Consider a variant of the matrix-chain multiplication problem in which the goal is to parenthesize the sequence of matrices so as to maximize, rather than minimize, the number of scalar multiplications. Does this problem exhibit optimal substructure

Answer:

Solving steps:

18) 16a²b - 8abc + 4ab²c²

=> 4ab(4a - 2c + bc²)

19) 3x³ + 3x² - 3x

=> 3x(x² + x - 1)

20) 2abx² + 3abx³ - 4abx\( {}^{4} \)

=> abx²(2 + 3x - 4x²)

Let x be the money used in the bank account that pays 4% and let y be the money used for the 10% certificates. We have that 1/3x is the money used to buy the bonds. Since the total investment is $10,000, then we have the following equation:

to find the return of each investment, we change the rate to decimals and multiply it to the amount of the investment:

since the total return of the investment is $885, then we have the following equation:

Now we have the following system of equations:

We can substract the second equation from the first to get the following:

we have that x=1500. This means that the money on the bankn account is $1500. Now we can use this value to find the money for the bonds and the money for the certificates:

finally, we have that the money used for the bonds is $500 and for the certificates is $8000.

Now, suppose that the controller don't buy the bonds. Then the equations would be the following:

Solving the system we get the following:

We can see that the solution changes with an increment on both quantities. Since the investments only were two, the money invested had to go up.

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

Tip: The symmetric property of equality states that no matter what side the equations and answer are it will still be equal, but it only works for the equal sign.

The math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

A number system is defined as a system of writing to express numbers.

Given that 12 = 17 - 5, then 17 - 5 = 12

we need to check which property will be used.

The math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

The symmetric property of equality is really quite simple. This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement.

Hence, the math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

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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

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

Answer:

C

Step-by-step explanation:

Approximate p-value assessing if the paleo group achieves greater weight reduction than the control group is 0.1957.

Null and Alternative Hypotheses:

All statistical tests have a null hypothesis. For most tests, the null hypothesis is that there is no relationship between your variables of interest or that there is no difference among groups.

The following null and alternative hypotheses need to be tested:

\(\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\ H_a: \mu_1 & > & \mu_2 \end{array}\)

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

\(t=\frac{\bar{X}_1-\bar{X}_2}{\sqrt{\frac{\left(n_1-1\right) s_1^2+\left(n_2-1\right) s_2^2}{n_1+n_2-2}\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}$$\\\\=\frac{7-6}{\sqrt{\frac{(400-1) 20^2+(400-1) 12^2}{400+400-2}\left(\frac{1}{400}+\frac{1}{400}\right)}}\\\\=0.857$\)

The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test). The p-value for: a lower-tailed test is specified by: p-value = P(TS ts | H 0 is true) = cdf(ts)

The p-value is p = 0.1957

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The value of r(s(4)) is -33.

What is a function?

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output.

To find the value of r(s(4)), we first need to find the value of s(4), and then use that as the input for the function r.

To find s(4), we substitute x = 4 into the expression for s(x):

s(4) = 3(4) - 1 = 12 - 1 = 11

Now that we have the value of s(4), we can use it as the input for the function r:

r(s(4)) = r(11) = -3(11) = -33

Therefore, the value of r(s(4)) is -33.

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Answer:

Step-by-step explanation:

d=vt, t=d/v, we are told they run for same amount of time so t=t and d2/v2=d1/v1

2/v=4/(v+4)

2v+8=4v

-2v+8=0

-2v=-8

v=4

So John jogs at 4 mi/hr

Data:

Loan=$278 at 10%

A simple interest is calculated for payments on the initial capital.

If the total interest was $174.12.

If the interest is on a year. You calculated the interes of one year. The 10% of $278:

In a year the interest is $27.8.

Then, $174.12 divided into $27.8 is the number of years of the loan:

Answer:

Step-by-step explanation:

Let the power is x, then we have the following inequality

Solving we get

Answer:

An answer is twenty.

