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Whitepunk [10]
3 years ago
12

Ane goes to a juice bar with her friend neil. she is thinking of ordering her favorite drink, 7/8 orange juice and 1/8 cranberry

juice, but the drink is not on the menu, so she decides to order a glass of orange juice and a glass of cranberry juice and do the mixing herself. the drinks come in two identical tall glasses; to avoid spilling while mixing the two juices, jane shows neil something she learned that day in class. she drinks about 1/8 of the orange juice, then takes the straw from the glass containing cranberry juice, sucks up just enough cranberry juice to fill the straw, and while covering the top of the straw with her thumb, carefully bends the straw and places the end over the orange juice glass. after she releases her thumb, the cranberry juice flows through the straw into the orange juice glass. jane has successfully designed a siphon. assume that the glass containing cranberry juice has a very large diameter with respect to the diameter of the straw and that the cross-sectional area of the straw is the same at all points. let the atmospheric pressure be pa and assume that the cranberry juice has negligible viscosity.
Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
3 0
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klio [65]
f<span>(x)</span>=<span>x^2</span>−<span>6

</span>Replace <span>f<span>(x)</span></span> with <span>yy</span>.

<span>y=<span>x^2</span>−<span>6

</span></span>Interchange the variables.

<span>x=<span>y2</span>−6

</span>Solve for <span>yy</span><span>.
</span>
Move <span><span>−6</span><span>-6</span></span> to the right side of the equation by subtracting <span><span>−6</span><span>-6</span></span> from both sides of the equation.<span><span><span>y2</span>=6+x</span><span><span>y2</span>=6+x</span></span>Take the <span><span>square</span><span>square</span></span> root of both sides of the <span><span>equation</span><span>equation</span></span> to eliminate the exponent on the left side.<span><span>y=±<span>√<span>6+x</span></span></span><span>y=±<span>6+x

</span></span></span>The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

<span>y=<span>√<span>6+x</span></span>,−<span>√<span>6+x</span></span></span>
Solve for y<span> and replace with </span><span><span>f^<span>−1</span></span><span>(x).
</span></span>
<span>Answer is f<span>−1</span></span><span>(x)</span>=<span>√<span>6+x</span></span>,−<span>√<span>6+<span>x</span></span></span>
3 0
3 years ago
Read 2 more answers
Danae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day worked. The second job pays an annu
Zigmanuir [339]

Answer:

C


Step-by-step explanation:


<u>Job A:</u>

  • Bonus of $1500
  • $120 per day for d days is 120 multiplied by d. Which is 120d
  • Total Payment = 1500+120d

<u>Job B:</u>

  • Bonus of $2500
  • $110 per day for d days is 110 multiplied by d. Which is 110d
  • Total Payment = 2500+110d

Solving these 2 equations for d would tell us after how many days both job would pay the same. Answer choice C is correct.

4 0
3 years ago
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3 years ago
The amount of money spent on textbooks per year for students is approximately normal.
Ostrovityanka [42]

Answer:a

a

   336.04    <  \mu < 443.96

b

  The  margin of error will increase

c

The  margin of error will decreases

d

The 99% confidence interval is  0.4107 <  p  < 0.4293

Step-by-step explanation:

From the question we are  told that

   The sample size  n =  19

    The sample mean is  \= x  = \$\  390

    The  standard deviation is  \sigma =  \$ \  120

 

Given that the confidence level is  95% then the level of significance is mathematically represented as

           \alpha = 100 -  95

          \alpha  =  5 \%

          \alpha  =  0.05

Next we obtain the critical value of \frac{\alpha }{2} from the normal distribution table

    So  

         Z_{\frac{\alpha }{2} } =  1.96

The  margin of error is mathematically represented as

      E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

=>    E = 1.96 *  \frac{120}{\sqrt{19} }

=>   E = 53.96

The 95% confidence interval is  

     \= x  -  E  <  \mu < \= x  +  E

=>   390  -   53.96   <  \mu < 390  -   53.96

=>  336.04    <  \mu < 443.96

When the confidence level increases the Z_{\frac{\alpha }{2} } also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

         n  \  \ \alpha  \ \  \frac{1}{E^2 }

So if the sample size increases the margin of error decrease

The  sample proportion is mathematically represented as

       \r p  =  \frac{210}{500}

       \r p  = 0.42

Given that the confidence level is 0.99 the level of significance is  \alpha =  0.01

The critical value of \frac{\alpha }{2} from the normal distribution table is  

      Z_{\frac{\alpha }{2} }  =  2.58

  Generally the margin of error is mathematically represented as

       E =  Z_{\frac{\alpha }{2} }*  \sqrt{ \frac{\r p (1- \r p )}{n} }

=>   E =  0.42 *  \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }

=>     E =  0.0093

The 99% confidence interval  is

     \r p  -  E <  p  < \r p  +  E

     0.42  -  0.0093 <  p  < 0.42  +  0.0093

     0.4107 <  p  < 0.4293

 

4 0
4 years ago
A homeowner measured her rectangular backyard as having a length of 40 yards and a width of 25 yards. Her measurements were accu
kotegsom [21]

Answer:

B.

Step-by-step explanation:

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3 years ago
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