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3 years ago

A trading card increases in value by 2% each year. In 2005, it was worth $8. About how much is it worth in 2011?

1 answer:

5 0

So for this, we will be using the exponential equation formula, which is y=ab^x, with a = initial value and b = growth/decay. Since the value is increasing, you would add 1 and 0.02(2% in decimal form) together to get 1.02, which will be the b variable. And since we are starting in 2005 with $8 and trying to figure out the value in 2011, 8 will be the a variable and 6 will be the x variable (2011-2005=6)

With this info, our equation will be: y = 8(1.02)^6

Firstly, solve 1.02^6: y = 8(1.12616242)

Next, multiply and your answer will be (rounded to the hundreths): y = $9.01

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My Notes A large manufacturing plant uses lightbulbs with lifetimes that are normally distributed with a mean of 1600 hours and

Evgen [1.6K]

Answer:

The bulbs should be replaced each 1436.9 hours.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 1600, \sigma = 70$

How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?

This is the first percentile of hours. So it is X when Z has a pvalue of 0.01.

So it is X when Z = -2.33.

$Z = \frac{X - \mu}{\sigma}$

$-2.33 = \frac{X - 1600}{70}$

$X - 1600 = -2.33*70$

$X = 1436.9$

The bulbs should be replaced each 1436.9 hours.

6 0

3 years ago

calculate the amount of money invested at 8.5% per annum when 2,488.80 simple interest was collected after three years. anyone

Mrac [35]

Answer:

2488.80 divided by 3=838.1

6 0

3 years ago

A large truck has two fuel tanks, each with a capacity of 150 gallons. Tank 1 is half full, and Tank 2 is empty.

12345 [234]

Answer:

1) $G(t) = 75 + \frac{23}{4}t\\$

2) After 8 minutes delivering fuel the tanks will have 121 gallons of fuel

Step-by-step explanation:

1) For generating the equation we have to take into account that in the tanks there is a initial volume of fuel that corresponds to 75 gallons, as it is stated that tank one is half full. As the capacity for tank 1 is of 150 gallons, half of the tank equals to:

$\frac{150}{2} = 75 gallons$

Now we have to convert the rate of delivery that is expressed as a mixed number to an improper fraction so:

$5\frac{3}{4} = \frac{(5x4)+3}{4} = \frac{23}{4}$

Then the pumping rate is of 23/4 gallons per minute, to get how many gallons are in the tank we just need to multiply this rate by the time in minutes, and as there is an initial volume we have to add it, so we have the following equation:

$G(t) = 75 + \frac{23}{4}t\\$

2) To know how much fuel is in the tank after 8 minutes we have to replace this time in the previous equation so we have

$G(t) = 75 + \frac{23}{4}t\\G(8) = 75 + \frac{23}{4}(8)\\G(8) = 75 + 23(2)\\G(8) = 75 + 46\\G(8) = 121 gallons$

After 8 minutes delivering fuel the tanks will have 121 gallons of fuel

8 0

3 years ago

Henrietta bought 5 cupcakes and 2 brownies for $16.25. She went back to the bakery the next day and bought 7 cupcakes and 6 brow

serious [3.7K]

Answer:

cost of one cupcake = $2.75

cost of one brownie = $1.25

Step-by-step explanation:

Let c = number of cupcakes

Let b = number of brownies

Equation 1: 5c + 2b = 16.25

Equation 2: 7c + 6b = 26.75

Multiply equation 1 by 3:

⇒ 15c + 6b = 48.75

Now subtract equation 2 from this equation to eliminate 6b:

⇒ 8c = 22

Divide both sides by 8:

⇒ c = 2.75

Substitute c = 2.75 into one of the original equations and solve for b:

⇒ 5(2.75) + 2b = 16.25

⇒ 13.75 + 2b = 16.25

⇒ 2b = 2.5

⇒ b = 1.25

Therefore, cost of one cupcake = $2.75 and cost of one brownie = $1.25

6 0

3 years ago

If 40% of the 25 students in mr.greggs class are boys how amny boys are in class

LiRa [457]

Answer:

10 boys

Step-by-step explanation:

0.4x25= 10

4 0

2 years ago