Step-by-step explanation:

0.35^20 is the expression the equation would be 0.35^20=7.609

or: 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times 0.35 times... until you multiply 0.35 times 0.35 twenty times. Not 0.35 times 20, 0.35 times 0.35 twenty times, don't forget to move the decimal! An exponent is 20.

hope this helps!

Answer:

a = -1 and

b = 10

Step-by-step explanation:

Given:

h(x) = (x – 1)³ + 10

h(x) = (g compose f)(x).

f(x) = x + a and

g(x) = x³ + b

To find:

The values of a and b = ?

Solution:

First of all, let us have a look at the composite functions.

(g compose f)(x) means we replace the value of \(x\) with \(f(x)\) in the function \(g(x)\).

We know that:

\(g(x) =x^3+b\) and

\(f(x) = x + a\)

Let us find (g compose f)(x) by replacing \(x\) with \(x+a\)

\((g\ compose\ f)(x) = (x+a)^3+b\)

Also, h(x) = (g compose f)(x) = (x – 1)³ + 10

Therefore,

\((x - 1)^3 + 10 = (x+a)^3+b\)

Comparing the corresponding elements of the above expressions:

we get a = -1 and

b = 10

Answer:

a: -1

b: 10

edge 2020

There are 2 rearrangements of abcd in which no two adjacent letters are also adjacent letters in the alphabet.

What is letter arrangements?

A sorting technique that allows the person to arrange alphabets as conditioned according to the question. Then total arrangements are calculated to know the result.

According to the given question:

Using XXXX as stencil for letters arrangement

We can't put B in either of the middle positions, as there would only be the far end at which to put both A and C and we can't put two things in one slot. That is, XBXX would require A and C to both be in the red X in order to avoid putting them next to B...can't do that, so B can't go in the middle.

Similarly, we can't put C in either of the middle positions, as there would only be the far end at which to put both B and D and we can't put two things in one slot.

So, B and C must go on the ends.

BXXC can only be filled in as BDAC.

CXXB can only be filled in as CADB.

Hence there are 2 such arrangements.

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The error was made in substituting the function and the problem has been solved correctly by using substitution method.

What is substitution method?

One strategy for solving equation-related problems is the substitution strategy. Get an expression for one variable in terms of the second variable using one equation before applying the substitution procedure. The expression in the second equation after that should be used in place of that variable.

We are given two functions as f(x) and g(x).

We need to calculate g (f(0)).

The error made was that the student substituted g(x) into f(x) whereas f(x) was to be substituted in g(x).

Now,

f(0) = \(\frac{3(0) - 7}{4}\)

f(0) = \(\frac{- 7}{4}\)

Now, on substituting, we get

⇒g (f(0)) = 2f(0) - 1

⇒g (f(0)) = 2 (\(\frac{- 7}{4}\))  - 1

⇒g (f(0)) = \(\frac{- 7}{2}\) - 1

⇒g (f(0)) = \(\frac{- 9}{2}\)

Hence, the correct solution has been obtained.

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Since there are multiple questions so, the question answered above is attached below

Rashaad's water proportion as a fraction is 4/7.

Mav's water proportion as a fraction is 5/9.

Mav's mix will be more watery than Rashaad's mix Since 5/9 is greater than 4/7.

To find Rashaad and Mav's water proportions as fractions, we shall compute the ratio of water to the total mixture for each of them.

Rashaad's water proportion:

Rashaad mixed 4 cups of water and 3 cups of powdered lemon mix, so the total mixture is 4 + 3 = 7 cups.

Rashaad's water proportion (out of total) as a fraction is 4/7.

Mav's water proportion:

Mav mixed 5 cups of water and 4 cups of powdered lemon mix, so the total mixture is 5 + 4 = 9 cups.

The water proportion  (out of total) as a fraction for Mav is 5/9.

