Explain why P(X = 2) = P(X = 3) in a binomial distribution where n = 5 and p = 0.5.

Numbers that have line symmetry would remain the same when reflected or rotated.

The numbers that have line symmetry are 3 and 8

There are 10 unit digits in algebra;

These numbers are 0 to 9

This is so because, they remain the same when rotated or flipped.

Hence, the numbers that have line symmetry are 3 and 8

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Answer:

3 and 8

Step-by-step explanation:

The pair of functions for which (f o g)(x) is equivalent to {12x} are f(x) = 4x and g(x) = 3x.

Given are the pair of functions f(x) and g(x) and it is asked to find (f o g)(x).

The pair of functions for which (f o g)(x) is equivalent to {12x} are -

f(x) = 4x and g(x) = 3x.

Proof :

g(x) = 3x

(f o g)(x) = f(x = 3x) = 4(3x) = 12x

(f o g)(x) = 12x

Therefore, the pair of functions for which (f o g)(x) is equivalent to {12x} are f(x) = 4x and g(x) = 3x.

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Answer:

D) f(x) = 4x and g(x) = 3x

Step-by-step explanation:

Answer:

-5 would Be your answer

Step-by-step explanation:

The range of the random variable is from 0 to 17,000.

The range of the random variable is the set of all possible values that the variable can take on. In this case, the variable is the number of people who carry the gene ifi202. Since 17,000 people are being tested, the range of the variable is from 0 to 17,000.

This is because it is possible that none of the people tested carry the gene, or that all 17,000 people tested carry the gene. Any number of people between 0 and 17,000 could also carry the gene, so the range of the variable is 0 to 17,000.

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Variables in mathematics are used to represent values or quantities that can change or vary.

The values are:

a) g(3b) = 9b² - 3b

b) f(2) + 1 = 9

What is a function?

A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as a range). The inputs are usually represented by variables, such as 'x' in the examples you provided.

The given functions are

f(x) = 3x +2 and g(x) = x² - x,

a) g(3b) = (3b)² - (3b) = 9b² - 3b

b) f(2) = 3(2) + 2 = 6 + 2 = 8

so f(2) + 1 = 8 + 1 = 9

Hence, the values are:

a) g(3b) = 9b² - 3b

b) f(2) + 1 = 9

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Answer:

d

Step-by-step explanation:

Answer:

40 mins

Step-by-step explanation:

time spent talking to his sister = (1 - 3/8) x 4/5 =

5/8 x 4/5 = 1/2

total fraction of time spent playing games and talking to his sister :

\(\frac{3}{8} + \frac{1}{2}\)

\(\frac{ 3 + 4}{8}\) = \(\frac{7}{8}\)

fraction of time remaining to complete the journey = 1 - 7/8 = 1/8

let t = total journey time

1/8 x t = 5

multiply both sides of the equation by 8

t = 5 x 8 = 40 minutes

Answer:

y = -4x + 29

Step-by-step explanation:

-3 = -4(8) + b

-3 = -32+b

29=b

The equation whose slope is -4 and passes through (8,-3) is y=-4x+29 where slope is -4.

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

We have been given slope of line being -4 and point through which it passes (8,-3) and we have to find the equation of line.

The equation from two points can be calculated through the following formula:

y-\(y_{1}\)=m(x-\(x_{1}\)) and slope is m.

Putting the values of points and slope in the formula given above.

y-(-3)=-4(x-8)

y+3=-4(x-8)

y+3=-4x+32

y=-4x+32-3

y=-4x+29

Hence the equation is y=-4x+29 where slope is -4.

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Answer:

x = 1 , y = 2

Step-by-step explanation:

Solve for substitution

The equation that calculates the length of the ladder is L^2 = 4^2 + 7^2

From the question, we have the following parameters

Base length to the ladder = 4 feet

From the base to the top of the ladder = 7 feet

These parameters can be represented as

Base = 4 feet

Height = 7 feet

The equation that calculates the ladder's length can be calculated using the following Pythagoras theorem

Length^2 = Base^2 + Height^2

Substitute the known values in the above equation

So, we have the following equation

L^2 = 4^2 + 7^2

Hence, the equation is L^2 = 4^2 + 7^2

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The equation for the volume of the prism will be given as  V=x^3+3x^2

The volume of the prism is given by the following formula

\(\rm Volume = Width\times Length\times hieght\)

Here we have a condition in the question that

The height of a right rectangular prism is 3 units greater than the length

\(h=x+3\)

length will be l = x

The width will be w=x

now by putting the value in the formula we get

\(\rm Volume = w\times L\times h\)

\(\rm Volume = x \times x \times (x+3)\)

\(\rm Volume = x^3+3x^2\)

Thus the equation for the volume of the prism will be given as  \(V=x^3+3x^2\)

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These forecasts illustrate bias.

Therefore, these forecasts illustrate bias.

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Answer:

£12000

Step-by-step explanation:

1 year = 1.5%

4 years = 6%

6% = 0.06

200000 times 0.06 = £12000

So, Katy will get £12000 interest rate at the end of 4 years.

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Answer:

£3,137

Step-by-step explanation:

First year: £200000 x 1.5% = £3,000

Second year: £203,000 x 1.5% = £3,045

Third year: £206,045 (because of 203,000+3,045) x 1.5% = £3,090.675

Last year: £209,135.675 x 1.5% = approximately £3,137

Answer:

The answers for this question are 1 and 0

Answer:

the correct answers are 1 and 0

Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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Answer:

3rd one

Step-by-step explanation:

The other ones are all wrong because if you look at the first graph, it says every rectangle is 10. And you can see that the number of lunches sold are far more larger.

