how many hexadecimal strings of length 9 have exactly three a’s, no b’sand two 7’s

Answers

Answer 1

There are approximately 368,739,406 possible hexadecimal strings of length 9 with exactly three a’s, no b’s and two 7’s.

Hexadecimal is a numbering system that uses 16 symbols (0-9 and A-F) instead of the standard 10 symbols in decimal.

A hexadecimal string of length 9 with exactly three a’s, no b’s and two 7’s can be represented as

=> XaXaXaX7X7,

where X can be any of the hexadecimal symbols other than a and 7.

To calculate the number of possible combinations, we need to calculate the number of possible values for X.

In total, there are 16 possible hexadecimal symbols, but we need to subtract 3 (a’s) and 2 (7’s) to find the number of possible values for X.

So, the number of possible values for X is

=> 16-3-2 = 11.

With 9 positions to fill and 11 possible values for X, the total number of combinations is 11⁹, which is approximately 368,739,406.

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Related Questions

Select 2 points in the solution of the inequality graphed below.
654
4
-241
2
X

Answers

The two points that represent the solution of the inequality graph are (-1,0) and (0,2).

What are the function and the solution to the inequality graph?

The function of an inequality graph obeys the linear slope intercept form y= mx + b, but the distinction here is that the equal to sign (=) is represented with >, <, ≥, and ≤, as the case may be. So, we use, > and < when the line is dotted or dashed and  ≥, and ≤, when we have a solid line on the graph.

So, using the two points on the (-1,0) and (0,2), the slope of the graph is 2, and the y-intercept is also 2.

The linear representation of the graph is: y = 2x + 2, in its inequality form, sInce the graph is increasing from the left to the right and the line is solid; we have:

y  ≥ 2x + 2

Therefore, we can conclude that the function of the graph is y  ≥ 2x + 2 and the two points that represent the solution of the inequality graph are (-1,0) and (0,2).

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help ima fail if i dont pass thisssssss

Answers

Answer:A

Step-by-step explanation:

Violet invested $5,900 in an account paying an interest rate of 7\tfrac{1}{2}% compounded quarterly. Nachelle invested $5,900 in an account paying an interest rate of 6\tfrac{7}{8}% compounded continuously. After 10 years, how much more money would Violet have in her account than Nachelle, to the nearest dollar?

Answers

The difference between the amounts of Nachelle and violet is $670.31

What is compound interest?

Starting young lets the students take advantage of the magic of "compound interest." Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

Given here: Violet invested $5900 at 7.5% interest and Nachelle invested the same amount but at 6.875 %

After 10 years Violets Amount when compounded quarterly we get

A= 5900×(1+7.5%)⁴⁰

  =$12,403.86

Similarly after 10 years Nachelle's amount if it is compounded contionously we get

[tex]P(t)=P_{0}e^{rt}[/tex]

[tex]P(10)=5900e^{0.06875*10}\\ =11733.55[/tex]

∴The difference between their amounts is$12,403.86-11733.55=$670.31

Hence, The difference between the amounts of Nachelle and violet is $670.31

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Answer:670

Step-by-step explanation:

ABCD is a parallelogram
CE=CF
Prove that y=x

Answers

Step-by-step explanation:

ABCD:-

CE=CF

Prove:y=x

y=x (x is opposite to y)

x=y

Hence,x=y and y=x.

-4x+7y=3
x intercept and y intercept
(,) (,)

Answers

rAnswer: x-intercept: (-0.75, 0)

y-intercept: (0, 3/7)

Step-by-step explanation: An x and y intercept is the point when the line crosses the x and y axis respectively. When a line crosses the x axis, the y value is 0 and when the line crosses y axis, the x value is 0. This means   we can set y and x equal to 0 and solve for the other variable.

To solve for the x intercept, we set y equal 0 so:

-4x + 7(0) = 3

-4x = 3

x = -(3/4)

so we get

(-3/4, 0) or (-0.75, 0) for our x int

For the y intercept we set x equal 0:

-4(0) + 7y = 3

7y = 3

y = 3/7

so we get

(0, 3/7) for our y int

Which ordered pair is a solution of the inequality y < 3x + 1

Answers

Answer:

C

Step-by-step explanation:

X has to be bigger than Y. For the first one Y is bigger. The next one Y is also bigger so find one where X is bigger. The answer is C.

