Consider a Gaussian random variable x ~ N(x, x), where a € RD. Furthermore, we have where y Є RE, A ɛ RE×D, b = RF, and w ~ N(w 0, Q) is indepen- dent Gaussian noise. "Independent" implies that x and w are independent random variables and that Q is diagonal.
a. Write down the likelihood p(yx).
b. The distribution p(y) = √ p(y | x)p(x)dæ is Gaussian. Compute the mean μy and the covariance Σy. Derive your result in detail.
c. The random variable y is being transformed according to the measure- ment mapping
z = Cy+v,

we are 90% confident that the true mean price of hard back statics is between $93.15 and $95.85.

What is statistics and its types?

Since the 90% confidence interuale tells that when you are going to construct a confidence interuale of size 30 100firmes , out of this 100, 90 times the truew means will lie in the confidence interuale.

So option 1) & 2) are incorrect.

Similarly option 4 will no be correct .

So option c is correct.

i.e. we are 90% confident that the true mean price of hard back statics is between $93.15 and $95.85.

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Step-by-step explanation:

3 coffees + 2 muffins = $7

therefore,

\(3x + 2y = 7\)

2 coffees + 4 muffins = $8

therefore,

\(2x + 4y = 8\)

Answer:

i think in every coast we're adding two shillings in the first sentence the total was 5 and we paid $7 and in the second sentence the total was 8 dollars meaning we added to shillings.

Step-by-step explanation:

in my school we are taughtthat we shouldn't mix goats with sheeps so we this the same way we can't mix x and y so in my opinion I guess you can say x + y =to that amount of money at the end you paid if it's 8 dollars or 7 dollars. we can say x represents the coffees and y represents the muffins that's how I get it I hope you want to be angry with me. for example 3 + 2 equals to 7 .3 + 2 is 5 so we'll carry five to the other side of equals where we will make it be minus so we'll say 7 - 5 where will get 2

\(\\ \sf\Rrightarrow Product=LCM(GCD)\)

\(\\ \sf\Rrightarrow 5070=390GCD\)

\(\\ \sf\Rrightarrow GCD=5070/390\)

\(\\ \sf\Rrightarrow GCD=13\)

Key words:-

Answer: D) the significance level of the test

=======================================================

Explanation:

The significance level of the test, also known as "alpha", is the probability of making a type 1 error. A type 1 error is where you reject the null hypothesis but it was true all along.

The null hypothesis is where we test a certain probability distribution (eg: normal distribution). Specifically we gather a sample of values and compute the test statistic. If the probability of getting that test statistic or more extreme is smaller than alpha, then we reject the null. This probability value is known as the p-value.

If you lower the alpha value, then that will make it more likely you do not reject the null. Consider an example where alpha = 0.10 to start with. If you get a p-value of 0.02, then you would reject the null. The same would apply for alpha = 0.05; however, with alpha = 0.01, the p-value is no longer smaller than alpha. At this point we do not reject the null. Your textbook may use the phrasing "fail to reject the null".

Going in the opposite direction, increasing the alpha value will make it more likely to reject the null. Each time you adjust the alpha value, keep the p-value to some fixed number (between 0 and 1).

The height of the equilateral triangle is 3√3 cm.

Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.

It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.

We have,

To minimize the probability of incorrectly rejecting the null hypothesis in a hypothesis test with a fixed sample size of 40, the statistician can adjust the significance level of the test.

The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.

By choosing a smaller significance level, the statistician can decrease the probability of making a Type I error (rejecting the null hypothesis when it is actually true).

However, decreasing the significance level also increases the probability of making a Type II error (failing to reject the null hypothesis when it is actually false).

Therefore,

The choice of significance level involves a trade-off between the two types of errors and should be based on the specific context of the problem and the consequences of each type of error.

Now,

The height of an equilateral triangle can be found using the formula:

height = (side length / 2) x √3

The side length = 6 cm

So,

height = (6 / 2) x √3

           = 3√3 cm

Therefore,

The height of the equilateral triangle is 3√3 cm.

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The point on the curve where the tangent line is parallel to the plane is (cos t0, sin t0, e^t0), where t0 is the solution of the equation et0/√3 = -2 sin t0.

To find t0, we need to take the derivative of r(t) with respect to t, which gives us the tangent vector: T(t) = (-2 sin t, 2 cos t, e^t).

