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devlian [24]
3 years ago
11

Dr. Tucker and his research team are interested in how aggression changes as we age. The team will recruit 100 3-year-old childr

en and assess their levels of aggression every three years until the participants turn 21. This is an example of cross-sectional research. True or false?
Mathematics
1 answer:
Rzqust [24]3 years ago
7 0

Answer:

False

Step-by-step explanation:

A cross sectional research examines changes between different population in a specific period of time. In this case the investigation of Dr. Tucker, is a longitudinal research. This research analyses changes in the same population in different periods of time which can provide data of changes of behavior of children over the time.

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If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.
Pie
Given that f^{(n)}(0)=(n+1)!, we have for f(x) the Taylor series expansion about 0 as

f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n

Replace n+1 with n, so that the series is equivalent to

f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}

and notice that

\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}

Recall that for |x|, we have

\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}

which means

f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}
\implies f(x)=\dfrac1{(1-x)^2}
5 0
3 years ago
Martin throws a ball straight up in the air. the equation h(t) = -16t^2 + 40t + 5 gives the height of the ball, in feet, t secon
Lisa [10]

Answer:

2.62 seconds

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> he height of the ball, in feet

we have

h(t)=-16t^2+40t+5

we know that

When the ball hits the ground, the height is equal to zero

so

-16t^2+40t+5=0

The formula to solve a quadratic equation of the form

at^{2} +bt+c=0

is equal to

t=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^2+40t+5=0

so

a=-16\\b=40\\c=5

substitute in the formula

t=\frac{-40\pm\sqrt{40^{2}-4(-16)(5)}} {2(-16)}

t=\frac{-40\pm\sqrt{1,920}} {-32}

t=\frac{-40+\sqrt{1,920}} {-32}=-0.12\ sec

t=\frac{-40-\sqrt{1,920}} {-32}=2.62\ sec

therefore

The solution  is t=2.62 seconds

4 0
2 years ago
Cecilia simplified an expression. Her work is shown below.
Citrus2011 [14]

Answer: second step.

Step-by-step explanation:

you then have to distribute the answer not subtract 9 1/4 from 1.5

you have to do the parenthesis next

4.5/0.5=45/5=9

then

1.5*9= 13.5

then

9.25-13.5 which I think you are capable of solving

4 0
3 years ago
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NikAS [45]

1.89871747424 heres the answer

3 0
2 years ago
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14 out of 22 students in 1st period passed the math assignment. What is the ratio of the students who passed to those who did NO
arlik [135]

Answer:

14:8

Step-by-step explanation:

5 0
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