Help me please with this

The solution to the system of equations using the substitution method is (7,2).

No, the substitution approach cannot be used to solve every system of equations. It can be challenging to replace one equation with another in some systems because they feature equations that are challenging or impossible to solve for one variable in terms of the other. Other approaches, such graphing or elimination, could be more useful in such circumstances.

Given that, the two equations are:

x= 4y - 1

3x + 2y = 25

Substitute x = 4y - 1 into the second equation:

3(4y - 1) + 2y = 25

12y - 3 + 2y = 25

14y - 3 = 25

14y = 28

y = 2

Substitute the value of y in equation:

x = 4y - 1

x = 4(2) - 1

x = 7

Hence, the solution to the system of equations using the substitution method is (7,2)

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Answer:

5 2/3

Step-by-step explanation:

all you need is to add because the fraction is the same.

We have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

We can use the properties of logarithms to show that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

First, recall that the arithmetic mean of two numbers is half their sum:
arithmetic mean = (v + w)/2

And the geometric mean is the square root of their product:
geometric mean = √(v*w)

Now, let's take the log of the geometric mean:
log(geometric mean) = log(√(v*w))

Using the property of logarithms that log(a*b) = log(a) + log(b), we can expand the expression:
log(√(v*w)) = log(√v) + log(√w)

Using the property of logarithms that log(a^b) = b*log(a), we can simplify the expression:
log(√v) + log(√w) = (1/2)*log(v) + (1/2)*log(w)

Now, we can see that the log of the geometric mean is the arithmetic mean of the logs of the two numbers:
log(geometric mean) = (log(v) + log(w))/2

So, if we let p = log(v) and q = log(w), we can see that the log of the geometric mean of v and w is the arithmetic mean of p and q:
log(geometric mean) = (p + q)/2

Therefore, we have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

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[tex]x=\textit{kgs of solution at 30\%}\\\\ ~~~~~~ 30\%~of~x\implies \cfrac{30}{100}(x)\implies 0.3 (x) \\\\\\ y=\textit{kgs of solution at 15\%}\\\\ ~~~~~~ 15\%~of~y\implies \cfrac{15}{100}(y)\implies 0.15 (y) \\\\\\ \textit{60 kgs of solution at 20\%}\\\\ ~~~~~~ 20\%~of~60\implies \cfrac{20}{100}(60)\implies 0.2 (60)\implies 12 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{kgs}{quantity}&\stackrel{\textit{\% of kgs that is}}{\textit{nitrogen only}}&\stackrel{\textit{kgs of}}{\textit{nitrogen only}}\\ \cline{2-4}&\\ \textit{1st Fert.}&x&0.3&0.3x\\ \textit{2nd Fert.}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&60&0.2&12 \end{array}~\hfill \begin{cases} x + y = 60\\\\ 0.3x+0.15y=12 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{x+y=60}\implies y=60-x \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 2nd equation}}{0.3x+0.15y=12}\implies \stackrel{\textit{substituting from above}}{0.3x+0.15(60-x)=12} \\\\\\ 0.3x+9-0.15x=12\implies 0.15x=3\implies x=\cfrac{3}{0.15} \\\\\\ \boxed{x=20}\hspace{5em}\stackrel{ 60~~ - ~~20 }{\boxed{y=40}}[/tex]

(2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗

The characteristic function of a random variable X is defined as ∅(t) = E[e^(√(-1)tx)]. To show that (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 is the Lebesgue density of X, we need to demonstrate that it is a probability density function.

We first calculate the integral to obtain (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 = (2π)^(-1) ∫▒〖E[e^(-√(-1) xt +√(-1) tx)]dt〗.

Since the expectation is a constant, we can pull it out of the integral to get (2π)^(-1)E[∫▒〖e^(-√(-1) xt +√(-1) tx)]dt〗.

Now, if we substitute t = y-x and rewrite the integral, we obtain (2π)^(-1)E[∫▒〖e^(-√(-1) x(y-x))e^(√(-1) xy)]dy〗.

This simplifies to (2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗.

