Solve the simultaneous equations 3x- 4y =20 and 4x-2y = 25

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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A series of rigid transformation that transform triangle EFG to produce an image that rests on the square ABCD to together form a simple drawing of a house are;

A translation and a counterclockwise rotation

A rigid transformation is one in which the lengths of corresponding points in the image are preserved.

A sequence of transformations (translations, rotations, and reflections that transform triangle EFG so that its image rest on square ABCD to together form a simple drawing of a house are;

The performance of the above transformations will produce the image of the simple drawing of the house consisting of the square base and the triangular top.

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Answer:

4/21

Step-by-step explanation:

I got the first probability and the second probabilty then multiplied them together.

Answer: P: (-3, -1), Q: (2, -1), R: (1, 2), S: (-3, 2)

Step-by-step explanation: the way I think about it is you have to run before you jump, so the third one let’s say, you have to “run” to 1, and then “jump” to 2. Now let’s take the first one, it’s the exact same thing just in the opposite direction, you “run” back to -3 and then “fall” to -1. Now let’s take the second one, first you would “run” to 2 and then “fall” (because it’s a negative) to -1, and if it was a negative first and then a positive, it would just be the opposite of the one O just explained

The probability that four of the first five patients will be helped by the medicine is 0.39. The probability that a particular medicine will help a person is an important aspect of medicine.

The probability that a certain medicine will help a person is 0.75. A doctor will be seeing 15 patients today.

To find out the probability of the following:

a) P(The medicine will help all 15 patients)When each patient is independent of the other, then the probability of the medicine helping all 15 patients can be calculated by multiplying 0.75 by itself 15 times.

Therefore:

= P(The medicine will help all 15 patients)

= 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75

= 0.0047.

Therefore, the probability that the medicine will help all 15 patients is 0.0047.

b) P(The medicine helps 9 or more patients)

To determine this, we have to calculate the probability of the medicine helping 9 patients, 10 patients, 11 patients, 12 patients, 13 patients, 14 patients and 15 patients.

We can calculate these probabilities using the binomial probability formula. The probability of the medicine helping at least 9 patients is the sum of the probabilities of the medicine helping 9 patients, 10 patients, 11 patients, 12 patients, 13 patients, 14 patients and 15 patients.

Therefore:

P(The medicine helps 9 or more patients) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= 0.196 + 0.326 + 0.305 + 0.176 + 0.066 + 0.018 + 0.003

= 0.99

Therefore, the probability that the medicine helps 9 or more patients is 0.99.

c) P(The medicine helps exactly 10 patients)Using the binomial probability formula, we can find that the probability that the medicine will help exactly 10 patients is:

P(X = 10) = nCx * p^x * q^(n - x), where n = 15, x = 10, p = 0.75 and q = 0.25

Therefore:

P(X = 10) = 15C10 * (0.75)^10 * (0.25)^5

= 0.20

Therefore, the probability that the medicine helps exactly 10 patients is 0.20.

d) P(Four of the first five patients will be helped by the medicine)

Using the binomial probability formula, we can find that the probability that 4 of the first 5 patients will be helped by the medicine is:

P(X = 4) = nCx * p^x * q^(n - x)y, where n = 5, x = 4, p = 0.75 and q = 0.25

Therefore:

P(X = 4) = 5C4 * (0.75)^4 * (0.25)^1

= 0.39

Therefore, the probability that four of the first five patients will be helped by the medicine is 0.39.

The probability that a particular medicine will help a person is an important aspect of medicine. The likelihood of the medicine helping all 15 patients is very low, and the likelihood of the medicine helping 9 or more patients is very high. The likelihood of the medicine helping exactly 10 patients is relatively low, and the likelihood of four of the first five patients being helped by the medicine is relatively high.

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Answers:

=======================================

Explanations:

Answer:

13.) 257.08

14.) 33.57

Step-by-step explanation:

Assume you mean the perimeter.

