Flying with the wind a plane went 227 km/h. Flying into the same wind the plane only went 165 km/h.
what is the speed of the wind?
How fast would the plane go if there would be no wind?

The instantaneous acceleration at any time t is given by 10t. The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point.

To use the limit definition of a derivative to calculate instantaneous acceleration, we need to find the derivative of the velocity function with respect to time. The derivative of velocity gives us acceleration.

The limit definition of a derivative is given by:

f'(x) = lim (h→0) [f(x+h) - f(x)] / h

To calculate instantaneous acceleration, we substitute the velocity function, v(t), into the limit definition. Let's say v(t) = 5t^2.

Using the limit definition, we have:

a(t) = lim (h→0) [v(t+h) - v(t)] / h

Substituting v(t) = 5t^2, we get:

a(t) = lim (h→0) [5(t+h)^2 - 5t^2] / h

Expanding and simplifying:

a(t) = lim (h→0) [10th + 5h^2] / h

Now, we can cancel out the h term:

a(t) = lim (h→0) 10t + 5h

Taking the limit as h approaches 0, we get:

a(t) = 10t

Therefore, the instantaneous acceleration at any time t is given by 10t.

The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point. By taking the limit as the change in input approaches zero, we are able to approximate the exact rate of change at that point. This concept is fundamental to calculus and is used in various applications such as physics, engineering, and economics.

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The statement that is true about J and K is that the expected values of J and K will be equal, and the variability of J will be greater than the variability of K. (Option E)

The sample size of J is 40 and sample size of K is 100. According to the central limit theorem if there is a population with mean μ and standard deviation σ and sufficiently large random samples is taken from the population with replacement, then the distribution of the sample means will be approximately normally distributed. Based on the theorem, both J and K will have the same expected value or mean.

As the standard deviation is inversely proportional to the same size, as the sample size increases, the standard deviation and related variability decreases. Hence, the variability of J will be greater than variability of K.

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(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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The total degrees of freedom is option (b) 29

Degrees of freedom refer to the number of values in a calculation that are free to vary. In the context of ANOVA, degrees of freedom represent the number of independent pieces of information that are available for estimating the population variance.

To find the total degrees of freedom in an ANOVA table, you need to add up the degrees of freedom for the different sources of variation. In this case, there are three sources of variation: between groups (processes), within groups (error), and total.

The total degrees of freedom is equal to the total sample size minus one

Total degrees of freedom = n - 1 = 30 - 1 = 29

Therefore, the correct option (b) 29

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Answer:

1/2

Step-by-step explanation:

Answer:

n=-20

Step-by-step explanation:

Answer:

n = -20

Step-by-step explanation:

n/-4 = 5

n/-4 (-4) = 5(-4)

n = -20

-20/-4 = 5

Answer:

1 and 1/8 of a batch

Step-by-step explanation:

First you multiply 1/2 by 4 and get for 8 and then you subtract 4/8 - 3/8 and you take the sum of that and add one hole

the probability that at least flights are on time is

P(7) + P(8) + P(9) + P(10)

To calculate the probability that at least a certain number of flights are on time using the binomial distribution, we need the probability of success (p), the number of trials (n), and the desired number of successful trials.

Let's assume we have the following information:

Probability of a flight being on time: p = 0.8 (80%)

Number of flights: n = 10

To find the probability that at least a certain number of flights are on time, we need to sum the probabilities of the desired number of successful trials and all higher numbers of successful trials.

Let's say we want to find the probability of at least 7 flights being on time.

P(at least 7 flights on time) = P(7) + P(8) + P(9) + P(10)

Using the binomial probability formula: P(x) = C(n, x) * p^x * (1-p)^(n-x)

where C(n, x) represents the number of combinations of n items taken x at a time.

Calculating the probabilities: P(7) = C(10, 7) * (0.8)^7 * (0.2)^(10-7) P(8) = C(10, 8) * (0.8)^8 * (0.2)^(10-8) P(9) = C(10, 9) * (0.8)^9 * (0.2)^(10-9) P(10) = C(10, 10) * (0.8)^10 * (0.2)^(10-10)

Finally, we sum up these probabilities to get the probability of at least 7 flights being on time.

P(at least 7 flights on time) = P(7) + P(8) + P(9) + P(10)

Performing the calculations will give us the specific probabilities and the final probability.

Complete Question :- According to an​ airline, flights on a certain route are on time 75​% of the time. Suppose 24 flights are randomly selected and the number of​ on-time flights is recorded.

​(a) Explain why this is a binomial experiment.

​(b) Find and interpret the probability that exactly 14 flights are on time.

​(c) Find and interpret the probability that fewer than 14 flights are on time.

​(d) Find and interpret the probability that at least 14 flights are on time.

​(e) Find and interpret the probability that between 12 and 14 flights, inclusive, are on time.

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The correct response variable is the amount of pain relief.

Given that,

A tall glass of ice water, according to some, can help migraine sufferers find relief. Multiple migraine sufferers will be recruited by researchers to participate in a test. The individual will either take a placebo pill or a common painkiller when they get a migraine. Additionally, only half of each group will take the pill with water; the other half will sip on a small amount of water. The quantity of pain relief is then reported by participants.

To find :  What is the response variable in this experiment.

Explanation :

Response variable or study variable, in general called as dependent variable  is the variable of main focus in study. We want to study the changes in explanatory or independent variables are associated with response variable. Sometimes we want to measure the effect of predictors i.e explanatory variables on response variable.

For example in hand, we want to determine whether the drinking ice water is associated with amount of pain relief. Hence in this study, response variable is the amount of pain relief.

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The nth term of the pattern is (1+n)/(18+n)

What is a sequence?

succession is the act of doing something after another. successional order: a list of books organized by title. a running or interconnected sequence: a series of sonnets. something that happens after; a following event; a result; or a repercussion. In contrast to a set, the order of the components in a sequence does important, and the same elements may occur more than once at various positions. A series can officially be described as a function from natural numbers.

We are given a sequence

1/18, 2/19, 3/20, 4/21

As we can see the second term is (1+1)/(18+1)

Third term is (1+2)/(18+2)

Hence the n th term of the sequence can be given as (1+n)/(18+n)

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The two-column proof are:

           Statements                                     Reasons

To begin the proof, we list our given information in the left column of the two-column format. The first two statements are simply the given parallelograms, so we can write them down as statements 1 and 2.

Next, we use the properties of parallelograms to make some additional statements about the sides of these shapes. Statements 3 and 4 use the fact that opposite sides of a parallelogram are parallel to one another. Statement 3 tells us that AB is parallel to CD and AD is parallel to BC, and statement 4 tells us that FE is parallel to CD and FD is parallel to CE.

Now that we have made some statements about the sides of the parallelograms, we can start to relate them to one another. Statement 5 tells us that the two parallelograms have the same base, CD. This means that the distance between CD and AB is equal to the distance between CD and FE.

Therefore, we have proven that AB = FE based on the given information and the properties of parallelograms.

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Answer: y= x- 10

Step-by-step explanation:

Nothing further can be solved

Answer:

49/12 or 4 1/12 or 4.083 (all the same answer in different forms)

Step-by-step explanation:

2m-14m+49=0

-12m+49=0

-12m+-49

m=49/12

Answer: m=7

Step-by-step-explanation:

m^2-14m+49=0

(m-7)^2=0

m-7=0

m=7      

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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the kangaroo real height is 3 feet and shadow height is 5 feet

if the height of the tree is 7 feet so the real height of the tree is 5 feet

Answer:

Oasis idiot and a good time in the day before

The correct answer is;

The volume of the triangular prism is equal to the volume of the cylinder

Given that there are two figures

1. A right triangular prism and

2. Right cylinder

Area of cross section of prism is equal to Area of cross section of cylinder.

Let this value be A.

Also given that Height of prism = Height of cylinder = 5

Hence, Volume of a prism is given as:

V (prism) = Area of cross section x height

V (prims ) = A x 6

Cross section of cylinder is a circle.

Area of circle is given as:

A = πr²

Area of cross section, A = πr²

Volume of cylinder is given as:

V = πr²h

V = A x h

V = A x 6

From equations (1) and (2) we can see that

Volume of prism is equal to the volume of cylinder.

Hence, the correct answer is:

Volume of prism is equal to the volume of cylinder.

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Answer:

Water is a compound. One molecule of water is made up of H2O or 2 hydrogen atoms and 1 oxygen atom. Water is colorless, tasteless, shapeless, and sizeless.