Because the integrand is 1, the integral is simply y. Then, the expectation becomes E[y] which is the mean of the random variable X. Thus, the Lebesgue density of X is (2π)^(-1)E[y], which is the probability density function of X.

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The result would be:
a) (og)(4) = 294
b) (gof)(2) = 433
c) (fof)(1) = 36
d) (gog)(0) = 4

Given f(x) = 6x and g(x) = 3x² + 1, we can find the following expressions:

a) (og)(4)
To find (og)(4), we first need to find g(4).
g(4) = 3(4)² + 1 = 3(16) + 1 = 49
Now we can find (og)(4) by plugging in 49 for x in f(x):
(og)(4) = f(49) = 6(49) = 294

b) (gof)(2)
To find (gof)(2), we first need to find f(2).
f(2) = 6(2) = 12
Now we can find (gof)(2) by plugging in 12 for x in g(x):
(gof)(2) = g(12) = 3(12)² + 1 = 3(144) + 1 = 433

c) (fof)(1)
To find (fof)(1), we first need to find f(1).
f(1) = 6(1) = 6
Now we can find (fof)(1) by plugging in 6 for x in f(x):
(fof)(1) = f(6) = 6(6) = 36

d) (gog)(0)
To find (gog)(0), we first need to find g(0).
g(0) = 3(0)² + 1 = 1
Now we can find (gog)(0) by plugging in 1 for x in g(x):
(gog)(0) = g(1) = 3(1)² + 1 = 4

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The value of the discriminant is 0 and the number of real solutions is 1

For the given equation, 36x^(2)-24x+4=0, we can find the value of the discriminant and the number of real solutions using the quadratic formula.

The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation.

The discriminant is the part of the formula under the square root, b^(2)-4ac.

In this equation, a = 36, b = -24, and c = 4. Plugging these values into the discriminant, we get:

Discriminant = (-24)^(2)-4(36)(4) = 576-576 = 0

Since the discriminant is equal to 0, there is only one real solution to this equation.

Therefore, the value of the discriminant is 0 and the number of real solutions is 1.

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The most appropriate formula to use in this situation (patient with a bacterial infection and prescribed with Amoxicillin) is Clark's rule, and the dose to administer every 12 hours would be 108.4 mg.

The best formula to use in this situation is the Clark's rule, which is used to calculate the dose of medication for a child based on their weight and the adult dose. The formula is as follows:

In this case, the weight of the child is 21.1 pounds and the adult dose is 771 mg every 12 hours. Plugging these values into the formula, we get:

Rounding to the nearest tenth of a milligram, the child dose would be 108.4 mg and to administer every 12 hours.

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Answer:

66 (at least if that is an answer choice)

Step-by-step explanation:

[tex]\frac{75*88}{100} = 66[/tex]

66 is your answer!

Answer:

Power – A power is an expression that represents repeated multiplication of the same number or variable, such as a raised to the power of n, denoted by aⁿ.

Base – The base is the number or variable that is raised to a power or exponent in a power expression.

Exponent – The exponent is the number that indicates how many times the base is to be multiplied by itself in a power expression.

Coefficient – The coefficient is the numerical factor of a term that contains a variable in an algebraic expression.

Exponential Form – The exponential form is a way of writing a number using a base and an exponent, such as aⁿ, where a is the base and n is the exponent.

Expanded Form – The expanded form is a way of writing an expression as the sum or difference of its individual terms, such as (a+b)² = a² + 2ab + b².

Standard Form – The standard form is a way of writing a number using digits, such as 1234 or 1.234 x 10³.

Exponent Laws – The exponent laws are a set of rules that describe how exponents can be manipulated in algebraic expressions, including the product law, quotient law, power law, and negative exponent law. These laws help simplify and solve equations involving exponents.

This property can be applied to any number of lines as long as they are all parallel to the same line.

The statement "if n I| m and m ll then 1 || n" is not valid as the symbols used are not correct. The correct statement should be "if l || m and m || n then l || n". This means that if line l is parallel to line m and line m is parallel to line n, then line l is also parallel to line n. This is known as the transitive property of parallel lines.

