Of the 75 employees in the office building in dc, 40 had taken the subway to work sometime during the past year, 22 had taken the bus sometime during the past year, and 55 had taken either the subway or the bus or both to work last year. If one person is selected at random, show you work and find the following:

a) The probability that the person had taken both the subway and the bus.

b) The probability that the person had taken the bus but not the subway.

c) The probability that the person had taken neither the bus nor the subway

d) The probability that the person had not taken both the bus and the subway

The right triangle, like the other triangles, has three sides, three vertices, and three angles. The difference between the other triangles and the right triangle is that the right triangle has a 90  angle.

To find missing angles and sides and round to the nearest tenth, you can use different methods depending on the given information and the type of triangle or shape involved.

Some common methods include:
Trigonometric ratios (sine, cosine, tangent) for right triangles.
Angle sum property or exterior angle property for triangles.
Pythagorean theorem for right triangles.
Law of cosines and law of sines for non-right triangles.
To help find the missing angles and sides of a triangle, you need certain information about the triangle, such as known angle and side measurements, or information about the properties of the triangle.

Without this information, no concrete calculations can be made.

Provide the necessary information or describe the problem in more detail and we will help you find the missing corners and sides of the triangle and round it to tenths.

Remember to always check if any additional information is given, such as side lengths or angles ' 7 and to apply the appropriate formula or property to find the missing value.

Round your answer to the nearest tenth as specified.

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The midpoint formula is used to find the center point of a line segment, given the coordinates of the two endpoints. The formula is as follows:

Midpoint = ( (x₁+ x₂) / 2, (y₁ + y2) / 2 )

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.

To find the missing coordinate using the midpoint formula, you would need to have the coordinates of one endpoint, as well as the coordinates of the midpoint. Then, you can use the formula to solve for the missing coordinate.

For example, if you have the coordinates of one endpoint as (3, 5) and the coordinates of the midpoint as (4, 6), you can use the formula to solve for the missing endpoint:

Midpoint = ( (3 + x₂) / 2, (5 + y₂) / 2 )

(4, 6) = ( (3 + x₂) / 2, (5 + y₂) / 2 )

So, by solving above equation we can get the missing coordinate

(x₂, y₂) = (5,7)

In conclusion, the midpoint formula can be used to find the missing coordinate of a line segment by using the coordinates of one endpoint and the midpoint. It is a simple and efficient way to find the missing coordinate when working with geometric shapes.

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we know that a has to be a number less than 0 and c has to be a number greater than 0. so a has to go before the number 0 and b can go before or after 0, as long as it satisfies the equation

Answer:

3

Step-by-step explanation:

1 / ( 1/14 + 1/10) = x      or    (1/14 + 1/10) x = 1

Step-by-step explanation:

For crossing chords in a circle, the products of the segments are equal

6 * 4  =   x   *   14 -x

24 = -x^2 + 14x

-x^2 + 14x - 24 = 0      Use quadratic Formula ( or factoring ) to find:

x = 2   or  12      ( drawing is not to scale)

Respuesta:

24 horas

Explicación paso a paso:

El primer medicamento se toma cada 8 horas.

El segundo medicamento se toma cada 12 horas.

Para Obtian el momento en que ambos medicamentos se volverán a tomar juntos:

Encontramos el mínimo común múltiplo de 8 y 12

Múltiplos de:

8 = 8, 16, 24, 32, 40, 48, 56

12 = 12, 24, 36, 48, 60

El mínimo común múltiplo de 8 y 12 es 24.

Por lo tanto, ambos medicamentos se volverán a tomar después de 24 horas.

Answer:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. In this case, the common difference between the terms 29, 37, 45, is 8.

To find the 59th term of an arithmetic sequence, you can use the formula:

a_n = a_1 + (n-1)d

Where:

a_n is the nth term of the sequence

a_1 is the first term of the sequence

n is the position of the term you are trying to find

d is the common difference between the terms of the sequence

In this case:

a_1 = 29

n = 59

d = 8

So, to find the 59th term of this arithmetic sequence, you would do:

a_n = 29 + (59-1)8 = 29 + (58)8 = 29 + 464 = 493

So, the 59th term of this arithmetic sequence is 493.