Answer:Answer is Letter C., check picture for steps

Step-by-step explanation:

If you need help please let me know at my discord

Acathia#0103

Please help precal problem!

Find the value of side a.

A) 2.770

B) 3.516

C) 5.760

D) 7.309

E) None of these

Answers

Therefore , the solution of the given problem of triangle comes out to be a value is 3.5154 unit.

What does a triangle actually mean?

Triangles are polygons because they have four sides or more. Its form is simple and geometric. An angle square with the letters ABC is known as a triangle. When the sides remain not collinear, Euclidean geometry generates a singular plane or square. Having three parts and three corners makes a triangle a polygon. The corners of a triangle are where the three sides meet. Angles in a triangle add up at 180 °.

Here,

Given :

=> Tan 38° =  a/4.5

=> 0.7812 = a /4.5

=> a = 4.5 * 0.7812

=> a = 3.5154 unit

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

a value is 3.5154 unit.

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the linear regression coefficient of x on y is beta. what is the range of regression coefficient of y on x?

Answers

The range of the regression coefficient of y on x is (-∞, ∞).

The parameter β (the regression coefficient) represents the amount by which change in x must be multiplied to give the interconnected average change in y or the amount y changes for a unit increase in x. In this manner, it represents the degree to which the line slopes upwards or downwards.

The regression coefficient of x on y, β, represents the change in y per unit change in x. The regression coefficient of y on x, β', represents the change in x per unit change in y.

The range of the regression coefficient of y on x is (-∞, ∞). This is because the relationship between x and y can be positive, negative, or zero, leading to positive, negative, or zero regression coefficients.

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Special right triangles pls help

Answers

Answer:

Step-by-step explanation:

4. short leg= 4

      hyp= 8

5. leg 2= 5

    hypotenuse= 5√2

6. both legs = 2√2

a triangular prism is 6.9 millimeters long. it has a triangular face with a base of 15 millimeters. the volume of the prism is 388.125 cubic millimeters. what is the height of its triangular face?

Answers

The height of its triangular face is 7.5 millimeters.

As per the given data:

A triangular prism is 6.9 millimeters long.

l = 6.9 millimeters

A triangular face with a base of 15 millimeters.

b = 15 millimeters

The volume of the prism is 388.125 cubic millimeters.

V = 388.125 cubic millimeters

Here we have to determine the height of its triangular face.

h = ?

A polyhedron with two triangular bases and three rectangular sides is referred to as a triangular prism. It is a three-dimensional shape with three connected side faces and two connected base faces.

The formula for the volume of the triangular prism is:

V = [tex]$\frac{1}{2}[/tex] × ( l × b × h)

388.125 = 0.5 × ( 6.9 × 15 × h)

388.125 = 51.75 × h

h = [tex]$\frac{388.125}{51.75}[/tex]

h = 7.5 millimeters.

Therefore height is 7.5 millimeters.

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using a discount rate of 6.5 percent, calculate the present value of a $1,000 profit payment to be received at the end of a. one year b. two years c. three years

Answers

​Future Value received at the end of  one year is 1065

Future Value received at the end of  two year is 1134.225

​Future Value received at the end of  three year is 1207.949

 discount rate of 6.5 percent

  present value of a $1,000

Present Value= [tex]\frac{FV}{(1+r)^{n} }[/tex]

​where:

FV=Future Value

r=Rate of return

n=Number of periods

Future Value received at the end of  one year

Future Value= Present Value * [tex](1+r)^{n}[/tex]

                      =  1000 * (1+ 6.5%)^1

                     =  1000* 1.065

                      = 1065

Future Value received at the end of  two year

Future Value= Present Value * [tex](1+r)^{n}[/tex]

                      =  1000 * (1+ 6.5%)^2

                     =  1000* 1.065^2

                      = 1000 * 1.134225

                      = 1134.225

​Future Value received at the end of  three year

Future Value= Present Value * [tex](1+r)^{n}[/tex]

                      =  1000 * (1+ 6.5%)^3

                     =  1000* 1.065^3

                      = 1000 * 1.207949

                      = 1207.949

Future Value received at the end of  one year is 1065

Future Value received at the end of  two year is 1134.225

​Future Value received at the end of  three year is 1207.949

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Are these equivalent? Please help!

Answers

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Solution:

We need to simplify the following expression: (5-7y+10)1/5

[tex]\frac{(5-7y+10)*1}{5}[/tex]

Grouping together numerical values

[tex]\frac{(-7y+5+10)*1}{5}[/tex]

We reduce the integers that can be added together: 5+10=15

= [tex]\frac{(-7y+5+10)*1}{5}[/tex]

By reorganizing/simplifying/expanding the terms that are amenable to

[tex]3 -\frac{7}{5}y[/tex]

Answer:

Yes they are in fact equivalent.

(Hope this helped!)

A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Progressive
Range ($)
Tax Rate
0
2000
2%
2001 - 9000
5%
9001 and
up
5.4%
Calculate the state income tax owed on a $60,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.

Answers

The amount of state income tax owed on a $60,000 per year salary is $3,000.

What should we know about Progressive tax?

A progressive tax is one in which the tax rate rises in proportion to the taxable amount. The term progressive refers to the manner in which the tax rate rises from low to high, resulting in a taxpayer's average tax rate being less than the person's marginal tax rate.

We are given that the income is $60,000. The applicable Progressive tax for this income range is 5%.

The state income tax owed on a $60,000 per year salary goes as follows:

= $60,000 * 5%

= $3,000

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Type the correct anwer in each box. Ue numeral intead of word. Conider thi expreion

Answers

Using numerals instead of words. Consider this expression |m² - 7| + n² is given by 28.

Given is the expression |m² - 7| + n²

where m = -2 and n = 5

so putting value in the expression

⇒|m² - 7| + n²

⇒|(-2)² - 7| + 5²

⇒|4-7| + 25

⇒| -3| +25

⇒3 + 25

⇒28

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between.

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The bar diagram shows how the circumference C of a circle relates to its diameter d. How does the bar diagram connect to the formula C = πd?​

Answers

The bar diagram connect to the formula C = πd by taking π as 3

How to determine teh connection between the bar diagram and the formula

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

C = πd

Also from the bar diagram, we have

C = 3d

When the equations are compared, we have

C = πd = 3d

This gives

π = 3

Hence, the value of π is 3

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-10(2m+1)=-50

solve for m

Answers

Answer:

Step-by-step explanation: Distributing the -10 to the parentheses, we get:

-20m -10 = -50

Adding 10 to both sides:

-20m = -40

dividing both sides by -20:

m = 2

So the solution for m is 2.

Answer:

-7

Step-by-step explanation:

Distribute the -10: -20-10m=50

Add 20 to both sides: -10m=70

Divide by -10 to isolate 70

m = -7

REGAN SOLD 14 NECKLACES AND MADE A TOTAL 210 IF EACH NECKLACE COST THE SAME COUNT HOW MUCH DID ONE NECKLACE COST

Answers

Answer: £15

Step-by-step explanation:

210/14 = 15

to check :14x15=210

Answer: One necklace costs $15

Step-by-step explanation:

We know Regan sold 14 necklaces but we do not know how many, we can use "x" to represent the amount of necklaces sold.

We will use the equation 14(x)=210 to represent our word problem

Use PEMDAS and divide both sides by 14, this will give you x=15

$15 per necklace is the answer

player a has a 50 sided die, player b as a 40 sided die. whoever gets the higher roll wins with the tie going to player a. what's the probability that player a wins?

Answers

The probability that player a wins is approximately 0.189 or 18.9%.

Probability of Winning Dice

The probability of Player A winning can be calculated by adding the probability of both players rolling different values and Player A getting a higher value, as well as the probability of both players rolling the same value (in which case Player A wins by default).

To calculate the probability of both players rolling different values and Player A getting a higher value, we can calculate the probability of each possible combination of rolls and sum them up. There are a total of 50 * 40 = 2000 possible combinations of rolls. Out of these, 50 of them result in Player A rolling the highest value, and 400 result in Player B rolling the highest value. Therefore, the probability of Player A winning in this scenario is 50 / (50 + 400) = 50 / 450 = 1/9.

The probability of both players rolling the same value can be calculated as the minimum of the number of sides of the two dice, which is 40, divided by the maximum number of sides, which is 50. Therefore, the probability of both players rolling the same value is 40/50 = 8/10.

Finally, the overall probability of Player A winning can be calculated as the sum of the above two probabilities:

P(Player A wins) = P(different values and Player A higher) + P(same values)

= 1/9 + 8/10

= 17/90

= approximately 0.189 or 18.9%.

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using (tr-tc) approach, what is the maximum number of workers to attain maximum profit. why?

Answers

The TR-TC approach helps firms determine the optimal level of output and the corresponding number of workers needed to maximize profit. By finding the level of output where MR = MC, firms can ensure that they are producing the right amount of output at the lowest possible cost, thereby maximizing their profit.

The Total Revenue (TR) and Total Cost (TC) approach is used to determine the optimal level of output and the corresponding number of workers for a business to maximize its profit. This approach is based on the principles of microeconomics, which states that a profit-maximizing firm will produce the level of output at which its marginal cost (MC) equals its marginal revenue (MR).

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Find the angle between 0 degrees and 360 degrees that is coterminal with the following angle 0=-1625 degrees

Answers

The angle between 0 degrees and 360 degrees that is coterminal with the following angle 0=-1625 degrees is 175.

What are coterminal angles?

Angles on the same side of the same quadrant are said to be coterminal angles. We repeatedly add or subtract a 360° full revolution from the supplied angle in order to discover an angle that is coterminal with it.

To determine a coterminal angle with the provided angle between 0tp 360 we add 360 to the given angle:

-1625 + 360(5) = 175

Hence, the angle between 0 degrees and 360 degrees that is coterminal with the following angle 0=-1625 degrees is 175.

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Triangle ABC i an iocele triangle. AB = BC
mB = 34°

What i mA?


A. 34°
B. 56°
C. 73°
D. 112°

Answers

In Triangle ABC which is an Isosceles triangle. AB = BC where mLB = 34° so mLA = 73°

Triangles that have at least two sides of equal length are said to be isosceles.

Sum of all angle of a traingle is 180°

So mLA + mLB +mLC = 180

2(mLA) + mLB = 180

2(mLA ) = 180 - 34

2(mLA ) = 146

mLA = 73°

An isosceles triangle has three angles, which, like other triangles, sum up to 180 degrees. The angles other than the apex angle among the three inner angles are identical in size. According to the isosceles triangle theorem, an isosceles triangle has equal-sized angles on either side of its equal sides. As a result, we have B = C in the isosceles triangle ABC where AB = AC.

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can anyone categorize these polynomials?

Answers

The given polynomials are discussed and grouped into each given category as given below.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

We can now look into each polynomial.

a) x³ + 125

   125 is a cube of 5 and also  x³  is the power of x.

So this is a perfect cube.

b) 8p³ - 27

    8p³ is a perfect cube of 2p and 27 is a perfect cube of 3.

So it is a perfect cube.

c) 12x³-9

    This is neither a cube nor a square.

d) a²-100

   100 is a perfect square and so is a².

So this is a difference of perfect squares.

e) 4m² + 25

4m² is a square of 2m and 25 is a square of 5.

But the operator is +

So this is neither a cube nor a difference of a perfect square.

f) 16x²-9

16x² is a square of 4x and 9 is a square of 3.

Also, the operator is -

So this is a difference of perfect squares.

Therefore the above polynomials are discussed and grouped into each given category accordingly.

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a group of 14 babies contains 6 boys and 8 girls, including evie and ben. in how many ways can i select 6 of the babies if i want to choose

Answers

There are ${14 \choose 6}$ ways to select 6 of the babies from the group of 14, including Evie and Ben.

The question is asking how many ways there are to select 6 of the 14 babies from the group if Evie and Ben are included. This can be solved using the formula for combinations, which is ${n \choose r}$, where n is the total number of items and r is the number of items being selected. In this case, n = 14 and r = 6. Therefore, the answer is ${14 \choose 6}$. This means that there are 1001 ways to select 6 of the 14 babies, including Evie and Ben. To solve this, first the formula is used. Then, the total number of items, 14, is plugged into the formula. Finally, the number of items being selected, 6, is plugged into the formula. This yields the final answer of ${14 \choose 6}$.

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what is the value of x A.26 B.39 C.67 D.78

Answers

The value of x is 39.

What are Alternate Interior Angles?

Alternate interior angles are the angles formed by the intersection of a transversal line with two parallel lines on the plane.

Alternate interior angles are formed on the inner side of the two parallel lines but are on the opposite side of the transversal line.

From the given figure, we have two parallel lines and two transversal lines and thus we can find alternate interior angles.

Alternate interior angles are always equal.

Angles formed by 2x° + 56° and the angle 134° are alternate interior angles and are thus equal.

2x° + 56° = 134°

2x = 134 - 56

2x = 78

x = 39

Hence the value of x is 39.

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to avoid a possible collision with a manned airplane, you estimate that your small ua climbed to an altitude greater than 600 feet agl. to whom must you report the deviation?

Answers

If you operate a small unmanned aircraft (UA) and deviate from your approved flight plan greater than 600 feet agl to avoid a possible collision with a manned airplane, you may need to report the deviation to;

the Federal Aviation Administration (FAA).

The FAA requires all small UAs to comply with certain regulations and guidelines, including the requirement to maintain an altitude of no more than 400 feet above ground level (AGL) unless otherwise authorized.

If you deviate from your approved flight plan, such as by climbing to an altitude greater than 600 feet AGL to avoid a possible collision with a manned airplane, you may need to report the deviation to the FAA.

It is important to follow all FAA regulations and guidelines for small UAs to ensure the safety of other aircraft and people on the ground. If you are unsure about how to report a deviation or what regulations apply to your specific UA, you can contact the FAA for guidance.

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dr. martinez conducted a survey to determine the frequency of sexual activity among the american middle class. he collected data from several individuals working at various multinational companies and concluded that an average middle-class american engages in sexual activity once in a week. in this scenario, dr. martinez's research sample is most likely a

Answers

If Dr.Martinez conducted a survey to determine the frequency of sexual activity among the American middle class and collected data from several individuals working at various multinational companies then the research sample is most likely a Convenience Sample .

A Convenience Sample is defined as a type of non-probability sampling method where the researcher selects the sample based on ease of access or availability.

In this survey , Dr. Martinez collected data from individuals who were readily available to him, such as people he knew working at various multinational companies, rather than using a method that would allow him to randomly select a representative sample of the middle class.

The results of this study cannot be generalized to the entire middle class population, as the sample may not be representative of the population.

Therefore , the the research sample is a Convenience Sample .

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write quadratic equation in standard form given vertex (-1, -6) (1 , 2)

Answers

The quadratic function with vertex (-1,-6), that passes through (1,2), is given as follows:

y = 2x² + 4x - 4.

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which:

h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.

Considering the vertex at x = -1, y = -6, the parameters h and k are given as follows:

h = -1, k = -6.

Hence:

y = a(x + 1)² - 6.

When x = 1, y = 2, hence the leading coefficient a is obtained as follows:

2 = a(2)² - 6

4a = 8

a = 2.

Hence:

y = 2(x + 1)² - 6.

In standard form, we have that:

y = 2x² + 4x + 2 - 6

y = 2x² + 4x - 4.

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This seems a bit long, but it's not really. I will be very grateful if you can help me ( ____'s need to be filled in )You go to the health center where both Doctor A and Doctor B independently (i.e. you have separate appointments with each of them) consider the possibility that you have cogscitis, a brain condition caused by a virus. Doctor A gives the hypothesis that you do have cogscitis a prior probability of 0.70 (so, the prior probability of the not-cogscitis hypothesis is 0.3). Doctor B gives the cogscitis hypothesis a prior probability of 0.20.The doctors each order three tests, and the results come back sequentially: the results of test 1 come back first, the results of test 2 come back second, and the test 3 results come back third. The Doctors both engage in Bayesian updating after seeing the results of each test.What is Doctor B's prior probability for the hypothesis that you do not have cogscitis? ___Test 1 comes back first, and it is positive. Here are the likelihoods for the positive result for Test 1:Hypothesis Probability of positive test result given hypothesiscogscitis 0.70not cogscitis 0.10After getting the results from Test 1, what is Doctor A's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.____After getting the results from Test 1, what is Doctor B's posterior probability for the hypothesis that you DO have cogscitis? Round your answer to two decimal places.____After observing the positive result for Test 1, what best explains the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis?a) Doctor B thought the false positive rate for test 1 was higher than Doctor A.b) Doctor A thought a positive test result was more likely, given the cogscitis hypothesis, than Doctor B.c) Doctor A thought the hypothesis that you have cogscitis was more probable than Doctor B before either of them saw the results from Test 1.d) Doctor B's prior prior probability for the cogscitis hypothesis was higher than Doctor A's.

