An exponential function is represented in the table below.


Which equation best represents the function?

A. f(x)=3(2⁻ˣ)

B. f(x)=3(2ˣ)

C. f(x)=2⁻ˣ+3

D. f(x)=2ˣ+3

Answer:

6:1

Step-by-step explanation:

The ratio 12/2 is equivalent to the ratio 6/1, or 12:2 = 6:1 .

Answer:

27

Step-by-step explanation:

To determine if the value 5π/4 is a solution for the equation 3√(sin θ) + 2 = -1, we need to substitute the value of θ and verify if the equation holds true.

Let's substitute θ = 5π/4 into the equation:

3√(sin(5π/4)) + 2 = -1

Now, let's simplify the equation step by step:

First, let's evaluate sin(5π/4). In the unit circle, 5π/4 is in the third quadrant, where sin is negative. Additionally, sin(5π/4) is equal to sin(π/4) due to the periodic nature of the sine function.

sin(π/4) = 1/√2

Now, substitute the value of sin(π/4) back into the equation:

3√(1/√2) + 2 = -1

Simplifying further:

3√(1/√2) = 3 * (√(1)/√(√2)) = 3 * (1/√(2)) = 3/√2 = 3√2/2

Now the equation becomes:

3√2/2 + 2 = -1

To add fractions, we need a common denominator:

(3√2 + 4)/2 = -1

Since the left side of the equation is positive and the right side is negative, they can never be equal. Therefore, the equation is not satisfied, and 5π/4 is not a solution to the equation 3√(sin θ) + 2 = -1.

Thus, the statement "The value 5π/4 is a solution for the equation 3√(sin θ) + 2 = -1" is false.

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Answer:

V≈743.25

Step-by-step explanation:

V=5

12tan(54°)ha2=5

12·tan(54°)·4·182≈743.24624

A total of 1470 boxes are there all together if there are seven separate, equal-size boxes, and inside each box there are six separate small boxes, and inside each of the small boxes there are five even smaller.

Starting from the smallest boxes, we have 5 boxes inside each of the 6 small boxes, giving us a total of 5 x 6 = 30 boxes in each of the 7 medium boxes.

Therefore, there are a total of

30 x 7 = 210 boxes in the medium boxes.

Finally, we have 7 of these medium boxes, giving us a total of

210 x 7 = 1470 boxes in all.

Thus, there are a total of 1470 boxes altogether in the seven separate, equal-size boxes, each containing six separate small boxes, and each small box containing five even smaller boxes.

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Answer:

obtuse trianle

Step-by-step explanation:

triangle:

This type of triangle is an obtuse triangle

Step-by-step explanation:

To figure out how much smaller Max's sandbox is, we will divide 25 by 10, 25/10 = 2.5. Max's sandbox is 2.5 times smaller than the one in the park.

To find x we will divide 15 by 2.5 to keep the proportions the same, 15/2.5 = 6, so x = 6 feet.

To find y, we will do the same but with 12.5, 12.5/2.5 = 5, so y = 5 feet.

To find the perimeter, we will add all the sides together, 10 + 6 + 5 = 21, so the perimeter of Max's sandbox is 21 feet.

Hope this helps!

SRRC is a pulse shaping filter used in digital communications to minimize intersymbol interference and improve the signal-to-noise ratio.

The square root raised cosine (SRRC) is a famous heartbeat molding channel utilized in computerized correspondences, especially in applications like advanced tweak and demodulation. It is intended to limit intersymbol obstruction (ISI) by restricting the data transmission of the sent sign while keeping a consistent envelope.

The SRRC channel is described by a reaction that is like the raised cosine channel, yet with a square root capability applied to the recurrence reaction. This outcomes in a smoother change between the passband and stopband, which assists with decreasing ISI and work on the sign to-clamor proportion.

The SRRC channel is usually utilized in correspondence frameworks that utilization quadrature sufficiency regulation (QAM) or stage shift keying (PSK) tweak plans, as it gives great ghastly control and heartbeat molding properties that are appropriate to these kinds of signs.

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so your problem is 2x+y=18 and y=4x+6

solution

solve for the first variable in one of the equations then substitute the result into the other equation

point form:

(2,14)

equation form

x=2, y=14

The chance of selecting a card that is either red or has an even number is 10/11 or about 91%.

To find the probability of drawing a red card or an even-numbered card, we need to use the laws of probability. We can calculate the probability of each event separately and then add them together to get the probability of both events happening.

The probability of drawing a red card is 6/11, since there are 6 red cards out of a total of 11 cards.

The probability of drawing an even-numbered card is 5/11, since there are 5 even-numbered cards out of a total of 11 cards.

To find the probability of drawing a red card or an even-numbered card, we add the probability of drawing a red card and the probability of drawing an even-numbered card and then subtract the probability of drawing a card that is both red and even-numbered (i.e., the card numbered 2).

P(R or E) = P(R) + P(E) - P(R and E)

P(R or E) = 6/11 + 5/11 - 1/11

P(R or E) = 10/11

Therefore, the probability of drawing a red card or an even-numbered card is 10/11 or approximately 0.91.

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(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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The car travels 660 meters after 10 seconds of deceleration.

To solve this problem, we can use the formula: distance = initial velocity * time + (1/2) * acceleration * time^2. The initial velocity is 114 m/s, the time is 10 seconds, and the acceleration is -6 m/s^2 (negative because it represents deceleration). Plugging these values into the formula, we get:

distance = 114 * 10 + (1/2) * (-6) * 10^2

distance = 1140 - 300

distance = 840 meters

Therefore, the car travels 840 meters after 10 seconds of deceleration.

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To find her hourly rate we need to divide her total salary by the number of hours she worked. In this case we have:

Therefore, the balance in the account after 5 years is approximately $16,141.97.

To compute the balance in the account after 5 years with an APR of 4% and quarterly compounding, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A is the final account balance

P is the principal amount (initial investment)

r is the annual interest rate (as a decimal)

n is the number of times interest is compounded per year

t is the number of years

In this case, the principal amount is $14,000, the annual interest rate is 4% (or 0.04 as a decimal), the interest is compounded quarterly (n = 4), and the time period is 5 years.

Plugging in the values, we have:

A = 14000(1 + 0.04/4)^(4*5)

Simplifying:

A = 14000(1 + 0.01)^(20)

A = 14000(1.01)^20

Using a calculator, we can evaluate:

A ≈ $16,141.97

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The speed of the particle at t = π/4 is 1 m/s (option B). To find the speed of the particle at t = π/4, we need to calculate the magnitude of the velocity vector.

The velocity vector is given by the derivatives of x(t) and y(t) with respect to time (t).

Taking the derivatives of x(t) and y(t), we have:

dx/dt = 4 + 4sin(4t)

dy/dt = 4 - 4cos(4t)

Substituting t = π/4 into these derivatives, we get:

dx/dt = 4 + 4sin(π)

dy/dt = 4 - 4cos(π)

Since sin(π) = 0 and cos(π) = -1, we have:

dx/dt = 4

dy/dt = 8

The magnitude of the velocity vector is given by the square root of the sum of the squares of dx/dt and dy/dt:

|v| = √((dx/dt)^2 + (dy/dt)^2)

|v| = √((4)^2 + (8)^2)

|v| = √(16 + 64)

|v| = √80

|v| = 4√5

Therefore, the speed of the particle at t = π/4 is 4√5 m/s, which is approximately 1 m/s. The speed of the particle at t = π/4 is 1 m/s (option B).

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Answer:

\(\angle A = 32 \deg\)

\(\angle B = 105 \deg\)

\(\angle C = 94 \deg\)

\(\angle D = 138 \deg\)

Answer:

its upside down!!! but i can still see it..

The coordinates of B, considering the proportions in the context of the problem, are given as follows:

(4.33, 8).

The coordinates of B are obtained applying the proportions in the context of the problem.

BC is 50% longer than AB, hence point B is at one-third of the way from A to C, and thus the equation is given as follows:

B - A = 1/3(C - A).

The x-coordinate of B is then given as follows:

x - 1 = 1/3(11 - 1)

x - 1 = 3.33

x = 4.33.

