multiply (2x – 3)(x2 – 5x + 3)

Answer:

(0,-2) (1,1) (2,4)

Step-by-step explanation:

To accumulate $100,000 over 20 years at a 10% annual interest rate compound annually, you would need to make annual payments of $8,218.64.

You can use the formula for the future value of an annuity to accumulate $100,000 over 20 years at a 10% annual interest rate compound on a yearly basis:

\(FV = Pmt * [(1 + r)^n - 1] / r\)

Where:

FV is future value, which is $100,000 in that case

Pmt: annual payment

r: annual interest rate, which is 10%

n: number of payment periods, which is 20

By plugging in values:

\($100,000 = Pmt * [(1 + 0.1)^(20) - 1] / 0.1\)

Solving for Pmt, we get:

\(Pmt = $100,000 / [(1 + 0.1)^(20) - 1] / 0.1\\Pmt = $100,000 / 12.167\\Pmt = $8,218.64\)

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Answer:

212

Step-by-step explanation:

Answer:

The slope is 1.

Step-by-step explanation:

The Chebyshev bound can be used to provide an upper bound on the probability that the total number of dots lies between 300 and 400.

The Chebyshev bound states that for any random variable with a finite mean and variance, the probability that the random variable deviates from its mean by more than a certain number of standard deviations is bounded. In this case, we can use the Chebyshev bound to estimate the probability that the total number of dots deviates from its mean by more than a certain amount.

To apply the Chebyshev bound, we need to know the mean and variance of the total number of dots. Once we have these values, we can calculate the standard deviation and determine the number of standard deviations that correspond to the interval between 300 and 400.

By using the Chebyshev bound, we can provide an upper bound on the probability that the total number of dots lies between 300 and 400. The bound becomes tighter as the sample size increases, and it approaches the actual probability as the sample size approaches infinity. Therefore, the Law of Large Numbers is indirectly invoked in using the Chebyshev bound to estimate the probability.

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Answer:

193.28 cm^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Refer to attached

The ares consists of half-circle and a triangle

Radius of circle:

Sided of the triangle:

Total area:

Answer:

240÷40 is your answer :)

Answer: 115%

Step-by-step explanation: ur welcome

Answer:

53.2%

Step-by-step explanation:

301x53.2%= 160.132 = 160.13

301-160.13=140.87

About 53.2%

Answer:

2 blueberry and 5 raspberry scones go in each bag

Step-by-step explanation:

34+85=119

119/17=7

34/85= 2/5

so 2 blueberry and 5 raspberry scones go in each bag

hope that helps :)

Answer:

2 Blueberry scones and 5 Raspberry scones

Step-by-step explanation:

Given:

34 Blueberry scones

85 raspberry scones

17 Bags to fit scones

34 Blueberry so 34 divided by the Bag 17 (34 ÷ 17 = 2)

85 Raspberry scones so 85 divided by the Bag 17 ( 84 ÷ 17 = 5)

Therefore Jason can put 2 Blueberry scones and 5 Raspberry scones in each Bag

Answer:

10^6

Step-by-step explanation:

The reason is because 2x5 = 10 and then you add the exponents when multiplying, making it 10^8

Answer: 2/3 hours

Step-by-step explanation:

okay so the speed now is 850, which is   850/340  = 2.5 times the original speed

Since It's 2.5 times the original speed,

2.5x = 5/3

so x = 5/3/2.5 = 2/3

Answer:

2/3 of an hour

Step-by-step explanation:

Here is the information that the question gives us.

A plane covers a distance in 5/3 of an hour at 340 km per hour. How long would it take for a plane to cover the same distance while traveling at 850 km per hour?

Remember, distance = speed * time. Using that formula, we can find the distance with this equation:

distance = 340 * 5/3

Multiply.

distance = 1700/3 km

Then, we can plug this distance in to find the time it would take for a plane going at 850 km/hour.

distance = speed * time

1700/3 = 850 * time

Divide both sides by 850

(1700/850) / 3 = time

time = 2/3 hour

Thus, the answer is 2/3 of an hour.

Just in case, let's check the answer. Because both the planes travel the same distance, then their speeds * time should both equal "distance". In other words, they should be equal.

340 * 5/3 = 2/3 * 850

Simplify.

1700/3 = 1700/3

So, the answer is correct.

I hope this helps! Feel free to ask any questions!

the product of x and a factor not depending on x

What is quadratic equation

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation given 3x(m-6n)²

This expression contains two factors:

1 factor: 3x

2 factor: (m-6n)²

Hence the product of x and a factor not depending on x.

