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3 years ago

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12 - x2? (4 points)

Mathematics

1 answer:

wolverine [178]3 years ago

7 0

Answer: 16 square units

Step-by-step explanation:

let the vertex in quadrant I be (x,y)

then the vertex in quadratnt II is (-x,y)

base of the rectangle = 2x

height of the rectangle = y

Area = xy

= x(12 - x²)

= -x³ + 12x

d(area)/dx = 3x² - 12 = 0 for a maximum of area

3x² = 12

x² = 4

x = ±2

y = 12-4 = 8

So, the largest area = 2 x 8 = 16 square units

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aleksandr82 [10.1K]

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

The parameters are given as follows:

$\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24$

Item a:

The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:

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

$Z = \frac{984 - 959}{263}$

Z = 0.1

Z = 0.1 has a p-value of 0.5398.

1 - 0.5398 = 0.4602.

Item b:

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

By the Central Limit Theorem:

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

$Z = \frac{984 - 959}{43.24}$

Z = 0.58

Z = 0.58 has a p-value of 0.7190.

1 - 0.719 = 0.281.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

8 0

2 years ago

$550.00 is what percent of $1580.00 ?

vodka [1.7K]

The answer is 35%. You just take 550.00/1580.00=0.34810127 then you turn that into percent (round up the 4 to a 5 since the next number is 8). And you get 35%

5 0

4 years ago

Your bag of rice says to mix 1 cup of rice with 2 cups of water. dela requ prov a. What is the ratio of rice to water? refer to

EastWind [94]

Answer:

(a) 1:2

(b) 6 cups

Step-by-step explanation:

(a) Given,

amount of rice mixture contains= 1 cup

amount of water mixture contains= 2 cups

$\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}$

$=\ \dfrac{1}{2}$

So, the ratio of rice to water is 1:2.

(b) Amount of rice in mixture = 3 cups

$\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}$

$=>\ \dfrac{1}{2}\ =\ \dfrac{3}{\textrm{amount of water in mixture}}$

=> amount of water in mixture = 3 x 2

= 6 cups

(c) $\textrm{amount of rice in mixture}\ =\dfrac{1}{3}$

$\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}$

$=>\ \dfrac{1}{2}\ =\ \dfrac{\dfrac{1}{3}}{\textrm{amount of water in mixture}}$

$=>\textrm{amount of water in mixture}\ =\ \dfrac{2}{3}$

So, the amount of water in the mixture will be $\dfrac{2}{3}$ cup.

7 0

3 years ago

The set of whole numbers is greater than -2

Law Incorporation [45]

Yes it because any positive number is greater a negative number

8 0

3 years ago

Read 2 more answers

What is the missing number???????

valina [46]

If you take 46.59 and subtract 43.8 you get 2.79. Therefore 2.79 is your answer.

5 0

3 years ago