The ratio of the width to the length of a flower is 10:19. How long is the flower bed if it’s width is 6 feet?

1 answer:

6 0

Just set up an equation comparing the two ratios and solve for the length, in this case x.

(10/19)=(6/x)
19/10=x/6
114/10=x

Answer= 11.4 feet for the length of the flower

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1/(x+1) - 1/(x+2) = 1/2

katen-ka-za [31]

Please include the instructions; I assume your job is to find the value of x.

1/(x+1) - 1/(x+2) = 1/2 would better be written as

1 1 1
-------- - ------------ = ----
x+1 x+2 2

Identify the LCD. It is (x+1)(x+2)(2). Mult. all 3 terms of the equation by this LCD:

2(x+2) - 2(x+1) = 2(x+1)(x+2)

We can factor out the 2 from all terms:

x+2 - x - 1 = x^2 + 3x + 2

Let's move all terms from the left to the right side:

0 = x^2 + 3x + 2 - x - 2 + x + 1

Then x^2 + 3x + 1 = 0. This is a quadratic with a=1, b=3 and c=1.

What is x?

-3 plus or minus sqrt( 9-4(1)(1) ) -3 plus or minus sqrt(5)
x = --------------------------------------------- = ---------------------------------
2 2

I rather expected to obtain an integer value for x.

Why don't you give this problem a try yourself? Suggestion: First mult. every term by 2. This will give you:

2 2
------- - ------- = 1 and this may be slightly easier to work with. Please
x+1 x+2 give it a try: try to find x that satisfies this equation.
Important: note that x cannot equal either -1 or -2.

8 0

3 years ago

The mean number of words per minute (WPM) read by sixth graders is 97 with a standard deviation of 19 WPM. If 75 sixth graders a

andrey2020 [161]

Answer:

0.0174 = 1.74% probability that the sample mean would be greater than 101.63 WPM

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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 $s = \frac{\sigma}{\sqrt{n}}$ ;