Suppose x has Poisson distribution. Find P(4 < x <8A = 4.4).

Step-by-step explanation:

Slope = ( y₂ - y₁) / (x₂ - x₁)

Slope of Line b = ( 6 - 1 ) ÷ ( 1 - 9 )

                         =  5  ÷  (- 8)

                         =   - ⁵/₈

Slope of Line c =  ( 12 - 7 )  ÷  ( 2 - 10 )

                         =  - ⁵/₈

⇒ Line b ║ Line c

Answer:

C

Step-by-step explanation:

Answer:

y3 - 120 y2 + 3600 y.

Step-by-step explanation:

Rearrange like terms to the same side of the equation:x2 yx = 60 - ySubstitute:60 - y2 yExpand the e.

hope this helps.

Answer & Step-by-step explanation:

(5√2 - 4√3)(5√2 - 4√3)

We can rewrite this equation into a more simpler form.

(5√2 - 4√3)²

Now, we multiply. When multiplying, its important we multiply each term instead of combining them together.

When you multiply a radical by itself, then the base number will be by itself as the product.

So......

(5)² = 25

(4)² = 16

(√2)² = 2

(√3)² = 3

So, now the equation looks like this..

(25 * 2) + (16 * 3)

Multiply the terms.

50 + 48

Add the numbers.

50 + 48 = 98

So, your answer will be answer choice D. The radical in choice D represents the radicals that are in the problem multiplied together.

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

Answer:

w+1.3=2.7

Step-by-step explanation:

the length of w+ the length of the other piece of tape (1.3) is equal to the length of the other tape which is 2.7

The answer is w+1.3=2.7  

Answer:

x = 4\(\sqrt{3}\) , y = 8\(\sqrt{3}\)

Step-by-step explanation:

The ratio of the sides of a 30- 60- 90 triangle are

x : x\(\sqrt{3}\) : 2x

From the diagram

x\(\sqrt{3}\) = 12 ( divide both sides by \(\sqrt{3}\) )

x = \(\frac{12}{\sqrt{3} }\) × \(\frac{\sqrt{3} }{\sqrt{3} }\) ( rationalising the denominator )

  = \(\frac{12\sqrt{3} }{3}\)

x = 4\(\sqrt{3}\)

Then

y = 2x = 2 × 4\(\sqrt{3}\) = 8\(\sqrt{3}\)

The approximate values of x and y are 4√3 and 8√3, respectively.

Given is a right triangle with base = x and the hypotenuse = y and the perpendicular side is 12, the acute angle between the base and the perpendicular side is 60°.

We need to find the value of x and y,

So, to find the value of x and y, we will use the concept of trigonometric ratios,

So, we know,

Sin = perpendicular / hypotenuse

Cos = base / hypotenuse

Tan = perpendicular / base

Let's denote the acute angle between the base and the perpendicular side as θ.

Angle θ = 60°

Using the sine ratio, we can write:

Sin(60°) = 12 / y

√3/2 = 12 / y

Cross-multiplying, we get:

√3 × y = 2 × 12

√3 × y = 24

y = 24 / √3

y = 8√3

To find the value of x, we can use the cosine ratio.

Cos(60°) = x / y

1/2 = x / 8√3

Cross-multiplying, we get:

2x = 8√3

x = 4√3

Hence, the value of x and y are:

x = 4√3

y = 8√3

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Altitude and perpendicular bisector of a side are always perpendicular to a side of a triangle.

How do triangles work?

A triangle is a three-sided polygon with three vertices. The angles of the triangle are formed by the three sides' end-to-end connections at a point.

               The triangle's three angles add up to a total of 180 degrees.

In a triangle, what is the altitude?

The perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude.

                       The altitude forms a right-angle triangle with the base and is also referred to as the triangle's height.

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Answer:

2m+3/5=3

2m+3= 5 x 3

2m+3=15

2m=15-3

2m=12

m=12/2

m=6

Answer:

A formula to express this would be:

60 = 32 + 4h

This simplifies down to 7 for h

Answer:

one dollar!?!??

Step-by-step explanation:

giiiiiirrrrrl u funny

The required value of the function at x = 3 is given as 7.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

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) = 5x - 8, a function is given we have to determine the value of the function for x = 3 so put x = 3 in the function,
f(3) = 5 (3)  - 8
f(3) = 15 - 8
F(3) = 7

Thus, the required value of the function at x = 3 is given as 7.

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The probability that a particular death is due to an automobile accident is 4%

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

total deaths in recent years = 1158

automobile accident resulted = 46 accidents

cancer deaths resulted = 226 accidents

heart disease deaths resulted = 388 accidents

the probability that a particular death is due to an automobile accident = 46/1158

                     = 0.04 or 4 % chances

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This quadratic equation has no real solution.

The given equation is 27 = -x⁴ - 12x².

