If θ is in Quadrant I and tanθ=5/12 , what is the value of tan 4θ/5 to the nearest hundredth?

(A) 18.10 (B) 0.33 (C) 0.32 (D) -23.90

Using the binomial distribution, it is found that there is a:

a) 0.3439 = 34.39% probability he will receive at least one upgrade during the next two weeks.

b) 0.8671 = 86.71% probability that in a set of 20 flights, Sam will be upgraded 3 times or fewer.

For each flight, there are only two possible outcomes, either he receives an upgrade, or he dos not. The probability of receiving an upgrade in a flight is independent of any other flight, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

An airline claims that there is a 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight, hence \(p = 0.1\).

Item a:

He takes 4 flights, hence \(n = 4\).

The probability is:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{4,0}.(0.1)^{0}.(0.9)^{4} = 0.6561\)

Then:

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.6561 = 0.3439\)

0.3439 = 34.39% probability he will receive at least one upgrade during the next two weeks.

Item b:

20 flights, hence \(n = 20\).

The probability is:

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

Then:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.1)^{0}.(0.9)^{20} = 0.1216\)

\(P(X = 1) = C_{20,1}.(0.1)^{1}.(0.9)^{19} = 0.2702\)

\(P(X = 2) = C_{20,2}.(0.1)^{2}.(0.9)^{18} = 0.2852\)

\(P(X = 3) = C_{20,3}.(0.1)^{3}.(0.9)^{17} = 0.1901\)

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1216 + 0.2702 + 0.2852 + 0.1901 = 0.8671\)

0.8671 = 86.71% probability that in a set of 20 flights, Sam will be upgraded 3 times or fewer.

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Answer:

Question 1. 1/2 hour

Question 2. 1/6

Question 3. 5/12 eggs

The pmf of M1 is \($P(M1=k) = \binom{20}{k} \cdot p^k \cdot (1-p)^{20-k}$\)

The probability that more than 11 passengers are riding on the bus is \($P(M > 11) = 1 - P(M\leq11) = 1 - \sum_{k=0}^{11} P(M=k)$\)

The value of E[R] is 20λp and the value of Var(R) is \($20\lambda p(1-p) + \lambda \cdot 20^2 p^2$\)

Given that the number of buses arriving at a station in a specific time interval follows a Poisson distribution with parameter λ, and each bus has 20 seats with a probability p that each seat is taken. The number of passengers in bus number 1, M1, follows a binomial distribution with parameters n=20 and p. Using these distributions, we can calculate the probabilities of different events, the expected value of the total number of passengers, and the variance of the total number of passengers.

The number of passengers on bus 1, M1, follows a binomial distribution with parameters n=20 and p. The pmf of M1 is:

\($P(M1=k) = \binom{20}{k} \cdot p^k \cdot (1-p)^{20-k}$\)

where k ranges from 0 to 20.

The range of M1 is 0 to 20.

When p=0.2, the probability that more than 11 passengers are riding on the bus can be calculated using the Poisson distribution. We can find \($P(M > 11) = 1 - P(M\leq11) = 1 - \sum_{k=0}^{11} P(M=k)$\)

where M is the number of passengers on the bus. We can also use Markov's inequality to find an upper bound on this probability, which is P(M>11) <= E[M]/11.

When p=0.8, we want to compute the probability that there are at most 10 passengers on the bus. We can use the binomial distribution to find P(M1<=10), where M1 is the number of passengers on bus 1. We can also use Chebyshev's inequality to find an upper bound on this probability, which is \(P(\left|M_1-E[M_1]\right|\geq3) \leq \frac{Var(M_1)}{3^2}\)

The expected value of the total number of passengers is \(E[R] = \lambda * E[M]\), where E[M] is the expected number of passengers on a bus. Since each seat has probability p of being taken, we have E[M]=20p. Therefore, E[R] = 20λp.

The variance of the total number of passengers is\($\mathrm{Var}(R) = \lambda\mathrm{Var}(M) + \mathrm{Var}(\lambda)\mathrm{E}(M)^2$\), where Var(M) is the variance of the number of passengers on a bus. Using the binomial distribution, we can find Var(M) = 20p(1-p). Since the Poisson distribution has variance equal to its mean, we have Var(λ) = λ.

Therefore, \($Var(R) = 20\lambda p(1-p) + \lambda \cdot 20^2 p^2$\)

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Answer:

g(4) = - 16

Step-by-step explanation:

Substitute x = 4 into g(x) , that is

g(4) = - 7(4) + 12 = - 28 + 12 = - 16

we know:  g(x) = -7x + 12

=> g(4) = -7.(4) + 12 = -28 +12 = -16

Ok done. Thank to me:>

Answer:

3/5 ÷ 5/6

3/5 × 6/5

3×6=18

5×5=25

18/25 is your answer

To solve graphically this set of equations, we should first draw both lines and see the value of x at which the lines crosses

Both graphs can be drawn as follows

We can see that both graphs intersect at a negative value of x. With a more accurate graph, we can determine that both lines intersect at x=-2.

