Each team in a soccer league has 43 players on it. There are 24 teams in the league. How many total players are in the league?

HOS

lianna [129]

Answer:

B

Step-by-step explanation:

5 0

3 years ago

Find the measures of the interior

Ainat [17]

Answer:

Angle 1 = 108°

Angle 2 = 72°

Angle 3 = 120°

Angle 4 = 96°

Angle 5 = 144°

Step-by-step explanation:

We need to find the measures of the interior angles in a pentagon if the measure of each consecutive angle is in the ratio 9:6:10:8:12.

Let x be the common ratio

So, we can write:

Angle 1 = 9x

Angle 2 = 6x

Angle 3 = 10x

Angle 4 = 8x

Angle 5 = 12x

We know that the <em>sum of all angles of pentagon = 540</em>

So, adding all angles and equal them to 540, we can find value of x

$9x+6x+10x+8x+12x=540\\45x=540\\x=\frac{540}{45}\\x=12$

So, we get the value of x: x=12

Now, calculating the angles by putting x=12:

Angle 1 = 9x = 9(12) = 108°

Angle 2 = 6x = 6(12) = 72°

Angle 3 = 10x = 10(12) = 120°

Angle 4 = 8x = 8(12) = 96°

Angle 5 = 12x= 12(12) = 144°

6 0

3 years ago

A self proclaimed psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the c

swat32

Answer:

The 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Description in words of the parameter p

$p$ represent the probability that the psychic correctly identifies the symbol on the card in a random trial

$\hat p$ represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

n=200 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the cases successful

$\hat p=\frac{46}{200}=0.23$ represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

Confidence interval

The confidence interval for a proportion is given by this formula:

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.23 - 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.172$

$0.23 + 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.288$

And the 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

6 0

3 years ago

ok so if you have 3 and 1/4 pizza and want to subtract 3/4 out of it,and get 3x more slices then you had from a friend after sub

Brilliant_brown [7]

Answer:

You have 2 and 1/2 pizzas and your friend has 5/6 of a pizza.

Step-by-step explanation:

You have 3 1/4 pizzas. If you get rid of 3/4 of a pizza, you will end up with 2 2/4 pizzas.

To make it easier, you can just change the values into improper fractions: 3 1/4 = 13/4

13/4 - 3/4 = 10/4

10/4 = 2 2/4 pizzas

(2 2/4 = 2 1/2)

Anyways! You now have 2 and a half pizzas. You have 3 times the amount of pizza that your friend has. In other words, your friend has 1/3 the amount of pizza that you have. You can solve for this in two ways, whichever way you solve it is up to you.

You can solve this problem by dividing the amount of food you have by 3: $\frac{2\frac{1}{2} }{3}$ which equals 0.8333... (the 3 is repeating). But you can just keep your final answer in fraction form if you want to: $\frac{2.5}{3} = \frac{5}{6}$
You can solve this problem by multiplying 1/3 to the amount of food you have: $\frac{1}{3} * 2 \frac{2}{4}\\=\frac{10}{12}\\ =\frac{5}{6}$