use a direct proof to show that every odd integer is the difference of two squares. [hint: find the difference of the squares of k 1 and k where k is a positive integer.]

The divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

To find the divergence and curl of the vector field F(x, y, z) = x²yi - (2²-3x) 5+uy³k, we can use vector calculus operations.

The divergence of a vector field measures the rate of outward flow from an infinitesimally small region surrounding a point. It is calculated using the divergence operator (∇·F), which is the dot product of the gradient (∇) with the vector field F. In this case, the divergence of F can be found as follows:

∇·F = (∂/∂x)(x²yi) + (∂/∂y)(- (2²-3x) 5+uy³k) + (∂/∂z)(0)

      = 2xyi - 15(2²-3x) 4+uy³k

The curl of a vector field measures the rotation or circulation of the field around a point. It is calculated using the curl operator (∇×F), which is the cross product of the gradient (∇) with the vector field F. In this case, the curl of F can be found as follows:

∇×F = (∂/∂x)(0) - (∂/∂y)(x²yi) + (∂/∂z)(- (2²-3x) 5+uy³k)

      = 0 - x²yi - 15u³k

Therefore, the divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

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The function h(t) = -16t^2 + 75 is a quadratic function, and the stick hits the ground at about 2.165 seconds

The function is given as:

h(t) = -16t^2 + 75

Next, we plot the graph of the function h(t)

From the graph of the function h(t) (see attachment), we have the following highlight:

t = -2.165 and t = 2.165 when h(t) = 0

Time cannot be negative.

So, we have:

t = 2.165

This means that the stick hits the ground at about 2.165 seconds

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Answer:

g(5) = -19

Step-by-step explanation:

Substitute 5 for x in the equation

Plug in 5 for the x's and get g(x)=-3(5)-4 and then -15-4 which is -19 so g(x)=-19

The formula for the standard error is: standard deviation / square root of sample size. In this case, since the population standard deviation is provided as ? = 226.83 and we are dealing with a sample size of 12 states, the standard error can be calculated as 226.83 / sqrt(12) = 65.49.

Compared to the standard deviation of the population, the standard error is much smaller. This is because the standard error takes into account the size of the sample, which reduces the variability in the estimates.
The shape of the sampling distribution is assumed to be normal due to the Central Limit Theorem, which states that as the sample size increases, the sampling distribution will approach a normal distribution regardless of the underlying population distribution.
To reduce the standard error, increasing the sample size would be the most effective method. This would reduce the variability in the estimates and provide a more accurate representation of the population. Additionally, ensuring that the sample is representative of the population and using random sampling methods can also help to reduce the standard error.

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The formula for the standard error is: standard deviation / square root of sample size. In this case, since the population standard deviation is provided as ? = 226.83 and we are dealing with a sample size of 12 states, the standard error can be calculated as 226.83 / sqrt(12) = 65.49.

Compared to the standard deviation of the population, the standard error is much smaller. This is because the standard error takes into account the size of the sample, which reduces the variability in the estimates.
The shape of the sampling distribution is assumed to be normal due to the Central Limit Theorem, which states that as the sample size increases, the sampling distribution will approach a normal distribution regardless of the underlying population distribution.
To reduce the standard error, increasing the sample size would be the most effective method. This would reduce the variability in the estimates and provide a more accurate representation of the population. Additionally, ensuring that the sample is representative of the population and using random sampling methods can also help to reduce the standard error.

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Answer:

$16.7

Step-by-step explanation:

501 dollars/1 week·1 week/30 hours

The weeks cancel out leaving 501 dollars/30 hours which can be simplified to $16.7 per hour

The evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8.

Let us evaluate ∫30(4f(t) - 6g(t)) dt.

Therefore,∫30(4f(t) - 6g(t)) dt = ∫30(4f(t) dt - 6g(t) dt) = 4 ∫30f(t) dt - 6 ∫30g(t) dt

Now, using the given values in the question we can say that,∫30(4f(t) - 6g(t)) dt = 4 ∫30f(t) dt - 6 ∫30g(t) dt = 4 (-8) - 6(8) = -32 - 48 = -80

Therefore, the evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Note: The given integrals ∫150f(t) dt, ∫30f(t) dt, ∫150g(t) dt, and ∫30g(t) dt are only intermediate steps in order to evaluate the final integral.

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Answer:

She knows that in the last week 30 customers paid cash, 40 custo… ... paid cash, 40 customers used a debit card, and 6 customers used a credit card. Based on these results, express the probability that the next customer will pay with something other than a debit card as a decimal to the nearest hundredth.

Step-by-step explanation:

Answer:

║⊕║·····∧····∨····Hola :D····∨····∧····║⊕║

Your answer should be:

47.37% or 36/76 as a fraction

Step-by-step explanation:

Hope this helped!

Brainliest appreciated!

Have a great day! :D

Answer:

The correct value is t* = 2.492.

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.98}{2} = 0.99\). So we have T = 2.492, which is the answer to this question.

The expected value of the sample sum of the ticket labels in 11 independent random draws with replacement from the box is -19.67 (option b.)

To find the expected value of the sample sum of the ticket labels in 11 independent random draws with replacement from the box, we can calculate the average of all possible sample sums.

Given that the box contains 12 tickets with the following numbers: -9, -9, -8, -8, -5, -5, -4, 3, 6, 6, 6, 7, we can find all the possible sample sums and their probabilities.

Let's denote the ticket labels as X1, X2, ..., X12.

To calculate the expected value, we sum up the product of each sample sum and its corresponding probability.

Expected value = Sum of (Sample sum * Probability)

The sample sums and their probabilities are as follows:

Sample sum: -9 + -9 + -8 + -8 + -5 + -5 + -4 + 3 + 6 + 6 + 6 = -43

Probability: (2/12)^11 = 0.00000017166 (There are 2 "-9" tickets and 12 total tickets in the box)

Sample sum: -9 + -9 + -8 + -8 + -5 + -5 + -4 + 3 + 6 + 6 + 7 = -42

Probability: (2/12)^10 * (1/12) = 0.0000017166 (There are 2 "-9" tickets, 1 "7" ticket, and 12 total tickets in the box)

Sample sum: -9 + -9 + -8 + -8 + -5 + -5 + -4 + 3 + 6 + 6 + 6 = -41

Probability: (2/12)^10 * (3/12) = 0.0000085832 (There are 2 "-9" tickets, 3 "6" tickets, and 12 total tickets in the box)

and so on for all the possible sample sums.

Calculating the expected value:

Expected value = (-43 * 0.00000017166) + (-42 * 0.0000017166) + (-41 * 0.0000085832) + ...

After performing the calculations, the expected value of the sample sum is approximately -19.67.

Therefore, the correct option is: b. -19.67

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Answer:

the system has no solutions

Step-by-step explanation:

the systems are shaded in different directions with no part of them intersecting

this means that there are no solutions

Answer:

18 seconds

Step-by-step explanation:

convert km/h to m/s and you get 22.22m/s. Then divide 400 by 22.22 and the answer is 18 seconds.

Hopefully this helps! Let me know if you have any questions!

Answer:

Perimeter of the park = 70 cm

Step-by-step explanation:

Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)

Perimeter = 2πr + 2(BC)

✔️Perimeter of the 2 semicircles = 2πr

Where,

radius (r) = ½(AB) = ½(7)

r = 3.5 cm

Perimeter = 2*π*3.5 = 7*π

Perimeter of the two semicircles = 21.9911486 ≈ 22 cm

✔️Find BC using Pythagorean theorem:

Thus,

BC = √(AC² - AB²)

AC = 25

AB = 7

BC = √(25² - 7²) = √576

BC = 24

✔️Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)

Perimeter of the park = 22 + 2(24)

= 22 + 48

= 70 cm

Answer:

horizontal asympote

Y:-4

Step-by-step explanation:

Both of the following statements are true about confidence intervals: Small samples produce large confidence intervals. Large samples produce small confidence intervals.

Confidence intervals are statistical estimations used in hypothesis testing. They are calculated from a random sample taken from a population, and they help to measure the accuracy and variability of the population parameter being tested.

The confidence interval is calculated by using a sample mean and a margin of error. In general, the larger the sample size, the smaller the margin of error and the narrower the confidence interval. The confidence interval is larger if the sample size is small, indicating that the sample mean is less likely to accurately represent the population parameter.

Small samples will produce larger confidence intervals because of greater uncertainty in the sample estimates. In contrast, larger samples will produce smaller confidence intervals because they provide more accurate estimates of the population parameter.

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Answer:

a = 4

b = 2√3

Step-by-step explanation:

Here, we want to get the missing side lengths

We start by looking at the values that we are given

from the question, a faces the right-angle and is called the hypotenuse; it is also the longest side

b faces the angle given and is also called the opposite

Lastly, the side marked 2 is the adjacent side

Now, the triangle given is called a 30-60-90 triangle

In a 30-60-90 triangle, the ratio of the sides are given as

1: √3:2

Thus, we have 1 as the adjacent

The opposite would be √3 * 2 = 2 √3 = b

Lastly , a = 2 * 2 = 4

Answer:

one hundred thirty four and zero nine

The value of sin a + cos a is √7/2.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows

Here we have

sin a × cos a = 3/8  

Multiply with 2 on both sides

=> 2(sin a × cos a) = 2(3/8)

=> 2 sin a cos a = 3/4  

Add sin²a + cos²a on both sides

=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a    

As we know (a + b)² = a²+ b² + 2ab  

=> (sin a + cos a)² = 3/4 + 1

=> (sin a + cos a)² = 7/4

=> sin a + cos a = √7/2

Therefore,

The value of sin a + cos a is √7/2.

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Answer:

a. \(\frac{x+2}{x+6}\)

Step-by-step explanation:

\(\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}\)

An oil tank is being filled at a constant rate.

In 0 minute, the depth of oil in the tank is 3, : (0,3)

In 10 minute, the depth of oil in the tank is 5, : ( 10, 5 )

In 15 minutes, the depth of oil in the tank is 6, : ( 15, 6 )

Since, the oil is filled at the constant rate, so the equation form by the depth of oil with the time is linear equation.

The general expression for the linear equation is :

Let x express the time and y express the depth of oil

Substitute any two set of value of time and depth from the table : ( 0, 3) & ( 10, 5 )

Since, we need to depth of the oil after, 45 minutes,

Substitute x = 45 in the equation :

as, y represent the depth of the oil

so, depth of the oil is 12 ft in 45 minutes

45 minutes after filling, the depth of the oil is 12 ft

Answer : 45 minutes after filling, the depth of the oil is 12 ft

Answr:

1.the y intercept is 4 as the base fee is $4

2.£28

3. 2(rate per mile driven)

Step-by-step explanation:

2.

2x7=14

14+4=28

The number of hamburgers sold on Sunday was 89

Let's assume that the number of hamburgers sold on Sunday was x.

According to the problem, the number of cheeseburgers sold was three times the number of hamburgers sold.

Therefore, the number of cheeseburgers sold can be expressed as 3x.

The total number of hamburgers and cheeseburgers sold was 356.

Therefore, we can write an equation to represent this information:

x + 3x = 356

Simplifying the left-hand side of the equation, we get:

4x = 356

Dividing both sides by 4, we get:

x = 89

Therefore, the number of hamburgers sold on Sunday was 89, and the number of cheeseburgers sold was 3 times that, or 267.

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer: A random variable.

Step-by-step explanation:

a numerical description of the outcome of an experiment is called a random variable.

Answer:

b 2，3，8

Step-by-step explanation:

Y=234678

Z=278910

X=12358

234678910 n 12358

=238

Answer: 80%

Step-by-step explanation:

To find percent error all you have to do is divide the estimate by the actual then multiply it by 100

8/10×100=80%

The percent error of the actual measurement of 10 fluid ounces is 25%.

Percent error:

Percent error means the difference between the exact or known value of something and its approximate or actual value, in percentage form.

The formula to calculate the percent id defined as

δ = |(A - E)/E| x 100%

Where

δ  = percent error

A  = actual value observed

E  = expected value

Given,

Derek filled the pitcher with 8 fluid ounces of lemonade.

Here we need to find the percent error if the actual measurement was 10 fluid ounces.

According to the percent error formula, the actual value in the given question is 10 and the expected value is 8.

Then we have to apply the value on the formula, then we get,

Percent error = [(10 - 8)/8] x 100%

Percent error = [2/8] x 100%

Percent error = 0.25 x 100%

Therefore, the percent error in the given situation is 25%.

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95.

As you see, the angle is a bit closer to 120. A right angle would be a perfect square, which is 90 degrees. So since it is so closer to 90 than the other answers, the answer is 95.

3/4+6/7 = (21 + 24)/28 = 45/28

The answer is C. 45/28