Use the unit circle to find the value of sin 3π/2 and cos 3π/2. Show work please!

Answer:0.68

Step-by-step explanation:

Given

Total of 600 employees out of which 400 had college degree ,100 are single

and 60 were single graduates

therefore out of 100, 60 were single and rest 40 are single undergraduate

and out of 400, 60 were single graduates thus 340 are married graduate.

Now out of 600, 100 were single i.e. 500 is married

thus Probability that an employee is married and has a college degree is

=[tex]\frac{Favourable outcome }{Total outcome}[/tex]

P=[tex]\frac{340}{500}[/tex]=0.68  

Answer:

V=8.5

Step-by-step explanation:

o=oil. vinegar=v. furniture polish=f

O=3v

34= 3v + v

Using a system of guessing and checking if that number fits equation you can tell that 8 causes the equation to be unequal and also 9. You can learn V must be between 8 and 9 so 8.5 might fit the equation. 8.5=V

Final answer:

To make 34 oz of furniture polish, 8.5 oz of vinegar and 25.5 oz of olive oil are needed, with the olive oil being three times the amount of vinegar.

Explanation:

To create 34 oz of nontoxic furniture polish, where the amount of olive oil should be three times the amount of vinegar, we need to solve a simple algebraic equation. Let's denote the amount of vinegar as v ounces. According to the conditions, the amount of olive oil will then be 3v ounces.

The total amount of furniture polish equals the amount of vinegar plus the amount of olive oil:

v + 3v = 34 oz

This simplifies to:

4v = 34 oz

Dividing both sides by 4 gives us:

v = 8.5 oz

Therefore, the amount of olive oil needed is:

3v = 3 Times 8.5 oz = 25.5 oz

To conclude, we need 8.5 oz of vinegar and 25.5 oz of olive oil to make 34 oz of furniture polish.

Answer: [tex]\dfrac{3}{4389}[/tex]

Step-by-step explanation:

Given : Number of math books = 5

Total number of books = 5+6+8+3=22

Number of books except math = 17

Number of ways to arrange 22 books in bookshelf = [tex]22![/tex]

When all math books are together , then we count whole set as one

Now, the number of objects in bookshelf = 17+1=18

Number of ways to arrange books such that all math books are together = [tex]18!5![/tex]

Now, the probability that all the math books are together :-

[tex]\dfrac{5!18!}{22!}=\dfrac{3}{4389}[/tex]

Hence, the probability that all the math books are together [tex]=\dfrac{3}{4389}[/tex]

Answer:

The answer is 27 on edge as well!

Step-by-step explanation:

The answer is 27

This is because 15x15 is 225 plus 8x8 is 64 which is 289 and the square root of that is 17 and that is the diameter of the circle and the hypotenuse of the triangle and since the kite has two congruent sides which are both radii or half of a diameter times two would be the same as the length of the diameter which is 17 plus the two bottom sides which are both 5 and 5 plus 5 is 10 and 10 plus 17 is 27 or the perimeter of the kite.

Your Welcome!

Answer:

27

Step-by-step explanation:

im taking the test right now on edg. 2020

Answer:

  B.  sin35/9=sin40/b

Step-by-step explanation:

The law of sines tells you ...

  sin(A)/a = sin(B)/b

Filling in the given values, you get ...

  sin(35°)/9 = sin(40°)/b

Answer:

B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]

Step-by-step explanation:

We are given that in a triangle ABC. [tex]m\angle =35^{\circ}[/tex]

[tex]m\angle B=40^{\circ}[/tex]

a=9

We have to find an equation  which solve for b

We know that a sine law

[tex]\frac{a}{sine A}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Using above formula of sine law

Substituting all given values in the above formula of sine law

Then we get

[tex]\frac{9}{sin 35}=\frac{b}{sin 40}[/tex]

By cross multiply then we get

[tex]sin 40\times 9=sin35 \times b[/tex]

[tex] \frac{sin 40 \times 9}{b}= sin 35[/tex]

Using division property of equality

[tex]\frac{ sin 40}{b}=\frac{sin 35}{9}[/tex]

Using division property of equality

Hence, option B is true option for solving b.

Answer:B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]

Answer:

He should word his statement as "Free replacement for tires that wear before 30875 miles."

Step-by-step explanation:

If he is willing to replace 10% of tires he should find the life of tires that gives an area of 10% in the normal distribution graph.

Now for 10% of area standard normal deviate Z can be obtained from normal distribution table

Using normal distribution table for 10% area we have Z = -1.28

Thus we have [tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}[/tex]

Applying given values we get

[tex]X=-1.28\times 2500+34000\\\\X=30875miles[/tex]

The mechanic would replace the tires that spoil without covering up to 30800 miles.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

For a mean of 34000 miles and standard deviation of 2500. The probability of 10% correspond with a z score of -1.28. Hence:

-1.28 = (x - 34000)/2500

x = 30800

The mechanic would replace the tires that spoil without covering up to 30800 miles.