Next, we need to find a vector normal to the given plane. We can do this by taking the coefficients of x, y, and z in the equation of the plane: N = (√3, 1, 0).

Since the tangent line is parallel to the plane, the dot product of the tangent vector and the normal vector should be zero: T(t0) · N = 0.

Substituting the components of T(t0) and N, we get:

-2sin(t0)√3 + 2cos(t0) + 0 = 0

Simplifying and rearranging, we get:

tan(t0) = 1/√3

Solving for t0 in the given range 0 ≤ t ≤ π, we get:

t0 = π/6

Substituting t0 into the equation of the curve, we get:

r(t0) = (2cos(π/6), 2sin(π/6), e^(π/6)) = (√3, 1, e^(π/6))

Therefore, the point on the curve where the tangent line is parallel to the plane √3x + y = 1 is (√3, 1, e^(π/6)).

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Answer:

1. 672 yds, 2. 117°, 3. 4.05 km, 4. 69.3 miles 5. 23 ft

Step-by-step explanation:

See attachment for 1 through 4

5. a²=b²+c²-2bc CosA

a²=(30)²+(20)²-2(20)(30) Cos50°

a=23 ft

Answer:

The last graph.

Step-by-step explanation:

The last graph because it shows the continum of time, and it shows him getting closer to the school (decrease in distance), then it shows him picking up Janet (staying constant), then it shows him going back home to grab his books (increase in distance), all as time goes on.

Answer:

(4, 4)

Step-by-step explanation:

y = 7/4 x - 3       graph (0, -3) (2, .5), (4, 4) (8, 11).  Draw the line

y = x                        graph (0,0)  (2, 2), (4, 4) , ( -2, -2).  Draw the line

The two lines intersect at point (4, 4)

Answer:

9.375 days

Step-by-step explanation:

Let d be the number of days the do 1 work(job). The speed A can do the job is (1/3)/(5)=1/3 × 1/5=1/15. The speed B can do the job is (2/5)/(10)=2/5 × 1/10=2/50=1/25. (These speeds have units work per 1 day)

So the amount of work done in d days for A is 1/15×d=d/15 and that same amount of days B does 1/25×d=d/25 work.

We are trying to figure out when they ddo 1 work together.

We need to solve

d/15+d/25=1

Multiply both sides by 75=least common multiple of 15 and 25.

75d/15+75d/25=75

Reducing:

5d+3d=75

Combine like terms:

8d=75

Divide both sides by 8:

d=75/8

d=9.375

The sum of the interior angles for a pentagon is 540°

Sum of Interior Angles of a Pentagon :

The interior angles of a pentagon sum up to 540 degrees.. Regardless of how regular or irregular the pentagon is, this is true. By dividing the whole amount by 5, we can calculate the size of each internal angle in the case of regular pentagons. To determine the measure of a missing angle in the situation of irregular pentagons, we must first know the measurements of other angles.

Any pentagon's internal angles add up to 540° in the same way. This holds true regardless of how regular or irregular the pentagon is. By using the polygon angle sum formula, the following sum is obtained:

(n-2)180(n−2)×180°

where n represents the polygon's number of sides. We have n = 5 in the case of a pentagon. Consequently, utilizing the formula:

=(n-2)180=(n−2) ×180°

= (5-2) 180= (5−2) ×180°

= (3) 180= (3) ×180°

= 540=540°

Consequently, a pentagon's interior angles add up to 540 degrees.

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Answer:

C

Step-by-step explanation:

-6(-2/3 + 2x)

= 12/3 = 4

4 is the answer to the first number times -6. This is because 2 negatives are equal to a positive.

-6 * 2x

= -12

So, it can be concluded that the answer is C

Answer:

$15

Step-by-step explanation:

Let A, B, C and D represent the four friends respectively.

Given the following data;

Amount earned by A = $15

Amount earned by B = $20

Amount earned by C = $25

Amount earned by D = $40

Total amount earned = 15 + 20 + 25 + 40

Total amount earned = $100

For an equal ration, each friend should be given;

Each earnings = total amount earned/number of friends

Substituting into the equation, we have;

Each earnings = 100/4

Each earnings = $25

Hence, for D with $40, would become;

D = $40 - $25

D = $15

Therefore, D would give A $10 and give B $5.

