please try this for answer my question please​

(1) Recall that

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

sin²(x) + cos²(x) = 1

Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have

• sin(α) < 0 and cos(α) < 0

• sin(β) < 0 and cos(β) > 0

Solve for cos(α) and sin(β) :

cos(α) = -√(1 - sin²(α)) = -3/5

sin(β) = -√(1 - cos²(β)) = -5/13

Then

sin(α - β) = sin(α) cos(β) - cos(α) sin(β) =  (-4/5) (12/13) - (-3/5) (-5/13)

==>   sin(α - β) = -63/65

(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,

sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)

==>   tan²(x) + 1 = sec²(x)

Rewrite the equation as

3 sec²(x) tan(x) = 4 tan(x)

3 (tan²(x) + 1) tan(x) = 4 tan(x)

3 tan³(x) + 3 tan(x) = 4 tan(x)

3 tan³(x) - tan(x) = 0

tan(x) (3 tan²(x) - 1) = 0

Solve for x :

tan(x) = 0   or   3 tan²(x) - 1 = 0

tan(x) = 0   or   tan²(x) = 1/3

tan(x) = 0   or   tan(x) = ±√(1/3)

x = arctan(0) + nπ   or   x = arctan(1/√3) + nπ   or   x = arctan(-1/√3) + nπ

x = nπ   or   x = π/6 + nπ   or   x = -π/6 + nπ

where n is any integer. In the interval [0, 2π), we get the solutions

x = 0, π/6, 5π/6, π, 7π/6, 11π/6

(3) You only need to rewrite the first term:

[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]

Then

[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]

Answer:

[tex]\sqrt{49}[/tex]

Step-by-step explanation:

Define a rational number by a number able to expressed a fraction where the denominator is not 0 or 1.

Non-terminating (never-ending) decimals cannot be expressed as a fraction and therefore are irrational. However, recall that [tex]\sqrt{49}=7[/tex], which can be expressed as a fraction (e.g. [tex]\frac{14}{2}[/tex], etc). Thus, the answer is [tex]\boxed{\sqrt{49}}[/tex].

Answer:

22608 mm³/s

Step-by-step explanation:

Applying chain rule,

dV/dt = (dV/dr)(dr/dt)............... Equation 1

Where dV/dr = rate at which the volume is increasing

But,

V = 4πr³/3

Therefore,

dV/dr = 4πr²............... Equation 2

Substitute equation 2 into equation 1

dV/dt = 4πr²(dr/dt).............. Equation 3

From the question,

Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm

Consatant: π = 3.14

Substitute these values into equation 3

dV/dt = 4×3.14×30²×2

dV/dt = 22608 mm³/s

Answer:

[tex]c = \frac{1}{12}[/tex]

The mean of the distribution is 0.25.

The variance of the distribution is of 0.6875.

Step-by-step explanation:

Probability density function:

For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:

[tex]3c + 3c + 6c = 1[/tex]

[tex]12c = 1[/tex]

[tex]c = \frac{1}{12}[/tex]

So the probability distribution is:

[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]

[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]

[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]

Mean:

Sum of each outcome multiplied by its probability. So

[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]

The mean of the distribution is 0.25.

Variance:

Sum of the difference squared between each value and the mean, multiplied by its probability. So

[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]

The variance of the distribution is of 0.6875.

Answer:

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A statistician calculates that 7% of Americans are vegetarians.

This means that [tex]p = 0.07[/tex]

Sample of 403 Americans

This means that [tex]n = 403[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.07[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127[/tex]

What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?

Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.

Probability the proportion is below 4%

p-value of Z when X = 0.04.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.04 - 0.07}{0.0127}[/tex]

[tex]Z = -2.36[/tex]

[tex]Z = -2.36[/tex] has a p-value of 0.0091

2*0.0091 = 0.0182

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Answer:

Area of ellipse=[tex]\pi ab[/tex]

Step-by-step explanation:

We are given that

[tex]x=acos\theta[/tex]

[tex]y=bsin\theta[/tex]

[tex]0\leq\theta\leq 2\pi[/tex]

We have to find the area enclose by it.

[tex]x/a=cos\theta, y/b=sin\theta[/tex]

[tex]sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2[/tex]

Using the formula

[tex]sin^2x+cos^2x=1[/tex]

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

This is the equation of ellipse.

Area of ellipse

=[tex]4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx[/tex]

When x=0,[tex]\theta=\pi/2[/tex]

When x=a, [tex]\theta=0[/tex]

Using the formula

Area of ellipse

=[tex]\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta[/tex]

Area of ellipse=[tex]-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta[/tex]

Area of ellipse=[tex]-4ba\int_{\pi/2}^{0} sin^2\theta d\theta[/tex]

Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta[/tex]

Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta[/tex]

Using the formula

[tex]1-cos2\theta=2sin^2\theta[/tex]

Area of ellipse=[tex]-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}[/tex]

Area of ellipse[tex]=-2ba(-\pi/2-0)[/tex]

Area of ellipse=[tex]\pi ab[/tex]

Answer:

To find the surface area of a cuboid we can also label the length, width and the height of the prism and use the formula SA=2LW+2LH+2HW to find the area of a cuboid

Answer:

202 cm²

Step-by-step explanation:

The opposite faces of a cuboid are congruent , then

SA = top/bottom + front/ back + sides , that is

SA = 2(9 × 4) + 2(9 × 5) + 2(4 × 5)

     = 2(36) + 2(45) + 2(20)

     = 72 + 90 + 40

    = 202 cm²

Answer:

f(6)=-42

f(0)=0

f(-1)=7

Step-by-step explanation:

since f(x) =-7x

it implies that f(6),f(0) and f(-1) are all equal to f(x)

which is equal to -7x .

so wherever you find x you out it in the

function

Answer:

y = -2(x + 3)² + 2

y = 2{ -(x + 3)²+ 1}

y = 2{ -(x² + 6x + 9) + 1}

y = 2{ -x² - 6x - 9 + 1}

y = 2{ -x² - 6x - 8 }

y = -2 { x² + 6x + 8}

OR

y = -2{(x + 4)(x + 2)}

Answer:

-18

Step-by-step explanation:

b = -6

c = 3

-4c + b = ?

Plug in the value of each variable into the equation

-4c + b = ?

= -4(3) + (-6)

= -12 - 6

= -18

Answer:

median

Step-by-step explanation:

Q is at the midpoint of RS and so PQ is a median

A median is a segment from a vertex to the midpoint of the opposite side.

We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.

First, let's analyze the image:

In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.

Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.

With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.

If you want to learn more, you can read:

https://brainly.com/question/2272632

Answer:

0.9936 = 99.36% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

Step-by-step explanation:

For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used 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.

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

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Assume that there is a 8​% rate of disk drive failure in a year.

So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]

Two disks are used:

This means that [tex]n = 2[/tex]

What is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive?

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

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

[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]

0.9936 = 99.36% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

Hi!

√80 = √(16 • 5) = √(4² • 5) = 4√5

Answer:

32P6  

Step-by-step explanation:

nPr

n=32

r=6

Answer:4778.3 cm^3

Step-by-step explanation: The formula for volume of a cone is V=1/3h pi r^2. By plugging in the height and the radius we get our answer.

Answer:

4778.4 :)

Step-by-step explanation:

Answer:

C. -4

Step-by-step explanation:

Answer:

(c) - 4

is your right answer

Answer:

x= - 1

Step-by-step explanation:

Answer:

see the attachment

Step-by-step explanation:

Hope it helps you

Answer:

78i+52j

Step-by-step explanation:

8(9i+2j)-6(-i-6j)

72i+16j+6i+36j

=78i+52j

===============================================

Explanation:

It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.

The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.

We add on 2 since we're adding two copies of "1" on either side of each dimension.

The larger rectangle's area is 92*82 = 7544 square feet

The smaller rectangle's area is 90*80 = 7200 square feet

The difference in areas is 7544-7200 = 344 square feet.

Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.

Answer:

(a)So, there are 2 kings in red- one of hearts and the other of diamonds. Therefore, the probability of selecting a red king from a deck of cards= 2/52 or 1/26.

(b) There are 6 red face cards in a 52-card deck (so 46 other cards). PROBABILITIES compare the number of favorable outcomes to the total number of possible outcomes: The PROBABILITY of getting a red face card is 6/52 = 3/26.

The odds in favor of getting a red king will be 1/26. And the odds against getting a red king will be 25/26.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

You are dealt one card from a 52-card deck.

Total events = 52

The odds in favor of getting a red king will be

Favorable events = 2

Then the probability will be

P = 2/52

P = 1/26

The odds against getting a red king will be

q = 1 – P

q = 1 – 1/26

q = 25/26

More about the probability link is given below.

https://brainly.com/question/795909

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Answer:

y = 4 x − 4

Step-by-step explanation:

Answer:

z = (2xy-x)

Step-by-step explanation:

Let the first number be x and the other number is z.

According to question,

The average of two number is xy i.e.

[tex]\dfrac{x+z}{2}=xy\\\\x+z=2xy\\\\z=2xy-x[/tex]

So, the value of z is (2xy-x) i.e. the other number is (2xy-x).

===============================================

Work Shown:

A = P*e^(r*t)

A = 47000*e^(0.0526*17)

A = 114,932.799077198

A = 114,932.80

Notes:

Mark's account balance after 17 years would be $114,932.8

[tex]A=Pe^{rt}[/tex]

where,

A = Accrued amount

P = Principal amount

r = interest rate as a decimal

R = interest rate as a percent

r = R/100

t = time in years

For given question,

P = $47000, t = 17 years

R = 5.26%

[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]

Using the Continuous Compounding Formula,

[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]

Therefore, Mark's account balance after 17 years would be $114,932.8

Learn more about the Continuous Compounding here:

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Answer:

80 students

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

60% of 500 = 300

72% of 500 = 360

40% of 500 = 200

28% of 500 = 140

300+360 = 660

660 - 2x = 500

660 - 500 = 2x

160 = 2x

2x = 160

x = 80

Answer:

11

Step-by-step explanation:

y-1=10

Any figure that crosses equal sign, the operational sign changes.

y=10+1

y= 11

Hi there!  

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I believe your answer is:  

Quadrant III

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Here’s why:  

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See the attached picture for reference.

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Hope this helps you. I apologize if it’s incorrect.  

Answer:

A and b Are in quadrant 2. F and D are in quadrant 1. F is in quadrant 3 and C is in quadrant 4

Step-by-step explanation:

each quadrant is in the boxes and the question is asking what is each  coordinate is in what quadrant

Answer:

(0, -9)

Step-by-step explanation:

The y intercept is the y value when x =0

(0, -9)