Solve for b.

-3b = 9 - 4b

B=

The amount Archie has to pay for his share of the cost is £605

The costs of the holiday will be shared equally between the 4 friends.

These are:

The 4 of them will share the total cost equally. This means Archie paid the same amount with his friends.

Therefore, the amount Archie have to pay for his share of the costs can be calculated as follows:

total cost = 1360 + 850 + 210

total cost = £2420

Amount Archie paid = 2420 / 4

Amount Archie paid = £605

Therefore, the amount Archie has to pay for his share of the cost is £605

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Therefore, we can classify the polynomial as a quadratic polynomial.

A polynomial is a mathematical expression that consists of variables and coefficients, and involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and may contain multiple terms. Each term consists of a coefficient and a variable raised to a power. The degree of a term is the power to which the variable is raised, and the degree of a polynomial is the highest degree of any of its terms. Polynomials are used in many areas of mathematics, science, and engineering, such as algebra, calculus, geometry, and physics. They are used to model real-world phenomena, to solve equations, and to approximate complex functions.

Here,

To write the polynomial 14y² - x² - 3xy in standard form, we need to arrange the terms in descending order of degree (highest degree term first) and combine like terms.

First, let's rearrange the terms:

x² - 3xy + 14y²

Now, the polynomial is in descending order of degree. We don't need to do anything else to put it in standard form.

To classify the polynomial, we count the number of terms and the highest degree of those terms. In this case, there are three terms and the highest degree term is 14y², which has degree 2.

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We can use different measures and properties of angles to determine the measures of angles in different types of polygons.

To find the measures of the angles in each figure, we need to remember the properties of angles in different types of polygons.
For the first figure, we can see that it is a trapezoid, and we know that the angles on the same side of the base of a trapezoid add up to 180 degrees. Therefore, the measures of the angles are 50, 50, 130, and 130 degrees.
For the second figure, we can see that it is a kite, and we know that the two angles between the congruent sides are equal, and the two angles between the non-congruent sides are also equal. Therefore, the measures of the angles are 50, 50, 130, and 130 degrees.
For the third figure, we can see that it is a regular hexagon, and we know that the interior angles of a regular hexagon add up to 720 degrees. Therefore, each angle measures 120 degrees.
For the fourth figure, we can see that it is a rhombus, and we know that the angles of a rhombus are equal. Therefore, each angle measures 115 degrees.
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Answer:

------------------------

Solve the equation in below steps:

Answer:

x = 16.3

Step-by-step explanation:

17 + 3.8 = x + 4.5

Combine like terms.

20.8 = x + 4.5

Subtract 4.5 from both sides.

20.8 - 4.5 = x

16.3 = x

Answer:

Inequality: 7.5v+55≥100

Answer: v≥6

Step-by-step explanation:

Have a good day :)

The inequality for the given situation is 7.5v+55≤100.

Given that, Mamadou receives 55 rewards points just for signing up. He earns 7.5 points for each visit to the movie theater. He needs at least 100 points for a free movie ticket.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The number of visits Mamadou can make to earn his first free movie ticket is v.

The inequality for the given situation is 7.5v+55≤100

Subtract 55 on both the sides of inequality.

That is, 7.5v+55-55≤100-55

⇒ 7.5v≤45

⇒ v=45/7.5

⇒ v=6

Therefore, the inequality for the given situation is 7.5v+55≤100.

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The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.

The function being used is;

f(x) = (x - 3)⁻²

If we separate this function according to x, we obtain;

f'(x) = -2/(x - 3)³

Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.

This suggests that;

0.06 - 0.25 = -2/(c - 3)³ x 6

-0.19 =  -12/(c - 3)³

(c - 3)³ = 63.157

c = 6.98

If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).

But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.

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The complete question is-

Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?

Answer:

No

Step-by-step explanation:

the ratio of 15:12 is not equivalent to the ratios above. The ratios above have a common factor of 3, while 15:12 does not.

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.

When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.

When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.

The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.

The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.

So, annual crossover sales are 1800 units.

Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.

Fixed cost ÷ variable cost

$90000÷50 =$1800

$9,000÷5=$1800

Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.

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Correct question:

A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.

