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vovikov84 [41]
3 years ago
13

The manager of a vacation resort believes that the ages of adult visitors to the resort can be modeled by a normal distribution.

The manager surveyed a random sample of 765 visitors and recorded their age. A summary of the responses is shown in the frequency table, where x represents the age of the visitor. a) Construct a histogram of the distribution of ages. (b) Write a few sentences to describe the distribution of ages of the adult visitors to the resort.

Mathematics
1 answer:
8090 [49]3 years ago
7 0

Step-by-step explanation:

(a) A histogram is like a bar graph, but with ranges instead of values.

(b) The distribution is approximately uniform, with slightly more people at the younger and older ends than in the middle.

(c) The ages do not appear to come from a normal distribution.  Normal distributions are bell-shaped, tall in the middle and short on the sides.

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Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the end behavior.
jenyasd209 [6]
The function is f(x)=x^3-11x^2+36x-36.

To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:

f(1)=1-11+36-36, not 0

f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).

Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).

We can also try some other factors of 36. Indeed we can check that 

f(3)=27-99+108-36=135-135=0, 
and
f(6)=216-396+216-36=0.

Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.

This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).


Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6. 

The y-intercept is f(0), which is -36.


Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly, 

we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.

Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity, 

and it goes to minus infinity as x goes to - infinity.
7 0
3 years ago
Please help, due tomorrow. will give brainlist
Tatiana [17]

Step-by-step explanation:

By Remainder Theorem, f(5) = 91.

=> (5)³ - 4(5) + k = 91

=> 125 - 20 + k = 91

=> 105 + k = 91

=> k = -14.

8 0
3 years ago
three friends jogged last month. Richard jogged 9 miles last month. Jena jogged 2 times as many miles as Richard. Brian jogged 4
ANTONII [103]

Answer:

Jena=18 miles Brian=36 miles

Step-by-step explanation:

well if you add what Richard got and double it (9+9=18 or 9x2=18) you get how much Jena ran. then if u add (9+9+9+9=36 or 9x4=36) you get Brians miles he ran


8 0
3 years ago
If y varies inversely as n and m = 8 when n = 3 find m whenn =12
zepelin [54]

Answer:

24

Step-by-step explanation:

m=8x4 n=3x4 so that is the answer

6 0
2 years ago
You can do both problems if want
Agata [3.3K]
A= π r2 and v=3.14d

---Volume(v=3.14d):

3.14(15) equals 47.1

47.1 rounds to 47

nearest hundreth would be 0 that rounds to .1 or .10,which rounds to 47
v=47

---Area(π r2)

3.14(7.5)^2 is 3.14(56.25)
176.625

176.625 rounded to the nearest hundreth is 176.630.

Answer:

The area of a circle with the diameter of 15 is 176.630.
4 0
3 years ago
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