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Anestetic [448]
3 years ago
12

Geoff has a bag that contains 4 red marbles and 6 blue marbles. He chooses two marbles at random and does not replace them. What

is the probability that the first marble is blue and the second marble is red? A. B. C. D.
Mathematics
1 answer:
posledela3 years ago
3 0

Total number of marbles = 10

Number of red marbles = 4

Number of blue marbles = 6

Probability = \frac{number of favorable outcomes}{total number of outcomes}

The probability that the first marble is blue = \frac{6}{10}

The probability that the first marble is red = \frac{4}{9} ; 9 because 1 marble has already been taken out.

Joint probability= probability of event A * Probability of event B

= \frac{6}{10}\times\frac{4}{9}=\frac{24}{90}= \frac{4}{15}

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If x = 4, y = 2 and z = 1 then xz (4y - 2z) is: 861, 24, 46, or 40. Help please.
dybincka [34]
(4)(1) * (4(2)-2(1))
4 * (8-2)
4*6
24
8 0
3 years ago
Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)
notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A <em>mathematical induction</em> consists in only 2 steps:  

<u>First step</u>: Show the proposition is true for the first one valid integer number.

<u>Second step</u>: Show that if any one is true then the next one is true  

Finally, if first step and second step are true, then the complete proposition is true.

So, given 2*n^3+3*n^2+n

First step: using and replacing n=2 (the first valid integer number >1)

2*(2)^3 +3*(2)^2+2=30

\frac{30}{6} =5

As the result is an integer number, so the first step is true.

Second step: using any next number, n+1, let it replace

2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)

As the First step is true, we know that

2*n^3+3*n^2+n=6*k,

So let it replace in the previous expression

6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]

Finally

\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)

where the last expression is an integer number

So the second step is true, and the complete proposition is True

5 0
3 years ago
On a coordinate plane, line A has a negative slope, line b is horizontal, line c is vertical, and line d has a positive slope.
Digiron [165]

Answer:

<u>Line b</u>

Step-by-step explanation:

It cannot be line a or line d because the line will have a constant rate of change. It cannot be line c because line c would be undifined. Therefore, it must be line b.

4 0
3 years ago
Felicia is buying a Crockpot that retails for $125. She has a coupon for $40 off of any item over $100. Calculate her percent sa
Juliette [100K]

Answer:

32%

Step-by-step explanation:

Given

Cost of Crockpot = $125

Coupon = $40

Coupon applies on items greater than $100

Required

Percent saved if coupon is applied.

If she applies coupon on the Crockpot, then she'll be saving $40.

Percent Savings = Amount Saved / Total Amount

Percent Savings = $40/$125

Percent Savings = 0.32

Convert to Percentage

Percent Savings = 0.32 * 100%

Percent Savings = 32%.

Hence, she'd save 32% if she applies the coupon of $40 on the Crockpot

7 0
3 years ago
Read 2 more answers
The perimeter of a rectangle is 46in and the diagonal is 17 in
dmitriy555 [2]

Answer + explaination

p=2*(L+l)=46

L+l=46:2

L+l=23

(L+l)^2=529

(L^2+l^2)+2l*L=529

D= V L^2+l^2= 17

L^2+l^2=289

so 289+2l*L=529

    2l*L=529-289=240

l*L=240:2

A=120

4 0
3 years ago
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