Does this situation represent a positive or negative number?<br><br> 23∘above0∘F

15. Suppose a box of 30 light bulbs contains 4 defective ones. If 5 bulbs are to be removed out of the box.

Naddika [18.5K]

Answer:

1) Probability that all five are good = 0.46

2) P(at most 2 defective) = 0.99

3) Pr(at least 1 defective) = 0.54

Step-by-step explanation:

The total number of bulbs = 30

Number of defective bulbs = 4

Number of good bulbs = 30 - 4 = 26

Number of ways of selecting 5 bulbs from 30 bulbs = $30C5 = \frac{30 !}{(30-5)!5!} \\$

$30C5 = 142506$ ways

Number of ways of selecting 5 good bulbs from 26 bulbs = $26C5 = \frac{26 !}{(26-5)!5!} \\$

$26C5 = 65780$ ways

Probability that all five are good = 65780/142506

Probability that all five are good = 0.46

2) probability that at most two bulbs are defective = Pr(no defective) + Pr(1 defective) + Pr(2 defective)

Pr(no defective) has been calculated above = 0.46

Pr(1 defective) = $\frac{26C4 * 4C1}{30C5}$

Pr(1 defective) = (14950*4)/142506

Pr(1 defective) =0.42

Pr(2 defective) = $\frac{26C3 * 4C2}{30C5}$

Pr(2 defective) = (2600 *6)/142506

Pr(2 defective) = 0.11

P(at most 2 defective) = 0.46 + 0.42 + 0.11

P(at most 2 defective) = 0.99

3) Probability that at least one bulb is defective = Pr(1 defective) + Pr(2 defective) + Pr(3 defective) + Pr(4 defective)

Pr(1 defective) =0.42

Pr(2 defective) = 0.11

Pr(3 defective) = $\frac{26C2 * 4C3}{30C5}$

Pr(3 defective) = 0.009

Pr(4 defective) = $\frac{26C1 * 4C4}{30C5}$

Pr(4 defective) = 0.00018

Pr(at least 1 defective) = 0.42 + 0.11 + 0.009 + 0.00018

Pr(at least 1 defective) = 0.54

3 0

3 years ago

Sam rented a truck for one day. There was a base fee of $16.95, and there was an additional charge of 73 cents for each mile dri

Naddik [55]

Answer: 134 miles

Step-by-step explanation:

f(m) = 16.95 + 0.92m

140.23 = 16.95 + 0.92m

0.92m = 140.23 - 16.95

0.92m = 123.28

m = 123.28/0.92

m = 134 miles

5 0

3 years ago

If f(x) = x2 + 7, what is the value of f(3)?

Mazyrski [523]

Plug in 3 for f(x)
f(3)=(3)²+7
f(3)=9+7
f(3)=16
Hoped this helped!

3 0

3 years ago

If $1,000 is invested at 4% simple interest, how much will the investment be worth after 2 years? Please explain how compound an

Novay_Z [31]

<h3>Answer:</h3>

simple interest: $1080.00
compounded annually: $1081.60

<h3>Step-by-step explanation:</h3>

<em>Simple Interest</em>

Simple interest is computed on the principal amount only. Each year, 4% of the principal is added to the balance. So, at the end of 2 years, the balance is ...

... $1000 + 0.04×$1000 + 0.04×$1000

... = $1000×(1 + 0.04×2) = $1000×1.08

... = $1080.00

_____

<em>Comment on the computation</em>

The added interest is the rate (per year) multiplied by the number of years. Here, that is 0.04×2×(principal amount). The formula for the simple interest earned is often seen as ...

... I = Prt . . . . . where I is the amount of interest, P is the principal amount, r is the interest rate for the time period, t is the number of time periods.

The account balance (A) with interest added is ...

... A = P + I = P + Prt

... A = P(1 +rt)

Here, the time period is years, and the rate given is an annual rate.

____

<em>Compound Interest</em>

Compound interest is computed on the <em>account balance</em> at the beginning of the period, not just the <em>principal</em> amount. After the first period, the account balance includes interest earned so far. So, the interest is earning interest. That is why it is called compounded interest.

Here, the balance at the end of the first year is the principal amount plus the interest that has earned:

... $1000 + 0.04×$1000 = $1000×1.04 = $1040.00

The balance at the end of the second year when the interest is compounded is this account balance plus the interest it earns:

... $1040 + 0.04×$1040 = $1040×1.04 = $1081.60

You may notice that the intial principal, $1000, has been multiplied by the factor 1.04 twice. Using exponents, the multiplier for a period of 2 years is 1.04×1.04 = 1.04².

_____

<em>Comment on the computation</em>

The multiplier of the account balance each year is raised to a power that is the number of years. Here, the account balance at the end of 2 years is (1+0.04)² times the principal amount. A formula that is seen for this is ...

... A = P(1 +r)^t . . . . . where A is the final account balance, P is the principal amount, r is the interest rate for the time period, and t is the number of time periods.

7 0

4 years ago

-3x+2-5x-7=4x+2 what is the first step solve this<br> equation?

Triss [41]

Answer: x = -0.58

Step-by-step explanation:

-3x+2-5x-7=4x+2

First step, collect like terms

-3x -5x-4x = 2-2+7

-12x = 7

x = 7/-12

x = -0.58

5 0

3 years ago

Does this situation represent a positive or negative number? 23∘above0∘F