Which recursively defined function represents the sequence?.

The exponential function y = \(3^x\) grows at a faster rate than the quadratic function for x > 0.

The exponential function that grows at a faster rate than the quadratic function for x > 0 is y = \(3^x\).

To see why, let's first look at the rate of change of the quadratic function.

We can find this by looking at the differences between consecutive y-values:
1 - 0 &= 1
3 - 1 &= 2
12 - 3 &= 9
27 - 12 &= 15
$$We can see that the rate of change is increasing as x increases.

For example, the rate of change between the first two points is 1, while the rate of change between the last two points is 15.

However, this rate of change is still constant within each interval of x-values.

y = \(3^x \\\)  

Let's take a look at its y-values for the same x-values as in the table:
\(3^0\) &= 1

\(3^1\) &= 3
\(3^2\) &= 9
\(3^3\) &= 27
$$We can see that the rate of change is not constant, but rather increasing, just like in the quadratic function.

However, the rate of change is greater for y = \(3^x\).

For example, the rate of change between the first two points is 2, while the rate of change between the last two points is 18.

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The distance the slower and faster car travelled are 360 km and 432 km respectively.

Two cars start at the same time from two towns 792 kilometres apart and meet in 9 hours.

One car can travel 8 km faster than the other car.

let

x = speed of the slower car

x + 8 = speed of the faster car

The cars meet in 9 hours and both cover a distance of 792 km.

Therefore,

speed = distance / time

distance = time × speed

Hence,

9x + 9(x + 8) = 792

9x + 9x + 72 = 792

18x = 792 - 72

18x = 720

divide both sides by 18

x = 720 / 18

x = 40

Therefore,

speed of the slower car = 40 km per hour

speed of the faster car = 48 km per hour

Hence,

how far the slower car go(distance) = 40 × 9 = 360 km

how far the faster car go(distance) = 48 × 9 = 432 km

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Answer:

Step-by-step explanation:

ITS RATIONAL!

Answer:

Rational

Explanation:

0.8 can be expressed as the ratio of two integers which is the definition of a rational number.

The error kelly made was that sin f is h/e and g = EF

The area of a triangle is given by 1/2 base × height. In the triangle base is g and height is h

In trigonometry, sin(tetha) =[opp/ hypotenuse)

cos (tetha) = adj/hypotenuse

tan(tetha) = opp/ hypotenuse

sinF = e/h

sinE = h/f

this two does not have g at all. so we either use tan or cos.

g is divided into two, let's name it g1 and g2

cos F = g1/e

cos E = g2/f

g1 = e(cos F)

g2 = f(cos E)

g = g1+g2

g = e(cos F) + f(cos E)

A = 1/2bh

A = 1/2 ×( e( cos F) + f(cos E) ) h

Therefore the actual value of the area is /2 ×( e( cos F) + f(cos E) ) h

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As there is less ambiguity when the population's standard deviation is known, the z interval with a value of 2.57 is preferable (the interval is too wide).

However, there is more uncertainty when the standard deviation is unknown, thus the t interval of 1.96 is more reasonable (the z-interval is too small). A z interval is a special kind of confidence interval that provides a range of possible values for a given mean or proportion. It can be determined using a standard deviation that is known. Calculate a t-interval when you don't know the standard deviation but still need to obtain a confidence interval. The only difference is that the interval is calculated using a different table: a t-table for a t-interval and a z-table for a z-interval. For more on the exact distinctions between the “T” and “Z”, see: T-scores vs. Z-scores.

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Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, Gregg cut 4 sections of pizza dough.

The first term, a1, in the geometric series is -3.

What is Geometric Series?

A geometric series is a series for which the ratio of two consecutive terms is a constant function of the summation index. The more general case of a ratio and a rational sum-index function produces a series called a hypergeometric series. For the simplest case of a ratio equal to a constant, the terms have the form

To find the first term, a1, in a geometric series given the sum, Sn = 93, the common ratio, r = 2, and the number of terms, n = 5, we can use the formula for the sum of a geometric series:

Sn = a1 * (1 - r^n) / (1 - r)

Plugging in the given values, we have:

93 = a1 * (1 - 2^5) / (1 - 2)

Simplifying the expression:

93 = a1 * (1 - 32) / (-1)

93 = a1 * (-31)

Now we can solve for a1 by dividing both sides of the equation by -31:

a1 = 93 / -31

a1 = -3

Therefore, the first term, a1, in the geometric series is -3.

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Answer:

A (c=1,900-163-259)

Step-by-step explanation:

This is right because this equation follows the PEMDAS rules in order to get the correct answer.

Answer:

False

Step-by-step explanation:

supplementary means 180 and right angle is 90 so 180-90 gives us 90 which is also a right angle. So false, acute angle is when the angle is less than 90. If it is excatly 90 then that would be right angle.

Answer:

3 horses and 4 ducks

Step-by-step explanation:

let h be the no. of horses and d be the no. of ducks

h+d=7

d=7-h

Since horses have 4 legs and ducks have 2 legs,

4h+2d=20

4h+2(7-h)=20

4h+14-2h=20

2h=6

h=3

d=4

50

(-1) + 2 + (-3) + 4 + ... + (-99) + 100 =

= 2 - 1 + 4 - 3 + .. + 100 - 99

= 1 + 1 + .. + 1

= 50×1

= 50

Answer:

50.

Step-by-step explanation:

Each pair of numbers add up to 1:

-1 + 2 =  1,  -3 + 4 = 1   and so on

There are 50 of theses pairs so the value is 50.

Answer:

yes, it is correct

Step-by-step explanation:

12 = 1/3 (21) + 5

12 = 5 + 7

12 = 12

yes

in the formula, =1+(2-3)+5/6-6^2,  The final result of the formula is -35.1667.

In the formula =1+(2-3)+5/6-6^2, the order of operations dictates that the exponentiation operator (^) is evaluated first, followed by multiplication and division from left to right, and then addition and subtraction from left to right.

So, access will evaluate 6^2 first, which equals 36. Then, it will evaluate the division 5/6, which equals 0.8333 (rounded to four decimal places).

Next, it will evaluate the subtraction (2-3), which equals -1. Then, it will evaluate the addition (1+(-1)), which equals 0. Finally, it will evaluate the multiplication (-6 * 6), which equals -36.

Putting it all together, we get:

=1 + (2-3) + 5/6 - 6^2

= 1 + (-1) + 0.8333 - 36

= -35.1667

Therefore, the final result of the formula is -35.1667.

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Answer:

thank you for points

Step-by-step explanation:

Answer:

(2 × 3 × 3) and (2 × 2 × 2 × 3).

2.15 is  value of binomial distribution and 2.15 is value of standard deviation.

In statistics, what is a binomial distribution?

The possibility that a variable would take one of two independent values under a certain set of factors or assumptions is expressed by the statistical distribution known as the binomial distribution.

                                 As an illustration, there are only two conceivable results from tossing a coin: heads or tails, and there are only two outcomes from taking a test: success or failure. The term "binomial probability distribution" is sometimes used to describe this distribution.

Given that,

p = 0.2

q = 1 - p =1-0.2=0.8

n = 29

Using binomial distribution,

  Standard deviation = σ = √n * p * q

                                          = √29 * 0.2 * 0.8 = 2.15

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The complete question is -

Find the standard deviation, σ, for the binomial distribution which has the stated valuesof n and p. Round your answer to the nearest hundredth.

n = 29; p = 0.2

σ = 2.15

σ = 6.27

σ = -0.26

σ = 5.42

Answer:

Step-by-step explanation:

We know that:

Work:

Now, let's substitute the value of b into any equation.

Hence, Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

Hoped this helped.

\(BrainiacUser1357\)

We can use the fact that 32 is equal to 2 raised to the power of 5:

32 = 2^5

Substituting this into the equation gives:

16^x = 2^5

We can then rewrite 16 as 2^4, since 16 is equal to 2 raised to the power of 4:

(2^4)^x = 2^5

Simplifying the left side of the equation gives:

2^(4x) = 2^5

Now we can see that the bases of both sides of the equation are equal, so we can set the exponents equal to each other:

4x = 5

Dividing both sides by 4 gives:

x = 5/4

Therefore, the solution to the equation 16^x = 32 is x = 5/4.

Answer:

y24

Step-by-step explanation:

Answer:

y24

Step-by-step explanation:

The value of an 8 in the tens place as a fraction of an 8 in the hundreds place is 1 / 10.

In the number system we use, each digit's value is determined by its position and is ten times the value of the digit to its right. Therefore, the value of an 8 in the tens place is 10 times the value of an 8 in the ones place.

Likewise, the value of an 8 in the hundreds place is 10 times the value of an 8 in the tens place, which in turn is 10 times the value of an 8 in the ones place. Therefore, the value of an 8 in the hundreds place is 10 x 10 times the value of an 8 in the ones place.

So in equation form, we have:

= 8 / 80

= 1 / 10

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Answer:

He makes 4 snowmen

Step-by-step explanation:

please mark brainliest

Answer:

It would be the first answer choice, 18+54

Step-by-step explanation:

6(3+9

6x3=18

6x9=54

18+54 would be the equation.

Please pick me for brainliest

Answer:

a

Step-by-step explanation:

If a hypothesis test is performed and fails to reject the null hypothesis, it would mean that there is not enough evidence to support the claim that less than 15% of the marketing organization's employees are paid minimum wage.

Therefore, it would not be concluded that the claim is true. The null hypothesis assumes that the claim is false or that the percentage of employees paid minimum wage is not significantly different from 15%.

The failure to reject the null hypothesis means that the evidence does not contradict the null hypothesis, but it does not necessarily prove it to be true.

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The variance of the discrete random variable X is equal to 70t.

The variance of discrete random variable X is given by Var(X) = E[X2] – (E[X])2. In this case, the probability function is given as P(X = k) = t (6 – k) for k = 1, 2, 3, 4, 5. Therefore, the expected value of X is the sum of the products of each possible value of X and its corresponding probability. This can be calculated as:

E[X] = 1 x P(X = 1) + 2 x P(X = 2) + 3 x P(X = 3) + 4 x P(X = 4) + 5 x P(X = 5)

E[X] = t (6 - 1) + 2t (6 - 2) + 3t (6 - 3) + 4t (6 - 4) + 5t (6 - 5)

E[X] = t (5) + 2t (4) + 3t (3) + 4t (2) + 5t (1)

E[X] = 5t + 8t + 9t + 8t + 5t

E[X] = 35t

The expected value of X2 is the sum of the products of each possible value of X and its corresponding probability, multiplied by X2. This can be calculated as:

E[X2] = 1 x P(X = 1) x (1)2 + 2 x P(X = 2) x (2)2 + 3 x P(X = 3) x (3)2 + 4 x P(X = 4) x (4)2 + 5 x P(X = 5) x (5)2

E[X2] = t (6 - 1) x (1)2 + 2t (6 - 2) x (2)2 + 3t (6 - 3) x (3)2 + 4t (6 - 4) x (4)2 + 5t (6 - 5) x (5)2

E[X2] = t (5) x (1)2 + 2t (4) x (2)2 + 3t (3) x (3)2 + 4t (2) x (4)2 + 5t (1) x (5)2

E[X2] = 5t + 16t + 27t + 32t + 25t

E[X2] = 105t

Therefore, the variance of X is given by Var(X) = E[X2] – (E[X])2 = 105t – (35t)2 = 70t.

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The probability that the two pets selected are of the same species  is 0.2426   .

In the question ,

it is given that ,

the number of puppies in the pet store = 6

the number of kittens in the pet store = 9

the number of lizards in the pet store = 4

the number of snakes in the pet store = 5

total animals = 24

the probability of selecting 2 puppies = ⁶C₂/²⁴C₂

the probability of selecting 2 kittens = ⁹C₂/²⁴C₂

the probability of selecting 2 lizards = ⁴C₂/²⁴C₂

the probability of selecting 2 snakes = ⁵C₂/²⁴C₂

So , the required probability is

= ⁶C₂/²⁴C₂  + ⁹C₂/²⁴C₂ + ⁴C₂/²⁴C₂  + ⁵C₂/²⁴C₂  

Simplifying further ,

we get ,

= 5/92 + 3/23 + 1/46 + 5/138

= 0.0543 + 0.1304 + 0.0217 + 0.0362

= 0.2426

Therefore , the required probability is 0.2426   .

The given question is incomplete , the complete question is

The pet store has 6 puppies , 9 kittens , 4 lizards and 5 snakes . if you select two pets from the store randomly, what is the probability that they are both the same species ?

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the sample is truly representative of all horses in the state, and that there are no biases or confounding factors that might affect the proportion of stallions in the sample.

If we assume that the horses constitute a random sample of all horses in the state, then we can estimate the probability that a randomly selected horse is a stallion by calculating the proportion of horses in the sample that are stallions. Let's assume that we have a sample of n horses, and that x of these horses are stallions. Then the estimated probability of selecting a stallion is:

x/n

For example, if we had a sample of 100 horses and 25 of them were stallions, the estimated probability of selecting a stallion would be:

25/100 = 0.25 or 25%

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