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2 years ago

prove that ( sin theta cos theta = cot theta ) is not a trigonometric identity by producing a counterexample

Mathematics

1 answer:

user100 [1]2 years ago

8 0

Answer:

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Assume θ with a value and substitute with it.

Let θ = 45°

So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2

R.H.S = cot θ = cot 45 = 1

So, L.H.S ≠ R.H.S

So, sin θ cos θ = cot θ is not a trigonometric identity.

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What is the value of the expression below when x=4x=4? 7x^2 +8x-7 7x 2 +8x−7

Vinil7 [7]

Answer: 137

Step-by-step explanation:

The given expression: $7x^2 +8x-7$

We need to find the value of the expression when x=4.

So we just use the substitution property and substitute the value of x= 4 in the given expression , we get

$7(4)^2+8(4)-7\\\\= 7(16)+32-7\\\\= 112+25\\\\=137$

Hence, the value of the expression at x=4 is 137.

3 0

2 years ago

A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations al

NeX [460]

Complete Question

The complete qustion is shown on the first uploaded image

Answer:

The correct option is B

Step-by-step explanation:

From the question we are told that

The sample size is $n = 49$

The mean is $\mu = 17ppb$

The standard deviation is $\sigma = 14 ppb$

Generally the standard error of this measurement is mathematically represented as

$\sigma_z = \frac{\sigma}{\sqrt{n} }$

substituting values

$\sigma_{\= x} = \frac{14}{\sqrt{49} }$

$\sigma_{\= x} = 2$ ppb

Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )

Next is to find the z value

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

$z = \frac{15-17}{2}$

$z = -1$

Now checking the z-table for the z-score of -1 we have

$P(X$

5 0

2 years ago

the table shows different ways that cameron can display his 12 model cars on shelves. How many shelves will display 2 cars if 8

Lera25 [3.4K]

Answer:

4 shelves

Step-by-step explanation:

if there is 8 shelves that display 1 car then that means there is 8 cars total.

so if you need a total of 12 cars then you would do (total of cars needed - total of cars you have).

(12-8) which would equal 4.

you need 4 cars left but on each shelf going forward needs to have 2 cars on it.

now since you have 4 cars you would divide that by the amount of cars on each shelf going forward.

4/2) which equals 2.

you need 2 more shelfs for the 4 cars needed.

3 0

2 years ago

An employee at a homemade wooden toy store earned $860 over the past week. The employee needs to pay 14% for Federal Income Tax

kari74 [83]

Answer:

$713.8

Step-by-step explanation:

14%of 860 = 120.4

3% of 860 = 25.8

so, subtract the sum of the above 2 values from 860.

860 - (120.4+25.8) = 860-146.2 = 713.8

Hope this helps

3 0

2 years ago

A study is being conducted in which the health of two independent groups of ten policyholders is being monitored over a one-year

uysha [10]

Answer:

46.91% probability that at least nine participants complete the study in one of the two groups, but not in both groups

Step-by-step explanation:

We use two binomial trials to solve this question.

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.

Probability of at least nine participants finishing the study in a group.

0.2 probability of a students dropping out. So 1 - 0.2 = 0.8 probability of a student finishing the study. This means that $p = 0.8$ .

10 students, so $n = 10$

We have to find:

$P(X \geq 9) = P(X = 9) + P(X = 10)$

Then

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

$P(X = 9) = C_{10,9}.(0.8)^{9}.(0.2)^{1} = 0.2684$

$P(X = 10) = C_{10,10}.(0.8)^{10}.(0.2)^{0} = 0.1074$

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.2684 + 0.1074 = 0.3758$

0.3758 probability that at least nine participants complete the study in a group.

Calculate the probability that at least nine participants complete the study in one of the two groups, but not in both groups?

0.3758 probability that at least nine participants complete the study in a group. This means that $p = 0.3758$

Two groups, so $n = 2$

We have to find P(X = 1).

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

$P(X = 2) = C_{2,1}.(0.3758)^{1}.(0.6242)^{1} = 0.4691$

46.91% probability that at least nine participants complete the study in one of the two groups, but not in both groups

5 0

2 years ago

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