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2 years ago

2. Solve for x: 2(x - 5) = x + 3(x + 2)

Mathematics

2 answers:

MrMuchimi2 years ago

5 0

Answer:

x=-8

Step-by-step explanation:

Artist 52 [7]2 years ago

5 0

Answer:

x = -8

Step-by-step explanation:

Firstly, distrubute 2 to our parentheses (2x - 10). Now, let's add our like terms, 2x - 10 = 4x + 6 since x alone is one we add this to 3x, equaling 4x. Then we're going to move our variable and sign, 2x - 10 - 4x = 6. Alright, now combine like terms and calculate (2x - 4x), we know when we subtract two and four, it's a negative 2, -2x = 6 + 10 = 16. Now divide both sides of the equation by -2, 16 divided by -2 is -8. Therefore, x = -8, hope this helped! Have a great day!

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Bob and Joe start from the same point and walk in opposite directions. Bob walks 2 km/h faster than Joe. After 3 hours, they are

valkas [14]

Answer:

Bob = 6km/h, Joe = 4km/h

Step-by-step explanation:

Bob walked 6km/h after 3 hours = 18 km
Joe walked 4km/h after 3 hours = 12 km

Finally, their distance is 30 km.

6 0

2 years ago

Zaid and Matias, two farmers, constructed a 792 foot fence around their very large garden. Zaid agreed to construct 20% more of

likoan [24]

Answer:

$1.2x +x =792$

$2.2x =792$

And we got finally:

$x =\frac{792}{2.2}= 360 ft$

And the amount for Zaid would be 1.2*360 ft= 432ft

So then Zaid construc 432 ft and Matias 360 ft

Step-by-step explanation:

For this case we know that Zaid and Matias, two farmers, constructed a 792 foot fence around their very large garden so then the total is represented by 792 ft

We also know that Zaid agreed to construct 20% more of the fence than Matias did. Let's assume that the amount that construct by Matias was x then the amount constructed by Zaid would be 1.2 x representing 20% more than Matias and we can set up the following equation:

$1.2x +x =792$

$2.2x =792$

And we got finally:

$x =\frac{792}{2.2}= 360 ft$

And the amount for Zaid would be 1.2*360 ft= 432ft

So then Zaid construc 432 ft and Matias 360 ft

7 0

3 years ago

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$