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2 years ago

6

Louise measured the perimeter of her rectangular scrapbook to be 156 cm. If the scrapbook is 43 cm wide, how long is the scrapbo

ok?

1 answer:

Montano1993 [528]2 years ago

8 0

Answer:

L=35cm

Step-by-step explanation:

Perimeter is 2(L+w)

156cm=2*(43+L)

L=35cm

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A) The y-intercept of the line with the largest slope

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Answer:

a) the largest y-intercept is 1

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2 years ago

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

$x=b^2+w^2$
$y=b^2+w^2+2bw$ so, y has an extra piece and it is larger
$k=b+w$ 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

2 years ago

..........................

QveST [7]

Answer:

x = 0.954

Step-by-step explanation:

We apply pythagorean to find x

(4-x)² = 1.2² + 2.8²

(4-x)² = 9.28

✓(4-x)² = ✓(9.28)²

4 - x = 3.046

- x = 3.046 - 4

- x = -0.954

x = 0.954

(Please heart and rate if you find it helpful, it's a motivation for me to help more people)

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2 years ago

how high up on a building will 15 foot ladder reach if the foot of the ladder is placed 5 feet from the building? (be sure to in

mezya [45]

Use the Pythagorean theorem:
$5^2+x^2=15^2 \\
25+x^2=225 \\
x^2=225-25 \\
x^2=200 \\
x=\sqrt{200} \\
x=\sqrt{100 \times 2} \\
x=10\sqrt{2} \\
x \approx 14.14$

The ladder will reach approximately 14.14 feet (exactly 10√2 feet) up on the building.

3 0

3 years ago