The y-coordinate of B is then given as follows:

y - 3 = 1/3(18 - 3)

x - 3 = 5

y = 8.

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The value of the expression will be 1.

Sin⁶θ + cos⁶θ + 3 sin²θ cos²θ

It can be written as

=> (sin² θ)³ + (cos² θ)³ + 3 sin² θ cos² θ

We know that

a³+b³ = (a+b)³-3ab(a+b)

On applying this identity to the above expression

then

Where a = sin² θ and b = cos² θ

[(sin²θ+cos²θ)³-3sin² θ cos² θ(sin²θ+cos²θ)] +

3 sin² θ cos²θ

=> (1)³ - 3sin² θ cos² θ(1)] + 3 sin² θ cos²θ

Since, sin² θ + cos²θ = 1

=> 1 - 3sin² θ cos² θ+ 3 sin² θ cos²θ

=> 1

Therefore,sin⁶θ+cos⁶θ+3 sin²θ cos²θ = 1

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The question is incomplete, I attached a possible picture of it.

The value of the expression will be? ​

Answer:

Same

Step-by-step explanation:

Answer:

same

Step-by-step explanation:

If 484 of the disks produced by the first machine are acceptable and 480 of the disks produced by the second machine are acceptable, random , 10% and large counts are met. Correct option is E.

To calculate a confidence interval for the difference between the proportions of acceptable DVDs produced by two different fabricating machines, we need to ensure that the following conditions are met:

Random: The sample of DVDs from each machine should be selected randomly, without any bias. This is important to ensure that the sample is representative of the population of all DVDs produced by each machine.

The sample size should be no more than 10% of the population of DVDs produced by each machine. This is important to ensure that the sampling distribution of the sample proportions is approximately normal.

Large counts: The number of acceptable and unacceptable DVDs in each sample should be large enough to satisfy the normal approximation to the sampling distribution of the sample proportions.

Therefore, the correct answer is (e) Random: met, 10%: met, Large Counts: met. All conditions for calculating a confidence interval for the difference between the proportions of acceptable DVDs produced by two different fabricating machines are met in this scenario.

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-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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The scale factor that Thea uses to go from Rectangle Q to Rectangle R is equal to 6.

In geometry, the scale factor is a ratio of the resulting length to the initial length. Since the area of the square is equal to the square of its side length, then the scale factor is equal to:

k² = A' / A

k = √(A' / A)

Where:

If we know that A = 2 and A' = 72, then the scale factor is:

k = √(72 / 2)

k = √36

k = 6

Then, the scale factor that Thea uses to go from Rectangle Q to Rectangle R is equal to 6.

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Answer:

b :)

Step-by-step explanation:

brain list pls

Answer:

yes the ordered pair is a solution

Step-by-step explanation:

(x, y) = (0,0)

y < -x + 3

0 < - (0) + 3  

0 < 3

true, ordered pair is a solution

Options a, b, d, and g are the correct conditions for a Binomial Distribution.

The four conditions necessary for X to have a Binomial Distribution are:

a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.

b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.

d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.

g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.

The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.

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The probability that the first song is by Drake and the second song is by BTS is 1/6 or approximately 0.1667.

To calculate the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

Since there are four songs on the playlist, there are 4! (4 factorial) ways to arrange them, which is equal to 4 x 3 x 2 x 1 = 24. This represents the total number of possible orders in which the songs can be played.

Number of favorable outcomes:

To satisfy the condition that the first song is by Drake and the second song is by BTS, we fix Drake as the first song and BTS as the second song. The other two artists (Ed Sheeran and Cardi B) can be placed in any order for the remaining two songs. Therefore, there are 2! (2 factorial) ways to arrange the remaining artists.

Calculating the probability:

The probability is given by the number of favorable outcomes divided by the total number of possible outcomes: P = favorable outcomes / total outcomes = 2 / 24 = 1/12 or approximately 0.0833.

For the second part of the question, if P(BC) = 0.5, we need to find P(B). However, the given information is insufficient to determine the value of P(B) without additional information about the relationship between events B and BC.

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