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Varvara68 [4.7K]
3 years ago
8

There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen. How many possibilities a

re there?
Mathematics
1 answer:
tester [92]3 years ago
3 0

Answer:

190 possibilities.

Step-by-step explanation:

The problem is called 20 choose 2, given by the formula for combinations

C(20,2) = 20! / (2! (20-2)!) = 190

alternatively, we can reason it this way:

there are 20 choices to choose a captain and 19 choices for an alternate captain for a total of 380 ways.

However, there are 20 choices to choose an alternate captain and 19 choices for a captain for a total of 380 ways.

Since we are essentially double counting every choice of the posts, we need to divide 380 by 2 to get 190 ways.

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Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor’s. A sample of 40 bab
Leviafan [203]

Answer:

z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936  

The p value can be founded with this formula:

p_v =P(z  

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

Step-by-step explanation:

Information given

\bar X_{1}=7.6 represent the mean for Gibbs products

\bar X_{2}=8.1 represent the mean for the competitor

\sigma_{1}=2.3 represent the population standard deviation for Gibbs

\sigma_{2}=2.9 represent the sample standard deviation for the competitor

n_{1}=40 sample size for the group Gibbs

n_{2}=55 sample size for the group competitor

\alpha=0.05 Significance level provided

z would represent the statistic

Hypothesis to verify

We want to check if babies using the Gibbs brand gained less weight, the system of hypothesis would be:  

Null hypothesis:\mu_{1}-\mu_{2}=0  

Alternative hypothesis:\mu_{1} - \mu_{2}< 0  

The statistic would be given by:

z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)  

Replacing the info given we got:

z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936  

The p value can be founded with this formula:

p_v =P(z  

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

5 0
3 years ago
Hellpppp Neeededd, How To Solve…<br><br> Quadratic Formula Equation To <br> x² +9x+8=0
mrs_skeptik [129]

Answer:

-8 or -1

Step-by-step explanation:

x*2+9x+8=0

(x+8)(x+1)=0

x+8=0 or x+1=0

x= -8 or x= -1

6 0
2 years ago
Help me fast please find the area???
goldfiish [28.3K]

1485 this is wrong I think

4 0
3 years ago
A child should no longer use a booster seat when they reach 4'9" tall. Jannet is 59 inches tall can she go without a booster sea
Alisiya [41]

Answer:

Yes

Step-by-step explanation:

4'9" is 57 inches. Jannet is taller than that, so should go without a booster seat.

___

<em>Feet to Inches</em>

1 foot is 12 inches, so 4 feet is 4×12 = 48 inches. Adding 9 inches to that gives ...

... 4' 9" = 57 inches

4 0
3 years ago
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Mindy has a total of 84 candy bars in a box. If the ratio
wolverine [178]
There are 35 snickers in the box
There is also 49 Twix bars
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