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Yuki888 [10]
3 years ago
8

Please help with this I am completely stuck on it

Mathematics
1 answer:
vaieri [72.5K]3 years ago
7 0

Answer:

f(x)=\sqrt[3]{x-4} , g(x)=6x^{2}\textrm{ or }f(x)=\sqrt[3]{x},g(x)=6x^{2} -4

Step-by-step explanation:

Given:

The function, H(x)=\sqrt[3]{6x^{2}-4}

Solution 1:

Let f(x)=\sqrt[3]{x}

If f(g(x))=H(x)=\sqrt[3]{6x^{2}-4}, then,

\sqrt[3]{g(x)} =\sqrt[3]{6x^{2}-4}\\g(x)=6x^{2}-4

Solution 2:

Let f(x)=\sqrt[3]{x-4}. Then,

f(g(x))=H(x)=\sqrt[3]{6x^{2}-4}\\\sqrt[3]{g(x)-4}=\sqrt[3]{6x^{2}-4} \\g(x)-4=6x^{2}-4\\g(x)=6x^{2}

Similarly, there can be many solutions.

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A thermometer shows a temperature of Negative 20 and three-fourths degrees. A chemist recorded this temperature in her notebook
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Answer:

The answer is C.

Step-by-step explanation:

3/4 is equal to 0.75. If you combine 0.75 with -20, then it is 20.75.

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3 years ago
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Among freshman at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 10
lina2011 [118]

Answer:

a) 6.68th percentile

b) 617.5 points

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

\mu = 550, \sigma = 100

a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.

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

Z = \frac{400 - 550}{100}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

So this student is in the 6.68th percentile.

b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.

He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.

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

0.675 = \frac{X - 550}{100}

X - 550 = 0.675*100

X = 617.5

6 0
3 years ago
HELP ME PLS stock worth $60 a share dropped in value by 20% on Monday. Then it dropped again by 10$ the next Tuesday. And finall
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Step-by-step explanation:

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Which team has the best winning percentage?
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Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20-%20%20%5Cfrac%7B2%7D%7B9%7D%20%29%28x%20%2B%20%20%5Cfrac%7B1%7D%7B2%7
Aleonysh [2.5K]
f(x) = (x -  \dfrac{2}{9} )(x +  \dfrac{1}{2} )

\text {When } f(x) = 0 :

(x -  \dfrac{2}{9} )(x +  \dfrac{1}{2} ) = 0

(x -  \dfrac{2}{9} ) = 0  \text { or }  (x +  \dfrac{1}{2} ) = 0

x =  \dfrac{2}{9}  \text { or } x =  -\dfrac{1}{2}

3 0
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