About 400 marbles. You simply set up a proportion and solve it as I did in the photo attached.
The ratio of runners to swimmers was 3:2. When 28 runners dropped out of the competition, the ratio became 5:6. How many total s
1 answer:
The total of 42 swimmers are competing
Step-by-step explanation:
The given is:
- The ratio of runners to swimmers was 3 : 2
- When 28 runners dropped out of the competition, the ratio became 5 : 6
We need to find how many total swimmers are competing
∵ The ratio of runners to swimmers was 3 : 2
- Multiply each term of the ratio by x
∴ There are 3x runners and 2x swimmers
∵ 28 runners dropped out of the competition
∴ The number of runners who complete = 3x - 28
∵ The ratio became 5 : 6
- Equate the ratio between the new number of runners and the
number of swimmers by 5 : 6
∵ The new number of runners = 3x - 28
∵ The number of swimmers = 2x
∴
- By using cross multiplication
∴ 6(3x - 28) = 5(2x)
- Simplify both sides
∴ 18x - 168 = 10x
- Add 168 to both sides
∴ 18x = 10x + 168
- Subtract 10x from both sides
∴ 8x = 168
- Divide both sides by 8
∴ x = 21
∵ The number of swimmers is 2x
∵ x = 21
∴ The number of swimmers = 2(21) = 42
The total of 42 swimmers are competing
Learn more:
You can learn more about the ratio in brainly.com/question/2707032
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Using the z-distribution, it is found that since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.
At the null hypothesis, it is <u>tested if the mean length of jail time is still of 2.5 years</u>, that is:
At the alternative hypothesis, it is <u>tested if it has increased</u>, that is:
We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:
The parameters are:
is the sample mean.
is the value tested at the null hypothesis.
is the standard deviation of the sample.
- n is the sample size.
For this problem, the values of the <u>parameters</u> are:
Hence, the value of the <u>test statistic</u> is:
The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05</u>, is of
Since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.
A similar problem is given at brainly.com/question/24166849
Answer:
Zach earns $10 and for the pair of boots Zach earns $15
Step-by-step explanation:
Let be x the number of pairs of shoes
Let be y the number of pairs of boots
Then we can establish the following system of equations with the data of the statement:
We subtract the second equation from the first equation to eliminate the variable y and solve for x, just like this:
For y replacing in the first equation the value of x and solving for y:
So for the pair of shoes Zach earns $10 and for the pair of boots Zach earns $15
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