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3 years ago

F(x) = 5x and g(x) = x + 11.

Mathematics

2 answers:

aleksklad [387]3 years ago

5 0

Answer:

$5x^2 + 55x$

Step-by-step explanation:

Let's review f(x)g(x) simply means you multiply both functions together.

So,

(5x)(x+11)

5x * x = 5x^2

5x * 11 = 55x

Hence, the answer is $5x^2 + 55x$

ratelena [41]3 years ago

3 0

Answer:

Step-by-step explanation:

f(x) × g(x)

= 5x(x + 11) = 5x² + 55x, thus

h(x) = 5x² + 55x → C

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A Government company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The s

Fofino [41]

Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

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.

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 $s = \sqrt{\frac{p(1-p)}{n}}$

In this question, we have that:

$\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2$

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when $X = 260$ . So

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

By the Central Limit Theorem

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

$Z = \frac{260 - 270}{21.2}$

$Z = -0.47$

$Z = -0.47$ has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

5 0

3 years ago

Gumawa ng bilog na grap (pie graph) na nagpa

Goshia [24]

Answer:

huh what does this mean

Step-by-step explanation:

8 0

3 years ago

An oil tanker can be emptied by the main pump in 5 hours. An auxiliary pump can empty the tanker in 7 hours. If the main pump is

r-ruslan [8.4K]

Answer:

so the answer will be 1

Step-by-step explanation:

An oil tanker can be emptied by the main pump in 5 hours.

An auxilary pump can empty the tanker in 14 hours.

If the main pump is started at 7pm, when should the auxilary pump be started

so that the tanker is emptied by 11pm?

Let t = no. of hrs to run the Aux pump

The main pump will run 4 hr (7 - 11 pm)

Let the completed job = 1; (an empty Tanker)

The shared work equation

4%2F5 + t%2F14 = 1

Multiply equation by 70 to get rid of the equation, results:

14(4) + 5t = 70

56 + 5t = 70

5t = 70 - 56

5t = 14

t = 14%2F5

t = 2.8 hrs to run the aux pump

2.8 hr = 2 + .8(60) = 2 hrs 48 min

Subtract 2:48 from 11:00 = 8:12 PM start the aux pump

;

Check solution

4/5 + 2.8/14 =

.8 + .2 = 1

6 0

3 years ago

Ali finished his history assignment in 1/4

Lina20 [59]

Hello there!

For this you simply need to give both fractions a common denominator!

The easiest way to do this specific problem would be to make the denominator 12. Why 12? Because 4 x 3 = 12.

So:

1/4 --> ?/12 --> 1 (3) / 12 --> 3/12

2/3 --> ?/12 --> 2 (4) / 12 --> 8/12

Total amount of time means the sum (adding them together).

When adding fractions, you MUST have a common denominator! (Which is what we just did).

So 3/12 + 8/12 = (8+3) / 12 = 11/12 hours

Notice how the denominator stayed the same? When adding/subtracting fractions, the denominator stays the same! :)

Hope this helped!

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4 0

3 years ago

Mark did 2/5 of a job and Alan did 1/3 of the remainder. The fraction of the job left undone

Evgesh-ka [11]

2/5=4/10=12/30 1/3=10/30 12/30+10/30=22/30 22/30=11/15

4 0

3 years ago