10 marbles what is the probability of drawing 2 blue marbles if the first marble is placed back in the bag before the second draw

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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The portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

To calculate the portfolio weights for stock A and stock B, we need to determine the total value of the portfolio and the proportion of each stock's value within that total.

The total value of the portfolio can be calculated as follows:

Total value = (Number of shares of stock A × Price per share of stock A) + (Number of shares of stock B × Price per share of stock B)

Total value = (135 × $84) + (110 × $82)

Total value = $11,340 + $9,020

Total value = $20,360

Now, we can calculate the portfolio weights for each stock:

Weight of stock A = (Value of stock A ÷ Total value) × 100%

Weight of stock A = (($84 × 135) ÷ $20,360) × 100%

Weight of stock A = $11,340 ÷ $20,360

Weight of stock A ≈ 0.5569 or 55.69%

Weight of stock B = (Value of stock B ÷ Total value) × 100%

Weight of stock B = (($82 × 110) ÷ $20,360) × 100%

Weight of stock B = $9,020 ÷ $20,360

Weight of stock B ≈ 0.4431 or 44.31%

Therefore, the portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

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The probability of having fifth tail occurring before the tenth head if a fair coin is flipped repeatedly is 0.377.

To solve this problem, we need to use the concept of negative binomial probability distribution.

The negative binomial probability distribution is a type of probability distribution that is used to describe the probability of k failures occurring before r successes in a sequence of independent and identical trials.

Let us consider the problem at hand.

We need to find the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly.

Let X be the number of trials required to obtain the fifth tail. Then, X follows a negative binomial distribution with parameters r = 5 (number of successes we want) and p = 0.5 (the probability of obtaining a tail in a single flip).

The probability of obtaining the fifth tail on the kth trial is given by: P(X = k) = ᵏ-¹C₄(1 - p)ᵏ-ʳ *

where ᵏ-¹C₄ denotes the number of combinations of (k - 1) trials that yield 4 tails before the kth trial.

Since X should occur before the tenth head, k should be less than or equal to 9.

Therefore, we can calculate the required probability as follows:

P(X ≤ 9) = ∑P(X = k) for k = 5 to 9

= (⁴C₄*0.5⁵) + (⁵C₄*0.5⁶) + (⁶C₄*0.5⁷) + (⁷C₄*0.5⁸) + (⁸C₄*0.5⁹)

= (1*0.03125) + (5*0.015625) + (15*0.0078125) + (35*0.00390625) + (70*0.001953125)

= 0.376953125

Therefore, the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly is 0.377.

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Step-by-step explanation:

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The energy that it takes to melt 2 kg of ice is; (2 kg * 1000 g/kg) * 1 mol/18.02 g * 6.03 kJ/mol = 669 kJ

We are given;

Mass of ice; m = 2 kg

Now, from tables showing constants for ice, we see that;

Molar heat of fusion for ice; Δ_fus.H = 6.03 kJ/mol at 0°C.

Molar mass of Ice which is water is; 18.02 g/mol

Formula to get the energy is;

E = (m/M) * Δ_fus.H

E = (2 kg * 1000 g/kg) * 1 mol/18.02 g * 6.03 kJ/mol = 669 kJ

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Answer:

x = -6 and y = -3

Step-by-step explanation:

x- 4y =6

x =4y +6......(i)

5x -4y =-18

20y +30 - 4y = -18

16y = -48

y = -3

x = -12+6

x = -6

Given paraboloid equation is z = 9 + 2x² + 2y² and plane equation is z = 15. Now, we need to find the volume of the given solid using polar coordinates in the first octant.

The given equations in polar coordinates are:
x = rcosθ, y = rsinθ and z = z, Using these equations we can rewrite the given equation as:
z = 9 + 2x² + 2y² ⇒ z

= 9 + 2r²cos²θ + 2r²sin²θ ⇒ z

= 9 + 2r² (cos²θ + sin²θ) ⇒ z

= 9 + 2r²......(1).

As per the given information, the volume of the given solid is bounded by the paraboloid z =9 + 2x2 +2y2 and the plane z = 15 in the first octant. Using these equations, we need to find the volume of the given solid using polar coordinates in the first octant. Given paraboloid equation is z = 9 + 2x² + 2y² and plane equation is z 15. Now, we need to find the volume of the given solid using polar coordinates in the first octant.

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\((5^{4} *\frac{1}{b^{10} }) ^{-6}\)

\((\frac{5^{4} }{b^{10} } )^{-6}\)

\(\frac{b^{60} }{5^{24} }\)

Answer:88

Step-by-step explanation:

Answer:

0.576

Step-by-step explanation:

0.08 x 720 /100   = 0.576

Answer:

40

Step-by-step explanation:

The one from the given option representing linear ordinary differential equations are ,

option a) ∂² u/∂x² + ∂² u/∂x² = 2x and option b) 2 dy/dx + 3y = e⁻ˣ.

