.
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Help me please and explain im so confused
The value of cos S to the nearest hundredth is 0.54
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Here in this triangle, the hypotenuse is 28
and the opposite to angle S is line TU
The adjascent is 15
therefore cos S = adj/hyp
= 15/28
= 0.54 ( nearest hundredth)
therefore the value of cos S is 0.54
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Solve using the zero product property. The problem has been factored for you.
The solution is, the solutions using the Zero Product Property: is x =0 and -5.
The expression to be solved is:
x(x + 5) = 0
we know that,
The zero product property states that the solution to this equation is the values of each term equals to 0.
now, we have,
x (x + 5) = 0
i.e. we get,
(x) × (x + 5) = 0
so, using the Zero Product Property:
we get,
(x) = 0
or,
(x + 5) = 0
so, we have,
x = 0 or, x = -5
The answers are 0 and -5.
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A softball is thrown at an angle of 45° with an initial speed of 49 ft/s and an initial height
of 5 ft.
i) Write a set of parametric equations for the motion of the softball.
ii) Determine how long the softball was in the air.
iii) Determine how far the softball traveled in the air.
iv) Determine when the softball reached its maximum height.
v) Determine the maximum height reached by the softball.
Answer:
i) The horizontal and vertical components of the softball's motion can be described by the following parametric equations:
x(t) = v0x * t
y(t) = v0y * t - 1/2 * g * t^2 + h0
where v0x and v0y are the initial horizontal and vertical velocities, respectively, g is the acceleration due to gravity (32.2 ft/s^2), h0 is the initial height (5 ft), and t is time.
We can find v0x and v0y by resolving the initial velocity vector into horizontal and vertical components:
v0x = v0 * cos(45°) = 49 ft/s * cos(45°) ≈ 34.65 ft/s
v0y = v0 * sin(45°) = 49 ft/s * sin(45°) ≈ 34.65 ft/s
Substituting these values into the parametric equations, we get:
x(t) = 34.65 * t
y(t) = 34.65 * t - 16.1 * t^2 + 5
ii) The softball will be in the air until it hits the ground, which occurs when y(t) = 0. We can solve for t using the quadratic formula:
16.1 * t^2 - 34.65 * t + 5 = 0
t ≈ 2.19 s (rounded to two decimal places)
Therefore, the softball was in the air for approximately 2.19 seconds.
iii) The horizontal distance traveled by the softball can be found by evaluating x(t) at the time when the softball hits the ground:
x(2.19) ≈ 75.8 ft (rounded to one decimal place)
Therefore, the softball traveled approximately 75.8 feet in the air.
iv) The softball reaches its maximum height when its vertical velocity is zero. We can find the time when this occurs by setting v0y - g * t = 0 and solving for t:
t = v0y / g = 34.65 / 32.2 ≈ 1.08 s (rounded to two decimal places)
Therefore, the softball reaches its maximum height after approximately 1.08 seconds.
v) The maximum height reached by the softball can be found by evaluating y(t) at the time when the softball reaches its maximum height:
y(1.08) ≈
Step-by-step explanation:
Which of the following is not a valid probability
A. 1
B. 1.1
C. 0
D. 0.001
Answer:
B
Step-by-step explanation:
It is impossible for a possibility to be more than 1, or 100%.
Find the two following values
The value of angle TUW is 32⁰.
The value of angle UTV is 25⁰.
What is the value of angle TUW?
The value of angle TUW is calculated by applying the following formula.
angle TVW = angle TUW (vertical opposite angles are equal)
angle TVW = 32⁰
So, angle TUW = 32⁰
The value of angle UTV is calculated as;
angle UTV = VWU (vertical opposite angles are equal)
3x + 4 = 2x + 11
3x - 2x = 11 - 4
x = 7
angle UTV = 3x + 4
= 3(7) + 4
= 25⁰
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Beth enlarged the triangle below by a scale of 5.
3.5 cm
4 cm
She found the area of the enlarged triangle. Her work is shown below.
(4)(3.5)(5)- 35 cm²
What was Beth's error?
O She should have divided (4)(3.5) by 5.
