How many unique ways are there to arrange the letters in a word OPAL.

Answer:

[tex] \cos \bigg( \frac{7\pi}{12} \bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } [/tex]

Step-by-step explanation:

[tex] \cos \bigg( \frac{7\pi}{12} \bigg) \\ \\ = \cos \bigg( \frac{7 \times 180 \degree}{12} \bigg)\\ \\ = \cos \bigg( {7 \times 15 \degree} \bigg)\\ \\ = \cos \bigg( {105 \degree} \bigg)\\ \\ = \cos \bigg( {60\degree + 45 \degree} \bigg) \\ \\ = \cos {60\degree .\cos 45 \degree} - \sin {60\degree .\sin 45 \degree} \\ \\ = \frac{1}{2} . \frac{1}{ \sqrt{2} } - \frac{ \sqrt{3} }{2} .\frac{1}{ \sqrt{2} } \\ \\ = \frac{1}{2 \sqrt{2} } - \frac{ \sqrt{3} }{2 \sqrt{2} } \\ \\ \huge \purple{ \boxed{ \cos \Bigg( \frac{7\pi}{12} \Bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } }}[/tex]

The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

We have to given that,

An equation is,

⇒ cos (7 pi/12)

Now, WE can change it into degree as,

⇒ cos (7 pi/12)

⇒ cos (7 × 180 / 12)

⇒ cos (7 × 15)

⇒ cos 105°

⇒ cos (90 + 15)°

⇒ - sin 15°

⇒ - (√3 - 1) / 2√2

⇒ - 0.2588

Thus, The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

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Answer:

Step-by-step explanation:

it is a downward parabola cutting x-axis at (-3,0),(1,0)

f(x)=-(x+3)(x-1)

=-(x²+2x-3)

=-(x²+2x+1-1-3)

=-(x+1)²+4

vertex is (-1,4)

Answer:

A: -11

B: Two complex solutions

Step-by-step explanation:

The discriminant of this equation is 3^2-20=9-20=-11. Since the discriminant is negative, its square root will be an imaginary number, and there will be two complex solutions. Hope this helps!

Answer:

A:-11

B: has no real solutions

Step-by-step explanation:

For this equation: a=1, b=3, c=5

1x2+3x+5=0

Step 1: Use quadratic formula with a=1, b=3, c=5.

x=

−b±√b2−4ac

2a

x=

−(3)±√(3)2−4(1)(5)

2(1)

x=

−3±√−11

2

Answer:

No real solutions.

Answer:

Volume of cone = 314 in³

Step-by-step explanation:

Radius of the cone (r) = 5 in

Height of the cone (h) = 12 in

[tex]Voume \: of \: the \: cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times {(5)}^{2} \times 12\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times 25 \times 12\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times 300 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times 100\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 314 \: {in}^{3} [/tex]

Answer:

Step-by-step explanation:

[tex]V=whl=3*4*2=24units^3[/tex](grey)

[tex]V=whl=6*8*4=192units^3[/tex](green)

They are similar, the green is just double in size so a ratio of 1:2

Answer:

.4 yards of fabric were used for each pillow.

Steps:

2/5=0.4 (or [tex]\frac{2}{5}[/tex])

[tex]\left \{ {{y=2} \atop {x=2}} \right. x^{2} x^{2} x^{2} x^{2} x^{2} x^{2}[/tex]Answer:

A

Step-by-step explanation:

question: when do you take the SAT test

Answer:

70 degrees

Step-by-step explanation:

total angle in a triangle is 180 degrees

180-40= 140

Angle b and c is total of 140 degrees

they are isosceles so their measurements would be same.

angle b and c is 140÷ 2 = 70

so angle b is 70 degrees

Answer:

P=462+66-9

=528-9

=519

Q=762-26-5

=762-31

: =731

Answer:

12.68

Step-by-step explanation:

76 degrees /2 = 38

Half the width of 15m forms the lower side of the triangle: 7.5 m

sin(38) = 7.5/h

=12.1820

12.18+.5

12.68

Answer:

0.25

Step-by-step explanation:

Probability is the chance you get a certain thing when you pick randomly. In this case, it's asking the probablility of picking someone from a whole student survey that does music or drama.