The circumference is 2\(\pi\)r, then just add the extra measurements

Answer:

I think it is 420 people

Step-by-step explanation:

Answer:

Volume of one prism; (1/16) unit³

Step-by-step explanation:

The given volume of the cube, v₁ = 1 unit cube

The height of the unit cube, h₁ = 1 unit

The length of the unit cube, w₁ = 1 unit

The height of the unit cube, l₁ = 1 unit

The number of identical prism located along the height = 2 identical prism

The number of identical prism located along the width = 2 identical prism

The number of identical prisms located along the length = 4 identical prism

Therefore;

The height of each identical rectangular prism that make up the unit cube, h₂ = h₁/2 = 1/2 unit

Similarly, for each identical rectangular prism, we have;

The width, w₂ = w₁/2 = 1/2 unit

The length, l₂ = l₁/4 = 1/4 unit

The volume of each one of the identical rectangular prism, v₂ = h₂ × w₂ × l₂

∴ v₂ = 1/2 unit × 1/2 unit × 1/4 unit = 1/16 unit³

The volume of one of the identical rectangular prisms = (1/16) unit³.

Answer: D

Step-by-step explanation:

Answer:D

Step-by-step explanation:

...

Answer: Distance: 9.43398113206

Find the equation of the dotted line:

1. Find the slope:

2. Find the y-intercept (b): the value of y when the line cross y-axis:

b=4

Then, the eqution of the line is: y=-2x+4

To write the inequality:

When the line is a dotted line you use > or <, whne it is a full line you use ≥ or ≤

When the sahdow area is under the line use < or ≤, when the shadow area is over the line you use > or ≥

Then, as you have a dotted line and the shadow area in under that line, you get the next inequality:

Answer:

2a +ab-9

Step-by-step explanation:

First, write out what you have:

3a-2b-ab-(a-b+ab)+3ab+b-9

Then, distribute the "-" to the "a-b+ab" inside the parenthesis:

3a-2b-ab-a+b-ab+3ab+b-9

Finally, combine like terms and simplify:

3a-a-2b+b+b-ab+3ab-ab-9

2a-2b+2b+3ab-2ab-9

2a+0+ab-9

2a+ab-9 is you equation fully simplified

Answer: x = -5

Step-by-step explanation:

Hey there, so you need to Solve for x.

x: 10 - 2x = -5x -5

Add All X's to the left side and All numbers to the right side

-2x+5x = -5 - 10

Add

3x = -15

Simplify

x = -5

~I hope I helped you! :)~

Answer:

B

Step-by-step explanation:

Answer:

A. \(10x^{2} + 33x^{2} +19x - 12\)

Explanation:

\((2x + 3) (5^{2} + 9x - 4)\\\)

Mutiply \(2x\) by each number on the second bracket

\((2x) (5^{2} ) = 10x^{3} \\(2x) (9x ) = 18x^{2} \\(2x) (- 4 } ) = -8x\)

Then mutiply 3 by each number on the second bracket

\((3) (5^{2} )= 15x^{2} \\(3) (9x) = 27x\\(3) (-4) = -12\)

New equation:

\(10x^{3} + 18x^{2} + -8x + 15^{2} + 27x - 12\)

Add all like terms

\(10x^{3} + 33x^{2} + 19x - 12\)

Answer:

B) x = √118 mi

Step-by-step explanation:

This is a right triangle, so we can the measure of x using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

Step 1:  Plug in x and √26 for a and b and 12 for c and simplify:

x^2 + (√26)^2 = 12^2

x^2 + 26 = 144

Step 2:  Subtract 26 from both sides to isolate x^2:

(x^2 + 26 = 144) - 26

x^2 = 118

Step 3:  Take the square root of both sides to isolate x:

√(x^2) = √118

x = √118 mi

A system of linear equations with zero solutions has a graph containing parallel lines.

Recall that a linear equation is displayed as a line, which means that all points on the line are solutions to that linear equation. There are an infinite number of solutions. If you have a system of linear equations, the solution to the system is the value that makes all the equations true.

Systems of equations

A solution to a system of equations is the value or values ​​that apply to all equations in the system. Graphing the equations in a system can tell you how many solutions there are for that system.

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The equation of a line is generally written in the form \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept. So from the parameters we were given, \(m = 2\) and \(c = -3\), thus the equation becomes \(y = 2x + (-3), y = 2x - 3\)

\(y = 2x - 3\)

The equation of the line with a Y-intercept of -3 and a slope of 2 is y = 2x - 3

The slope of the line is represented by m

m = 2

The y-intercept of the line is represented by c

c = -3

The slope-intercept for of the equation of a line is:

y = mx + c

Substitute m = 2 and c = -3 into the equation above

y = 2x - 3

Therefore, the equation of the line with a Y-intercept of -3 and a slope of 2 is:

y = 2x - 3

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Job sharing is the name for this type of arrangement as Annette and Nathan share their work at Wood Grove Elementary.

