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r-ruslan [8.4K]

3 years ago

10

The depth of a lake, dd, varies directly with rr, the amount of rainfall last month. if kk is the constant of variation, which e

quation represents the situation?

1 answer:

Murrr4er [49]3 years ago

4 0

Given that the depth varies directly with amount of rainfall, then we shall have:
let d be the depth and r be the rainfall amount
dαr
thus
d=kr
where, k is the constant of proportionality, thus the formula will be:
d=kr

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558/93=6 or also 558/6=93

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PLEASE HELP ILL MARK BRAINLIEST !!!

Alexus [3.1K]

Answer:

a) the common difference is 20

b) $x_8=115 , x_{12}=195$

c) the common difference is -13

d) $a_{12}=52, a_{15}=13$

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: $x_n=x_1+(n-1)d$

We know common difference d= 20, we need to find $x_1$

Using $x_3=16$ we can find $x_1$

$x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25$

So, We have $x_1 = -25$

Now finding $x_8$

$x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115$

So, $\mathbf{x_8=115}$

Now finding $x_{12}$

$x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195$

So, $\mathbf{x_{12}=195}$

c) what is the common difference of the sequence $a_m$

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: $a_n=a_1+(n-1)d$

We know common difference d= -13, we need to find $a_1$

Using $a_7=104$ we can find $x_1$

$a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195$

So, We have $a_1 = 195$

Now finding $a_{12}$ , put n=12

$a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52$

So, $\mathbf{a_{12}=52}$

Now finding $a_{15}$ , put n=15

$a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13$

So, $\mathbf{a_{15}=13}$

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3 years ago

Rewrite p(x)=x(x-1)+1 in standard form

mario62 [17]

Answer : p(x)= x^2 -x+1

*Mark brainliest*

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3 years ago

. There are 10 beads in a bag. 5 beads are black; 3 beads are white and the rest are red. A bead is picked at random. Find the p

Bingel [31]

Part A

P(white) = (3 white)/(10 total) = 3/10

<h3>Answer: 3/10</h3>

==============================================

Part B

10 total, 3 are white

10-3 = 7 are not white so they are either black or red

P(black or red) = 7/10

<h3>Answer: 7/10</h3>

==============================================

Part C

Earlier in part B we calculated 7 beads that weren't white

This means P(not white) = P(black or red) = 7/10

They are the same probability just phrased slightly different ways.

<h3>Answer: 7/10</h3>

==============================================

Part D

There aren't any blue beads (unless there's a typo somewhere). So the probability of picking not blue is 100% or we represent this as the value 1.

<h3>Answer: 1</h3>

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2 years ago