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anygoal [31]
3 years ago
14

Simplify the answer as much as possible​

Mathematics
1 answer:
RSB [31]3 years ago
6 0

Answer:

f(-5)=240

g(-7)=-33

Step-by-step explanation:

1) f(x)=3x^2 - 3x

f(-5)= 3×(-5)^2 - 3×(-5) = -15^2 + 15= 225 + 15=240

2) g(x)=5x + 2

g(-7)= 5×(-7) + 2= -35+2=-33

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A square has a side of 8cm. The area of the square increases by 50%. Work out the percentage increase in the length of the side.
sertanlavr [38]
Because the side has to be increased by 50% 
you find half of 8, which is 4 and you add 8+4 because you add the increased amount
8+4=12
you then just find the area.... so 12x12= 144
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3 years ago
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yuradex [85]

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Step-by-step explanation:

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7 0
3 years ago
Find the explicit formula for the given sequence.<br> 1,5, 25, 125, ....
Lyrx [107]

Answer:

you keep multiplying by five

Step-by-step explanation:

So 1 x 5 is five, 5 x 5 is 25, 25 x 5 is 125, so on and so forth.

8 0
3 years ago
Name a pair of complementary angles and a pair of supplementary angles
makkiz [27]

Answer:

Step-by-step explanation:

m<POQ + m<SOR = 90º. This makes these two angles complementary.

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hope this helps, reach out if you have more questions!

5 0
3 years ago
A manufacturer knows that their items have a normally distributed length, with a mean of 15.4 inches, and standard deviation of
Masteriza [31]

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

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 establishes 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.

Mean of 15.4 inches, and standard deviation of 3.5 inches.

This means that \mu = 15.4, \sigma = 3.5

16 items are chosen at random

This means that n = 16, s = \frac{3.5}{\sqrt{16}} = 0.875

What is the probability that their mean length is less than 16.8 inches?

This is the p-value of Z when X = 16.8. So

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

By the Central Limit Theorem

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

Z = \frac{16.8 - 15.4}{0.875}

Z = 1.6

Z = 1.6 has a p-value of 0.9452.

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

5 0
3 years ago
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