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Consider the first five terms of the following sequence

1, 10, 100, 1000, 10,000, ...

If the sequence defines a function, what is a reasonable domain and range of the function?

Question 8 options:

Domain: {1, 2, 3, 4, 5, ...}; Range: {1, 10, 100, 1000, 10,000, ...}


Domain: all real numbers; Range: all real numbers


Domain: all real numbers; Range: {1, 10, 100, 1000, 10,000, ...}


Domain: {1, 2, 3, 4, 5, ...}; Range: all real numbers

The Tesla Model S P100D, when pushed to its limit in "Ludicrous mode," can accelerate to 60 mph in an astonishingly short amount of time. The acceleration profile of the vehicle during the first 3.0 seconds can be modeled using the equation x = (35 m/s³)t + 14.6 m/s² - (1.5 m/s³)t² for 0 s ≤ t ≤ 0.40 s and x = 14.6 m/s² - (1.5 m/s³)t² for 0.40 s ≤ t ≤ 3.0 s.

Explanation:

During the initial phase of acceleration from 0 s to 0.40 s, the equation x = (35 m/s³)t + 14.6 m/s² - (1.5 m/s³)t² describes the motion of the Tesla Model S P100D. This equation includes a linear term, (35 m/s³)t, and a quadratic term, -(1.5 m/s³)t². The linear term represents the linear increase in velocity over time, while the quadratic term accounts for the decrease in acceleration due to drag forces.

After 0.40 s, the quadratic term dominates the equation, and the linear term is no longer significant. Therefore, the equation x = 14.6 m/s² - (1.5 m/s³)t² applies for the remaining duration until 3.0 s. This equation allows us to calculate the position of the car as a function of time during this phase of acceleration.

Now, to determine the time it takes for the Tesla Model S P100D to accelerate to 60 mph, we need to convert 60 mph to meters per second. 60 mph is equivalent to approximately 26.82 m/s. We can set the position x equal to the distance covered during this acceleration period (x = distance) and solve the equation x = 26.82 m/s for t.

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It takes around 2.34 seconds for the Tesla Model S P100D in "Ludicrous mode" to accelerate to 60 mph.

To find out how long it takes for the Tesla Model S P100D to accelerate to 60 mph, we need to convert 60 mph to meters per second (m/s) since the given acceleration equation is in m/s.

1 mile = 1609.34 meters

1 hour = 3600 seconds

Converting 60 mph to m/s:

60 mph * (1609.34 meters / 1 mile) * (1 hour / 3600 seconds) ≈ 26.82 m/s

Now, we can set up the equation and solve for time:

x = (35 m/s^3)t^3 + (14.6 m/s^2)t^2 - (1.5 m/s^3)t

To find the time when the velocity reaches 26.82 m/s, we set x equal to 26.82 and solve for t:

26.82 = (35 m/s^3)t^3 + (14.6 m/s^2)t^2 - (1.5 m/s^3)t

Since the equation is a cubic equation, we can use numerical methods or calculators to solve it. Using a numerical solver, we find that the time it takes to accelerate to 60 mph is approximately 2.34 seconds.

Therefore, it takes around 2.34 seconds for the Tesla Model S P100D in "Ludicrous mode" to accelerate to 60 mph.

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Answer:

Exponential growth

Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:

n = 100, p = 0.5.

The mean and the standard deviation are given by:

Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (59.5 - 50)/5

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

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The probability was broken by Bob is, 0.003 or 3%.

What is probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

Alonzo, Bob, and Casper are each assigned three chances to bus tables and to fix any broken dishes, respectively.

P(Alonzo bussing tables) = 50% = 0.5

P(Bob bussing tables) = 15% = 0.15

P(Casper bussing tables) = 35% = 0.35

P(Alonzo breaking a dish) = 6% = 0.06

P(Bob breaking a dish)  = 2% = 0.02

P(Casper breaking a dish)  = 4% = 0.04

As the likelihood of dish breakage does not change with the busing of the tables, this is all about independent events.

Consequently, P(A and B) = P(A) + P (B)

So, if a dish is broken, the likelihood that Bob broke it is;

P(Bob breaking dishes and busing tables) = P(Bob busing tables) x P (Bob breaking a dish)

                                                                       = 0.15 x 0.02

                                                                       = 0.003

P(Bob breaking dishes and busing tables)  = 0.003 0r 0.3%

Hence, the probability was broken by Bob is, 0.003 or 3%.

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Answer:

Step-by-step explanation:

For b

\(9\sqrt{3} = 3^{2} 3^{\frac{1}{2} }\)

add exponents

=\(3^{\frac{5}{2} }\)

so b= 5/2

For c

\(\frac{1}{\sqrt{3} } = 3^{-\frac{1}{2} }\)

so c= -1/2

Answer:

A.

While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.

Answer:

y=⁻ \(\\\frac{13}{21}\)  should be your answer in decimal form its y=-0.619047

Step-by-step explanation:

Answer:

Range: 20.

Step-by-step explanation:

Put in order:

12, 13, 13, 15, 16, 19, 32

Subtract smallest number from largest number

32 - 12 =20

Answer:

9 :  7, or 9/16 to 7/16

Step-by-step explanation:

We know that there are 9 blue hats.

We know there are 7 red hats.

This is a 9 : 7 ratio.

In fraction form, we must find the total ratio, use that as the denominator, then take the seperate amounts, such as bluei adn red hats, and use that as the numerator:

9+7=denominator

denominator = 16

Blue hats = 9

Ratio of red = 9/16

Red hats = 7

Ratio of red = 7/16

Hope this helps!

Answer:

\(\frac{400}{3} \pi\)

Step-by-step explanation:

Formula for Cone: π\(r^{2}\frac{h}{3}\)

Since we have all the components, we can find the volume of the cone.

R = 10

H = 4

π\(10^{2}\frac{4}{3}\)

10×10 = 100

100π\(}\frac{4}{3}\)

\(}\frac{4}{3}\)×100

4       100          400

---  ×   -----    =    ------

3          1              3

Answer: \(\frac{400}{3} \pi\)

Hope this helped.

Find the volume of a cone with radius 10 feet and height of 4 feet.

Given Data :

Radius = 10 feet

Height = 4 feet

Formulae :

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \blue{ \underline{ \overline{ \green{ \boxed{ \frak{{ \sf V}olume_{(Cone)} = \pi {r}^{2} \frac{h}{3}}}}}}}\)

Putting the values we get

\( \frak{ Volume_{(Cone)} = 3.14 × (10)² × \frac{4}{3} }\)

\( \frak{Volume_{(Cone)} = 3.14 × 100 × \frac{4}{3} }\)

\( \frak{Volume_{(Cone)} = 314 \times \frac{4}{3} }\)

\( \frak{Volume_{(Cone)} = 418.67 \: ft³ }\)

Henceforth, the volume is 418.67 ft³

Answer:

1+1=2

2+2=4

4+3=7

7+4=11

so the patter is number + natural numbers (serially)

Step-by-step explanation:

The value of the rate of change when we put a glass of water at room temperature is 1/3.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another.

The connection defining how one quantity changes in response to the change in another quantity is given by the rate of change formula. The formula for calculating the rate of change from y coordinates to x coordinates is y/x = (y2 - y1)/. (x2 - x1 ).

Rate of change  = change in temperature / time

= 10-5/15

=5 / 15

= 1/3

Therefore, the Rate of change is 1/3.

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Complete question;

What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is its temperature at 5 minutes and then at 10 minutes.

hope it helps this to you figthing sheeeeeeeeeeeeeeeeeeeeeeeesh!!!

Answer:

1 = Given

2 = Given

3 = Substitution Property

4 = Distributive Property

5 = Given

6 = Substitution Property

7 = Simplify

8 = Subtraction Property

9 = Addition Property

By substituting given c and d values inn the given equation and simplifying we get a=b. Hence, proved.

Given that, 2c =d-2b, c = a-b and d= a + b.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To prove: d=a+b

Proof:

1. 2c =d-2b (Given)

2. c=a-b (Given)

3. 2(a-b)=d-2b (Substitute c=a-b)

4. 2a-2b=d-2b

5. d=a+b (Given)

6. 2a-2b=a+b-2b (Substitute d=a+b)

7. 2a-2b=a-b

8. a-2b=-b (Transpose a to LHS and simplify)

9. a=b (Transpose a to RHS and simplify)

By substituting given c and d values inn the given equation and simplifying we get a=b. Hence, proved.

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9514 1404 393

Answer:

  540 cm³

Step-by-step explanation:

Apparently, the base of the prism is a parallelogram that is 15 cm wide and 3 cm from one side to the other. Its area is given by ...

  A= bh

  A = (15 cm)(3 cm) = 45 cm²

The volume of the prism is the product of its base area and height.

  A= Bh

  A = (45 cm²)(12 cm) = 540 cm³ . . . . volume of this prism

Answer:

2

Step-by-step explanation:

f(x) = 2x

Let x =1

f(1) = 2*1

f(1) = 2

Answer:

f(1)=2

Step-by-step explanation:

We are given the equation:

f(x)=2x

We also know that x=1. Therefore, we can substitute 1 in for every x.

f(1)= 2(1)

Multiply 2 and 1

f(1)=2

f(x) when x=1 is 2.

The measure of side length AB in the triangle is approximately 13.8 units.

The sine rule is expressed as:

\(\frac{c}{sinC} = \frac{b}{sinB}\)

From the diagram:

Angle B = 50 degrees

Angle C = 62 degrees

Side AC = b = 12

Side AB = c =?

Plug these values into the above formula and solve for c.

\(\frac{c}{sinC} = \frac{b}{sinB}\\\\\frac{c}{sin62^o} = \frac{12}{sin50^o}\\\\c = \frac{12 * sin62^o}{sin50^o}\)

c = 10.595 / 0.766

c = 13.832

c = 13.8

Therefore, side AB measures 13.8 units.

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If the slope of the line is 7 /10, the vertical change that will be present for a horizontal change of 63 ft is 44.1 ft

The slope of a line is the measure of its steepness. Therefore,

slope = change in y(vertical) / change in x(horizontal)

slope = y₂ - y₁ / x₂ - x₁

slope = 7 / 10

Therefore,

7  / 10 = y / 63

cross multiply

441 = 10y

divide both sides by 10

y = 441 / 10

y = 44.1 ft

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Answer:

A=S1+S2+S3+S4

Step-by-step explanation:

A=4(l*w)ft

Answer:

100

THIS IS FOR THE SECOND ONE ONLY THE SECOMD ONE

Answer:

Area= 4,200 square feet

Step-by-step explanation:

If I read your question correctly, I'm assuming the dots (".") mean a multiplication sign ("x").

If they are all being multiplied, use PEMDAS to solve this. First, find to value for any exponents you have (in this case, it's \(2^3\) and \(5^2\)).

\(2^3=2*2*2=8\\5^2=5*5=25\)

Now that you have the values for these two exponents, multiply all the numbers together.

8 x 3 x 25 x 7 = 4,200

The exact length of the curve is 4(2√2 - 1), which is approximately 7.656.

To find the length of the curve, we need to use the formula for arc length, which is given by: \(L = ∫a^b √(dx/dt)^2 + (dy/dt)^2 dt\)

Here, a = 0 and b = 1, and x = 5 + 6t^2 and y = 3 + 4t^3. Differentiating with respect to t, we get:

dx/dt = 12t

\(dy/dt = 12t^2\\\)

Substituting these values in the formula for arc length, we get:

\(L = ∫0^1 √(12t)^2 + (12t^2)^2 dt\)

\(L = ∫0^1 √(144t^2 + 144t^4) dt\)

\(L = ∫0^1 12t√(1 + t^2) dt\)

This integral can be solved using the substitution \(u = 1 + t^2\), du/dt = 2t, and the limits of integration become u = 1 and u = 2:

\(L = ∫1^2 6√u du\)

\(L = [4u^(3/2)]_1^2\)

\(L = 4(2√2 - 1)\)

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For the sample (a) Mean is 30.8, the median is 31 and the standard deviation is 3.96, (b) the coefficient of skewness using Pearson's method is -0.151, and (c) the coefficient of skewness using the software method is 0.075.

Given values,

36, 26, 33, 28, 31

no. of values, n = 5

(a)

Mean, μ = Σx/n

= (36+26+33+28+31)/5 = 30.8

Now, Median, M = (n+1)/2th value

M = (5+1)/2 th = 3rd value

M = 31

Standard deviation(s) = \(\sqrt{ }\)Σ(x-μ)²/n-1

= \(\sqrt{ \frac{(36-30.8)^{2}+(26-30.8)^2+(33-30.8)^2+(28-30.8)^2+(31-308)^2 }{4} }\)

s = 3.96

(b) the coefficient of skewness using Pearson’s method

= 3(μ-M)/s = 3(30.8-31)/3.96 = -0.151

(c) the coefficient of skewness using the software method

= 1/s³(n-1)Σ(x-μ)³ = \(\frac{(36-30.8)^{3}+(26-30.8)^3+(33-30.8)^3+(28-30.8)^3+(31-30.8)^3 }{4(3.96)^3}\)

= 0.075

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Answer:

90000011-00001002000020200.9 :3

Step-by-step explanation:

A popular way for people to share information and thoughts with others online is through blogging.

A blog is a conversation or informational website published on the World Wide Web that is composed of discrete, frequently informal diary-style text posts, according to the definition of a blog provided by Wikipedia.

This has given rise to a brand-new trend where everyone may now voice their opinions on a given subject.

Other phenomena and artefacts, such as analogue signals, poetry, photographs, music, or other sounds, as well as electrical currents, transmit information in a more continuous manner than do digital signals and other data, which employ discrete signs or algebras to do so.

Information itself is not knowledge, but how it is interpreted is crucial. Raw information can also take the shape of structured data. A collection of data may contain information that may be extracted through analysis by analysts who are experts in their field.

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Answer:

c) 2 2 over 5 = 2 2/5

Step-by-step explanation:

Forming the equation,

→ (1/3)b = 4/5

Now the value of b will be,

→ (1/3)b = 4/5

→ b = (4/5) ÷ (1/3)

→ b = (4/5) × (3/1)

→ b = (4 × 3)/(5 × 1)

→ b = 12/5

→ [ b = 2 2/5 ]

Hence, value of b is 12/5.

Answer:

I think the answer would be 33. I am not exactly sure though.

Answer:

Gradient = Change in y / Change in x

Gradient = (-7-3) / (0-4)

Gradient = -10/-4

Gradient = 2.5

So the answer is 10/4, which is 2.5

The slope of the line passes through the points (0.-7) and (-4, 3) is -5/2. The correct option is B.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is defined as the ratio of the rise to the run.

Given that the points are (0.-7) and (-4, 3). the slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 3 - (-7) / ( -4 - 0 )

Slope = 10 / -4

Slope = -5 / 2

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