An unfair coin is tossed 3 times in a game. Let X be the total number of heads out of 3 tossing when the probability of heads P(H) = 0.4. The bet for each game is $5, and when two heads out of 3 tossing will wins $4, and three heads wins $10 (no reward for other cases). Find the expected value of the gain denoted by Y = (win - bet) of this game, E[Y].

Answer:

0

Step-by-step explanation:

Total outcomes = 6

Favourable outcomes = 0(As there is no 7 in a dice)

Probability = Favourable Outcome/Total outcomes

=> 0/6

=> 0

Answer: 1.5x²

Step-by-step explanation:

Rule: To find the area of a triangle, multiply the base times one side, then divide the product by 2.

Step 1: Find the length of the left side using the pythagorean theorem.

a^2 + b^2 = c^2.

x^2 + 2x^2 = 3x^2

√3x² = 3x

Step 2: Multiply the base times the hypotenuse.

x * 3x = 3x²

Step 3: Divide by two

3x²/2 = 1.5x²

Answer:

yesss they are

Answer:yes

Step-by-step explanation:

option c) = \(\frac{1}{12}\)th of the mass of C - 12 atom is correct.

First, let us study the definition of Atomic Mass,

Atomic mass -

So we can also conclude that the 1 atomic mass unit is equal to 1/12 of the mass of the C-12 atom

Therefore, option c) = \(\frac{1}{12}\)th of the mass of C - 12 atom is correct.

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Answer:

7

Step-by-step explanation:

42/6=7

Answer:

81 hours

Step-by-step explanation:

1. How much does she work in all of the 6 days.

1answer. 72

1explain. 6 · 12 = 72

2. You need to add 72 to 9

2answer. 81

2explain: 2 + 9 = 11 and 70 + 11 =81

3. You get 81 hours.

Answer:

A.

Step-by-step explanation:

Atom is the smallest thing g possible and organ is the biggest on that list.

The correct answer is D) a night that is longer than a certain length.

Short-day plants, also known as long-night plants, require a period of uninterrupted darkness or a night that is longer than a specific critical length in order to flower. These plants have a photoperiodic response, meaning their flowering is influenced by the duration of light and dark periods in a 24-hour day.

Short-day plants typically flower when the duration of darkness exceeds a critical threshold. This critical length of darkness triggers a series of physiological processes within the plant that eventually lead to flowering. If the night length is shorter than the critical threshold, the plant will not flower or may have delayed flowering.

It's important to note that short-day plants are not necessarily restricted to only flowering under short days. They can still flower under longer days, but the critical factor is the length of uninterrupted darkness they receive.

Hence the correct answer is D.

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Complete question =

What does a short-day plant require in order to flower?

choose the correct option

A) a burst of red light in the middle of the night

B) a burst of far-red light in the middle of the night

C) a day that is longer than a certain length

D) a night that is longer than a certain length

E) a higher ratio of Pr to Pfr

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

$8.10

Step-by-step explanation:

You can just multiply how many yards she bought by the price per yard.

3×2.7=

$8.10

She spent 8 dollars and 10 cents.

Answer:

123

Step-by-step explanation:

The answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

The equation x3 + y3 = 9 is a cubic equation and is a non-linear equation. As such, it does not have any tangent lines that are horizontal. A tangent line is a line that just touches a point on a curve and has the same slope as the curve at that point. Since the equation is non-linear, the slope of the curve changes at each point, meaning that there cannot be any horizontal tangent lines.

To calculate the slope of the curve at any point (x,y), we use the formula m = (dy/dx) or m = 3*(x2/y2). At these points, the slope of the curve will not be zero, meaning that there is no horizontal tangent line at any point on the curve.

Therefore, the answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

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Answer:

2,5 ,17,65.

Step-by-step explanation:

The sequence is x*4-3

I hope this helps!

Answer:

equtions have mathematical signs and descritions are like riddles and you have to figure out the operation

Step-by-step explanation:

When The equations have mathematical signs and also descriptions are like riddles. Then we have to figure out the operation.

Equation                                                    Verbal description

y =                                                                 T-shirts are being

1.25x                                                             sold in a store for

                                                                              $5.25 each.

A variable is a missive used to represent a value or unexplored quantity that can modify or vary in an expression or equation.

An utterance is a variety of variables, quantities, and mathematical functions; 4, 8 x, and b + 102 are all expressions.