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Answer:

In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus  three over root seven

Step-by-step explanation:

Given that sin ∅ =3/4 It means the ratio of the opposite side to the hypotenuse side is 3:4.

Using the Pythagoras theorem we can calculate the hypotenuse adjacent as follows.

a²+b²=c²

a²=c²-b²

a²=4²-3²

a²=16-9

a²=7

a=√7

Then Cos ∅= opposite/ adjacent

=√7/4

Then Tan ∅ = opposite/adjacent

=3/√7

In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus  three over root seven.

Answer: The following statements are true:

It is symmetrical.

The first diagonal is all 1’s.

The second diagonal is the counting numbers.

Any number in the triangle is the sum of the two numbers directly above it.

Each row adds to a power of 2.

Answer:

They are all correct

Step-by-step explanation:

Answer:

Approximately 56.7%.

Step-by-step explanation:

Choose two people at random from the crowd and there will be two cases:

There's no third possible outcome. In other words, the two cases are mutually exclusive. Either the first or the second event is expected to happen. The sum of their probabilities shall equal to 1.

66 out of that 100 were rooting for the champion. The probability that both were rooting for the champion will be easier to find. The probability that the first person is rooting for the champion is equal to [tex]66/100[/tex].

After that first person was chosen from the crowd, the 65 out of the remaining 99 person in the crowd were chanting. The probability that the second person is rooting as well will equal to [tex]65/100[/tex].

Both event shall take place. The probability that both were rooting for the champion will equal to

[tex]\displaystyle \frac{66}{100} \times \frac{65}{99}[/tex].

The probability that one or zero out of the two persons were rooting will equal to

[tex]\displaystyle 1 - \frac{66}{100} \times \frac{65}{99} \approx \frac{17}{30} = 56.7\%[/tex].

Answer:

56.7% is correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

  (2x +3)² = (2x)² + 2(2x)(3) +(3)²

  = 4x² +12x +9

Comparing that to ax² +bx +c, we can identify ...

The values of a, b, and c are:

a   =  4

b  =  12

c  =  9

The given quadratic equation is:

y  =   (2x  +  3)²

A quadratic equation is of the form:

y  =  ax²  +  bx   +  c

Expand the equation y = (2x  +  3)²

y  =  (2x  +  3)(2x  +  3)

y   =  4x²  +  6x  +  6x   +  9

y  =  4x²  +  12x   +  9

Comparing y = 4x²  +  12x  +  9   with  y  =  ax²  +  bx  +  c

a   =  4

b  =  12

c  =  9

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Answer:

  f(x) = x^2

Step-by-step explanation:

The square root function is defined to have a non-negative range only. That corresponds to restricting the domain of f(x) = x^2 to positive values of x.

_____

The attached graph shows the domain-restricted f(x)=x² in solid red and the corresponding f⁻¹(x) = √x in solid blue. The other halves of those curves are shown as dotted lines (and are inverse functions of each other, too). The dashed orange line is the line of reflection between a function and its inverse.

Answer:

OH NANANA

Step-by-step explanation:

Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square.  

Step-by-step explanation:

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.

Step-by-step explanation:

Answer:

Cyclical unemployment.

Step-by-step explanation: It is not part of the natural unemployment rate.

It's caused by the contraction phase of the business cycle. That's when demand for goods and services generated by the company fall dramatically, forcing businesses to lay off large numbers of workers to cut or reduce costs.

Answer:

See below.

Step-by-step explanation:

Average rate of change =( R(1008) - R(1001) ) / (1008 - 1001)

=[ 12(1008) - 0.005(1008)^2 - (12(1001) - 0.005(1001)^2) ] / 7

Answer:

2

Step-by-step explanation:

Average rate of change is just the slope.

You want to find the slope of the line that goes through x=1001 and x=1008 while on R(x)=12x-0.005x^2.

So y=R(x)... R(x) will give your corresponding y values for the x's mentioned.

Just plug them in.

R(1001)=12(1001)-0.005(1001)^2=7001.995

R(1008)=12(1008)-0.005(1008)^2=7015.68

So now the question just becomes find the slope of the line that goes through

(1001,7001.995) and (1008,7015.68).

To find the slope of a line given two points: I just lined the points up and subtract vertically.  Afterwards I put the second number on top of the first number.

So let's do that!

(1008 ,  7015.68)

-(1001,    7001.995)

------------------------------

      7       13.685

So the slope also known as the average rate of change here is 13.685/7.

Putting 13.685 divided by 7 into my calculator returns the value 1.955.

This rounded to the nearest integer is 2.

Answer:

the probability that their minimum is larger than 5 is 0.2373

Step-by-step explanation:

For calculate the probability we need to make a división between the total ways to selected the 5 numbers and the ways to select the five numbers in which every number is larger than 5.