Given the following quadratic functions

[] y^2 + 12y - 36

[] x^2 + 121

[] x^2 - 6x + 9

[] y^2 - 64

[] 9x^2 - 121

[] 4y^2 + 20y + 25

We need to categorize them as perfect square trinomial, difference of squares, or neither

For the quadratic function y^2 + 12y - 36, 9x^2 - 121, 4y^2 + 20y + 25, and x^2 + 121, they are neither since there are no factors

For the function x^2 - 6x + 9

x^2 - 6x + 9

x^2 - 3x - 3+ 9

x(x-3)-3(x -3)

(x-3)(x-3)

(x-3)^2

This is  a perfect Square Trinomial

For the function y^2 - 64

y^2 - 8^2

(y-8)*(y+8)

This is a difference of squares.

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Answer:

80

Step-by-step explanation:

Answer: 80

Step-by-step explanation: Maybe research supplementary angle rules?

Answer:

88

Step-by-step explanation:

400*0.22=88

Answer:

C. \(x^{3}\) - 4\(x^{3}\) - 24x + 21

Step-by-step explanation:

(x - 7)(\(x^{2}\) + 3x - 3)

x(\(x^{2}\) + 3x - 3) + -7(\(x^{2}\) + 3x - 3)

(\(x^{3}\) + 3\(x^{2}\) - 3x) + (-7\(x^{2}\) + -21x + 21)

\(x^{3}\) - 4\(x^{3}\) - 24x + 21

Answer:

B

Step-by-step explanation:

divide them by 2

Answer:

x³ - 3x² + 5x - 6

Step-by-step explanation:

      1) (2x + y)(4x - 9) = 2x*(4x - 9) + y(4x - 9)

                                 = 2x*4x - 2x*9 + y*4x - y *9

                                = 8x² - 18x + 4xy - 9y

2) (3x + 5y)²

Identity : (a + b)² = a² + 2ab + b²

a = 3x and b = 5y

(3x +5y)² = (3x)² + 2 * 3x *5y + (5y)²

               = 9x² + 30xy + 25y²

3) (x -2)(x² - x + 3) = x*(x² - x + 3) - 2(x² - x + 3)

                             =x*x² - x*x + x*3 -2*x² + 2*x - 2*3

                            = x³ - x² + 3x - 2x² + 2x - 6

                            =x³ - x² - 2x² + 3x + 2x - 6

Combine like terms. Like terms have same variable with same exponent.

                           = x³ - 3x² + 5x - 6

Answer:

12

Step-by-step explanation:

you take 50 diveded by .24 (for 24%) which is 12

Answer:

48%, or 24 candies

Step-by-step explanation:

Since there is 50 candies, and the percentenc is based on 100%, you can double the percent of the amount of green candies to see how many there are.

Answer:

Step-by-step explanation:

You want to know which of various statements about f(x) = 4(x- 3)³ +6 are true.

The cubic function is symmetric about its point of inflection. The translation by (3, 6) moves that to coordinates (3, 6). The point of symmetry is not (6, 3). (False)

The domain of any polynomial function is (-∞, ∞). True.

The slope of f(x) never changes sign, so the inverse relation is a function. (False)

The range of the inverse relation is the same as the domain of the function. It is (-∞, ∞). (False)

__

Additional comment

The function is graphed in red; the inverse function is graphed in green. The orange dashed line is the line of reflection between the function and its inverse: y = x. Both have domain and range of (-∞, ∞).

<95141404393>

Answer: (b + 3)/2

\(\frac{b-5}{2b}.\frac{b^{2}+3b }{b-5}=\frac{b^{2}+3b }{2b}=\frac{b(b+3)}{2b}=\frac{b+3}{2}\)

Step-by-step explanation:

Answer:

(b + 3)/2

Step-by-step explanation:

At μ = 10.0932 level should the mean be set if it is required that only 1% of the bags weigh less than 9.5 kg.

Given Data:

σ = 0.04 kg

x = 9.5 kg

We want to determine μ such that: P(X ≤ 9.5)= 1% = 0.01

Thus, we know here probability of x is 0.1 which is  less than 9.5

so here Z is -2.326 by the standard table

Determine the z-score in the normal probability table in the appendix that has a probability closest to 0.01:

Then, we have here 1% to left when Z is - 2.326

Now,

The value corresponding to the z-score is then the mean increased by the product of the z-score and the standard deviation:

x = μ+ zσ

= μ− 2.33(0.04) = μ - 0.0932

Since , P(X ≤ 9.5) = 0.95% = 0.095, we know that x also has to be equal to 9.5:

   μ− 0.0932 = 9.5

Add 0.0932 to each side of the previous equation:

μ = 10+ 0.0932

= 10.0932

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Answer:

The answer is sometimes.