Similarly, the statement "if k 11,11 m and m In then k \ n" is not valid as the symbols used are not correct. The correct statement should be "if k || l, l || m, and m || n then k || n". This means that if line k is parallel to line l, line l is parallel to line m, and line m is parallel to line n, then line k is also parallel to line n. This is also an application of the transitive property of parallel lines.

In conclusion, the transitive property of parallel lines states that if two lines are parallel to the same line, then they are also parallel to each other. This property can be applied to any number of lines as long as they are all parallel to the same line.

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Therefore, the answers are:
a. 0.0498
b. 0.8008
c. 0.7745

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

a. The probability that none is sold on a particular day can be calculated using the formula:
P(X = 0) = (e^-λ)(λ^0) / 0!
Where λ is the mean and e is the base of the natural logarithm.
Substituting the values, we get:
P(X = 0) = (e^-3)(3^0) / 0!
P(X = 0) = (0.0498)(1) / 1
P(X = 0) = 0.0498

b. The probability that at least 2 automobiles are sold on a particular day can be calculated using the formula:
P(X ≥ 2) = 1 - P(X < 2)
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))
P(X ≥ 2) = 1 - ((e^-3)(3^0) / 0! + (e^-3)(3^1) / 1!)
P(X ≥ 2) = 1 - (0.0498 + 0.1494)
P(X ≥ 2) = 1 - 0.1992
P(X ≥ 2) = 0.8008

c. The probability that for five consecutive days at least one automobile is sold can be calculated using the formula:
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - (e^-3)(3^0) / 0!
P(X ≥ 1) = 1 - 0.0498
P(X ≥ 1) = 0.9502
The probability that for five consecutive days at least one automobile is sold is:
P(X ≥ 1)^5 = 0.9502^5 = 0.7745

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Thhe standard error of the sample mean is 0.208333.  The probability that the sample mean is within 0.5 units of the population mean is 0.9918. We need to take a sample size of at least 7 to be 98% confident that the sample mean is within one-half of the population mean.

(i) The standard error of the sample mean is calculated by dividing the standard deviation of the population by the square root of the sample size. In this case, the standard error of the sample mean is 1.25 / √36 = 1.25 / 6 = 0.208333.

(ii) To find the probability that the sample mean is within 0.5 units of the population mean, we need to use the standard normal distribution. We can find the z-score for 0.5 units away from the mean by dividing 0.5 by the standard error of the sample mean, which is 0.5 / 0.208333 = 2.4.

Using a standard normal table, we can find the probability that the sample mean is within 2.4 standard deviations of the population mean, which is 0.9918.

(iii) To be 98% confident that the sample mean is within one-half of the population mean, we need to find the sample size that corresponds to a z-score of 2.33 (the z-score for a 98% confidence interval). We can use the formula for the standard error of the sample mean to solve for the sample size:

0.5 = 1.25 / √n

√n = 1.25 / 0.5

n = (1.25 / 0.5)²

n = 6.25

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Answer:

To find how many more items the first plant produces daily than the second plant, we need to subtract the daily production levels of the two plants.

First plant: 5x + 11

Second plant: 2x - 3

Difference: (5x + 11) - (2x - 3)

= 5x + 11 - 2x + 3

= 3x + 14

Therefore, the first plant produces 3x + 14 more items daily than the second plant.

Let's say that the number of metal paperweights is "x", then the number of glass paperweights is "2x" since she has twice as many glass paperweights as metal.

We know that she has a total of 12 paperweights, so we can set up an equation:

x + 2x + 3 = 12

Simplifying the equation, we get:

3x + 3 = 12

Subtracting 3 from both sides, we get:

3x = 9

Dividing both sides by 3, we get:-

x = 3

So Teri has 3 metal paperweights, and since she has twice as many glass paperweights as metal, she has:

2x = 2(3) = 6 glass paperweights.

Therefore, Teri has 3 metal paperweights, 6 glass paperweights, and 3 wood paperweights in her collection.

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The first term of the product of (2x^(3)+4x-3) and (4x-1) in standard form will be 8[tex]x^{4}[/tex].

Since 4x is multiplied by 2x³, their product is 8x⁴. Then, distributing 4x to the terms inside the first bracket and -1 to the terms inside the second bracket, we have:

8x⁴ - 2x³ + 16x² - 13x + 3.

To write the above expression in standard form, we just need to arrange the terms of the polynomial in descending order of their degree.

Thus, the first term will be 8[tex]x^{4}[/tex].

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A conjecture which Carlos can make about the angles formed by line t and lines l, m, and n include the following: B. angles 1, 3, and 5 are congruent.

In Mathematics, corresponding angles postulate simply refers to a theorem which states that corresponding angles are always congruent (equal) if the transversal intersects two parallel lines.

This ultimately implies that, the corresponding angles would always be congruent (equal) if a transversal intersects two (2) parallel lines.

By applying corresponding angles postulate to both lines l, m, and n, we can reasonably infer and logically deduce that the following angles are congruent:

∠1 ≅ ∠3

∠3 ≅ ∠5

∠1 ≅ ∠5

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The required function is g(x) = f(x)-7

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is a graph of two functions, the functions are in a way related, we need to find the relation between the two,

f(x) = x²+5

g(x) = x²-2

We can write,

g(x) = x²+5-7

g(x) = f(x)-2

We can clearly see a vertical shift of 7 units down, of f(x),

Therefore, when we subtract 7 from the function f(x) we will get g(x) [graph attached]

Hence, the required function is g(x) = f(x)-7

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Var(θ3) = (a-1)(a-2) / λ^2 - θ^2.

First, let's find the method of moments estimate of θ based on Y1,...,Yn. We know that E(Y) = E(log(X/x0)) = E(log(X)) - log(x0) = θ^-1 - log(x0). Therefore, θ^-1 = E(Y) + log(x0) and θ3 = 1 / (E(Y) + log(x0)).

Next, let's find the distribution of Y. Since Y = log(X/x0), we can use the change of variables formula to find the density function of Y. Let g(y) = x0 * exp(y), then the Jacobian is |g'(y)| = x0 * exp(y). The density function of Y is fY(y) = fX(g(y)) * |g'(y)| = θ * (x0 * exp(y))^θ * (x0 * exp(y))^(-θ-1) * x0 * exp(y) = θ * x0^θ * exp(-θy).

Finally, let's find the mean and variance of θ3. We know that E(θ3) = E(1 / (E(Y) + log(x0))) = 1 / (E(Y) + log(x0)) = θ. To find the variance, we can use the fact that Var(θ3) = E(θ3^2) - E(θ3)^2. We can use the fact that if U follows a gamma distribution, then E(U^r) = Γ(a+r) / [λ^r * Γ(a)] to find E(θ3^2). Let U = E(Y) + log(x0), then E(θ3^2) = E(U^-2) = Γ(a-2) / [λ^2 * Γ(a)] = (a-1)(a-2) / λ^2. Therefore, Var(θ3) = (a-1)(a-2) / λ^2 - θ^2.

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Answer:

Try out

Step-by-step explanation:

1/4

1/2

1

1 1/2

Answer: 360 degrees

So basically when you spin around you make 360 degrees lol.

The secx equivalent of the two expressions are

tan²x = sec²x - 1

tan x =sec x * sin x

Generally, Equalities that utilize trigonometry functions and are true no matter what the values of the variables that are specified in the equation are what are referred to as trigonometric identities. There are many different trigonometric identities that may be found using the length of a triangle's side as well as the angle of the triangle.

a) Using the identity:

tan²x + 1 = sec²x

We can rearrange it to get:

tan²x = sec²x - 1

Therefore, in terms of secx:

tan²x = sec²x - 1

b) Using the identity:

tan x = sin x / cos x

We can rewrite it in terms of sec x as follows:

tan x = sin x / cos x

= (1/cos x) * sin x

= sec x * sin x

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1241 student tickets were sold. Below, you will learn how to solve the problem.

2566 concert tickets were sold for a total of $10,348, and if students paid $3 and nonstudents paid $5, then the number of student tickets sold can be calculated.

To solve this problem, we can set up an equation using the given information.

X + Y = 2566

3X + 5Y = 10348

Find the value of X:

Y = 2566 - X

3X + 5(2566 - X) = 10348

3X + 12830 - 5X = 10348

2X = 12830 - 10348

2X = 2482

X = 1241

Therefore, 1241 student tickets were sold.

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The expression can be expanded as a difference of two logarithms:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

What is the logarithms?

Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.

We can use the properties of logarithms to expand the expression as follows:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]ln(x^2) - ln(y^5/2)[/tex]

Next, we can simplify each logarithm using the property that log(a^b) = b log(a):

[tex]ln(x^2) - ln(y^5/2)[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

Hence, the expression can be expanded as a difference of two logarithms:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

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Step-by-step explanation:

when x=2

y=2(2)-1

y=4-1

Answer:

slope = -2, Y intercept = -1

Step-by-step explanation:

[tex]y = mx + c[/tex]

[tex]where \: m \: is \: the \: slope \: and \: c \: is \: the \: intercept[/tex]

So compare the equation with y= -2x-1

Therefore m = -2, c = -1

The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

Currency conversion can be stated as the process of converting one currency into another currency. This is usually done in order to make transactions or investments in another country or to keep track of the value of assets held in different currencies.

here, we have,

we know.

The value of one currency is generally expressed in terms of another currency using exchange rates, which means  the value of one currency in terms of another currency at a specific point in time.

We know that, exchange rate can fluctuate over time, and currency conversion can be done manually or through various financial services or tools.

we have,

To calculate that how many pounds Brian will get for R2 100,

At first we need to calculate the amount of commission he will have to pay to the agent.

Commission = 1.5% of R2 100

Commission = 0.015 x R2 100

Commission = R31.50

Now we can calculate how much money Brian will have left after paying the commission:

Amount left after commission = R2 100 - R31.50

Amount left after commission = R2 068.50

Next, we can use the exchange rate given to convert Rands to Pounds:

1 Rand = 0.075199 Pounds

Therefore, to find out how many Pounds Brian will get for R2 068.50, we can multiply R2 068.50 by the exchange rate:

2 068.50 x 0.075199 = 155.605265 pounds

Next Part:

The price of petrol is increased from R12, 58 per litre to R13, 28 per litre.

i.e. increase of price = 100

so, the percentage increase in the price = 100 * 100/1258

                                                                   =7.9%

Next Part:

A motor car drives at an average speed of 106 km/h.

the car travel in 2 hours 45 minutes = 106* 165 / 60

                                                           =291.5 km

So The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

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Cylinder B is taller which is 3.45 inches more than cylinder A.    

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases that are connected by a curved surface.

The formula for the volume of a cylinder is given by  

Where V is the volume of the cylinder, r is the radius of the circular base of the cylinder, and h is the height of the cylinder.

Here we have

Two cylinders have the same volume of 845π cubic inches.  

The radius of Cylinder A is 13 inches

Let 'h₁' be the height of th cylinder

By using the formula, V = π r² h₁

Volume of the cylinder A = π (13)² h₁ = 169πh₁

From the data, 169πh₁ = 845π

=> 169h₁ = 845

=> h₁ = 845/169

=> h₁ =  5  

The radius of Cylinder B is 10 inches.

Let h₂ be the height

Volume of the Cylinder B = π (10)² h₂ = 100πh₂  

From the data, 100πh₂ = 845π  

=> 100h₂ = 845

=> h₂ = 8.45

The difference between the heights of the two cylinders

= 8.45 inch - 5 inch = 3.45 inch  

Therefore,

Cylinder B is taller which is 3.45 inches more than cylinder A.  

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Answer:

20%

Step-by-step explanation:

600÷3 of 100 = 20%

600/3 of 100 = 20%