A six-sided die has an unknown number of faces marked with a six. Let k be this unknown number, which we would like to estimate. Our prior distribution fork is P(k = j) = -0.4, j=1 and 0.1, j = 0,2,3,4,5,6, When the die is thrown each face has an equal chance of showing. The observed data is that the die was thrown twice, and it did not show a six either time. (a) Write down the likelihood for the observed data. What is the maximum likelihood estimate for k? (b) Derive the normalized posterior distribution for k. What is the posterior mean for k? (e) Find the posterior predictive probability that if the die is thrown again, it will not show a six.

Note that the proof that ΔABC ≅ ΔEDC is given as follows:

According to the ASA rule, if any two angles and sides included between the angles of one triangle are comparable to the corresponding two angles and sides included between the angles of the second triangle, the two triangles are said to be congruent.

Thus, given the above statements, it is clear that ΔABC ≅ ΔEDC

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Full Question:

Angle BAC is congruent to Angle DEC: Given

C is the midpoint of AE: Given

Prove triangle ABC is congruent to triangle EDC

What are the statements and reasons for this proof?

The complete equation is 3 lb/sec ≈ 4897.0806 kg/h.

From the question, we have the following parameters that can be used in our computation:

3 Ib/sec ≈ ? kg/h

To convert pounds per second (lb/sec) to kilograms per hour (kg/h), we can use the conversion factor: 1 lb = 0.45359237 kg.

So, 3 lb/sec = 3 * 0.45359237 kg/sec = 1.361 kg/sec

To convert from per second to per hour, we multiply by the number of seconds per hour:

1.3607771 kg/sec * 3600 sec/hour = 4897.0806 kg/h

Therefore, 3 lb/sec ≈ 4897.0806 kg/h.

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A stick has a length of 5 units and the stick is then broken at two points, chosen at random, then the probability that all three resulting pieces are shorter than 3 units is 16%.

Total length of the stick = 5 units

The stick is broken into pieces = 3

The equal length of the stick = 5/3

The equal length of the stick = 1.67

The probability that all three resulting pieces are shorter than 3 units = 2/5 × 2/5

The probability that all three resulting pieces are shorter than 3 units = 4/25

The probability that all three resulting pieces are shorter than 3 units = 0.16

The probability that all three resulting pieces are shorter than 3 units = 16%

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The amount of RNA transcribed from promoter gene, which can consequently influence the amount of protein made from this gene. So the option c is correct.

A gene's DNA sequence is duplicated during transcription in order to create an RNA molecule.

The primary transcribed enzyme is called RNA polymerase.

RNA polymerase connects to a promoter sequence close to the start of a gene to start transcription (directly or through helper proteins).

A new, complementary RNA molecule is created by RNA polymerase using a template from one of the DNA strands (the template strand).

Termination is the procedure that brings transcription to a conclusion. The RNA sequences that indicate that the transcript is done are what determine when a process is terminated.

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The complete question is:

How frequently RNA polymerase binds to DNA sequence

a. length of RNA transcribed from the gene

b. precise sequence of RNA transcribed from this gene

c. amount of RNA transcribed from promoter gene, which can consequently influence the amount of protein made from this gene

A graph of the equality that models the number of pizzas they can make is shown in the image attached below.

The three (3) possible solutions include the following:

In order to write an equation that model this situation, we would assign variables to the small pizza shop and the large pizza shop respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that the small pizza makes use of 12 ounces and a large pizza uses 18 ounces of dough as follows;

12x + 18y = 4800

Next, we would use an online graphing calculator to plot the above algebraic equation as shown in the graph attached below

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Her bi-weekly gross earnings if she works 47 hours during a week of her pay period is $4110.525.

The answer is determined by calculating the income earned for the additional hours she works multiplied by the income earned for the additional hours. This is then added with the gross income for the week and the total is calculated by taking the sum of the two.

Given that her bi-weekly gross earnings are $913.45, and she earns additional compensation for all hours over 40 worked in one week.

For 47 hours, the extra hours worked are 7.

Hence, the compensation for additional hour is:

a = 7 (913.45/2)

a = 3197.075

The gross income would be:

Total = bi-weekly pay + additional hours

T = 913.45 + 3197.075

T = 4110.525

Hence, her bi-weekly gross earnings if she works 47 hours during a week of her pay period is $4110.525.

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The number of pounds in 32 kg would be 70.5479.

A pound is an imperial unit used to measure bulk or weight. A kilogram is a metric measuring unit. The letters lb and lbm stand for pounds. Kilo or kg are used to denote kilograms. 0.4535 kilograms make up one pound.

In both the British imperial system and the United States' customary system, weight is measured in pounds. Measuring a person's weight is one common application of pounds.

The weight of a kilogram is 2.2046 pounds. We convert kilograms (kg) to pounds (lb) using the formula 1 kg = 2.2 lb. By multiplying by 2.2, we may convert a kilogram to a pound. We divide by 2.2 to change a pound into a kilogram.

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The probability that both quartz and tourmaline will be found, but not aquamarine is P(A intersection B) = P(A)*P(B) = 0.80 * 0.36 = 0.29.

The Venn diagram for this situation is as follows:

A: Quartz specimens are found  _____

B: Tourmaline specimens are found  ____

C: Aquamarine specimens are found ____

The probability that both quartz and tourmaline will be found, but not aquamarine is P(A intersection B) = P(A)*P(B) = 0.80 * 0.36 = 0.29.

The probability that quartz will be found, but not tourmaline or aquamarine is P(A) – P(A intersection B) – P(A intersection C) = 0.80 - 0.29 - 0.24 = 0.27.

The probability that none of these types of specimens will be found is 1 – P(A) – P(B) – P(C) + P(A intersection B) + P(A intersection C) + P(B intersection C) = 1 - 0.80 - 0.36 - 0.28 + 0.29 + 0.24 + 0.16 = 0.17.

The probability of A intersection (B union C) is P(A)*P(B union C) = P(A)*(P(B) + P(C) – P(B intersection C)) = 0.80 * (0.36 + 0.28 – 0.16) = 0.41.

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A rectangle with sodes of lengrh 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon

(A) 41

(B) 46

(C) 43

(D) 45

(E)Other

A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure

(A) 40

(B) 25

(C) 60

(D) 35

(E)Other

A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q

(A) 5

(B) 19

(C) 37

(D) 47

(E)Other

The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence

(A) 25/12

(B) 9/4

(C) 7/4

(D) 2

(E)Other

one-sided limits of a function f(x) at x = 1 is  lim x → 2[f(x) - f(2)]/(x - 2) = 20

Since  function f(x) = 5(x² - 1) and we want to find its derivative, we can proceed thus.

Let x = h + 2

So,  

f(x) = 5(x² - 1)

f(2) = 5[(2)² - 1]

= 5[4 - 1]

= 5(3)

= 15

f(2 + h) = 5[(2 + h)² - 1)

= 5(4 + 4h + h² - 1)

= 5(3 + 4h + h²)

= 15 + 20h + 5h²

So, f(2 + h) - f(2) = 15 + 20h + 5h² - 15

= 20h + 5h²

So, we have that

[f(2 + h) - f(2)]/h = (20h + 5h²)/h

= 20 + 5h

Now, taking the limit as h → 0, we have

= 20 + 5(0)

= 20 + 0

= 20

So,  lim h → 0[f(2 + h) - f(x)]/h = lim x → 2[f(x) - f(2)]/(x - 2) = 20

So,  lim x → 2[f(x) - f(2)]/(x - 2) = 20

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Answer: I think you got number 1 correct.

Step-by-step explanation: I think you can search online XD.

Using the US customary system, 1 tablespoon is equivalent to 0.5 fluid ounces. A tablespoon is equivalent to 0.5 fluid ounces. According to the Imperial system, 1 imperial tablespoon is equal to 0.625 imperial ounces.

By multiplying the quantity of US tablespoons by 0.5—0.5 is a conversion factor—you can convert US tablespoons to fluid ounces:

the tablespoon times 0.5.

Multiply the amount of tablespoons by 0.625, where 0.625 is a conversion factor, to convert imperial tablespoons to imperial ounces:

by 0.625 times the tablespoon.

Consider an illustration. The US measurement system is applied to all computations below.

How many ounces are in two tablespoons?

2 tablespoons multiplied by 0.5 equals 1 fluid ounce, thus

two teaspoons make up one fluid ounce.

This table translates a quantity in teaspoons (tbsp) into fluid ounces (fl oz).

Tablespoons Ounces Tablespoons Ounces

8 tbsp of 1/2 teaspoon 0.25 fluid ounces

2 tbsp 1 fl ounce 10 tbsp 5 fl oz, 1 tbsp 0.5 fl oz, 9 tbs 4.5 fl oz, and 2 tbs 1 fl oz

3 tbsp 1.5 fl oz, 12 tbsp 6 fl oz

4 tbsp./2 fl. oz.

14 tbsp 7 fl oz, 5 tbsp 2,5 fl oz, and 16 tbsp 8 fl oz, along with 6 tbsp 3 fl ounce

17 tablespoons, 9 fluid ounces, 7 tablespoons, and 20 tablespoons

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Lisa’s average speed is: 11.4 miles/hours

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formulas and procedures we will use to solve this exercise are:

Where:

Given info:

Applying the time formula we get:

t2= 135 mi / 15 mi/h

t2= 9 h

Calculating t1 we get:

t1= 9h -1 h

t1= 8 h

Applying the average velocity formula we get:

vm= x(total)/t(total)

vm= (60 mil + 135 mil) /( 9h + 8h)

vm= 195 mil/17 h

vm= 11.4 mil/h

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Answer: the smallest number out of the four is 0.13

Step-by-step explanation:

First, let's think about the number 13. It's a whole number and it's pretty big. It's definitely larger than the other numbers we're looking at today.

Next, let's take a look at 0.13. This number is a decimal, which means it's a number that has a whole number part and a fractional part. The whole number part is 0 and the fractional part is 13. So, 0.13 is smaller than 13.

Now, let's move on to 1.03. This is also a decimal and it's a little bit bigger than 0.13, but smaller than 13.

Finally, we have 1.3. This number is a decimal with a whole number part of 1 and a fractional part of 3. It is bigger than 0.13 and 1.03 but smaller than 13.

So, we can see that the smallest number out of the four is 0.13.

Answer: 3x^2 + x + 2

Step-by-step explanation:

The intersection of events A and B is the event of exactly two tails. This is because event A is defined as exactly two tails and event B is defined as at least two tails.

Since two tails is both exactly two tails and at least two tails, the intersection of the two events is exactly two tails.

The intersection of two sets is the set of all elements that are common to both sets. This is also known as the intersection of two conjunctions. To find the intersection of two sets, you take the elements from both sets and keep only the elements that are found in both sets. For example, given the sets A = {1, 2, 3} and B = {2, 3, 4}, the intersection of A and B would be {2, 3}.

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The required total number of innings are 7.5.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

We have,

1 (2/3) innings on Monday and 3 (1/3) innings on Wednesday.

Total innings =  1 (2/3) +  3 (1/3)

= 5/2 + 10/2

= 15/2

= 7.5 innings.

Thus, total innings are 7.5.

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Answer:

B

Step-by-step explanation:

Linear equations are straight lines and exponential equations are curves. Since this is a curve, we can get rid of A and C

Looks like the graph is a downwards line, so decreasing

Answer: 10/12

Step-by-step explanation:

Make 1/4 have the same denominator as 7/12. 1/4=3/12. 7/12+3/12 = 10/12

The probability that she will select a chicken would be =7/23.

Probability is defined as the expression that represents that possible outcome of an event.

The amount of pigs in the farm = 6

The amount of chicken in the farm = 7

The amount of cows in the farm = 10

The total animals in the farm = 10+7+6 = 23

The probability of selecting a chicken out from the whole farm = 7/23.

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Complete question:

Giovanna owns a farm. She is going to randomly select one animal to present at the state fair. She has 6 pigs, 7 chickens, and 10 cows. What is P (chicken) ?

The equation of the line that passes through two points (1, 4) and (3, 10) is,

y = 3x + 1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line passes through two points (1, 4) and (3, 10).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

y - 4 = 6/2 (x - 1)

y = 3x + 1

Therefore, the equation of the line is y = 3x + 1.

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Answer:

it is B

Step-by-step explanation:

It is B the answer is B you can make sure by using distance formula.