Answer:

4/3

Step-by-step explanation:

Slope is calculated by \(\frac{y1-y2}{x1-x2}\) so now you pul the points (10,2) and (19,14) into that.

\(\frac{14-2}{19-10}\) = \(\frac{12}{9}\)

12/9 can be simplified to be 4/3

Answer:

4/3

Step-by-step explanation:

Given,

Two points are (10,2) and (19,14)

To find the slope of the line passing through these points.

Answer:

d(x)= -x/2 - 3

Step-by-step explanation:

According to the information we can infer that the coordinates of the rotated shape are: a. (2, -2), b. (3, -3), c. (3, -5), d. (1, -5), e. (1, 3).

To rotate a point 90° clockwise in the Cartesian plane, we need to identify the new coordinates. Also we have to take into account that the values of the y axis are going to be negative. In this case, we can infer that the new coordinates are:

Also, the new shape is going to be horizontal in the IV cuadrant of the cartesian plane.

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Answer

Explanation

Given:

To determine the value of g(f(x)), we substitute x with 1/3x^2+4 for g=9x-12:

Therefore, the value of g(f(x)) is C:

Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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1. Solving for t in terms of a, b, and c by completing the square. Given 2+ bt + c = 0, solve for t in terms of a, b, and c by completing the square. (Hint: You will derive the quadratic formula as the solution.)Since the formula is in the form at2 + bt + c = 0, the quadratic formula is useful for solving it, which is: t = (-b ± sqrt(b2 - 4ac)) / 2a.

Plugging in values for a, b, and c, we have: t = (-b ± sqrt(b2 - 4ac)) / 2a and t = (-b ± sqrt(b2 - 4ac)) / 2(2).Simplifying, we obtain t = (-b ± sqrt(b2 - 4ac)) / 2a and t = (-b ± sqrt(b2 - 4ac)) / 4.2. Solving for t using the quadratic formulaGiven 3t2 + 4t + 12 = 0, solve for t using the quadratic formula. (Hint: Simplify the final answers as much as you can, but leave them exact in terms of square roots.

Do not expand to decimal approximations.)The quadratic formula is t = (-b ± sqrt(b2 - 4ac)) / 2a.We have a = 3, b = 4, and c = 12 when plugging into the quadratic formula.t = (-4 ± sqrt(42 - 4(3)(12))) / 2(3)t = (-4 ± sqrt(-80)) / 6t = (-4 ± 4i*sqrt(5)) / 6Where i is the imaginary unit, which is sqrt(-1).3. Finding its derivative function and its second derivative functionGiven the function x(t) = 4t2 + 3t + 1, find its derivative function v(t) = dt / dx (t) and its second derivative function a(t) = dt / dv (t) = dt2 / d2 x (t).

We can differentiate x(t) term by term to obtain v(t) = 8t + 3.To find a(t), we can differentiate v(t) to obtain a(t) = 8, which is constant and does not depend on t. 4. Graphing each function Graph of x(t) = 4t2 + 3t + 1:  Graph of v(t) = 8t + 3: Graph of a(t) = 8:

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Answer

put 1 on top and exo on bottom

Step-by-step explanation:

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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the indentation diagonal length is approximately 0.0686 units.

What is Intention Diagonal Length?

The indentation diagonal d is determined by the mean value of the two diagonals d 1 and d 2 at right angles to each other: To avoid the risk of bulging of the material on the opposite side of the sample, the thickness should not fall below a certain minimum value. value. The minimum thickness depends on the expected hardness of the material and the test load.

To calculate the indentation diagonal length using the Vickers hardness value, you need to know the applied load and the hardness number. The Vickers hardness test measures the resistance of a material to indentation using a diamond indenter.

In this case, you have the following information:

Load: 0.700 kg

Vickers HV: 650

The Vickers hardness number (HV) is defined as the applied load divided by the surface area of the indentation.

The formula to calculate the indentation diagonal length (d) is:

d = 1.854 * sqrt(L / HV)

Where:

d = indentation diagonal length

L = applied load in kg

HV = Vickers hardness number

Plugging in the values:

d = 1.854 * sqrt(0.700 / 650)

Calculating the square root and performing the division:

d ≈ 1.854 * 0.0370262

d ≈ 0.0686

Therefore, the indentation diagonal length is approximately 0.0686 units. Please note that the specific unit (e.g., millimeters) was not provided in the question, so the answer is given in relative units.