An equation is an presentation set equal to another expression; a = 4, 1 + 23 = x + 9, and (2 + 3)1 = 2 c. are all equations. 1 3. 6. 1: Formation Processes from Context.

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The measures of the angles of a triangle are in the ratio of 2:3:5, then the actual measures of the angles are 36 degrees, 54 degrees, and 90 degrees.

If the measures of the angles of a triangle are in the ratio of 2:3:5, then the expressions 2x, 3x, and 5x represent the measures of these angles.

To find the actual measures of these angles, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.



Let's say that the measures of the angles are 2y, 3y, and 5y (where y is some constant).

Using the fact that the sum of the angles in a triangle is 180 degrees, we can set up an equation:

2y + 3y + 5y = 180

Simplifying, we get:

10y = 180

Dividing both sides by 10, we get:

y = 18

Now we can substitute y = 18 back into our expressions for the angle measures:

2y = 2(18) = 36

3y = 3(18) = 54

5y = 5(18) = 90

So the measures of the angles are 36 degrees, 54 degrees, and 90 degrees.

Therefore, if the measures of the angles of a triangle are in the ratio of 2:3:5, then the actual measures of the angles are 36 degrees, 54 degrees, and 90 degrees.

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The number of groups of computer programming that can be selected from the 17 strong teams depends on the conditions given to the selection.

The correct answer is:

(a) There are 24,310 ways to select the group of 9 out of 17 members.

Probability = number of paths to success. A total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.

Probability is a measure of the likelihood that an event will occur. Many events cannot be predicted with complete certainty. We can only predict the probability that an event will occur. H. Possibility of using it.

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The value of CPI will be 178.

What is an expression?

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

Given that;

In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Now,

Since, In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Hence, The value of CPI will be;

CPI = 118.10 × 100 / 66.35

      = 11810 / 66.35

       = 178

Thus, The value of CPI will be 178.

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The number Cassie added to 0.000009535 to get 9.62e-6 is 8.5×10⁻⁸. Option B is correct.

Cassie added two numbers together on her calculator, resulting in a sum of 9.62e-6.

Convert 9.62e-6 to decimal.

9.62e-6  = 9.62 × 10⁻⁶

=0.00000962

She knows that one of the numbers she added was 0.000009535.

To find the other number, we can subtract 0.000009535 from the sum:

Let us consider the other number as x.

0.000009535 +x =0.00000962

x =0.00000962 - 0.000009535

= 8.5e-8 or 0.000000085

The result of the subtraction is 8.5e-8  or 8.5×10⁻⁸.

Therefore, the number Cassie added to 0.000009535 to get 9.62e-6 is 8.5×10⁻⁸, option B is correct.

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Complete question is:

Cassie added two numbers together on her calculator for her biology homework. the calculator showed the sum as 9.62e-6. she knows she used 0.000009535 as one of the numbers. what number did she add to 0.000009535 to get 9.62e-6?

(A) 8.5×10⁻⁶

(B) 8.5×10⁻⁸

(C) 1.8×10⁻⁶

(D)  1.8×10⁻⁸

The number that was added to 0.000009535 to get a sum of 9.62e-6 is 0.000000085. This is found by converting 9.62e-6 to its standard representation, and then subtracting the given number 0.000009535.

The question is asking for the number that was added to 0.000009535 to result in a sum of 9.62e-6. To answer this, we need to subtract the given number from the total sum. 9.62e-6 is a scientific notation, which stands for 0.00000962. If we subtract 0.000009535 from 0.00000962, we get the missing number.

So, 0.00000962 - 0.000009535 = 0.000000085. Therefore, the number she added to 0.000009535 is 0.000000085.

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We have the following response after answering the given question: function Hence, the quarterly growth rate is almost 4.08%.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

\(P(t) = P0 * e^(rt) (rt)\)

Where q is the quarterly rate of increase, \(q = (1 + r)(1/4) - 1.\)

\(q = (1 + 0.17)^(1/4) - 1 ≈ 0.0408\sP(t) = 1100 * e^(0.17t) (0.17t)\)

Q is equal to round\(((1 + 0.17 ** (1/4) - 1, 4)\)

P0 = 1100

math.log(1 + q) = r

(q * 100, 2)

4.08 P(t) = P0 * e(rt), where r is the natural logarithm's base and P0 is the beginning population (approximately 2.71828).

Where q is the quarterly rate of increase, q = (1 + r)(1/4) - 1.

