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2 years 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 is written as:
f(x) = log(-20x + 12√x)
To find the maximum value, differentiate the equation in terms of x, then equate it to zero. The solution is as follows.

The formula for differentiation would be:
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
x = (6/20)² = 9/100

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

<em>The maximum value of the function is 0.2553.</em>

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Suppose students' ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 3 years. If we

natta225 [31]

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Mean of students' age = 24 years

Standard deviation of students' age = 3 years

Sample size = number of students = 350

So, according to options,

a. The shape of the sampling distribution is approximately normal.

It is true as n >30, we will use normal.

b. The mean of the sampling distribution is approximately 24-years old.

It is true as it is given.

c. The standard deviation of the sampling distribution is equal to 5 years.

It is not true as it is given 3 years.

Hence, Option 'c' is correct.

8 0

2 years ago

For the level 3 course, exam hours cost twice as much as workshop hours, workshop hours cost twice as much as lecture hours. How

natulia [17]

<h2>Answer</h2>

Cost of lectures = $7.33 per hour

<h2>Explanation</h2>

Let $e$ the cost of the exam hours

Let $w$ be the cost of the workshop hours

Let $l$ be the cost of the lecture hours.

We know from our problem that exam hours cost twice as much as workshop, so:

$e=2w$ equation (1)

We also know that workshop hours cost twice as much as lecture hours, so:

$w=2l$ equation (2)

Finally, we also know that 3hr exams 24hr workshops and 12hr lectures cost $528, so:

$3e+24w+12l=528$ equation (1)

Now, lets find the value of $l$ :

Step 1. Solve for $l$ in equation (3)

$3e+24w+12l=528$

$12l=528-3e-24w$ equation (4)

Step 2. Replace equation (1) in equation (4) and simplify

$12l=528-3e-24w$

$12l=528-3(2w)-24w$

$12l=528-6w-24w$

$12l=528-30w$ equation (5)

Step 3. Replace equation (2) in equation (5) and solve for $l$

$12l=528-30w$

$12l=528-30(2l)$

$12l=528-60l$

$72l=528$

$l=\frac{528}{72}$

$l=\frac{22}{3}$

$l=7.33$

Cost of lectures = $7.33 per hour

3 0

2 years ago

Read 2 more answers

Joaquin and Trisha are playing a game in which the lower median wins the game. Their scores are shown below.

iragen [17]

Median is defined as the middle term when the scores are arranged in increasing/decreasing order.

Joaquin's scores: 58, 62, 72, 75, 85, 91 Median: 73.5
Trisha's scores: 55, 74, 76, 90, 91, 92 Median: 83

The answer is letter A.

3 0

2 years ago

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In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed

sleet_krkn [62]

Answer:

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

Step-by-step explanation:

The interpretation of a confidence interval of level x% means that we are x% sure that the interval contains the true mean of the population.

In this problem, we have that:

The population are all the cell phone users.

The 95% confidence interval is (73.1%, 76.9%).

Which of the following is an appropriate interpretation of the 95% confidence interval?

D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

3 0

2 years ago

Charlie is watching hot air balloons. Balloon A has risen at a 56° angle. Balloon B has risen at an 81° angle. If the distance f

sweet [91]

Answer:

999 ft

Step-by-step explanation:

In the picture attached, the drawn of the situation is shown

∠x = 56°

∠y = 81°

distance from balloon A to the ground is 1,200 feet

From definition:

tan(∠x) = opposite/adjacent

tan(56°) = 1200/adjacent

adjacent to ∠x = 1200/tan(56°)

adjacent to ∠x = 809.41 ft

tan(∠y) = opposite/adjacent

tan(81°) = 1200/adjacent

adjacent to ∠y = 1200/tan(81°)

adjacent to ∠y = 190.06 ft

The distance from balloon A to balloon B is: 809.41 + 190.06 = 999.47 ≈ 999 ft

8 0

2 years ago

Read 2 more answers