So the solution for this system of equation is x=-2.

Answer:

The expression 6c + 4d - c - 7d can be simplified by combining like terms. 6c + 4d - c - 7d = (6c - c) + (4d - 7d) Simplifying further, we get: 6c + 4d - c - 7d = 5c - 3d So the simplified expression is 5c - 3d.

To simplify the expression 6c + 4d - c - 7d, we can first combine the like terms, which are the terms that have the same variable and the same exponent:

6c - c + 4d - 7d

Simplifying this expression further by combining the like terms, we get:

5c - 3d

Therefore, 6c + 4d - c - 7d simplifies to 5c - 3d.

The scale Giselle used to create the scale drawing of the school cafeteria is 1 inch : 8 feet.

Length is a measure of dis dancer size it can be measured in a variety of waste including inches sentiment of metres feet miles and more. Playing these an important concept mathematics science engineering and many others build it is used to calculate the dimensions of this area and more it is also used to measure the time it takes to travel A certain distance link this and important concept that is used to measure and compare objects.

To answer this question, we can use the ratio of the length of the cafeteria in the scale drawing compared to the actual length of the cafeteria. The ratio is 11 inches : 88 feet. We can simplify this ratio to 1 inch : 8 feet. Therefore, the scale Giselle used to create the scale drawing of the school cafeteria is 1 inch : 8 feet.

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Answer:

y = 5x + 6

Step-by-step explanation:

Write each equation in slope intercept form

-10x + 2y = 12

slope intercept form means solving for y:

-10x + 2y = 12

add 10x to both sides:

-10x + 2y + 10x = 12 + 10x

2y = 12 + 10x

rearrange right side:

2y = 10x + 12

divide both sides by 2:

2y/2 = (10x + 12)/2

y = 5x + 6

Answer:

f(-2) = 5

Step-by-step explanation:

Step 1: Define

f(x) = -3 + 2x²

f(-2) is x = -2

Step 2: Substitute and Evaluate

f(-2) = -3 + 2(-2)²

f(-2) = -3 + 2(4)

f(-2) = -3 + 8

f(-2) = 5

Answer:

The answer is -285

Step-by-step explanation:

Answer:

1)  -2x-11

2) 1.3x-3

3) 5k-20

4) 21.84

Step-by-step explanation:

-2x-7+(-4)          -2x-7-4           -2x-11

5.2x+9-12-3.9x          1.3x+9-12      1.3x-3

5(k-4)    distribute        5k-20

5.46÷0.25=21.84

Answer:

A washer and dryer cost a total of $964 . The cost of the washer is three times the cost of the dryer. Find the cost of each item.

Answer: 96$

Answer:

The washer costs $723 and the dryer $241.

Step-by-step explanation:

Represent the cost of the washer by w and that of the dryer as d.

Then w = 3d.

Since w + d + $964, we get 3d + d = $964, or 4d = $964, or d = $241.

Three times that is $723.

The washer costs $723 and the dryer $241.

Answer:

The arc length is 185.39 meters.

Step-by-step explanation:

The arc length is calculated by the following expression:

\(\Delta s = \Delta \theta \cdot r\)

Where:

\(r\) - Radius, measured in meters.

\(\Delta \theta\) - Central angle, measured in radians.

If \(r = 36.9\,m\) and \(\Delta \theta =\frac{8}{5}\pi\, rad\), the arc length, measured in meters, is:

\(\Delta s = \frac{8}{5}\pi\cdot (36.9\,m)\)

\(\Delta s = \frac{8}{5}\cdot (3.14)\cdot (36.9\,m)\)

\(\Delta s \approx 185.386\,m\)

\(\Delta s \approx 185.39\,m\)

The arc length is 185.39 meters.

Answer:

18

Step-by-step explanation:

6+3=9

9*2=18

sorry if not right

Given that radioactive element carbon-14 has a half-life of 5750 years. The bones from a mastodon had lost 78.3% of their carbon-14.

Thus, we are required to find how old were the bones at the time they were discovered, the bones were about years old. Let the number of years be x.Thus, amount of carbon-14 after x years will be 150g.

Now, the mass of the carbon-14 after 5750 years = 150/2 = 75 gThe mass of the carbon-14 left after x years will be 78.3% of 150 = 117.45gThus,117.45 = 150*(1/2)^(x/5750)Let's simplify the above equation:1/2^(x/5750) = 117.45/150 = 0.783Taking log on both sides,we get (x/5750)*log(1/2) = log(0.783)x/5750 = -0.286x = -0.286*5750x = 1648.9Thus, the bones were discovered approximately 1649 years ago.

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The length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.

Given that, in triangle GHJ, ∠G=25°, ∠H=46°, and h = 37 mm.

The sine rule of a triangle is sin A/a = sin B/b = sin C/c.

From triangle GHJ

∠G+∠H+∠J = 180°

⇒ 25°+46°+∠J = 180°

⇒ ∠J = 109°

Using sine rule

sin 109°/g = sin 25°/37

⇒ 0.945/g = 0.4226/37

⇒ 34.965 = 0.4226g

⇒ g = 82.73 mm

⇒ g ≈ 83 mm

Therefore, the length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.

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Answer:

y=3/5x-26/5

Step-by-step explanation:

y=mx+b

m=3/5

y=3/5x+b

2=x, -4=y

-4=3/5(2)+b

-4-6/5=b

b=-26/5

A-The first line has a direction vector of ⟨-2, 1, 3⟩, b-the second line has parametric equations x(t) = -4 - 2t, y(t) = 2 + t, z(t) = 17 + 5t, c-the two lines intersect at the point (1, 3, 10), d-the angle formed is 15.2 degrees, and e- the equation containing both lines is -2x + 7y - 5z = -59.

What is direction vector ?

A direction vector, also known as a directional vector or simply a direction, represents the direction of a line, vector, or a linear path in three-dimensional space. It is a vector that points in the same direction as the line or path it represents.

a) The direction vector for the first line is given by ⟨-2, 1, 3⟩.

b) The parametric equations for the second line, written in terms of the parameter t, are x(t) = -4 - 2t, y(t) = 2 + t, z(t) = 17 + 5t.

c) To find the intersection point, we set the x, y, and z coordinates of both lines equal to each other and solve for s and t:

4 - 2s = -4 - 2t

-2 + s = 2 + t

1 + 3s = 17 + 5t

Solving this system of equations yields s = 3 and t = 1. Therefore, the two lines intersect at the point (1, 3, 10).

d) The angle formed at the intersection point is given by the angle between their respective direction vectors. Using the dot product, the angle θ can be found as cos(θ) = (⟨-2, 1, 3⟩ · ⟨-2, 1, 5⟩) / (|⟨-2, 1, 3⟩| |⟨-2, 1, 5⟩|), which simplifies to cos(θ) = 0.96. Taking the inverse cosine, we find θ ≈ 15.2 degrees.

e) To find the equation of the plane containing both lines, we can use the point-normal form of a plane equation. We choose one of the intersection points (1, 3, 10) and use the cross product of the direction vectors of the two lines as the normal vector. The equation of the plane is given by -2x + 7y - 5z = -59.

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When we have a normal model for the sampling distribution, we cannot say that a sample mean or sample proportion is approximately 2 standard errors (ses) away from the population mean or the true proportion.

Instead, we can say that 95% of the sample proportions fall within two standard errors of the population proportion. Similar to this, the percentage of sample proportions decreases as the standard error distance decreases and increases as the standard error distance increases.

Therefore, the standard error distance will be greater than 2 standard errors (ses) if 99% of the sample proportions are within a given standard error distance of the population proportion.

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Milan drove the truck for approximately 147.06 miles. We determined this by subtracting the base fee from the total payment to find the cost for the miles driven and then dividing that amount by the additional charge per mile.

To find out how many miles Milan drove the truck, we need to subtract the base fee and divide the remaining amount by the additional charge per mile.

Given:

Base fee: $19.95

Additional charge per mile: $0.97

Total payment: $162.54

Subtracting the base fee from the total payment, we have $162.54 - $19.95 = $142.59. This remaining amount represents the cost for the miles driven.

Dividing the remaining amount by the additional charge per mile, we get $142.59 / $0.97 ≈ 147.06 miles.

Therefore, Milan drove the truck for approximately 147.06 miles.

In summary, Milan drove the truck for approximately 147.06 miles. We determined this by subtracting the base fee from the total payment to find the cost for the miles driven and then dividing that amount by the additional charge per mile.

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The formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase is given as follows: V (t) = Ct - rt, where C is the initial cost of the machine in thousands of dollars, r is the depreciation rate per year, and t is the time in years since the machine was purchased. V(t) = 710 - 13.7925t Answer: V(t) = 710 - 13.7925t

The value of an industrial milling machine after two years of purchase is $710,000 and after five years, the value is $180,000. Let us find the depreciation rate of the machine.

Linear Depreciation Method: Linear depreciation method is one of the methods used to calculate depreciation in accounting. It is also called straight-line depreciation. Under this method, the depreciation expense of an asset is the same for each year of its useful life.

The formula to calculate the depreciation expense using the straight-line depreciation method is:Depreciation Expense = (Cost of Asset - Salvage Value)/Useful Life Let,

The cost of the industrial milling machine = C = 710The value of the industrial milling machine after five years = S = 180The useful life of the machine in years = LWe have to find a formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase.

To find the useful life of the machine, use the following formula:Cost of Asset = Depreciation Expense x Useful Life + Salvage Value710 = (710 - 180)/L * L + 180

Simplifying the above equation, we get:710 = 530/L + 180Multiplying both sides of the equation by L and then subtracting 180 from both sides, we get:530L = 530L = 530 - 180L = 350/53.

Therefore, useful life, L = 350/53 yearsThe depreciation rate of the industrial milling machine is the difference between its cost and salvage value divided by its useful life.

Using the given information, the cost of the machine and the value of the machine after five years, we get: Depreciation Rate = (Cost of Machine - Salvage Value) / Useful LifeDepreciation Rate = (710 - 180) / (350/53)Depreciation Rate = 13.7925

Hence, the formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase is given as follows:V (t) = Ct - rt, where C is the initial cost of the machine in thousands of dollars, r is the depreciation rate per year, and t is the time in years since the machine was purchased. V(t) = 710 - 13.7925t Answer: V(t) = 710 - 13.7925t

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The missing statement in Step 5 include the following: B. AC/DC = BC/EC.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the angle, angle (AA) similarity theorem, we can logically deduce the following congruent triangles:

ΔABC ≅ ΔDEC  ⇒ Step 4

By the definition of similar triangles, we can logically deduce the following proportional and corresponding side lengths:

AC/DC = BC/EC ⇒ Step 5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

10

Step-by-step explanation:

100 divided by 10 = 10

Answer:

Step-by-step explanation:

7(9w)7(9w) = 11

(7 ×7)(9×9)(w×w) = 11

49 ×81 w² = 11

3969w² = 11

\(\frac{3969w^{2} }{3969}\) =  \(\frac{11}{3969}\)

w²   =  \(\frac{11}{3969}\)

\(\sqrt{w^{2} }\)   =   \(\sqrt{11/3969}\)

w = ± \(\frac{\sqrt{11} }{63}\)

Because the solution contains a square root the answer contains both a negative and a positive solution.  

The difference in the number of components assembled per day by the experienced and new employees can be described by the function D(t) = 704 - Sofa.

This function represents the gap between the productivity of an experienced employee, who can assemble 704 components per day, and a new employee, whose productivity is determined by the function N(t) = Sofa. The difference in the number of components assembled per day depends on the number of hours worked, represented by t.

In the given scenario, the function N(t) is not explicitly defined, as only the variable Sofa is mentioned. It is unclear how the productivity of a new employee is affected by the number of hours worked. However, regardless of the specific form of the N(t) function, the difference in productivity between the experienced and new employees can be expressed as D(t) = 704 - N(t). This function calculates the difference by subtracting the productivity of the new employee, represented by N(t), from the constant productivity of the experienced employee, which is 704 components per day. The result, D(t), provides an estimation of the additional output achieved by the experienced employee compared to the new employee.

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The number that makes the equation 0.54 + 17/100 = x/100 + 17/100 true is 54.

To solve this equation, we want to isolate x on one side of the equation.

Starting with:

0.54 + 17/100 = x/100 + 17/100

We can first simplify the left side by finding a common denominator for 0.54 and 17/100:

0.54 = 54/100

54/100 + 17/100 = 71/100

Now, we can simplify the right side by combining like terms:

x/100 + 17/100 = (x + 17)/100

Substituting these simplifications back into the original equation, we get:

71/100 = (x + 17)/100

To isolate x, we can multiply both sides by 100:

71 = x + 17

Subtracting 17 from both sides, we get:

x = 54

Therefore, the number that makes the equation true is 54.

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The question is -

Enter the number that makes the equation true.

0.54 + 17/100 = x/100 + 17/100

Answer:

  102.8 cm

Step-by-step explanation:

The perimeter of a semicircle is the sum of the length of the diameter and the length of the curved edge. The curved edge is half the circumference of a circle with the same radius.

  perimeter = diameter + curved edge

  = 2r +1/2(2πr) = r(2 +π)

  = (20 cm)(2 +π) ≈ 102.8 cm

The perimeter of the window is about 102.8 cm.