From a list of ten books, how many groups of 4 books can be selected

Answers

Answer 1

Answer:

From a list of ten books, 210 ways to select a group of 4 books.

What is a combination?

A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.

The number of ways to select a group of 4 books from a list of 10 books can be calculated using the combination formula:

nCr = n! / (r! x (n-r)!)

Where n is the total number of items (in this case, 10 books) and r is the number of items to be selected (in this case, 4 books).

Plugging in the values, we get:

10C4 = 10! / (4! x (10-4)!)

= 10! / (4! x 6!)

= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

= 210

Therefore, there are 210 ways to select a group of 4 books from a list of 10 books.

To learn more about the combination;

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Answer 2

Answer:

First you have all ten books, but then every time after, you loose one because you can't put the same book in the group twice.

10 * 9 * 8 * 7 = 5040 groups

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a catering service offers 4 appetizers, 6 main course, and 12 desserts. a banquet chairperson is to select 3 appetizers, 2 main course and 5 desserts or a banquet. in how many ways can this be done

Answers

If you have 4 appetizers and you need to choose just 3 of them, it would be the same amount of options as just choosing 1 out of the 4; so there are 4 ways to choose the appetizer. For the main course, you are choosing 2 out of 6. So there are 6 ways to choose the first main course, and assuming there is no repeats, there would be 5 ways to choose the next one. However, there will be some overlap, so you need to divide it by 2. So you have $(6*5)/(2) =15$ options for main course. Finally for dessert, you have 12 desserts to choose from and 5 desserts to choose. So you do a similar thing to the main courses. $(12*11*10*9*8)/(5*4*3*2*1)$ would be the equation you would use. Because there are 12 ways to pick the first dessert, 11 ways for the 2nd and so on until you reach 5 desserts. You divide it by 5*4*3*2*1 or 5! (Factorial) because there are overlaps for each of the 5 so you have to account for those. After solving the equation, there are 792 ways to pick desserts So you now know that you have 4 ways of picking the appetizer, 15 ways for the main course and 972 ways to pick desserts. So for options of the full meal, you need to multiply all these values together: $4*15*792=47520$ . Therefore, there are 47,520 possible ways this could be done.

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x7 – x5 + x3+6

Answers

According to the Fundamental Theorem of Algebra, the number of roots of a polynomial is equal to the degree of the polynomial. The degree of the polynomial is the highest exponent of a term in the polynomial.
Looking at the function, the term with the highest exponent is 8x7. The exponent is 7; therefore, the function has 7 roots.

According to the Fundamental Theorem of Algebra, the roots exist for the polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6 x$ is $\boxed7.$

Further explanation:

The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.

$f\left( x \right) = a{x^n} + b{x^(n - 1)} +\ldots + cx + d$

The polynomial function has n roots or zeroes.

Degree is highest power of the polynomial function.

Given:

The polynomial function is $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6.$

Explanation:

The polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6$ has seven zeroes as the degree of the polynomial is 7.

According to the Fundamental Theorem of Algebra, the roots exist for the polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6$ is $\boxed7.$

Learn more:

1. Learn more about inverse of the functionbrainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Polynomials

Keywords: quadratic equation, equation factorization. Factorized form, polynomial, quadratic formula, zeroes, Fundamental Theorem of algebra, polynomial, seven roots.

A livestock pen is built in the shape of a rectangle that is twice as long as it is wide. The perimeter is 48 feet. If the material used to build the pen is $1.85 per foot for the longer sides and $2.35 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.

Answers

Wow! This has to handled one step at a time.
Step 1). Find the actual dimensions of the pen.
Step 2). Decide the total amount on longer sides
and the total amount on shorter sides.
Step 3). Work out the costs.

Dimensions of the pen:
"Twice as long as it is wide".
Width = W feet
Length = 2W feet
Perimeter = W + 2W + W + 2W = 6W = 48 feet
Width = W = 8 feet
Length = 2W = 16 feet

Amount on long sides and short sides:
The longer sides are 16 feet.
There are 2 of them.
Total mount on longer sides = 32 feet.

The shorter sides are 8 feet.
There are 2 of them.
Total amount on shorter sides = 16 feet.

Costs:
Longer sides: (32 feet) x ($1.85 per feet) = $59.20
Shorter sides: (16 feet) x ($2.35 per foot) = $37.60
Total cost of material to build the pen = $96.80

Which of the following metals will react with water to produce a metal hydroxide and hydrogen gas? (2 points)Select one:
a. Al
b. Bi
c. Na
d. Fe

Answers

I think the correct answer from the choices listed above is option C. It is the metal Na that will react with water to produce a metal hydroxide and hydrogen gas. It reacts violently with water forming sodium hydroxide and the hydrogen gas.

Solve the following:2(x+3)=x-4

Answers

To solve the equation 2(x+3) = x-4, you can follow these steps:

1. Distribute the 2 on the left side of the equation to both terms inside the parentheses:
2x + 6 = x - 4

2. Now, let's isolate x on one side of the equation. You can do this by subtracting x from both sides:
2x - x + 6 = -4

3. Simplify the left side by combining like terms (2x - x):
x + 6 = -4

4. To isolate x, subtract 6 from both sides of the equation:
x + 6 - 6 = -4 - 6

5. Simplify both sides:
x = -10

So, the solution to the equation is x = -10.

N entry level technical writer's annual pay is $55,068 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its technical writers. If the firm cuts the work year to 51 weeks but keeps the same rate of pay, how much should the technical writer expect his annual pay to decrease? Round your answer to the nearest dollar.