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3 years ago

assume that a 150-pound person starts a diet loses 2 pounds per week for 15 weeks . write an equation modeling this situation

Mathematics

1 answer:

boyakko [2]3 years ago

8 0

Weight = w
no. of weeks = n

w = 150 - 2n

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What is the value of x? x=

elena-s [515]

Your answer could be -3 and 10

3 0

3 years ago

A certain type of aluminum screen has, an average, one flaw in a 100-foot roll. Assume the flaw distribution approximately follo

julsineya [31]

Answer:

a) 0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.

b) 0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.

c) 0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it.

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the Binomial distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

(a) Find the probability that a 100-foor roll has at most 2 flaws.

A certain type of aluminum screen has, an average, one flaw in a 100-foot roll, which means that $\mu = 1$ . Only one roll means that the Poisson distribution is used.

This is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-1}*1^{0}}{(0)!} = 0.3679$

$P(X = 1) = \frac{e^{-1}*1^{1}}{(1)!} = 0.3679$

$P(X = 2) = \frac{e^{-1}*1^{2}}{(2)!} = 0.1839$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3679 + 0.3679 + 0.1839 = 0.9197$

0.9197 = 91.97% probability that a 100-foor roll has at most 2 flaws.

(b) Suppose that I bought 10 200-foot rolls, find the probability that there are exactly 3 rolls that have no flaws in them.

Two parts.

Probability that a single 200-foot roll has no flaw.

This is $P(X = 0)$ , Poisson(single 200-foot roll) when $\mu = \frac{200*1}{100} = 2$ . So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353$

0.1353 probability that a single 200-foot roll has no flaw.

Probability that on 10 200-foot rolls, 3 have no flaws.

Multiple 200-foot rolls means that we use the binomial distribution.

0.1353 probability that a single 200-foot roll has no flaw means that $p = 0.1353$

10 200-foot rolls means that $n = 10$

We want $P(X = 3)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{10,3}.(0.1353)^{3}.(0.8647)^{7} = 0.1074$

0.1074 = 10.74% probability that there are exactly 3 rolls that have no flaws in them.

(c) What is the probability that the 15th roll he inspected was the 3rd one that have no flaws in it.

0.1353 probability that a single 200-foot roll has no flaw means that $p = 0.1353$

2 with flaws in the first 14, which is $P(X = 2)$ when $n = 14$

The 15th has no flaw, with probability of 0.1353. So

$P = 0.1353*P(X = 2) = 0.1353*(C_{14,2}.(0.1353)^{2}.(0.8647)^{12}) = 0.1353*0.2911 = 0.0394$

0.0394 = 3.94% probability that the 15th roll he inspected was the 3rd one that have no flaws in it

3 0

3 years ago

ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴀ ʙᴀꜱᴇʙᴀʟʟ ᴡɪᴛʜ ᴀ 3 ɪɴᴄʜ ᴅɪᴀᴍᴇᴛᴇʀ.

Tems11 [23]

Answer:

As Per Provided Information

We have to use π = 3.14

Diameter of baseball is 3 inch

So, Radius of Baseball will be

Radius = Diameter/2

Radius = 3/2 inch

Radius = 1.5 inch

we have been asked to determine the surface area of given baseball .

Using Formulae 

 $\boxed {\bf \: Surface \: Area_{(Baseball)} \: = 4 \pi {r}^{2} }$ 

substituting the value and let's solve it

$\longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = 4 \times 3.14 \times {1.5}^{2} \\ \\ \\ \longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = \: 4 \times 3.14 \times 2.25 \\ \\ \\ \longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = \: 12.56 \times 2.25 \\ \\ \\ \longrightarrow\tt \:Surface \: Area_{(Baseball)} \: = \: 28.26 \: {inch}^{2}$

Therefore,

Surface Area of baseball is 28.26 sq. inch .

So, your answer is 28.26 sq.in

4 0

2 years ago

Solve. 8+2=16106. 5+4=2091. 9+6=54153. 7+5=35122. 20+3=602317. 30+1=303129. 18+4=722214. 10+5=??

Sergio [31]

answer:

505155

step-by-step explanation:

multiply, add, and subtract the first two numbers of the equation in that order to get the final number

8 + 2 = 16106: 8 x 2 = 16, 8 + 2 = 10, 8 - 2 = 6 to get the number 16106

5 + 4 = 2091: 5 x 4 = 20, 5 + 4 = 9, and 5 - 4 = 1 to get the number 2091

9 + 6 = 54153: 9 x 6 = 54, 9 + 6 = 15, and 9 - 6 = 3 to get the number 54153

7 + 5 = 35122: 7 x 5 = 35, 7 + 5 = 12, and 7 - 5 = 2 to get the number 35122

20 + 3 = 602317: 20 x 3 = 60, 20 + 3 = 23, and 20 - 3 = 17 to get the number 602317

30 + 1 = 303129: 30 x 1 = 30, 30 + 1 = 31, and 30 - 1 = 29 to get the number 303129

18 + 4 = 722214: 18 x 4 = 72, 18 + 4 = 22, and 18 - 4 = 14 to get the number 722214

10 + 5 = 505155: 10 x 5 = 50, 10 + 5 = 15, and 10 - 5 = 5 to get the number 505155

6 0

3 years ago

Omg this is too hard, which is this one?

Juli2301 [7.4K]

Hi there!
So, to start you have to convert cups into ounces.
1 cup is 8 fluid ounces, so 3 cups are 8*3 which are 24 fluid ounces.
So, if she filled x amount of 2-ounce containers, then it would be 24/2 which are 12 containers that are full.

The answer is C) 12.

Hope it helps!

5 0

2 years ago