To determine which equations are linear ordinary differential equations (ODEs),

Check if they satisfy the linearity property. A linear ODE can be expressed in the form,

aₙ(x) dⁿ y / dxⁿ + aₙ₋₁(x) dⁿ⁻¹ y / dxⁿ⁻¹ + ... + a₁(x) dy / dx + a₀(x) y = f(x)

where aₙ(x),  aₙ₋₁(x), ..., a₁(x), a₀(x) are functions of x, y is the dependent variable, and f(x) is a function of x.

Let us check each given equation,

∂² u/∂x² + ∂² u/∂x² = 2x

This equation includes a term with the second derivative of u with respect to x, which is linear.

Therefore, equation a) is a linear ODE.

2 dy/dx + 3y = e⁻ˣ

This equation includes a term with the first derivative of y with respect to x, which is linear.

Therefore, equation b) is a linear ODE.

∂² y/∂x² + \(e^{y}\) = 0

This equation includes a term with the second derivative of y with respect to x,

but it also includes a non-linear term \(e^{y}\).

Therefore, equation c) is not a linear ODE.

Therefore, the linear ordinary differential equations are option a) ∂² u/∂x² + ∂² u/∂x² = 2x and option b) 2 dy/dx + 3y = e⁻ˣ.

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Answer: uh nt rlly helping i need sum help w hw and i need points to ask question so uh ye just thank me pls

Step-by-step explanation:

Answer:

The equation is graphed below.

Step-by-step explanation:

Please see attachment.

Hope this helps!

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Answer:

Step-by-step explanation: 24 smoothies

Answer:180

Step-by-step explanation:

If there are 6 kinds of fruit and three kinds of juice, lets say these are the only 2 choices so far. With 6 fruits and 3 juices, Clare can make 18 different smoothies. Next, lets take the 5 frozen yogurts. If Clare can make 18 different types of smoothies without the frozen yogurt, then we are now adding 5 variations to all 18, meaning there is now 90 different types of smoothies. Finally, she has 2 garnishes to top it with, so there are 2 different variations to the 90 existing smoothies, which in total, comes out to 180 different types of smoothies that Clare can make.

Answer:

i think its 58824.5

okay so since the area is 22cm^2 , you will need to simplify it.

Which you will get 22*22 and the total would be 484. Which u will divide by 4 ( Square) to get each of the side your looking for.

So your answer is... 121

Answer:

$5,102.05

Step-by-step explanation:

Present value of the car = $21,500

Present percentage value = 100% = 1

Percentage of Depreciation per year = 25% = 0.25

Years of depreciation = 5 years

The value of the car after 5 years = Present value of the car (Present percentage value - Percentage of Depreciation per year)^Years of depreciation

= 21,500(1 - 0.25)^5

= 21,500(0.75)^5

= 21,500(0.2373046875)

= 5,102.05078125

Approximately,

The value of the car after 5 years = $5,102.05

Distance is increasing with a speed of 0.2 Miles/Min

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time in Minutes      Distance in Miles

0                              0.0

2                              0.4

4                              0.8

6                              1.2

8                              1.6

Here, Myra’s distance is increasing as time increase with a constant Speed.

Now, In every 2 mins distance traveled = 0.4 Miles

Hence, In every 1 min Distance traveled = 0.4/2 = 0.2 Miles/Min

Thus, Distance is increasing with a speed of 0.2 Miles/Min.

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a) The linear equation expressing the average annual cost to employees y in terms of the number of years x

after 2000 is: y = 40x + 3140

b) The average annual cost in 2014 was approximately 3700.

c) The first full year in which costs exceed 7000 is 2097.

(a) To write a linear equation expressing the average annual cost to employees y in terms of the number of years x

after 2000, we need to find the slope and y-intercept of the line that passes through the points (9, 3500) and (14,

4500), where x represents the number of years after 2000 and y represents the average annual cost in dollars.

The slope of the line is given by:

m = (y2 - y1) / (x2 - x1) = (4500 - 3500) / (14 - 9) = 200 / 5 = 40

The y-intercept can be found by plugging in one of the points into the equation y = mx + b and solving for b:

3500 = 40(9) + b

b = 3500 - 360 = 3140

(b) To find the average annual cost in 2014, we need to plug in x = 14 into the equation we just found:

y = 40(14) + 3140 = 560 + 3140 = 3700

(c) To find the first full year in which costs exceed 7000, we need to solve the equation y = 40x + 3140 for x when

y = 7000:
7000 = 40x + 3140
3860 = 40x
x = 96.5

Since x represents the number of years after 2000, we need to add 2000 to get the actual year:

2000 + 96.5 = 2096.5

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Answer:

Step-by-step explanation:

O.    

\((-5)^2-(-6)^2\\25-36\\-11\)

P.

\(\frac{2}{(5)^2}\\ \frac{2}{25}\)

Q.

\(15-(-2)^4\\15-16\\-1\)

R.

\(2-12\\-10\)

Answer:

1) Mean = 6.28

2) Median = 7

3) Mode = 8

4) Range = 6

Step-by-step explanation:

We need to find Mean, Median, Mode and Range of data given in tables.

1) Mean

The formula used to calculate mean is: \(Mean=\frac{Sum\:of\:all\:data\:points}{Number\:of\:data\:points}\)

The data given is: 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9

Sum of all data points = 132

Number of data points = 21

Finding mean:

\(Mean=\frac{Sum\:of\:all\:data\:points}{Number\:of\:data\:points}\\Mean=\frac{132}{21}\\Mean=6.28\)

So, Mean = 6.28

2) Median

The formula used to calculate median is: \(Median=\frac{n+1}{2}\:th\: term\) because we have n = odd

Number of data points n = 21

Putting values and finding the position of median term

\(Median=\frac{n+1}{2}\:th\: term\\Median=\frac{21+1}{2}\:th\: term\\Median=\frac{22}{2}\:th\: term\\Median=11\:th\:term\)

So, in the given data : 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9

The 11 th term is 7

So, Median = 7

3) Mode

The mode is the most repetitive value of data set.

In the given data set: 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9

The most repetitive value is 8

So, Mode = 8

4) Range

The range can be calculated using formula: \(Range=Maximum\:Value-Minimum\:Value\)

In the given data set: 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9

Maximum value = 9

Minimum value = 3

So, the range is:

\(Range=Maximum\:Value-Minimum\:Value\\Range=9-3\\Range =6\)

So, Range = 6

Answer:

Step-by-step explanation:

got it right on Edge

Answer:

Which of the following statements is true about the dataset below?

4, 2, 0, 3, 2, 1, 9, 6, 4, 5

The mean is 3.6

The median is 3.5

The mode is 2 and 4

Thus the statements that are true are:

The mean is larger than the median.

- The mean and the median are equal. This is not true because the mean is 3.6 while the median is 3.5.

- There is only one mode. This is incorrect because there are 2 modes, 2 and 4 both repeat twice.

- The median is larger than the mean. This is also incorrect because 3.5 is not bigger than 3.6.

Step-by-step explanation:

You're welcome.

Answer:

The opposite sides of a rectangle are equal in length ⇒ perimeter = 2(3x +1) +2(x + 1) Also the perimeter = 28.

Answer:

P=2(L+W)

Step-by-step explanation:

p=2(L+W)

    2(2x+1)+2(3x-2)

    4x+2+6x-4

    10x-2

Answer:

la respuesta es 10.3199...

Step-by-step explanation:

solo divides 100 por 9.69

There is a probability of 66.5 % chance of it landing on a 5 at least once in 6 dice.

Because there are six faces on a die, you have an even chance of the dice landing on one of these faces each time you roll:

This means that each time that you roll, there is a 5/6 chance that you will not roll a 5.

The probability of not rolling a 6 twice is 5/6 or 69.4%.

Roll the die six times, and the probability of not rolling a 5 is

(5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6)

= (5/6)⁶

= 33.5%

Therefore, the probability of rolling a 5 at least once in 6 dice

= 100%  - 33.5%

= 66.5%

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Answer:

by the way and the answer is c for yhe reasin because the of tje by theand i thaith

Answer:

anor soi sena orka uzumo senda?

The only value for which the functions f(x) ≠ g(x) is: Option D: 3

A function is defined as a relation whereby each input value (x-value) will possess only one output value (y-value). Therefore, all functions are termed as relations. However, not all relations are functions due to the fact that it is not all that will meet the requirement that each unique input creates only one output .

From the graph, we see that the graph of f(x) and g(x) intersect at:

x = -1

x = -2

x = 2

These are the points where the output value of both functions are equal

Thus, looking at the options, only Option D does not represent an input value that makes both functions equal.

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Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

The solution to the given inequality as represented in the task content are; z < - 1.00485413 OR z > 1.00485413.

It follows from the task content that the solution of the given inequality; ( 29 / 289z ) < ( 16 / 161 ) z is to be determined.

Since the given inequality is;

( 29 / 289z ) < ( 16 / 161 ) z

By cross multiplication; we have;

161 × 29 < ( 16z × 289z )

( 161 × 29 ) / ( 16 × 289 ) < z²

1.00973183 < z²

Therefore;

1.00485413 < z. OR. -1.00485413 > z.

Ultimately, z < - 1.00485413 OR z > 1.00485413.

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