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The division of 16 - 8x - 7x² + 2x³ by x - 4 will have a quotient of 2x² + x - 4 and a remainder of 0 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall rearrange 16 - 8x - 7x² + 2x³ to become 2x³ - 7x² - 8x + 16 and then divide by x - 4 as follows;

2x³ divided by x equals 2x²

x - 4 multiplied by 2x² equals 2x³ - 8x²

subtract 2x³ - 8x² from 2x³ - 7x² - 8x + 16 will give x² - 8x

x² divided by x equals x

x - 4 multiplied by x equals x² - 4x

subtract x² - 4x from x² - 8x will give us -4x + 16

-4x divided by x equals -4

x - 4 multiplied by -4 equals -4x + 16

subtract -4x + 16 from -4x + 16 will result to a remainder of 0

Therefore by synthetic division, 16 - 8x - 7x² + 2x³ divided by x - 4 is equal to the quotient of 2x² + x - 4 with a remainder of 0.

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Answer:

Not me sorry I can't help nut I hope you get the answer

Answer:

Bowling ball

Step-by-step explanation:

A bowling ball has much more mass than all three of the other choices and the amount of kinetic energy is determined based on a object's mass and velocity, but in this case, all 4 balls are traveling at the same velocity. Therefore, we know that the bowling ball has much more mass so therefore it has the most kinetic energy.  

a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

18. a. If B is any echelon form of A, then the pivot columns of B form a basis for the column space of A.

This statement is true. An echelon form of a matrix is obtained by performing row operations on the original matrix to transform it into a specific triangular form. In this form, the pivot columns correspond to the columns containing the leading entries in each row. The pivot columns of an echelon form of matrix A will also be pivot columns of matrix A itself.

The column space of a matrix is the span of its column vectors. Since the pivot columns of B are a subset of the column vectors of A, they will also span the column space of A. Therefore, the pivot columns of B form a basis for the column space of A.

b. Row operations preserve the linear dependence relations among the rows of A.

This statement is true. When we perform row operations on a matrix, such as multiplying a row by a scalar, adding rows together, or swapping rows, the resulting matrix will have the same row space as the original matrix. This means that the linear dependence relations among the rows of the original matrix will be preserved in the transformed matrix.

c. The dimension of the null space of A is the number of columns of A that are not pivot columns.

This statement is false. The dimension of the null space of A, also known as the nullity of A, is the number of free variables in the reduced row echelon form of A. It is equal to the number of columns of A minus the number of pivot columns. Therefore, the dimension of the null space of A is the number of columns of A minus the number of pivot columns, rather than the other way around.

To summarize:
a. True. Pivot columns of an echelon form of A form a basis for the column space of A.
b. True. Row operations preserve linear dependence relations among the rows of A.
c. False. The dimension of the null space of A is the number of columns of A minus the number of pivot columns.

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Answer:

3x + 6y + 15z

Step-by-step explanation:

Use distributive property:

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

(3x) + (6y) + (15z)

3x + 6y + 15z

Hope this helped :)

Step-by-step explanation:

50

because 50*(30/100)=1500/100

then it gives 15

so the 30 percent of a number is 15 that number is 50.

The requried, 30 percent of 50 is 15, as of the given condition.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

We can use algebra to solve the problem.

Let's call the number we're looking for "x". Then we can translate the problem statement into an equation:

30% of x is 15:

0.3x = 15

To solve for x, we can divide both sides of the equation by 0.3:

x = 15 ÷ 0.3

x = 50

Therefore, 30 percent of 50 is 15.

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Initially, the tank contains 60 kg of salt, calculated by multiplying the salt concentration (0.06 kg/L) by the water volume (1000 L).

In the given scenario, the tank starts with a known salt concentration and water volume. By multiplying the concentration (0.06 kg/L) with the water volume (1000 L), we find that the initial amount of salt in the tank is 60 kg.

After 4.5 hours, considering the rate of water entering and leaving the tank, the net increase in solution volume is 810 L. Multiplying this by the initial concentration (0.06 kg/L), we determine that the amount of salt in the tank after 4.5 hours is 48.6 kg.

As time approaches infinity, with a constant inflow and outflow of solution, the concentration of salt in the tank stabilizes at the initial concentration of 0.06 kg/L.

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The series \(\sum n=17^{[\infty]} ln(n)/n^3\) is a convergent series.

To determine whether the improper integral

\(\int [\infty,17] ln(x)/x^3 dx\)

converges or diverges, we can use the Limit Comparison Test.

Let's compare it to the convergent p-series \(\int [\infty] 1/x^2 dx:\)

lim x→∞ ln(x)/\((x^3 * 1/x^2)\) = lim x→∞ ln(x)/x = 0

Since the limit is finite and positive, and the integral ∫[infinity] \(1/x^2\) dx converges, by the Limit Comparison Test, we can conclude that the integral \(\int [\infty,17] ln(x)/x^3 dx\) converges.

