Find the current price of the item and the price 10 years from today. Round your answer to the nearest dollar as necessary.

Find The Current Price Of The Item And The Price 10 Years From Today. Round Your Answer To The Nearest

Answers

Answer 1

Given the function

\(p(t)=800(1.039)^t\)

t= number of years from today

The current price (t=0) is

\(p(0)=800(1.039)^0\)\(p(0)=800*1\)\(p(0)=800\)

Current price= 800

Price 10 years from today (t=10)

\(p(10)=800(1.039)^{10}\)\(p(10)=1172.85\)

rounded to the nearest dollar the price in 10 years from today

p(10) = 1173


Related Questions

Find the value of 0.7 x 0.08

Answers

Answer:

0.056

Step-by-step explanation:

I used my calculator, not much work to show :)

Answer:

The answer for 0.7 x 0.08 is 0.056.

Explantion:

I am smart like that.

I am built different.

TIME REMAINING
44:54
The table below shows the number of cars sold each month for 5 months at two dealerships.

Cars Sold
Month
Admiral Autos
Countywide Cars
Jan
4
9
Feb
19
17
Mar
15
14
Apr
10
10
May
17
15


Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.

Answers

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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I need help with this math problem

I need help with this math problem

Answers

Step-by-step explanation:

given,

\( log_{7}(4) = 0.712 \\ log_{7}(12) = 1.277 \\ to \: find \: log_{7}( \frac{1}{3} ) \\ log_{7}( \frac{1}{3} ) = log_{7}( \frac{4}{12} ) \\ by \: logarithmic \: result \: log( \frac{a}{b} ) = log(a) - log(b) \\ implies \\ log_{7}( \frac{1}{3} ) \: = log_{7}(4) - log_{7}(12) \\ = 0.712 - 1.277 \\ = −0.565\)

I hope this is the answer.

pls mrk me brainliest, i rly worked hard on this i need to get the next rank

-5 = -36 / m + m
pls help me with this question hurry
This is 6 grade work

Answers

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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Mikael has a loan of $40 000.
He pays 1.6% simple interest for six months
How much interest does he pay altogether?

Answers

Step-by-step explanation:

Based on the given conditions,

\( formulate: 1.6\% \times 40000 \times 12 \div 12

\( formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}

\( formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}\)

\(Reduce the fraction: 2 \times320

\(Reduce the fraction: 2 \times320Calculate the product orquotient: 640[tex]

Answer 640

Answer:

\(\sf\longmapsto \: 640\)

Step-by-step explanation:

Based on given cases:

\( \sf \: Formulate: 1.6\% \times 40000 \times 12 \div 12\)

Reduce the fraction:

\( \sf \longmapsto \: \dfrac{2 \times 40000}{125}\)

\( \sf \longmapsto \: 320 \times 2\)

Calculate the product/quotient:

\( \sf\longmapsto \: 640\)

Hello! Could someone please help explain how to solve this to me please and an answer would be nice! Thanks! :)

Hello! Could someone please help explain how to solve this to me please and an answer would be nice!

Answers

if we notice the tickmarks on the triangle, we can see the all sides are equal, namely is an equilateral triangle, and if all sides are equal, then all interior angles are equal as well.

Let's recall that the sum of all interior angles in a triangle is 180°, now if we divide that by 3, that gives us 60, namely each angle in the equilateral triangle is 60°, that means

\(10x=60\implies x=\cfrac{60}{10}\implies \boxed{x=6} ~\hfill 12y=60\implies y=\cfrac{60}{12}\implies \boxed{y=5}\)

In a certain city, E Street, W Street, C Street, and D
Street are parallel streets that intersect K Street and
M Street. How long is K Street between C Street
and D Street?
600 ft
800 ft
540 ft
E St
W St
M St
C St
D St
1400 ft
K St

Answers

The length which lies from K Street between C Street and D Street is 337.5 ft.


How to find the distance

Given that,

E Street, W Street, C Street, and D Street are parallel streets that cross K Street and M Street in a particular city. It is unknown how far K Street is from C Street and D Street.

Let the distance of street K between C and D be x,

Now,

Taking the equality of the proportionality expression of triangles,

600 / 400 = 600 + x / 400 + 250

6 / 4 = 600 + x / 625

3750/4 = 600 + x

937.5 = 600 + x

x = 337.5 ft

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Area and perimeter assignment. (9th Grade geometry)

Area and perimeter assignment. (9th Grade geometry)

Answers

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

Explain about the perimeter:

A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.

