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enot [183]
2 years ago
14

Solve the equation 2cos^2x + 3sinx = 3

Mathematics
1 answer:
Bezzdna [24]2 years ago
6 0

Answer:

x = 2 π n_1 + π/2 for n_1 element Z

or x = 2 π n_2 + (5 π)/6 for n_2 element Z or x = 2 π n_3 + π/6 for n_3 element Z

Step-by-step explanation:

Solve for x:

2 cos^2(x) + 3 sin(x) = 3

Write 2 cos^2(x) + 3 sin(x) = 3 in terms of sin(x) using the identity cos^2(x) = 1 - sin^2(x):

-1 + 3 sin(x) - 2 sin^2(x) = 0

The left hand side factors into a product with three terms:

-(sin(x) - 1) (2 sin(x) - 1) = 0

Multiply both sides by -1:

(sin(x) - 1) (2 sin(x) - 1) = 0

Split into two equations:

sin(x) - 1 = 0 or 2 sin(x) - 1 = 0

Add 1 to both sides:

sin(x) = 1 or 2 sin(x) - 1 = 0

Take the inverse sine of both sides:

x = 2 π n_1 + π/2 for n_1 element Z

or 2 sin(x) - 1 = 0

Add 1 to both sides:

x = 2 π n_1 + π/2 for n_1 element Z

or 2 sin(x) = 1

Divide both sides by 2:

x = 2 π n_1 + π/2 for n_1 element Z

or sin(x) = 1/2

Take the inverse sine of both sides:

Answer: x = 2 π n_1 + π/2 for n_1 element Z

or x = 2 π n_2 + (5 π)/6 for n_2 element Z or x = 2 π n_3 + π/6 for n_3 element Z

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A coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces. A random sample of 15 co
Luda [366]

Answer:

We conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

Step-by-step explanation:

We are given that a coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces.

A random sample of 15 containers were weighed and the mean weight was 31.8 ounces with a sample standard deviation of 0.48 ounces.

Let \mu = <u><em>mean weight of coffee in its containers.</em></u>

SO, Null Hypothesis, H_0 : \mu \geq 32 ounces     {means that the mean weight of coffee in its containers is at least 32 ounces}

Alternate Hypothesis, H_A : \mu < 32 ounces      {means that the mean weight of coffee in its containers is less than 32 ounces}

The test statistics that would be used here <u>One-sample t-test statistics</u> as we don't know about population standard deviation;

                             T.S. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean weight = 31.8 ounces

             s = sample standard deviation = 0.48 ounces

             n = sample of containers = 15

So, <u><em>the test statistics</em></u>  =  \frac{31.8 -32}{\frac{0.48}{\sqrt{15} } }  ~ t_1_4  

                                      =  -1.614

The value of t test statistics is -1.614.

<u>Now, at 0.01 significance level the t table gives critical value of -2.624 at 14 degree of freedom for left-tailed test.</u>

Since our test statistic is more than the critical value of t as -1.614 > -2.624, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.

Therefore, we conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

8 0
3 years ago
A corporation has 11 manufacturing plants. Of these, seven are domestic and four are outside the United States. Each year a perf
nikdorinn [45]

Answer:

The probability that a performance evaluation will include at least one plant outside the United States is 0.836.

Step-by-step explanation:

Total plants = 11

Domestic plants = 7

Outside the US plants = 4

Suppose X is the number of plants outside the US which are selected for the performance evaluation. We need to compute the probability that at least 1 out of the 4 plants selected are outside the United States i.e. P(X≥1). To compute this, we will use the binomial distribution formula:

P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = total no. of trials

           x = no. of successful trials

           p = probability of success

           q = probability of failure

Here we have n=4, p=4/11 and q=7/11

P(X≥1) = 1 - P(X<1)

          = 1 - P(X=0)

          = 1 - ⁴C₀ * (4/11)⁰ * (7/11)⁴⁻⁰

          = 1 - 0.16399

P(X≥1) = 0.836

The probability that a performance evaluation will include at least one plant outside the United States is 0.836.

7 0
2 years ago
An airplane traveled 700 kilometers in two hours during a trip. What was the average speed of the plane during the trip?
Igoryamba

9514 1404 393

Answer:

  350 km/h

Step-by-step explanation:

Speed = distance/time

speed = (700 km)/(2 h) = 350 km/h

8 0
3 years ago
Please help me answer this
ohaa [14]

i did the awnser is 173,668.18 there you goStep-by-step explanation:

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What is the median weight of the fish
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It should be 16.

Hope this helps!
8 0
2 years ago
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