The value of a certain photocopying machine t years after it was purchased is defined by P(t) = le-0.25 where is its purchase value. What is the value of the machine 6 years ago if it was purchased 35"

Answers

Answer 1

The value of a photocopying machine t years after its purchase is given by the function P(t) = l * e^(-0.25t), where "l" represents the purchase value. To determine the value of the machine 6 years ago, we need to substitute t = -6 into the function using the given purchase value of 35".

By substituting t = -6 into the function P(t) = l * e^(-0.25t), we can calculate the value of the machine 6 years ago. Plugging in the values, we have:

P(-6) = l * e^(-0.25 * -6)

Since e^(-0.25 * -6) is equivalent to e^(1.5) or approximately 4.4817, the expression simplifies to:

P(-6) = l * 4.4817

However, we are also given that the purchase value, represented by "l," is 35". Therefore, we can substitute this value into the equation:

P(-6) = 35 * 4.4817

Calculating this expression, we find:

P(-6) ≈ 156.8585

Hence, the value of the photocopying machine 6 years ago, if it was purchased for 35", would be approximately 156.8585".

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Answer 2

The value of a photocopying machine t years after it was purchased is given by the function \(P(t) = l e^{-0.25t}\), where l represents its purchase value.

The given function  \(P(t) = l e^{-0.25t}\) represents the value of the photocopying machine at time t, measured in years, after its purchase. The parameter l represents the purchase value of the machine. To find the value of the machine 6 years ago, we need to evaluate P(-6).

Substituting t = -6 into the function, we have \(P(-6) = l e^{-0.25(-6)}\). Simplifying the exponent, we get \(P(-6) = l e^{1.5}\).

The value \(e^{1.5}\) can be approximated as 4.4817 (rounded to four decimal places). Therefore, P(-6) ≈ l × 4.4817.

Since the purchase value of the machine is given as 35", we can find the value of the machine 6 years ago by multiplying 35" by 4.4817, resulting in approximately 156.8585" (rounded to four decimal places).

Hence, the value of the machine 6 years ago, based on the given information, is approximately 156.8585".

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Related Questions

What is 300 - 25 divided by 3 subtracted by 200 plus 1000 minus 350 is

Answers

Answer:

741.(6)

Step-by-step explanation:

300 - 25 divided by 3 subtracted by 200 plus 1000 minus 350:

300 - 25/3 - 200 + 1000 - 350 = 300 - 8.(3) - 200 + 1000 - 350 = 741.(6)

Step-by-step explanation:

300-25/3-200+1000-350300-8.33-200+1000-350300+1000-8.33-200-3501300-558.33741.67

Howard bought 3/5 pound of granola. He divided the
granola evenly among 4 friends. How much granola did
each friend get?

Answers

Answer:

Step-by-step explanation:

So because Howard wants to divide the granola evenly among all of his friends, we have to divide the amount of pounds he has by the number of friends he has.

(3/5) / 4

Dividing by four is the same as multiplying by the reciprocal of 4 which is 1/4.

So (3/5) * (1/4) is 3/20 which is .15 pounds

Engineers and architects often use transformed shapes to design objects or structures. Analyze a building or structure around you, and describe the transformations that you see using geometric vocabulary. How does the transformed shape contribute to the design of the object?

Answers

Transformed shapes contribute to the design of objects by making them more efficient to get the most out of their characteristics.

What is architecture?

Architecture is a term to refer to the technique of projecting, designing and building, modifying the human habitat based on the proper use and function of spaces.

Engineering is a term for the use of scientific principles to design and create machines, structures, and other objects.

These two disciplines use modified shapes to design and build objects and structures, that is, they take geometric shapes and make modifications to them to get the most out of an element as needed.

For example, engineers and architects who design and build a house must modify the geometric figures of the square, rectangle and triangle to make their spaces with:

Appropriate amplitude, The most efficient lighting and Their roof is inclined so that on days of rain the water rolls to the sides of the house.

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Alan has a guessing game on his computer.

He estimates that the probability of winning each game is 0.35
Alan decides to play 20 of these games.
How many of these games should he expect to win?

Answers

Answer:7

Step-by-step explanation:

100/20 = 5

35/5 = 7

Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.
y = (smaller slope)

y = (larger slope)

Answers

Answer:

y = -x - 1 ;  y = 11x - 25

Step-by-step explanation:

y = x² + x

y-(-3) = m(x-2)


y = x²+x

y + 3 = mx - 2m


y = x² + x

y = mx - 2m - 3


x² + x = mx - 2m - 3

x² + x - mx + 2m + 3 = 0

x² + (1-m)x + 2m + 3 = 0

discriminant = m² + 1 - 2m -4 (2m + 3)

m² + 1 - 2m - 8m  - 12

m² - 10m - 11

the line is tangent so the discriminant must be equal to 0

m² - 10m - 11 = 0
(m-11)(m+1) = 0

m = 11

m = -1


y + 3 = -(x-2)

y+ 3 = -x + 2

y = -x + 2 - 3

y = -x - 1


y + 3 = 11(x-2)

y + 3 = 11x - 22

y = 11x -22 - 3

y = 11x - 25

Marty and Adam want to share 8/10 feet of rope, equally. What amount of rope should each person get?

Answers

Answer: 2/5 feet

Step-by-step explanation:

From the question, we are informed that Marty and Adam want to share 8/10 feet of rope, equally.

The amount of rope that each person would get would be calculated by dividing 8/10 by 2. This will be:

= 8/10 ÷ 2

= 8/10 × 1/2

= 8/20

= 2/5

Therefore, each person gets 2/5 feet of rope.

A water tank holds 320 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 480 gallons but is leaking at a rate of 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same?

Answers

Answer:

I think the two tanks will be the same in week 80

Step-by-step explanation:

Help the picture is above I’ll mark you as brainliest please show the work too.

Answers

Answer: what are you doing stepbro

Step-by-step explanation: i like doggos :)

The midpoint between (5, -6) and (-7, -1).

Answers

Answer:

(-1, -3.5)

Step-by-step explanation:

(5, -6) and (-7, -1) have a midpoint of (-1, -3.5)

The heights, in cm, of 32 female gymnasts were recorded:
148 152 147 149 150 147 151
142 156 148 148 149 150 152
155 154 151 154 148 150 149
145 147 148 161 152 162 149
146 151 150 157
a) Construct a grouped frequency table, using groups of 5 cm.
b) Draw a histogram to represent this data.

Answers

Step-by-step explanation:

142r4h+34-45=673cm2468228b288

Which correctly Applies the distributaries property to show an equivalent expression to (-2.1)(3.4)

Answers

Answer:

(–2.1)(3) + (–2.1)(0.4)

Step-by-step explanation:

It's D

Answer:

D

Step-by-step explanation:

Took the test ;)

Type the correct answer in the box. Round your answer to two decimal places.

Type the correct answer in the box. Round your answer to two decimal places.

Answers

Answer:

13 units

Step-by-step explanation:

\(3^2+2^2=\sqrt{13^2} \\9+4=13\)

Answer:

The length of BC is 3.61 units.

Step-by-step explanation:

√13=3.60555128=3.61 (Round off to two places)

According to Pythagoras theorem,

Hypotenuse²=Perpendicular²+Base²

H²=P²+B²

Perpendicular given=3 units

Base given=2 units

H²=3²+2²

H²=9+4

H²=13

H=√13 units

H=3.61 units (approx)

Use special products to multiply. 4x (4x+3)(4x-3) - (Simplify your answer. Use integers or fractions for any numbers in the expre
Multiply the binomials. (6x + 7)(x+6) (6x + 7)(x+6)= (Simplify your answer

Answers

4x (4x+3)(4x-3) is the given expression. Here we can use the formula of special products to multiply the given expression.The formula for special product is (a+b)(a-b)=a²-b² .

Consider a=4x and b=3. Substituting the values in the formula, we get

(a+b)(a-b)=a²-b² (4x+3)(4x-3) = (4x)² - (3)²  = 16x² - 9

The given expression 4x (4x+3)(4x-3) can be simplified as 4x(16x² - 9).The next step is to simplify the given expression. Multiply 4x by 16x² and 4x by -9. We get, 4x(16x²) + 4x(-9) = 64x³ - 36x.

Therefore, 4x (4x+3)(4x-3) simplified is 64x³ - 36x.The expression to be solved is (6x + 7)(x+6). Multiplying the given expression (6x + 7)(x+6), using special product method, we get

(6x + 7)(x+6)=6x(x+6) + 7(x+6)= 6x² + 36x + 7x + 42= 6x² + 43x + 42.

Therefore, (6x + 7)(x+6) = 6x² + 43x + 42.

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expression is equivalent to
14

17

Answers

Answer:

14/17

Step-by-step explanation:

14/17 as a fraction can't be simplified. 17 is a prime number, so it can't be divided by anything except 1.

If the question you're asking is 14-17, the answer would be -3...

I hope this helped you out!! Have an awesome day C:

Step-by-step explanation:

if you are subtracting it is -3

if you are dividing it is 0.823

if you are looking for an equivalent fraction it is 28/34

Help please + need explanation

Help please + need explanation

Answers

Answer: 18 dollars

Step-by-step explanation:

Let x be the amount of money each girl recevied. Then, in total, they received 4*x dollars.

We can set up an equation for the information given.

4x - 4*12 = 24

4x - 48 = 24

4x = 72

x = 18

Therefore, each girl received 18 dollars.

Properties of translation and reflation quiz iready answer guide

Answers

Step-by-step explanation:

The property of translations on a coordinate plane, is pretty easy to remember, if you go up, you add to the y, if you go down, subtract from the y

If you go left, subtract from the x, if you go right, add to the x.

Example: State the number of moves the x and y variable in each vertex had to go through and what direction, (-100, 27) to (100,0)

Answer:

The x had to go through 200 moves to the right to add 200 onto the x

The y had to go through 27 moves to the left to subtract 27 from y.

Hope this helps!

Circle D circumscribes ABC and ABE. Which statements about the triangles are true?



Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.
Statement II: The distance from C to D is the same as the distance from D to E.
Statement III: bisects CDE.
Statement IV: The angle bisectors of ABC intersect at the same point as those of ABE.
A.
I only
B.
I and II
C.
II and IV
D.
I and III
E.
III and IV

Answers

The true statements about these triangles are: B. I and II.

How to identify the true statements?

Based on the diagram (see attachment), we can logically deduce the following points in accordance with circle theorem:

The tangents drawn from a point out side the circle are the same (equal).The perpendicular bisectors of triangle ABC would have an intersection at the same point (center D) as those of triangle ABE.The distance from point C to point D is the same as the distance from point D to point E i.e CD = DE since both are radii of the circle.

In conclusion, we can logically deduce that the true statements about these triangles are I and II only.

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Circle D circumscribes ABC and ABE. Which statements about the triangles are true?Statement I: The perpendicular

pls help me answer this 12 to 15 questions​

pls help me answer this 12 to 15 questions

Answers

Answer:

Step-by-step explanation:

See attachment

12.  -23C

13.  28.9% Loss

14.  Diagram in the attachment.  The sides can be calculated with the Pythagorean Theorem.  Side = 3.61 cm

15.  Use trig relationships.  x = 5, y = 8.66

pls help me answer this 12 to 15 questions

Which table(s) show x and y in DIRECT PROPORTION?

Which table(s) show x and y in DIRECT PROPORTION?

Answers

Answer:

d and a

Step-by-step explanation:

URGENT!!!!! Will give brainliest if correct :)

A regression line has a slope of 1.885. If the mean of the x-coordinates of the data points is 3.448, and the mean of the y-coordinates is 12.318, what is the y-value of the y-intercept of the line to three decimal places?

A. -5.819
B. - 19.771
C.19.771
D. 5.819

URGENT!!!!! Will give brainliest if correct :) A regression line has a slope of 1.885. If the mean of

Answers

The equation of a regression line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope m is given as 1.885.

The y-intercept b can be found using the formula b = y_mean - m * x_mean, where x_mean and y_mean are the means of the x-coordinates and y-coordinates of the data points, respectively. Plugging in the given values, we get:

b = 12.318 - 1.885 * 3.448 b ≈ 5.819

So the y-value of the y-intercept of the line to three decimal places is approximately 5.819. The correct answer is D. 5.819.

What is the solution for the system of linear equations shown in the graph?

answers are in the second image

What is the solution for the system of linear equations shown in the graph?answers are in the second
What is the solution for the system of linear equations shown in the graph?answers are in the second

Answers

Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

A squirrel runs up and down a tree.
The graph shows the height of the squirrel, h (feet), as
a function of time, t (seconds).
What is the highest point the squirrel reaches solve h(t) =

Answers

Answer:5

Step-by-step explanation:

How many micrometers are in a centimeter?

Answers

There are 10000 micrometers are in a centimeter.

What is micrometers?

 Micrometers are commonly used to determine the thickness or diameter of microscopic objects such as microorganisms and colloidal particles. The International Bureau of Weights and Measures' symbol for a micrometre is m. The micrometer is a length unit derived from SI that equals 106 metre (SI standard prefix "micro-" = 106) and is equivalent to one millionth of a metre or one thousandth of a millimetre.

Here we know that ,

1 centimeter = 10000 micrometers.

If we want to convert 1 centimeter into micrometer we need to multiply by 10000.

Hence there are 10000 micrometers are in a centimeter.

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1. A new book bag costs $45. If it is on sale for 25% off and a tax of 7%, how much would it
cost?

Answers

Answer:

I believe it would be $31.39

Step-by-step explanation:

Original Price - $45

Price With Sale And Tax $31.39

Hope that helps!

Which Venn diagram has shading that represents the given set?
A^cnB

Answers

Answer:

b

Step-by-step explanation:

Show transcribed data
What valid conclusion can ve have in each of the following expressions: What comclusion can wre have? ∃x−R(x) 三 xR(x) ∃x×(x) ∃x−5(x)

Answers

We can have is that there exists at least one entity that is five less than another entity.

The following are the conclusions that can be drawn from the given expressions:

Conclusion for ∃x−R(x): This expression can be translated to "There exists an x such that x is not R."

Thus, the conclusion we can have is that there exists at least one entity that is not R.

Conclusion for 三xR(x):

This expression can be translated to "For all x, x is R." Thus, the conclusion we can have is that everything is R.

Conclusion for ∃x×(x):

This expression can be translated to "There exists an x such that x times x." Thus, the conclusion we can have is that there exists at least one entity that is squared.

Conclusion for ∃x−5(x):

This expression can be translated to "There exists an x such that x minus 5."

Thus, the conclusion we can have is that there exists at least one entity that is five less than another entity.

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what is the probability that a student has a gpa under 2.0 given that he or she has skipped many classes?

Answers

The probability that a student has a GPA under 2.0 given that he has skipped many classes is 8/11.

From the table we see that,

The student who have a GPA under 2.0 = 80

The student who has skipped many classes = 80 + 25 + 5

The student who has skipped many classes = 110

Hence, the probability that a student has a GPA under 2.0 given that he has skipped many classes = The student who have a GPA under 2.0/The student who has skipped many classes

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 80/110

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 8/11

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The complete question is:

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.

What is the probability that a student has a GPA under 2.0 given that he has skipped many classes?

A. 0.080

B. 0.281

C. 0.285

D. 0.314

E. 0.727

what is the probability that a student has a gpa under 2.0 given that he or she has skipped many classes?

Evaluate the function w(x) = -5x - 1 when x = -3, 0, and 4/5

Answers

w(x) = -5x - 1

___________

→ ←

w(-3) = -5(-3) - 1

= 15 - 1

= 14

w(0) = 5(0) - 1

= 0 - 1

= -1

consider the quadratic function y equals short dash x squared plus 6 x minus 5. what do we know about the graph of this quadratic equation, based on its formula?

Answers

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Do Now
Determine the coordinates of the midpoint of the line
segment with endpoints R(6,-2) and S(-3,-2).
O (1,2)
O (1.5, 2)
O (1.5, -2)
(3,-2)

Answers

Answer:

(1.5, -2)

Step-by-step explanation:

First subract -3 from 6 to find the total distance of the line segment.

6 - (-3)

Two negatives make a positive

6 + 3

9 units distance

Knowing this, the midpoint is 4 1/2 units away from either end. (1/2 * 9 = 9/2 = 4 1/2 units) Either add 4.5 to -3, or subtract 4.5 from 6 (keep the -2 though, as this line is straight!) to get the coordinates of the midpoint.

-3 + 4.5

-3 + 3 + 1.5

(1.5, -2)

6 - 4.5

6 - 4 - 0.5

2 - 0.5

(1.5, -2)

The midpoint of segment RS is (1.5, -2).

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