Therefore , the solution of the given problem of domain comes out to be its range is [2,-2] and domain is [-1.5,-4].

A function's domain is the range of possible arguments that it can receive. These integers indicate the cross of a functional like f. (x). The range of potential values that can be used with a function is known as its domain. The value that method returns after inserting the x value belongs to this set. The formula for a function with y as the predictor variables and x as the predictor variables is y = f. (x). When a single value of y can be successfully produced from a value of x, that value is said to be in the domain of the function.

Here,

Given :

A graph with the extreme values of 2 and -2.

So.

Its range is [2,-2]

and

its start from [-1.5,-4]  

so its domain is [-1.5,-4] .

Therefore , the solution of the given problem of domain comes out to be

its range is [2,-2] and domain is [-1.5,-4].

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The relation's domain is 0, 1, 2, 3, and 4.The relation's range is: 0, 1, 4, 9, and 16.

The set of x-values or relational inputs can be thought of as the domain of a relation.

The collection of all results, or y-values, that match an ordered set of pairs' x-values.

With respect to the relationship, (0, 0), (1, -1), (2, -4), (3, -9), and (4, -16)

The relation's range is 0, 1, 2, 3, and 4. (these are all the input of the relation).

The relation's range is: 0, 1, 4, 9, and 16 (these are all the output of the relation).

The relation's domain is 0, 1, 2, 3, and 4.The relation's range is: 0, 1, 4, 9, and 16

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Tthe required simplified solution of the given expression is -3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression
=  -3(9)⁰
= -3(1)     [a⁰ = 1]
= -3

Thus, the required simplified solution of the given expression is -3.

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Answer: The Fourth One

Step-by-step explanation:

Answer:

Bottom right corner

Step-by-step explanation:

The coordinate of the point P that lies on the line segment AB will be (-1, -1).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

Given the points A(-4, 1) and B(8, -7). AP to PB is in the ratio of 1 to 3. Then the coordinate of the point P is given as,

x = (1 × 8 + 3 × (-4)) / (1 + 3)

x = (8 - 12) / 4

x = -4 / 4

x = -1

y = (1 × (-7) + 3 × 1) / (1 + 3)

y = (- 7 + 3) / 4

y = -4 / 4

y = -1

The coordinate of the point P that lies on the line segment AB will be (-1, -1).

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The required simplified value of the f + g(x) =  3x² + 5x + 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x)=3x²-2x+6

g(x) = 7x - 4

f+g = f(x) + g(x)
      = 3x²-2x+6 + 7x - 4
      = 3x² + 5x + 2

Thus, the required simplified value of the f + g(x) =  3x² + 5x + 2.

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It takes the runner distance 15.625 seconds to get to the flagpole because 125m/8m/s equals 15.625s.

1. Determine the distance: 125 metres

2. Determine the velocity: 8 m/s

3. Calculate the time as follows: 125 m/ 8 m/s = 15.625 s

We must know the distance the runner must cover and their pace in order to determine how long it will take them to get to the flagpole. This time, the runner begins 125 metres west of the flagpole and moves east at a speed of 8.0 metres per second. The formula distance (in meters)/speed (in metres per second) = time can be used to determine how long it takes the runner to get to the flagpole (in s).  Given that the speed is 8 m/s and the distance is 125 m, the calculation is 125 m/ 8 m/s = 15.625 s. It follows that the runner needs 15.625 seconds to get to the flagpole. This formula can be used to determine how long it will take any object to go a specific distance at a specific speed. It is crucial to remember that in order to obtain the duration in s, the speed must be expressed in m/s and the distance must be expressed in m.

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The sketch of the function z = 6 − 2x − 3y is illustrated below graph.

The term in math called function is defined as special relationship where each input has a single output.

Here we have the function as z = 6 − 2x − 3y

Now, we have to plot the function into graph.

In order to plot the graph, first we have to identify the variable in the function here in the function we have 3 variable. then we plot the graph on the 3 dimensional plane.

If you want to understand how to draw 3−D plot, then assume one of the coordinate is zero and draw line of remaining two coordinate,

In a similarly draw for other two coordinates too, you will get purview of

3−D plot of that function that has been look like as follows.

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