Laura is 4 times as older as her daughter. In 16 years she will be only twice as old as her daughter. what is laura's percentage age?

Answer:

\(8x^2y-18y^3\)

\(=8x^2y-18yy^2\)

\(=4\cdot \:2x^2y+9\cdot \:2yy^2\)

\(=2y\left(4x^2-9y^2\right)\)

\(=2y\left(2x+3y\right)\left(2x-3y\right)\)

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

Hope it helps...

Have a great day!!

To compute the characteristic polynomial p(λ) for the matrix A, we need to find the determinant of (A - λI), where λ is the eigenvalue and I is the identity matrix.

The matrix (A - λI) is:

A - λI = [20 - λ, 16; -24, -20 - λ]

The determinant of (A - λI) is:

det(A - λI) = (20 - λ)(-20 - λ) - (16)(-24)

           = λ^2 + 20λ + 400 + 384

           = λ^2 + 20λ + 784

Therefore, the characteristic polynomial p(λ) is λ^2 + 20λ + 784.

To solve for the roots, we set p(λ) equal to zero and solve the quadratic equation:

λ^2 + 20λ + 784 = 0

Using the quadratic formula:

λ = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation, a = 1, b = 20, and c = 784. Substituting these values into the quadratic formula:

λ = (-20 ± √(20^2 - 4(1)(784))) / (2(1))

  = (-20 ± √(400 - 3136)) / 2

  = (-20 ± √(-2736)) / 2

  = (-20 ± √(2736)i) / 2

Since the discriminant is negative, the roots of the equation are complex numbers. Simplifying the expression:

λ1 = (-20 + √(2736)i) / 2

   = -10 + √(684)i

λ2 = (-20 - √(2736)i) / 2

   = -10 - √(684)i

Therefore, the two eigenvalues of the matrix A, with λ1 < λ2, are:

λ1 = -10 + √(684)i

λ2 = -10 - √(684)i

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Answer:

X = 101

Step-by-step explanation:

Add 11 to 90

90 + 11 = 101

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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Answer:

Jessica lived 10 months in Spain and 8 months in Colombia.

Step-by-step explanation:

Let x be the months Jessica spent in Spain, and y the months she spent in Colombia:

   1. x + y = 18

Using the information of words per month learned in each country, we can also write the equation:

    2. 160 * x + 200 * y = 3200

So now we have a system of two equations and two unknowns.

First we express y in terms of x, in the first equation:

We replace y in the second equation:

And solve for x:

Finally we use that value of x in the first equation and solve for y:

Jessica lived 10 months in Spain and 8 months in Colombia.

Answer: he'll make $99 from the one dude and $72 from the lady so 171 total

if this isnt right then im sorry:(

Step-by-step explanation:

\(3.8\times 10^4\qquad \times\qquad 2.7\times10^{-8}\qquad \implies \qquad (3.8\cdot 2.7)\times 10^4\times10^{-8} \\\\\\ 10.26\times 10^{4-8}\implies 10.26\times 10^{-4}\implies 10.26\times \cfrac{1}{10^4} \\\\\\ \cfrac{10.26}{10^4}\implies \cfrac{10.26}{1\underline{0000}}\implies 0.\underline{0010}26\)

(A) The percentage is approximately 62.07%.

(B) percentage of years will have an annual rainfall of more than 39 inches is 72.17%.

(C) the smaller percentage from the larger one: 50.48% - 22.17% = 28.31%.

First, let's recall that the normal distribution is characterized by the mean and standard deviation. In this case, the mean annual rainfall is 42.3 inches and the standard deviation is 5.6 inches.

To answer your questions, we'll use the Z-score formula: Z = (X - mean) / standard deviation. Then, we can use a Z-table or calculator to find the percentage.

a) For annual rainfall less than 44 inches:
Z = (44 - 42.3) / 5.6 = 1.7 / 5.6 ≈ 0.3036
Using a Z-table or calculator, the percentage is approximately 62.07%.

b) For annual rainfall more than 39 inches:
Z = (39 - 42.3) / 5.6 = -3.3 / 5.6 ≈ -0.5893
Using a Z-table or calculator, the percentage for LESS than 39 inches is approximately 27.83%. To find the percentage of years with more than 39 inches, subtract from 100%: 100% - 27.83% = 72.17%.

c) For annual rainfall between 38 and 43 inches:
Z1 = (38 - 42.3) / 5.6 ≈ -0.7679
Z2 = (43 - 42.3) / 5.6 ≈ 0.1250
Using a Z-table or calculator, the percentage for Z1 is 22.17%, and for Z2 is 50.48%. To find the percentage between these two Z-scores, subtract the smaller percentage from the larger one: 50.48% - 22.17% = 28.31%.

So, the answers are: a) 62.07%, b) 72.17%, and c) 28.31%.

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490

472 <490<500

it fits the criteria

9514 1404 393

Answer:

  x = 33

Step-by-step explanation:

The angles of a linear pair are supplementary.

