Construct a residual plot of the amount of money in a person’s bank account and their age that would indicate a linear model

The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).

       Now, we are required to find a member of the family that is a solution to the initial-value problem which is

                             y(0) = 0 and y′(0) = 5.

     The differential equation is y'' − y = 0

      The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1

     The general solution of the differential equation is y = c1ex + c2e−x

      Let us solve for the constants by using the given initial conditions:

                    At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0

                    means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2

                    Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2

                The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.

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On solving the question we can say that Therefore, the solutions to the inequality given inequality are: x < 4 or x > 6.

An inequality in mathematics is a relationship between two expressions or values ​​that are not equal. Imbalance therefore leads to inequality. An inequality establishes a connection between two values ​​that are not equal in mathematics. Equality is different from inequality. The inequality sign () is most commonly used when two values ​​are not equal. Various inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be solved by changing both sides until only variables remain. But many things contribute to inequality.

two inequalities

4x - 6 < 10

4x < 16

x < 4

2x - 4 > 8

2x > 12

x > 6

Therefore, the solutions to the given inequality are:

x < 4 or x > 6.

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Answer: Quadratic polynomial.

Step-by-step explanation: Polynomials with 2 as the degree.

Answer:

B. Isosceles right triangle

C. Quadrilateral

D. Parallelogram

Step-by-step explanation:

Answer:

The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.

Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.

To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.

The purchase price for 1,000 shares of stock was:

$35.50 x 1,000 = $35,500

The selling price for 1,000 shares of stock was:

$55.10 x 1,000 = $55,100

The capital gain is the difference between the selling price and the purchase price:

$55,100 - $35,500 = $19,600

To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:

($19,600 / $35,500) x 100 = 55.21%

In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.

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Answer:

Step-by-step explanation:

Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:

999n = 727272

To solve for "n", we divide both sides by 999:

n = 727272/999

Using a calculator or long division, we get:

n ≈ 728.56

Therefore, each pizza has approximately 728 slices.

An appropriate theorem to show that the given set, W, is a vector space. A specific example can be

[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s  and 3p = -2s - 3r

Sets represent values ​​that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.

The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.

The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.

The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.

Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is

S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties

u +v =y+ u and (u + v)+w=u + (v +W).

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The subsets B. The 3×3 matrices with all zeros in the third row. C. The diagonal 3×3 matrices, and F. The symmetric 3×3 matrices are subspaces of M3(R).

A subspace of a vector space is a portion of that space that meets the three criteria of closure under addition, closure under scalar multiplication, and the presence of the zero vector. If two vectors from the subspace are added, the resultant vector will still be in the subspace because of closure under addition. If a vector from the subspace is multiplied by any scalar, the resultant vector will still be in the subspace, according to the concept of closure under scalar multiplication.

The conditions of a subspace are: closure under addition, closure under scalar multiplication, and contains the zero vector.

For all the options we have:

A: The 3 x 3 matrices in reduced row-echelon form (A): As this subset is not closed under addition, M3(R), it is not a subspace of M3(R).

B. The 3 x 3 matrices with all zeros in the third row: Due to its closure under addition and scalar multiplication as well as the presence of the zero vector, this subset is a subspace of M3(R).

C. The diagonal 3 x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).

D. The invertible 33 matrices: Because this subset is not closed under addition, M3(R), it is not a subspace of M3(R).

E. The 3 x 3 matrices that are not invertible Due to the fact that it is not closed under scalar multiplication, this subset is not a subspace of M3(R).

F. The symmetric 3x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).

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Answer:

143°

When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.

Answer:

b ≈ 12.1

Step-by-step explanation:

using the tangent ratio in the right triangle

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )

7 × tan60° = b , then

b ≈ 12.1 ( to the nearest tenth )

Answer:

B

Step-by-step explanation

The height of the triangle is 1.12 units (rounded to two decimal places).

The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex. In other words, it is the length of the line segment that is perpendicular to the base and passes through the opposite vertex.

We can use the formula for the area of a triangle:

Area = (1/2) * base * height

And since we know the values of the base (b) and the area (a), we can rearrange the formula to solve for the height (h):

h = (2a) / b

Plugging in the values of a and b:

h = (2 * 14) / 25

h = 28 / 25

Therefore, the height of the triangle is 1.12 units (rounded to two decimal places).

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The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.

We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.

We need to find the probability that a randomly selected component is shorter than 7 inches long.

We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:

z = (7 - 8) / 1.5 = -0.67

Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:

P(z < -0.67) = 0.2514

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: In the problem, they tell us that

dL / dt = 7 cm/s (the rate at which the length is changing) and

dw / dt = 8 cm/s (the rate at which the width is changing)

Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm

The equation for the area of a rectangle is:

A = L·w, so will need the product rule when taking the derivative.

dA/dt = L (dw/dt) + w (dL/dt)

Now just plug in all of the given numbers:

dA/dt = (7)(7) + (5)(8) = 49+40 = 89  cm²/s

The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.

Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.

Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.

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If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%

To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.

Let the cost price of each article be "C" and the selling price of each article be "S".

Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:

20C = 16S

We can simplify this equation to:

S = (20/16)C = (5/4)C

Now, let's calculate the profit earned on the sale of 16 articles:

Profit = Total Selling Price - Total Cost Price

Profit = 16S - 20C

Profit = 16(5/4)C - 20C

Profit = 5C/2

The profit earned is 5C/2. The profit percent can be calculated as:

Profit Percent = (Profit / Cost Price) x 100

Profit Percent = (5C/2) / (20C) x 100

Profit Percent = 25%

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Answer:

x/8 + 6 = 4

Step-by-step explanation:

x / 8 + 6 = 4

x/8 = -2

x = 8*-2 = -16.

The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Hence, The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.

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Answer:

27.18

Step-by-step explanation:

Firstly, you must label the triangle.

r- opposite

13.85- adjacent

We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.

tan (63) = r/13.85

Then, times 13.85 on both sides so we only have our unknown on one side.

(x13.85)  tan(63)= r/13.85   (x13.85)

r= tan (63) x 13.85

r=27.18

:)

Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.

The time taken by Meredith to file 70% of the 10 reports given, given that each report takes an average of 75 minutes is 6 hours, 30 minutes. Therefore, the correct option is B. 6 hours, 30 minutes. How long will it take Meredith to file 70% of 10 reports, given that each report takes an average of 75 minutes to file?

Here, the total number of reports = 10

Average time to file one report = 75 minutes

To find out the time taken to file 70% of 10 reports, we will need to multiply the average time taken to file one report by the number of reports to be filed, which is 7 in this case:

75 × 7 = 525 minutes

We have calculated the time it will take Meredith to file 7 reports. Now, to convert this time to hours and minutes, we divide the total minutes by 60 to get the hours and then find out the remainder for the minutes:

525 ÷ 60 = 8 hours 45 minutes

Therefore, Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.

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Answer:

you need to show the numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Calculate fraction of boys

If girls =3/5, then boys = 1 - 3/5 = 2/5.

Calculate fraction of students absent

Girls - 2/5 of 3/5 = 6/25

Boys - 1/3 of 2/5 = 2/15

6/25+2/15=28/75

Calculate total number of students

If 28/75 = 280

280/28=10

10x75=750

Total number of students = 750

Answer:

To factor 30b³-54b², we can factor out the greatest common factor of 6b² to get:

30b³-54b² = 6b²(5b-9)

To factor 35-48y³, we can notice that it is a difference of cubes:

35-48y³ = (5)³ - (4y)³ = (5-4y)(25+20y+16y²)

To factor x³+8, we can use the sum of cubes formula:

x³+8 = (x+2)(x²-2x+4)

To factor 3-64, we can use the difference of squares formula:

3-64 = (1)² - (8)² = (1+8)(1-8) = -7(-9) = 63

To factor 8c³+343, we can use the sum of cubes formula:

8c³+343 = (2c)^3 + 7³ = (2c+7)(4c²-14c+49)

To add or subtract complex polynomials, we simply combine like terms. For example:

(3x²+2x-5) + (4x²-3x+7) = 7x²-x+2

To multiply complex polynomials, we can use the distributive property and FOIL method. For example:

(2x+1)(3x-4) = 6x²-5x-4

To factor complex polynomials, we can use various methods such as factoring out the greatest common factor, using the difference of squares formula, using the sum or difference of cubes formula, or factoring by grouping.

The formulas provided are for factoring the sum or difference of cubes:

These formulas can be useful for factoring complex polynomials that have a cube term or a constant term in addition to the quadratic and linear terms.

The complete table for the amount balance, A when P dollars is invested at rate r for t years and compounded n times per year is present in above figure 2.

The compound interest formula is written as A = P( 1 + r/n)ⁿᵗ

where, A--> total Amount of money after t years

P --> Principal

r --> Annual rate of interest (as a decimal)

t --> Number of years:

n--> number of times interest is compounded per year

Here, principle, P = $1300, rate of interest, r = 8.5% = 0.085 , time periods, t = 11 years. We have to complete the above table for compound interest.

Case 1: n = 1

Substitute the known values in above formula, A = 1300( 1 + 0.085/1)¹¹

= 1300( 1.085)¹¹

= 3,189.12

Case 2: n = 2

A = 1300( 1 + 0.085/2)²²

= 1300( 2.085/2)²²

= 1300( 1.0425)²²

= 3,248.01

I'll let you work out the cases where n = 4, 12 and 365 since all you need to do is place those in for n as done in the 1st 2 cases. For the Compounded continuously case, the formula becomes,

[tex] A = Pe^{rt}[/tex]

Where: A-> Total amount of money after t years

P --> Principal Amount

e --> Natural log constant:

r = Annual rate of interest (as a decimal)

Case: Continuous: e = 2.71828 (approx), r = 0.085

A = 1300( 2.71828)⁰·⁰⁸⁵⁽¹¹⁾

= 1300(e)⁰·⁹³⁵ = 3,311.34

Hence, required value is $3,311.3775.

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Complete question :

The above table completes the question.

Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. ) P = $1300, r = 8. 5%, t

= 11 years

The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].

Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.

Using the appropriate notation, the hypotheses can be expressed as:

$H_0: p = 0.08$

$H_a: p < 0.08$

Therefore, the appropriate set of hypotheses for the mayor's significance test are:

[tex]$$H_0: p = 0.08$$[/tex]

[tex]$$H_a: p < 0.08$$[/tex]

Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate

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Hence, the abbreviated formula is -7 + 0i, or just -7.

The terms in the parentheses can be immediately simplified. So, we can carry out the operations indicated by the brackets in the following order: multiplication, addition, subtraction, division. Note: The brackets should be shortened in the following order: (),, []. Simplify: 14 + (8 - 2 3) for Example 2.

We must combine like terms in order to make the phrase simpler.

First, we can individually merge the real and made-up parts:

The genuine parts add out to -3 - 4 = -7.

i - i = 0 is the imaginary part's total.

Hence, the abbreviated formula is -7 + 0i, or just -7.

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Complete question:

Please simplify the following expression while performing the given operation. (-3+i)+(-4-i)

Answer: View answer in explanation below.

Step-by-step explanation: Let's use variables to represent the unknown quantities.

Let x be the number of $5 clearance mystery books purchased.

Let y be the number of $12 regular-priced science fiction books purchased.

We can set up a system of equations based on the given information:

5x + 12y = 126 (total amount spent)

x + y = total number of books purchased

We need to solve for x and y.

Let's use the second equation to solve for one variable in terms of the other:

y = total number of books purchased - x

Now we can substitute this expression for y into the first equation:

5x + 12(total number of books purchased - x) = 126

Simplifying and solving for x:

5x + 12total number of books purchased - 12x = 126

-7x + 12total number of books purchased = 126

-7x = -12total number of books purchased + 126

x = (12total number of books purchased - 126)/7

Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:

If total number of books purchased is 10:

x = (12(10) - 126)/7 = -6/7 (not a whole number)

If total number of books purchased is 11:

x = (12(11) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 12:

x = (12(12) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 13:

x = (12(13) - 126)/7 = 12/7 (not a whole number)

If total number of books purchased is 14:

x = (12(14) - 126)/7 = 18/7 (not a whole number)

If total number of books purchased is 15:

x = (12(15) - 126)/7 = 24/7 (not a whole number)

If total number of books purchased is 16:

x = (12(16) - 126)/7 = 30/7 (not a whole number)

If total number of books purchased is 17:

x = (12(17) - 126)/7 = 36/7 (not a whole number)

If total number of books purchased is 18:

x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)

So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.

16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.

The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.

16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.

Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:

x + 2y = 14

2y = -x + 14

y = (-1/2)x + 7

The slοpe οf the line is -1/2.

Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.

Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:

y - y1 = m(x - x1)

where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.

y - 5 = (-1/2)(x - (-6))

y - 5 = (-1/2)x - 3

y = (-1/2)x + 2

17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)

perpendicular equations slope would be negative reciprocal to the current line.

The slope in y = -(2/3)x + 4, is m = -(2/3),

The negative reciprocal of -(2/3) is 3/2

Now, applying the x and y values in pοint-slοpe fοrm

y - 6 = 3/2(x - (-4))

y =  3/2(x+4) + 6

y =  (3/2)x + 6 + 6

y =  (3/2)x + 12

18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.

Lets find the slope using slope formula

[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]

[tex]\rm m = \dfrac{1}{3}[/tex]

Now, using the point slope form

y - 1 = 1/3(x - 3)

y = 1/3(x - 3) + 1

y = (1/3)x - 1 + 1

y = (1/3)x

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