If coefficients aren’t equal or opposite, you can do a little manipulation so that you can still use the elimination

Find the 78th term of the arithmetic sequence –4,-2,0,...

MArishka [77]

The number is increasing by 2 every time.

78 x 2 = 156

-4 + 156 = 152

The 78th term is 152

8 0

2 years ago

Your neighbor has a bag with 5 oranges and 7 apples in it. You will be receiving two pieces of fruit from your neighbor. What is

Snezhnost [94]

Answer:

31.82% probability that you will receive 2 apples.

Step-by-step explanation:

The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

5 + 7 = 12 total fruits, which means that $N = 12$

7 apples, which means that $k = 7$

You receive 2 fruits, which means that $n = 2$

What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?

This is, as a proportion, P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182$

0.3182*100% = 31.82%

31.82% probability that you will receive 2 apples.

4 0

3 years ago

Can someone explain 5. please ?

GuDViN [60]

Both denominators are 4, so we can add the numerators to place over the common denominator. The numerators are -3 and -3, which add to -6. One way to think of negative numbers is to think of IOUs, which are a way of expressing debt in money. For instance, if you go into a store and buy a $10 item, but only have $3 in your pocket, then you would have to owe the owner $7. This can be represented with -7. If you repeat the process, then you'd have 7+7 = 14 in IOUs total. This would be represented with -14

In short, adding negative numbers is really the same as adding positives, but the final result is negative

So that's why -3+-3 turns into -6. We add the two threes like normal but then make the final result negative. All throughout this process, the denominator stays at 4.

So we end up with -6 over 4 which reduces to -3 over 2. How is this reduction happening? We are simply dividing each piece by the greatest common factor 2.

-6 divided by 2 = -3

4 divided by 2 = 2

5 0

3 years ago

Can somebody help me evaluate this expression and solve the terms

yanalaym [24]

Step-by-step explanation:

3 0

2 years ago

Please help me with this math question

Svetach [21]

If the two rectangles are similar, their sides must be proportional. We can figure this out by setting up a proportion. We need to make sure to match up the correct sides though. We know the two longer sides must match up, so 6 goes with 60, and 3 goes with 30:

3/6=30/60

If we reduce the fractions, we get:

1/2=1/2

Therefore, the rectangles are similar. One of them is just rotated.

4 0

3 years ago