To find its value, we can integrate by parts:

Let u = ln(x) and dv = 1/x^3 dx, then du = 1/x dx and v = -1/(2x^2)

Using the formula for integration by parts, we get:

\(\int [\infty,17] ln(x)/x^3 dx = [-ln(x)/(2x^2)] [\infty,17] + ∫[\infty,17] 1/(x^2 \times 2x) dx\)

The first term evaluates to:

-lim x→∞ \(ln(x)/(2x^2) + ln(17)/(217^2) = 0 + ln(17)/(217^2)\)

The second term simplifies to:

\(\int [\infty,17] 1/(x^3 \times 2) dx = [-1/(4x^2)] [\infty,17] = 1/(4\times 17^2)\)

Adding the two terms, we get:

\(\int [\infty,17] ln(x)/x^3 dx = ln(17)/(217^2) + 1/(417^2)\)

\(\int [\infty,17] ln(x)/x^3 dx \approx 0.000198\)

Now, we can use the Integral Test to determine whether the series

\(\sum n=17^{[\infty]} ln(n)/n^3\)

converges or diverges.

Since the function\(f(x) = ln(x)/x^3\) is continuous, positive, and decreasing for x > 17, we can apply the Integral Test:

\(\int [n,\infty] ln(x)/x^3 dx ≤ \sum k=n^{[\infty]} ln(k)/k^3 ≤ ln(n)/n^3 + \int [n,\infty] ln(x)/x^3 dx\)

By the comparison we have just shown, the improper integral \(\int [\infty,17] ln(x)/x^3 dx\) converges.

Thus, by the Integral Test, the series also converges.

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Using the Integral Test, we can now determine whether the series ∑(from n=1 to infinity) (ln(n)/n^3) converges. Since the improper integral of the same function converges and the function is positive, continuous, and decreasing, the series also converges.

To determine whether the improper integral ∫[infinity]17ln(x)x3dx converges or diverges, we can use the integral test. Let's first find the antiderivative of ln(x):

∫ln(x)dx = xln(x) - x + C

Now, we can use integration by parts with u = ln(x) and dv = x^3dx:

∫ln(x)x^3dx = x^3ln(x) - ∫x^2dx
             = x^3ln(x) - (1/3)x^3 + C

Now, we can evaluate the improper integral:

∫[infinity]17ln(x)x^3dx = lim as b->infinity [∫b17ln(x)x^3dx]
                                 = lim as b->infinity [(b^3ln(b) - (1/3)b^3) - (17^3ln(17) - (1/3)17^3)]
                                 = infinity

Since the improper integral diverges, we can conclude that the series [infinity]∑n=17ln(n)n^3 also diverges by the integral test.

Therefore, the improper integral ∫[infinity]17ln(x)x^3dx diverges and the series [infinity]∑n=17ln(n)n^3 also diverges.

To determine whether the improper integral ∫(from 1 to infinity) (ln(x)/x^3) dx converges or diverges, we can use integration by parts. Let u = ln(x) and dv = 1/x^3 dx. Then, du = (1/x) dx and v = -1/(2x^2).

Now, integrate by parts:
∫(ln(x)/x^3) dx = uv - ∫(v*du)
= (-ln(x)/(2x^2)) - ∫(-1/(2x^3) dx)
= (-ln(x)/(2x^2)) + (1/(4x^2)) evaluated from 1 to infinity.

As x approaches infinity, both terms in the sum approach 0:
(-ln(x)/(2x^2)) -> 0 and (1/(4x^2)) -> 0.

Thus, the improper integral converges, and its value is:
((-ln(x)/(2x^2)) + (1/(4x^2))) evaluated from 1 to infinity
= (0 + 0) - ((-ln(1)/(2*1^2)) + (1/(4*1^2)))
= 1/4.

Using the Integral Test, we can now determine whether the series ∑(from n=1 to infinity) (ln(n)/n^3) converges. Since the improper integral of the same function converges and the function is positive, continuous, and decreasing, the series also converges.

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To maximize the likelihood function, we take the derivative with respect to θ and set it equal to zero: d/dθ[L(θ|X1,X2,...,Xn)]=−n/θ+(X1+X2+⋯+Xn)/θ2=0.

The MLE for θ in the exponential distribution is simply the sample mean of the observed data.

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson point process. X1,X2,...,XnX1,X2,...,Xn is a random sample of size n from this distribution, which means that each XiXi is an independent and identically distributed random variable with the same exponential distribution.

The probability density function (pdf) of the exponential distribution is given by f(x:θ)=(1/θ)e−x/θ, where θ is the scale parameter. This means that the probability of observing a value x from the distribution is proportional to e−x/θ, with the constant of proportionality being 1/θ.

To estimate the value of θ based on the observed data, we can use the method of maximum likelihood estimation (MLE). The likelihood function for the sample X1,X2,...,XnX1,X2,...,Xn is given by L(θ|X1,X2,...,Xn)=∏i=1n(1/θ)e−Xi/θ=(1/θ)n e−(X1+X2+⋯+Xn)/θ.

Solving for θ, we get θ=(X1+X2+⋯+Xn)/n, which is the sample mean.

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Answer:

An apportionment is the allocation of a loss between all of the insurance companies that insure a piece of property. This allocation is used to determine a percentage of liability for each insurer.

I'm new here! Sorry if this didn't help

Answer:

8

Step-by-step explanation:

12 ÷ 3 = 4

4 × 2 = 8

:) hope this helps

Answer:

The answer is is 8 inches.

Micro-organisms change large organic molecules to forms that can be absorbed and used inside the cell through the process of decomposition.

We have,

Different organic compounds decompose when plant residues are added back to the earth. Decomposition is a biological process in which complicated organic molecules found in dead matter are physically broken down and biochemically converted into less complex organic and inorganic molecules.

The biological activity and the process of cycling carbon in the soil are both aided by the ongoing increase of decomposing plant residues to the soil's surface. These processes are also aided by the decomposition of soil organic matter and the development and decay of roots. Carbon cycling is the ongoing transformation of organic and inorganic carbon compounds in the earth, plants, and the atmosphere by micro- and macro organisms.

The organic molecules in organic matter are broken down during decomposition into smaller organic molecules that need additional breakdown or into mineralized minerals. Different organic substances can be broken down by microorganisms in different ways. Amino acids and sugars are among the first organic substances to break down because they are simple to do so. Lignin, phenols, and waxes will last the longest in the earth, while cellulose will degrade more slowly.

In this question, the process that occurs when micro-organisms change large organic molecules to forms that can be absorbed and used inside the cell is decomposition.

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complete question:

How do micro-organisms change large

organic molecules to forms that can be

absorbed and used inside the cell

The system of equations is:

2b + 4.25s = 53.75

b - s = 5  

The number of bagels bought is 12 and the number of sandwiches bought is 7.

2b + 4.25s = 53.75 equation 1

b - s = 5  equation 2

Where:

The elimination method would be used to determine the required values.

Multiply equation 2 by 2

2b - 2s = 10 equation 3

Subtract equation 3 from equation 1 :

6.25s = 43.75

Divide both sides of the equation by 2.25

s = 43.75 / 6.25

s = 7

Substitute for s in equation 1:

2b + 4.25(7) = 53.75

2b + 29.75 = 53.75

2b = 53.75 - 29.75

2b = 24

b = 24 / 2

b = 12

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The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.9476

To determine the probability

The given parameters are:

True proportion and the mean (p) = 0.06

The samples size (n) = 235

Start by calculating the standard deviation using

\(\sigma = \sqrt{\frac{p(1-p)}{n} }\)

This gives

\(\sigma = \sqrt{\frac{0.06\;*\;(1-0.06)}{235} }\)

\(\sigma = \sqrt{\frac{0.06\;*\;(0.94)}{235} }\)

\(\sigma = \sqrt{\frac{0.0564}{235} }\)

\(\sigma = \sqrt{0.00024 }\)

\(\sigma = 0.01549\)

Next, we calculate the x values

\(x = x_{1} \pm x_{2}\)

where x₁ = 0.06 and x₂ = 0.03

x = x₁ + x₂ , x₁ - x₂

x = 0.06 + 0.03, 0.06 - 0.03

x = 0.09, 0.03

Calculate the z score for both x values

\(z = \frac{x\; - \; \mu}{\sigma}\)

\(z = \frac{0.09\; - \; 0.06}{0.01549}, \frac{0.03\; - \; 0.06}{0.01549}\)

\(z = \frac{0.03}{0.01549}, \frac{-0.03}{0.01549}\)

\(z = 1.94, -1.94\)

The p values at the z scores are:

p = 0.9738, 0.0262

Note: refer to z tables to find the p values

Calculate the difference

p = 0.9738 - 0.0262

p = 0.9476

Hence, the probability that the sample proportion will differ from the population proportion by less than 0.03 is 0.9476

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Answer:

4,324,386 students

Step-by-step explanation:

Student population in 2015 = 3,845,721

Percentage of students population in 2015 = 100%

Percentage increase of students each year = 1.18%

What will the student population of Algebra City be in the year 2025?

2025 population = 3,845,721(100% + 1.18%)^t

Where

t = number of years

= 2025 - 2015

= 10 years

2025 population = 3,845,721(100% + 1.18%)^t

= 3,845,721(1 + 0.118)^10

= 3,845,721(1.0118)^10

= 3,845,721(1.1244670934955)

= 4,324,386.7152646077555

Approximately,

= 4,324,386 students