Next, we compare the fractions:

We shall compare the water proportions to determine whose mix will be more watery,  

So, we compare the numerators of the fractions:

Rashaad's water proportion: 4/7

Mav's water proportion: 5/9

Therefore, since 5/9 is greater than 4/7, Mav's mix will be more watery than Rashaad's mix.

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We can multiply the second equation by 5 to eliminate the x-variable when the equations are added together.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To eliminate the x-variable when the equations are added together, we need to multiply the second equation by some number that will cause the x-coefficient to be equal to the x-coefficient in the first equation but with opposite sign.

The x-coefficient in the first equation is 1, and the x-coefficient in the second equation is 1/5. We can multiply the second equation by 5 to get:

5(1/5 x - 2y = -1) => x/1 - 10y = -5

Now we can add the two equations together:

x - 3u + x/1 - 10y = 9 - 5

Simplifying the left side, we get:

2x - 3u - 10y = 4

Therefore, we can multiply the second equation by 5 to eliminate the x-variable when the equations are added together.

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Data triangulation is a research method that involves using multiple data sources or methods to gather and analyze information, enhancing the validity and comprehensiveness of findings.

Data triangulation is a research method that involves using multiple sources or methods to gather and analyze data on a particular topic or research question. By combining different data sources, researchers aim to enhance the validity, reliability, and comprehensiveness of their findings.

Two real-world examples of data triangulation are:

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Answer:

Step-by-step explanation:

We need only identify the x- and y-coordinates of the point of intersection of these two graphs.  That point is (-4, 2).

Answer:

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

It is an isosceles triangle if two sides are same.

There are two possible triangles with given values.

If the 45° is between the two 8 cm sides, then as the isosceles triangle the other two angles have the measure:

So this is an acute triangle.

If the 45° angle is opposite to 8 cm side, then the other 8 cm side also has same opposite angle measure.

Then the third angle is:

It means it is a right triangle.

Given plane is \(z + 2y + \frac{1}{3}x = 1\).Therefore,  \(z = 1 - 2y - \frac{1}{3}x\).

According to the question, we need to find the area of the surface S in the first octant. The first octant is defined as the region in 3D space where x, y, and z are all positive.

Now, the limits of integration are given by the intercepts of the plane on the three axes as below:

x-intercept :

\($z + 2y + \frac{1}{3}$\)

\(x = 1  z = 0, y = 0 = > x = 3y = 0\)

z- intercept :

\(z + 2y + \frac{x}{3} = 1\)  \(x = 0, y = 0 = > z = 1\)

y-intercept :

\(z + 2y + \frac{x}{3} = 1\) \(x = 0, z = 0 = > y = 1/2\)

Therefore, the limits of integration are:

0 ≤ x ≤ 3y0 ≤ y ≤ 1/2

Now, we need to find the area of the surface S, which is given by the following integral:

\(\int!\int ds = \int!\int \sqrt{1 + \left(\frac{\partial z}{\partial x}\right)^2 + \left(\frac{\partial z}{\partial y}\right)^2} dA\)

where ds is the surface area element, and dA is the area element on the xy-plane.

Now, we need to find ∂z/∂x

\(\frac{\partial z}{\partial y} \cdot \frac{\partial z}{\partial x}\)

\(-\frac{1}{3} \frac{\partial z}{\partial y}\)

= -2

Now, the integral becomes:

\(= \int\!\int \sqrt{1 + \frac{1}{9} + 4} \, dxdy\\= \int\!\int \sqrt{\frac{46}{9}} \, dxdy\\= \frac{2}{3} \int\!\int \sqrt{46} \, dxdy\\= \frac{2}{3} \sqrt{46} \int\!\int \, dxdy\\= \frac{2}{3} \sqrt{46} \frac{1}{2} \frac{3}{2}\\= \frac{9}{4} \sqrt{46}\)

Therefore, the area of the surface S in the first octant is (9/4)√46 square units.

