Two chips are drawn at random without replacement from a bowl containing n chips numbered 1 through n where n ≥ 3.What is the probability that the greater of the two numbers obtained is 3?A. 4/n(n-1) B. 3/n(n-1)C.2/n(n-1)D. 4/n²E. 2/n

Answer: a

Step-by-step explanation: add 2 + 3 +28

An integral for the volume of the solid obtained by rotating the region bounded by the curves y = 1/(1 x2), y = 0, x = 0, and x = 2 about the

line x = 2 is v = 2.pi.∫(0,2) (2-x/1+[tex]x^{2}[/tex]).dx

we will use the method of cylindrical shells here as per the limits given to calculate the volume,

let us first find the volume of a cylindrical shell with thickness dx at a distance of x from y axis,

dV = 2.pi(2-x).y.dx

where (x,y) is a point on the curve y=1/1+[tex]x^{2}[/tex]

v = 2.pi.(2-x)(1/1+[tex]x^{2}[/tex]).dx

Therefore the total volume would be,

v = 2.pi.∫(0,2) (2-x/1+[tex]x^{2}[/tex]).dx

v = 2.pi.[2tan-1 x -(1/2).ln(1+[tex]x^{2}[/tex])] at 0,2

v = 2.pi.[2tan-1(2) - ln 5/2]

v = 4 .pi.tan-1(2) - pi.ln5

therefore volume = 8.8 approximately.

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Answer: 13.2%

Step-by-step explanation:

To find the percentage we need to use the formula: (original cost-new cost)/original cost *100

Plugging in the numbers: (38-33)/38*100=0.131578947368421*100=13.2%

Answer:

Step-by-step explanation:

sin(YZX)=opposite/hypotenuse

sin(YZX)=7.5/22.3

then apply sin inverse to find angle Z

Answer:

40,28,16,4, -8,-20... keep going

Step-by-step explanation:

use 40-12, then 40-2*12, so forth

The weight of gift is 5 pound extra with medium size of box.

In science and engineering, the weight of an object is the force acting on the object due to gravity.

Let the weight is W

The first company charged “$15 to ship a medium box, plus an additional $1 per pound”.

So, that the amount of certain weight is F =  $15 + $1*W

The second company charged “$10 to ship a medium box, plus an additional $2per pound”.

So, that the amount of certain weight is S  =  $10 + $2*W

The two shipping methods will cost the same amount

so that, F = S

$15 + $1*W = $10 + $2*W

$5  =  $1*W

W = 5 pound.

So that the weight of gift is 5 pound extra with medium size of box.

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The two integers required in the question are; 16 and 12

We are told that the sum of two positive integers is 28. Now, if the two integers are x and y, then we have;

x + y = 28   ------(1)

When the smaller integer is subtracted from three times the larger, the result is 36. Thus;

3x - y = 36  ------(2)

Add eq 1 and eq 2 to get;

4x = 64

x = 64/4

x = 16

16 + y = 28

y = 28 - 16

y = 12

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a) The probability that the specific engineer Jane and the specific manager Mary are on the committee is 2/45

b) The probability that the most experienced and least experienced engineers are on the committee is 2/45

The term called probability in math is known as the probability is the likelihood or chance that an event will occur

And it is calculated by using the general form that can be written as,

=> Probability = Expected/Total outcome

Here we know that if 2 managers were randomly selected from  10 managers, then the probability will be 2/10

AS we know that if 4 engineers were randomly selected from 18 managers, then the probability will be 4/18

On the other hand the probability that engineer Jane or manager Mary is on the committee will be calculated as,

=> 2/10 x 4/18

=> 8/180

When we simplify this then we get the value of the probability as 2/45.

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Answer:

4/3x + 9/2y

Step-by-step explanation:

2x + 3y - 2/3 x + 1 1/2y

1 1/2 = 3/2

2x + 3y - 2/3x + 3/2y

= 6/3x + 6/2y - 2/3x + 3/2y

= 4/3x + 9/2y

The system of equations are solved

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = x³ + 9

On simplifying the equation , we get

A = x³ + 9

So , it cannot be further factorized

b)

A = x² - 12

On simplifying the equation , we get

A = x² - 12

So , it cannot be further factorized

c)

A = 9x² - 16

On simplifying the equation , we get

A = ( 3x + 4 ) ( 3x - 4 )

On factorizing the equation ,

A = ( 3x )² - ( 4 )²

Hence , it is a difference of perfect squares

d)

A = 4x² + 9

On simplifying the equation , we get

A = ( 2x )² + ( 2 )²

So , it cannot be further factorized

e)

A = x³ + 8

On simplifying the equation , we get

A = ( x )³ + ( 2 )³

Hence , it is a perfect cube

f)

A = 25x² - 64

On simplifying the equation , we get

A = ( 5x + 8 ) ( 5x - 8 )

On factorizing the equation ,

A = ( 5x )² - ( 8 )²

Hence , it is a difference of perfect squares

g)

A = x² - 100

On simplifying the equation , we get

A = ( x + 10 ) ( x - 10 )

On factorizing the equation ,

A = ( x )² - ( 10 )²

Hence , it is a difference of perfect squares

h)

A = 216x³ - 27

On simplifying the equation , we get

A = ( 6x )³ + ( 3 )³

Hence , it is a perfect cube

i)

A = 8x³ - 512

On simplifying the equation , we get

A = ( 2x )³ - ( 8 )³

Hence , it is a perfect cube

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The number of feet away from the sprinkler where it could spread water would be the radius of the circle in which it is spraying.

The area of the circle is

[tex]\pi[/tex]r²=706.50

(3.14)r²=706.50

r²=706.50÷3.14

r²=225

Now, the square root will shift from LHS to RHS.

r=(225)²

r=15

Therefore, the sprinkler can spread the water 15 feet away .

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The values for x and y for the geometric system formed by two similar triangles are 9 / 2 and 15 / 4, respectively.

In this question we find the case of a geometric system formed by two similar triangles. Two triangles are similar when their angles are congruent and sides are not congruent though proportional. The situation represented in the figure is described by proportion formula:

5 / (5 + y) = 4 / 7 = 6 / (6 + x)

Now we proceed to find the values for x and y by algebra properties:

5 / (5 + y) = 4 / 7

5 · 7 = 4 · (5 + y)

35 = 20 + 4 · y

15 = 4 · y

y = 15 / 4

6 / (6 + x) = 4 / 7

6 · 7 = 4 · (6 + x)

42 = 24 + 4 · x

18 = 4 · x

x = 18 / 4

x = 9 / 2

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Answer: You should buy 7.5 pounds of pecan.

Step-by-step explanation: Each pecan pie needs 1.5 pounds each and 1.5 x 5 = 7.5

Answer:

13800

Step-by-step explanation:

First we suppose the cost price is X, so 15%x is lost

x-15%x=10200

85%x=10200

   x=12000

Now want 15% profit, so 100%+15%=1.15

12000x1.15=13800

The needed temperature continues to decline at this pace in 2 hours -6°C, 5 hours -15°C, and half an hour -1.5°C.

A weather station on a mountaintop says that the temperature is now 0°C and has been dropping at a consistent pace of 3°C every hour.

We must discover,

What will the temperature be in 2 hours, 5 hours, and half an hour if it continues to plummet at current rate?

In response to the question,

A weather station on a mountaintop says that the temperature is now 0°C and has been dropping at a consistent pace of 3°C every hour.

The temperature drops by 3°C in one hour = 0 – 3 = -3°C

The temperature drops in two hours = (2)(-3°C) = -6°C

Temperature drop in 5 hours = (5)(-3°C) = -15°C

In half an hour, the temperature drops = (0.5)(-3°C) = -1.5°C.

As a result, the needed temperature continues to decline at this pace in 2 hours -6°C, 5 hours -15°C, and half an hour -1.5°C.

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The required temperature will drop further at this rate in 2 hours at -6 °C, 5 hours at -15 °C, and 30 minutes at -1.5 °C.

A weather station on a mountaintop says that the temperature is now 0 °C and has been dropping at a consistent pace of 3 °C every hour.

A weather station is a place equipped with tools for measuring atmospheric conditions, gathering data for weather forecasts, and researching the weather and environment.

The temperature drops by 3 °C in one hour = 0 – 3 = -3 °C. The temperature drops in two hours = (2)(-3 °C) = -6 °C

Temperature drop in 5 hours = (5)(-3 °C) = -15 °C

In half an hour, the temperature drops = (0.5)(-3 °C) = -1.5 °C.

Therefore,  the needed temperature continues to decline at this pace in 2 hours -6 °C, 5 hours -15 °C, and half an hour -1.5 °C.

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The probability that a resident of this city who is 60 years old will survive until they are 80 will be 0.54 l.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

In this case, in the city of exactly 100,000 people, 90% can expect to live to (at least) age 60 and 60% can expect to live to (at least) age 80.

The probability that a resident of this city who is 60 years old will survive until they are 80 will be:

= 90% × 60%

= 0.54

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If E(X) = 6 and E(Y) = 10, and the random variables are independent variables, the value of E(X | Y) is 6

Given, E(X) = 6 and  E(Y) = 10.

It is also given that X and Y are independent variables.

So, if two random variables X and Y are independent, which means that if knowing the value of one of them does not change the probability of occurring of the other one. In other words, if X and Y are independent, we can write:

                           P(Y | X) = P(Y)

So, in the question, we are asked to determine the value of E(Y | X).

                        ∴ E(X | Y) = E(X)

                        ∴ E(X | Y) = 6

Hence, the value of E(X | Y) is 6

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Answer:

90 is 150% of 60

OR

90 is 50% greater than 60

Step-by-step explanation:

To find the percentage increase between two values, the first step is to find the difference between the final and initial value.

Final value: 90cm

Initial value: 60cm

Difference = 90 - 60 = 30cm

Next, you need to divide the difference between the two values by the initial value.

30 / 60 = 0.5

Lastly, you need to take the value previously found and multiply it by 100 to convert it from a decimal to a percentage.

0.5 * 100 = 50%

This value will be your percentage increase.

If you want to know what percentage the final value is of the initial value, you can take the percentage you have and add 100% to it.

50% + 100% = 150%

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Answer: 150%

Step-by-step explanation:

First, ask yourself what the difference between the two is: 90-60=30.

Secondly, 30 is 1/2 of 60. 1/2=50%.

You also need to add the hundred percent because we are adding 60 and 60 is 100% of 60. It increases by 50 and then 100. so 150%.

50% + 100% = 150%

79.1 mL is equal to 0.0791 liters with correct significant figures.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

79.1 mL is equal to 0.0791 litres. To convert millilitres to litres, we divide the number of milliliters by 1000:

79.1 mL / 1000 = 0.0791 liters

So, 79.1 mL is equal to 0.0791 litres with correct significant figures.

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The expected number of rolls until the first pair of consecutive sixes appears is 36.

This can be calculated using a geometric distribution, where each roll is considered a Bernoulli trial with success defined as rolling two sixes in a row, and failure defined as not rolling two sixes in a row. The probability of success in any given roll is 1/36, since there are 36 possible outcomes for rolling two dice and only one of them results in two sixes.

Using the formula for the expected value of a geometric distribution, we can calculate the expected number of rolls until the first success as:

where p is the probability of success in a single roll (1/36) and E is the expected number of rolls until the first success. So the expected number of rolls until the first pair of consecutive sixes appears is 36.

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If ten slices are cut from the cheese. each slice has a width of 1 cm , then the maximum possible volume of the remaining block is 729 cm³ .

The maximum possible volume of the remaining block of cheese can be found by considering the slices to be the minimum possible thickness, which is 1 cm. So, after each slice is cut, the dimensions of the cheese decreases by 1 cm.

the dimensions of the block of cheese is :  10 cm by 13 cm by 14 cm  .

number of slices cut is = 10 slices .

the dimension change by the 10 cut of cheese slices are as follows :

(10,13,14) → (10,13,13) → (10,12,13) → (10,12,12) → (10,11,12) → (10,11,11) → (10,10,11) → (10,10,10) → (9,10,10) → (9,9,10) → (9,9,9) .

So , after cutting 10 slices the dimensions of the remaining block is 9 cm by 9 cm by 9cm .

the volume of the remaining cheese  block is = 9×9×0 = 729 .

Therefore , the maximum possible volume of the remaining block is 729 cm³ .

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Answer:

x greater-than-or-equal-to negative 9.2

Step-by-step explanation:

Step by step in math notation here is what Marquis solved

Starting with -5.6 ≥ x + 3.6

Step 1

Step 2: Interpret the results

Since the question is asking only for the first step where the error was made, the rest of the actions taken have no relevance

The probability of getting at least 14 heads when flipping a fair coin 20 times is 0.25.

This can be calculated using the binomial distribution formula which states that the probability of obtaining exactly x successes in n trials is given by

P(x) = (n choose x) * p^x * (1-p)^(n-x),

where n is the total number of trials, p is the probability of success, and x is the number of successes.

For this problem, n=20, p=0.5, and x=14, so the probability of getting at least 14 heads is P(x) = (20 choose 14) * 0.5^14 * 0.5^6 = 0.25.

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"A music streaming service charges a flat monthly fee plus a per-song charge for each song downloaded. It cost $11 to download 2 songs during the month and $14 to download 8 songs during the month."

The equation in the form y = mx b for this function is:

y = (1/2)x + 10

To write an equation in the form y = mx + b for this function, we can use two sets of data points, (x, y), to find the slope (m) and the y-intercept (b) of the line.

Let x be the number of songs downloaded and y be the cost in dollars.

We can use the slope formula to find m:

Next, we can use one of the data points and the slope to find b:

Therefore, the equation of the line is:  y = (1/2)x + 10

This equation represents the cost y in dollars of downloading x number of songs, given the flat monthly fee and per song charge.

Complete Question:

"A music streaming service charges a flat monthly fee plus a per-song charge for each song downloaded. It cost $11 to download 2 songs during the month and $14 to download 8 songs during the month. Write an equation in the form y = mx + b for this function."

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The probability that both the father and mother are current smokers is 0.12.

The probability that the mother is a current smoker is, 0.3 and the father is a current smoker is, 0.4.

The events are independent, the probability that both the events will occur is the multiplication of probability of individual events.

Therefore, the required probability is product of probability that mother is a current smoker with the probability that father is a current smoker.

P(Father and Mother are current smokers) = P(Father is a current smoker) × P(Mother is a current smoker)

P(Father and Mother are current smokers) = 0.4 × 0.3

P(Father and Mother are current smokers) = 0.12

The required probability is 0.12.

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The equation for your savings account can be represented as:

y = 50 + 10x

The equation for your friend's savings account can be represented as:

y = 25 + 10x

where x is the number of weeks and y is the total amount of money in the account.

The equation for the savings account can be determined by taking the initial amount of money and adding the weekly deposit over a certain number of weeks. The initial amount of money in your savings account is $50, and you plan to deposit $10 each week, so each week your balance will increase by $10.

Starting from the initial balance, after the first week, the balance will be $50 + $10 = $60. After the second week, the balance will be $60 + $10 = $70, and so on. We can represent this pattern using an equation:

y = 50 + 10x

where y is the balance after x number of weeks.

Similarly, for your friend's savings account, the initial balance is $25 and the weekly deposit is $10. So, each week the balance will increase by $10. Using the same pattern, the equation for your friend's savings account can be represented as:

y = 25 + 10x

where y is the balance after x number of weeks.

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The temperature at 6 P.M. would be - 29 °F.

Given is that Casho spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -10.4°F. Between 9 am and noon, the temperature rose 9.5°F. Between noon and 3 pm, the temperature went down 10°F. Between 3 pm and 6 pm, the temperature went down 18.6°F.

Temperature at 9 A.M. = - 10.4°F.

At noon, the temperature would be = - 10.4°F + 10°F = - 0.4°F

At 3 P.M., the temperature would be = - 0.4°F - 10°F = - 10.4°F

At 6 P.M., the temperature would be = - 10.4°F - 18.6°F = - 29 °F

Therefore, the temperature at 6 P.M. would be - 29 °F.

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Answer: There are 29 freshman in the class

Step-by-step explanation:

Sophmore = x

Freshman = x+16

x + (x + 16) = 42

x + x + 16 = 42

2x + 16 = 42

2x = 26

x = 13

Sophmore = x = 13

Freshman = x + 16 = 29

Answer:

29 freshmen

Step-by-step explanation:

Freshmen = 16 + x

Sophomores = x

Equate the number of freshmen(16 + x ) and the number of sophomores( x ) to 42( the total number of students in the class)

(16 + x ) + x = 42

16 + 2x = 42

2x = 42 - 16

2x / 2 = 26/2

x = 13

Therefore, the number of freshmen

= 16 + x

= 16 + 13

= 29

Answer:

because yftythdetv y yvh bb jhh

Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.

At the banquet in Macbeth, Lady Macbeth fulfills a traditional feminine role in several ways. Firstly, she demonstrates her hospitality and generosity by welcoming the guests and providing them with food and drink. Secondly, she shows her nurturing nature by urging Macbeth to be more hospitable and to provide the guests with more generous servings. Thirdly, she shows her graciousness and hospitality by offering the guests timely compliments. Lastly, she shows her caring and supportive nature by encouraging Macbeth to be more gracious and generous. Altogether, Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.

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