(calculus) please help!! will mark brainliest

nika2105 [10]

There could be 35 toffees in the box.

8 0

2 years ago

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 800 voters i

Hunter-Best [27]

Answer:

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.

Based on this the correct system of hypothesis are:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis $p >0.3$

Step-by-step explanation:

We have the following info given from the problem:

$n= 800$ the random sample of voters selected from the town

$\hat p = 0.34$ represent the proportion of residents favored construction

$p_o = 0.30$ represent the value desired to test.

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 30%, so then that represent our claim and needs to be on the alternative hypothesis.

Based on this the correct system of hypothesis are:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis $p >0.3$

And in order to test this hypothesis we can use a one sample z test for a population proportion and the statistic would be given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

And with the data given we have:

$z=\frac{0.34 -0.3}{\sqrt{\frac{0.3(1-0.3)}{800}}}=2.469$

7 0

2 years ago

In 2000, the population of Big Springs was 13 thousand. Use the given doubling

trasher [3.6K]

Answer:

The answer is "26179.4".

Step-by-step explanation:

Assume year 2000 as t, that is t =0.

Formula:

$A= A_0e^{rt}$

Where,

$A_0 = \ initial \ pop \\\\r= \ rate \ in \ decimal \\\\t= \ time \ in \ year$

for doubling time,

$r = \frac{log (2)}{t} \\$

$r = \frac{\log (2)}{ 40} \\\\r= \frac{0.301}{40}\\\\r= 0.007$

Given value:

$A = A_0e^{rt} \\\\$

$A_0 = 13000$

$t= 40 \ years$

when year is 2000, t=0 so, year is 2100 year as t = 100.

$A = 13000 \times e^{et}\\\\A = 13000 \times e^{e \times t}\\\\A = 13000 \times e^{0.007 \times 100}\\\\A = 13000 \times e^{0.7}\\\\A= 13000\times 2.0138\\\\A = 26179.4$