Answer:

653005 = 653,005 in the International System of Numeration, the number is (Six hundred fifty-three thousand and five)

Answer:

15 × 14 = 210 of the 2,800 admitted patients remained longer than a week, so 2,800 - 210 = 2,590 of those patients were released within one week.

Answer:

10 steps

Step-by-step explanation:

Answer: Below :p

Step-by-step explanation:

-10 - (-3) is -7.

The opposite of -3 is 3 since there were parentheses around -3.

Tom might have added the negatives wrong to get -13 or he thought the subtraction symbol was an addition symbol.

Answer: Yes it does.

Step-by-step explanation:

The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

To determine the surface area from the net of the box, we simply calculate the area of each shape.

From the given figure, we have the following shapes and dimensions:

The area is then calculated using:

Area = Areas of the rectangle + Area of the triangle

So, we have:

Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7

Evaluate the sum of products

Area = 430.35

Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

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Answer:577.35 square feet

Step-by-step explanation:

‍♀️

The optimal allocation is x = -1/2, y = 3/2, with a shadow price of 1.50.

To maximize profit, the firm needs to determine the optimal allocation of inputs x and y within the budget constraint of $100.

Let's assume the firm uses 'a' units of input x and 'b' units of input y. Since each unit of x costs $2 and each unit of y costs $3, the total cost constraint can be expressed as:

2a + 3b ≤ 100

To maximize profit, we need to differentiate the profit function P(x, y) with respect to both inputs and set the derivatives equal to zero:

∂P/∂x = 2y - 3 = 0 ---> y = 3/2

∂P/∂y = 2x + 1 = 0 ---> x = -1/2

However, x and y cannot have negative values, so these values are not feasible. To find the feasible values, we can substitute the values of x and y into the cost constraint:

2(-1/2) + 3(3/2) = 0 + 9/2 = 9/2 ≤ 100

This constraint is satisfied, so the feasible allocation is x = -1/2 and y = 3/2.

To find the shadow price, we need to determine the rate at which the maximum profit would change with respect to a one-unit increase in the budget constraint. We can do this by finding the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = λ

Where λ represents the shadow price or the marginal value of an additional dollar in the budget. In this case, λ is the shadow price.

Taking the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = ∂(2xy - 3x + y)/∂(2a + 3b) = 0

2y - 3 = 0 ---> y = 3/2

Thus, the shadow price (λ) is 3/2 or 1.50 when rounded to two decimal places.

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The answers to the questions on how she would use the colored chips are given here:

For the first percentage

20 / 100 = x/20

= 20 * 20 = 100x

400 = 100x

divide through by 100

x = 400/100

x = 4

For the second percentage

30/100 = x/20

600 = 100x

x = 600/100

x = 6

For the last

50/100 = x/20

1000 = 100x

x = 10

The proof is that 6 + 4 + 10 still gives us 20

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Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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Answer:

Step-by-step explanation:

perpendicular bisector AB is dividing the line segment XY at a right angle into exact two equal parts,

therefore,

ΔABY ≅ ΔABX

also we can prove the perpendicular bisector property with the help of SAS congruency,

as both sides and the corresponding angles are congruent thus, we can say that B is equidistant from X and Y

therefore,

ΔABY ≅ ΔABX

Answer:

2(x²-13)

Step-by-step explanation:

the expression above gives 2x²-26

when expanded we get 2(x²-13)

This is because the determinant is a measure of how much the matrix changes the area or volume of the space it is applied to, and if two columns are the same, then the matrix does not change the area or volume of the space.

According to Theorem 3 in Chapter 3, if two rows or two columns in a square matrix are the same, then the determinant of that matrix is 0. This is because the determinant is a measure of how much the matrix changes the area or volume of the space it is applied to. If two rows or two columns are the same, then the matrix does not change the area or volume of the space, so the determinant is 0.

To show this, let's consider a square matrix A with two identical rows:

A = [a1, a2, a3; a1, a2, a3; b1, b2, b3]

The determinant of A can be found using the formula:

det(A) = a1 * det([a2, a3; b2, b3]) - a2 * det([a1, a3; b1, b3]) + a3 * det([a1, a2; b1, b2])

Since the first two rows are the same, the first two determinants in this formula will be the same:

det([a2, a3; b2, b3]) = det([a1, a3; b1, b3])

So the formula simplifies to:

det(A) = a1 * det([a2, a3; b2, b3]) - a2 * det([a2, a3; b2, b3])

= (a1 - a2) * det([a2, a3; b2, b3])

Since a1 = a2, the determinant is 0:

det(A) = 0

The same is true for two identical columns. The determinant will also be 0 in that case. This is because the determinant is a measure of how much the matrix changes the area or volume of the space it is applied to, and if two columns are the same, then the matrix does not change the area or volume of the space.

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Answer:

  (b)  1 - x - 2 + 2 x = 10 x - 25 - x

Step-by-step explanation:

The distributive property tells you the factor outside parentheses multiplies each term inside parentheses.

__

  1 -(x +2) +2x = 5(2x -5) -x

The minus sign outside the parentheses on the left side of the equal sign represents a factor of -1. Using the distributive property there, we have ...

  1 +(-1)(x) +(-1)(2) +2x = 5(2x -5) -x

  1 -x -2 +2x = 5(2x -5) -x . . . . . . simplify a bit

The 5 outside parentheses on the right side of the equal sign similarly multiplies each of the terms inside those parentheses:

  1 -x -2 +2x = (5)(2x) +(5)(-5) -x

  1 -x -2 +2x = 10x -25 -x . . . . . . . . matches the second choice

_____

Additional comment

It might be helpful to think of parentheses as a "bag." The factor outside tells you how many bags you have. (All are the same.) When you eliminate the parentheses, you are essentially dumping the contents of the bags into one pile. Since all of the bags have the same contents, the total is the product of what's in a bag and the number of bags.