Rearranging the equation :

x⁴+12x²+27=0

Lets use u=x².we can write the equation in terms of u:

u²+12u+27=0

To solve this Rearranging the equation:

x⁴ + 12x² + 27 = 0

Now, let's substitute a variable to make the equation more readable. Let's use u = x². We can rewrite the equation in terms of u:

u² + 12u + 27 = 0

To solve this *quadratic equation*, we can factor it:

(u + 9)(u + 3)=0

Setting each factor equal to zero and solving for u:

u+9=0 or u+3=0

solving for u:

u=-9 or u=-3

Substituting back the original variable:

x²=-9 & x²=-3

since both x²=-9 and x²=-3 have no real solutions(no real numbers can be squared to give negative values).

Therefore,the given equation has no real solution.

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Answer:

24

Step-by-step explanation:

The graph of x = sin(√(y)) from y extends infinitely in both directions. The length of the graph cannot be determined using the arc length formula.

The length of the graph of x = sin(√(y)) from y can be found using the arc length formula. The arc length formula for a function y = f(x) is given by:

L = ∫[a,b] √(1 + (f'(x))^2) dx

In this case, we have x = sin(√(y)). To find the length of the graph from y, we need to solve for x in terms of y.

Step 1: Rewrite the equation x = sin(√(y)) in terms of y.

Since sin(√(y)) is the input for x, we can square both sides of the equation to isolate y.

x^2 = sin^2(√(y))

Step 2: Use the trigonometric identity sin^2(θ) + cos^2(θ) = 1 to rewrite the equation.

sin^2(√(y)) + cos^2(s√(y)) = 1

Since sin^2(√(y)) = 1 - cos^2(√(y)), we can substitute this expression into the equation.

1 - cos^2(√(y)) + cos^2(√(y)) = 1

Simplifying the equation gives us:

1 = 1

This equation is true for all values of y.

Therefore, the graph of x = sin(√(y)) from y extends infinitely in both directions. The length of the graph cannot be determined using the arc length formula.

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Answer:

3rd degree binomial

-2x has a coefficient of -2

-x³  has a coefficient of -1

Step-by-step explanation:

-2x - x³ is typically written in decreasing exponent order:

-x³ - 2x  ⇒ this is a third degree binomial because of the value of the greatest exponent

there are two 'x' terms:

-2x and -x³

the coefficient of -2x is the integer which precedes the 'x', which is -2

the coefficient of -x³ is -1

There are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

To find the number of acres in a lot, you can use the following formula:

Number of acres = (length in feet) x (width in feet) / 43,560

First, convert the length and width from miles to feet. There are 5,280 feet in a mile, so:

Length in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet
Width in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet

Next, plug these values into the formula:

Number of acres = (2,640 feet) x (2,640 feet) / 43,560 = 174,240,000 / 43,560 = 160 acres

Therefore, there are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

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The root mean squared error (RMSE) of the wisdom of the crowd forecasts for 1960-2015 is 3.72. This is lower than the RMSE of any of the individual forecasting approaches, which were:

3-period moving average: 4.02

Exponential smoothing: 3.98

Rolling regression: 3.87

The wisdom of the crowd method is a forecasting technique that averages the forecasts of multiple individuals or models. This can often lead to more accurate forecasts than any of the individual forecasts.

In this case, the wisdom of the crowd method reduced the RMSE by 0.30, 0.26, and 0.15, respectively, compared to the 3-period moving average, exponential smoothing, and rolling regression models.

The reason why the wisdom of the crowd method can be more accurate than any of the individual forecasts is because it can help to correct for individual biases.

For example, if one individual is consistently over-forecasting, the wisdom of the crowd method will down-weight that individual's forecast. This can help to improve the overall accuracy of the forecast.

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The root mean squared error (RMSE) of the wisdom of the crowd forecasts for 1960-2015 is 3.72. This is lower than the RMSE of any of the individual forecasting approaches, which were:

3-period moving average: 4.02

Exponential smoothing: 3.98

Rolling regression: 3.87

The wisdom of the crowd method is a forecasting technique that averages the forecasts of multiple individuals or models. This can often lead to more accurate forecasts than any of the individual forecasts.

In this case, the wisdom of the crowd method reduced the RMSE by 0.30, 0.26, and 0.15, respectively, compared to the 3-period moving average, exponential smoothing, and rolling regression models.

The reason why the wisdom of the crowd method can be more accurate than any of the individual forecasts is because it can help to correct for individual biases.

For example, if one individual is consistently over-forecasting, the wisdom of the crowd method will down-weight that individual's forecast. This can help to improve the overall accuracy of the forecast.

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Answer:

1.5gallons

Step-by-step explanation:

Here,

no. of bottles(a) : 12

no. of cups (b) :a*2

=12*2

=24

Now,

No. of gallons. :24/16

:1.5gallons

.·.A cartoon contains 1.5 gallons of lemon tea.

Answer:

Step-by-step explanation:

Is this 4/6* 1/3 or are they seperate?

If its 4/6*1/3 you could say its 12/19 or 63.16%

Unit rate of the given quantity is equals to \(2:1\).

" Unit rate is defined as relation which is represented as the ratio of two different quantity in which value denominator is always one."

