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Ad libitum [116K]

3 years ago

12

Zach solved this problem. Maria had a spool of ribbon 68 inches long. She cut the ribbon into 8 equal-length pieces. How long wa

s each piece of ribbon? Zach said the answer was 0.85 inches. Is Zach's answer reasonable

2 answers:

VLD [36.1K]3 years ago

8 0

8 times 8.5 (or 8 1/2) is 68 so 8.5 would be the answer

Tom [10]3 years ago

4 0

<span> No, because 64 ÷ 8 = 8 and 72 ÷ 8 = 9, so the answer should be between 8 and 9.</span>

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A painter can paint 180 square feet in 1/2 an hour. How many square feet can the painter paint in 1 1/2 hours? (UNIT RATES QUEST

nirvana33 [79]

Well 1/2 is one quarter of 2 hours. so if he can paint 180 square feet is 1/2 hour multiply it by four to get 2 hours. so 180 times 4 is 720.
He can paint 720 square feet in 2 hours

3 0

3 years ago

The number of requests for assistance received by a towing service is a Poisson process with rate θ = 4 per hour.a. Compute the

aliya0001 [1]

Answer:

a) 9.93% probability that exactly ten requests are received during a particular 2-hour period

b) 13.53% probability that they do not miss any calls for assistance

c) 2

Step-by-step explanation:

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 time interval.

Poisson process with rate θ = 4 per hour.

This means that $\mu = 4n$ , in which n is the number of hours.

a. Compute the probability that exactly ten requests are received during a particular 2-hour period.

n = 2, so $\mu = 4*2 = 8$

This is P(X = 10). So

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

$P(X = 10) = \frac{e^{-8}*8^{10}}{(10)!} = 0.0993$

9.93% probability that exactly ten requests are received during a particular 2-hour period

b. If the operators of the towing service take a 30-min break for lunch, what is the probability that they do not miss any calls for assistance?

n = 0.5, so $\mu = 4*0.5 = 2$

This is P(X = 0). So

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

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

13.53% probability that they do not miss any calls for assistance

c. How many calls would you expect during their break?

n = 0.5, so $\mu = 4*0.5 = 2$

4 0

3 years ago

Which rule describes the translation below ? In the picture

rewona [7]

The translation rule which describes the given translation is $\fbox{\begin\\\math{(x,y)}\rightarrow(x+5,y-3)\\\end{minispace}}$ .

Further explanation:

Translation is defined as the shifting of the curve in which each point on the curve is shifted in such a way that the shape and size of the curve remains unchanged but the position of each point is changed by a fixed distance.

In the given figure there are two right angle triangle as $S'T'U'$ and $STU$ .

The coordinates of the right angle triangle $S'T'U'$ are $(-4,2),(-4,-2)$ and $(-1,-2)$ and the coordinates of the right angle triangle $STU$ are $(1,5),(1,1)$ and $(4,1)$ .

Consider that the triangle $STU$ is obtained after the translation of each point on the triangle $S'T'U'$ .

The coordinate of the point $S'$ in triangle $S'T'U'$ is $(-4,2)$ .

Step 1:

Use the translation $(x,y)\rightarrow(x-5,y-3)$ for the point $S'$ .

$\fbox{\begin\\\(-4,2)\rightarrow(-4-5,2-3)=(-9,-1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x-5,y-3)$ the coordinate of the point $S$ is $(-9,-1)$ , but in the given figure the coordinate of the point $S$ is $(1,5)$ .

So, the translation $(x,y)\rightarrow(x-5,y-3)$ is incorrect.

Step 2:

Use the translation $(x,y)\rightarrow(x-3,y-5)$ for the point $S'$ .

$\fbox{\begin\\\(-4,2)\rightarrow(-4-3,2-5)=(-7,-3)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x-3,y-5)$ the coordinate of the point $S$ is $(-7,-3)$ , but in the given figure the coordinate of the point $S$ is $(1,5)$ .

So, the translation $(x,y)\rightarrow(x-3,y-5)$ is incorrect.

Step 3:

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point $S'$ .

$\fbox{\begin\\\(-4,2)\rightarrow(-4+5,2+3)=(1,5)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $S$ is $(1,5)$ which is correct as the coordinate for the point $S$ given in the figure is $(1,5)$ .

Step 4:

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point $T'$ .

$\fbox{\begin\\\(-4,-2)\rightarrow(-4+5,-2+3)=(1,1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $T$ is $(1,1)$ which is correct as the coordinate for the point $T$ given in the figure is $(1,1)$ .

Step 5:

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point U’.

$\fbox{\begin\\\ (-1,-2)\rightarrow(-1+5,-2+3)=(4,1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $T$ is $(4,1)$ which is correct as the coordinate for the point $U$ given in the figure is $(4,1)$ .

As per the above calculation it is concluded that the translation $(x,y)\rightarrow(x+5,y+3)$ is correct for the shifting of each point on the triangle $S'T'U'$ to each point on the triangle $STU$ .

The translation of each point on the triangle $S'T'U'$ is shown in the image attached below.

Therefore, the correct translation rule for the shifting of the triangle $S'T'U'$ to the triangle $STU$ is $\fbox{\begin\\\math{(x,y)}\rightarrow(x+5,y-3)\\\end{minispace}}$

Learn more:

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: Translation, shifting, graph, geometry, coordinate geometry, coordinates, shifting of graph, triangle, right angle triangle, movement of curve, shifting of curve, translation of curve.

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3 years ago

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Find the GCF. 18x 3 and 30x 5 A. 6x 5 B. 90x 3 C. 6x 3 D. 90x 5

muminat

<span>GCF. 18x^3 and 30x^5 = 6x^3

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3 years ago

3 1/2+ 4 5/6 in simpleast form

Shtirlitz [24]

Answer:

23 is the answer.

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