Colin is painting figurines. He spends 20 minutes painting each figurine. After painting for 60 minutes, he still has 9 more fig
2 answers:
Answer:
Step-by-step explanation:
To solve this problem we must pay attention to the following data supplied:
- f It is the number of figurines that remain to be painted.
- t amount of time, in minutes, that Colin spends painting
- Colin takes 20 minutes painting each figurines.
- After painting 60 min, he still has 9 figurines left. f (60) = 9
If he takes 20 minutes painting 1, it means that in 60 minutes he has painted 3 and he has 9 left.
Then, at the beginning he has 9 +3 figurines to be painted.
With these two points we can find the function:
If m is the slope of the line, then:
Where by definition
Finally the formula is:
You might be interested in
Answer:
Step-by-step explanation:
Answer:
ON MONDAY: 35 mosquitos.
ON TUESDAY: 6 flies.
Step-by-step explanation:
As you can see in the diagram, the frog eats 3 flies for every 7 mosquitoes (for lunch). Then you can expresed this ratio as following:
3:7 or
Based on the table:
-If the frog eats 15 flies on monday, then the number of mosquitos that it eats can be calculated as following:
-If the frog eats 14 mosquitoes on tuesday, then the number of flies that it eats can be calculated as following:
Answer:
We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.
Step-by-step explanation:
<u>The complete question is</u>: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:
Number sampled: 1,000 (republican) , 800 (democrats)
Number in favor: 200 (republican) , 168 (democrats)
At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.
Let = <u><em>proportion of Republicans in favor of lowering the standards</em></u>.
= <u><em>proportion of Democrats in favor of lowering the standards</em></u>.
SO, Null Hypothesis, :
{means that there is an equal or larger proportion of Republicans in favor of lowering the standards}
Alternate Hypothesis, :
{means that there is a larger proportion of Democrats in favor of lowering the standards}
The test statistics that would be used here <u>Two-sample z-test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of Republicans in favor of lowering the standards =
= 0.20
= sample proportion of Democrats in favor of lowering the standards =
= 0.21
= sample of Republicans = 1000
= sample of Democrats = 800
So, <u><em>the test statistics</em></u> =
= -0.52
The value of z test statistics is -0.52.
<u>Now, P-value of the test statistics is given by the following formula; </u>
P-value = P(Z < -0.52) = 1 - P(Z 0.52)
= 1 - 0.6985 = 0.3015
Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.
Since our test statistic is more than the critical value of z as -0.52 > -2.054, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.
Therefore, we conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.