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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

xz_007 [3.2K]

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

∴ $\frac{3x-28}{2x}=\frac{5}{6}$

- 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

#LearnwithBrainly

7 0

3 years ago

What is the answer plz help

stira [4]

0.334 if you turn it to decimals... still acceptable?

4 0

4 years ago

If circumference and the area of a circle are numerically equal, find the diameter of the circle.

babunello [35]

Answer:

d = 4

Step-by-step explanation:

C = 2*pi r or C = pi * d

Area = pi *r^2= pi (d/2)^2 = pi * d^2 /4

So if they are numerically equal, you get

pi * d = pi * d^2 / 4 Divide both sides by pi

d = d^2 / 4 Multiply both sides by 4

4*d = d^2 Divide both sides by d

4 = d

8 0

3 years ago

HELP PLEASEE!!!!!!!!!!!!!

RideAnS [48]

I can’t see the picture

4 0

3 years ago

A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that yo

aev [14]

Answer:

1. M=108

2. μ=110

3. In the explanation.

4. Test statistic t = -1.05

5. P-value = 0.1597

Step-by-step explanation:

The question is incomplete: to solve this problem, we need the sample information: size, mean and standard deviation.

We will assume a sample size of 10 matches, a sample mean of 108 points and a sample standard deviation of 6 points.

1. The mean points is the sample points and has a value of 108 points.

2. The null hypothesis is H0: μ=110, meaning that the mean score is not significantly less from 110 points.

3. This is a hypothesis test for the population mean.

The claim is that the mean score is significantly less than 110.

Then, the null and alternative hypothesis are:

$H_0: \mu=110\\\\H_a:\mu< 110$

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=108.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{10}}=1.9$

4. Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{108-110}{1.9}=\dfrac{-2}{1.9}=-1.05$

The degrees of freedom for this sample size are:

$df=n-1=10-1=9$

5. This test is a left-tailed test, with 9 degrees of freedom and t=-1.05, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.1597) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean score is significantly less than 110.

7 0

3 years ago