Given that:

coordinates of triangle: A(5,3) , B(1,5) and C(3,0)

Perimeter = sum of all sides

Perimeter = AB + BC + CA

Estimate each distance using the distance formula:

d = √(x2 - x1)² + (y2 - y1)²

AB = √(1 - 5)² + (5 - 3)²

AB = √(-4)² + (-2)²

AB = √(16 + 4)

AB = √20

BC = √(3 - 1)² + (0 - 5)²

BC = √(2)² + (-5)²

BC = √(4 + 25)

BC = √29

CA = √(5 - 3)² + (3 - 0)²

CA = √(2)² + (3)²

CA =  √(4 + 9)

CA = √13

Perimeter = AB + BC + CA

Perimeter = √20 + √29 + √13

Perimeter = 4.47 + 5.38 + 3.60

Perimeter = 13.45 units.

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

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Describe the series of rigid motion transformations which map polygon A to Polygon A'''. Are the two polygons congruent? Explain how you know.

(someone please help me!)

Describe the series of rigid motion transformations which map polygon A to Polygon A'''. Are the two

Answers

The series of rigid motion transformations that map polygon A to Polygon A''' are;

A rotation of 145° about the origin to map A to A'A reflection across the x-axis to map A' to A'A translation of four units to the right and one unit down

What is a rigid transformation?

A rigid transformation is a transformation in which the distance between all pairs of points on the pre-image is preserved following the transformation.

The series of rigid motion transformations that map polygon A to polygon A''' are;

Transformation from A to A'

The angle in the diagram in the question indicates the rotation of polygon A to produce polygon A' is a rotation of 145° about the origin.

Transformation from A' to A''

The coordinates of the vertices of triangle, A' (0.9, 4.1), (3.1, 5.9), (5.5, (2.5) and the vertices of triangle A'' (0.9, -4.1), (3.1, -5.9), (5.5, -2.5), indicates that the transformation is a reflection about the x-axis

Transformation from A'' to A'''

The arrow of the translation transformation indicates that the transformation is a translation of four units to the right and 1 unit down.

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A steel safe with mass 2200 kg falls onto concrete. Just
before hitting the concrete its speed is 40 m/s, and it smashes
without rebounding and ends up being 0.06 m shorter than
before. What is the approximate magnitude of the force exerted
on the safe by the concrete? How does this compare with the
gravitational force of the Earth on the safe? Explain your analysis
carefully, and justify your estimates on physical grounds.

Answers

The kinetic energy of the safe increases the force exerted by the concrete

to several times the weight of the safe.

The magnitude of the force exerted on the safe by the concrete on the is approximately \(\underline{29.\overline 3 \, \mathrm{MN}}\)The concrete exerts a force that is approximately 1,359.16 times the weight of the safe.

Reasons:

First part

The mass of the steel safe, m = 2,200 kg

Velocity of the safe just before it hits the concrete, v = 40 m/s

The amount by which the safe was compressed, d = 0.06 m

The kinetic energy, K.E., of the safe just before it hits the round is therefore;

\(\displaystyle K.E. = \mathbf{\frac{1}{2} \cdot m \cdot v^2}\)

\(\displaystyle K.E._{safe} = \frac{1}{2} \times 2,200 \times 40^2 = 1,760,000 \ Joules\)

Work done by concrete, W = Force, F × Distance, d

\(\displaystyle Force, \, F = \mathbf{\frac{Work, \, W}{Distance, \, d}}\)

By the law of conservation of energy, we have;

The work done by the concrete, W = The kinetic energy, K.E. given by the safe

W = K.E. = 1,760,000 J

The effect of the work = The change in the height of the safe

Therefore;

The distance, d, over which the force of the concrete is exerted = The change in the height of the safe = 0.06 m

d = 0.06 m

Therefore;

\(\displaystyle The \ force \ of \ the \ concrete, \, F = \frac{1,760,000\, J}{0.06 \, m} = 29,333,333. \overline 3 \, N = 29.\overline 3 \ MN\)

The force of the concrete on the safe = \(\underline{29.\overline 3 \ MN}\)

Second part:

The gravitational force of the Earth on the safe, W = The weight of the safe

W = Mass, m × Acceleration due to gravity, g

W = 2,200 kg × 9.81 m/s² ≈ 21,582 N

The ratio of the force exerted by the concrete to the weight of the safe is found as follows;

\(\displaystyle Ratio \ of \ forces = \frac{29.\overline 3 \times 10^6 \, N}{21,582 \, N} = \frac{4,000,000}{2,943} \approx \mathbf{1359.16}\)

The force exerted by the concrete is approximately 1,359.16 times the weight of the safe.

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Does a point have any dimensions ?

Answers

Answer:

NO

Step-by-step explanation:

Points do not have dimensions.

