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Vlada [557]
4 years ago
7

Use the steps to determine the exact value of

Mathematics
2 answers:
Ede4ka [16]4 years ago
7 0
To solve for sin(-135), the reference angle will be obtained as follow:
sin(-135)
=-sin(135)
=-sin(180-135)
=-sin 45
hence
the reference angle θ=45°
UNO [17]4 years ago
7 0

Answer:

The reference angle will be {\theta}=45^{\circ}

Step-by-step explanation:

To solve for sin(-135), the reference angle can be obtained as follows:

= sin(-135)

=- sin(135) (Because sin(-{\theta})=-sin{\theta})

Thus, the above equation can be written as:

=-sin(180-135)

=-sin45

Hence , the reference angle will be {\theta}=45^{\circ}

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Suppose it is known that 60% of radio listeners at a particular college are smokers. A sample of 500 students from the college i
vladimir1956 [14]

Answer:

The probability that at least 280 of these students are smokers is 0.9664.

Step-by-step explanation:

Let the random variable <em>X</em> be defined as the number of students at a particular college who are smokers

The random variable <em>X</em> follows a Binomial distribution with parameters n = 500 and p = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

 np=500\times 0.60=300>10\\n(1-p)=500\times(1-0.60)=200>10

Thus, a Normal approximation to binomial can be applied.

So,  

X\sim N(\mu=600, \sigma=\sqrt{120})

Compute the probability that at least 280 of these students are smokers as follows:

Apply continuity correction:

P (X ≥ 280) = P (X > 280 + 0.50)

                   = P (X > 280.50)

                   =P(\frac{X-\mu}{\sigma}>\frac{280-300}{\sqrt{120}}\\=P(Z>-1.83)\\=P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that at least 280 of these students are smokers is 0.9664.

8 0
3 years ago
A rectangular swimming pool has a length of 50 m, a width of 25 m, and a depth of 1.75 meters. What is the volume of water neede
Ahat [919]

Answer:

2187.5 cubic meters of water

Step-by-step explanation:

Volume of rectangle = L * W * D

V = 50 * 25 * 1.75

V = 2187.5

5 0
3 years ago
Read 2 more answers
Question 13 (Essay Worth 8 points)
mixer [17]

9514 1404 393

Answer:

  geometric sequence

Step-by-step explanation:

The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...

  an = 3(-4)^(n-1)

so the sum can be written as ...

  \displaystyle\sum_{n=0}^\infty3(-4)^n

(Note the summation starts at n=0, corresponding to a first term of 3.)

3 0
3 years ago
It cost 17 and $.70 send 170 in text messages how many text messages did you send if you spent $19.10?
ZanzabumX [31]

Answer:

184

Step-by-step explanation:

17.70 / 170 = .104 per text

19.10 / .104 = 183.65 round up to 184

6 0
3 years ago
A new novel is selling for $17.95. If it is on sale at 40% off, find the amount of discount and the sale price.
nadya68 [22]

Answer:

A

Step-by-step explanation:

multiply $17.95 by 40% to get the discount ($17.95 x .4), which equals $7.18.

the sale price is the initial price of the book less the discount ($17.95-$7.18), which equals $10.77.

5 0
3 years ago
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