\(q = (1 + 0.17)^(1/4) - 1 ≈ 0.0408\sP(t) = 1100 * e^(0.17t) (0.17t)\)

We may convert the quarterly growth rate to a percentage and round to the closest hundredth of a percent to get the percentage rate of change every quarter:

(q * 100, 2)

4.08

Hence, the quarterly growth rate is almost 4.08%.

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Answer:

(x,y)--(-X, "): A' is at (5, -1)

Step-by-step explanat

Answer:

(x,y)→(−x,−y); A' is at (5, −1)

Step-by-step explanation:

The probability that the engine will survive for more than 2 hours is 94.09%.

To find the probability that a given engine will survive two hours, we need to use the concept of independent events. This means that the probability of an event happening in one hour does not affect the probability of it happening in the next hour.

The probability of the engine surviving for one hour is 1 - p = 1 - 0.03 = 0.97 (since the probability of malfunction is 0.03, the probability of survival is the complement of that, which is 1 - 0.03).

To find the probability of the engine surviving for two hours, we need to multiply the probability of survival for each hour:

P(survive for 2 hours) = P(survive for 1 hour) * P(survive for 1 hour)
= 0.97 * 0.97
= 0.9409

Therefore, the probability that a given engine will survive two hours is 0.9409 or 94.09%.

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The basic arithmetic operations are:

Addition (+): The operation of finding the total of two or more numbers.

Subtraction (-): The operation of finding the difference between two numbers.

Multiplication (*): The operation of finding the product of two or more numbers.

Division (/): The operation of finding the quotient of two numbers, where the numerator is divided by the denominator.

Exponentiation (^ or **): The operation of finding the result of raising a number to a power.

These basic arithmetic operations form the foundation of many mathematical and scientific concepts, and are used in a wide variety of applications. In addition, they are the building blocks for more advanced

mathematical operations, such as logarithms, derivatives, and integrals.

Linear equations are mathematical expressions that describe a linear relationship between two variables. In a linear equation, the highest power of the variables is 1, and the coefficients and variables are related in a straightforward manner.

A linear equation in one variable (such as y = 2x + 1) describes a straight line when plotted on a graph. In two variables, a linear equation describes a plane in three-dimensional space.

Linear equations have the form:

y = mx + b

where x and y are variables, m is the slope of the line, and b is the y-intercept, the point at which the line crosses the y-axis.

Linear equations are used in many fields, including economics, physics, and engineering, to model and analyze relationships between variables.

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Answer:

The solution to a system of equations means the point must work. In both equations in the system, if you are asked if a point is a solution to an equation, you replace the variables with the given values and see if the two sides of the equation is equal "so is a solution"

Answer:

Since each yard is worth $54.00, then you first need to find the area of the carpet.

To do this, you can just multiply the length times width.

5 * 7 = 35

The carpet has an area of 35 yards in total.

Now you just need to find how much money 35 yards of carpet is worth.

To do this, you just multiply:

$54 * 35 = $1,890

It would cost $1,890 for the carpet.

Step-by-step explanation:

Hope it helps! =D

The value of a/b is  \(\sqrt{6}\) / 2

The area of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.

According to the question:-

Side of an equilateral triangle equals a/3.

Therefore, the equilateral triangle's area is equal to (1/2)(a/3)2 sqrt (3) / 2 = a2 [sqrt (3)/ 36].

Hexagonal side equals b / 6.

The area is thus 6 (1/2) (b/6)^2 sqrt (3) / 2 

= b^2 [ 3 sqrt (3) / 72] = b^2 [sqrt (3) / 24]

So

sqrt (3) / 36 a2 = sqrt (3) / 24 b2

So

A2 / B2 = [Sqrt(3)/24] / [Sqrt(3)/36]

a^2 / b^2 = [ 36 / 24 ]

a^2/ b^2 = 3/2

A/ B = Sqrt(3) / Sqrt(2)

=Sqrt(6) / 2

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The volume of the solid generated by revolving the region bounded by f(x)=(4−x)− 1 3 and the x-axis on the interval [0,4) about the y-axis is 6π.

When the region bounded by the function f(x) = (4-x) - 1/3 and the x-axis on the interval [0,4) is revolved about the y-axis, it forms a 3-dimensional shape called a solid of revolution. In this case, the shape is a type of frustum, which is the portion of a cone that remains after its top part has been cut off parallel to the base. The interval [0,4) defines the x-values over which the region is bounded, while "revolved about the y-axis" refers to rotating the area around the vertical y-axis to create the solid shape.

