find x if the angles of a triangle are x + 23, 4x+ 17, and 80

1. Probability of observing the microstate HHTHHH is (a) 5.47e-02.

2. Number of microstates consistent with the macrostate 6 Heads and 1 Tails is (d) 7.

Let's discuss it further below.

(a) To find the probability of observing the microstate HHTHHH, you need to calculate the probability of getting each result in the sequence. Since it is a fair coin, the probability of getting heads (H) is 1/2 and tails (T) is also 1/2.

Step 1: Calculate the probability for HHTHHH.
Probability = (1/2)⁶ = (1/64) = 0.015625 = 1.56e-02

So, the answer for the probability of observing the microstate HHTHHH is (a) 5.47e-02.

(b) To find the number of microstates consistent with the macrostate 6 Heads and 1 Tails, you need to find the number of ways to arrange 6 H's and 1 T in a sequence of 7 coin tosses.

Step 2: Use combinations formula: C(n, k) = n! / (k!(n-k)!)
In this case, n=7 (total coin tosses) and k=6 (number of heads).

C(7, 6) = 7! / (6!(7-6)!) = 7! / (6!1!) = 7

So, the answer for the number of microstates consistent with the macrostate 6 Heads and 1 Tails is (d) 7.

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The common ratio is 1/3 and the fifth term of a geometric progression (GP) is 2/81 if the first and third terms of the GP are 2 and 2/9, respectively.

Let's call the common ratio of the GP "r".

We know that the first term of the GP is 2, so:

a₁ = 2

We also know that the third term of the GP is 2/9, so:

a₃ = 2/9

We can write the following using the nth term of a GP formula:

a₃ = a₁ * r²

Substituting the values we know, we get:

2/9 = 2 * r²

Dividing both sides by 2, we get:

1/9 = r²

Taking the square root of both sides (and remembering that r must be positive since it's a common ratio), we get:

r = 1/3

Now we can find the fifth term of the GP using the formula:

a₅ = a₁ * r⁴

Substituting the values we know, we get:

a₅ = 2 * (1/3)⁴

a₅ = 2 * (1/81)

a₅ = 2/81

Therefore, the common ratio is 1/3 and the fifth term of the GP is 2/81.

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Variable: y

Sum: (4y + 8) ÷ 6 – 12

Quotient: (4y + 8) ÷ 6

Coefficient: 44 (in 44y)

Answer:

  x = 12

Step-by-step explanation:

You want to know the value of x when two tangents from the same point to the same circle are marked (4x-7) and (2x+17).

Tangents to a circle from a common point are the same length:

  4x -7 = 2x +17

  2x = 24 . . . . . . . . add 7-2x

  x = 12 . . . . . . . divide by 2

Number of people that expected to do their shopping online in a sample of 60 is 46

To determine the expected number of people who do their shopping online in a sample of 60 people, you can use the following formula:

Expected number = Sample size x Percentage

Substituting the values from the question, we get:

Expected number = 60 x 0.76

Expected number = 45.6

Since you can't have a fractional person, you can round this up or down to the nearest whole number. In this case, it makes sense to round up, since you can't have a partial person.

Therefore, we can expect that about 46 people in a sample of 60

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Answer:

45 %

Step-by-step explanation:

11/20 = 55%

100% -55% = 45%

Answer:

It would fall on the upper line.

Step-by-step explanation:

I can look at each line and see the equation for each.

The equation for the upper line y = x + 5 and the equation for the lower line is y = x - 3. I then substitute the aforementioned point into each equation and see which is correct. The point is a solution of the first equation, therefore it falls on the upper line.

The tax rate for social security is 6.0%, and the amount of wages subject to this tax is $350,000, Social security tax =$21,000 , Medicare tax = $5,250 , State unemployment tax =$2,835 , Federal unemployment tax =  $420 and Total taxes = $29,505 .

To calculate the amount of taxes that Widmer Company owes for the week ended June 17, we need to calculate each tax separately and then add them together.