Caus and Exit
The error made by Beth is that:
She didn't apply the scale factor to each dimension of the triangle before multiplying
How to Interpret Enlargement Scale Factor?We are given the parameters as:
Initial height = 3.5cm
Initial width = 4cm
Formula for area of triangle is:
Area = ¹/₂ * base * height
If the triangle was enlarged by a scale factor of 5, then it means each of the dimensions should first be multiplied by 5 to get:
New width = 4 * 5 = 20 cm
New height = 5 * 3.5 = 17.5 cm
Thus:
New area = ¹/₂ * 20 * 17.5 = 175 cm²
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Find the coordinate vector of v relative to the basis S = (v1, V2, V3) for R^3 v = (40,36, 24); v1 = (2,0,0), v2 = (3,3,0), v3 = (8, 8, 8)
(v)s = ___ , ____, ____
To find the coordinate vector of v relative to the basis S = (v1, v2, v3) for R^3 with v = (40, 36, 24), v1 = (2, 0, 0), v2 = (3, 3, 0), and v3 = (8, 8, 8), follow these steps:
1. Write v as a linear combination of the basis vectors v1, v2, and v3: v = a * v1 + b * v2 + c * v3
2. Substitute the given vectors: (40, 36, 24) = a * (2, 0, 0) + b * (3, 3, 0) + c * (8, 8, 8)
3. This results in a system of linear equations:
2a + 3b + 8c = 40
3b + 8c = 36
8c = 24
4. Solve the system of linear equations:
From the third equation, we can find c: c = 24 / 8 => c = 3
Substitute c into the second equation: 3b + 8 * 3 = 36 => 3b + 24 = 36 => 3b = 12 => b = 4
Substitute b and c into the first equation: 2a + 3 * 4 + 8 * 3 = 40 => 2a + 12 + 24 = 40 => 2a = 4 => a = 2
So, the coordinate vector of v relative to the basis S is (a, b, c) = (2, 4, 3). Therefore, (v)s = (2, 4, 3).
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1.What does the series
[infinity]
Σ √n/n²
n=1
tell us about the convergence or divergence of the series
[infinity]
Σ √n/n²+n+3
n=1
2.
What does the series
[infinity]
Σ πn/n
n=1
tell us about the convergence or divergence of the series
[infinity]
Σ πn+√n/3n+n²
n=1
1. To determine the convergence or divergence of the series Σ(√n/n² + n + 3) from n=1 to infinity, let's first consider the series Σ(√n/n²) from n=1 to infinity.
Using the Comparison Test, we can compare Σ(√n/n²) with Σ(1/n), which is a known harmonic series and diverges. Since (√n/n²) ≤ (1/n) for all n ≥ 1, and Σ(1/n) diverges, Σ(√n/n²) also diverges.
Now, Σ(√n/n² + n + 3) can be rewritten as Σ(√n/n²) + Σ(n) + Σ(3). Since Σ(√n/n²) diverges, the whole series Σ(√n/n² + n + 3) diverges as well.
2. To determine the convergence or divergence of the series Σ(πn + √n)/(3n + n²) from n=1 to infinity, let's consider the series Σ(πn/n) from n=1 to infinity.
Using the Comparison Test again, we compare Σ(πn/n) with Σ(1/n). Since (πn/n) ≥ (1/n) for all n ≥ 1, and Σ(1/n) diverges, Σ(πn/n) also diverges.
Now, Σ(πn + √n)/(3n + n²) can be compared with Σ(πn/n). Since (πn + √n)/(3n + n²) ≤ (πn/n) for all n ≥ 1, and Σ(πn/n) diverges, the series Σ(πn + √n)/(3n + n²) diverges as well.
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Use the table of the probability distribution to find the variance
The variance of the given distribution is 0.9.
Calculating the anticipated value or distribution mean is the first step in determining a probability distribution's variance. The anticipated value is a weighted average of all potential outcomes, with each outcome's probability serving as the weight. The expected value can be expressed mathematically as follows:
[tex]E(X) =[/tex] Σ[tex][xi[/tex] × [tex]P(xi)][/tex]
where μ is the mean of the data.
Then, calculate μ:
μ [tex]= (1+2+3+4+5)/5[/tex]
[tex]=(15/5)[/tex]
[tex]= 3[/tex]
and replace this value and the values of xn and P(xn) into the formula for the variance, just as follow:
Hence, the variance of the given distribution is 0.9.
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the weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3315 grams and a variance of 391,876 . if a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4504 grams. round your answer to four decimal places.
The probability that the weight will be less than 4504 grams is 0.9713.
We need to standardize the value 4504 using the given mean and variance, and then use the standard normal distribution table to find the corresponding probability.
The standard deviation is the square root of the variance: √391876≈626.05
So, the z-score for a weight of 4504 grams is:
z=(4504−3315)/626.05≈1.8974
Using a standard normal distribution table, we find that the probability of a z-score being less than 1.8974 is approximately 0.9713.
Therefore, the probability that a newborn baby boy born at the local hospital will weigh less than 4504 grams is approximately 0.9713.
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Please help asap :( Find the exact length of arc ADC. In your final answer, include all of your calculations
Answer:
15 Pi m
Step-by-step explanation:
arc ADC = 360 Degrees - 60 Degrees divided by 360 Degrees Multiplied by 2 Pi Multiplied by 9
= 5/6 Times 18 Pi
=15 Pi m
This question has two parts.
A wooden block is a prism, which is made up of two cuboids with the dimensions shown. The volume of the wooden block is 427 cubic inches.
Part A
What is the length of MN?
Write your answer and your work or explanation in the space below.
Part B
200 such wooden blocks are to be painted. What is the total surface area in square inches of the wooden blocks to be painted?
A) The length MN of the given wooden block is: 12
B) 80400 in²
How to find the surface area and volume of the prism?1) The formula for volume of a cuboid is:
Volume = Length * Width * Height
Thus:
427 = (MN * 7 * 3) + (5 * 5 * 7)
427 = 21MN + 175
21MN = 252
MN = 252/21
MN = 12
2) Surface area of entire object is:
TSA = 2(12 * 3) + 2(12 * 7) - (5 * 7) + 2(7 * 3) + 3(5 * 7) + 2(5 * 5)
= 402 in²
For 200 blocks:
TSA = 200 * 402 = 80400 in²
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At a local gym with 800 members, 450 members take aerobics class, 200 members do weight training, and 125 members do both weight training and take an aerobics class. What is the probability that a randomly-selected member takes an aerobics class or does weight training? Round your answer to the hundredths place.
Answer:
0.66
Step-by-step explanation:
You want the probability that a randomly chosen member from the 800 members of a gym takes either an aerobics class, as 450 members do, or does weight training, as 200 members do. 125 members do both.
EitherAdding the numbers given for members who do aerobics or weight training will count the number who do both twice. Then the number who do either is ...
(# of aerobics) + (# of weights) - (# of both)
= 450 +200 -125 = 525
The probability that one of the 800 members is in this group is ...
P(either) = 525/800 ≈ 0.66
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Brody has a jar with 1000 g of sugar in it. Each day, he empties out half
of the sugar that is in the jar. At the end of the first day, he is left with
500 g of sugar.
a) How much sugar will be left in the jar at the end of the 5th day? Give
your answer in grams (g).
b) Write a sentence to explain whether or not the jar will ever be empty
31.25 g on the 5th day
no it will never by empty because even when it gets down to one singular piece of sugar you would technically just cut it in half, then that in half, yes it would get impossible, that's why you wouldn't actually do it, but if you typed it into a calculator it would just keep getting a smaller and smaller decimal.
Please help I have to do this before state testing this I one out of 32 questions also if you so happen to be mrs Billie from Alhambra traditional school I hate you
Answer:turn right 45 degrees, then turn right another 45 degrees. flip the figure x-axis wise/horizontally
Step-by-step explanation:
Vectors u = 6(cos 60°i + sin60°j), v = 4(cos 315°i + sin315°j), and w = −12(cos 330°i + sin330°j) are given. Use exact values when evaluating sine and cosine.
Part A: Convert the vectors to component form and find −7(u • v). Show every step of your work. (4 points)
Part B: Convert the vectors to component form and use the dot product to determine if u and w are parallel, orthogonal, or neither. Justify your answer. (6 points)
PART A: component form of the vector is:
u = <3, 3√3>
v = <2√2, -2√2>
w = <-6√3, 6>
-7(u • v) = 42(√6 - √2)
PART B: u and w are orthogonal
How to write vectors in component form?The component form of a vector is <x, y>.
