The two true statements are: b.) The value for the degrees of freedom for Mary's sample population is six, and e.) Mary would use the sample standard deviation to calculate a t-statistic.
a.) The t-distribution that Mary uses does not have skinnier tails than a standard distribution. In fact, the t-distribution has fatter tails, which accounts for the increased variability when working with small sample sizes.
b.) The degrees of freedom for Mary's sample population can be calculated as the number of subjects minus one, which in this case is 7 - 1 = 6. So statement b is true.
c.) The t-distribution that Mary uses is not taller than a standard distribution. The shape of the t-distribution is similar to the standard normal distribution, but it is slightly flatter.
d.) Mary would not use the population standard deviation to calculate a t-distribution. Instead, she would use the sample standard deviation, which provides an estimate of the population standard deviation.
e.) Mary would use the sample standard deviation to calculate a t-statistic. The t-statistic measures the difference between the sample mean and the hypothesized population mean, relative to the variability in the sample.
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Consider The Function And The Arc Of A Curve C From Point A (4,3) To Point B (5,5) Using The Fundamental Theorem For Line Integrals, G(X,Y)=2x²+3y² S Vg⋅Dr=
We know that the line integral of the curve C is equal to the difference between the anti-derivative at the final point B and the antiderivative at the initial point A. Therefore, Vg⋅dr= F(B) - F(A)⇒ Vg⋅dr= [2(5)²(5) + 3(5)² + C] - [90 + C]⇒ Vg⋅dr= 184
The question states that the function g(x,y) = 2x² + 3y² and the curve C is the arc of a curve from point A(4,3) to point B(5,5). The task is to find the value of the line integral along curve C.
Therefore, we need to use the fundamental theorem for line integrals to evaluate the line integral. To use the fundamental theorem for line integrals, we must first evaluate the gradient vector field of the function. Then we need to find the antiderivative of the gradient vector field of the function. We can obtain the antiderivative by integrating the gradient vector field along the curve C using the initial and final points of the curve. The value of the line integral of the curve C is equal to the difference between the antiderivative at the initial point A and the antiderivative at the final point B, i.e., Vg⋅dr= F(B) - F(A).
Step-by-step solution: Given, the function g(x,y) = 2x² + 3y²Let us calculate the gradient vector of the function g(x,y).∇g(x,y) = [∂g/∂x, ∂g/∂y]⇒ ∇g(x,y) = [4x, 6y]Therefore, the gradient vector field of g(x,y) is V = [4x, 6y].
Now, we need to find the antiderivative of the gradient vector field of the function. Let us integrate V along the curve C from A(4,3) to B(5,5). The curve C is given by y = x + 1.We know that the line integral along curve C is given by the formula, Vg⋅dr= ∫C V . dr = F(B) - F(A)
Therefore, we need to find the antiderivative F of V.F(x,y) = ∫V dx⇒ F(x,y) = 2x²y + 3y² + C. Since we have two variables, we need to find the value of C using the initial point A(4,3).F(4, 3) = 2(4)²(3) + 3(3)² + C⇒ F(4, 3) = 90 + C
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Given that the function is G(x, y) = 2x² + 3y² and Arc of a curve C from point A(4, 3) to point B(5, 5). The value of the line integral [tex]\int _C[/tex] (2x² + 3y²) ds is 106.67.
Solution: In the given question, we have a function G(x, y) = 2x² + 3y² and an arc of a curve C from point A(4, 3) to point B(5, 5).
We are to use the fundamental theorem for line integrals to find the value of [tex]\int _C[/tex] (2x² + 3y²) ds.
Step 1: First, we will find the parametric equations of the given curve.
The points A(4, 3) and B(5, 5) are given.
We can write the parametric equations of the curve C as: x = f(t) and y = g(t), where a ≤ t ≤ b, and f(a) = 4, g(a) = 3, f(b) = 5, g(b) = 5.
Here, the curve C is the straight line from A(4, 3) to B(5, 5), so we can choose any convenient parameterization.
A possible one is: t → r(t) = (4 + t, 3 + t), 0 ≤ t ≤ 1.
Step 2: Next, we will find dr/dt and ds/dt.
We have: r(t) = (4 + t)i + (3 + t)j
⇒ dr/dt = i + j.
Square of the magnitude of the tangent vector: |dr/dt|² = (1)² + (1)²
= 2.
Magnitude of the normal vector:
|n| = √(ds/dt)²
= √(2)
= √2.
Magnitude of the velocity vector:
|v| = √(dr/dt)²
= √2.
Step 3: Now, we will find the limits of integration and substitute the required values in the integral.
Given: [tex]\int _C[/tex] (2x² + 3y²) ds.
We have: r(t) = (4 + t)i + (3 + t)j
⇒ r'(t) = i + j
⇒ |r'(t)| = √2.
We know that the length of the curve C from A to B is given by:
Length of the curve = [tex]\int _C[/tex] ds
= [tex]\int_a^b[/tex] |r'(t)| dt
= [tex]\int_0^1[/tex] √2 dt
= √2.
Now, we have the value of ds: ds = √2 dt.
Then, we can write the integral as follows:
[tex]\int _C[/tex] (2x² + 3y²) ds = [tex]\int_0^1[/tex] (2(4 + t)² + 3(3 + t)²) √2 dt
= [tex]\int_0^1[/tex] (32 + 32t + 10t²) √2 dt
= [32t + 16t² + (10/3)t³[tex]]_0^1[/tex]
= 32 + 16 + (10/3)
= 106.67.
Thus, the value of the line integral [tex]\int _C[/tex] (2x² + 3y²) ds is 106.67.
The required answer is: 106.67.
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It costs $3 per hour to park in a parking lot, with a maximum cost of $12.
Explain why the amount of time a car is parked is not a function of the parking cost.
Answer:
It is not a function because there is a maximum.
Step-by-step explanation:
With 12 as the maximum it will not go on forever and functions do.
Mary has a toy which is in the shape of a right prism with triangular bases. The sides of its bases are each 4 feet and its approximate height is 3.5 feet. The length of the prism between the bases is 10 feet. What is the approximate surface area of this right prism? A. 134 B. 150.5 C. 210 D. 323.5
Answer:
B
Step-by-step explanation:
Answer:
C
Step-by-step explanation: 210 ft. 2
A property worth 10,480.00 is shared between Eugenia and her 10 brothers in ratio: 1:4 respectively.The 10 brothers shared their portion equally.Find each the brothers share.
Answer:
838.4
Step-by-step explanation:
From the question,
Total worth of the property = 10480.
Eugenia share: Her 10 brothers share = 1:4
Total ratio = 1+4 = 5.
Her 10 brother's share = (4/5)(10480)
Her 10 brother's share = 41920/5
Her 10 brother's share = 8384.
If the 10 brothers shared their portion equally,
Each brother's share = 8384/10
Each brother's share = 838.4
pls help and show work
Answer:
Step-by-step explanation:
3x^2 + 24x + 48 + 43 - 48
3(x^2 + 8x + 16) - 5
3(x + 4)^2 - 5
vertex at (-4,-5)
Answer:
vertex = (- 4, - 5 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = 3x² + 24x + 43 ← factor out 3 from the first 2 terms
= 3(x² + 8x) + 43
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 8x
y = 3(x² + 2(4)x + 16 - 16) + 43
y = 3(x + 4)² - 48 + 43
y = 3(x + 4)² - 5 ← in vertex form
with vertex = (- 4, - 5 )
Please hurry lol I’ll give brainliest
Answer:
this is true but what do we have to do?
Step-by-step explanation:
Answer: x = 35, angle 1 = 85, angle 2 = 70, angle 3 = 25
Step-by-step explanation:
Finding x: 85+2x+x-10=180
3x= 105
x= 35
x-10 = angle 3 due to a property of parallels lines so put x in to get that angle 3 is 25 degrees
angle 2x = 70 degrees
70 + 25+angle 1 = 180
angle 1 = 85
angle 2 = 180-85-25 = 70
12 + 6 − 4 ÷ (2 + 5)
Answer:
2
Step-by-step explanation:
14 / (7)
Answer all or none! Ty!
Determine the projection of u=1.6i+3.3j in the v=-2.1-.5j direction.
A.8i+.2j
B.2.3i+.5j
C. -.6i-1.3j
D. -1.2i-1.1j
Answer:
[tex]0.80i +0.2j[/tex]
Step-by-step explanation:
The projection of u on v is expressed as;
[tex]proj_{v} u = \dfrac{u*v}{|v|^2} * v[/tex]
Given
u=1.6i+3.3j
v=-2.1i-.5j
u*v = (1.6i+3.3j )*(-2.1i-0.5j )
u*v = 1.6i(-2.1i) + 3.3j(-0.5j)
u*v = -3.36 - 1.65
u*v = -5.01
|v|² = (√(-2.1)²+(-0.5)²)²
|v|² = (-2.1)²+(-0.5)²
|v|² = 4.41+0.25
|v|² = 4.66
Substitute into the formula;
[tex]= \frac{1.71}{-5.01} * (-2.1i - 0.5j)\\= -0.3413 (-2.1i - 0.5j)\\= 0.8i + 0.17j\\= 0.80i +0.2j[/tex]
Please help!! I am so confused on how to do this.
Answer:
its 62!
p-by-step explanation:
Answer:
62.
