The table shows the number of students graduating from a university in selected years. Use a calculator to write a cubic model for the number of graduates in a given year since 1990. Then use the model to estimate the number of graduates in 2001.

P(x) ≈ 27.13x3 − 473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 5,565.
P(x) ≈ −473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 4,133.
P(x) ≈ 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 3,535.
P(x) ≈ −27.13x3 + 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 2,504.

The diagonal matrix D has the eigenvalues 7, 2, and 3 along the diagonal.

To diagonalize matrix A, we first need to find the eigenvalues and eigenvectors.

The eigenvalues can be found by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue.

For the given matrix A, the characteristic equation is:

[tex]\begin{vmatrix}4 - \lambda & 1 & 2 \1 & 4 - \lambda & 2 \1 & 1 & 5 - \lambda\end{vmatrix} = 0[/tex]

Expanding the determinant and solving for λ, we find the eigenvalues are λ = 7, 2, and 3.

Now, we find the corresponding eigenvectors by solving the equation Av = λv for each eigenvalue. For each eigenvalue, we can write the equation as (A - λI)v = 0 and solve for v.

For example, for λ = 7, we have:

[tex]\begin{bmatrix}-3 & 1 & 2 \1 & -3 & 2 \1 & 1 & -2\end{bmatrix}\begin{bmatrix}v_1 \v_2 \v_3\end{bmatrix} = \mathbf{0}[/tex]

where the matrix on the left is (A - 7I) and the vector on the right is v.

Solving for v, we find that the eigenvector corresponding to λ = 7 is v = (1, 1, -2).

The diagonal matrix D can be written as:

[tex]\begin{bmatrix}7 & 0 & 0 \0 & 2 & 0 \0 & 0 & 3\end{bmatrix}[/tex]

So, the diagonal matrix D has the eigenvalues 7, 2, and 3 along the diagonal.

The diagonalization of a matrix A is given by [tex]A = SD^{-1} S[/tex], where D is a diagonal matrix with the eigenvalues along the diagonal, and S is the matrix of eigenvectors with the columns being the corresponding eigenvectors. [tex]S^ {-1}[/tex] is the inverse of S.

Did you mean Diagonalize the matrix [tex]A = \left[\begin{array}{ccc}4&1&2\\1&4&2\\1&1&5\end{array}\right][/tex]  by finding the eigenvalues of A listed in increasing order, the corresponding eigenvectors, a diagonal matrix D, and a matrix S such that [tex]A = SD^{-1} S[/tex].

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The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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Answer:

(-7, 8)

Step-by-step explanation:

Hope it helps! =D

The equation of the tangent at (2,7) is y = 4x - 1.y = x^2 + 3; t = 2

Given: y = x^2 + 3 and t = 2

We need to find the equation of the tangent at (2,7).

First, we find the slope of the tangent line by taking the derivative of the function:

y' = 2x

At x = 2, the slope is 2*2 = 4.

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

y - 7 = 4(x - 2)

Simplifying:

y = 4x - 1

Therefore, the equation of the tangent at (2,7) is y = 4x - 1.

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The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

2x3 - 36x² + 162x

=2x *(x^2-18x+81)                                            Factor out- 2x    

= 2x [x²-2(9)x+ (9)²]                                  Rewrite the trinomial.

=2x*(x-9)(x-9)                                              

= 2x*(x-9) ²                                                      Simplify.

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if the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is observational.

Two variables are said to be causally related in statistics if the occurrence of one variable influences or modifies the other variable. In this case, one variable is the cause and the other is the effect.

An outcome of a study is measured by a response variable. A response variable changes are explained by or affected by an explanatory variable. You will often find explanatory variables called independent variables and response variables called dependent variables.

So, we cannot conclude that the explanatory variable causes changes in the response variable when the study is observational.

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The solution to the given fraction 2 3/8 x 5 3/4 is 13 21/32

A fraction is a number which has a numerator and a denominator. A numerator is the top or upper value while a denominator is the bottom or lower value.

2 3/8 x 5 3/4

= 19/8 × 23/4

Multiply numerator and denominator respectively

= (19 × 23) / (8 × 4)

= 437 / 32

= 13 21/32

Therefore, 13 21/32 is the solution to the fraction.

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[tex]\cfrac{3}{8}+\cfrac{4}{5}\implies \cfrac{(5)3~~ + ~~(8)4}{\underset{\textit{using this LCD}}{40}}\implies \cfrac{15+32}{40}\implies \cfrac{47}{40}\implies 1\frac{7}{40}[/tex]

Answer:

47/40

Step-by-step explanation:

[tex](\frac{3}{8}\cdot\frac{5}{5})+(\frac{4}{5}\cdot\frac{8}{8})=\frac{15}{40}+\frac{32}{40}=\frac{47}{40}[/tex]

Option A and C, To draw accurate conclusions about change in an experiment, both experimental control and causation are required.

Experimental control means that the experiment is designed and conducted in a way that allows for a clear determination of the effect of the independent variable on the dependent variable, by controlling for extraneous variables and minimizing the effects of confounding variables.

Causation means that a relationship exists between the independent variable and the dependent variable, such that a change in the independent variable directly and consistently results in a change in the dependent variable.

Correlation refers to the statistical relationship between two variables, but does not necessarily imply causation. A single case study provides information about a specific individual or situation, but may not be generalizable to a larger population.

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To draw accurate conclusions about change in an experiment, which of the following is required?

a. experimental control

b. correlation

c. causation

d. single case study

The number of tornadoes in December and in May are : 22 and 341

Let x be the typical number of tornadoes in December.

The typical number of tornados in May is 11 + 14x.

The sum of the typical number of tornados in December and in May is x + (11 + 14x) = 341.

Combining like terms, we get 15x + 11 = 341.

Subtracting 11 from both sides, we get 15x = 330.

Dividing both sides by 15, we get x = 22.

So the typical number of tornados in December is 22, and the typical number of tornadoes in May is 11 + 14x = 11 + 14 * 22 = 341.

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The first four value of this set of 2s will be 2, 4, 6 and 8.

The set of numbers we use to learn how to count are called counting numbers. They are also known as natural numbers, maybe because they are the first numbers we naturally learn and hence feel natural to us. They are also sometimes referred to as positive integers.

Numbers that we can use to count things are called counting numbers, for example 1, 2, 3, and so on. They are also called natural numbers.

In this case, we are couting on 2s. The first four numbers will be:

= 2 × 1 = 2

= 2 × 2 = 4

= 2 × 3 = 6

= 2 × 4 = 8

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This triangle is similar by the rule of (d)SAS.

When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.

We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.

In this given diagram, there are two triangle ΔRST and ΔRUV

where, RS/SU = RT/RV

and ∠SRT = ∠URV

So ΔRST ~ ΔRUV by the rule of SAS

So that option (d) is correct answer.

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The situation that could not be represented by the algebraic expression b + 5 is given as follows:

If there are b ounces of water in a bottle, b + 5 could represent the amount of water after you drink 5 bottles.

The algebraic expression for this problem is defined as follows:

b + 5.

Meaning that an unknown amount b is increased by a value of 5.

For the answer of this problem, the correct expression would be of b - 5 instead of b + 5, hence it is the option that could not be represented by the algebraic expression b + 5.

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The slope intercept form of the inequality is y ≤ -3x - 6.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope intercept form of a linear equation is of the form y = mx + c.

m : slope and c : y intercept

In the case of inequalities, symbol change from equality sign to inequality sign.

Given linear inequality is,

y - 6 ≤ -3(x + 4)

y - 6 ≤ -3x - 12

y ≤ -3x - 12 + 6

y ≤ -3x - 6

Hence the slope intercept form of the inequality is y ≤ -3x - 6.

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The algorithm to calculate the sum of 9 and 4. is:

From the question, we have the following parameters that can be used in our computation:

algorithm to calculate the sum of 9 and 4

This implies that we write the steps to calculate the sum of 9 and 4

So, the steps are

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Answer:

x=3 and y=-¼

Step-by-step explanation:

3x + 4y=8-(x-4y=4)

4x and 4x out then left 4x=12 By simplified and x = 3

Answer:

Step-by-step explanation:

Error in the division of points is the error in this outline. Thus option (E) is correct. Each heading's first word needs to be capitalized. Any proper nouns contained within each header must be capitalized. period.

What is a division

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

In order to emphasize related ideas in a sentence, parallelism is the use of comparable words, clauses, phrases, sentence structure, or other grammatical characteristics. It makes the statement succinct, understandable, and simple to read. Particularly in series, pairs, and items in an outline or list, parallel structuring is crucial.

Therefore, Thus option (E) is correct.

B) About 90% of the confidence intervals will contain μ

The 90% confidence interval is a range of values that is constructed from a sample of data that has a 90% probability of containing the true population mean, μ. To calculate the 90% confidence interval from a sample, we use the formula:

[tex]CI = X ± z* (σ/√n)[/tex]

Where X is the sample mean, z is the z-score corresponding to a 90% confidence level, σ is the population standard deviation, and n is the sample size.

In this case, 110 students each selected a sample of 35 quiz scores from a population of 5000. So the sample size is n = 35. Assuming the population standard deviation is known, then we can use the formula to calculate the 90% confidence interval for each student. We expect that around 90% of the confidence intervals will contain μ, the true population mean.

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Note that the solution of the given inequalities [4x+2y ≤ 16 and x+y>4.] is (4, 0).

Inequalities are mathematical expressions in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is substituted by a less than (or less than or equal to), larger than (or greater than or equal to), or not equal to sign.

Part A: The solution of the inequalities is (4, 0)

Part B: In figure attached, we can see that the point (2, 3) included in the solution area for the system.

Therefore, the solution of the given inequalities is (4, 0).

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Answer: 1/6

Step-by-step explanation: there are 6 sides, so we know the answer will be something/6. There is only one 5 on this 6-sided cube which is why the probability of rolling it would be 1/6

Answer:

52$

Step-by-step explanation:

Well, because we know our price was originally 80 dollars and maya bought it 65% off, we know that our answer is 65% of 80. 65% can be rewritten as .65, and we can now write our new equation as 80 x .65 = Mayas new price. Using a calculator we can find out that the answer is 52$

The marginal cost of producing x units is equal to 300 multiplied by the sum of 6 and 4x dollars per unit.

The marginal cost for producing x units is calculated by taking the derivative of the cost equation with respect to x. The cost equation is C = 300(6 + 4x). Differentiating with respect to x, the marginal cost is found to be the derivative of the cost equation, which is equal to 300 multiplied by the derivative of the equation, 6 + 4x. The derivative of 6 + 4x is 4, so the marginal cost is 300 multiplied by 4, or 1200 dollars per unit. Therefore, the marginal cost for producing x units is 1200 dollars per unit.

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we need to use the concept of the right triangle formed by the angle and the point in the coordinate plane.

Let's call the angle in standard position θ. The point (-1, 5) lies on the terminal side of θ. We can use the Pythagorean Theorem to find the length of the adjacent side (x) and the opposite side (y) of the right triangle formed by θ and the point.

x = √((-1)^2 + 5^2) = √(1 + 25) = √26

y = 5

The values of the six trigonometric functions of θ can then be found as follows:

sin(θ) = y/r = 5/√26

cos(θ) = x/r = -1/√26

tan(θ) = y/x = 5/(-1) = -5

csc(θ) = 1/sin(θ) = √26/5

sec(θ) = 1/cos(θ) = -√26

cot(θ) = 1/tan(θ) = -1/5

where r is the distance from the origin to the point, which can be found using the distance formula:

r = √((-1)^2 + 5^2) = √26

So the values of the six trigonometric functions of the angle in standard position with a point of (-1, 5) on its terminal side are: sin(θ) = 5/√26, cos(θ) = -1/√26, tan(θ) = -5, csc(θ) = √26/5, sec(θ) = -√26, and cot(θ) = -1/5.

