There are 6 men and 8 women in a book club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.

A) In how many different ways can the committee be selected if exactly one of Mr Lan and Mrs Lan must be on the committee?

B) If a committee is selected at random, find the probability that there are more women than men on the committee, given that Mrs Lan was selected

The value "Sin 100°" is greater than "sin 250°", that is, sin 100° > sin 250°

To compare the values of sin 100° and sin 250°, we need to understand the behavior of the sine function. The sine function oscillates between -1 and 1 over a period of 360°, with its maximum value of 1 at 90° and its minimum value of -1 at 270°.

Using the sine wave, we can see that sin 100° is located in the second quadrant, where the sine values are positive, while sin 250° is located in the third quadrant, where the sine values are negative. Therefore, sin 100° is greater than sin 250°, because sin 100° has a positive value closer to the maximum value of 1, while sin 250° has a negative value closer to the minimum value of -1.

Read more about Sin

brainly.com/question/30232355

#SPJ1

Thus, the value of x for the given expression containing the mixed fractions is found as: x = 8/11.

A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls in between two whole numbers.

Multiply the whole integer by the denominator, then add the numerator to create an incorrect fraction out of a mixed number. The response here becomes the new numerator, while the denominator stays the same.

Given expression:

(x- 4 8/11) + 1 9/11 = 7 3/11

Solving all the mixed fractions in proper fractions:

4 8/11 = (4*11 + 8) / 11 = (44 + 8) /11 = 52/11

1 9/11 = (1*11 + 9) /11 = (11 + 9)/ 11 = 20/11

7 3/11 = (7*11 + 3) /11 = (77 + 3)/11 = 80/ 11

Put the obtained results in expression:

(x- 52/11) + 20/11 = 80/11

x - 52/11 = 80/11 - 20/11

x - 52/11 = (80 - 20)/11

x - 52/11 = 60/11

x = 60/11 - 52/11  

x = (60 -  52) / 11

x = 8/ 11

Thus, the value of x for the given expression containing the mixed fractions is found as: x = 8/11.

Know more about the mixed fractions:

https://brainly.com/question/1055953

#SPJ1

The null and alternative hypotheses that apply are as follows:

H0: p ≤ 0.54, which claims that the proportion of pupils finishing class with a grade of A, B, or C in this experimental curriculum is no greater than 54%.

H₁: p > 0.54, according to the alternative hypothesis, asserts that the rate of students concluding the course with an A, B, or C grade in its experimental form must be above 54%.

The letter "p" represents the proportion of student grades in the experimental program who reach either A, B, or C levels.

The null hypothesis is that the proportion of pupils finishing class with a grade of A, B, or C in this experimental curriculum is no greater than 54%.

Learn more about hypothesis on

https://brainly.com/question/606806

#SPJ1

To graph the solution set to the given system of inequalities, we first need to graph the functions f(x) = x^2 - 2 and g(x) = -x^2 + 5.

The graph of f(x) is a parabola that opens upward and has its vertex at (0, -2). The graph of g(x) is also a parabola, but it opens downward and has its vertex at (0, 5). We can plot these two graphs on the same coordinate plane as follows:

[Insert image of two parabolas on a coordinate plane]

Next, we need to shade the regions of the graph that satisfy the given inequalities. The first inequality y > x^2 - 2 represents the region above the parabola f(x) but below the line y = infinity. The second inequality y ≥ -x^2 + 5 represents the region at or above the parabola g(x). The solution set is the intersection of these two regions.  

The shaded region represents all the points (x, y) that satisfy both inequalities, and therefore, the solution set to the system of inequalities.

Answer:

there are 2,598,960 ways to deal 5 different cards from a standard 52-card deck.

Step-by-step explanation:

The number of ways 5 different cards can be dealt from a standard 52-card deck is given by the combination formula:

C(52,5) = 52! / (5! * 47!)

which simplifies to

C(52,5) = (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)

= 2,598,960

The answer for it is diagram B because it does not cross or have parallel lines

The perimeter of the new shape is 32 cm + 8 * sqrt(3) cm.

What is perimeter?

