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Andrei [34K]
3 years ago
7

: A new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.

Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
8 0

Answer:

2 bears in 2020.

Step-by-step explanation:

We have been given that a new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.

We will use exponential decay formula to solve our given problem as:

y=a\cdot (1-r)^x, where,

y = Final quantity,

a = Initial value,

r = Decay rate in decimal form,

x = Time

20\%=\frac{20}{100}=0.20    

Upon substituting our given values in above formula, we will get:

y=150(1-0.20)^x

y=150(0.80)^x, where x corresponds to year 2000.

To find the population in 2020, we will substitute x=20 in our equation as:

y=150(0.80)^{20}

y=150(0.011529215046)

y=1.7293822569    

y\approx 2

Therefore, 2 bears are there predicted to be in 2020.

Since population is decreasing so population is best described as exponential decay.

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Neika is saving her money to buy a DVD that costs $45. If she has a job that pays $8 per hour, write and solve an inequality tha
juin [17]

Answer:

8x6=48 so in 6 hours she will have enough money to buy it

Step-by-step explanation:

6 hours will give her 48 dollars if the dvd costs 45 so she will have to work 6 hours

6 0
2 years ago
How much change will you get back if you bought three $0.78 chocolate bars and paid with a 5$ bill
Crazy boy [7]

3 times 0.78 = 2.34 dollars

5.00 - 2.34 = 2.66

So your change is $2.66

8 0
3 years ago
Read 2 more answers
Many elementary school students in a school district currently have ear infections. A random sample of children in two different
Marta_Voda [28]

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school n_1 = 42

sample size for the second school n_2  = 34

so 16 out of 42 i.e x_1 = 16 and 18 out of 34 i.e x_2 = 18 have ear infection.

the proportion of students with ear infection Is as follows:

\hat p_1 = \dfrac{16}{42} = 0.38095

\hat p_2 = \dfrac{18}{34}  =  0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}

\bar p = \dfrac{16 +18}{42 +34}

\bar p = \dfrac{34}{76}

\bar p = 0.447368

\bar p + \bar  q = 1 \\ \\ \bar q = 1 -\bar  p \\  \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632

The pooled standard error can be computed by using the formula:

S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} +  \dfrac{\bar p \bar p}{n_2} }

S.E = \sqrt{ \dfrac{  0.447368 *  0.552632}{ 42} +  \dfrac{ 0.447368 *  0.447368}{34} }

S.E = \sqrt{ \dfrac{  0.2472298726}{ 42} +  \dfrac{ 0.2001381274}{34} }

S.E = \sqrt{ 0.01177284105}

S.E = 0.1085

The test statistics is ;

z = \dfrac{\hat p_1 - \hat p_2}{S.E}

z = \dfrac{0.38095- 0.5294}{0.1085}

z = \dfrac{-0.14845}{0.1085}

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

5 0
3 years ago
Create a tally chart with the data below
ladessa [460]
3 beach 2 skiing and 2 camp
5 0
3 years ago
Read 2 more answers
Evaluate 2^2⋅4^3=<br><br>Your answer<br><br><br>​
ivanzaharov [21]

Answer:

256

Step-by-step explanation:

First, handle the exponent:

2²=4 (2*2=4)     and     4³=64 (4*4=16*4=64)

Now multiply those two outcomes:

4*64=<u>256</u>

This equation is also known as 4⁴

6 0
2 years ago
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