(09.06)
Two functions are shown in the table below.

Function | 1 | 2 | 3 | 4 | 5 | 6

f(x) = -x^2 + 4x + 12
-
g(x) = x+8

Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points)

a) The number of ways to form a committee of 6 people from the department is 177,100.

b) The number of ways to form a committee of 6 people with an equal number of men and women is 54,600.

c) The number of ways to form a committee of 6 people with more women than men is 91,455.

a) To form a committee of 6 people from the department, we can choose 6 individuals from a total of 25 people (10 men + 15 women). The order in which the committee members are chosen does not matter, and we are not concerned with any specific positions within the committee. Therefore, we can use the concept of combinations.

The number of ways to choose 6 people from a group of 25 is given by the combination formula:

C(25, 6) = 25! / (6! * (25 - 6)!) = 25! / (6! * 19!) = 177,100

Therefore, there are 177,100 ways to form a committee of 6 people from the department.

b) In this case, we need to choose an equal number of men and women for the committee. We can select 3 men from the available 10 men and 3 women from the available 15 women. Again, the order of selection does not matter.

The number of ways to choose 3 men from 10 is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 120

Similarly, the number of ways to choose 3 women from 15 is:

C(15, 3) = 15! / (3! * (15 - 3)!) = 15! / (3! * 12!) = 455

To find the total number of ways to form a committee with an equal number of men and women, we multiply these two combinations:

Total = C(10, 3) * C(15, 3) = 120 * 455 = 54,600

Therefore, there are 54,600 ways to form a committee of 6 people with an equal number of men and women.

c) In this case, we need to form a committee with more women than men. We can choose 1 or 2 men from the 10 available men and select the remaining 6 - (1 or 2) = 5 or 4 women from the 15 available women.

For 1 man and 5 women:

Number of ways to choose 1 man from 10: C(10, 1) = 10

Number of ways to choose 5 women from 15: C(15, 5) = 3,003

For 2 men and 4 women:

Number of ways to choose 2 men from 10: C(10, 2) = 45

Number of ways to choose 4 women from 15: C(15, 4) = 1,365

The total number of ways to form a committee with more women than men is the sum of these two cases:

Total = (Number of ways for 1 man and 5 women) + (Number of ways for 2 men and 4 women)

     = 10 * 3,003 + 45 * 1,365

     = 30,030 + 61,425

     = 91,455

Therefore, there are 91,455 ways to form a committee of 6 people with more women than men.

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Answer:

a=99

Step-by-step explanation:

The answer is 99 square meters. I took this quiz, so I know the answers. I hope you get a good grade!!

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Answer:

\(1347\)

Step-by-step explanation:

Let's first figure out an expression for the sum of 3 consecutive integers

If \(n\)  is the smallest of the 3 consecutive integers, then the next consecutive integer would be \(n + 1\) and the next one after that, \(n + 2\)

The sum of these would be

\(n + (n +1) + (n +3) = 3n + 3\)

The next step is to find out many integers there are between 1 and 2019(since the question says less than 2020) that can be written as the sum of 3 consecutive integers

We get the following inequality:

\(3n + 3 < 2020\)

\(3n = 2017\)

\(n = 2017/3 = 672 \textrm{ (omit fractional part)}\)  

So there are 672 integers that can be expressed the sum of 3 consecutive integers

Since there are a total of 2019 integers between 1 and 2019, subtracting 672 from 2019 will give us the complement i.e. The  number of positive numbers less than 2020, which cannot be written as the sum of three consecutive positive numbers.

Answer:

\(2019 - 672 = \boxed{1347}\)

Answer:46 1/3

Explanation:

12 1/2 + 12 1/2 = 25

10 2/3 + 10 2/3 = 21 1/3

25 + 21 1/3 = 46 1/3

The equation of the line is y = (-1/5)x + 7.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

5y + x = 10

5y = -x + 10

y = (-1/5)x + 10  _____(1)

This is in the form of,

y = m(1)x + c

This means,

m(1) = (-1/5) ______(2)

The equation that is parallel to (1) can be assumed as a general equation as,

y = m(2)x + c _______(4)

Since (1) and (4) are parallel.

From (4) and (3)

m(1) = m(2)

So,

m(2) = (-1/5) _____(5)

And,

y-intercept = 7 _____(6)

Now,

From (4), (5) and (6)

y = (-1/5)x + 7

Thus,

The equation of the line is y = (-1/5)x + 7.

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Given:

Price before tax was $19.99.

To find:

The cost of the two DVDs after the 8.25% tax was added.

Solution:

We have,

Price of two DVDs before tax = $19.99

Rate of tax = 8.25%

Thus,

Tax = 8.25% of price of two DVDs before tax

\(Tax=\dfrac{8.25}{100}\times 19.99\)

\(Tax=1.649175\)

\(Tax\approx 1.65\)

Now,

\(\text{Cost of two DVDs after tax = Cost of two DVDs before tax + Tax}\)

                                         \(= \$19.99 + \$1.65\)

                                         \(= \$21.64\)

Therefore, the cost of 2 DVDs after the tax is $21.64.

Answer:

24

Step-by-step explanation:

the ratio of the triangle is 1/2. Let x be Segment SP

1/2 = 12/x

x = 24

(a) The generating functions together r times:\(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^5\)\)

(b) \(\(f(x) = (x^3 + x^4 + x^5 + x^6)^4\)\)

(c) \(\(f(x) = (\frac{x}{1-x})^{7r}\)\)

(d) \(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^3\)\)

(a) To build a generating function for selecting r items from five different boxes with at most five objects in each box, we can consider each box as a separate generating function and multiply them together.

The generating function for selecting objects from the first box is:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

Similarly, for the second, third, fourth, and fifth boxes, the generating functions are the same:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

To select r items, we need to choose a certain number of items from each box.

Therefore, we multiply the generating functions together r times:

\(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^5\)\)

(b) To build a generating function for selecting r items from four different boxes with between three and six objects in each box, we need to consider each box individually.

The generating function for selecting objects from the first box with three to six objects is:

\(\(x^3 + x^4 + x^5 + x^6\)\)

Similarly, for the second, third, and fourth boxes, the generating functions are the same:

\(\(x^3 + x^4 + x^5 + x^6\)\)

To select r items, we multiply the generating functions together r times:

\(\(f(x) = (x^3 + x^4 + x^5 + x^6)^4\)\)

(c) To build a generating function for selecting r items from seven different boxes with at least one object in each box, we need to subtract the case where no items are selected from the total possibilities.

The generating function for selecting objects from each box with at least one object is:

\(\(x + x^2 + x^3 + \ldots = \frac{x}{1-x}\)\)

Since we have seven boxes, the generating function for selecting from all seven boxes with at least one object is:

\(\((\frac{x}{1-x})^7\)\)

To select r items, we multiply the generating function by itself r times:

\(\(f(x) = (\frac{x}{1-x})^{7r}\)\)

(d) To build a generating function for selecting r items from three different boxes with at most five objects in the first box, we can consider each box separately.

The generating function for selecting objects from the first box with at most five objects is:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

For the second and third boxes, the generating functions are the same:

\(\(1 + x + x^2 + x^3 + x^4 + x^5\)\)

To select r items, we multiply the generating functions together r times:

\(\(f(x) = (1 + x + x^2 + x^3 + x^4 + x^5)^3\)\)

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Answer:

113 square feet

Step-by-step explanation:

Given

\(d = 24\) --- diameter

See attachment for complete question

Required

Determine the area of each color

First, we calculate the area of all colors

\(Area = \frac{\pi d^2}{4}\)

This gives:

\(Area = \frac{22 * 24^2}{7*4}\)

\(Area = \frac{12672}{28}\)

\(Area = 452.57\)

Since all 4 colors have equal areas, the area of 1 of them is:

\(A = \frac{1}{4}Area\)

\(A = \frac{1}{4} * 452.57\)

\(A = 113.14ft^2\)

\(A = 113ft^2\) --- approximated

The first step is to graph the line 2x + y = -8. To do this, we can graph the x and y-intercepts. Letting x = 0, we get y = -8, so the y-intercept is -8. Letting y = 0, we get 2x = -8, so x = -4.

Graph the line between the points (-4, 0) and (0, -8). The line should be dotted, because this is a strict inequality (the points on the line are not part of the solution).

The next step is to substitute a point - I like to use (0,0): when x and y are equal to zero, we have 2(0)+0>-8, which is true. Therefore, the right side of the graph (which contains the point (0,0)) should be shaded. Note: If the inequality was not true, you would want to shade the opposite side of the graph.

The probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7 is 28.43%. Correct option is D.

To calculate the probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7, we need to use the standard normal distribution and the z-score.

First, we can find the z-score for 82 using the formula:

z = (x - mu) / sigma

where x is the value of interest (in this case, 82), mu is the mean (78), and sigma is the standard deviation (7).

z = (82 - 78) / 7

z = 0.57

Next, we can use a z-table or a calculator to find the area under the standard normal curve corresponding to a z-score of 0.57. The area represents the probability that a score will be greater than 82.

Using a standard normal table, we find that the area to the right of z = 0.57 is 0.2843 or approximately 28.43%. Therefore , correct option is D.

In conclusion, by calculating the z-score and using a standard normal distribution table, we can find the probability that a score will be greater than a certain value in a normal distribution with a known mean and standard deviation.

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Complete question is:

A normal distribution with a mean of 78 and a standard deviation of 7, what is the probability that a score will be greater than 82?

group of answer choices

A. 23.89%

B. 26.11%

C. 76.11%

D. 28.43%

E. 52.22%

Answer:

x=52º

Step-by-step explanation:

A triangle's angles are equal to 180º.

Given the opposite angle to H is 66º, we can find the opposite angle of angle I. The opposite angle of angle K is 62º, assuming that it is equivalent to the opposite angle of angle I we can solve for x.

66+62+x=180

Add 66 and 62.

128+x=180

Subtract 128 from both sides of the equation.

x=52

Angle x is equal to 52º.

Hope this helps :)

1) Since the sum of interior angles yields 180º, no matter which type of triangle it is.

2) Then we can write

3x+12 +x +6x +8 = 180

10x +20 = 180º

10x = 180-20

10x = 160

x= 16

2.2 Let's find out the measurement of each angle

m∠ A= x Plug into that the value of x

m∠ A = 16º

m∠B= 3x+12 Plug into that the value of x

m∠B = 3(16) +12

m∠B = 48+12

m∠B =60

3) Then the answers are:

x = 16

m∠ A = 16º

m∠B =60

Answer:

385.8 I think sorry if wrong

Step-by-step explanation:

Well if the average student is 35 kg then 35kg times by 5 students is 175 kg so convert that to pounds and you get 385.8.

It will take 5.625 hours for both Darryl and Valerie to paint the room if they work together .

In the question ,

it is given that ,

Darryl can paint the room in 9 hours .

So , in 1 hour Darryl can paint 1/9 of the room .

Valerie can paint the room in 15 hours .

So , in 1 hour Valerie can paint 1/15 of the room .

So , the time taken to paint the room together can be calculated using ,

1/t = 1/9 + 1/15

1/t = 5/45 + 3/45

1/t = 8/45

Simplifying further ,

we get ,

t = 45/8

t = 5.625

Therefore , the time taken will be 5.625 hours .

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Answer:

Where is the ordered pair?

Step-by-step explanation:

Answer:

D- Quotient C- Product A-Difference B-Sum

Step-by-step explanation:

Hope this helps

The probability that Bentley selects a striped egg and Johnny selects a polka dotted egg is 35/132.

The probability of Bentley selecting a striped egg on the first pick is 7/12

After Bentley selects an egg, there are 11 eggs remaining in the basket, of which 5 are polka dotted.

So the probability of Johnny selecting a polka dotted egg on the second pick = 5/11.

To find the probability of both events happening, we multiply the probabilities:

P(Bentley selects striped and Johnny selects polka dotted) = (7/12) * (5/11)

P(Bentley selects striped and Johnny selects polka dotted) = 35/132

Therefore, the probability that Bentley selects a striped egg and Johnny selects a polka dotted egg is 35/132.

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Answer: 90 degrees

Step-by-step explanation:

The greatest common factor of 84 and 36 will be 2 × 2 × 3 that is 12.

The term that is common in the given terms.

The terms are given below.

84 and 36

The factor of the 84 will be

84 = 2 × 2 × 3 × 7

The factor of the 36 will be

36 = 2 × 2 × 3 × 3

Then the greatest common factor of 84 and 36 will be 2 × 2 × 3 that is 12.

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Answer:

\(\dfrac{1}{5}\ L\)

Step-by-step explanation:

It is given that,

A 2-liter bottle is filled completely with water from a faucet in 10 seconds.

We need to find how much water us filled in to the bottles each seconds.

In 10 s = 2 L bottle is filled

In 1 s, \(\dfrac{2}{10}\ L=\dfrac{1}{5}\ L\) of water is filled into the bottles.

Answer:

−49  / 8

decimal form- -6.125

Step-by-step explanation:

140−  167  / 8  (7)

=

140−  1169  / 8

=

−49  / 8

Answer:

$-6

Step-by-step explanation:

Spend

$36 on t-shirt

$20 hot dog

$50 shoes

Ramos money- $100

$36+$20+$50=$106

$100-$106=$-6

***Don't forget units***

Hope this was useful :)

Hi! I can help you with joy! :)

Answer:

2 terms

Hope it helps!

\(\rm{Stargazing{\bold{WithJoy:D}\)

Answer:

A,B and E

Step-by-step explanation:

Dilation =  was done on a rectangle.

→As Factor of Dilation is 0.4, which is less than 1.

→So, the image will be smaller in size than Pre image.

→As, the two rectangles , Pre image and image are similar so their sides will be proportional.

As in similar figures the interior angles are congruent.

As the images are similar , so Base of the image will be two fifths of the size of the base of preimage.

Option A,B and E are Correct.

A: The image is a reduction because n < 1.

B : The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.

E. The base of the image is two-fifths the size of the base of the pre-image.

ANSWER:

STEP-BY-STEP EXPLANATION:

By the statement Kevin always has $5 or more, which means that x can be 5 or all values greater than this. So the correct graph would be the first option: