Identify the like terms.

A researcher is interested in estimating the mean blood alcohol content of people arrested for driving under the influence. Base

UNO [17]

Answer:

We need a sample size of at least 650

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this problem:

We need a sample of size at least n

n is found when $M = 0.005, \sigma = 0.065$

So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.005 = 1.96*\frac{0.065}{\sqrt{n}}$

$0.005\sqrt{n} = 1.96*0.065$

$\sqrt{n} = \frac{1.96*0.065}{0.005}$

$(\sqrt{n})^{2} = (\frac{1.96*0.065}{0.005})^{2}$

$n = 649.23$

Rounding up

We need a sample size of at least 650

7 0

3 years ago

Kyle's family bought 4 adult tickets and 2 student tickets for $52. Maria's family bought 3 adult tickets and 5 student tickets

Troyanec [42]

Adult tickets cost $10 each and student tickets cost $6 each.

Given:
Kyle's family bought 4 adult tickets and 2 student tickets for $52
Maria's family bought 3 adult tickets and 5 student tickets for 60.

Let us assign x as the adult tickets and y as the students tickets

Kyle's family: 4x + 2y = 52
Maria's family: 3x + 5y = 60

Let us find the value of x using Kyle's equation:
4x + 2y = 52
4x = 52 - 2y
x = (52 - 2y)/4
x = 13 - y/2
Substitute the value of x in Maria's equation to find y.
3x + 5y = 60
3(13 - y/2) + 5y = 60
39 - 3y/2 + 5y = 60
- 3y/2 + 5y = 60 - 39
- 3y/2 + 5y = 21
2(-3y/2 + 5y) = 2(21)
-3y + 10y = 42
7y = 42
7y/7 = 42/7
y = 6

x = 13 - y/2
x = 13 - 6/2
x = 13 - 3
x = 10

To check:
Kyle's Family Maria's Family
4x + 2y = 52 3x + 5y = 60
4(10) + 2(6) = 52 3(10) + 5(6) = 60
40 + 12 = 52 30 + 30 = 60
52 = 52 60 = 60

3 0

3 years ago

Resolver el siguiente sistema de ecuación:

snow_tiger [21]

Answer:

$x=-1\\y=4$