Which expression fits this description

A teacher with 10 students has 30 lesson times available. She will teach exactly one of her students during each lesson time. Ho

natka813 [3]

There are $\frac{30!}{(3!)^{10} }$ ways for the teacher to decide which student she will teach during each lesson time if she must teach each student exactly 3 times. Here, "!" represents the factorial.

A number's factorial is the result of multiplying the integer by each natural number below it. Factorial can be symbolized by the letter "!". Thus, n factorial is denoted by n! and is the result of the first n natural numbers.

A whole number's "n" factororial is the sum of that number and each whole number up to one.

When a question asks you to determine how many different ways you can arrange or order a given number of items, you use a factorial.

Learn more about factorials here:

brainly.com/question/25997932

#SPJ1

5 0

2 years ago

1. The manager of FrozonAir Refrigerator factory notices that on Monday it cost the company a total of $25,000 to build 30 refri

Vinvika [58]

Answer:

The fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500

Step-by-step explanation:

Let

Cost per refrigerator (marginal cost) = r

Fixed costs per day for the factory = f

Total cost = variable cost + fixed cost

Monday

25,000 = 30r + f

Tuesday

30,000 = 40r + f

Using Monday,

f = 25000 -30r

Substitute f = 25000 - 30r into Tuesday

30,000 = 40r + f

30,000 = 40r + (25,000 -30r)

30,000 = 40r + 25,000 - 30r

Collect like terms

30,000 - 25,000 = 40r - 30r

5,000 = 10r

Divide both sides by 10

r = 5,000 / 10

= 500

r = $500

Substitute r= 500 into Monday equation

f = 25,000 -30r

= 25,000 - 30(500)

= 25,000 - 15,000

= 10,000

f = $10,000

Therefore, the fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500

7 0

3 years ago

Find the numbers b such that the average value of f(x) = 7 + 10x − 9x2 on the interval [0, b] is equal to 8.

barxatty [35]

Answer:

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

Step-by-step explanation:

The mean value of function within a given interval is given by the following integral:

$\bar f = \frac{1}{b-a}\cdot \int\limits^b_a {f(x)} \, dx$

If $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ , $a = 0$ , $b = b$ and $\bar f = 8$ , then:

$\frac{1}{b}\cdot \int\limits^b_0 {7+10\cdot x -9\cdot x^{2}} \, dx = 8$

$\frac{7}{b}\int\limits^b_0 \, dx + \frac{10}{b} \int\limits^b_0 {x}\, dx - \frac{9}{b} \int\limits^b_0 {x^{2}}\, dx = 8$

$\left(\frac{7}{b} \right)\cdot b + \left(\frac{10}{b} \right)\cdot \left(\frac{b^{2}}{2} \right)-\left(\frac{9}{b} \right)\cdot \left(\frac{b^{3}}{3} \right) = 8$

$7 + 5\cdot b - 3\cdot b^{2} = 8$

$3\cdot b^{2}-5\cdot b +1 = 0$

The roots of this polynomial are determined by the Quadratic Formula:

$b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

7 0

3 years ago

Bu soruyu yapın arkadaşlar acill lütfen yapanı en iyi seçip takip edicem 5 yıldız koyucam<br>

jok3333 [9.3K]

Step-by-step explanation:

bsbdbxbshzb jdjxhdjzbe

5 0

3 years ago

Please answer this. you will get branliest if u do

Shalnov [3]

Let’s first find the angle y
Angle y = 180-(140+10)(angle sum property)
Angle y = 180-150
Angle y = 30 degrees
Angle x = 180- 110 ( linear pair )
Angle x = 70
Angle z = 180-(70+90)( angle sum property)
Angle z = 180-160
Angle z = 20

8 0

3 years ago

Read 2 more answers