(x + 2)(x2 + 5x + + 1)

Sam wants to buy 8 pencils and 6 pens, which cost a total of $8.50. He realizes he doesn't have enough cash and instead takes on

lukranit [14]

The base equation is: 8x + 6y = 8.50. (x is pencils and y is pens)

We also know that 4x + 4y = 5.00. Let's solve this equation for y.

4x+4y = 5.00

4y = 5.00 - 4x

y = 5.00 - 4x /4

Plug this into the base equation.....

8x + 6 x 5-4x /4 = 8.50

8x + 3x 5-4x /2 = 8.50 (Reduce the fraction by dividing the numerator and denominator by 2)

8x + 3x5-3x4x /2 = 8.50 (multiply the values)

8x = 15-12x /2 = 8.50

2x8x + 2 x 15-12x /2 = 2x8.50 (multiply both equation sides by 2)

2x8x+15-12x=2x8.50 (reduce the fraction by dividing the numerator and denominator by 2)

16x + 15 - 12x = 2x8.50

4x + 15 = 2 x 8.50 (Calculate the difference)

4x + 15 = 2 x 85/10 (write the value as a fraction)

4x + 15 = 2x17/2 (reduce the fraction by diving the N and D by 5)

4x + 15 = 17 (reduce the fraction by diving the N and D by 2)

4x = 17 - 15 (rearrange the values)

4x = 2 (calculate the difference)

x= 2/4 (divide both equation sides by 4)

x = 2/4 (write as a fraction)

x= 1/2 (reduce the fraction by dividing the N and D by 2)

x = 0.5 (alternate decimal form) = in simple terms of cost is 50 cents

Plug that into either one of the equations to get y, which is .75 or 75 cents

8(.50) + 6y = 8.50

4.00 + 6y = 8.50

6y = 4.50

y = .75

OR

4(.50) + 4y = 5.00

2.00 + 4y = 5.00

4y = 3.00

y = .75

I'll take a chocolate bar as compensation, please. And you're welcome. :-)

3 0

3 years ago

HELP ME PLZ. I NEED THIS DONE TONIGHT.

Alekssandra [29.7K]

Answer:

7

Step-by-step explanation:

3 0

3 years ago

Under ideal conditions a certain bacteria population is known to double every four hours. Suppose that there are initially 50 ba

san4es73 [151]

Answer:

(b) a = 50 * 2^(t/4)

(c) 951

Step-by-step explanation:

After t hours

a = 50 * 2^(t/4)

After 17 hours

a = 50 * 2^(17/4)

a = 50 * 2^(4.25)

Use calculator

a = 951.3656920022

Rounded

a = 951

3 0

3 years ago

A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat

zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5$

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

$Z = \frac{X - \mu}{s}$

X = 205

$Z = \frac{X - \mu}{s}$

$Z = \frac{205 - 200}{5}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 195

$Z = \frac{X - \mu}{s}$

$Z = \frac{195 - 200}{5}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

$Z = \frac{X - \mu}{s}$

$Z = \frac{210 - 200}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

X = 195

$Z = \frac{X - \mu}{s}$

$Z = \frac{190 - 200}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0

3 years ago

What is the formula for the sum of an infinite geometric series

algol13

An infinite geometric series is the sum of an infinite geometric sequence . This series would have no last term. The general form of the infinite geometric series is a1+a1r+a1r2+a1r3+... , where a1 is the first term and r is the common ratio. We can find the sum of all finite geometric series.

3 0

3 years ago