Which square root could be the number shown on the number line?
O A. √15
O B. √17
O C. √26
O D. √24

Answer:

From sin²θ + cos²θ = 1, we have;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ

Step-by-step explanation:

The given equation is (sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ

We have;

(sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ gives;

(sin⁴θ + cos⁴θ) + 2 sin²θ·cos²θ= 1

Which is equivalent to sin⁴θ + 2 sin²θ·cos²θ +cos⁴θ  = 1

From which we can get;

(sin²θ + cos²θ)·(sin²θ + cos²θ)  = 1

Given that sin²θ + cos²θ = 1

Therefore;

1 × 1 = 1

To get to the initial equation in the question, we have;

sin²θ + cos²θ = 1

(sin²θ + cos²θ) × (sin²θ + cos²θ) = 1

(sin⁴θ + sin²θ·cos²θ + sin²θ·cos²θ + cos⁴θ = 1

∴ sin⁴θ + cos⁴θ = 1 - sin²θ·cos²θ + sin²θ·cos²θ  = 1 - 2·sin²θ·cos²θ

Therefore;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ.

Answer:

Ermmm.. What is a integer?

Step-by-step explanation:

Someone explain please

Answer:

x= -4

Step-by-step explanation:

2^x =1/16

2^x = 2^-4

x= -4

Given problem represent Fundamental Counting Theorem.

Fundamental Counting Theorem states that if an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m×n.

Here Taylor has 5 baskets and there are 6 balls in each basket.

That is m = 5 and n = 6

Therefore Taylor have m×n= 5×6 =30 balls

Hence here we use Fundamental counting theorem.

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The American Housing Survey is conducted annually by the Bureau of the Census to gather data on the distribution of occupied housing units in the United States.

Using data from the 2003 survey, the distribution of occupied housing units by the number of rooms can be found. To visualize this data, histograms can be drawn separately for owner-occupied and renter-occupied units.

It is important to note that "10 or more" mean 10 or 11, as very few units have more than 11 rooms.

(a) The This could be due to rounding errors or differences in sample sizes between the two groups.

(b) The percentage of one-room units is much smaller for owner-occupied housing. This is not necessarily because there are more owner-occupied units in total, but could be due to differences in the length preferences and financial means of renters versus owners.

(c) It is unclear which group, on the whole, has larger units without additional information about the distribution of rooms.

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By using the basic comparison test and limit comparison test for the series: 3Σn=1 to ∞ a₁n³e⁻ⁿ², The number π²/2 is a finite number, and the series 3Σn=1 to ∞ a₁n³e⁻ⁿ² is convergent.

Part 1: We need to identify whether the given series is converging or diverging.

Part II: We can use the basic comparison test to test the convergence of the given series. Let's compare the given series with another series that is easily recognizable and convergent. For

n ≥ 1, a₁n³e⁻ⁿ² > 0

We know that the series Σ a₁n³e⁻ⁿ² is convergent, which means that the sequence of terms must be converging to zero as well. This can be shown using the following limit statement.

lim n→∞ a₁n³e⁻ⁿ² = 0.

By comparing the series with a simpler convergent series, we can prove that the series is convergent. The simpler convergent series can be represented by the expression 3Σn=1 to ∞ 1/n². This series is known as the p-series with p = 2. We can use this series to perform a comparison test.

Let Sn be the nth partial sum of the given series. Thus,

3Σn=1 to ∞ a₁n³e⁻ⁿ² ≤ 3Σn=1 to ∞ 1/n²

Let's evaluate the second series using the formula for the sum of a p-series:

Σn=1 to ∞ 1/n² = π²/6

Thus, 3Σn=1 to ∞ a₁n³e⁻ⁿ² ≤ 3 x π²/6

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Step-by-step explanation:

once to understand how a function works, these are the most trivial questions to solve.

a function works that when you have a specific value for the input variable (here x), then you replace the name of the variable everywhere by that survival value. and then you simply calculate the result

p(-4) = 2×-4 - 5 = -8 - 5 = -13

that's it. there is nothing more to it.

Answer:

\(\huge\boxed{x^3-y^3=508}\)

Step-by-step explanation:

\(\underline{+\left\{\begin{array}{ccc}x+y=10\\x-y=6\end{array}\right}\qquad|\text{add the sides of the equations}\\.\qquad2x=16\qquad|\text{divide both sides by 2}\\.\qquad\boxed{x=8}\\\\\text{Substitute it to the first equation}\\8+y=10\qquad|\text{subtract 8 from both sides}\\\boxed{y=2}\\\\x^3-y^3=8^3-2^3=512-8=504\)

Answer:

A

Step-by-step explanation:

They are paid a fix rate for each item produced or action performed

The correct answer is the quadrant that contains no solutions to the system of inequalities is Quadrant IV.

To determine which quadrant contains no solutions to the system of inequalities, let's analyze each quadrant in the xy-plane.

Quadrant I: In this given quadrant, both x and y values are positive. Let's substitute values to check the inequalities:

For x = 1 and y = 1, we have:

y ≥ 2x + 1 ⟹ 1 ≥ 2(1) + 1 ⟹ 1 ≥ 3 (False)

y > 1/2x - 1 ⟹ 1 > 1/2(1) - 1 ⟹ 1 > 1/2 - 1 ⟹ 1 > -1/2 (True)

Since one inequality is false and the other is true, Quadrant I contains no solutions to the system.

Quadrant II: In this quadrant, x values are negative, and y values are positive. Substituting values:

For x = -1 and y = 1, we have:

y ≥ 2x + 1 ⟹ 1 ≥ 2(-1) + 1 ⟹ 1 ≥ -1 (True)

y > 1/2x - 1 ⟹ 1 > 1/2(-1) - 1 ⟹ 1 > -1/2 - 1 ⟹ 1 > -3/2 (True)

Both inequalities are true, so Quadrant II contains solutions to the system.

Quadrant III: In this quadrant, both x and y values are negative. Substituting values:

For x = -1 and y = -1, we have:

y ≥ 2x + 1 ⟹ -1 ≥ 2(-1) + 1 ⟹ -1 ≥ -1 (True)

y > 1/2x - 1 ⟹ -1 > 1/2(-1) - 1 ⟹ -1 > -1/2 - 1 ⟹ -1 > -3/2 (True)

Both inequalities are true, so Quadrant III contains solutions to the system.

Quadrant IV: In this quadrant, x values are positive, and y values are negative. Substituting values:

For x = 1 and y = -1, we have:

y ≥ 2x + 1 ⟹ -1 ≥ 2(1) + 1 ⟹ -1 ≥ 3 (False)

y > 1/2x - 1 ⟹ -1 > 1/2(1) - 1 ⟹ -1 > 1/2 - 1 ⟹ -1 > -1/2 (True)

Since one inequality is false and the other is true, Quadrant IV contains no solutions to the system.

Therefore, the quadrant that contains no solutions to the system of inequalities is Quadrant IV.

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The correct question is-

If the system of inequalities y≥2x+1 and y> 1/2x−1 is graphed in the xy-plane above, which quadrant contains no solutions to the system?

The dimensions of the rectangle is 25m × 25m.

Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth.

The three dimensions of a three-dimensional shape are length, width, and depth.

It is given that

Perimeter of the rectangle = 100m

Area is as large as possible if both the values are the same number.

The measurements must be equivalent for the rectangle to attain its maximum area.

Consider the dimensions as x

So perimeter can be written as

2 (x + x) = 100

2 (2x) = 100

By additional computation

4x = 100

Divide both sides by 4

x = 25

Therefore, the dimensions of a rectangle is 25m × 25m.

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After 17 tosses, you would expect to gain $7.50. In each toss, there are two possible outcomes: heads or tails. If the coin comes down heads, you win $2, and if it comes up tails, you lose $0.50.

Since the probability of getting heads or tails in a fair coin toss is equal (0.5), we can calculate the expected gain by multiplying the probability of each outcome by its corresponding value and summing them up.

For each toss, the expected gain is calculated as (0.5 * $2) + (0.5 * -$0.50) = $1.25. Therefore, after 17 tosses, the total expected gain is 17 * $1.25 = $21.25. However, since you start with zero dollars, the net gain would be $21.25 - $14.75 = $7.50. Thus, you would expect to gain $7.50 after 17 tosses.

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According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

$ 80.73

Step-by-step explanation:

You can find the complete solution in the given attachment

The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

A random sample is drawn from a population with mean μ=73 and standard deviation σ=6.1. To determine if the sampling distribution of the sample mean with n=18 and n=46 is normally distributed, we need to calculate the standard error for each sample size.

For n=18:
The standard error (SE) is calculated using the formula:

     SE = σ / √n
SE = 6.1 / √18

          ≈ 1.441 (rounded to 3 decimal places)

For n=46:
SE = 6.1 / √46 ≈ 0.901 (rounded to 3 decimal places)

To determine if the sampling distribution of the sample mean is normally distributed, we need to consider the Central Limit Theorem (CLT). According to the CLT, when the sample size is sufficiently large (typically n > 30), the sampling distribution of the sample mean tends to be approximately normally distributed, regardless of the shape of the population distribution.

Since both n=18 and n=46 are larger than 30, we can conclude that the sampling distribution of the sample mean with these sample sizes is approximately normally distributed.

Therefore, the sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

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Answer:

Sum of 100 terms of the sequence = 15050

Step-by-step explanation:

Given expression which represents a sequence is,

\(\sum_{r=1}^{100}(3r-1)\)

So the sequence will be,

2, 5, 8, 11, 14..........

So, the given sequence is an arithmetic sequence with,

First term of the sequence 'a' = 2

Common difference 'd' = 5 - 2 = 3

Sum of 'n' terms of an arithmetic sequence is given by,

\(S_n=\frac{n}{2}[2a+(n-1)d]\)

Here, n = number of terms

a = first term

d = common difference

\(S_{100}\) = \(\frac{100}{2}[2(2)+(100-1)(3)]\)

      = 50[4 + 297]

      = 15050

Therefore, sum of 100 terms of the sequence = 15050  

The solution is: 1) rate = 80 km/h and, 2.) rate = 15 km/h.

Here, we have,

given that,

1.) distance = 280 km

   time = 3.5 hours.

2.) distance = 7.5 km

   time = 30 mints.

now, we have to find the rate i.e. speed.

we know that,

Speed = Distance/ Time.

so, we get,

1.) distance = 280 km

   time = 3.5 hours.

so, rate = 280/3.5 = 80 km/h

2.) distance = 7.5 km

   time = 30 mints. = 1/2 hours

so, rate = 7.5/ 1/2 = 15 km/h

Hence, The solution is: 1) rate = 80 km/h and, 2.) rate = 15 km/h.

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Therefore , the solution of the given problem of speed comes out to be Tory will never keep pace to Juan because Juan has a one-minute head start on him.

We can estimate something's pace by observing it from a distance. The amount of distance an object can move in a specific amount of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most popular units of speed are miles per hour (mpg), kilometres per hour (kilometres), and metres for every second (m/s) (mph).

Here,

To resolve this issue, we can use the formula distance = rate x duration.

Assume Juan runs for t minutes prior to Tory beginning to run. Juan travels 704 feet in that period of time.

Juan has already travelled 704 feet when Tory begins to sprint. Since that time, Juan and Tory have been moving at the same pace of 704 feet per minute.

Suppose Tory needs x minutes to make up to Juan. In that period of time, Tory travels 704 feet.

Juan and Tory have travelled the same distance overall because they meet at the same location. Thus, we can construct the following equation:

=> 704t = 704x

If we simplify, we get:

=> t = x

Tory will never keep pace to Juan because Juan has a one-minute head start on him.

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Answer:

What is the question?

Step-by-step explanation:

Comment it

Answer:

same i feel you bru

Step-by-step explanation:

i'm actually, uh, procrastinating on brainly. can i vent? actually i will anyways so here: i have an science quiz on space and the moon phrases and i barely payed attention in class so i don't even know how to solve half of the problems. i normally always do ok on quizzes but i feel like this one is different and i'm going to fail. it's due by today at midnight and i'm procrastinating on brainly to take my mind away from reality. i know i'm being a total coward by trying to avoid what is my own consequences but... here i am haha ;-; it would be better if i at least started studying now even if it's short  to get my grade up just a little but i'm scared to even look at the quiz. i also have a lot of homework and an essay that's due tomorrow that i haven't started on yet... and yet i procrastinate. i don't understand myself and sometimes i want to cry because i don't know why i'm like this. i feel like the more homework i get, the more i procrastinate. i'm miserable really.

Answer:

cos(11π/3) = 1/2

Explanation:

To find the value of cos(11π/3), we first need to find a coterminal angle. This is because 11π/3 is greater than 2π, which is the angle of the complete circle. Then, we can find the coterminal angle as

11π/3 - 2π = 5π/3

Now, we need to find cos(5π/3), so we will use the unit circle as follows

Therefore, the value of cosine is the first coordinate of the point in the unit circle. It means that

cos(5π/3) = 1/2

Then, cos(11π/3) = 1/2

So, the answer is

cos(11π/3) = 1/2

Yes, it's possible. We need to consider alternative explanations.

It's possible that the new computer skills caused the better outcome for these welfare recipients, but it's also important to consider other factors that may have contributed to the improved outcomes. Some alternative causal explanations could include:

Selection bias: It's possible that the welfare recipients who chose to participate in the computer skills class were already more motivated and/or had more job-relevant skills than those who did not participate. This could explain why they were more likely to get off welfare and find a job.

Unobserved variables: There may be other factors that influenced the outcomes for these welfare recipients, such as their level of education, their personal networks, or their prior work experience. These factors could have contributed to their success in finding employment.

Reverse causality: It's also possible that the improved outcomes for these welfare recipients were a result of finding a job, rather than the computer skills class causing them to find a job. In other words, finding a job may have motivated these individuals to take the computer skills class, rather than the class causing them to find a job.

Therefore, It's important to carefully consider these and other potential explanations when trying to understand the causal relationship between the computer skills class and the improved outcomes for these welfare recipients.

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Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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Step-by-step explanation:

Hi Ariana. There is no solution to this question as no line has the equation 2x-3y=92x-3y=9. Perhaps you copied wrongly. Kindly look at the source and come again for assistance

An ordered pair is a solution of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.

In mathematics, an equation in two variables represents a relationship between two quantities. An ordered pair consists of two values, typically denoted as (x, y), that represent the coordinates of a point in a two-dimensional plane.

When these values are substituted into the equation, if the equation holds true, then the ordered pair is considered a solution or a solution set to the equation. This means that the relationship described by the equation is satisfied by the values of the ordered pair. In other words, the equation is true when evaluated with the values of the ordered pair.

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Answer:

A' = (-3, 0)

Step-by-step explanation:

The coordinates of point A are (-6, 2).

The translation adds 3 to x and subtracts 2 from y.

A'(-6 + 3, 2 - 2) = A'(-3, 0)

Answer: A' = (-3, 0)

Answer:

Step-by-step explanation:

yeah

Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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Answer:

Step-by-step explanation:

Answer:

2%

Step-by-step explanation: