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2 years ago

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Jackson has 180 pieces of gum. He wants to share the pieces equally with his friends. Which table shows the relationship between

n, the number of people who received gum, and p the number of pieces of gum each person receives?

1 answer:

mars1129 [50]2 years ago

6 0

Answer:

Step-by-step explanation:

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Is (A) correct or no????

Maslowich

Answer:

no

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A moving van changes a flat rate of $25 per day plus $0.12 per mile for every mile over 100 driven.If Millie’s bill was $29.46 h

Damm [24]

Answer: 137.17 miles

Step-by-step explanation: To know the driven miles, we will have to find the extra money paid divided by the unitary price of each driven mile.

Extra money=$29.46-$25=$4.46

Miles= $\frac{4.46}{0.12}$ =31.17 miles

However, this price per mile is only charged after 100 miles, therefore we will have to sum the extra miles driven and the 100 miles for the basis

Total=100 miles+31.17 miles=137.17

5 0

3 years ago

Consider these functions:

valkas [14]

I think the answer might be B

6 0

2 years ago

What is Permutations and Combinations?

marissa [1.9K]

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

$\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }$

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

$\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}$

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

$\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }$

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

$\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}$

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

5 0

2 years ago

Use Laplace transform methods to solve the differential equation: The initial conditions are f(0) = 0 and <img src="https://tex.

Llana [10]

Answer:

Step-by-step explanation:

$\frac{d^2 y}{dt^2} +12\frac{dy}{dt} +32y = 10e^{-2t}$ where f(x) is replaced by y

Take Laplace on both sides

$s^2 Y -s(0)-0 +12s Y-0+32Y = \frac{10}{s+2} \\Y(s^2+12s+32) = \frac{10}{s+2}\\Y = \frac{10}{(s+2)(s+4)(s+8)}$

We can resolve into partial fraction to get Y = L(y)

Let this equals

$\frac{A}{s+2} +\frac{B}{s+4} +\frac{C}{s+8} \\10 = A(s+4)(s+8) + B(s+2)(s+8) +Cs+4)(s+2) \\$

Solving we get

s=-9

24C = 10 or C =5/12

s=-2: A=10/12=5/6

s=-4: B = -5/4

Taking inverse Laplace

$y(t) = \frac{-5e^{-4t} }{4} + \frac{5e^{-8t} }{12} +\frac{-5e^{-2t} }{6}$

6 0

3 years ago