If the two lines have the same slope, then there will be 0 solutions, and if the two lines are the same, then there will be infinite solutions.

Hope this helps!

the current age of the house is 7 years old

Let's assume that the current age of the house is represented by x years.

According to the problem, when the mortgage is completely paid off, the age of the house will be 6 times its current age, which can be expressed as:

Age of house when mortgage is paid off = 6x

We also know that they have 35 years left on the mortgage, which means that they have already been paying it for x - 35 years.

Since the mortgage term is the same as the age of the house, we can write:

x - 35 = age of house when mortgage is paid off = 6x

Solving for x, we get:

5x = 35

x = 7

what is age?

Age typically refers to the length of time that a person or living organism has existed since birth or the point of origin. In the context of demographics, age is often used to describe the chronological age of a population, group, or individual.

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a) To construct the table showing the values of the joint probability distribution of X and Y, we need to consider all possible combinations of X and Y based on the given information. Let's denote "S" for statistics, "M" for mathematics, and "P" for physics. The possible combinations are as follows:

X = 0, Y = 0: No statistics texts and no mathematics texts

X = 0, Y = 1: No statistics texts and one mathematics text

X = 0, Y = 2: No statistics texts and two mathematics texts

X = 1, Y = 0: One statistics text and no mathematics texts

X = 1, Y = 1: One statistics text and one mathematics text

X = 1, Y = 2: One statistics text and two mathematics texts

X = 2, Y = 0: Two statistics texts and no mathematics texts

X = 2, Y = 1: Two statistics texts and one mathematics text

X = 2, Y = 2: Two statistics texts and two mathematics texts

Now, let's calculate the probabilities for each combination:

P(X = 0, Y = 0) = (3/8) * (2/7) = 6/56

P(X = 0, Y = 1) = (3/8) * (2/7) = 6/56

P(X = 0, Y = 2) = (3/8) * (5/7) = 15/56

P(X = 1, Y = 0) = (3/8) * (3/7) = 9/56

P(X = 1, Y = 1) = (3/8) * (2/7) = 6/56

P(X = 1, Y = 2) = (3/8) * (5/7) = 15/56

P(X = 2, Y = 0) = (5/8) * (3/7) = 15/56

P(X = 2, Y = 1) = (5/8) * (2/7) = 10/56

P(X = 2, Y = 2) = (5/8) * (5/7) = 25/56

The table for the joint probability distribution of X and Y is as follows:

X = 0 6/56 6/56 15/56

X = 1 9/56 6/56 15/56

X = 2 15/56 10/56 25/56

b) To find the marginal distributions of X and Y, we sum the probabilities across the rows and columns, respectively.

The marginal distribution of X:

P(X = 0) = (6/56) + (6/56) + (15/56) = 27/56

P(X = 1) = (9/56) + (6/56) + (15/56) = 30/56

P(X = 2) = (15/56) + (10/56) + (25/56) = 50/56

The marginal distribution of Y:

P(Y = 0) = (6/56) + (9/56) + (15/56) = 30/56

P(Y = 1) = (6/56) + (6/56) + (10/56) = 22/56

P(Y = 2) = (15/56) + (15/56) + (25/56) = 55/56

The marginal distribution of X is (27/56, 30/56, 50/56), and the marginal distribution of Y is (30/56, 22/56, 55/56).

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only option (c) satisfies the criteria of a probability distribution.

Among the options given, only (c) represents a probability distribution. A probability distribution is a function that assigns probabilities to each possible value of a random variable, ensuring that the probabilities sum to 1. In option (c), the random variable Z takes values 1, 2, 3, 4, and 5, and the corresponding probabilities assigned to these values are 0.1, 0.2, 0.3, 0.4, and 0.0, respectively. These probabilities satisfy the requirement that they sum to 1, making it a valid probability distribution.

In option (a), the random variable X has repeated values, which violates the requirement that each value should have a unique probability. For example, X takes the value 2 with a probability of 0.1 twice, which is not a valid probability distribution.

In option (b), the probabilities assigned to the values of the random variable Y are not non-negative, as there is a negative probability (-1.25). Negative probabilities are not allowed in probability distributions.

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The particular solution of the given differential equation with the initial condition x(0) = 4.