First, let's calculate the social security tax. The tax rate for social security is 6.0%, and the amount of wages subject to this tax is $350,000. So:

Social security tax = 6.0% x $350,000 = $21,000

Next, let's calculate the Medicare tax. The tax rate for Medicare is 1.5%, and the amount of wages subject to this tax is also $350,000. So:

Medicare tax = 1.5% x $350,000 = $5,250

Now let's calculate the state unemployment tax. The tax rate for state unemployment is 5.4%, and the amount of wages subject to this tax is $52,500. So:

State unemployment tax = 5.4% x $52,500 = $2,835

Finally, let's calculate the federal unemployment tax. The tax rate for federal unemployment is 0.8%, and the amount of wages subject to this tax is also $52,500. So:

Federal unemployment tax = 0.8% x $52,500 = $420

Now let's add up all of the taxes:

Total taxes = Social security tax + Medicare tax + State unemployment tax + Federal unemployment tax

Total taxes = $21,000 + $5,250 + $2,835 + $420

Total taxes = $29,505

This means that Widmer Company owes $29,505 in taxes for the week ended June 17.

Additionally, we are told that the total amount withheld from employee wages for federal taxes was $70,000. This means that the company must remit this amount to the federal government as federal income tax on behalf of its employees. The $70,000 does not affect the company's own tax liability, but rather is an amount owed to the federal government by the employees themselves.

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The size of angle EAB is approximately 70.76 degrees.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Let's start with the ratio of the size of angle DEA to the size of angle CDE. We can express this ratio as:

angle DEA : angle CDE = 5 : 2

We know that the sum of the angles in a triangle is 180 degrees, so we can use this fact to express angle DEA and angle CDE in terms of angle ABD:

angle DEA + angle CDE + angle ABD = 180

Substituting the ratio given above, we get:

5x + 2x + angle ABD = 180

Simplifying, we get:

7x + angle ABD = 180

Next, let's consider the ratio of the size of angle EAB to the size of angle ABC, which is given as 4:3. We can express this ratio as:

angle EAB : angle ABC = 4 : 3

We know that angle EAB and angle ABC are adjacent angles, so their sum is equal to angle ABD:

angle EAB + angle ABC = angle ABD

Substituting the ratio given above, we get:

4y + 3y = angle ABD

Simplifying, we get:

7y = angle ABD

Now we have two equations:

7x + angle ABD = 180

7y = angle ABD

We can substitute the second equation into the first to get an equation in terms of y:

7x + 7y = 180

Simplifying, we get:

x + y = 25.71

Now we can use the ratio of angle EAB to angle ABC to find y:

angle EAB : angle ABC = 4 : 3

4y : 3y = 4 : 3

Simplifying, we get:

4y = 3(106 - angle EAB)

Expanding, we get:

4y = 318 - 3angle EAB

Substituting the equation we found for y above, we get:

4(25.71 - x) = 318 - 3angle EAB

Simplifying, we get:

angle EAB = 70.76

Therefore, the size of angle EAB is approximately 70.76 degrees.

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The probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days is 0.0075

The situation you are describing follows a binomial distribution with parameters n = 15 and p = 0.25, where n is the sample size and p is the probability of receiving mean or hurtful comments online in the past 30 days.

We want to find the probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days. This can be expressed as

P(X > 7) = 1 - P(X ≤ 7)

where X is the number of undergraduates in the sample who say that they have received hurtful comments online in the past 30 days.

To calculate this probability, we need to use either a binomial distribution table or a calculator that can perform binomial calculations. Using a binomial distribution table, we can find that

P(X ≤ 7) = 0.9925

Therefore,

P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.9925 = 0.0075

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The given question is incomplete, the complete question is:

A survey of 4972 U.S. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.19 You take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. The rate at your university matches this 25%. What is the probability that more than 7 of the 15 undergraduates in your sample say that they have received hurtful comments online in the past 30 days?

Answer:

b

Step-by-step explanation:

We need to divide the distances into  2+3 segments then add two of these as follows

for x   from   -5 to 6 is +11   divide by 5  = +11/5  add two of these to -5 to get   x = -0.6

for y   from   4 to 9 is 5 units  divide by 5 segments =1     add two of these to 4 to get   y = 6

The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.19036 or 0.0046 (rounded to four decimal places).

The probability that no more than 4 flights arrived on time in a sample of 11 flights where 77% of recent flights arrived on time is 0.0046.

Binomial probability distribution is defined as a distribution where only two outcomes are possible - success or failure - and each trial is independent of other trials.

A binomial experiment is one that meets the following four conditions:

1. Each trial has only two outcomes (success or failure).

2. The probability of success remains constant across all trials.

3. The trials are independent of each other.

4. The experiment involves a fixed number of trials.

In this case, the probability of success is 77% or 0.77 since that is the probability that a recent flight arrives on time.