Perimeter is a measurement of the distance around a two-dimensional shape. It is the total length of the boundary or outer edge of the shape. In other words, it is the sum of the lengths of all the sides of the shape.

First, let's find the length of each side of the equilateral triangle, which was cut out of the square. Since the triangle was cut from a square, its sides have the same length as the sides of the square. Therefore, each side of the equilateral triangle is 8 cm.

Now, let's find the perimeter of the new shape, which is made by joining two of these shapes together. The new shape consists of two equilateral triangles and a rectangle. The length of the rectangle is the same as the side length of the equilateral triangle, which is 8 cm. The width of the rectangle is the same as the height of the equilateral triangle, which can be found by applying the Pythagorean theorem to one of the triangles:

[tex]height^2 = side^2 - (1/2 * side)^2\\\\height^2 = 8^2 - (1/2 * 8)^2\\\\height^2 = 64 - 16\\\\height^2 = 48\\\\height = \sqrt{(48)}\\\\height = 4 * \sqrt{(3)}[/tex]

Therefore, the width of the rectangle is also [tex]4 * \sqrt{(3)} cm.[/tex]

The perimeter of the new shape can be found by adding up the lengths of all four sides:

Perimeter = 2 * (side of equilateral triangle) + 2 * (length of rectangle + width of rectangle)

[tex]Perimeter = 2 * 8 cm + 2 * (8 cm + 4 * \sqrt{(3)} cm)\\\\Perimeter = 16 cm + 16 cm + 8 * \sqrt{(3)} cm\\\\Perimeter = 32 cm + 8 * \sqrt{(3)} cm[/tex]

Therefore, the perimeter of the new shape is [tex]32 cm + 8 * \sqrt{(3)} cm.[/tex]

To learn more about perimeter visit:

https://brainly.com/question/397857

#SPJ1

it would take Cody 40 bushels / 5.26 bushels per hour = 7.61 hours to pick 40 bushels of apples alone.

To begin, let's determine Lisa's individual work rate, or the amount of work she can complete in an hour.

The work formula states that the amount of work completed is equal to the product of the work rate and the amount of time spent working. Lisa's work rate is 40 bushels divided by 13 hours equals 3.08 bushels per hour.

Let C represent Cody's work rate, and let t represent the amount of time it takes him to pick 40 bushels on his own.

At the point when Lisa and Cody cooperate, they pick 40 bushels, so we can compose:

Lisa's work + Cody's work = Total work

3.08 bushels/hour * 4.8 hours + C * 4.8 hours = 40 bushels

14.78 + 4.8C = 40

4.8C = 25.22

C = 5.26 bushels per hour

Consequently, it would take Cody 40 bushels/5.26 bushels each hour = 7.61 hours to pick 40 bushels of apples alone.

know more about fraction visit :

https://brainly.com/question/6201432

#SPJ1

The term 4.59  is the y-intercept of the linear equation and represents the flat rate (or flat cost).

We know that the linear function:

f(x)=0.75x+4.59

models the cost of shipping x packages.

Remember that the general line is:

y = ax + b

Where a is the slope and b the y-intercept.

if x ≈ 0, then you ship no packages, and in that case the value of the function becomes equal to the second term:

f(x ≈ 0) = 4.59

So the term 4.59 represents the flat rate (or flat cost).

Learn more about linear equations at.

https://brainly.com/question/1884491

#SPJ1

The quadratic functions that have a graph with x-intercepts of -8 and 2 are:

y = (x + 8)(x - 2)

f(x) = -7(x + 8)(x - 2)

Options A and C are the correct answer.

We have,

To find the quadratic functions that have a graph with x-intercepts of -8 and 2, we can start by using the fact that the x-intercepts occur when y = 0.

We know that the x-intercepts are -8 and 2, so we can set up two equations:

(x + 8) = 0 and (x - 2) = 0

Solving for x in each equation, we get:

x = -8 and x = 2

Therefore, the factors of the quadratic function that has x-intercepts of -8 and 2 are (x + 8) and (x - 2).

Now we can use these factors to determine which quadratic functions have a graph with these x-intercepts.

