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3 years ago

Which proportion would you use to solve the following problem?

2 answers:

6 0

1 cm : 5km
4 cm : 5 x 4 km
4 cm : 20 km

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Answer: The city is 20km apart.
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alex41 [277]3 years ago

4 0

Answer:

1 cm : 5km

4 cm : 5 x 4 km

4 cm : 20 km

Answer: The city is 20km apart.

Step-by-step explanation:

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The perimeter of a rectangle must be less than 156 feet. If the length is known to be 66 feet, find the range of possible widths

balu736 [363]

x = perimeter

x<156

length = 66

so, in order to calculate perimeter you need to add two lengths and two widths

156 (perimeter) - 2 (66) = two widths

156 - 132 = 24 (remember this number is two widths added together)

so 24 twice the width SO 12 would be the number that the width can't be larger than

the width has to be less than 12

w < 12

5 0

3 years ago

in a given classroom the number of girls is 10 greater than number of boys if the ratio of the number of girls to the number of

Xelga [282]

Answer:

a) 35, b) 25, c) 60

Step-by-step explanation:

The number of girls is 10 more than the number of boys, so it's a good thing to choose a variable to represent the number of boys.

Number of boys: b

Number of girls: b + 10

Ratio of girls:boys is 7:5, so

$\frac{b+10}{b}=\frac{7}{5}$

"Cross multiply" to get

$7b=5(b+10)\\7b=5b+50\\2b=50\\b=25$

There are 25 boys. There are 10 more girls, so the number of girls is 35, and the total number of students is 60.

That's a packed classroom!

8 0

3 years ago

If the number of professors in a college is P and the number of students is S, and there are 19 times as many students as profes

morpeh [17]

Answer:

$S =19P\\S-19P = 0$

Step-by-step explanation:

We are given the following in the question:

Let P be the number of professor and S be the student in a college.

According to the question:

There are 19 times as many students as professors.

We have to write an equation to show the given relationship between professors and students.

$S =19P\\S-19P = 0$

The above situation is the situation that represents the given relationship.

5 0

3 years ago

At a specific point on a highway, vehicles arrive according to a Poisson process. Vehicles are counted in 12 second intervals, a

morpeh [17]

Answer: a) 4.6798, and b) 19.8%.

Step-by-step explanation:

Since we have given that

P(n) = $\dfrac{15}{120}=0.125$

As we know the poisson process, we get that

$P(n)=\dfrac{(\lambda t)^n\times e^{-\lambda t}}{n!}\\\\P(n=0)=0.125=\dfrac{(\lambda \times 14)^0\times e^{-14\lambda}}{0!}\\\\0.125=e^{-14\lambda}\\\\\ln 0.125=-14\lambda\\\\-2.079=-14\lambda\\\\\lambda=\dfrac{2.079}{14}\\\\0.1485=\lambda$

So, for exactly one car would be

P(n=1) is given by

$=\dfrac{(0.1485\times 14)^1\times e^{-0.1485\times 14}}{1!}\\\\=0.2599$

Hence, our required probability is 0.2599.

a. Approximate the number of these intervals in which exactly one car arrives

Number of these intervals in which exactly one car arrives is given by

$0.2599\times 18=4.6798$

We will find the traffic flow q such that

$P(0)=e^{\frac{-qt}{3600}}\\\\0.125=e^{\frac{-18q}{3600}}\\\\0.125=e^{-0.005q}\\\\\ln 0.125=-0.005q\\\\-2.079=-0.005q\\\\q=\dfrac{-2.079}{-0.005}=415.88\ veh/hr$

b. Estimate the percentage of time headways that will be 14 seconds or greater.

so, it becomes,

$P(h\geq 14)=e^{\frac{-qt}{3600}}\\\\P(h\geq 14)=e^{\frac{-415.88\times 14}{3600}}\\\\P(h\geq 14)=0.198\\\\P(h\geq 14)=19.8\%$

Hence, a) 4.6798, and b) 19.8%.

7 0

4 years ago

X+6 /3 = 2+x-2/5

olasank [31]

We can treat this problem like you regularly subtract fractions. First find the common denominator, which is 15.

So:

5(x+6)/15 = 30/15 + 3(x-2)/15

(5x+6)/15 - (30/15) - (3x - 6)/15

As you already know the answer, I'm assuming you can do the rest.

Hope this helps!

3 0

3 years ago