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The correct question is

What is the 59th term of the arithmetic sequence 29, 37, 45?

The entire interval over which the function f(x), is negative is (c) (-∝, -6)

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

The table of values

From the table, we can see that

The function f(x), is negative when x is less than or equal to -6

So, we have

x ≤ -6

As an interval, we have

(-∝, -6)

Hence, the interval is (-∝, -6)

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The probability of the message being "hi" given the ciphertext "st" is 0.

Consider a shift cipher with three possible messages, with a distribution of probabilities. The three possible messages are as follows:

Pr[M=‘hi’] = 0.3,

Pr[M=‘no’] = 0.2, and

Pr[M=’in’] = 0.5.

To solve this problem, we can use Bayes' theorem. We want to find the probability of the message being "hi" given the ciphertext "st".

Using Bayes' theorem, we have:

Pr[M=‘hi’ | C=‘st’] = Pr[C=‘st’ | M=‘hi’] * Pr[M=‘hi’] / Pr[C=‘st’]

We can break this down into three parts:

Pr[C=‘st’ | M=‘hi’]:

This is the probability that the ciphertext is "st" given that the message is "hi".

To find this probability, we need to encrypt the message "hi" using the shift cipher. If we shift each letter in "hi" by one (i.e., a becomes b, h becomes i, and i becomes j), we get the ciphertext "ij". Since "ij" does not contain the letter "s", we know that Pr[C=‘st’ | M=‘hi’] = 0.Pr[M=‘hi’]:

This is the probability of the message "hi", which is given as 0.3.Pr[C=‘st’]:

This is the probability of the ciphertext "st". We can find this probability by considering all the possible messages that could have been encrypted to produce "st".

There are three possible messages: "hi", "no", and "in". To encrypt "hi" to "st", we need to shift each letter in "hi" by two (i.e., a becomes c, h becomes j, and i becomes k). This gives us the ciphertext "jk".

To encrypt "no" to "st", we need to shift each letter in "no" by five (i.e., n becomes s and o becomes t). This gives us the ciphertext "st". To encrypt "in" to "st", we need to shift each letter in "in" by three (i.e., i becomes l and n becomes q). This does not give us the ciphertext "st", so we can ignore it.

Therefore, Pr[C=‘st’] = Pr[C=‘st’ | M=‘hi’] * Pr[M=‘hi’] + Pr[C=‘st’ | M=‘no’] * Pr[M=‘no’] = 0 + 0.2 * 1 = 0.2

Now we can plug in the values we have found:

Pr[M=‘hi’ | C=‘st’] = 0 * 0.3 / 0.2 = 0

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The sequence of transformations that will map figure H onto figure H' is: Option B:  the rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6.

We are given the coordinates of the hexagon as:

Points of Hexagon H  →  (2,2), (2,6), (6,7), (8,6), (8,2), (6,1)

Points of Hexagon H' →  (2,-8), (2,-4), (4,-3), (8,-4), (8,-8), (4,-9)

The steps that can be used to transform the hexagon H into hexagon H' are:

Step 1 - Translate the hexagon in the positive x-axis direction by a factor of 10.

Step 2 - Translate the graph obtained in the above step by factor 2 in the downward direction.

Step 3 - Rotate the graph obtained in the above step 180 degrees about the origin.

Step 4 - Then take the reflection of the graph obtained in the above step about y = -6. The resulting graph shows the graph of Hexagon H'.

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Hey there! :)

Answer:

f(-2) = -148.

Step-by-step explanation:

To calculate f(-2), simplify substitute -2 for x in the equation. Therefore:

f(x) = 4x³ -12x² + 40x + 12

Becomes:

f(-2) = 4(-2)³ - 12(-2)² + 40(-2) + 12

Simplify:

f(-2) = 4(-8) - 12(4) - 80 + 12

f(-2) = -32 - 48 -80 + 12

Finally, you get:

f(-2) = -148.

Answer:

64 Is the correct answer right

The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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The clinic should hire at least 7 doctors in order to serve 122 patients per day.

To determine how many doctors the clinic should hire in order to serve 122 patients per day, we need to calculate the number of patients each doctor can see within their working hours.

Let's start by calculating the total number of minutes each doctor works per day. Since each doctor works 8 hours per day and there are 60 minutes in an hour, the total minutes worked by a doctor per day would be 8 hours × 60 minutes = 480 minutes.

Next, we need to find out how many patients a doctor can see within their working hours. Given that each patient requires an average of 27 minutes with a doctor, the number of patients a doctor can see per day would be 480 minutes ÷ 27 minutes per patient = 17.7778 patients.

Since we can't have a fractional number of patients, we need to round this number up to the nearest whole number to ensure that each patient gets the required attention. Therefore, each doctor can see approximately 18 patients per day.

To serve 122 patients per day, we divide the total number of patients by the number of patients each doctor can see per day: 122 patients ÷ 18 patients per doctor = 6.7778 doctors.

Again, we can't have a fractional number of doctors, so we need to round this number up to the nearest whole number. Therefore, the clinic should hire at least 7 doctors to serve 122 patients per day.

In summary, the clinic should hire at least 7 doctors in order to serve 122 patients per day.

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Answer:

4. the square root of 36 should also be an integer

Answer:

The ball will hit the ground in 1.33 s if no one touches it. The equation has 2 real solutions.

Step-by-step explanation:

The ball will hit the ground when its height is equal to 0 meters, therefore using this value in the expression and solving for "t" will give us the correct solutions.

\(h = -4.9*t^2 + 5*t + 2\\\\-4.9*t^2 + 5*t + 2 = 0\\\\t_{1,2} = \frac{-5 \pm \sqrt{5^2 - 4*(-4.9)*(2)}}{2*(-4.9)}\\\\t_{1,2} = \frac{-5 \pm \sqrt{64.2}}{-9.8}\\\\t_{1,2} =\frac{-5 \pm 8.0125}{-9.8}\\\\t_1 = \frac{-5 - 8.0125}{-9.8} = 1.33 \text{ s}\\\\t_2 = \frac{-5 + 8.0125}{-9.8} = -0.3 \text{ s}\)

The ball will hit the ground in 1.33 s if no one touches it. The equation has 2 real solutions.

Answer:

1300

Step-by-step explanation:

130×10 thats the answer yoo

Answer:

7 17/99

Step-by-step explanation:

The integral ∫(2/3)3e^(9x)dx can be expressed as ∫e^(9x)^(2/3)dx. By substituting u = 9x, we can transform the integral into the I-function.

For the integral \(∫(2/3)3e^(9x)dx\), substitute u = 9x, which leads to du = 9dx. Rearranging, we have dx = (1/9)du. Substituting these values into the integral, we obtain ∫e^(9x)^(2/3)dx = (2/3)∫e^u^(2/3) * (1/9)du. The resulting integral is expressed in terms of the I-function.

For the integral ∫(Sqrt(cos(x)))^3dx, substitute u = cos(x), which leads to du = -sin(x)dx. Rearranging, we have dx = -du/sin(x). Substituting these values into the integral, we get ∫(cos(x))^(-3/2)dx = ∫u^(-3/2) * (-du/sin(x)).

The resulting integral is expressed in terms of the I-function.

By numerically evaluating both the I-function and the original integral, we can determine their respective values.

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Given data ; Initial distance between cars, d = 960m Speed of Car A, vA = 50 m/sSpeed of Car B, vB = 30 m/sSpeed of sound, vS = 340 m/s

Let's solve the parts given in the question;

a) Find vAB; Relative speed, \(vAB = vA + vBvAB = 50 m/s + 30 m/svAB = 80 m/s\)

b)Let t be the time until the two cars collide.In time t, the distance traveled by Car A = vA0t

The distance traveled by Car B = vBt

The total distance covered by both cars is d:

Therefore, \(vAt + vBt = dd/t = (vA + vB)t = 960 mt = d / (vA + vB)t = 960 / 80t = 12 s\)

Let ΔsSound be the displacement of the sound during that time.

