Answer:
There would need to be at least 1,800 entries in order for them to meet their goal.
Step-by-step explanation:
To find this, we must write an equation that helps solve it. We know that for every entry (x), we gain 75 and lose 25. We can express this as the following.
75x - 25x
Then we can add the number of donations.
75x - 25x + 10,000
Then we can set it as greater than or equal to the goal number.
75x - 25x + 10,000 ≥ 100,000
Now we solve this using the order of operations.
75x - 25x + 10,000 ≥ 100,000 ----> Combine like terms
50x + 10,000 ≥ 100,000 ------> Subtract 10,000
50x ≥ 90,000 -----> Divide by 50
x ≥ 1,800
Using the z-distribution, the p-value would be given as follows:
b) 0.0086.
<h3>What are the hypothesis tested?</h3>
At the null hypothesis we test if the means are equal, hence:
At the alternative hypothesis, it is tested if they are different, hence:
<h3>What are the mean and the standard error for the distribution of differences?</h3>
For each sample, they are given as follows:
Hence, for the distribution of differences, they are given by:
.
<h3>What is the test statistic?</h3>
The test statistic is given by:
In which 
is the value tested at the null hypothesis.
Hence:
z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
Hence option B is correct.
More can be learned about the z-distribution at brainly.com/question/13873630
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Hope this helps.................
You can because you already know the number is 3 and the blank number is n
Answer:
Hence, a carpenter can paint a maximum of 7 chairs.
Hence, option A is correct.
Step-by-step explanation:
A carpenter has less than 120 min. to spend painting furniture each day.
Today, he has spent 30.5 min. painting a desk.
Now he will paint x chairs, each of which takes 12.5 min.
i.e. he will take a total of 12.5x minutes in painting 'x' chairs.
Also total time spent on painting furniture each day will be equal to time spent on painting a desk and all of the chairs.
Hence,
30.5+12.5x<120 (since the total time he spends on painting is less than 120 mins.)
⇒ 12.5 x<120-30.5
⇒ 12.5 x<89.5
⇒ x<7.16 ( on dividing both side of the inequality with 12.5)
Hence, a carpenter can paint a maximum of 7 chairs.