Any mathematical equation that connects a function and its derivatives to one or more independent variables is known as a differential equation. Many different physical phenomena, including as the behaviour of particles, fluids, and electrical circuits, are modelled using differential equations. They are used extensively in physics, engineering, and other disciplines. Differential equations' solutions frequently provide light on the behaviour of complicated systems and can be used to forecast how they will behave in the future.

Step 1: Write down the given differential equation and initial condition.
\(dx/dt = 4x\\x(0) = 4\)

Step 2: Rewrite the differential equation in a separable form.
\((1/x)dx = 4dt\)

Step 3: Integrate both sides of the equation.
\(\int\limits {x} \, dx (1/x)dx = \int\limits {x} \, dx 4dt\)

Step 4: Find the antiderivatives.
\(ln|x| = 4t + C\)

Step 5: Solve for x.
\(x = e^(4t + C)\\x = e^(4t) * e^C\)
Step 6: Apply the initial condition x(0) = 4.
\(4 = e^(4*0) * e^C\\4 = e^C\)

Step 7: Write the general solution, substituting the value of e^C.
\(x(t) = e^(4t) * 4\)

That's the particular solution of the given differential equation with the initial condition x(0) = 4.

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The number of teams and matches in the soccer league illustrates permutation and combination

There are 12 teams in the soccer league in the first season

The number of teams in the soccer league is given as n.

So, the total number of matches played in a season is:

Matches = n(n-1)/2

When the number of teams increases by 2, we have:

Matches = (n + 2)(n + 2 -1)/2

Also, the number of matches increases by 27.5%.

So, we have:

Matches = n(n-1)/2 * (1 + 27.5%)

Equate both equations

\(\frac{(n + 2)(n + 2 -1)}{2} = \frac{n(n-1)}{2} * (1 + 27.5\%)\)

Simplify

\(\frac{(n + 2)(n + 1)}{2} = \frac{n(n-1)}{2} * (1.275)\)

Multiply through by 2

\((n + 2)(n + 1) = n(n-1) * (1.275)\)

Expand

\(n^2 + 3n + 2 = 1.275n^2 - 1.275\)

Collect like terms

\(n^2 -1.275n^2+ 3n + 2 +1.275 = 0\)

Evaluate the like terms

\(-0.275n^2+ 3n + 3.275 = 0\)

Using a graphing calculator, we have:

n = -1 or n = 11.909

n cannot be negative.

So, we have:

n = 11.909

Approximate

n = 12

Hence, there are 12 teams in the soccer league in the first season

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Answer:

Your answer is A

y≤ 1/2x + 3

y≥ 1/2x - 4

Step-by-step explanation:

6.14 Checkpoint: Systems of Linear Inequalities

I took the test

Answer:

Which systems of inequalities does the graph show?

A

O y ≤ 1/2x + 3

   y ≥ 1/2x - 4

Step-by-step explanation:

You're welcome.

Answer:

y=-5x+19

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Answer:

in this case the answer is D

Step-by-step explanation:

your welcome

Answer:

last years garden had a grather ratio

Step-by-step explanation:

The number of tomatoes and pepper produced last year ratio is greater than this year number of tomatoes and pepper produced last year ratio.

It is given that, last year Craig planted

Number of tomatoes rows = 3

Number of pepper rows = 5

Ratio of the rows of both tomatoes and peppers = \(\frac{3}{5}\)

Similarly, this year Craig also wanted to plant squash. So, as the land he has is fixed, so in order to plant one more variety of vegetable, Craig thought of reducing the number of rows of peppers and tomatoes he had been planting this whole time.

Therefore, this year Craig planted

Number of tomatoes rows = 2

Number of pepper rows = 4

Ratio of the rows of both tomatoes and peppers = \(\frac{2}{4}\) = \(\frac{1}{2}\)

Now, the given question asked to find which year has the greater ratio of number of tomatoes and pepper produced. So, we'll compare the both year ratios in order to find the answer

Here,

Ratio of the rows of both tomatoes and peppers = \(\frac{3}{5}\)

Ratio of the rows of both tomatoes and peppers = \(\frac{1}{2}\)

Here, clearly it can be observed that,

\(\frac{3}{5} > \frac{1}{2}\)

So, we concludes that the number of tomatoes and pepper produced last year ratio is greater than this year number of tomatoes and pepper produced last year ratio.

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