Step-by-step explanation:

Water is a compound made up of two hydrogen and one oxygen.

Compounds are chemical substances formed by the combination of two or more different elements.

Here consider the compound Water.

A Water molecule is made up of two hydrogen atoms and one oxygen atom.

The molecular formula is H₂O.

Consider the element hydrogen from water.

Hydrogen is an element which does not have any smell and does not have color.

In the room temperature, hydrogen exists in gaseous state. It will turn in to liquid at low temperature and high pressure.

Hence water is a compound made up of two hydrogen and one oxygen.

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Answer:

answer is C the means and the standard deviation because the data sets are normally disturbed

Answer: d

Step-by-step explanation:

To prove that if n²x² - 2mnx + m² = n², then x is rational, we can use a direct proof by assuming that x is irrational and arriving at a contradiction.

Assume that x is irrational. We will show that this leads to a contradiction.Since x is irrational, we can express it as x = a/b, where a and b are integers with no common factors and b ≠ 0. Substituting x = a/b into the given equation, we have: n²(a/b)² - 2mn(a/b) + m² = n².  Multiplying through by b², we get: n²a² - 2mna + m²b² = n²b².  Rearranging the terms, we have: n²a² - n²b² + 2mna - m²b² = 0

Now, let's consider the left-hand side of this equation as a quadratic expression in terms of a: (n²)a² + (2mn)a + (-n²b² - m²b²) = 0. This is a quadratic equation in a, and its discriminant is given by: Δ = (2mn)² - 4(n²)(-n²b² - m²b²). Simplifying this expression, we have: Δ = 4m²n² - 4n⁴b² - 4m²b²n². Δ = 4(m²n² - n⁴b² - m²b²n²). Since m, n, a, and b are integers, the discriminant Δ must be a perfect square. However, it is clear that the expression inside the square root (m²n² - n⁴b² - m²b²n²) will generally not be a perfect square unless certain conditions are satisfied. Therefore, we have reached a contradiction. Our initial assumption that x is irrational cannot hold, which implies that x must be rational. Hence, if n²x² - 2mnx + m² = n², then x is rational.

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Answer:

  P(-0.2, 2.2)

Step-by-step explanation:

You want the coordinates of point P that divides AB into segments with the ratio AP/PB = 3/7. The end points are A(-2, 1) and B(4, 5).

The point that divides AB in the ratio m/n is ...

  P = (mB +nA)/(m+n)

  P = (3(4, 5) +7(-2, 1))/(3+7) = (12 -14, 15 +7)/10

  P = (-0.2, 2.2)

Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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Answer:

$20

Step-by-step explanation:

let x be the original cost

0.85x = 17

divide both sides by 0.85

x = 20

Answer:

This function is an even-degree polynomial, so the ends go off in the same directions, just like every quadratic I've ever graphed. Since the leading coefficient of this even-degree polynomial is positive, the ends came in and left out the top of the picture, just like every positive quadratic you've ever graphed. All even-degree polynomials behave, on their ends, like quadratics.

Step-by-step explanation:

Jessica has 5 cupcake cases left.

First, divide 50 into groups of five. Next, subtract two groups of five from 50. Third, divide the remaining cases into groups of six. Finally, subtract 5 groups of six from the remains from the last subtraction equation.

The number of cupcake cases that Janissa has left will be 5.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Janissa bought 50 cupcake cases for baking.

She used 2/5 of the cases to bake vanilla cupcakes. Then the number of vanilla cupcakes will be

⇒ 50 x 2 / 5

⇒ 20 vanilla cupcakes

Then the remaining cupcake cases will be

⇒ 50 - 20

⇒ 30 cupcake cases

She then used 5/6 of the remaining cases to bake chocolate cupcakes. Then the number of chocolate cupcakes will be

⇒ 30 x 5 / 6

⇒ 25 chocolate cupcakes

Then the remaining cupcake cases will be

⇒ 30 - 25

⇒ 5 cupcake cases

Then the number of cupcake cases that Janissa has left will be 5.

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Answer:

f(30°) = \(\frac{1}{2}\)

Step-by-step explanation:

using the 30- 60- 90 triangle with legs 1 , \(\sqrt{3}\) and hypotenuse 2 , then

substitute x = 30° into f(x)

f(30°) = sin30° = \(\frac{1}{2}\)

Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation: