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1 month ago

If xy + 5ey = 5e, find the value of y'' at the point where x = 0.

Mathematics

1 answer:

Zina [12.3K]1 month ago

6 0

Response:

1 (only applicable if e is not zero)

Detailed explanation:

xy + 5ey = 5e

0y + 5ey = 5e

y = 5e/5e

y = 1

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A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, thi

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In this case, the dimensions of 12 inches in width and 4 inches in length are not crucial for solving the problem. An equation has been provided already, and it clearly states that A, as a function of θ, represents the area of the opening. We are specifically instructed to find this area, and the value of θ has been given. Therefore, the initial details seem to serve merely as a distraction.

Hence, we can directly substitute θ=45° into the given function.
A = 16 sin 45° ⋅ (cos 45° + 1)

Since 45° is a notable angle in trigonometry, remembering its functions is straightforward. The sine of 45° is √2/2, and the cosine of 45° is also √2/2.

A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8 + 8√2
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22 days ago

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A store sold a case of scented candles for $17.85 that had been marked up 110%. What was the original price?

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1.1x = 17.85 x ≈ 16.227272727272727... Rounded to $16.23

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29 days ago

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In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1,014 adults aged 18 and

babunello [11817]

Answer:

(b)E(x)=1.3087

(c)Variance of x =1.7119

(d)E(y)=2.0447

Step-by-step explanation:

The random variable x refers to the average number of cups of coffee consumed daily.

The total number of respondents equals 1014

(a) Probability distribution for x.

$\left|\begin{array}{c|cccccc}x&0&1&2&3&4\\\\P(x)&\dfrac{365}{1014}&\dfrac{264}{1014}&\dfrac{193}{1014}&\dfrac{91}{1014}&\dfrac{101}{1014} \end{array}\right|$

(b) Expected value for x

$E(x)=\left(0\times\dfrac{365}{1014}\left)+\left(1\times\dfrac{264}{1014}\left)+\left(2\times\dfrac{193}{1014}\left)+\left(3\times\dfrac{91}{1014}\left)+\left(4\times\dfrac{101}{1014}\right)$

E(x)=1.3087

Variance $=\sum (x-\mu)^2P(x)$

$\left|\begin{array}{c|cccccc}x&0&1&2&3&4\\(x-\mu)^2&1.7167&0.0953&0.4779&2.8605&7.2431\\\\P(x)&\dfrac{365}{1014}&\dfrac{264}{1014}&\dfrac{193}{1014}&\dfrac{91}{1014}&\dfrac{101}{1014} \\\\(x-\mu)^2P(x)&0.6179&0.0248&0.0910&0.2567&0.7215\end{array}\right|$

$Variance, \sum (x-\mu)^2P(x)=1.7119$

(d)

$\left|\begin{array}{c|cccccc}y&1&2&3&4\\\\P(y)&\dfrac{264}{649}&\dfrac{193}{649}&\dfrac{91}{649}&\dfrac{101}{649} \end{array}\right|$

$E(y)=\left(1\times\dfrac{264}{649}\left)+\left(2\times\dfrac{193}{649}\left)+\left(3\times\dfrac{91}{649}\left)+\left(4\times\dfrac{101}{649}\right)$

E(y)=2.0447

The expected value for y surpasses that of x.

6 0

1 month ago

In a study of hormone supplementation to enable oocyte retrieval for assisted reproduction, a team of researchers administered t

lawyer [12517]

Answer:

Please note: The provided question lacks completeness; the full question is below along with multiple choice options, and Option 3 is the right answer.

Step-by-step explanation:

Note: The question is incomplete, and presents several options.

1. The research team anticipates that 80% of comparable intervals will encompass the actual mean number of oocytes retrievable from the female population aged 36-40 years.

2. It is expected that 80% of similar intervals will cover the mean number of oocytes gathered from a sample of 98 women aged 36-40 years.

3. There is an 80% probability that the true average of retrievable oocytes from the 36-40 age group falls within the defined interval.

4. The expectation is that 80% of similarly constructed intervals will represent the possible range of oocytes that can be extracted from that demographic.

To select the proper option, we first need to clarify the concept of a confidence interval.

A Confidence Interval indicates the range where we can reasonably expect our true values to reside. In this scenario, the 80% confidence interval suggests that there is an 80% likelihood the actual values will reside within that interval. Let's compute it.

The data we possess from the question includes:

Sample Size = 98

Mean = 9.7

Confidence Level = 80%

Z Score = 1.282

The formula for the confidence interval is:

Mean ± Z x SD/ $\sqrt{n}$

We have all variables except for SD, which is the standard deviation. First, we will determine that.

The standard deviation is derived from the square root of the variance, so we need to calculate the variance first.

Mean = Total/Sample Number

9.7 = Total/ 98

Total = 950.6

For calculating variance, we will utilize this total.

s² = (950.6 (1 - 9.7)²) ÷ (98-1)

s² = 741. 762 = Variance.

Now, let's find the Standard deviation

SD = $\sqrt{variance}$

SD = $\sqrt{741.762}$

SD = 27.23 = Standard Deviation.

Now we have all the necessary data for computing the 80% confidence interval range.

Mean ± Z x SD/ $\sqrt{n}$

The Z-score, which we use is set for different confidence levels; in our case, for 80%, Z has a value of 1.282.

By inputting the numbers into the equation above, we can derive the range of values or the 80% confidence interval where our true value is likely to sit.

9.7 ± 1.282 x 27.23/ $\sqrt{98}$

9.7 ± 3.52 Or

9.7 + 3.52 = 13.22

9.7 - 3.52 = 6.18

The Range of Values with 80% confidence interval = (6.18 to 13.22).

This indicates that our true mean is most likely found within this range.

Therefore, Option 3 is the accurate choice fulfilling the correct definition and context of the question.

6 0

1 month ago

The pillars in front of Mr. Jefferson's home are shaped like cylinders. The pillars have a height of 24 ft and a radius of 8 in.

tester [12383]

Answer:

Option A. approximately 100.5ft²

Explanation:

As the bases should not be painted, their areas are not counted in the overall calculation.

The area that requires painting on each pillar corresponds to the lateral area of a cylinder given its dimensions.

The formula for calculating the lateral area of a cylinder is:

$Lateral\text{ }area=2\pi \times radius \times height$

Substituting with the conversion factor to transform inches to feet:

$Lateral\text{ }area=2\pi \times 8in\times 1ft/12in \times 24ft=100.5ft^2$

7 0

1 month ago