An airplane, flying in the direction 20° east of north at 325 mph in still air , encounters a 40-mph tail wind acting in the direction 40° west of north. The airplane maintains its compass heading but, because of the wind, acquires a new ground speed and direction. What are they?

Two events are mutually exclusive if the probability of their intersection is 0 and they have no sample points in common. Hence, option D is the correct answer.

The two events are called mutually exclusive when they have no sample points in common. Thus, the probability of event A and event B happening is zero. this means that their intersection set is the empty set.

let us take an example-

Let A be a set of odd numbers and B be a set of even numbers.

A = {1,3,5,7,9}

B = {0,2,4,6,8}

A ∩ B = { }

Hence, the two sets - A and B are mutually exclusive of each other.

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In order to finish the task in the allotted time, you would therefore need to ascend more quickly or decide to only climb the first two walls.

The Latin term minute, which means "small," is the root of both the adjective instant (my-NOOT), which denotes something that is incredibly small, and the substance minute (MIN-it), which denotes 60 seconds of time. Although the two terms have different pronunciations, they both refer to small sizes.

We can compute the overall time needed to scale all three barriers and compare it to the time available, which is 71/2 minutes or 450 seconds, to determine if you have enough time.

One wall takes 155 seconds to scale, so climbing three walls would take:

3 walls x 155 seconds per wall = 465 seconds

You wouldn't have enough time to scale all three walls inside the allotted time restriction because 465 seconds is longer than the amount of time that is accessible, which is 450 seconds.

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The book that weighs 3/4 pounds is greater than 1/2 pounds.

To compare the weights of the two books with 1/2 pound, we need to convert 1/2 pound into a fraction with a common denominator as the given weights. The common denominator of 8 and 4 is 8. So, we can convert 1/2 pound to 4/8 pound.

Now we can compare the weights of the two books with 4/8 pounds. The weight of the first book is 3/8 pounds, which is less than 4/8 pounds. The weight of the second book is 3/4 pounds, which is greater than 4/8 pounds.

Therefore, the book that weighs 3/4 pounds is greater than 1/2 pound.

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Answer:

A

Step-by-step explanation:

Put '0' in for 's' and solve :

0 = -p^2 + 75 p + 1200

 Use Quadratic Formula with a = -1      b=75      c = -1200

      to find p = ~ 24  OR  52       THE LEAST NUMBER WOULD BE 24

Answer:

In order to be a linear function, a graph must be both linear (a straight line) and a function (matching each x-value to only one y-value).

Step-by-step explanation:

I hope this helps, sorry if it doesn't good luck

It is false that Every relation that is linear, must also be a function.

Given that,
A statement is to be justify that, whether is true and false that Every relation that is linear, must also be a function.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Linear functions are defined as functions whose graph is a straight line. A linear function has the following form. example f(x) = 1 + 2x. A linear function has only independent variable and only a dependent variable.

Let's understand with an example,
If y = 1 *\(x^0\) , is a linear function but it's a verticle straight line. for every value of x, y is independent of x so for the function it is necessary that the function should be consist of an independent variable and a dependent variable,
Implies every function that is linear must not also a function.

Thus, It is false that Every relation that is linear must also be a function.

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Answer:

3, no

Step-by-step explanation:

Median of the following list of 4040 numbers is 1976.5

If we solve 45² = 2025, this value is greater than 2020.

If we solve 44² that would result in 44x44 =1936, this value is less than 2020.

If we subtract 44 from 2020: 2020 - 44 = 1976

There are 1976 of the 4040 numbers that are greater than 2020.

If we add 44 into 2022: 2020 + 44 = 2064

So, there are 2064 numbers which are less than or equal to 2020.

As there are 44 duplicates, it will shift up the median's placement down 44.

List of numbers had been 1, 2, 3, ....,4040

Median of the entire given set would be:

= 1+4040/2

= 2020.5

The median of the following list of 4040 numbers is:

2020.5 - 44= 1976.5

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Answer:

0, -2/3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Explicación paso a paso:

calcular la longitud de AB usando la fórmula de la distancia

re =

con (x₁, y₁ ) = A (4, 2 ) y (x₂, y₂ ) = B (9, 10 )

AB =

     =

     =

     =

     ≈ 9.4 (a 1 decimal)

For the D-operator P(D) = Da + CD + k to be stable and underdamped, we need c ≠ 0 and Δ < 0.

To determine the values of 'c' for which the D-operator P(D) = Da + CD + k is stable and underdamped, we need to analyze the characteristic equation associated with the operator.

The characteristic equation for the D-operator is obtained by substituting P(D) with 's', where 's' is a complex variable. The characteristic equation is given by s² + cs + k = 0.

To ensure stability, we require the real part of the roots of the characteristic equation to be negative. Additionally, for the system to be underdamped, the roots must be complex conjugate with a non-zero imaginary part.

We can determine the stability and damping conditions by examining the discriminant of the characteristic equation.

The discriminant is given by Δ = c² - 4k.

For stability, we require Δ > 0. This condition ensures that the roots are real and negative, indicating stability.

For underdamping, we require Δ < 0 to have complex conjugate roots. Additionally, we need c ≠ 0 to ensure non-zero imaginary parts in the roots.

Considering the conditions, we have two cases:

1. c ≠ 0:

  For stability and underdamping, we require Δ < 0 and c ≠ 0. This condition ensures complex conjugate roots with non-zero imaginary parts.

2. c = 0:

  If c = 0, the characteristic equation becomes s² + k = 0. In this case, the system can be stable or unstable, depending on the value of k. However, it cannot be underdamped since there are no complex roots.

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Answer:

A

Explanation:

A rectangle is a stretched out square and squares have 4 congruent angles (Congruent means the same or equal to), so a rectangle has 4 congruent angles.

Answer:

0,1,2

Step-by-step explanation:

you have to go in numerical order starting from zero and going forward with no fractions.

The percentage of data that is roughly greater than 66, as displayed in the box plot, is 100%.

In a box plot, we have the following displayed five-number summary which tells what percentage of the data distribution for each part of the data distribution:

Upper quartile (Q3): This is the value at where the box in the box plot ends at the edge of the box. From this point to the left, all data values that fall within the bracket make up 75% of the data.

Lower quartile (Q3): This is the value at where the box in the box plot starts at the edge of the box. From this point to the left, all data values that fall within the bracket make up 25% of the data.

Median: this is the middle value at the point where the line divides the box and data below this point make up 50% of the data.

The other five-number summary are the maximum and the minimum values that are represented by the whiskers.

On the box plot given, 66 is at the extreme whisker at the left. This means that the percentage of data that is roughly greater than 66 is 100%.

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Answer:

correct value of x = 5

Step-by-step explanation:

\( \frac{ {( - 2)}^{4x + 2} }{ {( - 2)}^{2x} } = {( - 2)}^{12} \\ = \frac{ {( - 2)}^{4 \times 5 + 2} }{ { ( - 2)}^{2 \times 5 } } \\ = \frac{ {( - 2)}^{22} }{ { ( - 2)}^{10} } \\ = \frac{4194304}{1024} \\ = 4096 = 4096(i.e \: {( - 12)}^{12} = 4096) \\ \)

each hot dog is 50 cents. Because .50+.50+.50+.50+.50+.50+.50.50=4 We know each hot dog is worth .50 cents because a pack of 8 HD cost $4 so each HD would need to cost less that a dollar. hope this helps!

Answer:

he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).

Step-by-step explanation:

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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Answer: A

Step-by-step explanation:

Each gallon costs 3 dollars.

8(gallons) times $3(for each gallon) = 24(dollars).

A system of n number of linear equations in n unknowns has an many number of solutions if the coefficients of matrix is unique. The assertion is always accurate. The given statement is always true.

From the question, the given statement is:

A system of n linear equations in n unknowns has an endless number of solutions if the matrix of coefficients is unique. The assertion is always accurate.

The given statement is always true.

Consider the system of equations Ax = b. If A is single, there is no A-inverse. As a result, there is no one approach to solve the system. Then, there are still two options:

We can't tell which condition is right only examining the matrix [A b]. There exists an endless number of solutions if [A b] is equal to A's rank.

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Answer:

the width is 3

Step-by-step explanation:

you divide the 4 by 12

Answer:

2 units

Step-by-step explanation:

Area = Length × Width of a rectangle

If Length = L

Width = L-4

So 12 units = L×(L-4)

12 = L^2 -4L

L^2 -4L -12=0

Simplify this equation

L^2 + 2L -6L -12 = 0

L( L+2) - 6(L+2) = 0

(L+2) (L-6) = 0

L+2 =0 Or L-6=0

L=-2 Or L= +6

But L can't take a negative value

therefore L= 6

Now if we substitute and check,

L× (L-4) = 6×2=12 units

width = 6-4 =2 units

Answer:

Step-by-step explanation:

Step-by-step explanation:

Familiarize yourself with perfect squares in the neighborhood of 140:

10^2 = 100

11^2 = 121

12^2 = 144

Note that 140 is much closer to the perfect square than it is to the perfect square 121.  The value of √140 must lie closer to 12 than to 11.

Place a point on the number line about 3/4 of the way from 11 to 12.

Answer:

x = 29/12, I don't think it's any of those choices because none of those choices fit x to be 8.

Step-by-step explanation:

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

10

Step-by-step explanation:

nCr = 5!/(3! × (5 - 3)!)

= 10

123/ 124/ 125/ 134/ 135/ 145/ 234/ 235/ 245/ 345

The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made. In our example, we have 52 cards; therefore, n = 52.

Answer: get 2 more frames

Step-by-step explanation:

The probability that a randomly selected firm will earn less than $100 million is 0.9525 or 95.25% (rounded to four decimal places).

We can standardize the income value of $100 million to a z-score by using the formula

z = (x - mu) / sigma

where x is the income value, mu is the mean income, and sigma is the standard deviation.

Substituting the given values, we get

z = (100 - 85) / 9 = 1.6667

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected firm will have an income less than $100 million by looking up the area to the left of the z-score of 1.6667.

The area to the left of 1.6667 is approximately 0.9525.

Therefore, the probability is 0.9525 or 95.25% (rounded to four decimal places).

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The correct statement about their work is: Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.

Adler started with the equation (13/8) = k(1/2) and subtracted 1/2 from both sides to get (13/8) - (1/2) = k(1/2) - (1/2). Then simplifying, Adler obtained (9/8) = k.

Erika started with the equation (13/8) = k(1/2) and multiplied both sides by -1/2 to get (13/8)(-1/2) = k(1/2)(-1/2). Simplifying, Erika obtained (9/8) = k.

Both Adler and Erika arrived at the correct value of k = 9/8, despite using slightly different approaches. The inverse of addition (subtracting 1/2) and the opposite of one-half (multiplying by -1/2) were correctly applied in their respective calculations.

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Answer:

y = 1/2x - 2.5

Step-by-step explanation:

(15, 5) and (42, 18.5)

Slope:

m=(y2-y1)/(x2-x1)

m=(18.5 - 5)/(42 - 15)

m = (13.5)/27

m = 1/2

y - y1 = m(x - x1)

y - 5 = 1/2(x - 15)

y - 5 = 1/2x - 7.5

y = 1/2x - 2.5

Answer:

2   or    1/2

Step-by-step explanation:

change in y over change in x

you didnt define what what x and what was y so ill provide both answers and you can figure which is correct

42-15/18.50-5   =27/13.5   =2

18.50-5/42-15    =13.5/27  =1/2

Answer: A random variable.

Step-by-step explanation:

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