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a bag contains 8 blue chips, 7green chips and 2 white chips. if two chips are drawn without replacement, what is the probability

defon

b=8, g=7, w=2, total=17

(8/17)(7/16)=56/272=7/34

3 0

3 years ago

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Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set o

Korolek [52]

Answer:

B

Step-by-step explanation:

10(10m+6)<=12

100m+60<=12 Distributive Property

100m <=12-60

100m <=-48

m <=-48/100

m <=-.48

This says values for m that are less than or equal to -.48

-.48 is between -1 and 0 so the answer is B

6 0

4 years ago

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Solve the differential equation <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6x%7D%20%2A%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%2

ExtremeBDS [4]

This ODE is separable as

1/(6x) dy/dx = y √(3x ² - 1)

→ dy / y = 6x √(3x ² - 1) dx

Integrate both sides:

∫ dy / y = ∫ 6x √(3x ² - 1) dx

The left side is trivial. For the right side, substitute u = 3x ² - 1 and du = 6x dx :

∫ dy / y = ∫ √u du

ln|y | = u ³′² + C

(that is, u is raised to the 3/2 power)

ln|y | = (3x ² - 1)³′² + C

Solve for y by taking the exponential of both sides:

exp(ln|y |) = exp((3x ² - 1)³′² + C )

y = exp((3x ² - 1)³′²) × exp(C )

y = C exp((3x ² - 1)³′²)

which can be written as

y = C exp(√((3x ² - 1)³))

which makes the answer none of these; this solution can't be expressed as either option given in A or B.

6 0

3 years ago

A new library, L, is to be built at some point along a straight road, R, such that its distance from train station, T, is the sh

andreyandreev [35.5K]

Answer:

Coordinates of the new library is (150, 70)

Step-by-step explanation:

To get the shortest possible distance means that line from point T to point R has to be perpendicular.

Now, the equation of R is given as;

y = x - 80 - - - (1)

For T to be perpendicular, it means it will have a slope equal to the negative reciprocal of line R.

Thus, slope of T is -1/1 = - 1

Thus, using line - slope intercept of y = mx + c, we can find equation of T as;

140 = -1(80) + c

140 = -80 + c

c = 140 + 80

c = 220

Thus, equation is;

y = -x + 220 - - - (eq 2)

Adding equation 1 to equation 2,we have;

y + y = 220 - 80

2y = 140

y = 140/2

y = 70

Putting 70 for y in eq 1 gives;

70 = x - 80

x = 70 + 80

x = 150

Thus;

Coordinate of the new library is (150, 70)

8 0

3 years ago

Which of the following expressions are equivalent to (6.2+6.2)+9.4(6.2+6.2)+9.4left parenthesis, 6, point, 2, plus, 6, point, 2,

ELEN [110]

Answer:

6.2 + (6.2 + 9.4) ⇒ A

6.2 - (-6.2 - 9.4) ⇒ E

Step-by-step explanation:

* Lets revise some definitions to solve the problem

- Associative property states that you can re-group numbers and you

will get the same answer [(a + b) + c = a + (b + c)]

- Additive inverse of a number means reverse the sign of the number

the additive inverse of x is -x

- The expression is (6.2 + 6.2) + 9.4

- We want to find which of the following expressions are equivalent

to this expression

- By using associative property we can write the expression as

6.2 + (6.2 + 9.4)

∴ (6.2 + 6.2) + 9.4 = 6.2 + (6.2 + 9.4)

- Multiply (-) by the additive inverse of number is the number itself

If a number is x and its additive inverse is -x, then (-) × (-x) = x

∵ -6.2 is additive inverse of 6.2

∵ (-)(-6.2) = 6.2

∵ -9.4 is additive inverse of 9.4

∵ (-)(-9.4) = 9.4

∴ 6.2 - (-6.2 - 9.4) = 6.2 + 6.2 + 9.4

∴ (6.2 + 6.2) + 9.4 = 6.2 - (-6.2 - 9.4)

* The answers are A and E

8 0

4 years ago