So the number of possibilities to select 5 numbers from 20 is:

20                 *      20         *          20     *        20         *       20

First number  2nd number   3rd number  4th number   5th number

Taking into account that a number can be chosen more than once, and the order in which you select the numbers matters, for every position we have 20 options so, there are  [tex]20^{5}[/tex] ways to select 5 numbers.

Then the number of possibilities in which their minimum number is larger than 5 is calculate as:

15                 *      15         *             15     *        15          *       15

First number  2nd number   3rd number  4th number   5th number

This time for every option we can choose number from 6 to 20, so we have 15 numbers for every option and the total ways that satisfy the condition are  [tex]15^{5}[/tex]

So the probability P can be calculate as:

[tex]P=\frac{15^{5} }{20^{5} } \\P=0.2373[/tex]

Then the probability that their minimum is larger than 5 is 0.2373

Answer:

  x = -0.5 or x = 2

Step-by-step explanation:

Finding solutions graphically is often easier if the equation can be put in the form f(x) = 0. Here, we can do that by subtracting the right-side expression to give ...

  (-2x^2 +2) -(-3x) = 0

This could be put in standard form, but there is no need. A graphing calculator can deal with this directly.

The solutions are x = -0.5 and x = 2.

Answer:

125 minutes of calling

It will cost $32.25 when the plans cost the same.

Step-by-step explanation:

The first plan's expression would be:

11+.17x       x being the number of minutes

The second plan's expression would be:

16+.13x

You must set the expressions equal to one another. So:

11+.17x=16+.13x

Then solve for x:

.17x=5+.13x

.04x=5

x=125

So the plans will cost the same after 125 minutes. To find the cost of the plans at that time, substitute 125 in for the x in one of the equations.

11+.17(125)=y        y being the overall cost of the plan

11+21.25=y

32.25=y

To check your answer, you can substitute again in the other equation:

16+.13(125)=y

16+16.25=7

32.25=7

Answer:

8

Step-by-step explanation:

167.39 is right but it can be simplified.

1.61 was replaced by (161/100).

3 more similar replacement(s)

  839          2      161

 (——— +  (0 -  —)) +

  100          1      100

639 + 161     8

—————————  

   100        1

Sorry if it looks confusing

Answer:

[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]

Step-by-step explanation:

Since each number is the sum of it's 2 preceding numbers thus mathematically it can be written as

[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]

Fibonacci Series can be written as

1,1,2,3,5,8,13...

Answer:

(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1 where a > b

- So lets collect x in a bracket and make it a completing square and

  also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x + 16y - 31 = 0

∴ (x² - 2x) + (-4y² + 16y) - 31 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y² - 4y) - 31 = 0

∴ (x² - 2x) - 4(y² - 4y) - 31 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵  (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

   the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1

- We will do the same withe bracket of y

- Lets make 4(y² - 4y) completing square

∵ √y² = y

∴ The 1st term in the bracket is x

∵ 4y ÷ 2 = 2y

∴ The product of the 1st term and the 2nd term is 2y

∵ The 1st term is y

∴ the second term = 2y ÷ y = 2

∴ The bracket is 4(y - 2)²

∵ 4(y - 2)² = 4(y² - 4y + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out

   the bracket to keep the equation as it

∴ 4[y² - 4y + 4) - 4]

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify

∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms

∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides

∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - (y - 2)²/4 = 1

∵ 16 = (4)² and 4 = (2)²

∴ The standard form of the equation of the hyperbola is

   (x - 1)²/4² - (y - 2)²/2² = 1

Answer:

Refer to attachment below.

Answer:

14

Step-by-step explanation:

An isosceles triangle has two sides that are the same.  If one side is 7 and another is 14, then the two possibilities are 7, 7, and 14, or 14, 14, and 7.

It can't be 7, 7, and 14, because the sum of the shortest sides of a triangle must be greater than the longest side.

Therefore, it must be 14, 14, and 7.  So the third leg is 14.

The length of third side of the isosceles triangle is 14.

An isosceles triangle is a triangle that has two sides of equal length. Also the property of isosceles triangle states that the base angle of the isosceles triangle subtends angle of equal measure.

It is given that the two sides of the triangle have lengths 7 and 14.

Thus for the triangle to be isosceles, the third side of the triangle will have the length as 7 or 14.

We know that the sum of any two sides of a triangle must be greater than the third side.

Thus if the third side is 7, then the sum of the sides will be (7 + 7) = 14 which is not greater than the other side. So, third side will not be of length 7 units.

The third side of the isosceles triangle is of 14 units .

Therefore, the length of third side of the isosceles triangle is 14.

To learn more about isosceles triangle, refer -

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Answer:

Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Let A be the event "sum of numbers is multiple of 3"

and B be the event "sum is an even number".

