Compare Linear & Exponential Functions Activity

Fiona earns $10 for mowing each lawn and $5 per hour for her work. Write an inequality to show how many lawns she needs to mow i

KatRina [158]

Answer: $\geq$ 9 lawns, assuming Fiona spends 1 hour per lawn.

Step-by-step explanation:

Let Y = the amount earned from mowing a lawn. Let z be the number of hours worked on that lawn.

Y = $10 + $5(z)

We need to know the number of hours, z, for any particular lawn to be able to make this a valid equation. Not having that, we really can't set up a valid equation.

But let's assume z=1 for each and every lawn and see what we'd have.

Y = $10 + $5

Y = $15/lawn.

Fiona needs at least $135 for her Broadway ticket.

Let L be the number of lawns mowed. We need:

L*($15/lawn) $\geq$ $135

L $\geq$ 9 lawns

8 0

3 years ago

The average yield of the standard variety off soybeans per acre on a farm in a region is 48.8 bushels per acre, with a standard

I am Lyosha [343]

Answer:

$z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3$

$p_v =P(Z>2.3)=1-P(Z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.

Step-by-step explanation:

1) Data given and notation

$\bar X=53.4$ represent the sample mean

$\sigma=12$ represent the population standard deviation assumed

$n=36$ sample size

$\mu_o =48.8$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is higher than 48.8, the system of hypothesis would be:

Null hypothesis: $\mu \leq 48$

Alternative hypothesis: $\mu > 48$

Since we assume that know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3$

4)P-value

Since is a right tailed test the p value would be:

$p_v =P(Z>2.3)=1-P(Z$

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.

3 0

4 years ago

Combine like terms: 1/4g+7+1/2g-8

jek_recluse [69]

The answer to this question should be 55

6 0

3 years ago

Determine which score corresponds to the higher relative position. Which is better, a score of 92 on a test with a mean of 71 an

ss7ja [257]

Answer:

The score of 92 on a test with a mean of 71 and a standard deviation of 15 is better.

Step-by-step explanation: