What is the measure of angle DEF to the nearest degree?

If you invest $250.00 in an account that pays a simple interest rate of 4%, how long will you need to leave the money in the acc

labwork [276]

Answer:

Step-by-step explanation:

1. A = P(1 + rt) is the formula for simple interest where A is the final amount, P is the principal amount, r is the interest rate (annual), and t is the number of time periods, or time in years (most often)

2. $25 of interest means your total amount will be $275, so A = $275. P = $250. r = .04. We are trying to find t.

3. $275 = $250(1+.04t)

4. (275/250)(1.04) = t t = 1.05

5. This means you will need to wait 2 years to earn $25 in interest

8 0

3 years ago

A customer at Marty’s Fruit Stand picks a sample of 3 oranges at random from a crate containing 60 oranges, of which 4 are rotte

pychu [463]

Answer:

340 ways

Step-by-step explanation:

Given:

Total number of oranges = 60

Number of rotten oranges = 4

Number of oranges picked = 3

Now, number of good oranges = Total number - Rotten oranges

= 60 - 4 = 56

Now, we need to pick at least two rotten oranges.

So, the possible outcomes can be as follows:

2 rotten oranges + 1 good orange = 3 oranges
3 rotten oranges + 0 good orange = 3 oranges

Now, number of ways of picking 'r' distinct objects from a total of 'n' objects is given as:

$^nCr=\frac{n!}{r!(n-r)!}$

Now, picking 2 rotten oranges from a total of 4 rotten oranges is:

$^4C_2=\frac{4!}{2!2!}=\frac{4\times 3\times 2}{4}=6$

Similarly, picking 3 rotten oranges from a total of 4 rotten oranges is:

$^4C_3 =\frac{4!}{3!\times1!}=\frac{4\times 3!}{3!}=4$

Now, picking 1 good orange from a total of 56 good oranges is:

$^{56}C_1=56$

Picking 0 good oranges means picking no good oranges.

Therefore, the total number of ways of picking at least 2 rotten oranges is the sum of the above two possibilities and is given as:

At least 2 rotten out of 3 picked = (2 rotten and 1 good) or 3 rotten

= 6 × 56 + 4

= 336 + 4 = 340 ways

Therefore, there are 340 ways of picking at least 2 rotten oranges when 3 oranges are picked from a total of 60 oranges.

8 0

4 years ago

Find the values of a, b, and c in the equation

MatroZZZ [7]

I believe you have to use power rules for these so for the numerator (x^5yz^4)^3 the power outside of the bracket will multiply with the powers inside the bracket in order to simplify this part so the numerator of the fraction would be x^15y^3z^12 (because 5x3=15, 1x3=3, 4x3=12)
Next simplify the fraction this is done by subtracting the powers so x^15y^3z^12/x^3yz =x^12y^2z^11 (because any singular letter term ie y can also be seen as y^1, using this 15-3=12, 3-1=2, 12-1=11) this is your final answer so a=12 b=2 and c=11

3 0

3 years ago

3(x – 2) = 18 help bro.

liubo4ka [24]

Answer:

x = 8

Step-by-step explanation:

3x-6=18

+6 to both sides

3x=24

÷3 on both sides

x = 8