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masya89 [10]
3 years ago
15

The vertex form of an equation is y = 3(x + 2)2 + 1. What is the standard form of the

Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0

Answer:

y=3x^2+12x+13

a=3

b=12

c=13

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A company developing a new cellular phone plan intends to market their new phone to customers who use text and social media ofte
Ber [7]

Answer:

A customer who sends 78 messages per day would be at 99.38th percentile.

Step-by-step explanation:

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.

Average of 48 texts per day with a standard deviation of 12.

This means that \mu = 48, \sigma = 12

a. A customer who sends 78 messages per day would correspond to what percentile?

The percentile is the p-value of Z when X = 78. So

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

Z = \frac{78 - 48}{12}

Z = 2.5

Z = 2.5 has a p-value of 0.9938.

0.9938*100% = 99.38%.

A customer who sends 78 messages per day would be at 99.38th percentile.

8 0
2 years ago
What are the domain and range of the function f(x)= square rootx-7+9?
FinnZ [79.3K]

Answer:

Domain: [7, ∞)

Range: [9, ∞)

Step-by-step explanation:

1) This question may be easily answered if you are aware of the shape of the graph of sq. root x, and the effect of translations to graphs.

1. x - 7 means that the original graph is translated 7 units in the positive direction of the x-axis (ie. to the right), thus the minimum value for x is also shifted from 0 to 7

2. the + 9 means that the graph is translated 9 units in the positive direction of the y-axis (ie. up), thus the minimum y-value is also shifted from 0 to 9

3. We know that the graph will continue to infinity, both in the x- and y-direction

Thus, the domain would be [7, ∞) and the range [9, ∞)

2) Another way to think about it is to ask yourself when it would make sense for the graph to exist. For this, we must consider that you cannot take the square root of a negative number.

Thus, if we have the square root of (x - 7), for what value of x would (x - 7) be negative? If x = 7:

x - 7 = 7 - 7 = 0

Therefor, any x-value less than 7 will lead to a negative answer, which wouldn't be practical. Any value equal to or greater than 7 will lead to a positive answer, thus the permissible values for x are from 7 to infinity, and so the domain is [7, ∞) (note that square brackets are used for 7 as it is included in the domain, whereas infinity is always closed with round brackets).

If we have already found the domain, then we can simply substitute the values for this into the equation to obtain the range (note that this will work for a square root function, however some functions will have turning points and in this case you must calculate the range based on the turning points as well as the minimum and maximum x-values):

if x = 7: y = sq. root (7-7) + 9

= 9

This is the minimum value for y

if we have x = ∞, then the y value will also be infinitely great, therefor the maximum y-value is also ∞. Thus, the range is [9, ∞).

These questions are much easier to solve however if you are already aware of the basic graph and the effect of dilations, translations and reflections so that you may visualise it better.

4 0
3 years ago
NEED HELP ASAP WILL GIVE BRAINLY IF CORRECT
Rama09 [41]

Answer:

I think it's the 3rd one but tell me if I'm wrong

7 0
3 years ago
Read 2 more answers
Simplify the expression: 2/3 (6e+9f-21g)
Natasha_Volkova [10]

Answer:

4e + 6f - 14g

Step-by-step explanation:

4 0
3 years ago
Pleaseeeeeeeeee help
Anna35 [415]

Answer:

the answer is 240

Step-by-step explanation:

6x10=60

60x8=480

480÷2=240

7 0
3 years ago
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