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andrezito [222]
3 years ago
10

The weight of male Americans between the ages of 18 and 25 is normally distributed, with a mean of 160.4 lb and a standard devia

tion of 27 lb. One definition of obesity states that a person is obese if the z-score of his or her weight is greater than 2. What is the obesity threshold weight for a young adult American male? Round your answer to the nearest tenth. A. 200.9 lb B. 187.4 lb C. 173.9 lb D. 214.4 lb
Mathematics
2 answers:
torisob [31]3 years ago
6 0

you need to substitute.... then do: 160.4(mean)+2(x)*27(z)= 214.4lb

Nataliya [291]3 years ago
3 0

Answer:

Step-by-step explanation:

We know that z=\frac{x-{\mu}}{\sigma}            (1)

and also we are given that a person is obese if the z-score of his or her weight is greater than 2.

Thus, using this information we can rewrite the above equation (1),

2\geq\frac{x-160.4}{27}

Solving this equation, we have

⇒54\geq(x-160.4)

⇒54+160.4\geq x

⇒214.4\geq x

Thus,  the obesity threshold weight for a young adult American male is 214.4lb\geq x.

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Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression.
vitfil [10]

Answer:

(A) e^2

(b) e^{-3}

(c) e^2

(d) e^3

Step-by-step explanation:

We have given expression and we have to simplify the expression using exponent property

(A) (\frac{1}{e})^{-2}

So (\frac{1}{e})^{-2}=\frac{1}{e^{-2}}=e^2

(b) (\frac{e^5}{e^2})^{-1}

So (\frac{e^5}{e^2})^{-1}=(e^{3})^{-1}=e^{-3}

(c) \frac{e^5}{e^3}

So \frac{e^5}{e^3}=e^2

(d) \frac{1}{e^{-3}}=e^3

7 0
3 years ago
Passes through (1,12) and has a vertex (10,-4)
agasfer [191]

Answer: 16/81 (x-10)^2 -4

Step-by-step explanation:

To write a vertex equation with just a point and the vertex, you have to figure out the variables.

In vertex form, the equation is y = a (x-h)^2 + k

Your y is 12, x = 1, h = 10, and k = -4

Plug everything into equation

12 = a (1 - 10)^2 -4

12 = a (-9)^2 - 4

12 = 81a - 4

16 = 81a

16/81 = a

Now you know what the 'a' value is.

If you graph 16/81 (x-10)^2 -4 , you will get a point at (1,12) and a vertex of (10,-4)!

I hope this helps!

3 0
3 years ago
The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont
BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)

and its cumulative distribution function (CDF) is

\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so  A∩B = B and  

\bf P(A | B) = P(B)P(B) = (P(B))^2

We have  

\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237

hence,

\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection =  </em>

\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021

5 0
3 years ago
If the translation of (x,y)-&gt;(x-5, y+2) was applied to the triangle ABC below, what would be the coordinates for A' after the
Rainbow [258]

Answer: (-3,0)

To get this answer, we subtract 5 from the x coordinate and add 2 to the y coordinate. Point A is located at (x,y) = (2,-2) so we see that x = 2 and y = -2

Subtract 5 from the x coordinate: x-5 = 2-5 = -3. The new x coordinate is -3

Add 2 to the y coordinate: y+2 = -2+2 = 0. The new y coordinate is 0.

Therefore, using the rule (x,y) --> (x-5,y+2) has the mapping (2,-2) ---> (-3,0)

Check out the attached image.


4 0
3 years ago
Zx and Zy are supplementary angles. Zy measures 108°,
gulaghasi [49]

Answer:

72°

Step-by-step explanation:

Given

Zy = 108°

Zx = ?

We know

Zx + Zy = 180° {being supplementary angles }

Zx + 108° = 180°

Zx = 180° - 108°

Zx = 72°

Hope it will help :)

4 0
3 years ago
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