 (2x -18)° +(4x)° = 180°

  6x -18 = 180 . . . . . . . . divide by °, simplify

  x -3 = 30 . . . . . . . . . divide by 6

  x = 33 . . . . . . . . . . add 3

_____

Additional comment

The two angles are 48° and 132°.

Answer:

\(y = \frac{Pa}{b} - za\)

Step-by-step explanation:

See picture below :)

The law of syllogism, also called reasoning by transitivity, is a valid argument form of deductive reasoning that follows a set pattern. It is similar to the transitive property of equality, which reads: if a = b and b = c then, a = c. ... If they are true, then statement 3 must be the valid conclusion.Answer:

Step-by-step explanation:

The given series is a geometric series with first term a = 10x and common ratio r = 2x. The series converges for the domain (-1/2, 1/2) and the sum is given by 10x/(1 - 2x).

The series 10x + 20x^2 + 40x^3 + 80x^4 + ... is a geometric series with first term a = 10x and common ratio r = 2x.

For a geometric series to converge, the absolute value of the common ratio must be less than 1, so we have:

|2x| < 1

Solving for x, we get:

-1/2 < x < 1/2

Therefore, the domain of x for which the series converges is (-1/2, 1/2).

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

sum = a/(1 - r)

Substituting a = 10x and r = 2x, we get:

sum = 10x/(1 - 2x)

This formula is valid only when |r| < 1, which is the case when x is in the domain (-1/2, 1/2).

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Answer:

240=386+b

Step-by-step explanation:

So ¨equal to the total of ¨ would mean that a number is the same as the sum of some other numbers.

In this case it would mean that 240 is the same as the sum of 386 and b, which would mean it equals itself.

Given the point (6,6) on the line and a slope of m = 0, three additional points that the line passes through can be determined. One possible set of points is (6,6), (5,6), (7,6), and (6,0).

When the slope (m) of a line is zero, it indicates that the line is a horizontal line. In this case, the line is parallel to the x-axis and does not have any vertical change. Therefore, the y-coordinate of any point on the line will remain constant.

Given the point (6,6) on the line, we can see that the y-coordinate is 6. Since the slope is zero, the y-coordinate will remain the same for any x-coordinate. Hence, three additional points on the line can be determined by varying the x-coordinate while keeping the y-coordinate constant at 6.

One possible set of points is (6,6), (5,6), (7,6), and (6,0). In this case, we keep the y-coordinate constant at 6 and choose different x-coordinates to form the points. These points lie on the horizontal line passing through (6,6) and have the same y-coordinate.

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Answer:

1

Step-by-step explanation:

If there is nothing by the (x) in the equation there is always an invisible 1 next to it. The full equation is f(x)= 1x+3. The answer is 1. Hope that helps!

Answer:

m=1; slope is 1

Step-by-step explanation:

..........

Answer:

Step-by-step explanation:

y = 5x - 4

y = 6x $\Rightarrow$ x = y/6

y = 5*y/6 - 4

y = 5y/6 - 4

6y = 5y - 24

y = -24.

So, x = -4

In a situation when the experimental data on alcohol consumption from the same 100 individuals, a matched pairs design is used. The correct option is B.

An experiment is a procedure that is carried out to support or refute a hypothesis, or to determine the efficacy or likelihood of something that has never been tried before. Experiments shed light on cause-and-effect relationships by demonstrating what happens when a specific factor is changed.

A matched pairs design is an experimental design in which participants are matched in pairs based on shared characteristics before being assigned to groups; one participant from the pair is randomly assigned to the treatment group and the other to the control group.

It is one in which each member of a sample is matched with a corresponding member in every other sample based on characteristics other than those under investigation.

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the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

How to solve?

To solve this problem, we can use the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence.

Let lambda be the expected rate of customer arrivals per minute. If exactly two customers arrive in the first minute, then the expected number of customers to arrive in three minutes is lambda ×3. We can use this expected value to calculate the probability of at least seven customers arriving in three minutes:

P(X ≥ 7 | X ~ ∝(λ×3))

= 1 - P(X ≤ 6 | X ~ ∝(λ×3))

= 1 - ∑[k=0 to 6] (e²(-λ3) ×(lλ3)²k / k!)

where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.

To find lambda, we can use the fact that exactly two customers arrive in the first minute. The Poisson distribution assumes that the number of events in a fixed interval of time or space follows a Poisson distribution with parameter lambda, which represents the expected rate of occurrence. Therefore, lambda is equal to the number of customers arriving per minute, which is 2.

Substituting lambda = 2 into the formula, we get:

P(X ≥ 7 | X ~ ∝(2×3))

= 1 - P(X ≤ 6 | X ~ ∝(6))

= 1 - ∑[k=0 to 6] (e²(-6) ×6²k / k!)

Using a calculator or computer software, we can evaluate this expression to get:

P(X ≥ 7 | X ~ ∝(6)) ≈ 0.081

Therefore, the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

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Answer:

1. 4,2

2. 1/2,2

3.-7.7,-1.3

4. a=4, b=-13, c=3

5. \(\frac{-7+-\sqrt{x} 89}{4}\)

Step-by-step explanation:

(a) The average rate the water leaves the tub between t=1 and t=2 is -3 m^3/min.

(b) The average rate the water leaves the tub between t=1 and t=1.1 is -23.1 m^3/min.

(c) The estimated exact rate at t=1 is -2 m^3/min.

(d) The average rate the water leaves the tub between t=1 and t=1+h is -2 - h m^3/min.

(e) The result when h=0 in part (d) is -2 m^3/min.

(a) To find the average rate the water leaves the tub between t=1 and t=2, we need to calculate the change in volume divided by the change in time. The change in volume is f(2) - f(1) = (4 - 2^2) - (4 - 1^2) = 1 m^3. The change in time is 2 - 1 = 1 min. Therefore, the average rate is 1 m^3/min.

(b) Similarly, for t=1 to t=1.1, the change in volume is f(1.1) - f(1) = (4 - 1.1^2) - (4 - 1^2) ≈ 0.69 m^3. The change in time is 1.1 - 1 = 0.1 min. The average rate is 0.69 m^3/0.1 min ≈ 6.9 m^3/min.

(c) At t=1, we can estimate the exact rate by calculating the derivative of the function f(t) = 4 - t^2 with respect to t. The derivative is -2t, so at t=1, the rate is -2 m^3/min.

(d) When h is a very small number, we can approximate the average rate by taking the derivative at t=1. The derivative is -2t, so the average rate between t=1 and t=1+h is approximately -2 m^3/min.

(e) When we substitute h=0 in the answer to part (d), we get -2 m^3/min, which is the exact rate of water leaving the tub at t=1.

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Answer:

x > 6

Step-by-step explanation:

2x + 4 > 16

2x > 16 - 4

2x > 12

x > 12/2

x > 6

Answer:

Estimation: 300 Billion times bigger

Actual: 290 Billion times bigger

Step-by-step explanation:

Lets group the coefficients together and the exponents together.

\((\frac{6.1}{2.1})(\frac{10^7}{10^{-4} })\)

We can round 6.1 to 6.

We can round 2.1 to 2.

\((\frac{6}{2})(\frac{10^7}{10^{-4} })\)

\((3)(\frac{10^7}{10^{-4} })\)

Subtract the exponent from the denominator from the exponent of the numerator.

\((3)(10^{7-4*1} )\)

\((3)(10^{7+4} )\)

\((3)(10^{11} )\)

\(3*10^{11}\)

\(10^{11}\) is 100 billion.

3 times 100 billion is 300 billion.

Answer:

no

Step-by-step explanation:

Answer:

Yes they are equivalent

Step-by-step explanation:

8 ÷ 2 = 4

\(8*\dfrac{1}{2}=\dfrac{8}{2}=4\)

Each of the statements should be completed as follows;

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values approach negative infinity (-∞) to positive infinity (∞).

In this context, the purple line on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 1.

Additionally, the base value of this exponential growth function f(x) = 3^x + 1 is equal to 1 and its domain includes all real numbers while its range includes all real numbers that are greater than 1 i.e 1 < y < ∞.

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The expected value of an unbiased estimator is equal to the parameter whose value is being estimated. This is FALSE statement.

Because, An unbiased estimator's anticipated value is the same as the parameter whose value is being calculated.

The acquisition, organization, measurement, explanation, and display of data are all covered by figures. A data object is a feature (or characteristic) data that would be measured or tallied, such as peak, origin nation, salary, etc. Data can also be referred to this as variables due to their ability to differ from one another and they may vary over time.

Statistics is a method of interpreting, analyzing and summarising the data. Hence, the types of statistics are categorized based on these features: Descriptive and inferential statistics. Based on the representation of data such as using pie charts, bar graphs, or tables, we analyse and interpret it.

If the disparity between the estimator and the parameter decreases with increasing sample size, the estimator is said to be consistent.

Real as An unbiased estimator's anticipated value is the same as the parameter whose value is being calculated.

The given statement is FALSE

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Let \(a\) be the first term in the series and \(r\) the common ratio. Then the infinite series converges to

\(a + ar + ar^2 + ar^3 + ar^4 + ar^5 + \cdots = \dfrac a{1-r}\)

Removing the first three terms from the left side effectively multiplies the right side by 27, so

\(ar^3 + ar^4 + ar^5 + \cdots = \dfrac{27a}{1-r}\)

By elimination,

\(a + ar + ar^2 = -\dfrac{26a}{1-r}\)

Solve for \(r\). We can eliminate \(a\) so that

\(1 + r + r^2 = -\dfrac{26}{1-r} \\\\ \implies 1-r^3 = -26 \\\\ \implies r^3 - 27 = 0 \\\\ \implies r^3 = 27 \implies \boxed{r=3}\)

The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

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