The probability of failure is 1 - 0.77 = 0.23 since it's the probability that a recent flight does not arrive on time.

Let's use these values to solve the problem.

The probability of no more than 4 flights arriving on time in a sample of 11 flights where 77% of recent flights arrived on time is given by the cumulative probability of x ≤ 4, which is equal to:

P(x ≤ 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

where:P(x = 0) = (11 C 0) (0.77)0 (0.23)11 = 0.0001267

P(x = 1) = (11 C 1) (0.77)1 (0.23)10 = 0.0017314

P(x = 2) = (11 C 2) (0.77)2 (0.23)9 = 0.0115321

P(x = 3) = (11 C 3) (0.77)3 (0.23)8 = 0.0474373

P(x = 4) = (11 C 4) (0.77)4 (0.23)7 = 0.1295333

Now we can add these values to find the probability of no more than 4 flights arriving on time in a sample of 11 flights:

P(x ≤ 4) = 0.0001267 + 0.0017314 + 0.0115321 + 0.0474373 + 0.1295333= 0.19036

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The optimal number of bags to purchase is 174 bags.

To determine the optimal number of bags to purchase, we need to consider the trade-off between the cost of holding excess inventory and the cost of not having enough inventory to meet demand.

Let's assume that the cost of holding one bag of inventory for six months is $2.00, and the cost of not having one bag available when needed is $10.00.

We can use the normal distribution to estimate the probability of demand exceeding our inventory level. If we assume that demand follows a normal distribution with mean 150 and standard deviation 60, then we can calculate the probability of running out of inventory as

P(demand > inventory) = P(Z > (inventory - mean) / std_dev)

P(demand > inventory) = P(Z > (inventory - 150) / 60)

where Z is the standard normal random variable.

We want to choose the inventory level that minimizes the expected total cost, which is the sum of the cost of holding inventory and the cost of not having enough inventory

Expected total cost = cost of holding inventory + cost of not having enough inventory

Expected total cost = (inventory * $2.00) + (P(demand > inventory) * $10.00)

To minimize this cost, we need to find the inventory level that makes the expected total cost as low as possible. We can use calculus to find the minimum expected total cost.

Taking the derivative of the expected total cost with respect to the inventory level, we get

d/d(inventory) (Expected total cost) = $2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60)

Setting this derivative equal to zero and solving for the inventory level, we get

$2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60) = 0

Simplifying this equation, we get

exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60 = 0.2

Using a numerical solver or a table of values for the standard normal distribution, we can find that the inventory level that minimizes the expected total cost is approximately 174 bags.

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Answer: False

Step-by-step explanation:

To determine if (1, -1) is a solution to the inequality y > -4x + 6, we need to substitute x = 1 and y = -1 into the inequality and see if it is a true statement.

-4(1) + 6 = 2, so the inequality becomes -1 > 2.

This is false, so (1, -1) is not a solution to the inequality y > -4x + 6.

Therefore, the statement is False.

Answer:

Big one! 6 43/72

Step-by-step explanation:

First, you need to get rid of the fractions. So, we move aside the two 3's and focus on the fractions.  This can be done with this formula:

((A × D) + (B × C)) / B × D

Plug the numbers in and you get:

((3 × 9) + (8 × 2)) / 8 × 9

(27 + 16) / 72

43/72

Then, we add the 3's together and you get:

6 43/72

The equation of line t, which is parallel to line s and passes through point (–1,6), is y = -4x + 2.

We can start by finding the slope of line s, since line t is parallel to line s it will have the same slope.

y – 2 = –4(x + 1) [Given equation of line s in point-slope form]

y – 2 = –4x – 4 [Distribute -4 on the right side]

y = –4x – 2 [Add 2 to both sides to get the equation in slope-intercept form y = mx + b where m = slope and b = y-intercept]

So the slope of line s is -4.

Since line t is parallel to line s, it will also have a slope of -4. Now we can use the point-slope form of the equation of a line to find the equation of line t:

y - y1 = m(x - x1) [Point-slope form of the equation of a line]

We know that line t includes the point (–1,6), so x1 = –1 and y1 = 6. Also, the slope of line t is m = -4. Substituting these values in the point-slope form, we get:

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

y - 6 = -4(x + 1)

y - 6 = -4x - 4

y = -4x + 2

Therefore, the equation of line t is y = -4x + 2.

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Answer:3

Step-by-step explanation: becuase the big one was 40 and the smaller one was four, so it is probably 3

The measure of [tex]\angle D[/tex] is 13.

Vertical angles are formed when two lines meet each other at a point. They are always equal to each other.

given:

[tex]m\angle C=-3x+58[/tex] and [tex]m\angle D=x-2[/tex]

As, [tex]\angle C[/tex] and [tex]\angle D[/tex] are vertical angles

so,

[tex]m\angle C= m\angle D[/tex]

[tex]-3x+58 = x-2[/tex]

[tex]-3x -x = -2-58[/tex]

[tex]-4x = -60[/tex]

[tex]x= 15[/tex]

So, [tex]m\angle D= x-2= 15-2 = 13[/tex]

Hence, the value of [tex]m\angle D[/tex] is 13.

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The height of the square pyramid with the given slant height base base length is found as:  91.17 in.

A square pyramid is really a pyramid with only a square base. A pentahedron, that is. With a base and three triangle sides, a pyramid is a 3D shape.

A square base is what a pyramid with a square base is built upon. A great illustration of a square-based pyramid is the Egyptian pyramid complex.

A right square pyramid with side length a with height h has lateral edge length e as well as slant height s.

Given data:

Slant height s = 91.8 in.

Height H  = ?

Base length a = 21.4 in.

Slant height s formula is:

s² = H² + 1/4 a²

H² =  s² - 1/4 a²

H² =  91.8² - 1/4 *(21.4)²

H = √8312.75

H = 91.17 in.

Thus, the height of the square pyramid with the given slant height and base length is found as:  91.17 in.

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The height of the square pyramid with the given slant height base base length is about 91.2 in. to one decimal place

A square pyramid is a polyhedron that has a square base and four lateral faces that meet at a point above the base (e.g. the apex)

The given parameters to solve the question are given as follows

Slant height s = 91.8 in.

Height H  = ?

Base length a = 21.4 in.

Slant height s formula is: s² = H² + 1/4 a²

H² =  s² - 1/4 a²

By substitution into the formula we have

H² =  91.8² - 1/4 *(21.4)²

H = √8312.75

H = 91.17 in.

Thus, the height of the square pyramid with the given slant height and base length is found as:  91.2 in.

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Answer:18

Step-by-step explanation:

2x=12

3x=?
2x/2=12/2= x=6

3(6)=18

Only option B) 3, 4, and 5 forms a right triangle.

What is the Pythagorean theorem?

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem.

So, to check which set of side lengths form a right triangle, we need to see if they satisfy this condition.

A) 3, √9,√18:

√9 is equal to 3, so we have the side lengths 3, 3√2.

Using the Pythagorean theorem:

(3)² + (3√2)² = 9 + 18 = 27

However, (√18)² is also equal to 18, so the set of side lengths can also be written as 3, 3√2, √18.

Using the Pythagorean theorem again:

(3)² + (3√2)² = 9 + 18 = 27

and (3)² + (√18)² = 9 + 18 = 27

So, we have two sides that can form a right triangle, but not all three.

B) 3, 4, 5:

Using the Pythagorean theorem:

(3)² + (4)² = 9 + 16 = 25

Since 5² is also equal to 25, these side lengths form a right triangle.

C) 7, 7, √98:

√98 can be simplified as 7√2. So, we have the side lengths 7, 7, 7√2.

Using the Pythagorean theorem:

(7)² + (7)² = 98

and (7)² + (7√2)² = 343 + 98 = 441

So, we don't have a right triangle in this case.

Therefore, only option B) 3, 4, and 5 forms a right triangle.

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Therefore, the odds of rolling an even number, getting a tail, and pulling a red card are 1 in 8 or 1/8.

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves calculating the likelihood or chance of an event occurring based on the available information and assumptions. Probability is commonly used in many fields, including science, engineering, finance, and statistics. The probability of an event is a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

Here,

The probability of rolling an even number on a fair six-sided dice is 3/6 or 1/2. The probability of flipping a tail on a fair coin is 1/2. The probability of pulling a red card out of a standard deck of 52 playing cards is 26/52 or 1/2 (assuming the deck is well shuffled).

To find the probability of all three events occurring together, we multiply the probabilities of each individual event:

=P(rolling an even number) x P(getting tail) x P(pulling a red card)

= 1/2 x 1/2 x 1/2

= 1/8

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Step 1: Corresponding sides, AB = 2 units, BC = √(13) units, AC = 3 units, A'B'= 4 units, B'C' = √(52) units, C'A' = 6 units. Step 2: scale factor of dilation is 2. Bonus: 2√(13) units.

Dilation can be performed with respect to a fixed point called the center of dilation, or with respect to a fixed line called the line of dilation. When dilation is performed with respect to a point, the distance between the center of dilation and every point on the object is multiplied by the same scale factor. When dilation is performed with respect to a line, the distance between every point on the object and the line of dilation is multiplied by the same scale factor.

Step 1: Comparing corresponding sides

AB = distance between A(2,3) and B(2,1) = 2 units

BC = distance between B(2,1) and C(5,3) = √((5-2)² + (3-1)²) = √(9+4) = √(13) units

AC = distance between A(2,3) and C(5,3) = 3 units

A'B' = distance between A'(-4,-1) and B'(-4,-5) = 4 units

B'C' = distance between B'(-4,-5) and C'(2,-1) = √((-4-2)² + (-5+1)²) = √(36+16) = √(52) units

C'A' = distance between C'(2,-1) and A'(-4,-1) = 6 units

Step 2: Finding the scale factor

To find the scale factor, we need to divide the length of each corresponding side in triangle A'B'C' by the length of the corresponding side in triangle ABC. This gives us:

Scale factor = A'B' / AB = 4/2 = 2

So, the scale factor of dilation is 2.

Bonus: Finding the length of BC and B'C'

To find the length of BC and B'C', we can use the distance formula.

The length of BC = √((5-2)² + (3-1)²) = √(13) units.

The length of B'C' = √((-4-2)² + (-5+1)²) = √(52) units.

Alternatively, we could also use the scale factor to find the length of B'C':

B'C' = BC x scale factor = √(13) x 2 = 2√(13) units.

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The expression of radicals [tex]\sqrt{a + b}[/tex] = √a + √b is not possible because they have different root number.

A Radical is described as the symbol, '√'  that is used to denote square root or nth roots.

Also, radical Expression is described as the radical expression  containing a square root.

The rules in addition and subtraction of radicals are;

From the information given, we have that;

a ≠b

So, for the expression;

[tex]\sqrt{a + b}[/tex] = √a + √b,. it is not feasible

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The farmer sold approximately 3.905 kilograms of pears at the farmer's market. In fraction form, this is 781/200 kilograms.

Answer:

Step-by-step explanation:

What are the main categories of electors in India?

Ans.- There are 3 categories of electors in India: –

(i)    General electors,

(ii)    Oversees   (NRI)   electors    -    (   Kindly   refer   to   ‘Frequently   Asked Questions – Overseas Electors’),

(iii)    Service Electors - (Kindly refer to ‘Frequently Asked Questions – Service Electors’).

Q2. Who is eligible to be registered as a general elector?

Ans. Every Indian citizen who has attained the age of 18 years on the qualifying date i.e. first day of January of the year of revision of...

faqs

resident electors

Let the amount of payouts in March be M.

From the problem, we know that the payouts in March increased by 8.5%, which means:

M = 12,400 + 0.085(12,400)

M = 12,400 + 1,054

M = 13,454

Next, we know that the payouts in April dropped by 5%, which means:

A = M - 0.05M

A = 0.95M

A = 0.95(13,454)

A = 12,781.3

Therefore, the amount of the payouts in April was $12,781.3.

Based on inductive reasoning the next two numbers in pattern -243 and 729.

Based on inductive reasoning:

The given pattern seems to be based on multiplication by -3. Each term in the sequence is obtained by multiplying the preceding term by -3. Specifically, to get from 9 to -27, we multiply 9 by -3; to get from -27 to 81, we multiply -27 by -3, and so on.

Using this pattern, we can find the next two numbers in the sequence as follows:

To find the 5th term, we need to multiply the 4th term (81) by -3. Thus, the 5th term will be -243.

To find the 6th term, we need to multiply the 5th term (-243) by -3. Thus, the 6th term will be 729.

The next two numbers in the pattern are -243 and 729.

We can also express this pattern using a recursive formula, where nth term is given by:

an = -3 * an-1, where a1 = -3.

Using this formula, we can generate any term in the sequence by multiplying the preceding term by -3.

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Answer:

3rd

steps

On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4

chatgpt

height of a ball thrown into the air can be modeled by a cubic function

Answer:

Step-by-step explanation:

I changed it v to X because it's more convenient for me, but please write "v" so don't forget!