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Basile [38]
3 years ago
9

Phil is buying a sandwich. He has the following choices.

Mathematics
2 answers:
MrRa [10]3 years ago
4 0

Answer:

its WG, WS, WC, WT

Step-by-step explanation:

goblinko [34]3 years ago
4 0

Answer:

wgt, wgf, wsc, wsh

Step-by-step explanation:

You might be interested in
An urn contains n white balls andm black balls. (m and n are both positive numbers.) (a) If two balls are drawn without replacem
Genrish500 [490]

DISCLAIMER: Please let me rename b and w the number of black and white balls, for the sake of readability. You can switch the variable names at any time and the ideas won't change a bit!

<h2>(a)</h2>

Case 1: both balls are white.

At the beginning we have b+w balls. We want to pick a white one, so we have a probability of \frac{w}{b+w} of picking a white one.

If this happens, we're left with w-1 white balls and still b black balls, for a total of b+w-1 balls. So, now, the probability of picking a white ball is

\dfrac{w-1}{b+w-1}

The probability of the two events happening one after the other is the product of the probabilities, so you pick two whites with probability

\dfrac{w}{b+w}\cdot \dfrac{w-1}{b+w-1}=\dfrac{w(w-1)}{(b+w)(b+w-1)}

Case 2: both balls are black

The exact same logic leads to a probability of

\dfrac{b}{b+w}\cdot \dfrac{b-1}{b+w-1}=\dfrac{b(b-1)}{(b+w)(b+w-1)}

These two events are mutually exclusive (we either pick two whites or two blacks!), so the total probability of picking two balls of the same colour is

\dfrac{w(w-1)}{(b+w)(b+w-1)}+\dfrac{b(b-1)}{(b+w)(b+w-1)}=\dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

<h2>(b)</h2>

Case 1: both balls are white.

In this case, nothing changes between the two picks. So, you have a probability of \frac{w}{b+w} of picking a white ball with the first pick, and the same probability of picking a white ball with the second pick. Similarly, you have a probability \frac{b}{b+w} of picking a black ball with both picks.

This leads to an overall probability of

\left(\dfrac{w}{b+w}\right)^2+\left(\dfrac{b}{b+w}\right)^2 = \dfrac{w^2+b^2}{(b+w)^2}

Of picking two balls of the same colour.

<h2>(c)</h2>

We want to prove that

\dfrac{w^2+b^2}{(b+w)^2}\geq \dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

Expading all squares and products, this translates to

\dfrac{w^2+b^2}{b^2+2bw+w^2}\geq \dfrac{w^2+b^2-b-w}{b^2+2bw+w^2-b-w}

As you can see, this inequality comes in the form

\dfrac{x}{y}\geq \dfrac{x-k}{y-k}

With x and y greater than k. This inequality is true whenever the numerator is smaller than the denominator:

\dfrac{x}{y}\geq \dfrac{x-k}{y-k} \iff xy-kx \geq xy-ky \iff -kx\geq -ky \iff x\leq y

And this is our case, because in our case we have

  1. x=b^2+w^2
  2. y=b^2+w^2+2bw so, y has an extra piece and it is larger
  3. k=b+w which ensures that k<x (and thus k<y), because b and w are integers, and so b<b^2 and w<w^2

4 0
3 years ago
2 3/4 x 8 = blank/4 x 8/1
Alex

Answer: 11

Step-by-step explanation:

2 3/4 × 8 = p/4 × 8/1

Let p be the missing number

Convert the mixed fraction 2 3/4 to proper fraction, multiply 4 x 2, then add 3= 11/4

11/4 × 8 = p/4 ×8

p= 11

I hope this helps.

5 0
3 years ago
Read 2 more answers
Question 29 of 30
frozen [14]

Answer:

7/10

Step-by-step explanation:

this is the simplest form

3 0
2 years ago
Use the formula for interest P=750 r=7% Y=25 A=?
Over [174]

Answer:

2062.50

Step-by-step explanation:

Interest = (Principle x rate x time)/100

Amount = Principle + interest

Principle = 750

Rate = 7%

Time = 25 years

(750 x 7 x 25)/100

= 131250/100

=1312.50

Principle = 750

Interest = 1312.50

Amount = 750 + 1312.50

Amount = 2062.50

7 0
3 years ago
Which pair of expressions represents inverse functions?
faust18 [17]

In this question , we have to find, which option represents inverse functions.

Let's check out option b

Let it be y

So we have

y = \frac{x+3}{4x-2}

Switching x and y and solving for y,

x = \frac{y+3}{4y-2}

Performing cross multiplication

4xy -2x = y+3

Combining like terms

y(4x-1) = 3+2x

y = \frac{2x+3}{4x-1}&#10;\\&#10;f^{-1} (x) = \frac{2x+3}{4x-1}

Which is same as of the other function.

So correct option is b .

6 0
3 years ago
Read 2 more answers
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