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Answer:

Step-by-step explanation:

Perimeter:

2(9x) + 2(2x + 7)

18x + 4x + 14 = 22x + 14

Area:

9x(2x + 7)

18x^2 + 63x

9x(2x + 7)

Using compound interest, The future value of this investment at the end of year 1 is $16321.6.

Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.

Every six months, or every semi-annually, the compound interest is added up.

Thus,

Rate = 4% / 2 = 2% =0.02

P = $16,000

n = 2

The compound interest is given by:

[tex]A = P (1 + \frac{r}{n})^n[/tex]

[tex]A = 16000(1 + \frac{0.02}{2})^2[/tex]

A = 16321.6

Hence, the future value of this investment at the end of year 1 is $16321.6.

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For the given transactions, the general journal, T accounts, and trial balance is attached.

In the given case, it is required to record all transactions using the general journal, post them into corresponding T accounts. After posting all transactions, ending balances are calculated. The ending balances are used to create a Trial Balance.

The general journal is a book of original entries where the raw business transactions is recorded according to the date events occur. It is the first place where data is recorded . The general journal for the provided data is attached (figure 1).

Each transaction from the journal to corresponding T-accounts and their ending balances are calculated by subtracting credits from debits for accounts with debit balance and subtracting debits from credits for account with credit balance. A T-account is an informal term which is used for a set of financial records that use double-entry bookkeeping.  It is a graphical representation of a general ledger where business’ transactions are recorded. It consists of the an account title at the top, a debit side on the left, and a credit side on the right. It is called a T-account because the bookkeeping entries are laid out in a way that resembles a T-shape. The T-account for the given data is attached (figure 2 and 3).

Trial balance is prepared by entering corresponding ending balances from T accounts and calculating the sums of debit and credit. A trial balance refers to a bookkeeping worksheet where the balances of all ledgers are compiled into debit and credit account column totals that are equal. The general purpose is to ensure that the entries in a company’s bookkeeping system are mathematically correct. The trial balance for the given data is attached (figure 4).

Note: The question is incomplete. The complete question probably is: Boilermaker House Painting Company incurs the following transactions for September. Record each transaction. Boilermaker uses the following accounts: Cash, Accounts Receivable, Supplies, Equipment, Accounts Payable, Deferred Revenue, Common Stock, Retained Earnings, Service Revenue, Salaries Expense, Advertising Expense, and Rent Expense. 2. Post each transaction to T-accounts and compute the ending balance of each account. 3. After calculating the ending balance of each account, prepare a trial balance.

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Answer:

-8.58

Step-by-step explanation:

-3.28+4.4-9.7=-8.58

The chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom, which allows for more independent observations and more reliable results.

The degrees of freedom for a chi-square test for equality of proportions are calculated using the following formula: df = (r-1)(c-1). In this formula, r represents the number of populations and c represents the number of categories. In the case of 6 populations, the degrees of freedom would be calculated as df = (6-1)(1-1) = 5. This means that the chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom. This is necessary because the chi-square test measures the difference between the expected and observed frequencies of a given variable, and degrees of freedom are used to determine the number of independent observations that can be made. The higher the number of degrees of freedom, the more independent observations that can be made, and thus the more reliable the results of the chi-square test are.

Therefore, the chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom, which allows for more independent observations and more reliable results.

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The points of the plane do not correspond to a function because they do not have any constant relationship between them.

A function is a mathematical term that refers to a quantity being a function of another if the value of the first depends on the value of the second. For example, the area A of a circle is a function of its radius r.

According to the above, if the points of the plane were a function, they would all have a location relationship, for example, they would mark a constant line or a parabola.

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Answer:
The correct answer option is $195

Step-by-step explanation:

2000 * 13% / 9 months * 9 months

2000 * 0.13 / 9 * 9 = 2000 * 0.014444 * 9 = 195