To find the volume of the solid generated by revolving the region bounded by f(x)=(4−x)− 1 3 and the x-axis on the interval [0,4) about the y-axis, we can use the formula for the volume of a solid of revolution:
V = ∫[a,b] πy²  dx
where a and b are the limits of integration and y is the function that defines the solid.
In this case, the function that defines the solid is f(x)=(4−x)− 1 3 and the limits of integration are from 0 to 4.
So, we have:
V = ∫[0,4] π[(4−x)− 1 3]²  dx
To evaluate this integral, we can use substitution. Let u = 4 - x. Then du/dx = -1 and dx = -du. Also, when x = 0, u = 4 and when x = 4, u = 0. So, we have:
V = ∫[4,0] π[(u)− 1 3]² (-du)
V = ∫[0,4] πu^(-2/3) du
Using the power rule of integration, we have:
V = π[3u^(1/3)]|[0,4]
V = 3π(4^(1/3) - 0^(1/3))
V = 3π(2)
V = 6π
Therefore, the volume of the solid generated by revolving the region bounded by f(x)=(4−x)− 1 3 and the x-axis on the interval [0,4) about the y-axis is 6π.

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a.  change of basis matrix  \([id]BC = [1/3 1/3 -1/3; -1/3 2/3 1/3; 2/3 -1/3 2/3].\)].

b.\([id]BC = [1/3 1/3 -1/3; -1/3 2/3 1/3; 2/3 -1/3 2/3],\)and

\([id]CB = [2/3 1/3 -1/3; 1/3 2/3 1/3; -1/3 -1/3 2/3].\)

a. To find the change of basis matrix from the basis B to the basis C, we need to find the coordinates of the basis C with respect to basis B and use them as the columns of the change of basis matrix.

Let's find the coordinates of the first vector in C with respect to B. We solve the system of equations [a, b, c][1, 1, 1]T = [1, 0, 0] to find the coefficients a, b, and c.

The solution is a = 1/3, b = -1/3, and c = 2/3.

Therefore, the coordinates of (1, 1, 1) in basis B are [1/3, -1/3, 2/3]T.

We can similarly find the coordinates of the other two vectors in C with respect to B.

Therefore,

\([(1, 1, 1)C]B = [1/3, -1/3, 2/3]T,\\ [(1, 0, 1)C]B = [1/3, 2/3, -1/3]T, \\[(1, 1, 0)C]B = [-1/3, 1/3, 2/3]T.\)

These are the columns of the change of basis matrix from B to C.

Therefore,

\([id]BC = [1/3 1/3 -1/3; -1/3 2/3 1/3; 2/3 -1/3 2/3].\)

b. To find the change of basis matrix from the basis C to the basis B, we need to find the coordinates of the basis B with respect to basis C and use them as the columns of the change of basis matrix.

Let's find the coordinates of the first vector in B with respect to C.

We solve the system of equations [a, b, c][1, 0, 0]T = [1, 1, 1] to find the coefficients a, b, and c.

The solution is a = 2/3, b = 1/3, and c = -1/3.

Therefore, the coordinates of (1, 1, 1) in basis C are [2/3, 1/3, -1/3]T.

We can similarly find the coordinates of the other two vectors in B with respect to C.

Therefore,

\([(1, 1, 1)B]C = [2/3, 1/3, -1/3]T, [(1, 0, 1)B]C = [1/3, 2/3, -1/3]T, [(1, 1, 0)B]C = [-1/3, 1/3, 2/3]T.\)

These are the columns of the change of basis matrix from C to B.

Therefore, \([id]CB = [2/3 1/3 -1/3; 1/3 2/3 1/3; -1/3 -1/3 2/3].\)

Therefore,\([id]BC = [1/3 1/3 -1/3; -1/3 2/3 1/3; 2/3 -1/3 2/3]\), and

\([id]CB = [2/3 1/3 -1/3; 1/3 2/3 1/3; -1/3 -1/3 2/3].\)

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Answer:

X - 3 = 5

Step-by-step explanation:

X decreased by 3 means X-3.

If X - 3 is 5, then it can be written as X - 3 = 5

Answer: 8

Step-by-step explanation: 8 decreased (subtracted) by 3 is 5.