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guapka [62]
3 years ago
9

A function is given. h(t) = t2 + 3t; t = −1, t = 2

Mathematics
2 answers:
kicyunya [14]3 years ago
7 0

Answer:

Step-by-step explanation:

h(t)=t ^2+3t  

t= -1, t=2

(a) Net Change of the function between given values  

h(t)=t ^2+3t  

h(-1)=( -1)^2+3(-1)

       = 1+(-3)

       =-2

h(2)=( 2)^2+3(2)

       = 4+(6)

       =10

net change =h(2) - h(-1)  

                   =10 -(-2)

                    =12

b, average of change  

net change divided by the change in the x- values  

12/(2-(-1) )

12/(2+1)

12/3= 6  

Average of change =6

Arlecino [84]3 years ago
5 0

Answer:

(a) The net change of the function is 12.

(b) The average rate of change of the function 4.

Step-by-step explanation:

The average rate of change of function f(x) over the interval a\leq x\leq b is given by this expression:

average rate of change =  \frac{net \:change \:in \:y}{change \:in \:x} = \frac{f(b)-f(a)}{b-a}

It is a measure of how much the function changed per unit, on average, over that interval.

Given:

h(t)=t^2+3t\\\\t=-1\\t=2

(a) To find the net change of the function, first we calculate the values of h(2) and h(-1)

h(-1)=(-1)^2+3(-1)=-2\\\\h(2)=(2)^2+3(2)=10

The net change is simply the difference

h(2)-h(-1)=10-(-2)=12

(b) The average rate of change takes the net change and divides it by the change in the t value.

\frac{12}{2-(-1)} =\frac{12}{3}=4

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What’s the answer to 8-10?
vovangra [49]

Answer:

-2

Step-by-step explanation:

When you have equations with smaller number subtracting bigger numbers, it means that you are always going to end up with a negative answer. So if you do 10-8 it would just be 2, but if you flip it , it will be a negative so the the answer would be

8-10= -2

Hope that helped or it probaly just made you more confused lol

4 0
3 years ago
At least 96.00​% of the data in any data set lie within how many standard deviations of the​ mean? Explain how you arrived at yo
zheka24 [161]

The answer assumes that the question is about the <em>normal distribution</em>.

Answer:

96% of the data in any data set <em>normally distributed</em> is 2.05 <em>standard deviations</em> <em>above</em> and <em>below</em> the mean.

Step-by-step explanation:

The key to solving this question is having into account that exists the <em>standard normal distribution</em> that permits obtaining any probability from any normally distributed data, doing the following transformation:

\\ z = \frac{x-\mu}{\sigma}

That is, in this case, we subtract a given value <em>x</em> from the <em>population mean</em> and then divide the result by the <em>population standard deviation</em>. This is a z-score, and this value is associated with the probability for a <em>standard normal distribution</em>, with a population mean = 0 and population standard deviation = 1.

Fortunately, for the <em>standard normal distribution</em>, there is associated a ubiquitous <em>standard normal table</em> for possible values of <em>z</em> and the corresponding probability. Then, knowing that the data are <em>normally distributed</em> and having both distribution <em>parameters</em>, namely, the <em>population mean</em> and <em>population standard deviation</em>, we can consult any standard normal table to find the probabilities for any data distributed following the normal distribution.

However, even without previously know the values of the normal parameters, the standard normal distribution can tell us how many standard deviations from the mean are 96.00% of the data for every normally distributed population.

<h3>Solving the question</h3>

Having all this information at hand, we know that <em>the z-score value tells us how many standard deviations</em> <em>from the mean</em> are the data normally distributed. As a result, we can determine how many standard deviations below and above the population mean represent the 96.00% of the cases for this normal distribution consulting a <em>cumulative standard normal table from the mean</em>.

If we divide 96.00/2 = 48, that is, 0.48, we need to find the z-score for this probability consulting a <em>cumulative standard normal table from the mean</em>. The values for a z-score for that probability is z=2.05, approximately. So, since the normal distribution is also symmetrical, those values are above and below the mean, that is, z =2.05 (above) and z=-2.05(below).

Thus, 96% of the data in any data set normally distributed is 2.05 <em>standard deviations</em> <em>above</em> and <em>below</em> the mean.  

 

5 0
3 years ago
would Annabelle be able to pay off the loan with the lower montly payment in 5 years by setting aside $200 each month​
NISA [10]

Answer:

no

Step-by-step explanation:

3 0
3 years ago
Urgent!! please help )):​
alisha [4.7K]

The 16th term is: 53

Further explanation:

We have to find the general formula first

The general form is:

a_n=a_1+(n-1)d\\Given\\a_1=8\\d=3\\Putting\ the\ values\ in\ the\ formula\\a_n=8+(n-1)(3)\\a_n=8+3n-3\\a_n=5+3n\\For\ 16th\ term, put\ n=16\\a_n=5+3(16)\\a_n=5+48\\a_n=53

The 16th term is: 53

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

  • brainly.com/question/5510873
  • brainly.com/question/5461619

#LearnwithBrainly

4 0
3 years ago
Geometry math question no Guessing and Please show work
MAXImum [283]

If the point P(x, y) partitions the segment AB in the ratio 1 : 1, then the point P is midpoint of segment AB.

The formula of a midpoint of segment:

A(x_A;\ y_A),\ B(x_B,\ y_B)\\\\P_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)

We have:

A(13,\ 1)\to x_A=13,\ y_A=1\\B(-5,\ -3)\to x_B=-5,\ y_B-3\\\\P\left(\dfrac{13+(-5)}{2};\ \dfrac{1+(-3)}{2}\right)\to P\left(\dfrac{8}{2};\ \dfrac{-2}{2}\right)\to P(4,\ -1)

Answer: C. (4, -1)

3 0
3 years ago
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