I need help with converting this to get the answer!! Please help!! :D

The formula for the variance of a binomial distribution is:
Variance = n * p * q
Plugging in the values, we get:
Variance = 30 * (1/6) * (5/6) ≈ 4.17
So, the variance of the probability distribution of the number of 5's obtained in this experiment is approximately 4.17 when rounded off to the second decimal place.

To find the variance of the probability distribution for the number of 5's obtained in this experiment, we'll use the binomial distribution formula. The terms in the binomial distribution are:
1. n = number of trials (30 rolls)
2. p = probability of success (rolling a 5) on each trial (1/6, since there are 6 faces on a fair die)
3. q = probability of failure (not rolling a 5) on each trial (5/6)

To find the variance of the probability distribution of the number of 5's obtained when a fair die is rolled 30 times, we need to use the formula:
Variance = ∑(x-μ)^2 P(x)
where x represents the number of 5's obtained, μ represents the expected value of x (which is the mean of the distribution), and P(x) represents the probability of getting x 5's in 30 rolls.

Since the die is fair, the probability of getting a 5 on any given roll is 1/6. Therefore, the probability of getting x 5's in 30 rolls can be calculated using the binomial distribution formula:
P(x) = (30 choose x) * (1/6)^x * (5/6)^(30-x)

We can use this formula to calculate P(x) for each possible value of x (i.e. x = 0, 1, 2, ..., 30). However, since we only need the variance of the distribution, we can simplify the formula using the expected value of x:
μ = np = 30 * (1/6) = 5

Now we can calculate the variance using the simplified formula:
Variance = ∑(x-μ)^2 P(x)
        = ∑(x-5)^2 * (30 choose x) * (1/6)^x * (5/6)^(30-x)
        ≈ 1.36

Therefore, the variance of the probability distribution of the number of 5's obtained in 30 rolls of a fair die is approximately 1.36 (rounded off to the second decimal place).

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Answer:

37.0                         Your answer is 28.9 Celsius  

- 8.1

---------

 28.9

Step-by-step explanation:

Fahrenheit:

90.5 Fahrenheit

Celsius:

23.7

then the order of a in the group G is 30. This can be guessed using the formula provided above, after calculating the least common multiple (lcm).The explanation is limited to 250 words.

Let us consider a group G with an element a such that the order of a5 is 12. In the group G,

can we make any guess about the order of the element a?Solution:Let G be a group and a be an element in G. Let's suppose the order of a5 is 12.

That means (a5)12 = e, where e is the identity element in G.Now we can calculate the order of a. For this, we need to find the smallest positive integer n such that an = e.To do this, we can use the following identity: (an)m = amn for all m and n in Z+.Let's calculate the order of a:an = (a5)2n/5 = a2n.

Therefore, a2n = e.The smallest positive integer n such that a2n = e is called the order of a. Thus, the order of a is equal to 5 × lcm(2, 12/5) = 60/2 = 30.This result is a consequence of the fact that for any x and y in Z+, lcm(x, y) = xy/gcd(x, y).Therefore, if the order of a5 is 12,

then the order of a in the group G is 30. This can be guessed using the formula provided above, after calculating the least common multiple (lcm).

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Answer:

a postulate is a mathematical statement taken as fact

a definition is a formal statement declaring the meaning of a word

a theorem is a mathematical statement proven by postulates and definitions

a diagram is a visual tool representing mathematical ideas to be represented

Answer:

35/100

Step-by-step explanation:

You have to find how many juniors there are, so if you add 13, 20, and 2 you get 35. For the denominator you have to find the total number of students, so just add all of the numbers together to get 100. So there is a 35/100 chance that a randomly selected student is a junior.

Answer: 7/20

Step-by-step explanation:

Answer:

Supplementary angles are angles that have a sum of 180°. When two angles are supplementary, we say that one angle is the supplement of the other.

Complementary angles are angles that add up to 90°. When two angles are complementary, we can say that one angle is the complement of the other

Step-by-step explanation:

The area of the composite figure is 89.065 ft^2

We can divide the figure into 3 simpler ones, these are:

A rectangle of 5ft by 2 ft

A rectangle of 8ft by 9 ft

A fourth of a circle of radius R = 3ft

Remember that the area of a circle of radius R is:

A = 3.14*R^2

Then the area of the fourth a circle of radius R = 3ft is:

a = (1/4)*3.14*(3ft)^2 = 7.065 ft^2

And the areas of the rectangles are equal to the product between the dimensions, so the areas are:

a' = 5ft*2ft = 10ft^2

a'' = 8ft*9ft = 72 ft^2

The total area is the sum of these:

7.065 ft^2 + 10ft^2 +72ft^2 = 89.065 ft^2

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By applying dilatation and congruency theorem, it can be concluded that the distance between points R and R' is 3 units (option A).

Dilation is a transformation of a geometric shape, either becoming larger or smaller, without changing the original shape using a certain scale factor.

Two shapes are said to be congruent if a pair of corresponding sides have the same ratio and the corresponding angles have the same measure.

From the problem we obtained the following information:

QR is dilated to create Q'R' ⇒ QR // Q'R'

The dilatation factor is 1.5 ⇒ Q'R'/QR = 1.5

Now we look at the ΔTRQ and ΔTR'Q':

QR // Q'R'

∠TRQ = ∠TR'Q'

So ΔTRQ is congruent to ΔTR'Q' and TR'/TR = Q'R'/QR

Now we can calculate y using this equation:

   TR'/TR = Q'R'/QR

(6 + y) / 6 = 1.5

      6 + y = 9

            y = 3

Thus, the distance between points R and R' is 3 units.

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Answer:

6

Step-by-step explanation:

Using the formula for velocity of money:

Velocity of money = (Price level x Real output) / Money supply

Plugging in the given values, we get:

Velocity of money = (120 x 300 billion) / 6 trillion

Velocity of money = 6

Therefore, the velocity of money is 6.

The expression 70x-40x^4 if  factor is:-10x (4x^3-7).

Expressions  can be defined as equation that has both number that are known as well as numbers that are not known .

Example of expression is the sum of 9 and 1  will gives us 10  which is calculated as (9+1 =10).

Given data:

Expression: 70x-40x^4

Now let factor the expression using the given expression

70x-40x^4

Rearrange the expression

-40x^4 +70x

Common factor

-10(4x^4 -7x)

So the expression is:

-10x (4x^3-7)

Therefore we can conclude that the expression is -10x (4x^3-7).

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Answer:

If i go to the park then it will stop raining

Step-by-step explanation:

I think

hope this help have a good night

Answer:

26.6 minutes

Step-by-step explanation:

Set up a proportion

3/8 = 10/x

cross multiply

3x = 80

x = 26.6

hope it will be helpful.......

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Amelia made a mistake in Step 2. She should have squared the expression (r+2) before taking the square root of both sides.

A circle is a two-dimensional shape that is defined as the set of all points in a plane that are at a constant distance, called the radius, from a given point, called the center. It can be thought of as a closed curve or a line forming a closed loop. The distance around the circle is known as its circumference, and it is equal to 2 times pi times the radius, where pi is an irrational number approximately equal to 3.14159. The area enclosed by a circle is given by the formula A = pi times the radius squared. Circles have many important applications in mathematics, geometry, and physics, and they are used to represent many real-world objects, including wheels, gears, planets, and celestial objects.

Amelia made a mistake in Step 2. She should have squared the expression (r+2) before taking the square root of both sides.

The correct solution process is:

Step 1: A = π (r+2)²

Step 2: ±√(A/π) = r+2

Step 3: (± √(A/π)) - 2 = r

In Step 2, we first divide both sides by pi, and then take the square root of both sides. In Step 3, we subtract 2 from both sides to isolate r. This process correctly solves for the radius of the original circle based on the given area covered in oil.

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Answer: 30 costumes

Step-by-step explanation:

Let x be the total amount of costumes.

In order to get 30% , we need to divide 9 by the total amount of costumes (x), but first we need to change 30% to its multiplier:

30% ÷ 100 = 0.3 (multiplier).

\(\frac{9}{x} =30\)%

\(\frac{9}{x} =0.3\)

\(x=\frac{9}{0.3}\)

\(x=30\) costumes

Or if that is confusing:

\(\frac{9}{x} =30\)%

\(\frac{9}{x} =0.3\)

\(\frac{x}{9} =\frac{1}{0.3}\)

\(x=9 *\frac{1}{0.3}\)

\(x=\frac{9}{0.3}\)

\(x=30\) costumes

The above equations are exactly the same, they are just written differently.

We can now check if our answer is correct:

\(\frac{9}{30} = 0.3\\0.3*100=30\)%

Hope you understand!

Answer:

18) a^5b^-3c

19) -3xy^1z^-2

20) -5r^4s^-2t^-3

Answer:

So heres what I think

C=2pie r

C=2*3.14*4

c=25.12

So basically half the circle is the radius and the whole is the circumference. So what you are doing is changing pie to 3.14 (since pie=3.14), since half the circle its radius so all you have to do is 2 times 3.14 times 4 to get 25.12 as your circumference.

Hope this helps!

Step-by-step explanation:

Answer: It is roughly 25.12 or 8π

Step-by-step explanation:

Well, it depends if you are using 3.14 as a subsitute for Pi, or you are just using the Pi symbol (π). Let me explain better:

The equation for solving the circumference of a circle is C=2πr

R is the radius, which is the 4 in the problem. If you were just using the Pi symbol, you would multiply 2*4 because you plugged 4 into the equation above. This would result in C=8π.

If you were using 3.14, you would subsitute both 3.14 and 4. So it would be C=2(3.14)(4) which would be 25.12

Hope this helped! (By the way, if it is wrong, I have not gotten this in my math class yet). ALSO remember to check whether the homework is using 3.14 for Pi or you just using the Pi symbol. And to put the squiggly equation symbol which means about.

Answer: Anything greater then -16 (EX: -15, -14)

Work: This is a One-Step Inequality equation, meaning you just need to divide. You need to get x by itself, so you divide the 6 on both sides, but since there is a negative, you have to flip the sign. So, the answer is x > -16.

Check: 6(-15) > -96;   -90 > -96 < It's correct.

The graph of f(x) = x^3 -6x^2 + 4x +1 hits 3 times to the x-axis

Hence, option (D) is the correct choice.

We have the function:

f(x) = x^3-6x^2+4x+1

The values of the variable in a function that cause the function to equal zero are known as the zeros of the function. The places on the x-axis where the graph crosses the x-axis are known as a function's zeros graphically. In other words, we may say that a function's zeros are the graph's x-intercepts.

The zeros of the function will be:

x^3-6x^2+4x+1 = 0

Since the last term is positive, so (x-1) will be the factor of the above equation.

Factorising, we will get,

(x-1)(x^2-5x-1)=x^3-6x^2+4x+1

So, one factor will be x = 1

Now solving the quadratic equation,

The roots will be: \(x^2 = \frac{( 5 \pm \sqrt 29)}{2}\)

So, the value of both roots will be: (x-5.19)(x+0.192)

Therefore, the graph will hit x-axis at these three points.

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Answer:

h=4cm

Area of triangle=1/2bh

1/2×8×6=72

Answer:

180

Step-by-step explanation:

xdcjuggggggggggggggggggggg

Answer:

-3 3/7

Step-by-step explanation:

Hope this helps!:)

The third term of the arithmetic sequence is 18.

The arithmetic sequence formula can be represented as follows:

nth term = a + (n - 1)d

where

Therefore, 4 numbers are inserted between 4 and 39.

Hence,

a = 4

39 = 4 + 5d

39 - 4 = 5d

35 = 5d

d = 35 / 5

d = 7

Hence, the common difference of the arithmetic sequence is 7.

Therefore, the sequence of the arithmetic sequence is as follows:

4, 11, 18, 25, 32, 39

Therefore, the third term of the arithmetic sequence is  18

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Answer:

2.77083333333

Step-by-step explanation:

I assume. Do not hold me account for mistakes, I apologize if my work is incorrect. Have a good day/night :}

Area of polygon = 1/2 * product of diagonals

Area of polygon = 1*10*8/2 = 40 unit square

Answer:

A. 23, 37.....

B. 26, 42......

Step-by-step explanation:

have a great day!

The weightage is given to the most recent values in the time series.

SES is a simple forecasting technique that is easy to implement and can be used with data that has a consistent trend. However, it is not well suited for data that is highly volatile or has a lot of noise.

One of the simplest forecasting techniques is single exponential smoothing (SES). It is a weighted average of past time-series values, where the weightage is given to the most recent values in the time series. This technique is easy to implement and can be used with data that has a consistent trend. However, it is not well suited for data that is highly volatile or has a lot of noise.

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A spontaneous reaction can occur even if the calculated ΔH is positive.

When a reaction occurs spontaneously, it means that the overall change in Gibbs free energy (ΔG) is negative. ΔG represents the energy available to do useful work, and it's calculated as follows:

ΔG = ΔH - TΔS

Where T is the temperature in Kelvin. A negative ΔG indicates that the reaction is thermodynamically favorable, while a positive ΔG means that the reaction is not favorable.

To answer this question, let's rearrange the equation for ΔG:

ΔG = ΔH - TΔS

ΔH = ΔG + TΔS

Since ΔG is negative for a spontaneous reaction, we can rewrite the equation as:

|ΔH| = -ΔG + TΔS

From this equation, we can see that if ΔH is positive, then -ΔG must be greater than TΔS. Since -ΔG is negative, then TΔS must be negative as well.

In other words, a spontaneous reaction can still occur even if it absorbs heat (ΔH is positive) as long as the increase in disorder (ΔS) is negative enough to overcome the positive ΔH.

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Kirsten had to drive 5 miles north, and then turn to the east for 12 miles where she found a nice parking spot at the Movie Theater :)

If the image represents the road she drove, she did travel 5 + 12 miles, thus she finally travelled 17 miles.