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Harrizon [31]
2 years ago
5

In 2007 the population of the town of Cartersville was 24,455. The population growth can be represented by the formula P = 24,45

5(1.03)x, where x represents the number of years after 2007. When will the population of the town first exceed 30,000?
Mathematics
1 answer:
Triss [41]2 years ago
3 0
P = 24455 (1.03)x
30,000/24455 (1.03) < x
The year must be > 1.19 + 2007, or 2008.19, which means in 2009, or in 2008 + 3 months
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Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, nor
kenny6666 [7]

Answer:

a) 0.0167

b) 0

c) 5.948

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6.16 ounces

Standard Deviation, σ = 0.08 ounces

We are given that the distribution of fill volumes of bags is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) Standard deviation of 23 bags

\displaystyle\frac{S.D}{\sqrt{23}} = \frac{0.08}{\sqrt{23}} = 0.0167

b) P( fill volume of 23 bags is below 5.95 ounces)

P(x < 5.95)

P( x < 5.96) = P( z < \displaystyle\frac{5.95 - 6.16}{0.0167}) = P(z < -12.57)

= 1 - P(z < 12.57)

Calculation the value from standard normal z table, we have,  

P(x < 5.95) = 1 - 1 = 0

c) P( fill volume of 23 bags is below 6 ounces)  = 0.001

P(x < 6)  = 0.001

P( x < 6) = P( z < \displaystyle\frac{6 - \mu}{0.0167})

Calculation the value from standard normal z table, we have,  

P( z \leq -3.09) = 0.001

\displaystyle\frac{6 - \mu}{0.0167} = -3.09\\\\\mu = 6 + (0.0167\times -3.09) = 5.948

If the mean will be 5.948 then the probability that the average of 23 bags is below 6.1 ounces is 0.001.

7 0
3 years ago
Can you solve the inequality 2(x-3) is less than or equal to 10 without using the distributive property? Explain.
STatiana [176]

Answer:

Yes, without using the distributive property, we get the value for the given expression 2(x - 3)  ≤ 10  as   x ≤ 8

Step-by-step explanation:

Here, the given expression is:

2(x - 3)  ≤ 10

Yes, the given expression can be solved without using the DISTRIBUTIVE Property

Here, consider the given expression:

2(x - 3)  ≤ 10

Now, divide the  inequality by 2 on both sides, we get:

\frac{2(x-3)}{2}  \leq  \frac{10}{2}\\\implies (x - 3)  \leq 5

Now adding (+3) on both the sides, we get:

(x - 3)  ≤ 5    ⇒  (x - 3  + 3 )  ≤ 5 + 3  

or, x ≤ 8

Hence, without using the distributive property, we get the value of x ≤ 8 for the given expression 2(x - 3)  ≤ 10

6 0
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