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3 years ago

If sinA=1/2 what is cosA

Mathematics

1 answer:

sergejj [24]3 years ago

4 0

Answer:

$\frac{\sqrt3}{2}$

Step-by-step explanation:

$sin(A)=\frac{1}{2}$

$A = \frac{\pi}{6}$ //this is retrieved from looking at the unit circle

$cos(A) = cos(\frac{\pi}{6}) = \frac{\sqrt3}{2}$

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Genetic Defects Data indicate that a particular genetic defect occurs in of every children. The records of a medical clinic show

Dovator [93]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that there exist 60 or more defected children is $P(x \ge 60)=0.0901$

Looking at the value for this probability we see that it is not so small to the point that the observation of this kind would be a rare occurrence

Step-by-step explanation:

From the question we are told that

in every 1000 children a particular genetic defect occurs to 1

The number of sample selected is $n= 50,000$

The probability of observing the defect is mathematically evaluated as

$p = \frac{1}{1000}$

$= 0.001$

The probability of not observing the defect is mathematically evaluated as

$q = 1-p$

$= 1-0.001$

$= 0.999$

The mean of this probability is mathematically represented as

$\mu = np$

Substituting values

$\mu = 50000*0.001$

$= 50$

The standard deviation of this probability is mathematically represented as

$\sigma = \sqrt{npq}$

Substituting values

$= \sqrt{50000 * 0.001 * 0.999}$

$= \sqrt{49.95}$

$= 7.07$

the probability of detecting $x \ge60$ defects can be represented in as normal distribution like

$P(x \ge 60)$

in standardizing the normal distribution the normal area used to approximate $P(x \ge 60)$ is the right of 59.5 instead of 60 because x= 60 is part of the observation

The z -score is obtained mathematically as

$z = \frac{x-\mu }{\sigma }$

$= \frac{59.5 - 50 }{7.07}$

$=1.34$

The area to the left of z = 1.35 on the standardized normal distribution curve is 0.9099 obtained from the z-table shown z value to the left of the standardized normal curve

Note: We are looking for the area to the right i.e 60 or more

The total area under the curve is 1

$P(x \ge 60) \approx P(z > 1.34)$

$= 1-P(z \le 1.34)$

$=1-0.9099$

$=0.0901$

3 0

3 years ago

A cone with a radius of 6 cm has a volume of 1200 cm3. What is the height of the cone? (The volume of a cone is given by the for

Rina8888 [55]

Answer:

31.8 cm

Step-by-step explanation:

Volume of a cone:

V = 1/3πr²h

We have:

V = 1200 cm³
r = 6 cm
h = ?

Substitute values and solve for h:

1200 = 1/3*3.14*6²h
1200 = 37.68h
h = 1200/37.68
h = 31.8 cm (rounded)

None of the choices is correct

5 0

3 years ago

Read 2 more answers

Find an expression for the function f(x) whose graph is a line passing through the points (8,-5) and (-9,2). f(x)=

pentagon [3]

Answer:

Step-by-step explanation:

hello : look this solution

3 0

3 years ago

A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense he

Orlov [11]

Answer:

We conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are effective.

Step-by-step explanation:

We are given that in a 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field.

Among 264264 trials, the touch therapists were correct 105105 times.

Let p = proportion that touch therapists uses a random guess method.

Here, random guess means; p = 50%

So, Null Hypothesis, $H_0$ : p = 50% {means that the touch therapists use a method equivalent to random guesses}

Alternate Hypothesis, $H_A$ : p $\neq$ 50% {means that the touch therapists does not use a method equivalent to random guesses}

The test statistics that would be used here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of touch therapists were correct = $\frac{105}{264}$ = 0.39

n = sample of trials = 264

So, test statistics = $\frac{\frac{105}{264} -0.50}{\sqrt{\frac{\frac{105}{264}(1-\frac{105}{264})}{264} } }$

= -3.395

The value of z test statistics is -3.395.

Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are effective.

3 0

3 years ago

Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work.

amm1812

Answer:

X=6

Step-by-step explanation:

5(x+2)=6x+3x−1

Step 1: Simplify both sides of the equation.

5(x+2)=6x+3x−14

(5)(x)+(5)(2)=6x+3x+−14(Distribute)

5x+10=6x+3x+−14

5x+10=(6x+3x)+(−14)(Combine Like Terms)

5x+10=9x+−14

5x+10=9x−14

Step 2: Subtract 9x from both sides.

5x+10−9x=9x−14−9x

−4x+10=−14

Step 3: Subtract 10 from both sides.

−4x+10−10=−14−10

−4x=−24

Step 4: Divide both sides by -4.

−4x / -4= −24 / −4

x=6

8 0

3 years ago

Read 2 more answers

If sinA=1/2 what is cosA​

If sinA=1/2 what is cosA