Simplify the expression

Find the longitude and latitude for the points on the globe with angular coordinates ( θ , ϕ ) = ( π 4 , 11 π 12 ) (θ,ϕ)=(π4,11π

DedPeter [7]

Answer:

For (45,165.02) Latitude and longitude is (45 0' 0",165 1' 12")

Hence latitude and longitude are 4 degrees 35' 59.94" and 2 degrees 47' 59.994 "

Step-by-step explanation:

Given:

The angular coordinates of the point on globe as (θ,∅)=(π/4,11π/12)

To find : longitude and latitude for this points:

Solution:

For finding this Longitude and latitude we should convert it into decimal degrees

Given that 1rad =57.295 deg.

we get for

θ=π/4

=3.142/4

=0.7855 *57.295

=45 degrees.

Now for φ=11π/12

=(11*3.142)/12=2.8801*57.295

=165.02 degrees

Now convert in longitude and latitude as ,

as degrees +min/60+seconds/3600

Now latitude =45 degrees

i.e. 45 degrees 0' 0"

And longitude as

165.02 degrees becomes

165 degrees 1' 12".

Hence For the angular co-ordinates (45,165.02)

Longitude and latitude is (45 0' 0",165 1' 12")

Now for the (4.6, 2.8)

we get using same

degrees+min/60+seconds/3600

=4 degrees 35' 59.94"

And for 2.8 means, (similar to clock analog )

=2 degrees 47' 59.94"

Hence latitude and longitude are 4 degrees 35' 59.94" and 2 degrees 47' 59.994 "

8 0

4 years ago

Convert 8/9 to its decimal form and round to the nearest thousandth

kolezko [41]

Answer:

0.888

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

HELP PLS I NEED TO PASS THIS CLASS

musickatia [10]

The correct answer is a

8 0

3 years ago

Sue wants to plan a meal with 71 grams of fat and 1755 calories. If hot dogs have 13 grams of fat and 145 calories each and if b

Lena [83]

Answer:

Sue must use 3 hotdogs and 4 half-cup serving of baked beans.

Step-by-step explanation:

Let the number of hot dogs be represented by h

Let the number of baked beans be represented by b

Hot dogs have 13 grams of fat and 145 calories each

Baked beans have 8 grams of fat and 330 calories per half cup serving

Sue wants to plan a meal with 71 grams of fat and 1755 calories.

Grams of Fat from Hotdog + grams of fat from baked beans=71

13h+8b=71....(I)

Similarly,

Calories from hot dog + Calories from baked beans=1755

145h+330b=1755....(II)

We then solve Equations (I) and (II) simultaneously.

13h+8b=71....(I)

145h+330b=1755....(II)

Multiply equation 1 by 145 and equation 2 by 13

1885h+1160b=10295

1885h+4290b=22815

Subtracting

-3130b=-12520

b=4

Substitute b=4 into (I)

13h+(8X4)=71

13h=71-32

13h=39

h=3

Sue must use 3 hotdogs and 4 half-cup serving of baked beans.

4 0

4 years ago

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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 normally distributed samples are 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.

In this problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

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

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

4 years ago