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3 years ago

Brenda can deliver 644 newspapers in 7 hours. How many newspapers can Brenda deliver in 9 hours?

Mathematics

1 answer:

Mademuasel [1]3 years ago

7 0

Answer:

828

Step-by-step explanation:

644 :7 =92 newspapers for hour

9 ×92 =828 newspapers in 9 hours

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Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

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 $1 - \alpha$ .

That 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.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So

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

$0.5 = 1.96\frac{2}{\sqrt{n}}$

$0.5\sqrt{n} = 2*1.96$

Dividing both sides by 0.5

$\sqrt{n} = 4*1.96$

$(\sqrt{n})^2 = (4*1.96)^2$

$n = 61.5$

Rounding up

We would have to take a sample of 62 to achieve this result.

8 0

3 years ago

Given the system of linear equations.

Karo-lina-s [1.5K]

Part A:

x + y = 9

4x + y = 6

To solve this system using substitution, begin by isolating either x or y in the first equation. I'll isolate x.

x + y = 9

x = 9 - y

Substitute this expression (9 - y) into the second equation for x and solve.

4x + y = 6

4(9 - y) + y = 6

36 - 4y + y = 6

36 - 3y = 6

-3y = -30

y = 10

To find x, substitute 10 for y into either of the original equations.

x + y = 9

x + 10 = 9

x = -1

Finally, check all work by substituting the x- and y-values into each original equation.

x + y = 9 --> -1 + 10 = 9 --> 9 = 9 --> True

4x + y = 6 --> 4(-1) + 10 = 6 --> -4 + 10 = 6 --> 6 = 6 --> True

The answer for Part A is x = -1 and y = 10; (-1, 10).

Part B:

For graphing, it's easier to get the equations into slope-intercept form. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To get our equations into slope-intercept form, we must simply isolate y.

x + y = 9

y = 9 - x

y = -x + 9

4x + y = 6

y = 6 - 4x

y = -4x + 6

Now that we have our slope-intercept equations, we can easily graph them, since their slopes and y-intercepts are readily visible.

Let's start with the y-intercepts. They are (0, 9) and (0, 6). You can plot those points on the graph.

Now, the slopes. The slope of the first line is -1, this means it declines. To plot this, start where you plotted the y-intercept, count one unit down, and then one unit to the right, and plot that point. Continue doing that and connect the dots, and you will have plotted the first line. The slope of the second line is -4, so it also declines. For this line, count four units down, and then one to the right and plot that point. Likewise, continue this and connect the coordinates, and you will have your line. (See attachment for graph.)

The lines do indeed intersect at (-1, 10); our answer is verified by graphing.