In a survey of 125 people, it was found that 60 people like chocolate ice cream, 25 people like vanilla ice cream, and 20 people like both chocolate and vanilla ice cream. Create a Venn diagram to represent this data and answer the following questions: a) How many people like only chocolate ice cream? b) How many people like only vanilla ice cream? c) How many people don't like either chocolate or vanilla ice cream? d) How many people like either chocolate ice cream or vanilla ice cream or both?

Answers

Answer 1

Answer:

To create a Venn diagram for this data, we need to represent the number of people who like chocolate ice cream, vanilla ice cream, and both.

Let's start by drawing two overlapping circles. The left circle represents chocolate ice cream, the right circle represents vanilla ice cream, and the overlapping region represents people who like both.

To find the number of people who like only chocolate ice cream (a), we subtract the number of people who like both from the total number of people who like chocolate ice cream. So, 60 - 20 = 40 people like only chocolate ice cream.

To find the number of people who like only vanilla ice cream (b), we subtract the number of people who like both from the total number of people who like vanilla ice cream. So, 25 - 20 = 5 people like only vanilla ice cream.

To find the number of people who don't like either chocolate or vanilla ice cream (c), we subtract the total number of people who like chocolate or vanilla ice cream from the total number of people surveyed. So, 125 - (60 + 25 - 20) = 60 people don't like either flavor.

To find the number of people who like either chocolate ice cream or vanilla ice cream or both (d), we add the number of people who like only chocolate ice cream, the number of people who like only vanilla ice cream, and the number of people who like both. So, 40 + 5 + 20 = 65 people like either chocolate ice cream or vanilla ice cream or both.

In summary:

a) 40 people like only chocolate ice cream.

b) 5 people like only vanilla ice cream.

c) 60 people don't like either chocolate or vanilla ice cream.

d) 65 people like either chocolate ice cream or vanilla ice cream or both.

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Answer:

Step-by-step explanation:

Check the attachment for solution

Can I get the answer for 3 4 5 6

Answers

3) x=190, <BOC=85

4) x=177, <TOU=31

5) x=61, <LOM=110

6) x=55, <DOE=117

Find the length of the curve. R(t) = 2 i + t2 j + t3 k, 0 ≤ t ≤ 1

Answers

Length of a curve is the length of its plot its curve. The length of the given curve for given range of t is: L = 1.44 units approx.

How to find the length of a curve?

If the curve has position vector p(x) for value of x ranging from x = a to x = b,

then, the curve's length is calculated as:

$L = \int_a^b ||p'(x)||dx\n$ units.

For the given case, we have:

Position vector = $R(t) = 2\hat i + t^2 \hat j + t^3 \hat k$

Its differentiation gives:

$R'(t) = 2t\hat j + 3t^2\hat k$

Its non negative magnitude is: ||R'(t)|| = $√((2t)^2 + (3t^2)^2) = t√(4+9t^2)$

Thus, as t ranges from a = 0 to b = 1, thus, length of the curve is:

$L = \int_0^1 (t√(4+9t^2))dt\n\n\text{Let v = 4+9}t^2, \text{then dv = 18tdt}\nand\nt=0\implies v = 4\nt=1 \implies v = 13\nThus,\nL = \int_4^(13)((√(v))/(18))dv = (1)/(18) [(2(v)^(3/2))/(3)]^(13)_4 \approx (38.87)/(27) \approx 1.44 \: \rm units$

Thus,

The length of the given curve for given range of t is: L = 1.44 units approx.

Learn more about length of the curve here:

brainly.com/question/4464059

curve equation is

$\n \vec{R}\left ( t \right ) = 2\hat{i}+t^(2)\hat{j} + t^(3)\hat{k}$ ,0≤ t≤ 1

now taking the differentiation

$\n{R}'t = 2t\hat{i} + 3t^(2)\hat{j}$

now taking the modulus

$\left \| {R}'(t) \right \|=$ $\sqrt{4t^(2) +9t^(4)}$

= $\sqrt{4 + 9 t^(2) } .t$

now taking the integration

length of the curve = $\n\int t\sqrt{4 + 9 t^(2)} dt\n$

now put the value v= 4 + 9t²

dv= 18 tdt

now put this value in the above equation

we get

length of the curve = $\n(1)/(18)\int √(v)dv\n$

now taking integation we get and put the value of the v

we get

= $(1)/(18)$ × $(2)/(3)$ × $(4 + 9t^(2) )^{(3)/(2) }$

= $(1)/(27) ( 4 + 9 t^(2) )^{(3)/(2) }$

now find out the length of the curve in the interval from 0 to 1.

length of the curve $= (1)/(27) (13^{(3)/(2)} -4^{(3)/(2)} )\n=(1)/(27) (13√(13) -8)$

Hence proved

CAN SOMEONE PLEASE HELP ME IVE ASKED MORE THAN 20 TIMES. A wildlife society is taking a sampling of the lengths of bluegill fish at a local lake.

If the survey resulted in the data above, the distribution of fish lengths would be best described as...
A.
symmetrical with multiple modes.
B.
symmetrical with one mode.
C.
skewed to the right.
D.
skewed to the left.