A job share arrangement is a full-time of work of  job  and it is split between two individuals, each with responsibility for the success of the total job. Work sharing, sometimes known as work sharing, is a work arrangement in which two persons, or occasionally more, are kept on a part-time or reduced-time basis to carry out tasks that are typically completed by one person working full-time of job.

As a result, there is a net decrease in per-employee income. The individuals who share the job are jointly accountable for the workload of the shared job and work together to fulfill the task.

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The subshell designated by each set of quantum numbers is as follows:

a) n=3, l=1 -> 3p subshell

b) n=4, l=2 -> 4d subshell

c) n=2, l=0 -> 2s subshell

d) n=5, l=3 -> 5f subshell

In the electron configuration of an atom, each electron is described by a set of four quantum numbers, which includes the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). The second quantum number (l) determines the shape of the subshell, which in turn influences the energy level and chemical behavior of the atom. The letter designation for each subshell is based on the value of the angular momentum quantum number (l): s (l=0), p (l=1), d (l=2), f (l=3), and so on. Therefore, for a given set of quantum numbers, we can determine the subshell designation by identifying the value of l.

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Answer:Z

cos x dx = sin x + C

Z

sec2 x dx = tan x + C

Z

sec x tan x dx = sec x + C

Z

1

1 + x2

dx = arctan x + C

Z

1

√

1 − x2

dx = arcsin x + C

8.1 Substitution

Needless to say, most problems we encounter will not be so simple. Here’s a slightly more

complicated example: find

Z

2x cos(x

2

) dx.

This is not a “simple” derivative, but a little thought reveals that it must have come from

an application of the chain rule. Multiplied on the “outside” is 2x, which is the derivative

of the “inside” function x

2

. Checking:

d

dx sin(x

2

) = cos(x

2

)

d

dxx

2 = 2x cos(x

2

),

so Z

2x cos(x

2

) dx = sin(x

2

) + C.

Even when the chain rule has “produced” a certain derivative, it is not always easy to

see. Consider this problem:

Z

x

3

p

1 − x

2 dx.

There are two factors in this expression, x

3

and p

1 − x

2, but it is not apparent that the

chain rule is involved. Some clever rearrangement reveals that it is:

Z

x

3

p

1 − x

2 dx =

Z

(−2x)

−

1

2

(1 − (1 − x

2

))p

1 − x

2 dx.

This looks messy, but we do now have something that looks like the result of the chain

rule: the function 1 − x

2 has been substituted into −(1/2)(1 − x)

√

x, and the derivative

Step-by-step explanation:Z

cos x dx = sin x + C

Z

sec2 x dx = tan x + C

Z

sec x tan x dx = sec x + C

Z

1

1 + x2

dx = arctan x + C

Z

1

√

1 − x2

dx = arcsin x + C

8.1 Substitution

Needless to say, most problems we encounter will not be so simple. Here’s a slightly more

complicated example: find

Z

2x cos(x

2

) dx.

This is not a “simple” derivative, but a little thought reveals that it must have come from

an application of the chain rule. Multiplied on the “outside” is 2x, which is the derivative

of the “inside” function x

2

. Checking:

d

dx sin(x

2

) = cos(x

2

)

d

dxx

2 = 2x cos(x

2

),

so Z

2x cos(x

2

) dx = sin(x

2

) + C.

Even when the chain rule has “produced” a certain derivative, it is not always easy to

see. Consider this problem:

Z

x

3

p

1 − x

2 dx.

There are two factors in this expression, x

3

and p

1 − x

2, but it is not apparent that the

chain rule is involved. Some clever rearrangement reveals that it is:

Z

x

3

p

1 − x

2 dx =

Z

(−2x)

−

1

2

(1 − (1 − x

2

))p

1 − x

2 dx.

This looks messy, but we do now have something that looks like the result of the chain

rule: the function 1 − x

2 has been substituted into −(1/2)(1 − x)

√

x, and the derivative

Answer:

ok so it is e because

Step-by-step explanation: n 1950, the population of the United States

was 152 million people. In 1990, it was 250

million. Use a linear model to estimate the

population of the United States in 2030.

