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3 years ago

11

Billy has been to three more than four times as many baseball games as Brendan. Brendan has been to 11 baseball games. Complete

the equation below to find out how many baseball games Billy has been to.

1 answer:

Masteriza [31]3 years ago

8 0

3 + 4 * y, y = 11
= 47

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India has a population density of 840 people per sq. mile. If we estimate the population of the US to be 300,000,000 and the tot

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A. 85.7 people/ sq mi

Step-by-step explanation:

<u>Population density is:</u>

Pd = population / area
Pd = 300000000 people / 3500000 sq mi = 85.7 people/ sq mi

Correct option is A

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Researchers are interested in the effect of a certain nutrient on the growth rate of plant seeding. Use a hydroponics grow proce

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Answer:

The 95% confidence interval for the mean would be given by (56.604;68.596)

The 99% confidence interval for the mean would be given by (53.196;72.004)

Step-by-step explanation:

1) Previous concepts

When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.

2) Basic operations

The sample mean can be calculated with the following formula

$\sum_{i=1}^n \frac{x_i}{n}$

Using excel we can use this function to calculate the mean:

=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $\bar X=62.6$

In order to find the sample deviation we can use this formula

$s=\sqrt{\sum_{i=1}^n \frac{(x_i-\bar X)^2}{n-1}}$

And using excel we can use this function to calculate the sample standard deviation:

=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $s=5.713$

The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case $df=n-1=6-1=5$

The formula for the confidence interval would be given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

3) Part a

If we want a 95% or 0.95 of confidence, then the value for the signficance is $\alpha=1-0.95=0.05$ , and $\alpha/2=0.025$ , and $1-\frac{\alpha}{2}=0.975$ so we can find the critical t value with the following formula in excel:

=T.INV(0.975,5)

And we got $t_{\alpha/2}= 2.571$

And we can replace into equation (1) and we got:

$62.6 \pm 2.571\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-2.571*(5.713/SQRT(6)) = 56.604

=62.6+2.571*(5.713/SQRT(6)) = 68.596

So the 95% confidence interval for the mean would be given by (56.604;68.596)

4) Part b

If we want a 99% or 0.99 of confidence, then the value for the signficance is $\alpha=1-0.99=0.01$ , and $\alpha/2=0.005$ , and $1-\frac{\alpha}{2}=0.995$ so we can find the critical t value with the following formula in excel:

=T.INV(0.995,5)

And we got $t_{\alpha/2}= 4.032$

And we can replace into equation (1) and we got:

$62.6 \pm 4.032\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-4.032*(5.713/SQRT(6)) = 53.196

=62.6+4.032*(5.713/SQRT(6)) = 72.004

So the 99% confidence interval for the mean would be given by (53.196;72.004)

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3 years ago

Factor the following polynomial completely.<br><br>y squared plus 5 zy plus 4 z squared<br><br>

sweet [91]

Answer:

(y + z)(y + 4z)

Step-by-step explanation:

${y}^{2} + 5zy + 4 {z}^{2} \\ = {y}^{2} + zy + 4zy + 4 {z}^{2} \\ = y(y + z) + 4z(y + z) \\ = (y + z)(y + 4z)$

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3 years ago

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Answer:

1. x = -6, -8, -90

2. solutions for $-2x\geq 10$ include -5, while -5 is not a solution for $-2x>10$

Step-by-step explanation:

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2 years ago