Looking at the two way table is easy! Out of all grades, 65 are in sports, 25 have music or drama, and 10 has work. Add them all up and get 100.

However, we only found the people in the survey. We need to find the probability of someone in music and drama. So we divide the number of people in all grades who take that class and divide it by the total amount- 25/100, this turns out for the probability to be 0.25.

Answer:

Natalie arrived at 3:55 pm or 15:25

Step-by-step explanation:

Start time is 3:00

The first two friends arrived at 10 minutes after 3. Arrival time = 3:10

Natalie arrived 45 minutes later. Arrival time is 3:10 + 45 = 3:55

Natalie arrived at 3:55, using 24-hour formats, the arrival time is 15:55

Answer:

C.I = 0.108 ± 0.022

Step-by-step explanation:

In this case, we are given a symmetric confidence interval, and the sample proportion p', is derived by finding the average of the two values.

Therefore, the sample proportion will be:

[tex] p' = \frac{0.086 + 0.130}{2} [/tex]

[tex] = \frac{0.216}{2} [/tex]

= 0.108

p' = 0.108

To find the margin of error, we have:

M.E = ½ * length of confidence interval

Where length of confidence interval = 0.130 - 0.086

= 0.044

Therefore,

[tex] M.E = \frac{1}{2} * 0.044 = 0.022 [/tex]

Margin of error = 0.022

The confidence interval is expressed as:

p' ± M.E

= 0.108 ± 0.022

Answer:

a postulate

Step-by-step explanation:

a postulate which states that through any two points, there is exactly one line

Yes indeed. That is so. Your statement is a fact. It virtually pulsates with  veracity and truthiness. You can take it to the bank and hang your hat on it. Truer words are seldom written or spoken.

Do you have a question to ask ?

Answer:

1 pizza is 18 dollars

Step-by-step explanation:

The cost of a pizza will be;

⇒ $18

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The Kennedy Middle School cafeteria charges students $3 for 1/6 of a pizza.

Now,

Since, The Kennedy Middle School cafeteria charges students $3 for 1/6 of a pizza.

Hence, The cost of a pizza = $3 × 6

                                         = $18

Thus, The cost of a pizza will be;

⇒ $18

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Answer:

8.9%

Step-by-step explanation:

Probability of picking a red marble first: [tex]\frac{2}{10}=\frac{1}{5}[/tex]

Probability of picking a blue marble (no replacement): [tex]\frac{4}{9}[/tex]

[tex]\frac{4}{9} *\frac{1}{5} =\frac{4}{45} = 8.8888888888...%[/tex] % ≈ 8.9%

Answer:

[tex]\frac{8 cupcakes}{1 box}[/tex]

Step-by-step explanation:

All we have to do for this problem is divide.

48 / 6 = 8

There are 8 cupcakes per box.

Answer: 8 cupcakes per box

Step-by-step explanation: "Per box" means in 1 box, so we can rewrite the given statement using fractions as

48 cupcakes/6 boxes = __ cupcakes/1 box.

To find out what goes in the blank, notice that we

have a 1 in the denominator of our second fraction.

So we want to find a fraction that is equivalent

to 48/6 that has a 1 in the denominator.

If we divide the numerator and denominator of 48/6 by 6,

we get the equivalent fraction 8/1 or 8 cupcakes/1 box.

So now we have 8 cupcakes/1 box = __cupcakes/1 box.

So an 8 must go in the blank which means that the unit rate

for 48 cupcakes in 6 boxes is 8 cupcakes per box.

Step-by-step explanation:

4x - 3 = 4x + 5

4x - 4x = 5 + 3

0 = 8

x is disappear and 2 both sides are not equal

Answer:

If you subtract 4x from both sides there are different numbers so the equation isn't equal so the equation is impossible

4x-4x=3

4x-4x=5

3≠5

Hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

These are independent events, so we will just multiply the two probabilities together.

1/6 x 1/6 = 1/36

I'm always happy to help :)

The probability should be [tex]1\div 36[/tex].

Since You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a six.

So here the probability should be

[tex]= 1\div 6 \times 1\div 6 = 1\div 36[/tex]

Hence, we can conclude that The probability should be [tex]1\div 36[/tex].

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Answer:

Circle Equation: ( x - 3.8 )^2 + ( y - 7.8 )^2 = 25/36

Step-by-step explanation:

* Knowing a circle equation is in the format (x – h)^2 + (y – k)^2 = r^2, with the center being at the point (h, k) and the radius being "r" *

Let us substitute values into this equation; provided ( 3.8, 7.8 ) is the center:

( x - 3.8 )^2 + ( y - 7.8 )^2 = r^2,

Now substitute value of r, or rather the radius 5/6:

( x - 3.8 )^2 + ( y - 7.8 )^2 = ( 5/6 )^2 ⇒

Circle Equation: ( x - 3.8 )^2 + ( y - 7.8 )^2 = 25/36

* Sorry this wasn't answered earlier *

Answer:

The answer is -3.1, or 3 1/10.Since diving a negative and a positive equals a negative, your quotient will be negative. You can start by removing the 0.5, and divide 15 by 5 which is 3. Then with the 0.5 from -15.5, divide it by 5 and you get 0.1. 3 plus 0.1 is 3.1, and since it has to be negative, it's -3.1.

Step-by-step explanation:

i tried, have a nice day (:

Answer:

[tex]\large \boxed{(-1,-6),(-1,10)}[/tex]

Step-by-step explanation:

Point A must be on a circle with centre at (5,2) and radius 10.

The centre-radius form for the  equation of a circle is  

(x – h)² + (y – k)² = r², where

(h,k) = the coordinates of the centre and

     r = the radius

Thus, the equation for this circle is

(x - 5)² + ( y - 2)² = 10²

Substitute the value for x and solve for  y:

[tex]\begin{array}{rcl}\\(x - 5)^{2} +( y - 2)^{2} &=& 10^{2}\\(-1 - 5)^{2} +( y - 2)^{2} &=& 100\\(-6)^{2} +( y - 2)^{2} &=& 100\\36 +( y - 2)^{2} &=& 100\\( y - 2)^{2} &=& 64\\y - 2 = -8 & \qquad & y - 2 = 8\\y = \mathbf{-6} & \qquad & y = \mathbf{10}\\\end{array}\\\text{The possible coordinates of A are $\large \boxed{\mathbf{(-1,-6),(-1,10)}}$}[/tex]

The figure below shows the circle intersecting the line x = -1 at (-1,-6) and (-1,10).

Answer:

Lower Quartile: 23

Median: 30

Upper Quartile: 43

Interquartile range: 20

Answer:

3/2 Per wall

Step-by-step explanation:

There are four walls in a room.

6/4 = 3/2

To check your work, you can do 3/2 *4

3/2*4 = 6

Hope this helps!! :)

The number of rolls that each wall requires is 1.5.

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

There are four walls in a room.

He is able to cover of the walls in the room using 6 rolls of wallpaper.

let x as the number of rolls that each wall requires.

So, 4x =6 rolls

x=6/4

x= 1.5 rolls

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4 - x < 9

Subtract 4 from both sides

4 - x - 4 < 9 - 4

Now we have:

- x < 5

Divide both sides by -1

x < -5

When you divide an inequality by -1, the sign flips

Thus, your answer would be:

x > -5

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Answer:

x=0.885622

Step-by-step explanation:

Dont forget to round

Answer:

0.77

Step-by-step explanation:

7=9x

9x/9

7=x

7/9=0.77777777777

Answer: 1/125,000

Step-by-step explanation:

If the lenght of the building is L, the height is H, and the width is W, the volume of the building is V = L*H*W

Then for the model we will have that each measure is 1/50 times the original, this is:

lenght = L/50

height = H/50

widht= W/50

The volume of the scale model is:

V' = (L/50)*(H/50)*(W/50) = L*H*W/50^3

So we have the volume of the actual building divided 50^3

This means that the volume of the scale is 1/50^3 = 1/125,000 times the volume of the actual building.

Answer:

y=8

n=1.5

Step-by-step explanation: