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3 years ago

5x + 38 ≤ 4(2 – 5x)?

Mathematics

2 answers:

kherson [118]3 years ago

3 0

False, that is not greater than

damaskus [11]3 years ago

3 0

Answer:

The value of x should be less than or equal to -6/5 or -1.2

In interval notation: (-∞,-6/5)

Step-by-step explanation:

Consider the provided inequality.

$5x + 38 \leq 4(2 - 5x)$

We need to solve the inequity for x.

$5x + 38 \leq 8-20x$

Subtract 38 from both sides.

$5x+38-38\le \:8-20x-38$

$5x\le \:-20x-30$

Add 20x to the both sides.

$5x+20x\le \:-20x-30+20x$

$25x\le \:-30$

Divide both sides by 25.

$\frac{25x}{25}\le \frac{-30}{25}$

$x\le \:-\frac{6}{5}$ or $x\le \:-1.2$

Hence, the value of x should be less than or equal to -6/5 or -1.2

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X2 - 8x + 15 = 0<br> quadratic formula

ivanzaharov [21]

The quadratic formula is x=(-b+-sqrt(b^2-4(a)(c)))/2a

Using the quadratic formula, we get:

x=(-(-8)+-sqrt((-8)^2-4(15)(1)))/2(1)

x=(8+-sqrt(64-60))/2

x=(8+-sqrt(4))/2

x=(8+-2)/2

x=10/2 and x=6/2

x=5 and x=3

We could do it way faster by completing the square:

x^2-8x+15=0

(x-5)(x-3)=0

x=5 and x=3

Hope both methods make sense! BTW, the +- thing means add or subtract

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igor_vitrenko [27]

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3 years ago

How do I find domain?

attashe74 [19]

Find the domain by finding where the expression is defined.

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4 years ago

When a snake hatched 4 years ago, it was only 5 inches long. Suppose it is now 3 foot 9 inches long. Given that the annual perce

chubhunter [2.5K]

The most important thing here is converting the length into the same units. So:

3 feet 9 inches = 45 inches

now, we know that compound 'growth' can be worked out by multiplying the initial value by the decimal to the power of the years. So, relating to this question, the equation would be:

5 x α⁴ = 45

Now, we have to solve for α!

α⁴ = 45/5
α⁴ = 9
α = ⁴√9
α = 1.732050808

This is the increase every year written as a decimal so, if we want to work out the pure percentage, we have to subtract 1 and then multiply by 100:

1.732050808 - 1 = 0.732050808
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Rounded to 2 decimal places the answer would be 73.21% !

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3 years ago

The body temperatures of adults are normally distributed with a mean of 98.6degrees° F and a standard deviation of 0.60degrees°

Schach [20]

Answer:

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples can be 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$