Please use the following image for the next 7 questions. Keep in mind
that because XY is tangent to circle M, XY and XM form a right angle. XY is tangent to circle M at point X.

XM = 12 and YM = 43.


Questions:

1. What is the area of circle M?

2. What is the circumference of circle M?

3. Find the length of XY.

4. Find the measure of angle M.

5. Find the area of triangle XYM.

6. Find the area of the minor sector that has been created as a part of triangle XYM.

7. Find the arc length of the minor arc from point C to the point where YM intersects with the circle.

9514 1404 393

Answer:

  19

Step-by-step explanation:

The evaluation is easier if we simplify the expression first.

  9(n +2) -5n = 9n +18 -5n = 4n +18

For n = 1/4, this is ...

  = 4(1/4) +18 = 1 +18

  = 19

The value of the expression for n = 1/4 is 19.

Answer:

[tex]Range = 85[/tex]

[tex]\sigma = 28.71[/tex]

[tex]Interval = [666.78, 781.62][/tex]

Step-by-step explanation:

Given

The data for 25 undergraduates

Solving (a): Range and Standard deviation

The range is:

[tex]Range = Highest - Least[/tex]

From the dataset:

[tex]Highest = 772[/tex]

[tex]Least = 687[/tex]

So:

[tex]Range = Highest - Least[/tex]

[tex]Range = 772-687[/tex]

[tex]Range = 85[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]

First, calculate the mean

[tex]\bar x = \frac{769 +691 +............+715}{25}[/tex]

[tex]\bar x = \frac{18105}{25}[/tex]

[tex]\bar x = 724.2[/tex]

So, the standard deviation is:

[tex]\sigma = \sqrt{\frac{(769-724.2)^2 +(691-724.2)^2 +(699-724.2)^2 +(730-724.2)^2 +............+(715-724.2)^2}{25}}[/tex]

[tex]\sigma = \sqrt{\frac{20604}{25}}[/tex]

[tex]\sigma = \sqrt{824.16}[/tex]

[tex]\sigma = 28.71[/tex]

Solving (b): The interval of the 95% of the observation.

Using the emperical rule, we have:

[tex]Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma][/tex]

[tex]Interval = [724.2 - 2*28.71, 724.2 + 2*28.71][/tex]

[tex]Interval = [666.78, 781.62][/tex]

Answer:

Yeah

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

9514 1404 393

Answer:

  y -4 = -2(x -3)

Step-by-step explanation:

The point-slope form of an equation for a line through point (h, k) with slope m is ...

  y -k = m(x -h)

You have (h, k) = (3, 4) and m = -2, so your equation is ...

  y -4 = -2(x -3)

Answer:

likely

Step-by-step explanation:

Answer:

102.37

Step-by-step explanation:

.29*353=102.37

Answer:

Total selling price= $663.82

Selling price per liter= $1.69

Step-by-step explanation:

Giving the following information:

Proportion of oil and gasoline:

Oil= 3/14= 0.21

Gasoline= 11/14= 0.79

The oil costs $0.75 per liter.

The gasoline costs $1.60 per liter.

First, we need to calculate the number of liters of oil and gasoline required:

Oil= 0.21*392= 82.32 liters

Gasoline= 0.79*392= 309.68

Now, the total cost to produce 392 liters:

Total cost= 82.32*0.75 + 309.68*1.6

Total cost= $577.23

Finally, the total and unitary selling price:

Total selling price= 577.23*1.15= $663.82

Selling price per liter= 663.82 / 392= $1.69

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Answer:

  (a) 10

Step-by-step explanation:

Attached is a graphical solution using "substitution." An expression was written for z using the first equation, and it was substituted into the remaining two equations. This gave two equations in x and y, easily solved graphically.

We found x = 10, y = 3, so ...

  z = 3(10) -4(3) -14 = 30 -12 -14 = 4

The whole solution is (x, y, z) = (10, 3, 4).

Answer:

[tex]x-2y=-12[/tex]

Step-by-step explanation:

Hi there!

1) Determine the equation of the line in slope-intercept form

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

Plug in the slope [tex]\frac{1}{2}[/tex]

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

Plug in the given point (6,9) and solve for b

[tex]9=\frac{1}{2}(6)+b\\9=3+b[/tex]

Subtract 3 from both sides

[tex]9-3=3+b-3\\6=b[/tex]

Plug 6 back into [tex]y=\frac{1}{2}x+b[/tex]

[tex]y=\frac{1}{2}x+6[/tex]

2) Rearrange the equation into standard form

Standard form: [tex]Ax+By=C[/tex] where A, B and C are integers and A is typically positive

[tex]y=\frac{1}{2}x+6[/tex]

Multiply both sides by 2 to remove the fraction

[tex]2y=1x+12\\2y=x+12[/tex]

Subtract x from both sides to isolate 12 as C

[tex]2y-x=x+12-x\\2y-x=12\\-x+2y=12[/tex]

Multiply both sides by -1 to make A positive

[tex]x-2y=-12[/tex]

I hope this helps!

9514 1404 393

Answer:

  c  1, 2, 4, 8

Step-by-step explanation:

It can work well to look at the first differences.

  a: 4 -2 = 2; 6 -4 = 2 ⇒ differences are 2, 2, 2

  b: differences are 0, 1, 1

  c: differences are 1, 2, 4

  d: differences are 2, 2, 2

__

Sequences 'a' and 'd' have common differences that are constant. These are arithmetic sequences. Sequence 'b' is of no named type.

Sequence 'c' has first differences that have a common ratio, the same as the sequence itself. This is an indication the sequence is geometric. The ratios of values are 2/1 = 2; 4/2 = 2; 8/4 = 2, so the terms have a common ratio.

Sequence c is a geometric progression.

Answer:

z = 3a + 4

Step-by-step explanation:

Add 4 to both sides

Answer:

One equation can be y = 3/4X +2

Step-by-step explanation:

Any equation that has a slope of 3/4 will be parallel to the line 4Y = 3X + 5 because the slope is the same. This can also be shown visually using any graphing calculator.

Answer:

Step-by-step explanation:

floor = 12*10 = 120 sq ft

rug = π[tex]r^{2}[/tex] = 9π

120-9π = 91.74 sq ft

The amount of floor left uncovered by the circular area rug in a rectangular living room is 91.74 ft²

Area is the space occupied by a 2 dimensional figure.

The room is rectangular and its 12 ft by 10 ft. Therefore,

area of the room = lw

where

l = length

w = width

area of the room = 12 × 10 = 120 ft²

The rug is circular and its use to cover the room. Therefore,

area of rug = πr²

where

r = 3 ft

Therefore,

area of rug = 3.14 × 3² = 28.26 ft²

The amount of floor left uncovered by the circular area rug in a rectangular living room can be calculated as follows:

learn more on area here; https://brainly.com/question/1389611

Answer:

Z = 51º

Step-by-step explanation:

sinZ/12.5 = sin76/15.5

multiply both sides by 12.5

sinZ = sin76/15.5 * 12.5

Use calculator

sinZ = 0.782496553448384

Z = arcsin 0.782496553448384

Use calculator again

Z = 51.48972926377471º

Rounded

Z = 51º

Answer:

20º

Step-by-step explanation:

Total parts

2  + 7 + 9 = 18

Value of each part given 180º in a triangle

180 / 18 = 10º

Smallest angle

2 * 10 = 20º

Answer:

20

Step-by-step explanation:

Multiply each angle by x

2x: 7x: 9x

The sum of the angles in a triangle is 180

2x+7x+9x = 180

Combine like terms

18x = 180

Divide by 18

18x/18 = 180/18

x =10

The smallest angle is 2x

2x = 2(10) =20

Answer:

[tex]-48x^5 y^{10} z^3[/tex] should be the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

1- digit numbers:

2- digit numbers:

3- digit numbers:

This is more than we have, but we know the number of pages is 3-digit.

Let it be x, then we have:

Answer:

wat

Step-by-step explanation:

Answer:

60m^2 is the answer im pretty sure

Step-by-step explanation:

yeah man thats it

9514 1404 393

Answer:

  180 in³

Step-by-step explanation:

  V = Bh

  V = (6 in × 3 in)(10 in) = 180 in³

The volume is the product of the cross section area (6 in × 3 in) = 18 in² and the height perpendicular to that cross section, 10 in.

Answer:

The total pay would be $50, But there would also be tax to consider in this situation.

Answer:

625

Step-by-step explanation:

First, you have to convert 0.2 grams to mg.  To do this, multiply 0.2 by 1000.  This yield 200.  Now 200 is what percent of 32.  

200 * 100 / 32

= 625

Answer:

f(x) = 2x - 6

Step-by-step explanation:

positive slope = 2

y- intercept = -6

Answer:A

Step-by-step explanation:

I tried every combination. there seems to be something wrong with the informations you gave.

the second equation contains errors, and none of these 4 points can be solutions to the first equation alone

Answer:

14,000 feet.

Step-by-step explanation:

A parallelogram has 4 total sides and the opposite sides are characterized as having the same length. Therefore, If we are provided the lengths of two adjacent sides we can easily calculate the perimeter by multiplying these provided lengths by 2 and then adding them together. Since we are asked to round each number to the nearest hundred, it would be the following...

(5,500 * 2) + (1,500 * 2) = x

11,000 + 3000 = x

14,000 = x

Finally, we can estimate that the perimeter of the parallelogram is 14,000 feet.

Answer:

[tex] - \frac{4}{5}[/tex]

Step-by-step explanation:

Line is passing through the points (-3, 1) & (2, - 3)

Therefore,

Slope of line

[tex] = \frac{ - 3 - 1}{2 - ( - 3)} \\ \\ = \frac{ - 4}{2 + 3} \\ \\ = - \frac{4}{5} [/tex]