Justin purchased his dream car worth 18500 on a finance for 4 years. He was offered 6% interest rate.assuming no other chargers and no tax,we want to find his monthly installment.

Justin Purchased His Dream Car Worth 18500 On A Finance For 4 Years. He Was Offered 6% Interest Rate.assuming

Answers

Answer 1

Answer:

To calculate Justin's monthly installment, we need to use the formula for calculating the monthly payment for a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where P is the monthly payment, r is the monthly interest rate, A is the loan amount, and n is the total number of payments (in months).

In this case, A = 18500, r = 0.06/12 = 0.005 (since the annual interest rate is 6%, we divide by 12 to get the monthly rate), and n = 4*12 = 48 (since the loan is for 4 years, or 48 months).

Plugging in these values, we get:

P = (0.005 * 18500) / (1 - (1 + 0.005)^(-48))

P ≈ $432.85

Therefore, Justin's monthly installment would be approximately $432.85


Related Questions

Y=3x-4 4x+3y=1 what does X and y equal?

Answers

Answer:

{y,x}={-1,1}

to leave and take

Will tracks the high and low tempters in his town for five days during a cold spell in January his results are shown in the table below

Answers

Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.

Define change in temperature

calculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.

Change in temperature on Monday from High to low

=15-10=5°F

Change in temperature on Tuesday from High to low

=8-(-4)=12°F

Change in temperature on Wednesday from High to low

=-2-(-5)=3°F

Change in temperature on Thursday from High to low

=-3-(-7)=4°F

Change in temperature on Friday from High to low

=-1-(-12)=11° F

Days when change in temperature more than 10° F are Tuesday and Friday.

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The Complete question is attached below:

what the answer of this

Answers

The correct option for this question is (d) "No, none of the sides are parallel."

why it is and what is a Quadrilateral?

To determine if quadrilateral CDEF is a trapezoid, we need to check if it has exactly one pair of parallel sides.

We can find the slopes of the line segments CD and EF as follows:

slope of CD = (5 - (-6)) / (-8 - (-1)) = 11 / (-7) = -1.57 (approx.)

slope of EF = (8 - 5) / (3 - 4) = 3 / (-1) = -3

Since the slopes are different, CD and EF are not parallel, and therefore, CDEF is not a trapezoid.

Alternatively, we can also find the slopes of the line segments CF and DE as follows:

slope of CF = (-5 - (-6)) / (4 - (-1)) = 1/5

slope of DE = (8 - 5) / (3 - (-8)) = 3/11

Since the slopes are different, CF and DE are not parallel, and therefore, CDEF is not a trapezoid.

Therefore, the answer is option (d) "No, none of the sides are parallel."

A quadrilateral is a geometric shape that has four straight sides and four vertices (corners). It is a two-dimensional polygon with four sides and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.

There are many types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.

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In a certain company, employees contribute to a welfare fund at the rate of 4% of the first $1000 earned, 3% of the next $1000, 2% of the next $1000 and 1% of any extra monies. How much will an employee who earned $20,000 contribute to the fund?​

Answers

The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.

An employee who earned $20,000 will contribute $260 to the welfare fund.

To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.

The first $1000 will have a contribution rate of 4%.

Contribution for the first $1000 = 4% of $1000 = $40.

The next $1000 will have a contribution rate of 3%.

Contribution for the next $1000 = 3% of $1000 = $30.

The next $1000 will have a contribution rate of 2%.

Contribution for the next $1000 = 2% of $1000 = $20.

The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.

Contribution for the remaining amount = 1% of $17,000 = $170.

Now, let's sum up the contributions for each tier:

$40 + $30 + $20 + $170 = $260.

Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.

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The mean time to admit an emergency patient to the Mount Nittany Medical Center is 5 minutes with a standard deviation of 3 minutes. Only trauma patients are admitted to this center. Also, assume that the admission process is in fact the radiography process via an X-Ray machine.
(a) What is the natural coefficient of variation for one patient?
C0 : ______________
(b) If the admission times of patients are independent, what will be the mean and variance of admitting a group of 50 emergency patients? What will be the coefficient of variation of a group of 50 emergency patients?
t0 : ______________ σ02 : ______________ C0 :______________
(c) The X-Ray machine in the center may fail at any time randomly. The time to failure is exponentially distributed with a mean of 80 hours and the repair time is also exponentially distributed with a mean of 4 hours. What will be the effective mean and coefficient of variation of the admission time for a group of 50 trauma patients?
te : ______________ σe 2 :____________ Ce :______________
(d) Determine the variability class of the squared-coefficients of variation in Parts a-c (e.g., low variability, moderate variability, or high variability.)
C0 2(Part a): ______________ C0 2(Part b): ______________ Ce 2(Part c): ______________
(e) In two sentences, describe how the manager of center can improve the inflated effective admission time in Part c?

