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nexus9112 [7]
3 years ago
14

30 points

Mathematics
1 answer:
alina1380 [7]3 years ago
6 0
A savings account helps you save for retirement and college while a CD isn’t typically used for that. A savings account is much more beneficial because it is also an emergency fund when you need it.
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Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u
soldier1979 [14.2K]

x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}

\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}

\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}

Therefore:

\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]

Recall that at t=25, p(25)=\dfrac { 5800 } {13} \approx 446.15

Therefore:

\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009

The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

8 0
3 years ago
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compression strength of more than 130
nekit [7.7K]

Answer:

The null hypothesis is: u >= 1300 KN/m^2

And the alternative hypothesis is:

u < 1300 KN/m^2.

Step-by-step explanation:

The null hypothesis describes hat there is no difference or assiciation between variables of a specific population or that it is a particular average value while the alternative hypothesis states otherwise.

In this case study, the null hypothesis is: u >= 1300 KN/m^2

And the alternative hypothesis is:

u < 1300 KN/m^2.

7 0
3 years ago
Every day, Luann walks to the bus stop and the amount of time she will have to wait for the bus is between 0 and 12 minutes, wit
Nana76 [90]

Answer:

a. 341.902.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n instances of a normal variable:

For n instances of a normal variable, the mean is n\mu and the standard deviation is s = \sigma\sqrt{n}

60 days, for each day, mean 6, variance of 12.

So

\mu = 60*6 = 360

s = \sqrt{12}\sqrt{60} = 26.8328

What is the 25th percentile of her total wait time over the course of 60 days?

X when Z has a p-value of 0.25, so X when Z = -0.675.

Z = \frac{X - \mu}{s}

-0.675 = \frac{X - 360}{26.8328}

X - 360 = -0.675*26.8328

X = 341.902

Thus, the correct answer is given by option A.

3 0
2 years ago
Multiply.Write each product in simplest form
xz_007 [3.2K]
1. 5/16
2. 1/3
3. 3/20
4. 38
5. 3/4
6. 6
4 0
3 years ago
Read 2 more answers
I WILL AWARD BRAINLIEST!! PLEASE HELP!!!<br> Find the areas of the trapezoids.
Galina-37 [17]

Answer:

A = 12 units ^2

Step-by-step explanation:

The area of the trapezoid is found by

A = 1/2 (b1+b2)h

b1 = 2

b2 = 4

h = 4

I found these by looking at the graph

A = 1/2(2+4) 4

A = 1/2(6*4)

A = 12 units ^2

8 0
3 years ago
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