If sample proportion is 0.476 and margin of error is given as 0.044 then find the respective confidence interval

Answers:

(a) p + m = 5
0.8m = 2

(b) 2.5 lb peanuts and 2.5 lb mixture

Explanations:

(a) Note that we just need to mix the following to get the desired mixture:

- peanut (p) - peanuts whose amount is p
- mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as

By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.

Hence,

p + m = 5

Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).

Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.

Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m).
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.

In terms mathematical equation,

0.8m = 2

Hence, the system of equations that models the situation is

p + m = 5
0.8m = 2

(b) To solve the system obtained in (a), we first label the equations for easy reference,

(1) p + m = 5
(2) 0.8m = 2

Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have

m = 2.5

Then, we substitute the value of m to equation (1) to solve for p:

p + m = 5
p + 2.5 = 5 (3)

To solve for p, we subtract both sides of equation (3) by 2.5. Thus,

p = 2.5

Hence,

m = 2.5, p = 2.5

Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.

7 0

3 years ago

2x/x-3 - 6/x-3 . I need a step by step explanation , please

Harman [31]

When adding/subtracting fractions you need a common denominator, but you already have one, which is x-3. So in general:

a/c-b/c=(a-b)/c so you just have:

(2x-6)/(x-3) now if you factor 2 from the numerator

2(x-3)/(x-3) the (x-3)s cancel out leaving

2

However! Note that division by zero is undefined, so x cannot equal 3. (because both original fractions had denominators of x-3)

What this all means is that that expression will equal 2 for all real values of x other than 3.

8 0

2 years ago