A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.23, P(A2) = 0.25, P(A3) = 0.29, P(A1 ∩ A2) = 0.09, P(A1 ∩ A3) = 0.11, P(A2 ∩ A3) = 0.07, P(A1 ∩ A2 ∩ A3) = 0.02. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.)

a. P(A2 | A1)
b. P(A2 ∩ A3 | A1)
c. P(A2 ∪ A3 | A1)
d. P(A1 ∩ A2 ∩ A3 | A1 ∪ A2 ∪ A3)

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

A. Real numbers, rational numbers

Note:

Real numbers are numbers that can be found on the number line. They include all rational and irrational numbers

Natural numbers are counting numbers. They include 0 and all whole numbers (1, 2, 3, ....)

Rational numbers are numbers that can be expressed as fractions of two integers. eg 2/3, 5/4, etc

Irrational numbers are numbers that cannot be expressed a s fractions of two integers. eg √7, π, etc

2/7 is a real number because it can be found on the number line, and is continuous

Also, 2/7 is a rational number because it is expressed as a fraction of two integers (2 and 7)

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

As the number of sides of the bases of a prism increases, the shape of the prism becomes more complex and closer in form to a cylinder. For example, a prism with two identical polygonal bases, such as a rectangular prism or a triangular prism, will have a more blocky or pyramidal shape. However, as the number of sides of the base increases, the shape of the prism becomes more cylindrical and less pyramidal in appearance. This is because the more sides a polygon has, the more closely it approximates a circle, and the cross-section of the prism becomes more circular in shape.

When the number of sides of the base of a prism increases, the prism becomes more like a cylinder.

The approximate sales price for a home in 2020 would be 480

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

Year Avg. Sales Price (Thousands)

1990 149

1995 158

2000 207

We can see that there is an upward trend as the year increases

However, the table does not follow a linear or an exponential pattern

From 2000 and 1990, the change in price is 58

Using this as a guide, we have

2020 = 207 + 58 * 2

2020 = 323

The closest to 323 in the option is 480

Hence, the sales price is 480

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2/7 or 2:7 or about 28.5%

Answer: 2/7 or 2 out of 7

Step-by-step explanation: because there are 2 y's in the word synonym

The angle 7 is the alternative interior angle to angle 2.

Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.

They are the angles that are on opposite sides of the transversal and inside the two parallel lines.

Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.

We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.

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Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

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The volume of the cone is 314cm³

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.

The volume of the cone is 1/3πr²h

h²= 13²-5²

h = √169 - 25

h = √144

h = 12 cm

V = 1/3πr²h

V = 1/3 ×3.14 × 5² × 12

V = 942/3

V = 314 cm³

therefore the volume of the cone is 314cm³

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Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

On solving the provided question, by the help of BODMAS we can say that - Subtract 22 from both sides is the answer to the given question.

BODMAS and PEDMAS are both names for it in various places. This stands for exponents, parenthesis, division, multiplication, addition, and subtraction. The BODMAS rule states that parentheses must be answered before powers or roots (that is, of), divisions, multiplications, additions, and lastly subtractions. The BODMAS rule states that the degree (52 = 25), parenthesis (2 + 4 = 6), any division or multiplication (3 x 6 (bracket response) = 18), and any addition or subtraction (18 + 25 = 43) come before any other operations.

\(f/3 +22 = 17\)

\(f/3 +22 -22 = 17 -22\) Subtracting the same value from both sides keeps the equation equal.  

Then simplify. The \(+22 and -22= 0\) They "cancel"   \(17-22 = -5\)

\(f/3 = -17 f/3\) is now isolated-- by itself-- in the equation.

If we have to solve  f, the next step we to take is to multiply on the both sides by  3.

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The restrictions on the width is that it must be between 14.1 yards and 17.3 yards

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

Area = between 240 yd² and 360 yd²

Also, we have

Length = 1.2 times the width

This means that

l = 1.2w

The area is then calculated as

Area = lw

So, we have

Area = 1.2w²

This means that

240 < 1.2w² < 360

Divide through by 1.2

200 < w² < 300

Take the square roots

14.14 < w < 17.32

Approximate

14.1 < w < 17.3

Hence, the width must be between 14.1 yards and 17.3 yards

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Answer:

-2i

Step-by-step explanation:

= √-4-√-16

= 2i - 4i

= -2i

Answer:

1, 2, 4

Step-by-step explanation:

Answer:

Los números son 23 y 35.

Step-by-step explanation:

Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?

Set the numbers as x and y. Using the given information, we have two equations:

x+y=58

x=y+12

Solving using substitution, we have:

y+y+12=58 -> y=23

Substituting, x=23+12=35

The numbers are 23 and 35.

In the Cell Styles gallery, the Currency [0] style and the Comma [0] style format the selected cell with 0 decimal places.

When numbers have values over 1000, they are formatted with commas using the comma style. For instance, the outcome displayed if we apply this style to data with a value of 100000 will be as (100,000). The 1000 (,) separator, often known as the comma style in Excel, may be found under the "Home" tab in the number section. Clicking on it will access this formatting style.

The "Accounting" format frequently uses the comma style.

The dollar sign is locked to the far left half of the cell in the normal comma style format, which also allows for up to two decimal places and 1,000 separators. In the enclosures, negative numbers are displayed.

Hence, in the Cell Styles gallery, the Currency [0] style and the Comma [0] style format the selected cell with 0 decimal places.