Answers

The best explanation for the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis is that Doctor A thought the hypothesis that you have cogscitis was more likely than Doctor B before either of them saw the results from Test 1.

After getting the results from Test 1, Doctor A's posterior probability for the hypothesis that you have cogscitis can be calculated as follows:

P(cogscitis|test 1 positive) = (P(test 1 positive|cogscitis) × P(cogscitis)) / P(test 1 positive)

where P(cogscitis) = 0.70 (Doctor A's prior probability) and P(test 1 positive|cogscitis) = 0.70 (probability of positive test result given cogscitis).

P(test 1 positive) can be calculated as the sum of probabilities of getting a positive result for both hypotheses:

P(test 1 positive) = P(test 1 positive|cogscitis) × P(cogscitis) + P(test 1 positive|not cogscitis) × P(not cogscitis)

where P(not cogscitis) = 0.3 (Doctor A's prior probability for not cogscitis).

Substituting the values, we get:

P(cogscitis|test 1 positive) = (0.70 × 0.70) / (0.70 × 0.70 + 0.10 × 0.30) = 0.87 (rounded to two decimal places).

So, Doctor A's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 is 0.87.

Similarly, Doctor B's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 can be calculated as follows:

P(cogscitis|test 1 positive) = (P(test 1 positive|cogscitis) × P(cogscitis)) / P(test 1 positive)

where P(cogscitis) = 0.20 (Doctor B's prior probability) and P(test 1 positive|cogscitis) = 0.70 (probability of positive test result given cogscitis).

P(test 1 positive) can be calculated as the sum of probabilities of getting a positive result for both hypotheses:

P(test 1 positive) = P(test 1 positive|cogscitis) * P(cogscitis) + P(test 1 positive|not cogscitis) × P(not cogscitis)

where P(not cogscitis) = 0.8 (Doctor B's prior probability for not cogscitis).

Substituting the values, we get:

P(cogscitis|test 1 positive) = (0.70 × 0.20) / (0.70 × 0.20 + 0.10 × 0.80) = 0.15 (rounded to two decimal places).

So, Doctor B's posterior probability for the hypothesis that you have cogscitis after seeing the positive result of Test 1 is 0.15.

The best explanation for the difference between Doctor A’s and Doctor B’s posterior probability for the hypothesis that you have cogscitis is c) Doctor A thought the hypothesis that you have cogscitis was more likely than Doctor B before either of them saw the results from Test 1.

Hence, the correct answer is c.

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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answers

The Three options are

1.  m∠5 + m∠6 = 180°

2. m∠2+ m∠3 = m∠6.

3. m∠2 + m∠3 + m∠5 = 180°.

What is an angle measure?

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Consider ΔABC with Exterior angles as

∠ 1, ∠ 4 , and ∠ 6

Exterior angle Property of Triangle:

A triangle's exterior angle is equal to the sum of its inner angles on either side.

For Exterior ∠ 1 we have

m∠1 = m∠ 5 + m∠ 3

Similarly,

For Exterior ∠4 we have

∠ 4 = ∠ 5 + ∠ 2.

Similarly,

For Exterior ∠ 6 we have

∠ 6 = ∠ 2 + ∠ 3.

Triangle Sum Property:

The total of all the angles of a triangle equals 180°.

∴ m∠2 + m∠3 + m∠5 = 180°

Linear Pair:

A linear pair of angles must add up to 180 degrees since a straight angle has a measure of 180 degrees.

∴ m∠5 + m∠6 = 180°

Therefore, all the required values are given above.

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A triangle has a 6 cm side, a 7 cm side, and a 45°.
• The 6 cm side is adjacent to the 45° angle.
• The 7 cm side is opposite the 45° angle.
How many triangles can be made with these conditions?
One
No
One
Two
More than 2
?triangle(s) can be made.
K

Answers

One triangles can be made with these conditions.

What is the 45 degree triangle's formula?Pythagorean theorem application The Pythagorean Theorem makes it simple to determine the length of the sides of a 45 45 90 triangle as it is a right angle triangle. The Pythagorean Theorem's formula is as follows: A 2 + B 2 = C 2 A2 + B 2 = C 2When the two legs of an isosceles right triangle are congruent to one another and the non-right angles are both 45 degrees, the triangle is known as a 45 45 90 triangle. The Pythagorean theorem may frequently be used to locate the missing legs or hypotenuse of 45 45 90 triangles.

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