I need help for this khan pleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeese

the value of sin ∅ is 12/ 13

From the given question,

We have,  cos ∅= 5/13

From the trigonometric identities, we have that

[tex]sin^2\alpha + cos^2\alpha = 1[/tex]

Then , let's substitute the value of cos ∅

[tex]sin^2\alpha +(\frac{-5}{13} )^2 = 1[/tex]

Let make sin the subject of formula and find the squares of the fraction

sin²∅ = [tex]1 - \frac{25}{169}[/tex]

Find the LCM

sin²∅ = [tex]\frac{169 - 25}{169}[/tex]

Find the difference

sin²∅ = [tex]\frac{144}{169}[/tex]

Find the square root

sin∅ = [tex]\sqrt{\frac{144}{159} }[/tex]

sin∅ = [tex]\frac{12}{13}[/tex]

In quadrant II , sin is positive, so we have

sin ∅ = 12/ 13

Thus, the value of sin ∅ is 12/ 13

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Answer:

x = 30 degrees

Step-by-step explanation:

angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees

KNL = 30 degrees

angle KLN is 90 degrees, a triangle is equal to 180 degrees

2x+30+90 = 180

2x = 60

x = 30 degrees

After the tax and the tip are counted, we conclude that each friend must pay $30.

We know that the meal cost is $72.50.

Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).

Then the total meal cost is:

C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39

Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:

C' = $77.39*(1 + 15%/100%) = $88.998 = $90

(Where we rounded up).

Then, if there are 3 friends, each one must pay:

$90/3 = $30

Each friend must pay $30.

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Answer:

D.  I, II, and III

Step-by-step explanation:

A discontinuous function is a function which is not continuous.  

If f(x) is not continuous at x = a, then f(x) is said to be discontinuous at this point.

To prove whether a function is discontinuous, find where it is undefined.

A rational function is undefined when the denominator is equal to zero.

Therefore, to find the values that make a rational function undefined, set the denominator to zero and solve.

Function I

Denominator:  x - 2

Set to zero:  x - 2 = 0

Solve:  x = 2

Therefore, this function is undefined when x = 2 and so the function is discontinuous.

Function II

Denominator:  4x²

Set to zero:  4x² = 0

Solve:  x = 0

Therefore, this function is undefined when x = 0 and so the function is discontinuous.

Function III

Denominator:  x² + 3x + 2

Set to zero:  x² + 3x + 2 = 0

Solve:  

⇒ x² + 3x + 2 = 0

⇒ x² + x + 2x + 2 = 0

⇒ x(x + 1) + 2(x + 1) = 0

⇒ (x + 2)(x + 1) = 0

⇒ x = -2, x = -1

Therefore, this function is undefined when x = -2 and x = -1, and so the function is discontinuous.

Therefore, all three given functions are discontinuous.

The solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

The first inequality is (x² - 25)/(x + 10) ≥ 0

⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

∴ x ≥ 5

Thus the domain of the given inequality from method of interval is x = [5,∝).

The second inequality is (x + 2)(x² - 64)/(x² + 45) ≤ 0

⇒ (x + 2)(x² - 64)≤ 0

Either (x + 2)≤ 0 or (x² - 64)≤ 0

Either x ≤ -2 or x ≤ 8

Thus , the combined domain of the given inequality from method of interval is x = [-2,0]∪[8,-∝) .

Therefore, the solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

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The value of the car after 5 years is 8527.02 dollars

Depreciation is the reduction in the value of an asset over time due to elements such as wear and tear. For example a car is said to "depreciate" in value after a discovery of a faulty transmission.

The value after 5 years can be found as follows:

Rate = 18% = 18 / 100 = 0.18

Initial Value  = $23,000

time = 5 years

Therefore,

y = 23000(1 + 18%)⁵

y = 23000(1 - 0.18)⁵

y = 23000(0.82)⁵

y = 23000 × 0.3707398432

y = 8527.0163936

y = 8527.02 dollars

Therefore, the value of the car after 5 years is 8527.02 dollars

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Using an exponential function, it is found that the value of the car after 5 years will be of $8,527.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the initial cost and the decay rate are given as follows:

A(0) = 23000, r = 0.18.

