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ollegr [7]
3 years ago
13

Find the value of x .Find the measurements of

Mathematics
1 answer:
Nastasia [14]3 years ago
3 0

Answer:

17

Step-by-step explanation:

42+x=5x

-5        - 5

=17

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It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 househo
BartSMP [9]

Complete Question

It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 households in Iowa City is taken, would you be surprised to find that fewer than 3% of households in the sample recycle their garbage? Use the fact that p-hat has an approximately normal distribution.

Group of answer choices

A I would not be surprised because there are lots of lazy students in Iowa City.

B I would not be surprised because 3% is not that far away from 9%.

C I would be surprised because Iowa City is a very clean community which means lots of people recycle their garbage.

D I would be surprised because if the 9% average is true, the chance of a sample proportion being less than 3% is very small (only 1%). Who cares? It's only garbage!

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

    The sample size is  n  = 120

    The  mean of the proportion is  p =  0.09

   

Generally the standard deviation is mathematically represented as

      \sigma  =  \sqrt{\frac{p(1-p)}{n} }

=>   \sigma  =  \sqrt{\frac{0.09(1-0.09)}{120 } }

=>   \sigma  = 0.02612

Generally the chance that fewer than 3%   of households in the sample recycle their garbage is mathematically represented as

    P(X < 0.03) =  P( \frac{X - p}{\sigma}  <  \frac{0.03 -0.09}{0.02612} )

    P(X < 0.03) =  P( Z  < -2.297 )

From the z-table  

     P( Z  < -2.297 ) = 0.01

=> [tex]P(X < 0.03) = 0.01/tex]

=>   [tex]P(X < 0.03) = 1\% /tex]

4 0
3 years ago
F(x)=x^2+4x and g(x)= 2x+2, find f(5)+ g(6)
Lubov Fominskaja [6]
F(5) = 5² +4*5=25+20 = 45
g(6) = 2*6 +2 =12+2=14

f(5) + g(6)
= 45 +14 =59
3 0
3 years ago
Can anyone help me integrate :
worty [1.4K]
Rewrite the second factor in the numerator as

2x^2+6x+1=2(x+2)^2-2(x+2)-3

Then in the entire integrand, set x+2=\sqrt3\sec t, so that \mathrm dx=\sqrt3\sec t\tan t\,\mathrm dt. The integral is then equivalent to

\displaystyle\int\frac{(\sqrt3\sec t-2)(6\sec^2t-2\sqrt3\sec t-3)}{\sqrt{(\sqrt3\sec t)^2-3}}(\sqrt3\sec t)\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\sec^2t-1}}\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\tan^2t}}\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{|\tan t|}\,\mathrm dt

Note that by letting x+2=\sqrt3\sec t, we are enforcing an invertible substitution which would make it so that t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3} requires 0\le t or \dfrac\pi2. However, \tan t is positive over this first interval and negative over the second, so we can't ignore the absolute value.

So let's just assume the integral is being taken over a domain on which \tan t>0 so that |\tan t|=\tan t. This allows us to write

=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\tan t}\,\mathrm dt
=\displaystyle\int(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\csc t\,\mathrm dt

We can show pretty easily that

\displaystyle\int\csc t\,\mathrm dt=-\ln|\csc t+\cot t|+C
\displaystyle\int\sec t\csc t\,\mathrm dt=-\ln|\csc2t+\cot2t|+C
\displaystyle\int\sec^2t\csc t\,\mathrm dt=\sec t-\ln|\csc t+\cot t|+C
\displaystyle\int\sec^3t\csc t\,\mathrm dt=\frac12\sec^2t+\ln|\tan t|+C

which means the integral above becomes

=3\sqrt3\sec^2t+6\sqrt3\ln|\tan t|-18\sec t+18\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|-6\ln|\csc t+\cot t|+C
=3\sqrt3\sec^2t-18\sec t+6\sqrt3\ln|\tan t|+12\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|+C

Back-substituting to get this in terms of x is a bit of a nightmare, but you'll find that, since t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3}, we get

\sec t=\dfrac{x+2}{\sqrt3}
\sec^2t=\dfrac{(x+2)^2}3
\tan t=\sqrt{\dfrac{x^2+4x+1}3}
\cot t=\sqrt{\dfrac3{x^2+4x+1}}
\csc t=\dfrac{x+2}{\sqrt{x^2+4x+1}}
\csc2t=\dfrac{(x+2)^2}{2\sqrt3\sqrt{x^2+4x+1}}

etc.
3 0
3 years ago
Which statement regarding the diagram is true?
Sergeu [11.5K]
Answer

<span>m∠WXY + m∠YXZ = 180°</span>
7 0
3 years ago
Read 2 more answers
Write 14/5 as a mixed number in simplest terms.
VladimirAG [237]
The answer you are looking for is 2 4/5. Hope this helps.
3 0
3 years ago
Read 2 more answers
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