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Answer:

r = 6 mph and f = 11 mph

Step-by-step explanation:

Representations:  

1) speed of faster cyclist:  f = r + 5

2) speed of slower cyclist:  r

Distances covered:

(r + 5)(5 hr) + r(5) = 55 mi (total distance covered)

Then 5r + 25 + 5r = 55, or, after reducing this equation:

r + 5 + r = 11, or

2r = 6

Then r = 6 mph and f = 11 mph

Answer:

The equivalent expression is  \(8.25\cdot y -14\).

Step-by-step explanation:

Let \(4\cdot (1.75\cdot y -3.5)+1.25\cdot y\), we proceed to simplify the expression by like terms and other algebraic operations:

1)  \(4\cdot (1.75\cdot y -3.5)+1.25\cdot y\)  Given

2) \([1.75\cdot y +(-3.5)]\cdot 4 + 1.25\cdot y\) Commutative property/Definition of subtraction.

3) \((1.75\cdot 4) \cdot y +(-3.5)\cdot 4 + 1.25\cdot y\) Distributive and associative properties.

4) \(7\cdot y +(-14)+1.25\cdot y\) Definition of multiplication/\(a\cdot (-b) = - a\cdot b\)

5) \((7+1.25)\cdot y -14\) Commutative and distributive properties/Definition of subtraction.

6) \(8.25\cdot y -14\) Definition of addition/Result

The equivalent expression is  \(8.25\cdot y -14\).

Answer:

the price of one gallon of milk has increased by 25%.

Step-by-step explanation:

The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:

(0.81 / 3.24) * 100% = 25%

Therefore, the price of one gallon of milk has increased by 25%.

The solution is 25 %

The percentage increase in the price of one gallon of milk is given by the equation P = 25 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the original price of the milk be A = $ 3.24

Let the increased price of the milk be B = $ 4.05

Let the percentage increase in the price be = P

Now , the equation will be

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Substituting the values in the equation , we get

Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100

On simplifying the equation , we get

Percentage increase P = ( 0.81 / 3.24 ) x 100

Percentage increase P = 0.25 x 100

Percentage increase P = 25 %

Therefore , the value of P is 25 %

Hence , the percentage increase is 25 %

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Tysm! Hope you have a nice day!! ^.^

The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).

The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).

It then crosses the -6 root to turn positive until it again crosses the -2 root.

(It crosses because the odd multiplicity of both roots)

The function remains negative from -2 until root 4, where it crosses into the positive, where it does not cross since there is an even multiplicity.

In light of the aforementioned, only the first option makes sense. because the leading coefficient is positive and the highest degree is odd (9) the function is negative for (-inf, -6).

Then it crosses the -6 root to become positive until it crosses again the root -2.

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(a)   g(x) = 2f(x) + 3.

b.)

the inverse functions are:

f-1(x) = x/2

g¹(x) = (x - 3)/2

c.)

g¹(x) = 2*f-1(x+3).

d. ) we obtain the graph of g¹(x) = 2f-1(x+3). and  g(x) = 2f(x) + 3.

(b) The inverse function of f(x) = 2*x is f-1(x) = x/2.

We found the  inverse function of g(x) = 2f(x) + 3 = 2(x) + 3, by isolating f(x):

g(x) = 2*f(x) + 3

(g(x) - 3)/2 = f(x)

f-1(x) = (x - 3)/2

(d)   we work on this graph f-1(x) and g¹(x),  by graphing f(x) = 2x and y = x/2 on the same set of axes.

shift the graph of f(x) to the right by 3 units to obtain the graph of f-1(x+3), and stretch it vertically by a factor of 2 to obtain the graph of g¹(x) = 2f-1(x+3).

The resulting graph should have a horizontal asymptote at y = 3 and pass through the points (0, -1.5) and (6, 4.5).

To produce g(x) from f(x), we will use  a vertical stretch by a factor of 2, which results in 2f(x). Then, we shift the graph 3 units upward, which results in g(x) = 2f(x) + 3.

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The range of the function \(y=4e^{x}\) will be all option A) All real numbers greater than 0.

The given function is  \(y=4e^{x}\), we know that the domain of this function is all real numbers i.e. from -∞ to +∞, It can take all values. Now, plotting the graph of the function gives us :  

When we take -∞ , the value of y tends towards 0 but never reaches exactly 0 or below zero  because exponential functions never become 0.

When we take 0 in x, term \(e^{x}\) = 1 so y = 4

When we take +∞, the value of y tends towards ∞

Therefore we can conclude that the given function has range of all real numbers greater than 0 or all positive real numbers.

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The complete question will be :

What is the range of the function \(y=4e^{x}\)?

A) All real numbers greater than 0

B) All real numbers less than 0

C) All real numbers less than 4

D) All real numbers greater than 4

Answer:

Since the Frog makes a Jump every 10 seconds

   ( using the digits on a random number table )

Step-by-step explanation:

A frog sitting exactly in the middle of a board which is 5ft long : frog is 2.5 ft from the edge of the board

every 10 seconds the frog jumps ; L or R

If he jumps ; LLRLRL ( still on Board on the left-most square )

if he jumps ; LLRLL ( He is off the Board in fifty seconds )

Since the Frog makes a Jump every 10 seconds

   ( using the digits on a random number table )

Answer:

answer is -1

sorry for bad handwriting

the answer to 1 is d and the answer to 2 is 471,284. Please review this topic when you get time.hope this helps

Answer:

k = 29

Step-by-step explanation:

5k - 3 + 9 + k = 180

6k + 6 = 180

6k = 180 - 6 = 174

k = 174/6 = 29

Answer:

last one

Step-by-step explanation:

since the only letters that both sets have