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Sophie [7]
2 years ago
7

A 12-yard-long pipe is cut into three equal sections. Two of the resulting sections are cut in half, and one of the halves is cu

t into thirds. If two pipe sections are chosen and combined end to end, what is the difference between the longest possible and shortest possible combinations? (Note: 1 yard = 3 feet)
Mathematics
1 answer:
valentinak56 [21]2 years ago
3 0

Answer:

14ft

Step-by-step explanation:

12 yard pipe equals 36ft. Divided equally 3 times gives 3 pipes at 12ft per pipe. 2 of those are divided in half, making 4 6ft pipes. 1 of the 6ft pipes is cut into 3 2ft pipes. you now have 3 pipes at 2ft, 3 pipes at 6ft and 1 pipe at 12ft. the longest 2 pieces are 12ft and 6ft making 18ft. 2 shoetest pieces equal 4ft. 18ft minus 4ft equals 14ft.

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A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample
suter [353]

Answer:

The expected frequency for the cell E2,2 is = 33

Step-by-step explanation:

The given data is

Gender               | 0-30| 30-60| 60-90| 90+       Totals

Male                    | 23    |    35   |   76    |  46        180

<u> Female               |   31   |    42   |   46    |  16         135    </u>

<u>Totals                    54         77        122    62          315  </u>

<u />

The expected frequency for the cell E2,2 is :

Expected for the (30-60 box for females)   =  Total of (30-6)/ (total )* females

                                                                      = ( 77/315)135= 33

Here p= 77/315 and n= 135

therefor X= pn = 33

χ²=  (33-42)²/33= 2.455  ( for the single value of E2,2=33)

Expected for the (30-60 box for males)   =  Total of (30-6)/ (total )* males

                                                                      = ( 77/315)180= 44

χ²=  (44-42)²/44= 0.09

The critical region is  χ² (0.05) 3 ≥  χ²= 11.34

Let the null and alternate hypothesis be

H0:the number of minutes spent online per day is not related to gender

against

Ha: the number of minutes spent online per day is related to gender

The single value of χ² for E2,2 = 2.45 is less than the critical value of 11.34.  

6 0
3 years ago
Anyone please help:&lt;
insens350 [35]

Answer:

y= 4x^2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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
Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio. A (-5, 12) B (11, 0)
zhenek [66]

Answer:

(7, 3)

Step-by-step explanation:

Using the midpoint formula

M(X, Y) = {(ax1+bx2/a+b), ay1+by2/a+b}

X = ax1+bx2/a+b

X = -5(1)+3(11)/1+3

X = -5+33/4

X = 28/4

X = 7

Y = ay1+by2/a+b

Y = 1(12)+3(0)/1+3

Y = 12/4

Y = 3

Hence the coordinate of P is at (7, 3)

7 0
3 years ago
Find the missing value <br> 3/8 +1/?=5/8<br> 3/4-1/?=1/4<br> ?/6 + 1/8= 23/24
steposvetlana [31]
1st one : is 1/4 ( subtract 3/8 from both sides and simplify 5/8 - 3/8 to 1/4. )

2nd one : is 1/2 ( subtract 3/4 from both sides, simplify 1/4 - 3/4 to 1/-2, and then multiply both sides by -1 )

3rd one : is 5/6 ( subtract 1/8 from both sides and simplify 23/24 - 1/8 to 5/6).
6 0
3 years ago
Read 2 more answers
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