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Answer:

F=-6

Step-by-step explanation:

2f/2=-12/2

f=-6

Answer: -6

Step-by-step explanation:

what times 2 = -12

2 * -6 = -12

Answer: kelsea 4 apples left

Step-by-step explanation:

Profit fall in one year = 116.8$

What is profit?

In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are several profit metrics that are frequently used.

Let cost price = C

And selling price before reducing = S

Profit for 1 day = S-C

Now, After reducing selling price to = S-0.32

Profit= S - 0.32 - C for 1 day

Profit fall by = (S-C)-(S - 0.32 - C)

                     = S - C - S + 0.32 + C

Profit fall by = 0.32 for 1 day

Profit fall by one year = 0.32×365

                                    = 116.8$

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a multiple regression model, the error term `e’ is assumed to be a random variable with a mean of is A) zero. This means that in a multiple regression model, the errors are assumed to have a mean of zero. This assumption is necessary to ensure that the model is unbiased and accurate in predicting the outcome variable.

this assumption is that the error term represents the unexplained variation in the outcome variable that is not accounted for by the predictor variables. If the error term had a mean value other than zero, this would indicate that there is a systematic bias or error in the model, which would affect the accuracy of the predictions.

the assumption of a zero mean error term is a critical aspect of multiple regression modeling and helps to ensure that the model is reliable and valid for predicting the outcome variable.

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The difference in the shortest collection times before and after the well installation is 20 minutes, calculated by subtracting the shortest time after installation (25 minutes) from before (45 minutes), as shown in the box and whiskers plot.

This is calculated by subtracting the shortest collection time after well installation (25 minutes) from the shortest collection time before well installation (45 minutes):

45 - 25 = 20 minutes.

This can be seen in the box and whiskers plot provided, where the lowest value for each distribution is denoted by the beginning of the whiskers.

So, the difference is before and after the well installation is 20 minutes.

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--The given question is incomplete, the complete question is given

" What is the difference in minutes between the shortest collection times before and after the well was installed"--

Answer:

where the boys are verbs

Answer:

(-x-3y)

Step-by-step explanation:

I look at subtraction of binomials like its a regular subtraction problem
in this case, we should re-write the equation as so

Answer: Part A:

To find the x-intercepts of the graph of f(x), we need to set f(x) equal to zero and solve for x:

-16x2 + 60x + 16 = 0

Divide both sides by -4 to simplify:

4x2 - 15x - 4 = 0

We can use the quadratic formula to solve for x:

x = (-b ± sqrt(b2 - 4ac)) / 2a

Where a = 4, b = -15, and c = -4.

x = (-(-15) ± sqrt((-15)2 - 4(4)(-4))) / 2(4)

x = (15 ± sqrt(385)) / 8

Therefore, the x-intercepts are approximately 0.256 and 3.194.

Part B:

The coefficient of the x2 term in f(x) is -16, which is negative. This means that the graph of f(x) opens downward, so the vertex is a maximum.

The x-coordinate of the vertex can be found using the formula:

x = -b / 2a

Where a = -16 and b = 60.

x = -60 / 2(-16) = 1.875

To find the y-coordinate of the vertex, we can plug in this value of x into the equation for f(x):

f(1.875) = -16(1.875)2 + 60(1.875) + 16 = 80.25

Therefore, the coordinates of the vertex are (1.875, 80.25).

Part C:

To graph f(x), we can use the information we obtained in Part A and Part B. We know that the x-intercepts are approximately 0.256 and 3.194, and the vertex is at (1.875, 80.25).

We can also find the y-intercept by plugging in x = 0:

f(0) = -16(0)2 + 60(0) + 16 = 16

Therefore, the y-intercept is (0, 16).

Using all of this information, we can sketch the graph of f(x) as a downward-opening parabola with x-intercepts at approximately 0.256 and 3.194, a vertex at (1.875, 80.25), and a y-intercept at (0, 16).

Step-by-step explanation: