What is the third quartile of the following data set? 15, 18, 20, 21, 23, 24, 26, 29, 34, 37, 40

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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The standard deviation of the weight distribution is approximately 20.31 pounds.

Let's denote the mean of the distribution as μ (mu) and the standard deviation as σ (sigma).

From the given information, we can calculate the z-scores corresponding to the weights of 154 pounds and 213 pounds.

For the weight of 154 pounds:

The proportion of players weighing less than 154 pounds is 10%, which corresponds to a cumulative probability of 0.10. To find the z-score, we can use a standard normal distribution table or a calculator:

z = invNorm(0.10) ≈ -1.28

For the weight of 213 pounds:

The proportion of players weighing more than 213 pounds is 5%, which corresponds to a cumulative probability of 0.95 (1 - 0.05). To find the z-score, we can again use a standard normal distribution table or a calculator:

z = invNorm(0.95) ≈ 1.64

In a standard normal distribution, the z-scores represent the number of standard deviations away from the mean.

Now, we can set up two equations using the z-scores:

1.28 = (154 - μ) / σ --> (1)

-1.64 = (213 - μ) / σ --> (2)

Solving these equations simultaneously will give us the mean (μ) and the standard deviation (σ) of the weight distribution.

Let's solve these equations:

From equation (1):

1.28σ = 154 - μ

From equation (2):

-1.64σ = 213 - μ

Adding equation (1) and equation (2):

1.28σ - 1.64σ = 154 - μ + 213 - μ

-0.36σ = 367 - 2μ

Simplifying:

-0.36σ = 367 - 2μ

0.36σ = 2μ - 367

Dividing by 0.36:

σ = (2μ - 367) / 0.36

Substituting this value of σ in equation (1):

1.28σ = 154 - μ

1.28[(2μ - 367) / 0.36] = 154 - μ

Simplifying:

1.28(2μ - 367) = 0.36(154 - μ)

2.56μ - 470.16 = 55.44 - 0.36μ

Combining like terms:

2.56μ + 0.36μ = 470.16 + 55.44

2.92μ = 525.6

Dividing by 2.92:

μ = 525.6 / 2.92

μ ≈ 180.00

Now that we have the value of μ, we can substitute it into equation (1) to find σ:

1.28σ = 154 - μ

1.28σ = 154 - 180

1.28σ = -26

Dividing by 1.28:

σ = -26 / 1.28

σ ≈ -20.31

Since standard deviation cannot be negative, we can disregard the negative sign. The standard deviation of the weight distribution is approximately 20.31 pounds.

To summarize:

Mean (μ) ≈ 180 pounds

Standard Deviation (σ) ≈ 20.31 pounds

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Answer:

25.2% of the boys want to play inside

Step-by-step explanation:

Answer:

1/125 probability for each student so, a 0.8 percent probably of winning per student.

Step-by-step explanation:

Answer:

the second one

Step-by-step explanation:

if you subtract 180-47-90= 43

since 47 is a vertical angle of a missing angle you subtract it from 180 to find x.

180-47=133

Answer:

Total Number of students taking Math and History and not music are 68.

Number of students who took both math and history at the same time is 6.

Step-by-step explanation:

History = 30

Math = 32

Music= 33

Math and Music= 9

History and Music= 13

History and Music and Math = 2

History but not math = 14

We have to find students taking history and math but not music.

Total number of students = 125

From the figure  number of students taking Math and History and not music are

=30+6+32= 68

Number of students who took both math and history at the same time is 6.

Answer:

58°

Step-by-step explanation:

x and the angle adjacent to x are supplementary, so the angle adjacent to x measures 180 - x.

180 - x = (1/2)(100 + 144)

180 - x = 122

58 = x

Answer:

D.20

Step-by-step explanation:

4*5=20

Answer:

5.0

Step-by-step explanation:

Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

Answer:

the first two and last one

Step-by-step explanation:

To graph an equation as given:

The absolute value of a number (positive or negative) is always the positive number:

Give values to x and calculate the corresponding value of f(x) or y

x= -4

x= -2

x=0

x= 2

x= 4

Use the next points to grpah the equation: (x,y)

(-4,4) (-2, 2) (0, 0) (2, 2) (4 , 4)

Graph of the equation:

Answer:

361

Step-by-step explanation:

\(3 \times {11}^{2} - 2 = 361\)

Answer:

361

Step-by-step explanation:

3(7+4)^2-14÷7

PEMDAS says parentheses first

3(11)^2-14÷7

Then exponents

3(121)-14÷7

Then multiply from left to right

363 -14÷7

363 -2

Subtract

361

Answer:

Step-by-step explanation:

120=10*12

120=5*2*4*3

120=5*2*2*2*3

120=(2^3)*3*5

A general linear equation is given by:

\(y = a*x + b\)

Where a is the slope and b is the y-intercept.

Here we will find that the linear equation that represents the situation is

\(y = 0.033*x + 1.269\)

And we can expect that the median salary in 2048 is $2.853 million

If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

Here we know that:

in 2007 (x = 7) the median player salary was y = $1.5 million

in 2013 (x = 13) the median player salary was y = $1.7 million.

Then we have two points that we can write as:

(7, 1.5)

(13, 1.7)

Note that the y-value is in millions.

Then the slope of the linear equation will be:

\(a = \frac{1.7 - 1.5}{13 - 7} = 0.033\)

So the linear equation is something like:

\(y = 0.033*x + b\)

To find the value of b, remember the point (7, 1.5), this means that when we have x = 7, we also have y = 1.5, then we can replace these in the above equation:

\(1.5 = 0.033*7 + b\\\\1.5 - 0.033*7 = b = 1.269\)

Then the linear equation is:

\(y = 0.033*x + 1.269\)

b) Now we want to predict the median salary in 2048. For 2048 the x-value is x = 48

So we just need to evaluate this in the linear equation:

\(y = 0.033*48 + 1.269 = 2.853\)

Then the median salary in 2048 will be $2.853 million

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Answer:

60, plz mark me brainliest

Step-by-step explanation:

The time required to fill the cone is approximately 40096.7 minutes.

The hose dispenses 1413 cm³ of water every minute into a cone with a radius of 60 cm and a height of 150 cm.

we can use the formula for the volume of a cone which is:

V = 1/3πr²h

where V is the volume of the cone, r is the radius of the cone, h is the height of the cone and π is the value of Pi.

For the given cone, radius = 60 cm and height = 150 cm.

The volume of the cone can be calculated using the formula as:

V = 1/3 × π × r² × h

V = 1/3 × π × 60² × 150V = 1/3 × π × 360000 × 150V = 56637028.317

Now we can find the time taken to fill the cone using the formula as:

Time = Volume / Rate

Here, Rate is the amount of water dispensed in 1 minute = 1413 cm³/min

Therefore, Time = 56637028.317 / 1413Time = 40096.7 minutes (Approx)

Therefore, the time required to fill the cone is approximately 40096.7 minutes.

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The profit from the sales of the 10th month from the signature item Ratatouille is $24.81 hundreds of thousands of dollars.

In statistics, a regression equation is used to determine whether or not there is a link between two sets of data. It is given by the equation,

y =a+bx

where y is the dependent variable, x is the independent variable, and a and b are the constant values.

We know that the regression equation that is related to profit from the signature item Ratatouille is given by the equation y=7.21+1.76x, therefore, the profit from the sales of the 10th month can be written as,

\(y=7.21+1.76x\\\\y= 7.21 + 1.76(10)\\\\y=24.81\)

Hence, the profit from the sales of the 10th month from the signature item Ratatouille is $24.81 hundreds of thousands of dollars.

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The correct option is option (b) . The statement that mean of the sampling distribution is same as the population parameters is not true .

Sampling Distribution:

A statistical sampling distribution is a type of probability distribution constructed by drawing a large number of random samples of a specified size from the same population. These distributions are useful for understanding how sample statistics vary from sample to sample. Mean of sampling distribution:

The distribution of the values of the sample mean (x- bar) in replicate samples is called the x -bar sampling distribution.

Central Limit Theorem :

For populations with finite mean μ and finite nonzero variance σₓ, the sampling distribution of the mean approaches a normal distribution with mean μ and variance σₓ/N, and for large N (sample size) become.

distribution is depends on sample size

Hence, the correct option is option (c) which gives the false or not true statement about mean of sampling distribution.

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The value of the line integral is \(\pi .\)

We want to calculate the line integral of the vector field F(x, y, z) = <0, 2, z> over the curve C given by C(t) = (cos(t), sin(t), t),

where 0 <= t <= pi.

First, we need to parameterize F along C by replacing x, y, and z with their expressions in terms of t:

F(C(t)) = F(cos(t), sin(t), t) = <0, 2, t>

Next, we need to calculate the derivative of C with respect to t:

C'(t) = (-sin(t), cos(t), 1)

We can now set up the line integral:

∫C F · dr = ∫[0, pi] F(C(t)) · C'(t) dt

= ∫[0, pi] <0, 2, t> · (-sin(t), cos(t), 1) dt

= ∫[0, pi] (2cos(t) - tsin(t)) dt

= [2sin(t) + tcos(t)]|[0,pi]

= 2sin(pi) + picos(pi) - 2sin(0) - 0cos(0)

\(= \pi .\)

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To calculate the energy change associated with an electron transitioning from the n = 4 energy level to the n = 2 energy level, we can use the equation for the energy of an electron in an atom, which is given by:

Where E_n is the energy of the electron in the nth energy level, and eV is the unit of energy called the electronvolt.

Substituting the values of n = 4 and n = 2 into this equation gives us:

The energy change associated with the transition from n = 4 to n = 2 is given by

To convert this energy change from electronvolts to joules, we can use the fact that 1 eV is equal to 1.602176634 x 10^-19 joules.

Multiplying -2.55 eV by this conversion factor gives us an energy change of -2.55 eV * 1.602176634 x 10^-19 joules/eV = -4.13 x 10^-18 joules.

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Answer:

48 cents

Step-by-step explanation:

Answer:

48 cents

Step-by-step explanation:

you can do a proportion i think

\(\frac{19}{57} = \frac{16}{x}\)

19x = 912

x = 48

Answer:

25 or 26 depending if your rounding if you're not rounding it's 25.7495

Answer:

The equation in slope-intercept form is \(y=\frac{1}{14}x\).

Step-by-step explanation:

Given points are;

(-14, -1 ) and (0,0)

Slope of a line is given by;

m = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{0-(-1)}{0-(-14)}\)

m = \(\frac{1}{14}\)

General equation in slope intercept form is,

y = mx + b

Putting (-14, -1) and m = 1/14 in Equation to find b

-1 = \(\frac{1}{14}(-14) +b \\\)

-1 = -1 + b

b = -1 + 1

b = 0

As y-intercept is 0, the equation in slope-intercept form would be

\(y = \frac{1}{14}x\)

Hence,

The equation in slope-intercept form is \(y=\frac{1}{14}x\).

Answer:

The 3 integers are 44, 46, 48

Step-by-step explanation:

The integers are:

Let the three consecutive even integers be denoted as :

x,x+2,x+4

x+x+2+x+4=138

3x+6=138

3x=138−6

3x=132

x=132/3

x=44

The integers are:

x=44

x+2=46

x+4=44+4=48

Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

In the Poisson distribution, the probability that x = 0 is 0.0150.

The probability that x > 1 is 0.9220.

The Poisson probability mass function is given by:

P(x; μ) = e^(-μ) * (μ^x)/ x!

where x is the number of events, and μ is the average number of events in a given interval.

For this problem, μ = 4.20.

To find the probability that x = 0, we plug in x = 0 and μ = 4.20:

P(x= 0) = e^(-4.20) * (4.20^0) / 0!

                         = e^(-4.20) * 1 / 1

                         = 0.0150

To find the probability that x > 1, we need to use the complement rule. That is:

P(x > 1) = 1 - P(x ≤ 1)

To find P(x ≤ 1), we can use the Poisson cumulative distribution function:

P(x ≤ 1) = P(x=0) + P(x=1)

           = [e^(-4.20) * (4.20^0) / 0!] + [e^(-4.20) * (4.20^1) / 1!]

           = 0.0150 + 0.0630

           = 0.0780

Therefore,

P(x > 1) = 1 - P(x ≤ 1) = 1 - 0.0780 = 0.9220

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Answer:

The distance between (3, -1) and (0, 3) is 5

Step-by-step explanation:

The reason why Verifone Systems would have a valuation allowance almost equal to its deferred tax assets is to avoid the risk of having a significant deferred tax liability.

In 2015, Verifone Systems reported deferred tax assets of $398 million and a valuation allowance of $332 million.

A valuation allowance is an accounting approach that is used to create a contra-asset account on a company's balance sheet. A contra-asset account is a ledger account that offsets the balance of another account. A valuation allowance is used to account for the uncertainty regarding the recoverability of a deferred tax asset.

In essence, a valuation allowance serves as an offsetting contra account to the deferred tax asset that is created when a company has more tax deductions or credits than it has taxable income.

This is why Verifone Systems reported a valuation allowance almost equal to its deferred tax assets.

The rationale behind using a valuation allowance is to ensure that a company does not have a significant deferred tax liability that could affect its financial position. It also ensures that a company's balance sheet accurately reflects the tax consequences of its transactions.

A valuation allowance can also be used to show that a company has reduced its deferred tax assets, which can be beneficial for tax planning and compliance purposes.

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