Pi/6 is the reference angle for:
A 13pi/6
B 5pi/6
C 3pi/6
D 8pi/6
Check all that apply

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8 - (-4)]^2 + [7 - (-3)]^2}\implies d=\sqrt{(-8+4)^2 + (7+3)^2} \\\\\\ d=\sqrt{(-4)^2 + 10^2}\implies d=\sqrt{116}\implies d\approx 10.77[/tex]

Answer:

The mean absolute deviation of this sample is 13.

Step-by-step explanation:

Mean absolute deviation is the sum of the absolute value of the differences between data values and the mean, divided by the sample size.

Answer:

2, 3, 6

Step-by-step explanation:

Simply try each value using long division.

2:

Since 5,238 ends in an even number, that automatically means it is divisible by 2.

5238/2=2619

Now for 3:

5238/3=1746 no remainder or decimal, so 3 also works

4:

You can either do long division again with 4, or you can see if 5238 divided by 2 (5238/2) is also divisible by 2. Since 2619 doesn't end in an even number, 4 is a no go.

Long division 5238/4=1309.5 decimal here, so 4 isn't an answer

5:

This is also very easy, simply check if the number ends in 0 or 5. Since 5,238 does not, 5 doesn't work either.

6:

You can do the same thing as with 4, except this time trying to find if 5238 divided by 3 (5238/3) is divisible by 2. Since 1746 ends in an even number, 6 also works.

Long division: 5238/6=873

9:

You can do the same thing as with 6, except this time trying to find if 5238 divided by 3 (5238/3) is divisible by 3.

1746/3=548 with a remainder of 2, which means 9 doesn't work

Long division: 5238/9=548.66 repeating

10:

Finally, 10 is another easy one. Simply check if the number ends in 0. 5,238 does not, so 10 doesn't work.

The value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length which is 8 units.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

Here the diagram and some data are missing.

But using Pythagoras or trigonometric ratio we can find the length.

We have:

17sinA-15-0

sinA = 15/17

Using Pythagoras theorem:

Base length = √(17² - 15²) = 8 units

= tanA = 15/8

= 1 - cosA = 1 - 8/17 = 9/17

We can find the rest of the trigonometric ratio.

Thus, the value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length, which is 8 units.

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The possible values of x in the diagram are x = 25 and x = -1

The given parameters are:

Both angles are congruent and adjacent angles.

So, we have:

∠DAB = ∠DAC

Substitute known values

x² - 24x = 25

Subtract 25 from both sides

x² - 24x - 25 = 0

Expand

x² + x - 25x - 25 = 0

Factorize

x(x + 1) - 25(x + 1) = 0

Factor out x + 1

(x - 25)(x + 1) = 0

Expand

x - 25 = 0 or x + 1 = 0

Solve for x

x = 25 or x = -1

Hence, the possible values of x are x = 25 and x = -1

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All circles are similar because radius is constant throughout the circle.

Every point on a circle's perimeter is equidistant from its center. We utilize the radii to get the scale factor since the size of each circle is specified by its radius.

A quality of at least two forms in relation to each other is similarity. When two forms are similar, their qualities in relation to one another remain the same.

A circle is characterized by two properties: its center and radius.Because similarity is unaffected by location  the similarity of circles is solely determined by their radii.

Hence,all circles are similar because radius is constant throughout the circle.

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The volume of the solid objects are 612π in³ and 1566πcm³

The given objects are composite figures consisting of two shapes.

The volume of the blue figure is expressed as;

Volume = Volume of cylinder + volume of hemisphere

Volume = πr²h + 2/3πr³

Volume =  πr²(h + 2/3r)

Volume =  π(6)²(13+2/3(6))

Volume = 36π(13 + 4)

Volume = 612π in³

For the other object

Volume = Volume of cylinder + volume of cone

Volume = πr²h + 1/3πr²h

Volume =  π(9)²(15) + 1/3π(9)²(13)

Volume=  81π (15+13/3)
Volume= 1566πcm³

Hence the volume of the solid objects are 612π in³ and 1566πcm³

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The number of night of work each performers will have equal amount is 1 night

The buskers gets permit which cost $30. They can make an average of $45 per night (n),

Therefore,

y = 45n - 30

Without a permit they may only make an average of $15 per night.

Therefore,

y = 15n

The number of night the money made are both equal.

45n - 30 = 15n

45n - 15n  = 30

30n = 30

n = 30 / 30

n = 1

Therefore, the number of night of work each performers will have equal amount is 1 night

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Answer:

C

Step-by-step explanation:

[tex]\textsf {Given :}[/tex]

[tex]\mathsf {x - 5 \leq -13}[/tex]

[tex]\textsf {Add 5 to each side of the inequality : }[/tex]

[tex]\mathsf {x - 5 + 5 \leq -13 + 5}[/tex]

[tex]\mathsf {x \leq -8}[/tex]

Step-by-step explanation:

So here...two triangle is measured in 78° and 30° ..here to find the value of third angle...

we need to subtract 180° from the sum of 78° and 30° ...cause the sum of all angle of triangle is 180° ..

x + 78° + 30° = 180°

x + 108° = 180°

x = 180° - 108°

x = 72°

hence the value of third angle is 72°....

The volume of the pyramid would be 2406.16 cubic cm.

Supposing that:

The length of the sides of the square base of the pyramid has = b units

The height of the considered square-based pyramid = h units,

The pyramid below has a square base.

h = 24.4 cm

b = 17.2 cm

Then, its volume is given by:

[tex]V = \dfrac{1}{3} \times b^2 \times h \: \rm unit^3[/tex]

[tex]V = \dfrac{1}{3} \times 17.2^2 \times 24.4 \: \rm unit^3\\\\V = 2406.16[/tex]

Therefore, the volume of the pyramid would be 2406.16 cubic cm.

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The length of the bike path, to the nearest meter, is effectively illuminated by the light is 138 m

The missing diagram is attached with the answer.

The angle formed between the horizontal line and line of sight is called Angle of Elevation.

It can be seen in the diagram that

It is a right angled triangle if extended and

cos 23 degree = (length of the bike path)/Hypotenuse

Hypotenuse here is the point on a bike path is 150 m from the light

Therefore

cos 23 ° = x / 150

x = 0.92 * 150

x = 138 m

Therefore The length of the bike path, to the nearest meter, is effectively illuminated by the light is 138 m.

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The original height  of the water in a pool is 5 ft , Option B is the correct answer.

An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.

It is given in the question that

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.

the height of the water is 4.75 feet.

The equation

4.75 = x + (negative 0.25)

can be used to find x, the original height of the water in a pool.

4.75 = x - 0.25

x = 5

Therefore the original height  of the water in a pool is 5 ft , Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

Answer:

5-y/5y

Sorry Im not to sure but maybe this will help?

Step-by-step explanation:

Answer:

100.05

Step-by-step explanation:

9.5 and multiple it by 5

The algebraic expression of the situation above is 4x - 100 = 400

Let

the amount of ice cream they serve in July = x + 100

the amount of ice cream they serve in June = x

They served twice as many customers in august as they did in June.

Therefore,

the amount of ice cream they serve in August = 2(x)

the amount of ice cream they serve in August = 2x

Therefore,

2x + x  + x + 100 = 400

4x - 100 = 400

4x = 500

x = 500 / 4  

x = 125  

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We can see that g(x) is a translation of 4 units to the left of f(x), then:

g(x) = log₃(x + 4).

Here we can see that g(x) is a shift of f(x). Is clear that the asymptote of g(x) is 4 units to the left of the asymptote of f(x), so we can say that g(x) is a shift of 4 units to the left of f(x).

Remember that for a given function f(x), an horizontal shift of N units is given by:

g(x) = f(x + N).

Then a shift of 4 units to the left is written as:

g(x) = log₃(x + 4).

Then the correct option is the last one.

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Answer:

x-4*2

Step-by-step explanation:

Since we dont know the number, we can make it a variable. So, x is the unknown number.

4 less will mean subtraction. So. x-4.

Next we have to multiply with 2.

So, the expression is x-4*2.

Answer:

5.3 is 5.259 rounded into the tenths place.

Answer:

$1,144.57

Step-by-step explanation:

1,451.54 + 393.03 = 1844.57

1,844.57 - 700 = 1,144

Answer:

7 years

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

You can not know the original price unless you know the taxes percentage.

Answer:

$12

Step-by-step explanation:

x+2y=82........(1)

3x+y=96.........(2)

y=96-3x...........(3)

x+2y=82

x+2(96-3x)=82

x+192-6x=82

-5x=82-192

-5x=-110

x=-110÷-5

x=22

y=96-3x

y=96-3(22)

y=96-66

y=30

Therefore,x=22 and Y=30

so silver= x =22

gold= y = 30

y=30;x=22

=30-22

-12

Therefore $12

Answer:

it's 15

Step-by-step explanation:

just do ( 5× 2) = (10+5)=15

Answer:

B. y=-0.5x + 1

Step-by-step explanation:

first look at the slope: slop = rise over run. for every 2 units right, the point goes 1 unit down. so the slope if -1/2 or -0.5

next look at the y-intercept. the y-intercept of this graph is 1

plug these into the equation y= mx + b to get y = -0.5x + 1

Answer:

A. y = -0.5x + 1

Step-by-step explanation:

Hello!

An equation of a line is written in slope-intercept form: [tex]y = mx + b[/tex]

The y-intercept is found when x=0, or then the line crosses the y-axis.

Over here, we can see that the line crosses the y-axis at point (0,1), so the y-intercept is positive 1.

Slope is calculated by rise over run, or the ratio of how much the graph rises over how much the graph runs. Use points to determine how the graph changes. (For simple calculations, use integer points, such as (0,1) and (0,2)

Now that we have the slope and the y-intercept, we can plug those values to make our equation.

The correct answer is Option A. y = -0.5x + 1