Max travels to see his brother's family by car. He drives 216 miles in 4 hours.

Given the values of the linear functions f (x) and g(x) in the tables, where is (f – g)(x) positive?

alexandr402 [8]

Comparing the functions, from the tables, it is found that (f - g)(x) is positive in the interval (–∞, 9) .

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For the subtraction function, we simply subtract both functions, thus:

$(f - g)(x) = f(x) - g(x)$

It is positive if f is greater than g, that is: f(x) > g(x).
It is a linear function, so one function is greater before the equality, one after.
They are equal at x = 9.
If x < 9, f(x) > g(x), and thus, (f - g)(x) is positive, which means that the desired interval is:

(–∞, 9)

A similar problem is given at brainly.com/question/24610273

4 0

1 year ago

In 154 N38 what digit should be replaced to N to make the number divisible by 3,6 and 9?

JulsSmile [24]

Answer:

$N = 6$ so that number becomes divisible by 3, 6 and 9.

Step-by-step explanation:

In Number Theory there is a rule of thumb which states that sum of digits of a multiple of 3 equal 3 or a multiple of three. If we know that $n = 154N38$ , then its sum of digits is:

$x = 1 + 5+4+N+3+8$

$x = 21+N$ (Eq. 1)

We have to determine which digits corresponds to multiples of three, there are four digits:

N = 0

$x = 21+0$

$x = 21$ ( $3\times 7 = 21$ )

N = 3

$x = 21+3$

$x = 24$ ( $3\times 8 = 24$ )

N = 6

$x = 21+6$

$x = 27$ ( $3\times 9 = 27$ )

N = 9

$x = 21+9$

$x = 30$ ( $3\times 10 = 30$ )

We get the following four distinct options: 154038, 154338, 154638, 154938. Now we find which number is divisible by 6 and 9 by factor decomposition:

$154038 = 2\times 3\times 25673$

$154338 =2\times 3\times 29 \times 887$

$154638 = 2\times 3\times 3\times 11\times 11\times 71$

$154938 = 2\times 3\times 7\times 7\times 17\times 31$

It is quite evident that $N = 6$ so that number becomes divisible by 3, 6 and 9.

6 0

2 years ago

share one tip or suggestion on how others can represent real-life situations using rational functions

posledela

Answer:

The answer is below

Step-by-step explanation:

There are various tips or suggestions on how others can represent real-life situations using rational functions, one of them is the application of a work problem formula.

By using the work problem formula, one can measure the time it will take different people working at different speeds to complete the work. With the formula w =r*t. Where w = work done, r = rate of work donee, and t = time

7 0

2 years ago

Solve the equation for x.

anzhelika [568]

32x+64 = 160
32x = 96
x = 3

8 0

2 years ago

Read 2 more answers

A 12 ounce bottle of beer contains 355 mL. The Random Brewing Company programs its machinery so that the amount of beer in a bot

erica [24]

Answer:

a) 79.67% probability that a randomly selected bottle has at least 355 ml

b) 99.29% probability that the bottles of a randomly selected 6-pack of beer have an average of at least 355 ml.

c) 88.88% probability that the total amount of beer in the 6-pack is less than 2131.5 ml

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 $s = \frac{\sigma}{\sqrt{n}}$ .