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21 day ago

Find the value of $x$ that maximizes $$f(x) = \log (-20x + 12\sqrt{x}).$$ If there is no maximum value, write "NONE".

1 answer:

5 0

The function can be expressed as:
f(x) = log(-20x + 12√x)
To ascertain the maximum value, differentiate the equation with respect to x and set the derivative to zero. The procedure unfolds as follows.

The differentiation formula is:
d(log u)/dx = du/u ln(10)
Thus,
d/dx = (-20 + 6/√x)/(-20x + 12√x)(ln 10) = 0
-20 + 6/√x = 0
6/√x = 20
From which we derive x = (6/20)² = 9/100

Therefore,
f(x) = log(-20(9/100)+ 12√(9/100)) = 0.2553

The function's maximum value is 0.2553.

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Micah rows his boat on a river 4.48 miles downstream, with the current , 0.32 hours. He rows back upstream the same distance, ag

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Short Answer: Current speed = 3 miles per hour. Given details for downstream distance of 4.48 miles at time 0.32 hours and upstream distance of the same 4.48 miles taking 0.56 hours. Using the equation d = r*t, we equate distances for both directions leading to a function in terms of the current speed. With each correction to solve ultimately yields the current speed as 3 mph.

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4 days ago

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

AnnZ [9104]

Answer: 0.1289

Step-by-step explanation:

Given: The proportion of students absent on Mondays at a large university.: $p=0.15$

Sample size: $n=12$

Mean: $\mu=np=12\times0.15=1.8$

Standard deviation = $\sigma=\sqrt{np(1-p)}$

$\Rightarrow\ \sigma=\sqrt{12(0.15)(1-0.15)}=1.23693168769\approx1.2369$

Let x represent a binomial variable.

Referencing the standard normal distribution table,

$P(x=4)=P(x\leq4)-P(x\leq3)$ (1)

Z score for normal distribution:-

$z=\dfrac{x-\mu}{\sigma}$

For x=4

$z=\dfrac{4-1.8}{1.2369}\approx1.78$

For x=3

$z=\dfrac{3-1.8}{1.2369}\approx0.97$

Thus, from (1)

$P(x=4)=P(z\leq1.78)-P(z\leq0.97)\\\\=0.962462-0.8339768\approx0.1289$

Consequently, the likelihood of four students being absent = $0.1289$

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23 days ago

The Spirit Team will be selling popcorn as a fundraiser at the next basketball game to earn funds to go to Orlando for a competi

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Response:1 and 2

Step-by-step Explanation:

Provided data

Volume required $V=220\ in.^3$

For the initial cylinder

$r=3\ in.$

$h=4\ in.$

$V=\pi r^2h$

$V_1=\pi (3)^2(4)$

$V_1=113.11\ in^3$

For the second cylinder

$r=4\ in.$

$h=4\ in.$

$V=\pi r^2h$

$V_2=\pi (4)^2(4)$

$V_2=201.08\ in^3$

For the third cylinder

$r=9\ in.$

$h=9\ in.$

$V=\pi r^2h$

$V_3=\pi (9)^2(9)$

$V_3=2290.51\ in^3$

For the fourth cylinder

$r=4\ in.$

$h=9\ in.$

$V=\pi r^2h$

$V_4=\pi (4)^2(9)$

$V_4=452.448\ in^3$

Thus, cylinders $1$ and $2$ meet the requirement as they remain under $220\ in.^3$

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1 month ago

Alonso brings \$21$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost \$2.50$2.50dollar sign, 2, p

PIT_PIT [9121]

Answer:

B ≤ 11 bags

Step-by-step explanation:

Alonso starts with $21. After purchasing eggs for $2.50, he has $21 - $2.50 left = $18.50

Thus, the remaining money for avocados is $18.50.

Each 3 bags of avocados cost $5, making the price for 1 bag $(5/3)

Consequently, if B represents the quantity of avocado bags purchased by Alonso, it could be expressed as:

B ≤ $18.50 ÷ $(5/3)

B ≤ 11.1

B ≤ 11

B ≤ 11 bags

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2 days ago

How do you use a number line to solve 235+123

AnnZ [9104]

<span>A number line is a visual method for performing addition using points on a line.
=> 235 + 123
Begin at 0 and move to 235. From 235, move forward another 123 units.
Then from zero mark the position you reach after adding 123 to 235.

This gives:
=> 235 + 123
=> 358.
See the attached image for a number line depiction.</span>Answer:

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5 days ago