Distance traveled by Car \(A = vA x t = 50 m/s x 12 s = 600 mDistance traveled by Car B = vB x t = 30 m/s x 12 s = 360 m\)

Therefore, the distance between the cars will be \(960 - (600 + 360) = 0 m.\) So, the sound wave will have traveled the displacement of 4080 m from Car B to Car A.

Hence, ΔsSound = 4080 m.

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\(\textbf{a)}\\\\~~~(x+8)(2x-3)\\\\=2x^2 -3x + 16x - 24\\\\=2x^2 +13x -24\\\\\textbf{b)}\\\\~~~(x-5)^2\\\\=(x-5)(x-5)\\\\=x^2 -5x -5x+25\\\\=x^2 -10x +25\)

The given statement "two vectors are linearly dependent if and only if they are collinear." is True, because these vectors lie on same plane.

Two vectors are linearly dependent if and only if one of them can be expressed as a scalar multiple of the other. In other words, if there exist scalars a and b such that av + bw = 0, where v and w are the two vectors in question, and at least one of a and b is not zero, then the vectors are linearly dependent.

If the vectors are collinear, it means that they lie on the same line and can be expressed as scalar multiples of each other. In this case, a and b can be chosen to be the coefficients of the vector components along the line, and the equation av + bw = 0 holds. Therefore, if two vectors are collinear, they are linearly dependent.

Conversely, if two vectors are linearly dependent, then one of them can be expressed as a scalar multiple of the other, which means that they lie on the same line and are collinear. Therefore, if two vectors are linearly dependent, they are also collinear.

Hence, we can conclude that two vectors are linearly dependent if and only if they are collinear.

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Complete question is:

Two vectors are linearly dependent if and only if they are collinear.

True/False.

Answer:

12

Step-by-step explanation:

Given That:

1 gray t-shirt for every 2 black shirt

Number of gray shirts bought = 6 to ensure that number of gray and black t-shirts are the same

Before:

If x = number of gray t-shirt

Number of black t-shirts = 2x

Now :

After buying 6 gray t-shirts

x + 6 = 2x

6 = 2x - x

6 = x

x = 6

Hence,

Numbe of gray and black t-shirt now is :

x + 6 = 6 +6 = 12

2(x) = 2 * 6 = 12

Answer:

It would be 12 1/2. (12.5%)

\((x+11)x(x-5)=0 \\\\[-0.35em] ~\dotfill\\\\ (x+11)x(x-5)=0\implies x=\cfrac{0}{(x+11)(x-5)}\implies x=0 \\\\[-0.35em] ~\dotfill\\\\ (x+11)x(x-5)=0\implies x-5=\cfrac{0}{(x+11)x}\implies x-5=0\implies x=5 \\\\[-0.35em] ~\dotfill\\\\ (x+11)x(x-5)=0\implies x+11=\cfrac{0}{x(x-5)}\implies x+11=0\implies x=-11 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x= \begin{cases} 0\\ 5\\ -11 \end{cases}~\hfill\)

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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Answer:

84 pairs of shoes

Step-by-step explanation:

Since Cici has  pairs of shoes, use this equation to solve for the number of pairs of shoes Aubree has

The "general-solution" of differential-equation, "x(dy/dx) + 6y = x³ - x" is y(x) = (x³/9) - (x/7) + c/x⁶.

The differential-equation is given as : x(dy/dx) + 6y = x³ - x,

We first divide the whole "differential-equation" by variable "x",

So, we get,

dy/dx + (6/x)y = x² - 1,

The next-step, we integrate, it can be written as :

y×\(e^{\int{\frac{6}{x} } \, dx }\) = ∫\(e^{\int{\frac{6}{x} } \, dx }\).(x² - 1),

y.x⁶ = ∫(x⁸ - x⁶).dx

y.x⁶ = x⁹/9 - x⁷/7 + c,

Dividing both the sides by x⁶, we get

y = (x⁹/9)/x⁶ - (x⁷/7)/x⁶ + c/x⁶,

So, y(x) = (x³/9) - (x/7) + c/x⁶,

Therefore, the required general-solution is y(x) = (x³/9) - (x/7) + c/x⁶.

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The given question is incomplete, the complete question is

Find the general solution of the given differential equation. x(dy/dx) + 6y = x³ - x.