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Doss [256]
3 years ago
13

Determine the exact value of sin 150 degrees

Mathematics
1 answer:
avanturin [10]3 years ago
7 0

Answer:

\frac{1}{2}

Step-by-step explanation:

Use the identity:

\sin(180-\theta)=\sin \theta

We were given:\sin 150\degree

We can rewrite this as:

\sin(180-30)\degree=\sin 30\degree

On the unit circle, \sin 30\degree=\frac{1}{2}

This implies that:

\sin(180-30)\degree=\sin 150\degree=\sin 30\degree=\frac{1}{2}

Therefore the exact value of \sin 150\degree is \frac{1}{2}

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Gordon types 1,972 words in 29 minutes<br> Gordon types _______ words per minute<br> PLSSS HELPP ME
Xelga [282]

Answer:

68 words

Step-by-step explanation:

To find how many words Gordon types per minute :

1972 ÷ 29 = 68 #

8 0
3 years ago
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS
Strike441 [17]
can u help me with mine thx
8 0
2 years ago
62% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 48 owned dogs are r
dedylja [7]

Answer:

a) 0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b) 0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c) 0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d) 0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

Step-by-step explanation:

To solve this question, we use the binomial probability distribution, and also it's approximation to the normal distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

62% of owned dogs in the United States are spayed or neutered.

This means that p = 0.62

48 owned dogs are randomly selected

This means that n = 48

Mean and standard deviation, for the approximation:

\mu = E(x) = np = 48*0.62 = 29.76

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{48*0.62*0.38} = 3.36

a. Exactly 30 of them are spayed or neutered.

This is P(X = 30), which is not necessary the use of the approximation.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 30) = C_{48,30}.(0.62)^{30}.(0.38)^{18} = 0.1180

0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b. At most 33 of them are spayed or neutered.

Now we use the approximation. This is, using continuity correction, P(X \leq 33 + 0.5) = P(X \leq 33.5), which is the pvalue of Z when X = 33.5. So

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

Z = \frac{33.5 - 29.76}{3.36}

Z = 1.11

Z = 1.11 has a pvalue of 0.8665

0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c. At least 31 of them are spayed or neutered.

Using continuity correction, this is P(X \geq 31 - 0.5) = P(X \geq 30.5), which is 1 subtracted by the pvalue of Z when X = 30.5. So

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

Z = \frac{30.5 - 29.76}{3.36}

Z = 0.22

Z = 0.22 has a pvalue of 0.5871

1 - 0.5871 = 0.4129

0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d. Between 24 and 30 (including 24 and 30) of them are spayed or neutered.

This is, using continuity correction, P(24 - 0.5 \leq X \leq 30 + 0.5) = P(23.5 \leq X \leq 30.5), which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 23.5.

X = 30.5

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

Z = \frac{30.5 - 29.76}{3.36}

Z = 0.22

Z = 0.22 has a pvalue of 0.5871

X = 23.5

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

Z = \frac{23.5 - 29.76}{3.36}

Z = -1.86

Z = -1.86 has a pvalue of 0.0314

0.5871 - 0.0314 = 0.5557

0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

8 0
3 years ago
Help quickly as possible thank you :) ​
garri49 [273]

Answer:

3/10 liter for one glass. 6 glasses total would be how many liters? Just multiply what one glass would have by 6. Lemme know the answer you get

7 0
2 years ago
The weight Wkg of a metal bar varies jointly
maria [59]

Answer:

d = \sqrt{\frac{216W}{35L} }

Step-by-step explanation:

Given that W varies jointly as L and d² then the equation relating them is

W = kLd² ← k is the constant of variation

To find k use the condition W = 140 when d = 4 and L = 54, thus

140 = k × 54 × 4² = 864k ( divide both sides by 864 )

\frac{140}{864} = k , that is

k = \frac{35}{216}

W = \frac{35}{216} Ld² ← equation of variation

Multiply both sides by 216

216W = 35Ld² ( divide both sides by 35L )

\frac{216W}{35L} = d² ( take the square root of both sides )

d = \sqrt{\frac{216W}{35L} }

6 0
3 years ago
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