Answer:

B. (-3, -17)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

there are 7 blocks in the whole

the green portion is 3/7

1/2 times 6/7 is equal to 3/7

the answer is B

a) There is not enough information  b) We can conclude that W≻R and W≻G.  c) The probabilities p(G), p(W), and p(R) are the probabilities of getting each drink in the lottery L.  d) The decision would be whether to drink Whisky or Gin.

(a) There is not enough information to determine whether Cohen prefers a glass of Gin to a glass of Whisky because the lotteries L1 and L2 are indifferent. This means that Cohen is equally likely to prefer one lottery to the other. In other words, his utility for Gin is equal to his utility for Whisky.

(b) If we are also told that Cohen prefers Rum to Gin, R≻G, then we can say that he prefers L3 to L1 and L2. This is because L3 has a higher probability of giving him his most preferred drink, Rum, than either L1 or L2. Therefore, we can conclude that W≻R and W≻G.

If G≻R, then we would have L1≻L3 and L2≻L3. This is because L1 and L2 have a higher probability of giving him his most preferred drink, Gin, than L3. However, we know that L3≻L1 and L3≻L2, so this is a contradiction. Therefore, G≻R cannot be true.

(c) A VNM utility function is a function that represents a person's preferences over lotteries. It takes as input a lottery and outputs a real number that represents the person's utility for that lottery. In the case where W≻G, a VNM utility function for Cohen would be of the form:

u(L) = w * p(G) + g * p(W) + r * p(R)

where w is Cohen's utility for Whisky, g is his utility for Gin, and r is his utility for Rum. The probabilities p(G), p(W), and p(R) are the probabilities of getting each drink in the lottery L.

(d) A VNM utility function cannot be used to represent Cohen's preferences because his preferences are not stable. In other words, his preferences change depending on his mood. When he is happy, he prefers Whisky to Gin. But when he is depressed, he prefers Gin to Whisky. This means that his utility for Gin and Whisky cannot be represented by a single number.

To model Cohen's preferences, we would need to use a more complex model that takes into account his mood. One possible model would be a Markov decision process. A Markov decision process is a model that describes how a person's preferences change over time. It takes as input the person's current mood and outputs a decision about what to do.

In the case of Cohen, the decision would be whether to drink Whisky or Gin. The person's mood would be represented by a state variable. The state variable would take on one of two values: happy or depressed. The transition probabilities would describe how likely it is for the person's mood to change from one state to the other. The reward function would describe how much utility the person gets from drinking each drink.

This model would allow us to capture the fact that Cohen's preferences change depending on his mood. It would also allow us to make predictions about how he would behave in different situations.

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Answer: b

Step-by-step explanation:

its b i just did the work

This, compute f30  = (832040, 1346269)t.

To solve the given problem in MATLAB

Define the matrix f.

f = [0 1; 1 1];

Find the eigenvalues and eigenvectors of matrix f.

[V, D] = eig(f);

Obtain the invertible matrix p and the diagonal matrix d.

p = V;

d = D;

Verify that pdp^(-1) equals f.

result = p * d * inv(p);

Compute f^10 and pd^10p^(-1).

f_10 = f^10;

result_10 = p * (d^10) * inv(p);

Compute ff, f2f, f3f, f4f, and f5f.

f_1 = f * f;

f_2 = f_1 * f;

f_3 = f_2 * f;

f_4 = f_3 * f;

f_5 = f_4 * f;

The pattern in the answers can be observed as follows:

ff = (1, 1)t

f2f = (1, 2)t

f3f = (2, 3)t

f4f = (3, 5)t

f5f = (5, 8)t

To compute f30, we can use the same pattern and repeatedly multiply f with itself. However, computing f^30 directly might result in large numbers and numerical errors. Instead, we can utilize the Fibonacci sequence properties.

Given that f = (f0, f1)t = (1, 1)t, we know that fnf = (fn, fn+1)t. So, to find f30, we can calculate f30f = (f30, f31)t. Since f30 is the 31st term in the Fibonacci sequence, we can conclude that f30 = fn+1 = 832040.

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The answer is 5.

Simple question

Answer:

The answer is B or -3.132

Step-by-step explanation:

You are multiplying 2 negatives and a positive, so it guarantees it will be negative! Hope this helps!