Hence the value of the boat after t years is given as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 23000(1 - 0.18)^t[/tex]

[tex]A(t) = 23000(0.82)^t[/tex]

The value after 5 years will be of:

[tex]A(5) = 23000(0.82)^5 = 8527[/tex]

The value of the car after 5 years will be of $8,527.

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Solving a quadratic equation, the correct option is given by:

Yes, they intersect at the coordinates (0, 8) and (6, 26).

A quadratic function is given according to the following rule:

y = ax² + bx + c

The solutions are:

x1 = (-b + sqrt(Delta))/2a

x2 = (-b - sqrt(Delta))/2a

In which:

Delta = b² - 4ac

The equation for this system if:

-x² + 9x + 8 = 3x + 8

x² - 6x = 0

x(x - 6) = 0

Then:

Which means that the correct option is:

Yes, they intersect at the coordinates (0, 8) and (6, 26).

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Using it's concept, there is a 20% probability that a customer ordered a large given that he or she ordered a cold drink.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 8 + 12 + 5 = 25 people ordered a cold drink, and of them, 5 were large, hence the probability is:

p = 5/25 = 0.2 = 20%.

20% probability that a customer ordered a large given that he or she ordered a cold drink.

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The converse, inverse and contrapositive of each conditional statement include:

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."

Where:

P and Q represent sentences.

In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:

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The value of angle 20 is as follows:

m∠20 = 50.9 degrees.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line l and m are parallel lines cut by the two transversal.

Hence,

m∠6 ≅ m∠20 (alternate angles)

Therefore, alternate angles are congruent

m∠20 = 2x - 4

m∠19 + m∠20 = 180 (angles on a straight line)

5x - 8 + 2x - 4 = 180

7x - 12 = 180

7x = 180 + 12

7x = 192

x = 192 / 7

x = 27.4285714286

x = 27.43

Therefore,

m∠20 = 2(27.43) - 4

m∠20 = 50.8571428571

m∠20 = 50.9 degrees.

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The first function is a type of cubic function and the second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

A function assigns the value of each element of one set to the other specific element of another set.

The function given in the problem is:

f(x) = x³ + x² – 3x + 4

The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.

The second function given in the problem is:

g(x) = 2x – 4

The highest degree (power) of this function is 1. Thus, this function is a type of linear function.

Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).

Thus, the first function is a type of cubic function  and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

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The largest possible total area of the four pens is 285610 ft²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the length of the pen and x represent the width of the pen.

Hence:

Perimeter = x + y + x + y + x + x + x = 2y + 5x

2y + 5x = 3380    

y = (3380 - 5x)/2      (2)

Area (A) = xy

A = x * (3380 - 5x)/2      

A = (3380x - 5x²)/2      

The maximum area is at A' = 0, hence:

A' = (1/2)(3380 - 10x)

0 = (1/2)(3380 - 10x)

10x = 3380

x = 338 ft.

2y + 5(338) = 3380    

y = 845 ft.

Largest possible total area = 338 * 845 = 285610 ft²

The largest possible total area of the four pens is 285610 ft²

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The equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

The expression is given as:

1/2 * 1/2 *1/2

Apply the product law of indices

1/2 * 1/2 *1/2 = (1/2)^3

Apply the power law of indices

1/2 * 1/2 *1/2 = (2^-1)^3

This gives

1/2 * 1/2 *1/2 = 2^-3

Hence, the equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

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hi

f°g  mean apply  g(x) and  then use result of  g(x) as  "x" in f(x)

so as  g(x) = x² +1   and  f(x) = 3x+2

so if we call  g(x)   X  we have  

f( X) =  3 X +2

now we replace  " X"  for it's value

f(X) =  3 ( x² +1) +2

f(X) =  3x² +3 +2

f(X) = 3x² +5

so  f°g = 3x² +5

The real engine is 65.25 feet long

The scale is given as:

Scale = 87 feet to 1 foot

The scale length is given as

Scale length = 9 inches

Convert inches to feet

Scale length = 9/12 feet

The actual length is then calculated as:

Actual = 87 * 9/12 feet

Evaluate

Actual = 65.25 feet

Hence, the real engine is 65.25 feet long

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The probability that at least 8 patients show improvement is; 0.94

The formula for Binomial Probability Distribution is;

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

where;

n = number of trials

r = number of specific events you wish to obtain

p is  probability of success

From the question, we have;

n = 12

r = 8

p = 81% = 0.81

The probability that at least 8 patients show improvement is expressed as;

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

Using online binomial probability calculator gives us;

P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977

P(X ≥ 8) = 0.94

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Answer: (5,1)

Step-by-step explanation:

Adding the equations gives 2d=10, and thus d=5.

So, it follows e=1.

Therefore, the solution is (5,1).

The solution is (5,1)

Given that d+e =6 and d-e =4

We need to find the solution of the given equations

Elimination method is used to eliminate a variable in an equation to find the value of another variable

Now here ,

We we will solve the equation i.e

d+e = 6

d-e = 4

Solving this equation We get,

2d = 10

Therefore,

d= 5

Now substituting the value of d in equation d+e =6

therefore,

5+e =6

Therefore e = 1

Hence the solution is (5,1)

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Answer:

1.  x = -1  y= -2
2. infinitely many solutions

3. x = 6 y= -7

4.no solution

5. x = -3 y = -17

6. x= 3 y = 7

Step-by-step explanation:

1) y=x-1

7x+6y= -19

6y= -19 -7x

y= (-7x-19)/6

since x-1 and (-7x-19)/6 are both equal to y they are equal to each other

this is how to get x

x-1 = (-7x-19)/6

6x-6 = -7x-19

13x = -13

x = -1

now put back -1 in the equation to get y

y=x-1

y = -1 -1

y= -2

2)-10x+2y=-12

y=5x-6

2y= -12 + 10x

y= -6 + 5x

y = 5x - 6

5x-6 = 5x - 6

0 = 0

when something is

equal to itself its

infinitely many solutions

(when something is not equal to something its no solution)

((when something is equal to just one answer its one solution)

3) y= -4x+17

y=x-13

-4x+17 = x-13

30 = 5x

x = 6

y=x-13

y=6-13

y= -7

4) -3x-15y=8

x+5y=5

-3x-15y=8 -> y = -1/15(3x-8)

5y=5-x -> y= 1/5 (5-x)

-1/15(3x-8) = 1/5 (5-x)

-x-8/3 = 5-x

0 = 23/3

(when something is not equal to something its no solution)

5) -3x+6y=-3

3x-y=8

-3x+6y= -3 -> y = 1/6(3x-3)

3x-y=8 -> y = 3x-8

1/6(3x-3) = 3x-8

3x-3 = 18x-48

x-1 = 6x - 16

5x = -15

x = -3

3x-y=8

3(-3)-y=8

-9-8 = y

y = -17

6) -6x+6y=24

-3x-8y=1

-6x+6y=24 -> y = 1/6(6x+24) -> y = x+4

-3x-8y=1 -> -3x-1 = 8y -> y = 1/8 (-3x-1)

1/8 (-3x-1) = x+4

-3x-1 = 8x+32

11x = 33

x= 3

-6x+6y=24

-6(3)+6y=24

-18 + 6y = 24

6y = 24 + 18

6y = 42

y = 7

The number of dogs in the animal shelter which comprise of cats, dogs, and rabbits is 84 dogs.

Total animals = 5 × 47

= 235

235 = d + (d + 20) + 1/2(d + 20) - 5

235 = d + d + 20 + 1/2d + 10 - 5

235 = 2 1/2d + 25

235 - 25 = 2 1/2d

210 = 2 1/2d

d = 210 ÷ 2 1/2

d = 210 ÷ 5/2

= 210 × 2/5

= 420/5

d = 84 dogs

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1. The average daily balance for this credit card account is $187.74.

2. The finance charge for the month of April is $249.22.

The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.

A billing cycle for a credit card account is usually one month.

Interest rate = 16.15% compounded monthly

Date       Activity            Amount     Balance  

April 1    Beginning Balance          $1,000.00

April 5   Purchase           29.10         1,029.10

April 12  Payment      −225.00           804.10

April 15  Purchase         97.25            901.35

April 23 Purchase         19.00           920.35

April 26 Purchase        28.40           948.75

April 30 Ending Balance                  948.75

Total                                            $5,632.05

Average daily balance = $187.735 ($5,632.05/30 days)

Daily interest rate = 0.04425 (16.15%/365)

Finance charge = $249.22 ($187.74 x 0.04425 30 days)

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Answer:

The product would be: -22/3 = 16/3, if true or false: false the left side -7.3 does not equal to the right side 5.3 which means the given statement is false, if it is evaluated -22/3 = 16/3, if multiplied it would still be -22/3 = 16/3 (you never said how to solve it so here are ways)

The length of the line segment SR is 15 units.

In Δ SRQ as seen in the attached image, we see that;

∠SRQ is a right angle

SQ is the hypotenuse

RT ⊥ SQ

Thus, by triangular rules, we know that;

(RQ)² = TQ × SQ

RQ = 20 units and TQ = 16 units

Thus;

(20)² = 16 × SQ

400 = 16 × SQ

SQ = 400/16

SQ = 25 units

By using Pythagoras theorem in Δ SRQ, we have;

(SR)² + (RQ)² = (SQ)²

RQ = 20 units and SQ = 25 units

Thus;

(SR)² + (20)² = (25)²

(SR)² + 400 = 625

(SR)² = 225

SR = √225

SR = 15 units

The length of the line segment SR is 15 units.

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Answer: answer is B

Step-by-step explanation:

use Pythagorean theorem to find other side. And sine is opposite side over hypotenuse.

The weighing of the man on the earth given the ratio is 174 pounds

Equate the ratio

6 : 1 = x : 29

6/1 = x/29

6 × 29 = 1 × x

174 = x

x = 174 pounds

Complete question:

The ratio of the weight of an object on the earth to the moon is 6:1. If a man weighs 29 pounds on the moon, calculate his weighing on the earth.

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The equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = 3(x + 5)^2 - 4

Express f(x) as y

So, we have

y = 3(x + 5)^2 - 4

Swap the positions of x and y

So, we have

x = 3(y + 5)^2 - 4

Add 4 to both sides of the equation

So, we have

x + 4 = 3(y + 5)^2

Divide through by 3

So, we have

1/3(x + 4) = (y + 5)^2

Take the square root of both sides

So, we have

√[1/3(x + 4)] = y + 5

Subtract 5 from both sides of the equation

So, we have

y = -5 + √[1/3(x + 4)]

Rewrite as

f-1(x) = -5 + √[1/3(x + 4)]

Hence, the equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

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Answer:

18.4 units

Step-by-step explanation:

We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of the line segment.

d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] = [tex]\sqrt{(5+12) ^{2} +(-10+3) ^{2}}[/tex] = [tex]\sqrt{(17) ^{2} +(7) ^{2}}[/tex]=[tex]\sqrt{338}[/tex]=18.38

The probability that all 3 books would be nonfiction is 0.1846.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)

9 /15 x 8/14 x 7/13 = 0.1846

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Answer:

Step-by-step explanation:

hello here is an solution