Answers

(a) The natural coefficient of variation for one patient is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(b) If the admission times of patients are independent, the mean and variance of admitting a group of 50 emergency patients can be calculated as follows:

mean = n x mean time = 50 x 5 = 250 minutes

variance = n x variance of individual patient / sample size = 50 x (3)^2 / 50 = 9

The coefficient of variation for a group of 50 emergency patients is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(c) The effective mean and coefficient of variation of the admission time for a group of 50 trauma patients can be calculated using the following formula:

te = n x mean time / (1 - p1 x p2)

where p1 is the probability of machine failure and p2 is the probability of repair completion. Assuming the machine can fail at any time, p1 can be calculated as 1 / (mean time between failures / mean admission time) = 1 / (80 x 60 / 5) = 0.001042. Assuming the repair time is also exponentially distributed, p2 can be calculated as 1 / mean repair time = 1 / 4 = 0.25. Therefore, te = 50 x 5 / (1 - 0.001042 x 0.25) = 250.14 minutes. The variance of the admission time can be calculated using the formula:

σe^2 = n x variance of individual patient / (1 - p1 x p2)^2 = 50 x (3)^2 / (1 - 0.001042 x 0.25)^2 = 10.81. The coefficient of variation for a group of 50 trauma patients is the ratio of the standard deviation to the mean, expressed as a percentage:

Ce = (standard deviation / mean) x 100% = (sqrt(10.81) / 250.14) x 100% = 2.60%.

(d) The variability class of the squared coefficients of variation can be determined as follows:

C0² (Part a): (0.6)^2 = 0.36 (low variability)

C0² (Part b): (0.6)^2 = 0.36 (low variability)

Ce² (Part c): (0.026)^2 = 0.000676 (low variability)

(e) The manager of the center can improve the inflated effective admission time in Part c by implementing preventive maintenance measures to reduce the probability of machine failure, such as regular inspection and cleaning of the X-Ray machine, and by improving the repair process to reduce the mean repair time, such as hiring more skilled technicians or improving the repair procedures.

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What percent of 28 is 77?

Answers

Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Help. I dont understand this math question and need help please and thank you.

Answers

Answer:

●B. The numbers -1,0,1 are zeros of multiplicity 1.

Step-by-step explanation:

So first, understand that when you are asked for roots, zeros, solutions, or x-intercepts...all of these, they are essentially asking for the same thing. Roots ARE solutions ARE zeros ARE x-intercepts. Maybe its oversimplifying a little bit; there are tiny nuanced differences to a mathematician but if you are just learning this, go ahead and over simplify. They are all the same. So you set it equal to 0 and solve.

Yes, literally, change y to a 0 and solve. See image.

You can factor out a 2x and then you have a "difference of squares" so factor that too.

see image.

"multiplicity" is a cool word. It just means how many times a number is the answer. It sort of doesn't even apply here. 0, -1, and 1 are the answer just one time each...so multiplicity 1. Also, on the graph, the curve will cross the x-axis like a line, so there's that. (See multiplicity 2 is cooler, because the curve will "bounce" at the x-intercept instead, but that's not happening here)

Anyway, set the problem equal to 0 and solve. Ta-da! You're done! Hope this helps! See image.

Need help answering all 3 of these please anyone

Answers

a. The slope of AB is  [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. The mid-point of Diagonal AC is  [tex](0, -1/2)[/tex]

What are the Quadrilaterals?

A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.

a.

Slope is given by

[tex]A = (-2, 3) and B = (-5, 0)[/tex]

[tex]m = 1[/tex]

[tex]B = (-5, 0) and C = (2, -4)[/tex]

[tex]m = -4/7[/tex]

Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex]  .

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y

Thus, Diagonal  [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]

Midpoint  [tex]= ((-2 + 2), (3 + -4))[/tex]

[tex]= ((0), (-1))[/tex]

Now divide them by 2

[tex]= ((0/2), (-1/2))[/tex]

[tex]= (0, -1/2)[/tex]

Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]

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What was your recommended intake of carbohydrates (grams), and how far were you from it? Show the mathActual Intake Recommended Intake Percentage159.00 115-166 100%

Answers

The actual intake of carbohydrates is 138% as compare to recommended intake.

Recommended intake of carbohydrates or any other nutrient are,

Based on the information provided,

Consumed 159 grams of carbohydrates,

Recommended intake is between 115 and 166 grams.

Calculate the percentage of actual intake compared to the recommended intake, use the following formula,

Percentage = (Actual Intake / Recommended Intake) x 100%

Substituting the values in the formula we have,

⇒Percentage = (159 / 115) x 100%

⇒Percentage ≈ 138.3%

Therefore,  the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.

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What is the meaning of "Euclidean geometry"?

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The concept of Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different theorems and axioms.

What is the concept of Euclidean geometry?

The concept of Euclidean geometry as required to be discussed is basically introduced for flat surfaces or plane surfaces. The postulates of the Euclidean geometry are as follows!

1 : A straight line may be drawn from any one point to any other point.

2 :A terminated line can be produced indefinitely.

3 : A circle can be drawn with any centre and any radius.

4 : All right angles are equal to one another (Congruent).

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If F1 = 4y - 6, F2 = 9y + 3 and F3 = -y - 8, simplify F1 × F2 - F3 in terms of y.

Answers

Answer:

To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.

F1 × F2 can be expanded using the distributive property:

F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3

= 36y^2 + 12y - 54y - 18

= 36y^2 - 42y - 18

Now we can subtract F3 from the result:

F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)

= 36y^2 - 42y - 18 + y + 8

= 36y^2 - 41y - 10

Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.

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Question 11 (1 point)

(06.03 LC)


What is the product of the expression, 5x(x2)?


a

25x2


b

10x


c

5x3


d

5x2

Answers

The expressiοn 5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³). Thus, οptiοn (c) 5x3 is the cοrrect respοnse.

Hοw are prοducts οf expressiοn determined?

The cοefficients (the numbers in frοnt οf the variables) οf the expressiοn 5x(x²) can be multiplied, and the expοnents οf the variables can be added, tο determine the prοduct.

The first cοefficient we have is 5 times 1, giving us 5. Sο, using the secοnd x², we have x tο the pοwer οf 2 multiplied by x tο the pοwer οf 1 (frοm the first x). Expοnents are added when variables with the same base are multiplied. Sο, x¹ multiplied by x² results in x³.

Cοmbining all οf the parts, the phrase becοmes:

5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³).

Thus, οptiοn (c) 5x³ is the cοrrect respοnse.

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find two positive numbers that satisfy the given requirements. the sum of the first and twice the secind is 100 and the product is a maximum

Answers

Answer: The two positive numbers that satisfy the given requirements are 25 and 50.

Step-by-step explanation:

Let's call the two positive numbers x and y. We want to maximize their product while satisfying the condition that "the sum of the first and twice the second is 100", or mathematically:

x + 2y = 100

We can use algebra to solve for one of the variables in terms of the other:

x = 100 - 2y

Now we want to maximize the product xy:

xy = x(100 - 2y) = 100x - 2xy

Substituting x = 100 - 2y:

xy = (100 - 2y)y = 100y - 2y^2

To find the maximum value of this expression, we can take the derivative with respect to y and set it equal to zero:

d(xy)/dy = 100 - 4y = 0

Solving for y gives:

y = 25

Substituting y = 25 into the equation x + 2y = 100, we get:

x + 2(25) = 100

x = 50

Therefore, the two positive numbers that satisfy the given requirements are x = 50 and y = 25, and their product is:

xy = 50(25) = 1250

write a quadratic function in standard form that passes through the points (-8,0) ,(-5, -3) , and (-2,0) .
F(x)=

Answers

A quadratic function in standard form that passes through the points [tex](-8,0), (-5,-3), and (-2,0)[/tex] is equals to the [tex]f(x) = (1/3)( x^{2} + 10x + 16)[/tex].

What are some examples of quadratic functions?

f(x) = ax2 + bx + c, in which a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.

How do you determine whether an equation is quadratic?

In other terms, you have a quadratic equation if a times the squares of the expression after b plus b twice that same equation not square plus c equals 0.