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Answer:

the volume at 606k is 2.22....the third one

Step-by-step explanation:

v1=1.00 t1=273 v2=? t2=606

v1/t1=v2/t2

1.00/273=v2/606

1.00×606=273v2

606=273v2

606/273=v2

2.21 L=v2

Answer: Points A, D, and G are collinear, meaning they all lie on the same line.

Step-by-step explanation:

Answer:

b.a rotation 270 clockwise

Step-by-step explanation:

The answers to the multiple-choice questions are as follows:

Converse: C. If you are not awake, then you are in class.

Inverse: OB. If you are not in class, then you are awake.

Contrapositive: OC. If you are awake, then you are not in class.

The converse, inverse, and contrapositive of the given statement "If you are in class, then you are not awake" are as follows:

Converse: If you are not awake, then you are in class.

The converse swaps the positions of the hypothesis and conclusion.

Inverse: If you are not in class, then you are awake.

The inverse negates both the hypothesis and the conclusion.

Contrapositive: If you are awake, then you are not in class.

The contrapositive negates both the hypothesis and the conclusion and swaps their positions.

Therefore, the answers to the multiple-choice questions are as follows:

Converse: C. If you are not awake, then you are in class.

The converse statement reflects the swapped positions of being awake and being in class.

Inverse: OB. If you are not in class, then you are awake.

The inverse statement reflects the negation of both being in class and being awake.  

Contrapositive: OC. If you are awake, then you are not in class.

The contrapositive statement reflects the negation of both being in class and being awake, while swapping their positions.

Note: The provided option "You are not in place or you are not awake" does not correspond to any of the converse, inverse, or contrapositive statements.

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The mean and standard deviation of the data sets are;

a. 60.83, 15.11

b. 44, 4.03

c. 7.2, 3.7

d. 114.4, 10.74

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The mean of a data is the average of the data across the points.

a. data set; 35, 50, 60, 75, 65, 80

mean = 60.83

standard deviation = 15.11

b. data set; 51, 48, 47, 46, 45, 43, 41, 40, 40, 39

mean = 44

standard deviation = 4.03

c. data set; 11, 7, 14, 2, 8, 13, 3, 6, 10, 3, 8, 4, 8, 4, 7

mean = 7.2

standard deviation = 3.7

d. data set; 135, 115, 120, 110, 110, 100, 105, 110, 125

mean = 114.4

standard deviation = 10.74

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Answer: 126 outfits

Step-by-step explanation: multiply all the numbers above

Step-by-step explanation:

Multiply all of the choices

  2 x 3 x 7 x 3 = 126 outfits

The correct answer is D. setne 23 47. Based on the provided information, I understand that you have a comparison function in C code and its corresponding assembly code. You are asked to fill in the blanks by selecting the appropriate instructions based on the given values of a and b and the status flags SF, OF, ZF, and CF. Let's go through the options:

A. setg 47 23: This option is incorrect because setg is used to set a byte to 1 if the Greater flag (ZF=0 and SF=OF) is set, but the given values of a and b are 47 and 23, respectively, so it does not satisfy the condition for setg to be set.

B. setl 23 47: This option is incorrect because setl is used to set a byte to 1 if the Less flag (SF≠OF) is set, but the given values of a and b are 23 and 47, respectively, so it does not satisfy the condition for setl to be set.

C. sete 23 23: This option is incorrect because sete is used to set a byte to 1 if the Zero flag (ZF=1) is set, but the given values of a and b are 23 and 23, respectively, so it does not satisfy the condition for sete to be set.

D. setne 23 47: This option is correct. setne is used to set a byte to 1 if the Zero flag (ZF=0) is not set, which means the values of a and b are not equal. In this case, the given values of a and b are 23 and 47, respectively, so they are not equal, and setne should be used.

Therefore, the correct answer is D. setne 23 47

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Answer:  30 students in the class.

Step-by-step explanation:

Domain is the set of all input values.

Given : A teacher writes a function to model the rate  of completion on a test .

C(n) represents  the completion rate

n represents the  number of students who have completed the  test over a class period.

Here , input variable = n

So, Domain= set of values for n

Since class has 30 students.

So, Domain = 30 students.

Hence, the appropriate domain of the function : 30 students.