PART A:
u = 6(cos 60°i + sin60°j)
x = 6(cos 60) = 6 * 1/2 = 3
y = 6(sin 60) = 6 * (√3)/2 = 3√3
In component form, u = <3, 3√3>
v = 4(cos 315°i + sin315°j)
x = 4(cos 315°) = 4 * (√2)/2 = 2√2
y = 4(sin 315°) = 4 * (-√2)/2 = -2√2
v = <2√2, -2√2>
w = −12(cos 330°i + sin330°j)
x = -12(cos 330°) = -12 * (-1/2) = -6√3
y = -12(sin 330°) = -12 * (√3)/2 = 6
w = <-6√3, 6>
The dot product of two vectors is given by:
A•B = A[tex]_{x}[/tex]B[tex]_{x}[/tex] + A[tex]_{y}[/tex]B[tex]_{y}[/tex]
−7(u • v) = -7 * [(3 * 2√2) + (3√3 * -2√2)]
= -7 * [6√2 - 6√6]
= 42(√6 - √2)
Part B:
The vectors will be parallel if the dot product is equal to the product of the magnitudes which means the angle between the vectors is 0 or 180.
The vectors will be orthogonal if the dot product = 0. This means the angle between them = 90.
The dot product of the vectors (u) and (w) will be as follows:
u = <3, 3√3>
w = <-6√3, 6>
u • w = (3 * -6√3) + (3√3 * 6)
= -18√3 + 18√3
= 0
Since the result of the dot product = 0. The vectors (u) and (w) are orthogonal.
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The amount of water on barrel deceased 9 5/8 pints in 7 weeks what was the change of water in 12 weeks
Answer:
To solve this problem, we can use a proportion.
Let x be the change of water in 12 weeks.
We know that in 7 weeks, the water decreased by 9 5/8 pints.
So, we can set up the proportion:
9 5/8 pints / 7 weeks = x / 12 weeks
To solve for x, we can cross-multiply and simplify:
9 5/8 pints * 12 weeks = 7 weeks * x
115 1/2 pints = 7 weeks * x
x = 115 1/2 pints / 7 weeks
x = 16 1/2 pints per 12 weeks
Therefore, the change of water in 12 weeks is 16 1/2 pints.
Step-by-step explanation:
xon the following graph, use the orange points (square symbol) to plot points along the portion of the firm's short-run supply curve that corresponds to prices where there is positive output.
To plot points along the portion of the firm's short-run supply curve that corresponds to prices where there is positive output, we need to identify the portion of the graph where the firm is producing output.
We can observe from the graph that the firm's short-run supply curve is the component of the marginal cost curve that is higher than the average variable cost curve. The company will shut down and create no production if prices fall below the minimum point of the average variable cost curve. However, as long as the price is above the marginal cost of production, the company will create output at prices above the minimum point of the average variable cost curve.
We may use the orange square symbols to represent the price and matching amount provided at each point where the company is generating output to plot points along this segment of the short-run supply curve. We may advance up the marginal cost curve from the last point of the average variable cost curve until we reach the maximum price at which the company is generating output. The firm's short-run supply curve may then be created by marking each price and quantity combination along this segment of the curve.
It is important to note that the firm's short-run supply curve is a reflection of its marginal cost curve above the average variable cost curve, and will shift as the firm's costs of production change or its technology improve.
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Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. (If it diverges to infinity, state your answer as inf. If it diverges to negative infinity, state your answer as -inf. If it diverges without being infinity or negative infinity, state your answer as div )limn→[infinity] −8n6+sin2(7n)/n7+9
The sequence converges to 0.
To determine the convergence or divergence of the given sequence, we can use the limit comparison test.
Let's consider the series a_n = -8n^6 + sin^2(7n) and b_n = n^7 + 9.
Since sin^2(7n) is always between 0 and 1, we have 0 ≤ sin^2(7n) ≤ 1 for all n. Therefore,
-8n^6 ≤ -8n^6 + sin^2(7n) ≤ -7n^6
Dividing all terms by n^7 + 9, we get
-8n^-1/(n^7+9) ≤ (-8n^6 + sin^2(7n))/(n^7 + 9) ≤ -7n^-1/(n^7+9)
Now, taking the limit as n approaches infinity, we have
lim n→∞ -8n^-1/(n^7+9) = 0
lim n→∞ -7n^-1/(n^7+9) = 0
Since both the upper and lower bounds go to 0, the limit comparison test tells us that the series a_n and b_n have the same convergence behavior.
