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Julli [10]
3 years ago
13

A town has a population of 12000 and grows at 4% every year. To the nearest tenth of a year, how long will it be until the popul

ation will reach 18500?
Mathematics
1 answer:
ch4aika [34]3 years ago
7 0

Answer:

  11.0 years

Step-by-step explanation:

The exponential function describing the population growth can be written ...

  population = (initial population)×(1 +growth rate)^years

If t represents the number of years, we can fill in the values to get ...

  18500 = 12000×1.04^t

Dividing by 12000 gives ...

  18500/12000 = 1.04^t

Taking logarithms, we have ...

  log(18500/12000) = t×log(1.04)

  t = log(185/120)/log(1.04) ≈ 11.037 ≈ 11.0

It will be 11.0 years until the population reaches 18,500.

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Lorico [155]

Answer:

id-2614656691

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5 0
3 years ago
Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.
Allisa [31]

Answer:

The  condition  are

           The  Null hypothesis is  H_o  :  \mu = 5

           The  Alternative hypothesis is  H_a  :  \mu <  5

The  check revealed that

             There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

     The  population mean is  \mu =  5 \ year

      The sample size is  n =  20

      The sample mean is  \=  x  =  4.6 \  years

       The  standard deviation is \sigma  =  2.2  \ years

   The  Null hypothesis is  H_o  :  \mu = 5

   The  Alternative hypothesis is  H_a  :  \mu <  5

So i will be making use of  \alpha =  0.05 level of significance to test this claim

    The critical value of  \alpha from the normal distribution table is  Z_\alpha  =  1.645

 

Generally the test statistics is mathematically evaluated as

                 t =  \frac{\= x  - \mu}{ \frac{\sigma }{\sqrt{n} } }

substituting values

                 t =  \frac{ 4.6  - 5}{ \frac{2.2}{\sqrt{20} } }

                t =  -0.8131

Looking at the value of  t and Z_{\alpha } we see that  t <  Z_{\alpha } so we fail to reject the null hypothesis  

  This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

4 0
3 years ago
How do i find the volume of a cone with a radius of 9ft and a height of 24ft​
ycow [4]

Answer: V≈2035.75ft³

That is a small 3 after ft

HOPE THIS HELPS

8 0
3 years ago
Help pls i don’t understand graphs!! &lt;3
spayn [35]
C is correct answer I think :)
8 0
3 years ago
Find the average distance each data value in the set is from the mean. Round your answer to the nearest tenth, if necessary. Pri
sineoko [7]

Answer:

The average distance of each observation from the mean is 0.                

Step-by-step explanation:

We are given the following in the question:

$7, $20, $9, $35, $12, $15, $7, $10, $20, $25

Formula:

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{160}{10} =16

Difference from the mean value of each term:

-9, 4, -7, 19, -4, -1, -9, -6, 4, 9

Average distances =

\text{Average distance} =\displaystyle\frac{0}{10} =0

Thus, the average distance of each observation from the mean is 0.

3 0
3 years ago
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