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3 years ago

How do you solve 2 (5-6) < 8f - 130

Mathematics

1 answer:

irga5000 [103]3 years ago

3 0

2(5-6)<8f-130
(2x5)-(2x6)<8f-130
10-12<8f-130
-2<8f-130
-2+130<8f-130+130
128<8f
128/8<8f/8
16<f
f>16

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Find the slope that is PARALLEL and PERPENDICULAR to the equation of the line y = -1/2x+6.

kifflom [539]

Answer:

parallel: -1/2

perpendicular: 2

Step-by-step explanation:

lines that are parallel have the same slope because they never intersect

lines that perpendicular, have the opposite reciprocal slope.

y = mx + b

where m is the slope

y = -1/2x + 6

-1/2 is the slope.

the slope in the equation given: -1/2

the slope parallel to the line given : -1/2

the slope perpendicular : opposite reciprocal, so the opposite of -1/2 is 1/2 and the reciprocal of 1/2 is 2.

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3 years ago

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly s

GaryK [48]

Answer:

The bill size can be considered usual.

Step-by-step explanation:

Mean (μ) = $108.43

Standard deviation (σ) = $36.98

Now, consider the distribution to be normal distribution :

$P(Z=\frac{X-\mu}{\sigma}>\frac{a-\mu}{\sigma})=P(Z>\frac{173-108.43}{36.98})\\\\\implies P(Z>1.75)$

Now, finding values of z-score from the table. We get,

P(Z > 1.75) = 0.9599

⇒ 95.99%

So, only 4.01 % of the people in the city wastes water.

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3 years ago

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Find the taylor polynomial t3(x) for the function f centered at the number

Vlad [161]

$e^{-3x}=\displaystyle\sum_{n=0}^\infty\frac{(-3x)^n}{n!}=1-3x+9x^2+\cdots$
$\sin2x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^n(2x)^{2n+1}}{(2n+1)!}=2x-\dfrac{4x^3}3+\cdots$

$e^{-3x}\sin2x=\left(1-3x+9x^2+\cdots\right)\left(2x-\dfrac{4x^3}3+\cdots\right)$
$\approx T_3(x)=(1-3x+9x^2)\left(2x-\dfrac{4x^3}3\right)$
$T_3(x)=2x-6x^2+\left(18-\dfrac43\right)x^3$
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3 years ago

Find the area. The figure is not drawn to scale.

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area of a triangle is 1/2 x base x height

base = 19

height = 3

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3 years ago

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Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long.

givi [52]

<h2>Hello!</h2>

The answer is: There are a total of 16 skits in the video.

From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).

So, we need to write the following equations:

First equation:

$TotalDuration=Introduction+n*Skit$

Second equation:

$Skit=6Minutes$

Where,

$TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes$

So, replacing and substituting the second equation into the first equation we have:

$101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16$

So, there are a total of 16 skits in the video.

Let's prove it substituting "n" into the first equation:

$101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes$

Have a nice day!

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3 years ago