A.

y = (x + 8)(x - 2)

Expanding this quadratic function gives:

y = x² + 6x - 16

This function has x-intercepts of -8 and 2, so it is a valid option.

B.

y = (x - 8)(x - 2)

Expanding this quadratic function gives:

y = x² - 10x + 16

This function does not have an x-intercept of -8, so it is not a valid option.

C.

f(x) = -7(x + 8)(x - 2)

Expanding this quadratic function gives:

f(x) = -7x² - 42x - 96

This function does have x-intercepts of -8 and 2, so it is a valid option.

D.

f(x) = -2x² - 12x + 32

To find the x-intercepts of this quadratic function, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-12) ± √((-12)² - 4(-2)(32))) / 2(-2)

x = (-(-12) ± √(144 + 256)) / (-4)

x = (6 ± √(100)) / 2

x = 3 ± 5

So the x-intercepts are -2 and 8, which means this function is not a valid option.

E.

y = x² - 5x + 8

To find the x-intercepts of this quadratic function, we can again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-5) ± √((-5)² - 4(1)(8))) / 2(1)

x = (5 ± √(9)) / 2

x = 4 or x = 1

So the x-intercepts are 4 and 1, which means this function is not a valid option.

F.

f(x) = x² - 8x + 2

To find the x-intercepts of this quadratic function, we can once again use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values from the given function, we get:

x = (-(-8) ± √((-8)² - 4(1)(2))) / 2(1)

x = (8 ± √(60)) / 2

x = 4 ± 2√(15)

So the x-intercepts are 4 + 2 √(15) and 4 - 2 √(15), which means this function is not a valid option.

Therefore,

The quadratic functions that have a graph with x-intercepts of -8 and 2 are:

A. y = (x + 8)(x - 2)

C. f(x) = -7(x + 8)(x - 2)

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

The equation for the orange graph is the one in the last option:

f(x) = -3x³

We can see that the orange graph seems to be:

From the given options, the only one that matches all these options is the last one:

f(x) = -3x³

Learn more about cubic functions at:

https://brainly.com/question/20896994

#SPJ1

The number that needs to be added to complete the square is 169/4

To complete the square for the quadratic equation x² + 13x - 32 = 0, we need to add (13/2)² = 169/4 to both sides.

This is because the coefficient of x in the quadratic term is 13, so half of that is 6.5, and the square of that is 42.25, which simplifies to 169/4.

The equation will then become:

x² + 13x - 32 + 169/4 = 0 + 169/4

So the number that needs to be added to complete the square is 169/4, or 42.25.

Read more about complete the square at

https://brainly.com/question/13981588

#SPJ1

Answer:

1) -8m

2) -x

3) -4y

4)

[tex] - 17x {y}^{3} [/tex]

5) p

6) 0

7) 15m + 10

8) r - 7

9) 5x - 22

10)

[tex]3 {m}^{2} [/tex]

11)

[tex]7 {x}^{2} - x[/tex]

12) 22pq - 8p

13)

[tex] - 13 {r}^{2} - 6r[/tex]

14) -19

15) 0

16) 3.07y

17)

[tex] - 4 {m}^{2} - 35m[/tex]

18)

[tex]x {y}^{2} - 3 {x}^{2} y[/tex]

19) .3mn + 4.7m

20) 3r + 2j + m + 3

21)

[tex] - 4 {x}^{2} - 16x + 11[/tex]

22)

[tex]3 {y}^{4} - {y}^{2} + 11[/tex]

The x-intercept represents:

"The number of hours the taxi was driven before running out of fuel"

In standard notation, the variable x is the independent variable in the horizontal axis, here we can see that in the horizontal axis we are measuring the time (in hours) that the taxi was driving.

Then the x-intercept (the time when y = 0) is the number of hours until the fuel is down to zero, then the correct option is B i guess, but it should be worded as:

"The number of hours the taxi was driven before running out of fuel"

Learn more about x-intercepts at:

https://brainly.com/question/3951754

#SPJ1

Answer: x = -11

Step-by-step explanation:

Sub in y= 3-1/2x into 3x+4y=1 for y, and solve for x.

[tex]3x+4(3-\frac{1}{2}x) =1\\3x + 12 - 2x =1\\\\\ x = -11[/tex]

Answer:

C or D it’s hard to see if the bottom of the shape is a square or rectangle.

Step-by-step explanation:

If rectangle C if squared D

I would go with C

Step-by-step explanation:

You are looking for the hypotenuse of a right triangle with legs of 12 and

 11 feet

Using Pthagorean theorem

hypot^2 = 12^2 + 11^2

hypot^2 = 265

hypot = sqrt (265) = 16.28 ft

Answer:

955 11 7 11

3101 thats my answer

Step-by-step explanation:

10 and 3 thank you

Answer:

Using the FOIL method to multiply (x + 80)(x - 20), we get:

(x + 80)(x - 20) = x^2 - 20x + 80x - 1600

Simplifying the expression, we get:

(x + 80)(x - 20) = x^2 + 60x - 1600

Therefore, the answer is x^2 + 60x - 1600.

The probability of selecting 3 boys for the relay team given that the first selection was a girl is approximately 0.055945 or 8/143.

Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.

Let's start by calculating the probability of selecting a girl first. Since there are 7 girls and 14 team members in total, the probability of selecting a girl first is:

P(Girl first) = 7/14 = 1/2

Now, we need to calculate the probability of selecting 3 boys from the remaining 13 team members (6 boys and 7 girls). We can do this using combinations:

Number of ways to select 3 boys from 6 = C(6,3) = 20

Number of ways to select 1 girl from 7 = C(7,1) = 7

Total number of ways to form a relay team of 4 from 13 = C(13,4) = 715

Therefore, the probability of selecting 3 boys from the remaining 13 team members is:

P(3 boys from 13) = (20*7)/715 = 4/143

Finally, we can use conditional probability to calculate the probability of selecting 3 boys given that the first selection was a girl:

P(3 boys | Girl first) = P(3 boys from 13)/P(Girl first)

= (4/143)/(1/2)

= 8/143

= 0.055944...

Rounded to the nearest millionth, the probability is 0.055945.

Therefore, the probability of selecting 3 boys for the relay team given that the first selection was a girl is approximately 0.055945 or 8/143.

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

Therefore, a sharpening costs Dollar 1.85.

The US, Canada, Australia, and some nations in the Pacific, Caribbean, Southeast Asia, Africa, and South America all use the dollar as their primary unit of exchange. The word "$" is used to denote it.

Let's use $a for the sharpener's price. We can state that the price of a book is $a + 1.95 because it costs $1.95 more than a sharpening.

We are aware of the $26.10 total cost of 10 sharpeners and 2 books. This can be expressed as an equation:

10a + 2(a + 1.95) = 26.10

If we simplify this equation, we get:

12a + 3.90 = 26.10

3.90 less from each side results in:

12a = 22.20

By multiplying both sides by 12, you get:

a = 1.85

Therefore, a sharpening costs $1.85.

To know more about dollar visit:

brainly.com/question/28547396

#SPJ1

Answer:

60 seconds

Step-by-step explanation:

Let's start by finding how much more water needs to be added to the solution to reach a total of 10 ml of water:

10 ml - 5.8 ml = 4.2 ml

Now we can use the formula:

time = amount of water added / rate of addition

to calculate the time it will take to add 4.2 ml of water at a rate of 0.07 ml/s:

time = 4.2 ml / 0.07 ml/s

time = 60 seconds (rounded to the nearest second)

Therefore, it will take 60 seconds to add enough water to the solution to make a total of 10 ml of water.

Can you mark me asbrainliest if you appreciate my effort just for favor. Thank you^^

Bank B would be the best option since it offers a higher interest rate than Bank A and does not have any fees.

To compare different bank accounts, we need to know the interest rates offered by each bank. Let's assume that we have three local banks, each with a different interest rate: Bank A offers 2% interest, Bank B offers 2.5% interest, and Bank C offers 3% interest.

Using the formula for simple interest, we can calculate the amount of interest earned on the initial deposit of $2000 over four years for each bank:

Bank A: 2% interest per year

After four years, the interest earned is:

$2000 x 2% x 4 = $160

Bank B: 2.5% interest per year

After four years, the interest earned is:

$2000 x 2.5% x 4 = $200

Bank C: 3% interest per year

After four years, the interest earned is:

$2000 x 3% x 4 = $240

So, Bank C offers the highest interest rate and would earn the most interest over the four-year period. However, we also need to consider any fees associated with each account. Let's assume that Bank A and Bank B have no fees, but Bank C charges a $50 annual fee.

Bank A: Total amount after four years = $2000 + $160 = $2160

Bank B: Total amount after four years = $2000 + $200 = $2200

Bank C: Total amount after four years = $2000 + $240 - $50 x 4 = $1960

Even though Bank C offers the highest interest rate, the annual fee significantly reduces the total amount earned over four years. Therefore, Bank B would be the best option since it offers a higher interest rate than Bank A and does not have any fees.

Learn about interest rate here https://brainly.com/question/25793394

#SPJ1

According to the given data the unit rate of hamburgers per hour is 9 hamburgers per hour.

The unit rate is the rate of change of the number of hamburgers produced per hour.

To find the unit rate, we can use the formula:

Unit rate = (Number of hamburgers produced) / (Number of hours)

Using the information provided in the table, we can find the unit rate for the restaurant:

For 3 hours, the restaurant produced 27 hamburgers.

Unit rate = 27 / 3 = 9 hamburgers per hour

For 5 hours, the restaurant produced 45 hamburgers.

Unit rate = 45 / 5 = 9 hamburgers per hour

For 7 hours, the restaurant produced 63 hamburgers.

Unit rate = 63 / 7 = 9 hamburgers per hour

For 9 hours, the restaurant produced 81 hamburgers.

Unit rate = 81 / 9 = 9 hamburgers per hour

Therefore, the unit rate of hamburgers per hour for the restaurant is 9 hamburgers per hour.

To know more about unit rate visit:

https://brainly.com/question/29781084

#SPJ1

Answer:

Step-by-step explanation:

b

Answer:

47 + 9f [tex]\leq[/tex] 120

Step-by-step explanation:

B is the correct answer.

The surface area of the square base pyramid is 132 cm².

The surface area of the square pyramid can be found as follows:

A square pyramid is a pyramid that has its base as square.

Therefore,

surface area of the square pyramid = base area + 2al

where

Therefore,

surface area of the square pyramid = 6² + 2 × 6 × 8

surface area of the square pyramid = 36 + 96

surface area of the square pyramid = 132 cm²

learn more on surface area here: brainly.com/question/24022178

#SPJ1

the formula for the exponential function N(t) is N(t) = 14 * 59in power (t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

How to solve the question?

Let N(t) be the exponential function we are trying to find, where N is the population at time t.

From the given information, we know that when t=0, N(0) = 14, which is the initial value of N.

We also know that when t is increased by 6, N is multiplied by 59. In other words,

N(t+6) = 59N(t)

We can use this relationship to express N(t+6) in terms of N(t) by substituting N(t+6) with 59N(t) in the above equation, giving us:

59N(t) = N(t+6)

Now, we can use this equation to solve for N(t) in terms of N(0) by repeatedly substituting N(t) with 59N(t-6), 59²N(t-12), 59³N(t-18), and so on.

N(t) = 59  in power (t/6) * N(0)

Using the initial value of N(0) = 14, we get:

N(t) = 14 * 59 in power (t/6)

Therefore, the formula for the exponential function N(t) is N(t) = 14 * 59^(t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

To know more about function visit :-

https://brainly.com/question/11624077

#SPJ1

The length or of the segment AD or  distance from point A to point D is 16.6 ft.

Given that Mr. Rose is remodeling his house by adding a room to one side

In order to determine the length of the boards he needs for the roof of the room, he must calculate the distance from point A to point D

We have to find the distance of AD

Sin 25 = 7/x

x is the distance of AD

x=7/sin 25

x=16.6 ft

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1