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2 years ago

What is the solution to the trigonometric inequality 2sin(x)+3>sin^2(x) over the interval 0<=x<=2pi radians?

Mathematics

1 answer:

densk [106]2 years ago

5 0

Answer:

A 2-column table with 6 rows. Column 1 is labeled x with entries 1.99, 1.999, 1.9999, 2.0001, 2.001, 2.01. Column 2 is labeled f (x) with entries 0.505, negative 0.827, 0.306, negative 0.306, 0.827, negative 0.506.

Find Limit of f (x) as x approaches 2 f(x), if it exists.

0.3

DNE

Step-by-step explanation:

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Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is t

svet-max [94.6K]

Answer:

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 450, \sigma = 100$

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

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

$Z = \frac{550 - 450}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

X = 350

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

$Z = \frac{350 - 450}{100}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

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

$1.88 = \frac{X - 450}{100}$

$X - 450 = 1.88*100$

$X = 638$

A score of 638(or higher).

c. Find the 60th percentile of the test scores.

X when Z has a pvalue of 0.60. So it is X when Z = 0.253

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

$0.253 = \frac{X - 450}{100}$

$X - 450 = 0.253*100$

$X = 475.3$

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

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

$-0.385 = \frac{X - 450}{100}$

$X - 450 = -0.385*100$

$X = 411.5$

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

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

$0.385 = \frac{X - 450}{100}$

$X - 450 = 0.385*100$

$X = 488.5$

The middle 30% of the test scores is between 411.5 and 488.5.

7 0

3 years ago

If a track is 400 meters around, how many laps around the track would it take to run 3.1 miles? Round to the nearest tenth. (Hin

zaharov [31]

Answer:

3200 meters

Step-by-step explanation:

because it is

4 0

2 years ago

Jonesville and smithville each have a population of size 2600 at time t = 0, where t is measured in years. Suppose jonesville'

ehidna [41]

Answer: B. Jonesville is growing linearly and Smithville is growing exponentially.

Step-by-step explanation:

Linear growth :

Population grow by a constant amount after each time period.
The rate of change of dependent variable with respect to independent variable is a constant.
It is represented by line on graph.
Equation for linear growth : $y=mx+c$ , c = initial value and m is the rate of change of y with respect to x.

Exponential growth :

Population grow by a constant ratio .
It is represented by a curve on graph.
Equation for exponential growth : $y=a(1+r)^x$ , a = initial value and r is rate of growth ( in decimal ) and x is time period.

Given : Jonesville's population grows by 170 people per year.

i.e .Population grow by a constant amount per year.

⇒ Jonesville is growing linearly.

The population of smithville grows by 7% per year.

i.e. Population grow by a constant ratio.

⇒Smithville is growing exponentially.

Hence, the true statement is "B. Jonesville is growing linearly and Smithville is growing exponentially."

5 0

3 years ago

A motocross ramp is 16 feet tall and 24 feet long what is the slope of the ramp

xxTIMURxx [149]

384 step by step explanation:

8 0

3 years ago

19/2 - 11/2 as an improper fraction

rjkz [21]

Answer:9 1/2 and 5 1/2

I hope that’s what your looking for

8 0

2 years ago