[tex]f(x) = ax^{2} + bx + c ----(1)[/tex]

is determined by three points and must be [tex]a[/tex] not equal [tex]0[/tex]. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs [tex](-8,0), (-5,-3)[/tex], and [tex](-2,0)[/tex] and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point[tex]( -8,0), x = -8, y = f(x) = 0[/tex] in equation [tex](1)[/tex],

[tex]= > 0 = a(-8)^{2} + b(-8) + c[/tex]

[tex]= > 64a - 8b + c = 0 -------(2)[/tex]

Similarly, for second point [tex]( -5,-3) , f(x) = -3, x = -5[/tex]

[tex]= > - 3 = a(-5)^{2} + (-5)b + c[/tex]

[tex]= > 25a - 5b + c = -3 --(3)[/tex]

Continue for third point [tex](-2,0)[/tex]

[tex]= > 0 = a(-2)^{2} + b(-2) + c[/tex]

[tex]= > 4a -2b + c = 0 --(4)[/tex]

So, we have three equations and three values to determine.

Subtract equation [tex](4)[/tex] from [tex](2)[/tex]

[tex]= > 64 a - 8b + c - 4a + 2b -c = 0[/tex]

[tex]= > 60a - 6b = 0[/tex]

[tex]= > 10a - b = 0 --(5)[/tex]

subtract equation [tex](4)[/tex] from [tex](3)[/tex]

[tex]= > 21a - 3b = -3 --(6)[/tex]

from equation (4) and (5),

[tex]= > 3( 10a - b) - 21a + 3b = -(- 3)[/tex]

[tex]= > 30a - 3b - 21a + 3b = 3[/tex]

[tex]= > 9a = 3[/tex]

[tex]= > a = 1/3[/tex]

from [tex](5)[/tex] , [tex]b = 10a = 10/3[/tex]

from [tex](4)[/tex], [tex]c = 2b - 4a = 20/3 - 4/3 = 16/3[/tex]

So,[tex]f(x)= (1/3)( x^{2} + 10x + 16)[/tex]

Hence, required values are [tex]1/3, 10/3,[/tex] and [tex]16/3[/tex].

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Answer:

f(x) = (1/3)x² + (10/3)x + 16/3

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

Given 3 points of a quadratic function and two of them lie on the x-axis:

(-8, 0) and (-2, 0)

These two points are representing the roots of the function. With known roots we can show the function in the factor form:

f(x) = a(x - x₁)(x - x₂), where a - coefficient, x₁ and x₂ are roots

Substitute the roots into the equation and use the third point with coordinates x = - 5, f(x) = - 3, find the value of a:

-3 = a(- 5 + 8)((-5 + 2)- 3 = a(3)(-3)3a = 1a = 1/3

This gives us the function in the factor form:

f(x) = (1/3)(x + 8)(x + 2)

Convert this into standard form of f(x) = ax² + bx + c:

f(x) =  (1/3)(x + 8)(x + 2)f(x) =  (1/3)(x² + 10x + 16)f(x) = (1/3)x² + (10/3)x + 16/3

Venell put together a model train with 25 train cars. Each train car is 80 millimeters long. How many meters long is Venell's model train if there are no gaps between cars? (1 meter = 1,000 millimeters)

Answers

Answer: 2 meters

Step-by-step explanation:

The length of one train car is 80 millimeters. Therefore, the length of the entire train is:

25 cars × 80 mm per car = 2000 mm

To convert millimeters to meters, we need to divide by 1000:

2000 mm ÷ 1000 = 2 meters

Therefore, Venell's model train is 2 meters long.

P, Q, R, S, T and U are different digits.
PQR + STU = 407

Answers

Step-by-step explanation:

There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:

P = 2

Q = 5

R = 1

S = 8

T = 9

U = 9

With these values, we have:

PQR = 251

STU = 156

And the sum of PQR and STU is indeed 407.

7. Complete the comparison: 17>?
O A. 18
O B. 17
O C. 39
O D. 1
O Mark for review will be highligh

Answers

Answer: 39

39 is the only answer option greater than 17

graph each system of equations. solve each system and clearly mark the solutions on your graph. assume 0\le \theta \le 2\pi : r

Answers

The system of equation is now written as:

y = −2x−8

y = x+ 1

First, we will plotting two system of  equations on the same axis, and then we'll explore the different factors to consider when plotting two linear inequalities on the same axis. The technique for drawing a system of linear equations is the same as for drawing a single linear equation. We can draw two lines on the same axis system using an array of values, slope and y-intercept or x-y-intercept.

Now,

these using slope-intercept form on the same set of axes. Remember that slope-intercept form looks like

y = mx+ b,  so we will want to solve both equations for y.

First, solve for y in 2x+y=−8

2x+ y = −8

OR, y = −2x− 8

Second, solve for y in

x− y = −1

Or, y = x+1

The system is now written as

y = -2x - 8

y = x + 1

Now you can plot the two equations using their slope and intercept on the same set of axes as shown in the figure below. Note that these charts have one thing in common. It is their intersection, the point that lies on the two lines. In the next section we will verify that this point is the solution of the system.

Complete Question:

Graph each system of equations. Solve each system and clearly mark the solutions on your graph and consider the following system of linear equations in two variables.

                            2x+ y = −8 and x− y = −1

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Tell me which brand or which size is a better buy.

Answers

Answer:

The answer is brand B

Step-by-step explanation:

You divide $14.88 by 24 which equals 68 cents per item.

Then brand B is 60 cents per item which is the better buy!

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If the triangles above are reflections of each other, then BC ≅ to:
A) DE.
B) ED.
C) EF.
D) DF.
E) AC.

Answers

Answer:

D

Step-by-step explanation:

If their reflections are congruent to each other then looking at the diagram we can see a reflection just like a mirror where its flipped on the other side of the dotted line. When flipping it and aligning one triangle to the other we find that BC is congruent to DF

Use the diagram shown. Lines p and q are parallel.

How many degrees is the measure of ∠4?

Answers

Answer:

61°

Step-by-step explanation:

∠4 is the vertical angle to the 61° angle. This means they will have the same measure, so ∠4 is 61°.

in nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by

Answers

The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)

where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.

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Complete question:

In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by

A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'

B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---

C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°

D. ΔY = f(x₁ +Xq, X2, Xk).

What quadratic function is represented by the graph?

A. f(x) = −2x²+x+6
B. f(x) = 2x²x+6
C. f(x) = 2x²+x+6
D. f(x) = − 2x² - x - 6

Answers

Answer:

Answer: C. f(x) = 2x²+x+6

For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).

Answers

Answer:

Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...

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complete the table below. ​

Answers

4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569

Answer:

?

Step-by-step explanation:

Let f be the function given by f(x) = e-2x2.
a) Find the first four nonzero terms and the general termof the power series for f(x) about x = 0.
b) Find the interval of convergence of the power series forf(x) about x = 0. Show the analysis that leads to yourconclusion.
c) Let g be the function given by the sum of the first fournonzero terms of the power series for f(x) about x = 0. Show thatabsolute value(f(x) - g(x)) < 0.02 for -0.6<= x <=0.6.

Answers

a) The first four nonzero terms of the power series for f(x) about x=0 are

e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!

The general term of the power series is (-2)^n (2x)^(2n) / (2n)!

b) The interval of convergence of the power series is (-∞, ∞).

c) To estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series, we can use the Lagrange form of the remainder

|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!

a) To find the power series for f(x) about x = 0, we can use the Maclaurin series formula

f(x) = Σ[n=0 to ∞] (fⁿ(0)/n!) xⁿ

where fⁿ(0) denotes the nth derivative of f evaluated at x=0.

In this case, we have

f(x) = e^6(-2x^2)

fⁿ(x) = dⁿ/dxⁿ(e^6(-2x^2)) = (-2)^n(2x)^ne^6(-2x^2)

So, we can write the power series as

f(x) = Σ[n=0 to ∞] ((-2)^n(2x)^n e^6(0))/n!)

= Σ[n=0 to ∞] ((-2)^n (2x)^n /n!)

To find the first four nonzero terms, we substitute n = 0, 1, 2, and 3 into the above formula

f(0) = e^6

f'(0) = 0

f''(0) = 24

f'''(0) = 0

So, the first four nonzero terms of the power series are:

e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!

The general term of the power series is

(-2)^n (2x)^(2n) / (2n)!

b) To find the interval of convergence of the power series, we can use the ratio test

lim [n→∞] |((-2)^(n+1) (2x)^(2n+2) / (2n+2)! ) / ((-2)^n (2x)^(2n) / (2n)!)|

= lim [n→∞] |-4x^2/(2n+1)(2n+2)|

= lim [n→∞] 4x^2/(2n+1)(2n+2)

Since this limit depends on the value of x, we need to consider two cases

i) If x = 0, then the power series reduces to the constant term e^6, and the interval of convergence is just x=0.

ii) If x ≠ 0, then the series converges absolutely if and only if the limit is less than 1 in absolute value

|4x^2/(2n+1)(2n+2)| < 1

This is true for all values of x as long as n is sufficiently large. So, the interval of convergence is the entire real line (-∞, ∞).

c) We can use the Lagrange form of the remainder to estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series

|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!

where M is an upper bound for the fifth derivative of f(x) on the interval [-0.6, 0.6].

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Construct triangle PQR in which angle Q = 30 deg , angle R=60^ and PQ + QR + RP = 10cm​

Answers

We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm​, here is a guide:

Draw a line segment AB = 10 cm.Construct angle 30° at point A and angle 60° at point B.Draw angle bisectors to angles A and B.Make sure these angle bisectors intersect at point P.Draw perpendicular bisector to line segment AP.Let this bisector meet AB at Q.Then draw perpendicular bisector to line segment BP.Let this bisector meet AB at R.Join PQ and PR.PQR is the required triangle.

What is a triangle?

A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.

Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.

Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.

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On the day a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. Assume the
number of viewers continues to double each day.

1. On which day will 640 people see the video? Explain or show your reasoning.

2. What strategy would you use to find the first day when more than 20,000 people will see the video (if the trend continues)?

Answers

On the 7th day after the videο was pοsted, 640 peοple will see the videο.

What is Statistics?

Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data.

1 Let's start by finding the pattern in the number οf viewers. We knοw that οn the first day, 5 peοple watched the videο. On the next day, the number οf viewers dοubled tο 5 x 2 = 10. On the third day, the number οf viewers dοubled again tο 10 x 2 = 20. We can see that the number οf viewers is dοubling each day, which means we can write the number οf viewers as:

[tex]V = 5 x 2^n[/tex]

where n is the number οf days after the videο was pοsted.

Nοw we want tο find οn which day the number οf viewers will be 640. Sο we can set V equal tο 640 and sοlve fοr n:

[tex]640 = 5 x 2^n[/tex]

[tex]2^n = 128[/tex]

n = lοg2(128) = 7

2.   Tο find the first day when mοre than 20,000 peοple will see the videο, we can set V equal tο 20,000 and sοlve fοr n:

[tex]20,000 = 5 x 2^n[/tex]

2^n = 4,000

n = lοg2(4,000) ≈ 11.29

Since n represents the number οf days after the videο was pοsted, we can rοund up tο the next whοle number tο find the first day when mοre than 20,000 peοple will see the videο. Therefοre, οn the 12th day after the videο was pοsted, mοre than 20,000 peοple will see the videο if the trend cοntinues

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Pls help There is a 20% chance that a customer walking into a store will make a purchase. A computer was used to generate 5 sets of random numbers from 0 to 9, where the numbers 0 and 1 represent a customer who walks in and makes a purchase.
A two column table with title Customer Purchases is shown. The first column is labeled Trial and the second column is labeled Numbers Generated.

What is the experimental probability that at least one of the first three customers that walks into the store will make a purchase?

A) 60%

B) 13%

C) 40%

D) 22%

Answers

The experimental probability that at least one of the first three customers that walks into the store will make a purchase is 60%.

What is experimental probability?

It is determined by counting the number of times an event occurs in a given experiment and dividing the total number of trials by the number of successful outcomes.

The experimental probability that at least one of the first three customers that walks into the store will make a purchase is calculated by dividing the total number of customers who make a purchase by the total number of customers who enter the store.

In this case, there are 3 trials and 2 customers who make a purchase.

The experimental probability is 3 by 5 which is the total number of trials.

Thus, the experimental probability

=3/5

= 60%.

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Kingsley knows that 1inch is about 2.45 centimeters. He wants to write an equation he can use to convert any given length in inches (i) to centimeters (c)

How should Kingsley write his equation?

A.) c/i = 2.54
B.) c = 2.54i
C.) i = c/2.54

Answers

Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.

What is equation ?

An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.

Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.

Let's call the length in inches "i" and the length in centimeters "c".

We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:

1 inch = 2.45 centimeters

To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:

c = 2.45i

This is the equation Kingsley can use to convert any given length in inches to centimeters.

Alternatively, we can rearrange this equation to solve for i:

c = 2.45i

Divide both sides by 2.45:

c/2.45 = i

So the equation for converting from centimeters to inches is:

i = c/2.45

Therefore,  since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.

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