Step-by-step explanation:
A=2(wl+hl+hw)=2·(3·5+2·5+2·3)=62
The price of crude oil, per barrel, in the year 2006 was estimated at $66.02. There was a 9.5% increase in the year
2007 and a 38.83% increase in the year 2008. Determine the approximate value for a barrel of crude oil in the year
2008. Round your answer to the nearest cent.
a. $128.74
c. $179.27
b. $91.66
d. $100.36
Answer:
D.) $100.36
Step-by-step explanation:
66.02/100 = 0.6602
0.6602 x 109.5 = 72.2919
72.2919/100 = 0.722919
0.722919 x 138.83 = 100.36
Help and an explanation would be greatly appreciated.
Answer:
the answer is D
hope it help
Answer: D, x²-6x+9
Step-by-step explanation:
(x-3)² is the same as (x-3)(x-3).
So you would do:
x times x=x²
x times -3=-3x
-3 times x=-3x
-3 times -3=9
The equation would look like this:
x²-3x-3x+9
Then you would have to collect the like terms. Like terms are terms that have the same variables and powers. So it would look like this:
x²-6x+9
Hope this helps :)
la suma de los tres terminos de una sustraccion es 720. calcula el minuendo
Answer:
i dont know
Step-by-step explanation:
hi can someone help me with this
Answer:
86 degrees
Step-by-step explanation:
180 - (74 + 20) = 86
36kg in the ratio 1:3:5
the answer are 4kg ,12kg and 20 kg
What is the equation of the horizontal line?
Answer: y = 1
y = 2x+7 x = -3
y = 2(-3) + 7
y = 1
PLEASE HELP!!!!!
Taylor's computer randomly generate numbers
between 0 and 4, as represented by the given uniform
density curve.
What percentage of numbers randomly generated by
Taylor's computer are between 1.5 and 3.25?
O 0%
1.75%
Random Number Generated
by Computer
25%
O 43.75%
1
2
3
Random Number
Answer: D
Step-by-step explanation:
just got it correct.
A rectangular playground has length of 120 m and width of 6 m. Find its length, in metres, on a drawing of scale 1 : 5
Answer:
I. Length = 600 meters
II. Width = 30 meters
Step-by-step explanation:
Given the following data;
Length = 120m
Width = 6m
Drawing scale = 1:5
To find the length and width using the given drawing scale;
This ultimately implies that, with this drawing scale, the length and width of the rectangle would increase by a factor of 5 (multiplied by 5) i.e the rectangle is 5 times bigger in real-life than on the diagram.
For the length;
120 * 5 = 600 meters
For the width;
6 * 5 = 30 meters
Therefore, the dimensions of the rectangle using the given drawing scale is 600 meters by 30 meters.
Help... do it now if you can pls...
Answer:
1.A,B,C,D
2. AB, CD
3. AC, BD
4. Line AD (don't take my word for this one)
Step-by-step explanation:
ATHEMATICS CURRICULUM
Lesson 3 Homework
time Zachary starts playing with his action figures.
the start playing with his action figures?
Start
1
12
11
1
31
10
on figures for 23 minutes.
Ish playing?
Finish
Answer:
guru gossip and you can you invite me to the heading
A coin is tossed until 3 consecutive heads appear. Show that the
expected number of tosses is 14. Find the PGF of the number of
tosses until the sequence HTH appears.
The PGF of the number of tosses until the sequence HTH appears is given by G(t) = (G × t / (1 - (1/2) × t).
To find the expected number of tosses until three consecutive heads appear, we can approach the problem using the concept of the probability generating function (PGF).
Let's define a random variable X as the number of tosses until three consecutive heads appear. We want to find E(X), the expected value of X.
To determine the PGF of X, we consider the possible outcomes at each toss. There are three possible outcomes: T (tails), H (heads), and the sequence HTH (three consecutive heads).
At the first toss, the possible outcomes are T and H. The PGF for this situation is given by:
[tex]G1(t) = Pr(X = 1) \times t^1 + Pr(X = 2) \times t^2[/tex]
Since we can have either T or H on the first toss, we have Pr(X = 1) = 1/2 and Pr(X = 2) = 1/2. Therefore:
[tex]G1(t) = (1/2) \times t + (1/2) \times t^2[/tex]
Now, let's consider the situation after the first toss:
If the first toss resulted in T, we are back to the starting point. Therefore, the PGF is G(t).
If the first toss resulted in H, we are one step closer to our goal (HTH). The PGF for this situation is G(t) × t.
Combining these two cases, we have:
[tex]G(t) = (1/2) \times t + (1/2) \times t^2 \times G(t)[/tex]
Simplifying the equation, we get:
[tex]G(t) = (1/2) \times t / (1 - (1/2) \times t^2)[/tex]
Next, let's consider the situation after the second toss:
If the second toss resulted in T, we are back to the starting point. Therefore, the PGF is G(t).
If the second toss resulted in H, we are still one step closer to our goal (HTH). The PGF for this situation is G(t) × t.
Combining these two cases, we have:
G(t) = (1/2) × t + (1/2) × t × G(t)
Simplifying the equation, we get:
G(t) = (1/2) × t / (1 - (1/2) × t)
Finally, we can calculate the expected value E(X) using the PGF:
E(X) = G'(1)
To find the derivative of G(t), we can use the quotient rule:
G'(t) = [(1 - t) × 1 - t × (-1/2)] / (1 - (1/2) × [tex]t)^2[/tex]
Simplifying the equation, we get:
G'(t) = 1 / (1 - (1/2) × [tex]t)^2[/tex]
Evaluating G'(1), we have:
[tex]E(X) = G'(1) = 1 / (1 - (1/2) \times 1)^2 = 1 / (1 - 1/2)^2 = 1 / (1/2)^2 = 1 / (1/4) = 4[/tex]
Therefore, the expected number of tosses until three consecutive heads appear is 4.
Additionally, the PGF of the number of tosses until the sequence HTH appears is given by:
G(t) = (G × t / (1 - (1/2) × t)
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please help, I need help understanding this. May someone explain this?
what is the mx of a slope of -1 and a y-intercept of 4
y=-1x+4
---
hope it helps
sorry I had no idea how to explain
Find the output, h, when the input, x, is -18
h = 17+x/6
h=?
Answer:
i think h=17
Step-by-step explanation:
-18h = 17 = xh/6
Subtract xh/6 from both sides of the equation.
-18 - xh/6 = 17
Answer:
Step-by-step explanation:8
guys what is m=4 i really need help
Answer:
m equals four means that you need to multiply the 4 by what is infront of the m aka the 4
Assume that the population is normally distributed. Construct a 95% confidence interval estimate of the mean numbers. Round to at least two decimal places.
17 14 16 13 15 15 14 11 13
Margin of Error:
Confidence Interval:
Based on the given data, a 95% confidence interval estimate of the mean number falls between 12.22 and 16.78.
To construct a confidence interval for the mean, we need to calculate the sample mean and the margin of error. The formula for the margin of error is:
Margin of Error = Z * [tex]\frac{standard deviation}{\sqrt{n} }[/tex]
where Z is the critical value corresponding to the desired confidence level (for 95% confidence level, Z ≈ 1.96), Standard Deviation is the sample standard deviation, and n is the sample size.
From the given data, we calculate the sample mean to be 14.33 and the sample standard deviation to be 1.91. Since the population is assumed to be normally distributed, we can use the Z-distribution.
Using the formula for the margin of error, we find:
Margin of Error = 1.96 * (1.91 / √9) ≈ 1.39
The confidence interval is calculated by subtracting and adding the margin of error to the sample mean:
Confidence Interval = (14.33 - 1.39, 14.33 + 1.39) = (12.94, 15.72)
Rounded to at least two decimal places, the 95% confidence interval estimate of the mean number is approximately (12.22, 16.78). This means that we can be 95% confident that the true mean number falls within this interval.
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Look at the sample space below.
{1, 2, 3, 7, 9, 10, 15, 19, 20, 21}
When chosen randomly, what is the probability of picking an odd number?
Plodd number) =
1
21
옮
3
10
름
7.
10
Answer:
There are 10 odd numbers: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} There are 4 factors of 8: {1, 2, 4, 8} There is 1 number in both lists: {1} Probability of an odd or a factor of 8 = (10 + 4 - 1)/20 = 13/20
Find the distance between the points (9,3) and (–5,3).
Answer:
The answer to the question provided is 14.
Step-by-step explanation:
》The Distance Formula:
[tex] d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} } [/tex]
》Plug in.
[tex]d = \sqrt{( - 5 - 9)^{2} + (3 - 3) ^{2} } \\ d = \sqrt{( - 14)^{2} + (0) ^{2} } \\ d = \sqrt{196 + 0} \\ d = \sqrt{196} \\ d = 14[/tex]
Urgent !!!! Can someone please help me
Answer:
The answer is D
Step-by-step explanation:
They are using 135 times the weeks, but the car already had 100 miles on it to start. Juan buys a car that has 40 miles originally on it and he drives it 150 miles per week. So, the word problem is D
On a school field trip, there will be one adult for every 12 students. Which equation could be used to find a, the number of adults, if s, the number of students, is unknown?
There is no good answer for this.
You would do s/12, since there is 1 adult for every 12 kids. Then, round the number to the nearest 1. (if it is a decimal, there is a number and remainder of students.)