Since the series b_n = n^7 + 9 is a p-series with p = 7 > 1, it converges. Therefore, the given sequence
(-8n^6 + sin^2(7n))/(n^7 + 9)
also converges by the limit comparison test.
To evaluate its limit, we can use algebraic manipulation and the squeeze theorem.
-8n^6 ≤ -8n^6 + sin^2(7n) ≤ -7n^6
Dividing all terms by n^7 + 9 and taking the limit as n approaches infinity, we get
lim n→∞ (-8n^6)/(n^7 + 9) ≤ lim n→∞ (-8n^6 + sin^2(7n))/(n^7 + 9) ≤ lim n→∞ (-7n^6)/(n^7 + 9)
Using the squeeze theorem, we know that
lim n→∞ (-8n^6)/(n^7 + 9) = lim n→∞ (-7n^6)/(n^7 + 9) = 0
Therefore,
lim n→∞ (-8n^6 + sin^2(7n))/(n^7 + 9) = 0
Hence, the sequence converges to 0.
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The total cost for funding a trip for the senior class to go to the fall fair, C(x), is a function of the number of students that will make the trip, x. The trip will not be taken until at least 5 students sign up to go. This relationship can be modeled by the function shown.
C(x) = 350 + 7.50x
What is the domain and range for this situation?
The value of domain and range for this situation are,
Domain = (- ∞, ∞)
Range = (- ∞, ∞)
We have to given that;
The total cost for funding a trip for the senior class to go to the fall fair, C(x), is a function of the number of students that will make the trip, x.
Now, We have;
⇒ C (x) = 350 + 7.5x
Clearly, the function is a polynomial.
Hence, The value of domain and range for this situation are,
Domain = (- ∞, ∞)
Range = (- ∞, ∞)
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According to a poll of adults, about 46% work during their summer vacation. Assume that the true proportion of all adults that work during summer vacation is p=0.46. Now consider a random sample of 400 adults. Complete parts a and b below.
a. What is the probability that between 39% and 53% of the sampled adults work during summer vacation?
The probability is. (Round to three decimal places as needed.)
b. What is the probability that over 63% of the sampled adults work during summer vacation?
The probability is (Round to three decimal places as needed.)
To find the probability we do the following:
I need help on this 40 points I need to turn it in in like 5 min
Answer:
Step-by-step explanation:
13. B
14. A
15. D
if he sees a wolf, a boy will cry wolf with probability 0.8. if he does not see a wolf, the boy will cry wolf anyway with probability 0.4. if the probability that there is a wolf would otherwise be 0.25, what is the probability that there really is a wolf when the boy crys wolf?
The probability that there really is a wolf when the boy cries wolf is 0.54.
Let A be the event that the boy cries wolf and B be the event that there is a wolf. We are given the following probabilities:
P(A|B) = 0.8 (the probability that the boy cries wolf when there is a wolf)
P(A|B') = 0.4 (the probability that the boy cries wolf when there is no wolf)
P(B) = 0.25 (the probability that there is a wolf)
We want to find P(B|A), the probability that there really is a wolf given that the boy cries wolf.
We can use Bayes' theorem to calculate this:
P(B|A) = P(A|B) * P(B) / [P(A|B) * P(B) + P(A|B') * P(B')]
Substituting the given values, we get:
P(B|A) = 0.8 * 0.25 / [0.8 * 0.25 + 0.4 * 0.75] = 0.54
Therefore, the probability that there really is a wolf when the boy cries wolf is 0.54.
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a researcher conducts an experiment comparing two treatment conditions with 10 scores in each treatment condition. how many participants are needed for the study if an independent-measures design is used, if a repeated-measures design is used, and if a matched-subjects design is used?
If an independent-measures design is used, a total of 20 participants would be needed, with 10 participants in each treatment condition.
If a repeated-measures design is used, only 10 participants would be needed since each participant would serve as their own control and be tested in both treatment conditions. If a matched-subjects design is used, the number of participants needed would depend on how many pairs of matched subjects are needed. For example, if 5 pairs of matched subjects are needed, then a total of 10 participants would be needed.
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How much greater is the value of the 6 inand 4786.53 Denton 3821.69
pls help ASAP 20 points
Answer:
A. Bay Side: mean = 17.1, median = 16; Seaside: mean = 19.5, median = 18
B. Bay Side: σ = 8.96, IQR = 12, range = 37; Seaside: σ = 9.03, IQR = 16, range = 31
C. Bay Side has lower center values and less variation.
Step-by-step explanation:
Given stem and leaf plots for 15 class sizes at each of two schools, you want to know (a) their measures of center, (b) their measures of variation, and (c) which would be preferred for lower class size.
A. CenterThe first attachment shows the statistics for Bay Side School. It tells you the measures of center for Bay Side are ...
Mean: 17.1Median: 16The second attachment shows the statistics for Seaside School. The measures of center there are ...
Mean: 19.5Median: 18We note the measures of center indicate smaller classes at Bay Side.
B. VariationFor Bay Side School, the measures of variation are ...
Standard deviation: 8.96IQR: 22 -10 = 12Range: 42 -5 = 37; with outlier removed, 25 -5 = 20For Seaside School, the measures of variation are ...
Standard deviation: 9.03IQR = 27 -11 = 16Range: 36 -5 = 31The measures of variation are generally smaller for Bay Side.
C. Smaller ClassesThe measures of center and the measures of variation both favor Bay Side School as the school of choice for smaller classes.
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Additional comment
The arithmetic for these descriptive statistics can be tedious and error-prone. It is convenient to let a calculator do it. The lists of data points are given as L1 and L2 for the calculator screens attached. L1 is Bay Side data, and the result of the 1-Var Stats calculation is shown in the first attachment. Seaside data was put in L2, which was used for the calculations shown in the second attachment.
The Q1 and Q3 data values are the 4th lowest and 4th highest data values in each of the lists. The median is the 8th data value, counted from either end.
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An investment portfolio is shown below.
Investment
Money Market Account $3,200
Government Bond
$1,750
Preferred Stock
$1,235
Common Stock
$2,300
O 0.5%
O 1.1%
Amount Invested ROR
02.3%
O 3.5%
2.1%
Using technology, calculate the difference between the arithmetic average ROR and the weighted average ROR. Round to
the nearest tenth of a percent.
4.4%
-7.8%
10.5%
Using a calculator, the difference between the arithmetic average ROR and the weighted average ROR is Option B) 0.1%
How did we arrive at this conclusion?arithmetic average ROR is given as
(2.1% + 4.4% - 7.8% + 10.5%) / 4 = 0.02300
The Weighted Average ROR
[(0.021 x 3200 ) + (0.044 x 1750) + (-0.078 x 1235) + (0.105 x 2300)] / (3200 + 1750 + 1235 + 2300) = 0.0341037124337065
Thus:
The Weighted Average ROR - arithmetic average ROR
= 0.0341037124337065 - 0.02300
= 0.01110371243 x 100
= 1.11037124337%
≈ 1.1%
So we are correct to state that Option B is the right answer.
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NEED ANSWERS ASAP!! PLS
The US government monitors the consumption of different products. The table shows y, the amount of ice cream consumed, in millions of pounds, for * years since 2010. The quadratic equation that models the amount of ice cream consumed, in millions of pounds, since 2010 is shown. y = 12(¢ - 6)2 + 3922 Determine when the amount of ice cream consumed in the United State would be 5,650 millions of pounds.
The amount of ice cream consumed in the United State would be 5,650 millions of pounds in 2028.
How to determine when the amount of ice cream is 5,650 millions of pounds?Based on the information provided about the mount of ice cream consumed in the United State, a quadratic equation that models the amount of ice cream consumed, in millions of pounds, since 2010 is given by;
y = 12(x - 6)² + 3922
Where:
y is the amount of ice cream consumed, in millions of pounds.x is the number of years since 2010.By substituting the value of y, the number of years can be calculated as follows;
5,650 = 12(x - 6)² + 3922
5,650 - 3922 = 12(x - 6)²
1728 = 12(x - 6)²
144 = (x - 6)²
12 = x - 6
x = 12 + 6
x = 18 years.
Since 2010; 2010 + 18 = 2028.
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