Find the exact location of all the relative and absolute extrema of the function. HINT [See Examples 1 and 3.] (Order your answers from smallest to largest x.)
h(x) = 3(x − 1)2/3 with domain [0, 2]
h has a (relative min, relative max, absolute min, absolute max, no extremum) at (x, y) = ( , )
h has a (relative min, relative max, absolute min, absolute max, no extremum) at (x, y) = ( , )
h has a (relative min, relative max, absolute min, absolute max, no extremum) at (x, y) = ( , )

Answer:

\( \frac{2b}{a} \)

Step-by-step explanation:

\( \frac{2}{a} \div \frac{1}{b} \)

\(\frac{2}{a} \: \times \:b\)

\( \frac{2b}{a} \)

Answer:

The equation that model the projectile's height is \(h(t) = -16.087\cdot t^{2}+900\cdot t +200\)

Step-by-step explanation:

We know that projectile is fired vertically upward from a height of 200 feet above the ground with an initial velocity of 900 feet per second and projectiles experiment a parabolic motion, which combines horizontal uniform motion and vertical uniform accelerated motion due to gravity, whose equation of motion is:

\(h(t) = \frac{1}{2}\cdot g \cdot t^{2}+v_{o}\cdot t + y_{o}\)

Where:

\(h(t)\) - Current height above the ground at instant t, measured in feet.

\(y_{o}\) - Initial height, measured in feet.

\(v_{o}\) - Initial velocity, measured in feet per second.

\(g\) - Gravitational acceleration, measured in feet per square second.

\(t\) - Time, measured in seconds.

If we know that \(g = -32.174\,\frac{ft}{s^{2}}\), \(v_{o} = 900\,\frac{ft}{s}\) and \(y_{o} = 200\,ft\), the equation that model the projectile's height is

\(h(t) = -16.087\cdot t^{2}+900\cdot t +200\)

The sum of the series ∑n=1 to infinity of \(\frac{1}{n} \cdot 9^n \cdot 11^n\) is a divergent series, which means it does not converge to a finite value.

To determine if the series converges or diverges, we can use the limit comparison test.

Let's compare the given series to the harmonic series, which is known to diverge. The harmonic series is given by ∑n=1 to infinity of 1/n.

We can take the limit as n approaches infinity of the ratio between the terms of the given series and the harmonic series:

\(\[\lim_{{n\to\infty}} \left( \frac{1}{n} \right) \left( 9^n \right) \left( 11^n \right) \div \left( \frac{1}{n} \right)\]\)

Using algebraic properties of limits, we can simplify this expression:

\(\lim_{{n \to \infty}} (9^n)(11^n)\)

As n approaches infinity, both 9ⁿ and 11ⁿ grow exponentially, and their product also grows exponentially without bound. This means that the ratio between the terms of the given series and the harmonic series does not approach zero, and therefore the given series does not converge.

Therefore, the sum of the series ∑n=1 to infinity of  \(\frac{1}{n} \cdot 9^n \cdot 11^n\)  is a divergent series.

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Answer and Step-by-step explanation:

Pythagorean theorem

Half of 4 is 2.

2^2 + 9^2 = l^2

4 + 81 = l^2

Square root of 85 = l

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Answer:

answer for parabola is pink

The numbers of questions answered correctly by various students on a 10-question quiz are an example of discrete numerical data. The correct answer is c.

Discrete numerical data refers to values that can only take on specific, separate, and distinct numerical values. These values typically represent counts or whole numbers and cannot be subdivided further.

In the context of the quiz, the number of questions answered correctly by students can only be whole numbers ranging from 0 to 10. Each possible value represents a distinct outcome and does not allow for intermediate values.

Discrete numerical data is different from continuous numerical data, which can take on any value within a certain range and allows for fractions or decimals. In the case of the quiz, if the scores were measured on a continuous scale (e.g., percentage), it would be considered continuous numerical data.

However, since the number of questions answered correctly is discrete and can only take specific values, it falls under the category of discrete numerical data. The correct answer is c.

Your question is incomplete but most probably your full question was

The numbers of questions answered correctly by various students on a 10 question quiz are an example of which type of data?

Neither

Discrete

Continuous

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Answer:  x > -8

Step-by-step explanation:

3x - 17 < 4x -  9   subtract 3x from both sides, and add 9 to both sides

-3x + 9 < -3x + 9

0  - 8   <  x  +  0      Rewrite and reverse the sign to simplify

     x > -8

The side of the first square will be √2 times the side of the second square. The relation of the sides is represented as a₁ = √2a₂.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the function expresses the area of another square whose area is twice the area of the original square.

The relation between the areas will be calculated as,

A₁ = 2A₂

a₁² = 2a₂²

a₁ = √2a₂

Therefore, the side of the first square will be √2 times the side of the second square. The relation of the sides is represented as a₁ = √2a₂.

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The probability that the player will receive a blackjack from  a player is dealt 2 cards from a standard deck of 52 well-shuffled cards is 0.0483.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

Combinations of drawing 1 ace * combinations of drawing 1 face cards / all possible 2 card combinations

4C1 * 16C1 / 52C2

4 * 16 / (52 * 51/2)

=64/1326

=.0483

When a player is dealt two cards from a standard deck of 52 properly shuffled cards, the likelihood that they will get a blackjack is 0.0483.

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The symbol M! for any positive integer M represents the result of adding the integers 1 through M. The largest integer n for which 5ⁿ is a factor of the sum 98! + 99! + 100 is 26.

A factorial multiplies a number (n) by each number that comes before it. It is represented by the symbol "!".

If the sum is 98! + 99! + 100, then

\(\begin{aligned}98! + 99! + 100&=(1+99+9900)\cdot 98!\\&=10000\cdot98! \end{aligned}\)

The formula yields the highest exponent m, such that 5m divides 98! is,

\(\begin{aligned}m&=\Bigl\lfloor\frac{98}{5}\Bigr\rfloor+\Bigl\lfloor\frac{98}{5^2}\Bigr\rfloor+\Bigl\lfloor\frac{98}{5^3}\Bigr\rfloor+\cdots\end{aligned}\)

However, only the first two terms exceed zero, thus we get,

\(\begin{aligned}m&=\Bigl\lfloor\frac{98}{5}\Bigr\rfloor+\Bigl\lfloor\frac{98}{5^2}\Bigr\rfloor\\&=19+3\\&=22\end{aligned}\)

Also, 10,000 now has four factors of five. Then,

\(n&= 22+4\\n&=26\)

The required answer is n = 26.

The complete question is -

For any positive integer M, the notation M! Denotes the product of the integers 1 through M. What is the largest integer n for which 5ⁿ is a factor of the sum 98! + 99! + 100?

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The tangential component of acceleration is approximately 205.26 m/s².

To calculate the tangential component of acceleration, we can use the formula:

at = (v^2 - v0^2) / (2r)

Where:

at is the tangential component of acceleration,

v is the final linear velocity,

v0 is the initial linear velocity (which is 0 since the hammer starts from rest),

and r is the radius of rotation.

Given that the radius of rotation is 1.52 m and the final linear velocity is 25 m/s, we can substitute these values into the formula:

at = (25^2 - 0^2) / (2 * 1.52)

Calculating the expression:

at = (625 - 0) / 3.04

  = 625 / 3.04

  ≈ 205.26

Therefore, the tangential component of acceleration is approximately 205.26 m/s².

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Answer:

y = -30

Option A

Step-by-step explanation:

y = -2x - 10

y = -5x + 20

We just need to substitute the values of y.

We have to equate both the equation.

-2x -10 = -5x + 20

-2x + 5x = 20 + 10

3x = 30

x = 10

Plug x as 10 in any one of the equation

Let's take the first equation

y = -2x  - 10

y = -2(10) - 10

y = -20 -10

y = -30

Answer:

(-1,-4) is the vertex

x = -1 is the equation of symmetry;

Step-by-step explanation:

See attached image.

Answer:

(- 1, - 4 ) and x = - 1

Step-by-step explanation:

given a parabola in standard form

y = ax² + bx + c ( ax≠ 0 )

then the x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

y = x² + 2x - 3 ← is in standard form

with a = 1, b = 2 , then

x = - \(\frac{2}{2}\) = - 1

substitute x = - 1 into the equation for corresponding y- coordinate

y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4

vertex = (- 1, - 4 )

this is an upward opening parabola ( a > 0 )

the axis of symmetry is a vertical line passing through the vertex with equation

x = c ( c is the value of the x- coordinate of the vertex ), then equation is

x = - 1

The third term of the arithmetic sequence is 18.

The arithmetic sequence formula can be represented as follows:

nth term = a + (n - 1)d

where

Therefore, 4 numbers are inserted between 4 and 39.

Hence,

a = 4

39 = 4 + 5d

39 - 4 = 5d

35 = 5d

d = 35 / 5

d = 7

Hence, the common difference of the arithmetic sequence is 7.

Therefore, the sequence of the arithmetic sequence is as follows:

4, 11, 18, 25, 32, 39

Therefore, the third term of the arithmetic sequence is  18

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Answer:

Your answer will be the third function

Step-by-step explanation:

The base function you need to know is h(t)= 1/2at^2

Your acceleration in this problem is going to be gravity which they give to you, 32 feet per second squared. Since the ball is falling, it means it will have negative acceleration. Now you have the equation h(t)= -16t^2. The final step is to add the initial height from which the ball was dropped giving you: h(t)= -16t^2 +12

Answer:

12394, −12322

Step-by-step explanation:

The population of interest is all students at her high school

The community or group that a researcher attempts to draw conclusions from is known as a population of interest. The surveyor is interested in learning additional information about a segment of the general population. Numerous research projects call for particular interest groups to make decisions in light of their findings.

When researching the opinions of students at her high school over the new school hours suggested by the school board, Kristen is interested in "all students at her high school." She wants to know what high school students think, and the only way to find out is to ask the students themselves. The other choices are incorrect because the study is focused on the opinions of the children at her school rather than theirs.

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Answer:

9c + 45

Step-by-step explanation:

The distributive property also known as distributive law of multiplication and division.

In the given expression, distributive law of multiplication is applied where we can multiply first before addition.

Given

9(c+5)

Using distributive property

9(c+5)

= (9 × c) + (9 × 5)

= 9c + 45

9(c+5) = 9c + 45

Answer:

slope = -10

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

Questions

6-(2x-4)=3x+5

Expanding the bracket

6-2x+4=3x+5

Rearranging the equation

6+4-2x=3x+5

10-2x=3x+5

Collecting like terms

10-5=3x+2x

5=5x

Dividing both sides by the quoefficient of x which is 5

5/5=5x/5

x=1

Answer:

Step-by-step explanation:

                            Mixed number          Improper fraction

a) 1 + 1 + 1/3 =            \(2\frac{1}{3}\)                                7/3

b) 1 + 1 + 1 + 5/8 =     \(3\frac{5}{8}\)                                 29/8

c) 1 + 1 + 1 +2/4 =      \(3\frac{2}{4}\)                                  14/4

Answer:

2x squared - 8

Step-by-step explanation:

For this kind of equation, we use the distributive property

So in the image below I used a box method (that's how I learned it in school)

So since -4x and 4x cancel each other out, or amount to 0, we don't put anything for those. So the equation left is 2x squared - 8

Answer: 41,224

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

The probability that X falls within 0.5 in. of the true mean is approximately 0.9042, or 90.42%.

To find the standard error of X (the sample mean), we can use the formula:

SE = σ / √n,

where σ is the population standard deviation and n is the sample size.

In this case, the population standard deviation (σ) is 2.65 in. and the sample size (n) is 81. Plugging these values into the formula, we get:

SE = 2.65 / √81 = 2.65 / 9 = 0.2944.

So, the standard error of X is approximately 0.2944 inches.

To find the probability that X falls within 0.5 in. of the true mean, we need to calculate the probability of observing a sample mean within that range. Since the population distribution is assumed to be normally distributed, we can use the properties of the normal distribution.

First, we need to calculate the z-scores corresponding to the upper and lower bounds of the range. The z-score can be calculated using the formula:

z = (x - μ) / (σ / √n),

where x is the upper or lower bound, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For the upper bound, we have:

z_upper = (μ + 0.5 - μ) / (2.65 / √81) = 0.5 / 0.2944 ≈ 1.698.

For the lower bound, we have:

z_lower = (μ - 0.5 - μ) / (2.65 / √81) = -0.5 / 0.2944 ≈ -1.698.

Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to these z-scores.

The probability of X falling within 0.5 in. of the true mean is given by:

Probability = P(-1.698 < Z < 1.698),

where Z is a standard normal random variable.

Using a standard normal distribution table or a calculator, we find that P(-1.698 < Z < 1.698) is approximately 0.9042.

Note: In this calculation, we assume that the sample is a simple random sample and that the sample size is sufficiently large for the Central Limit Theorem to apply.

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Based on the information provided, you have a closed-end lease.

A closed-end lease, also known as a "walk-away" lease or a "non-recourse" lease, is a type of lease where the lessee has no further financial obligations at the end of the lease term. In this case, you intend to turn in the car and not pay any additional amount based on the residual value of the car.

With a closed-end lease, the residual value of the car is predetermined at the beginning of the lease agreement. The residual value represents the estimated worth of the car at the end of the lease term. At the end of the lease, you have the option to return the car to the lessor without any additional payments, as long as you have complied with the terms and conditions of the lease agreement.

Unlike an open-end lease, where the lessee may be responsible for any difference between the actual value and the predetermined residual value, a closed-end lease provides more certainty and financial protection to the lessee.

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Answer:

121.9 squared centimeters

Step-by-step explanation:

Use the formula A = \(\frac{1}{2}\)h (\(b_{1} + b_{2}\)).

h = height

\(b_{1}\) = base 1

\(b_{2}\) = base 2

A = \(\frac{1}{2}\) (9.2) (18.2 + 8.3)

A = 121.9

Answer:

8, 9, and 10

Step-by-step explanation:

see attachment