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3 years ago

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Select the correct answer. Write (21 − 4i) − (16 + 7i) + 28i as a complex number in standard form. A. 5 + 39i B. 5 + 17i C. 5 −

39i D. 5 − 17i

1 answer:

Anastasy [175]3 years ago

8 0

Answer:

<em>b. 5 + 17i</em>

Step-by-step explanation:

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Concerns about the climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g. from r

natta225 [31]

Answer:

a) 99% of the sample means will fall between 0.933 and 0.941.

b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?

Samples of 34 means that $n = 34$

We have that $\mu = 0.937, \sigma = 0.009$

By the Central Limit Theorem, $s = \frac{0.009}{\sqrt{34}} = 0.0015$

Within what interval will 99% of the sample means fail?

Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

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

By the Central Limit Theorem

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

$-2.575 = \frac{X - 0.937}{0.0015}$

$X - 0.937 = -2.575*0.0015$

$X = 0.933$

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

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

$2.575 = \frac{X - 0.937}{0.0015}$

$X - 0.937 = 2.575*0.0015$

$X = 0.941$

99% of the sample means will fall between 0.933 and 0.941.

(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?

By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

6 0

3 years ago

Can someone help me with this problem??

Pavlova-9 [17]

Find the slope first by doing (6+2)/(4-3)=8/1 or just 8. Next use a set of coordinates into the equation so 6=8(4)+b then solve so 6=32+b next subtract 32 from both sides which would equal -24=b. Then plug it all into the equation so y=8x-24

8 0

3 years ago

The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate,

Brrunno [24]

Answer:

192 $ft^2$

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

$\pi$ is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. $Volume =\frac{4}{3}\pi r^3$

2. $Surface\ Area = 4\pi r^2$

Given volume is 256 ft³.

$256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}$

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

$Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}$

So, approximate surface area of sculpture is 192 $ft^2$ .

3 0

2 years ago

Look at the photo plz !!

sergejj [24]

Answer:

11 0ver 54

Step-by-step explanation:

4 0

3 years ago

sid and Jill hiked 4 1/8 miles in the morning and 1 1/7 miles in the afternoon.how many times as far did they hike in the mornin

mote1985 [20]

Your answer is ..
First,
we have to turn our mixed fractions into an improper fraction.
=4 1/8 which is 33/8(4 x 8 + 1).

Our next mixed fraction,
we have 1 1/7 which is 8/7(1 x 7 + 1).

Now, we have the get the same denominator in order to subtract.
SO, both 8 and 7 goes in to 56. So we multiply both mixed fractions to get the same denominator.
(Tip: what ever you do to do numerator, you do to the denominator; and the other way around).
33/8 : 33*7=231 and our denominator, 8*7=56
So our improper fraction now,
231/56

Our next fraction 8/7,
7*8= 56 and our numerator 8*8=64.
=64/56

So, now we subtract.
231-64= 167 and our common denominator. 167/56

Now we divide 167 by 56 which is 2 and remainder is 55.
So, you should end up with a mixed fraction, 2 55/56.

7 0

3 years ago