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3 years ago

Find the common difference in the arithmetic sequence where p35 =-9p + 4 and p28 = 5p - 17?

1 answer:

6 0

P(35) = -9p + 4 = -9(35) + 4 = -315 + 4 = -311
p(28) = 5p - 17 = 5(28) - 17 = 140 - 17 = 123

a + 34d = -311
a + 27d = 123

7d = -434
d = -62

Therefore, the commpm difference is -62.

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A. One player places 1 red, 5 green and 3 blue tiles in Bag A, and 6 red, 4 green, and 2 blue in Bag B. What is the probability

cupoosta [38]

Answer:

$\frac{8}{27}$ is the probability that a player draws out two tiles of the same color assuming they are drawing one tile from each bag.

Step-by-step explanation:

In each bag there are red, green, and blue tiles, meaning that no matter which color is pulled out first there is always some probability that the second tile will be the same color. So, we can set up three possible outcomes:

Red: The player pulls out a red tile first. This has a $\frac{1}{9}$ probability of happening. Then in order to succeed for the problem, the next tile also needs to be red which has a $\frac{6}{12}$ probability attached to it. $\frac{1}{9}$ × $\frac{6}{12}$ = $\frac{1}{18}$ probability of happening.

Green: There is a $\frac{5}{9}$ probability of the player pulling out a green tile first. In this case we want to calculate the probability of the second tile being green, which would be $\frac{4}{12}$ . $\frac{5}{9}$ × $\frac{4}{12}$ = $\frac{5}{27}$ .

Blue: There is a $\frac{3}{9}$ probability of the first tile being blue in which case we are hoping for the second tile to be blue as well. The probability of the second tile being blue is $\frac{2}{12}$ on its own, and them both being blue is $\frac{3}{9}$ × $\frac{2}{12}$ = $\frac{1}{18}$

Adding $\frac{1}{18}$ + $\frac{1}{18}$ + $\frac{5}{27}$ we get the answer $\frac{8}{27}$ .

4 0

3 years ago

Please help! i dont understand

kvv77 [185]

QUESTION 1

The given inequality is

$y\leq x-3$ and $y\geq -x-2$ .

If (3,-2) is a solution; then it must satisfy both inequalities.

We put x=3 and y=-2 in to both inequalities.

$-2\leq 3-3$ and $-2\geq -3-2$ .

$-2\leq 0$ :True and $-2\geq -5$ :True

Both inequalities are satisfied, hence (3,-2) is a solution to the given system of inequality.

QUESTION 2

The given inequality is

$y\:>\:-3x+3$ and $y\:>\: x+2$ .

If (1,4) is a solution; then it must satisfy both inequalities.

We put x=1 and y=4 in to both inequalities.

$4\:>\:-3(1)+3$ and $4\:>\: 1+2$ .

$4\:>\:0$ :True and $4\:>\: 3$ :True

Both inequalities are satisfied, hence (1,4) is a solution to the given system of inequality.

Ans: True

QUESTION 3

The given inequality is

$y\leq 3x-6$ and $y\:>\: -4x+2$ .

If (0,-2) is a solution; then it must satisfy both inequalities.

We put x=0 and y=-2 in to both inequalities.

$-2\leq 3(0)-6$ and $-2\:>\: -4(0)+2$ .

$-2\leq -6$ :False and $-2\:>\:2$ :False

Both inequalities are not satisfied, hence (0,-2) is a solution to the given system of inequality.

Ans:False

QUESTION 4

The given inequality is

$2x-y\:$ and $x+y\:>\:-1$ .

If (0,3) is a solution; then it must satisfy both inequalities.

We put x=0 and y=3 in to both inequalities.

$2(0)-3\:$ and $0+3\:>\:-1$ .

$-3\:$ :True and $3\:>\:-1$ : True

Both inequalities are satisfied, hence (0,3) is a solution to the given system of inequality.

Ans:True

QUESTION 5

The given system of inequality is

$y\:>\:2x-3$ and $y\:$ .

If (-3,0) is a solution; then it must satisfy both inequalities.

We put x=-3 and y=0 in to both inequalities.

$0\:>\:2(-3)-3$ and $0\:$ .

$0\:>\:-9$ ;True and $0\:$ :True

Both inequalities are satisfied, hence (-3,0) is a solution to the given system of inequality.

Ans:True

3 0

3 years ago

Describe the graph that would be used to solve the equation-x^2 + 4 = x+2

Rzqust [24]

Answer:

The values of x are x = -2 and x= 1.

Step-by-step explanation:

The given equation -x²+4 = x+2 can be written in the form of two functions as

y = -x²+4 which is a function representing parabola and

y = x+2 which is a straight line.

Now we will solve the given equation to find their points of intersection on graph. Their points of intersections will be the answer.

-x²+4 = x+2

-x²+4-x = x+2-x

-x²-x+4 = 2

-x²-x+4-2 = 2-2

-x²-x+2 = 0

Or x²+x-2=0

Now we will factorize the equation.

x²+2x-x-2=0

x(x+2)-1(x+2) = 0

(x+2)(x-1) = 0

x+2 = 0 ⇒x = -2

x-1 = 0 ⇒x = 1

For x = 1, y will be 3

and for x = -2, y will be 0

Now we can see the graph for the given coordinates (-2,0) and (1,3).

5 0

3 years ago

Sofia drew a scale drawing of a theater. The stage, which is 48 feet long in real life, is 16

Zigmanuir [339]

First, you multiply 4 by 1. Then that's your answer, 4. I hope it helped!

5 0

3 years ago

Evan’s family drove to a theme park for vacation. Assume they drove the same speed throughout the trip. The first day, they drov

nadezda [96]

300/6 = 50
250/5 = 50
x/3 = 50
x = 150 miles

4 0

4 years ago