Answer:

no

Step-by-step explanation:

I was never taught how to do this... some one help me.

I was never taught how to do this... some one help me.

Answers

\($\cos X = \frac{\text{adjacent}}{\text{hypotenuse}} = \boxed{\frac{15}{17}}$\)

So cos means adjacent over hypotenuse which would be 15/17 and you can’t simplify it down farther so 15/17 is your final answer.

Given the individual rates of workers, to find the combined rate of all the individuals working together you must
the individual rates.
Fill in the blank

Given the individual rates of workers, to find the combined rate of all the individuals working together

Answers

To find the combined rate of all the individuals working together, you must add the individual rates.

How to calculate combined rate of individuals working together?

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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A ring-shaped region shown below. Its inner diameter is20 yd. The Width of the ring is 3 yd. Find the area. Of the shaded region.

A ring-shaped region shown below. Its inner diameter is20 yd. The Width of the ring is 3 yd. Find the

Answers

9514 1404 393

Answer:

  216.66 yd²

Step-by-step explanation:

One way to find the area of a ring like this is to multiply its centerline length by the width of the ring.

Here, the diameter of the circle that is the centerline of the ring is 23 yd. The circumference of that circle is ...

  C = πd = 3.14(23 yd) = 72.22 yd

Then the ring area is ...

  (72.22 yd)(3 yd) = 216.66 yd² . . . area of shaded region

Kyle buys a bag of cookies that contains 4 chocolate chip cookies, 9 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies. What is the probability that Kyle randomly selects a sugar cookie from the bag, eats it, then randomly selects a peanut butter cookie

Answers

Multiply all them then stubbtrac to number

Given f(x) = x² - 5x - 6 and g(x) =
x² - 6x, what are the domain restrictions
for (-)(x)?
A) x # +6
B) x = 0
C) x = 0,6
D) x = -2,6

Answers

The domain restrictions for (f/g)(x) are (c) x = 0, 6

How to determine the domain restrictions for (f/g)(x)?

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

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Can someone help me and explain how I get the answer?

Can someone help me and explain how I get the answer?

Answers

Answer:

-9 is your answer.

I HOPE IT WILL HELP YOU.

Thank you.

Answer:

-9

Step-by-step explanation:

45/(-5) = -9

How did the Persian Wars affect the Greek army?

The Greek army was destroyed.
The Greek army defeated the Persians.
The Greek army overthrew the Persian government.
The Greek army suffered more losses than the Persians.

Answers

During the Persian Wars, the Greek army was weakened and then defeated by the Persians. This led to a decrease in the influence of Greece in Asia Minor.

During this time, Macedonia was one of the strongest states in Greece, and it had control over most of mainland Greece. The empire that emerged from this period is called Macedonian Empire. This empire lasted for another 300 years until its conquest by Rome around 148 BC.

The rise of Macedonia as a major power during this period also gave way to many internal conflicts between different tribes within the kingdom which led to increased military spending on them (cavalry). However, when Roman legions were sent into Asia Minor they easily crushed these armies and destroyed much of their infrastructure including fortifications and roads (roads were built under Alexander's reign but they fell apart quickly). This made it very difficult for any future armies or empires to hold onto territory once conquered.

So I think your question has been answered! Thanks!

Answer: The answer is B:The Greek army defeated the Persians.

Step-by-step explanation: I have my ways ;>

Does anyone understand this?

Does anyone understand this?

Answers

Answer:

\( x = - 1\)

\(x + 1 = 0\)

\( {(x + 1)}^{2} = {x}^{2} + 2x + 1 = 0\)

So m = 2 and n = 1, meaning m + n = 3.

What is the image of (-3,-7) under a rotation of 90 degrees

Answers

The new coordinate (- 7, 3 ) of the image of (-3,-7) under a rotation of 90 degrees.

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Let the coordinate Z is (-3, -7)

Under a clockwise rotation about the origin of  90 degrees

A coordinate ( x, y ) → ( y, - x ),

The coordinate Z is (-3, -7) and is translated using the rule

Then simply plug in the values of x and y which are x = -3 and y = -7

Thus ( -3, - 7 ) → (- 7, 3 )

This is the new coordinate for Z  (- 7, 3 )

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12x + 7 < −11
OR
5x-8>40

Answers

Answer:

x <-1.5

or

x <9.6

Step-by-step explanation:

12x + 7 < - 11

12x < -11 - 7

12x < - 18

12x/12 < -18/12

x = -1.5

OR.

5x - 8 > 40

5x > 40 + 8

5x > 48

5x/5 > 48/5

x > 9.6.

Calculate the bearing of Y from X

Calculate the bearing of Y from X

Answers

Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

The Answer to This Question

The Answer to This Question

Answers

Recall the Trigonometric Ratio below:

\( \tt{ \large{sin \theta = \frac{opposite}{hypotenuse} } }\\ \tt{\large{cos \theta = \frac{adjacent}{hypotenuse} }} \\ \tt{ \large{tan \theta = \frac{opposite}{adjacent} }}\)

For csc, sec and cot - they are reciprocal of sin,cos and tan.

\( \tt{ \large{csc \theta = \frac{1}{sin \theta} } }\\ \tt{ \large{sec \theta = \frac{1}{cos \theta} }} \\ \tt{ \large{cot \theta = \frac{1}{tan \theta} }}\)

What we know now is our hypotenuse, adjacent and opposite length.

hypotenuse = 15opposite = 12adjacent = 9

Therefore,

\( \large{sin \theta = \frac{12}{15} \longrightarrow \frac{4}{5} } \\ \large{cos \theta = \frac{9}{15} \longrightarrow \frac{3}{5} } \\ \large{ tan \theta = \frac{12}{9} \longrightarrow \frac{4}{3} }\)As for the reciprocal of three trigonometric ratio. We just swap the numerator and denominator.

\( \large{csc \theta = \frac{15}{12} \longrightarrow \frac{5}{4} } \\ \large{sec \theta = \frac{15}{9} \longrightarrow \frac{5}{3} } \\ \large{cot \theta = \frac{9}{12} \longrightarrow \frac{3}{4} }\)

Answer

sin = 12/15 —> 4/5cos = 9/15 —> 3/5tan = 12/9 —> 4/3csc = 15/12 —> 5/4sec = 15/9 —> 5/3cot = 9/12 —> 3/4

The first is non-simplifed form while the second that has the arrow pointing is the simplest form.

Let me know if you have any doubts.

to nem ai se vc excluiu minha respostpa q soud o5  oa

n

Which point is not on the graph of the function y = x - 1?



(9, 8)
(8, 7)
(5, 6)
(4, 3)

Answers

Answer:

C. (5,6)

Step-by-step explanation:

Hope this helps. please give brainliest

Find the prime factorization of 234.

Answers

Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

What is the place value of 1 of 574.8931.

Answers

In the number 574.8931, the 1 is in the thousandths place.

The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4

Answers

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

What is a translation?

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The graph of = y=xy, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right

8. Simon is saving his money to buy an Xbox. He earn money by mowing lowns for his
neighbors. The situation can be represented using the equation 35x - 2y = -42 where x
represents the number of lawns mowed and y represents the amount of money Simon has in his
bank account.

( explainations are muc appreciated:) )

a. How much money does Simon earn for mowing each lawn?

b. How much money was in Simon's bank account before mowing any lawns?

Answers

Answer:

a. $35

b.$21

Step-by-step explanation:

a. It is what your are multiplying the number of lawns mowed by

b. -2y = -42

divide by -2 on each side

y=21

(you don't need the 35x because we are trying to find how much before he started mowing)

Determine the mean, median, mode and midrange for the following data:
13 15 18 18 21
Your answers should be exact numerical values.
The mean of the data is
The median of the data is
The mode of the data is
The midrange of the data is

Answers

The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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Find an equation for the surface with all points which are equidistant of (−1,0,0)and the plane x=1. Draw the surface.

Answers

The equation for the surface with all points which are equidistant of (−1,0,0)and the plane x=1 is x² - 2x + y² + z² = 2.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=).

To start with, let's consider the given information. We have been given that all points on the surface are equidistant from (-1,0,0) and the plane x=1. This means that the distance between any point on the surface and (-1,0,0) is the same as the distance between that point and the plane x=1.

We can use the formula for the distance between a point and a plane to derive an equation for the surface. The formula for the distance between a point (x1, y1, z1) and a plane Ax + By + Cz + D = 0 is given by:

distance = |Ax1 + By1 + Cz1 + D| / √(A² + B² + C²)

In our case, the plane is x=1, which can be written as x - 1 = 0. So, A=1, B=0, C=0, and D=-1. The point (-1,0,0) can be substituted as x1=-1, y1=0, and z1=0.

We can simplify the distance formula to:

distance = |x-1|

Now, since all points on the surface are equidistant from (-1,0,0) and x=1, we can set up the following equation:

|x-1| = √( (x+1)² + y² + z² )

Squaring both sides and simplifying, we get:

(x-1)² = x² + 2x + 1 + y² + z²

Rearranging and simplifying, we get the final equation for the surface:

x² - 2x + y² + z² = 2

This is the equation of the surface that contains all points that are equidistant from (-1,0,0) and x=1.

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