As our dice has six sides, so the sample space of two dices will be of 36 ordered pairs.

|sample space | = 36

Out of which 11 pairs have the sum multiple of 3 and 18 pairs having sum even.

So Pr(A)= [tex]\frac{11}{36}[/tex]

and Pr(B)= [tex]\frac{18}{36}[/tex]

and Pr(A∩B) = [tex]\frac{5}{36}[/tex], as 5 pairs are common between A and B.

So now Pr(A or B)= Pr(A∪B)

                            = Pr(A)+Pr(B) - Pr(A∩B)

                            = [tex]\frac{11}{36}[/tex] + [tex]\frac{18}{36}[/tex] - [tex]\frac{5}{36}[/tex]

                            = [tex]\frac{24}{36}[/tex]

                            = [tex]\frac{2}{3}[/tex]

Answer:

2/3 and NOT mutually exclusive

Step-by-step explanation:

plato

Answer:

cos(x) = square root 2 over 2; tan(x) = 1

Step-by-step explanation:

[tex]\frac{\sqrt{2} }{2}[/tex]

was, before it was rationalized,

[tex]\frac{1}{\sqrt{2} }[/tex]

Therefore,

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

The side opposite the reference angle measures 1, the hypotenuse measures square root 2.  That makes the reference angle a 45 degree angle.  From there we can determine that the side adjacent to the reference angle also has a measure of 1.  Therefore,

[tex]cos(x)=\frac{1}{\sqrt{2} }=\frac{\sqrt{2} }{2}[/tex] and

since tangent is side opposite (1) over side adjacent (1),

tan(x) = 1

Answer:

  Converges; 51 3/7

Step-by-step explanation:

The common ratio is -10/60 = (5/3)/-10 = (-5/18)/(5/3) = -1/6.

Then the sum of the sequence is given by ...

  S = a1/(1 -r) = 60/(1 -(-1/6))

  S = 60/(7/6) = 360/7

  S = 51 3/7

_____

If you erroneously evaluate the formula for the sum using +1/6 as the common ratio, then you will get S=60/(1-1/6) = 60·6/5 = 72.

Answer:

  a) r(x) = 28x

  b) p(x) = -x^2 +30x +9

  c) 15

Step-by-step explanation:

a) Let x represent the number of items sold. Each sale results in $28 of revenue, so the revenue function r(x) is ...

  r(x) = 28x

__

b) p(x) = r(x) - c(x) = 28x -(x^2 -2x -9)

  p(x) = -x^2 +30x +9

__

c) The axis of symmetry of ax^2 +bx +c is -b/(2a). Here, the axis of symmetry of the profit function is ...

  x = -30/(2(-1)) = 15

15 is the quantity of sales that maximizes profit.

Answer:

Step-by-step explanation:

yes 30

Answer:

Mr Johnson will receive 1024 mL IV in 8 hours.

Step-by-step explanation:

Mr Johnson has an IV that is infusing at 32 gtt per minute.

So in 1 hour patient will get the drug = 32×60 = 1920 gtt

Now in 8 hours drug received by the patient = 1920 × 8

= 15360 gtt

Since IV tube is calibrated for 15 gtt per mL which means in 1 mL amount of drug is 15gtt.

Therefore, total volume of infusion (in mL) will be

= [tex]\frac{\text{Total drug infused}}{\text{Total drug in 1 mL}}[/tex]

= [tex]\frac{15360}{15}[/tex]

= 1024 mL.

Therefore, 1024 mL IV will be infused in 8 hours.

Answer:

∠4

Step-by-step explanation:

The angle of elevation is the measure of the angle from the horizontal upwards.

The angle of elevation from C to B is ∠4

Angle of elevation from C to B will be ∠4. Option (1) will be the answer.

Angle of elevation of an object from a point on the ground is defined by,

   "Angle between the horizontal line and line of site (line joining the observer and the object above the horizontal line)"

Following the definition,

Angle of elevation of an object at B from C will be → ∠4

   Therefore, Option (1) will be the answer.

Learn more about angle of elevation here,

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Answer:

Step-by-step explanation:

very interesting question. The temptation is to say that n should be 11 and that likely is divisible by 11 but it may not be the smallest.

100 + 100^2 = 100 + 10000 = 10100

The pattern of the series goes 101010101 ... 00...

100 / 11 = The remainder is 1/11

10100 / 11 = the remainder is 2/11

1010100 /11 the remainder is 3/11

The pattern suggests that the remainder will be 0 then n = 11

There might be other ways of doing this, but I don't know them.

Answer:

B

Step-by-step explanation:

In step 1, we found ∠GAC ≅ ∠AFD.

In step 2, we found ∠GAC ≅ ∠AFE.

Therefore, by transitive property of equality, ∠AFD ≅ ∠AFE.