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2 years ago

A baseball team played 130 games in a season. If it won sixteen more games

Mathematics

1 answer:

egoroff_w [7]2 years ago

4 0

Answer:

The team has 92 wins and 38 losses.

Step-by-step explanation:

In a season 130 games are played by a baseball team.

Let us assume that the team wins x games and losses y games.

Therefore, we can write, x + y=130....... (1)

It is given that if the team won sixteen more games twice as many games as it lost.

So, we can conclude that x =2y+16 ......(2)

Hence, solving equations (1) and (2) we get, (2y+16) + y =130

⇒ 3y = 114

⇒ y =38

And from equation (2), x = 2×38 + 16 = 92

Therefore, the team has 92 wins and 38 losses. (Answer)

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A positive real number is 5 more than another. When - 10 times the smaller is added to the square of the larger, the result is 5

salantis [7]

Answer:

4√2 and 5+4√2

Step-by-step explanation:

Let the two numbers be x ad y

Smaller = y

Bigger = x

If a positive real number is 5 more than another, then;

x = 5 + y ... 1

When - 10 times the smaller is added to the square of the larger, the result is 57, then;

-10y + x² = 57 ...2

Substitute 1 into 2;

-10y + (5+y)² = 57

-10y + 25+10y+y² = 57

y²+25 = 57

y² = 57 - 25

y² = 32

y = √32

y = 4√2

Since x = 5 + y

x = 5 + 4√2

Hence rhe numbers are 4√2 and 5+4√2

8 0

2 years ago

You estimated the average rental cost of a 2 bedroom apartment in Denton. A random sample of 16 apartments was taken. The sample

Zigmanuir [339]

Answer:

The new sample size required in order to have the same confidence 95% and reduce the margin of erro to $60 is:

n=28

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=160)$

And the distribution for $\bar X$ is:

$\bar X \sim N(\mu, \frac{160}{\sqrt{n}})$

We know that the margin of error for a confidence interval is given by:

$Me=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The next step would be find the value of $\z_{\alpha/2}$ , $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$

Using the normal standard table, excel or a calculator we see that:

$z_{\alpha/2}=\pm 1.96$

If we solve for n from formula (1) we got:

$\sqrt{n}=\frac{z_{\alpha/2} \sigma}{Me}$

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And we have everything to replace into the formula:

$n=(\frac{1.96(160)}{78.4})^2 =16$

And this value agrees with the sample size given.

For the case of the problem we ar einterested on Me= $60, and we need to find the new sample size required to mantain the confidence level at 95%. We know that n is given by this formula:

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And now we can replace the new value of Me and see what we got, like this:

$n=(\frac{1.96*160}{60})^2 =27.32$

And if we round up the answer we see that the value of n to ensure the margin of error required $Me=\pm 60$ $ is n=28.

5 0

2 years ago

Alice needs to rent a car while on vacation. The rental company charges $17.95, plus 15 cents for each mile driven. If Alice onl

Readme [11.4K]

Answer:

Alice can drive 147 miles

Step-by-step explanation:

At first you subtract $17.95 from $40.

Then you are left with $22.05

Finally, you divide $22.05 by $0.15

And you get 147, so she can drive 147 miles without going over her limit.

7 0

3 years ago

Tickets to a play cost $5 at the door and $4 in advance. The theater club wants to raise $400 from the play.

natima [27]

The theatre needs to sell 100 tickets in advance. or 80 tickets at the door to reach $400.
They would need to sell 48 tickets at the door to reach their goal.

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3 years ago

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6 0

3 years ago