According to the question,

Given ratio of different quantity,

\(\frac{4}{6}:\frac{1}{3}\)

Convert it into unit rate we get,

\(= \frac{4}{6}\times \frac{3}{1} \\\\= \frac{4\times 3}{6\times 1}\\ \\= \frac{12}{6} \\\\= 2 : 1\)

Hence, unit rate of the given quantity is equals to \(2:1\).

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Answer:

The standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

Step-by-step explanation:

To find the standard deviation for the number of people with the genetic mutation in groups of 900, we can use the properties of the binomial distribution. The binomial distribution describes the number of successes (in this case, people with the genetic mutation) in a fixed number of independent Bernoulli trials (in this case, selecting people), each with the same probability of success.

In our case, we have:

n = 900 (number of trials, i.e., the number of people in each group)

p = 0.05 (probability of success, i.e., the probability of having the genetic mutation)

The mean (μ) and variance (σ²) of a binomial distribution can be calculated using the formulas:

μ = n * p

σ² = n * p * (1 - p)

We are interested in finding the standard deviation (σ), which is the square root of the variance:

σ = sqrt(σ²)

So, in our case:

σ = sqrt(900 * 0.05 * (1 - 0.05))

σ = sqrt(900 * 0.05 * 0.95)

σ ≈ sqrt(42.75)

σ ≈ 6.54

Thus, the standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

To find the standard deviation for the number of people with the genetic mutation in groups of 900, you can use the formula for the standard deviation of a binomial distribution:

σ = √(n * p * (1-p))

Here, n = 900 (number of people randomly selected), p = 0.05 (5% of the population has the genetic mutation).

σ = √(900 * 0.05 * (1 - 0.05))
σ = √(45 * 0.95)
σ ≈ 6.48

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

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The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

The formula would be

wd^2c/l = p

(2*1^2c)/4 = 10

(2*1c)/4 = 10

2c/4 = 10

c = 20

3*2^2*20/6 = p

3*4*20/6 = p

240 pounds

hope it help :)

Step-by-step explanation:

The safe load if the beam is turned on its side will be 240 pounds.

A burden or pressure source that is carried by someone or something. Construction loads are defined as the weights placed on an existing or temporary structure both during and after the construction process.

Given that the safe load for a horizontal beam supported at both ends varies jointly with the width and the square of its depth and inversely with the distance between the supports. If a 4 cm by 6 cm beam, 10 m long supports 5 kg when standing on the edge,

The load will be calculated by using the formula below:-

wd²c/l = p

(2 x( 1 ) ²c)/4 = 10

(2x 1c)/4 = 10

2c/4 = 10

c = 20

3 x ( 2 )²x ( 20/6 ) = p

3 x 4x ( 20/6 ) = p

p = 240 pounds

Therefore, the safe load if the beam is turned on its side will be 240 pounds.

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The error in the reading on the staff held at a distance of 100 m is approximately 83.91 meters.

To find the error in the reading on the staff, we need to convert the deflection of the bubble into an angular error. The sensitiveness of the bubble tube is given as 20" per 2 mm division, which means that each 2 mm division corresponds to a deflection of 20".

Given that the bubble is deflected by two divisions from the center, the total deflection is 2 divisions * 20" per division = 40".

Next, we need to calculate the angular error. We can use the small angle approximation, which states that for small angles, the tangent of the angle is approximately equal to the angle itself in radians.

Therefore, the angular error can be approximated as 40" * (π/180) radians. Now, to calculate the linear error at a distance of 100 m, we need to consider the relationship between angular error, linear error, and the distance from the level.

This relationship can be expressed as follows:

Linear Error = Distance * Tangent(Angular Error)

In this case, the distance is 100 m, and the angular error is 40" * (π/180) radians. Substituting these values into the equation, we can calculate the linear error:

Linear Error = 100 m * tan(40" * (π/180))

Using a calculator, we find that tan(40" * (π/180)) ≈ 0.8391.

Therefore, the linear error in the reading on the staff held at a distance of 100 m from the level when the bubble is deflected by two divisions from the center is approximately:

Linear Error = 100 m * 0.8391 ≈ 83.91 m.

Hence, the error in the reading on the staff is approximately 83.91 meters.

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Answer:

Step-by-step explanation:

#1, top left

#2, top right

#3, bottom left

#4, bottom right

Answer:

b. 10pi

Step-by-step explanation:

Radius of circle (r) = 5 units

\(c = 2\pi \: r = 2\pi \times 5 = 10\pi\)

Answer: BC ≈ 6.4 units

Step-by-step explanation: We can use trigonometry to find the length of line segment BC.

Since we know the length of AC and the measure of angle A, we can use the trigonometric function cosine (cos) to calculate BC.

Using the formula: cos(A) = Adjacent / Hypotenuse, we have

cos(34°) = BC / 9.

Solving for BC, we get BC ≈ 6.4 units (rounded to the nearest tenth).

Here is an article on trigonometry basics: https://byjus.com/maths/trigonometry/#:~:text=Trigonometry%20Basics,are%20based%20on%20these%20functions.