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Kobotan [32]
2 years ago
5

Round 0.99999999 to four decimal places?

Mathematics
1 answer:
natali 33 [55]2 years ago
7 0
1.0000!

if this is rigtht please give brainliest, if you need an explication let me know :)
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Which equation in point-slope form contains the point (4, –1) and has slope 3?
Andrew [12]

Answer:

y+1=3(x-4)

Step-by-step explanation:

Hi there!

We are given a slope of 3 and a point (4,-1).

We need to find the equation of the line in point-slope form

Point-slope form is given as y-y1=m(x-x1), where m is the slope, and (x1,y1) is a point

We have all of the needed information to substitute into the formula

First, let's label the values of everything to avoid any confusion

m=3

x1=4

y1=-1

now substitute into the formula *remember, the formula has SUBTRACTION, and we have a NEGATIVE number, so we'll end up subtracting a negative*

y--1=3(x-4)

simplify

y+1=3(x-4)

That's it!

Hope this helps :)

4 0
3 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

  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
PLZ SOMEONE HELP ME AND EXPLAIN <br> THX
ELEN [110]
The graph of g is one-fifth as steep as the graph of f.

The function g basically takes the inputs for f and multiplies them by one-fifth, which means the outputs are one-fifth times those of f. Multiplying by one-fifth makes something smaller (it's the same as dividing by five). It helps to visualize this relationship, so I've attache the graphs below.

7 0
3 years ago
Which equation represents the line that passes through the points (-3, 7) and (9,-1)? oy--3x+5 o y=-x-7 o y=zx-7 oy - 12 2x+5​
nekit [7.7K]

Answer:

use the slope equation (y2-y1) / (x2 -x1). plug in values and solve

(-1 -7) / (9 -(-3)) (subtracting a negative is the same as adding a positive)

-8 / 12 (simplify)

m = -2/3

then, plug in one of the points and the slope into the slope-point equation.

(y - y1) = m (x - x1) (the point-slope form)

y - 7 = -2/3( x - (-3)) (plug in the slope and point 1 values, then solve)

y - 7 = -2/3x - 2 (add 7 to both sides)

y = 2/3x +5 (the answer)

Step-by-step explanation:

I hope this helps :))

4 0
3 years ago
What is the length and width of the rectangle if the area is 72 squre meters?
cupoosta [38]

Answer:

sorry

Step-by-step explanation:

5 0
2 years ago
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