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Step2247 [10]
3 years ago
15

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or par

allel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

Mathematics
1 answer:
Aleks [24]3 years ago
6 0
The equation of the line segment through A and B is given as
-7x + 3y = -21.5

In standard form,
3y = 7x - 21.5
  y = (7/3)x - 7.1667
Line AB has a slope of 7/3.

Let the equation of line segment PQ be
y = mx + b

Because line segments AB and PQ are perpendicular, therefore
(7/3)*m = -1
m = -3/7

The equation of PQ is 
y = -(3/7)x + b
To find b, note that the line passes through the point (7,6). Therefore
6 = -(3/7)*7 + b
6 = -3 + b
b = 9
The equation of PQ is
y = - (3/7)x + 9
or
7y = -3x + 63
3x + 7y = 63

Answer: 3x + 7y = 63

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A certain flight arrives on time 8484 percent of the time. Suppose 143143 flights are randomly selected. Use the normal approxim
Troyanec [42]

Answer:

a) P(x=108)=0.0020

b) P(x≥108)=0.9980

c) P(x<124)=0.7794

d) P(124≤x≤128)=0.1925

Step-by-step explanation:

We know the population proportion, that is p=0.84.

We take a sample of size n=143.

We will use the normal approximation to the binomial distribution to model this problem.

The mean and standard deviation of the normal approximation to the binomial distribution will be:

\mu=np=143*0.84=120.12\\\\\sigma=\sqrt{np(1-p)}=\sqrt{143*0.84*0.16}=\sqrt{19.22}=4.38

a) We have to calculate the probability that exactly 108 flights are on time.

As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.

In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):

P(x=108)=P(107.5

b) Now we have to calculate that at least 108 flights are on time.

As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:

P(x\geq108)=P(x>107.5)=P(z>-2.88)=0.9980

c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.

P(x

d) We have to calculate the probability that between 124 and 128 flights, inclusive, are on time.

This interval corresponds to the probability P(123.5<x<128.5)

P(123.5

5 0
3 years ago
The sum of two numbers is 46 and the difference is 10 . What are the numbers?
EastWind [94]

Answer: 28 and 18


Step-by-step explanation:

I used the guess and test strategy to find that:

28 - 10 = 18

28 + 18 = 46

6 0
3 years ago
a room in a form of a cuboid has a length of 5cm, height 8cm and breadth 0.07m. if one person can occupy a volume of 14cm3(cube)
Over [174]

Answer:

20 people

Step-by-step explanation:

The volume of a cuboid is equal to length * breadth * height.

First, we want to figure out the values relative to each other. Everything is in centimeters except the breadth, which is 0.07m. To convert meters to centimeters, we can multiply by 100: 0.07 * 100 = 7, so the breadth is 7cm.

Next, the volume is  length * breadth * height = 5cm * 7cm * 8cm = 280cm³. Each person occupies 14cm³. To find how many people can occupy the cube, we can divide the volume by the space each person takes, so

280cm³/14cm³ = 20 people

Note that we can divide because each person takes x amount of space, and the total space, z, can be represented by x * y = z, with y representing the amount of people, because we add x space for each person. Dividing both sides by x, we get y = z/x

5 0
3 years ago
Send help for this question!!!
neonofarm [45]

Answer:

m is greater than or equal to -9 the inequality sign flips when u divide by negative number

7 0
3 years ago
Read 2 more answers
Find, corrrect to the nearest degree, the three angles of the triangle with the given vertices. D(0,1,1), E(-2,4,3), C(1,2,-1)
Sholpan [36]

Answer:

The three angles of the triangle given above are 23, 73 and 84 correct to the nearest degree. The concept of dot product under vectors was applied in solving this problem. The three positions forming the triangle were taken as positions vectors. The Dot product also known as scalar product is a very good way of finding the angle between two vectors. ( in this case the sides of the triangle given above). Below is a picture of the step by step procedure of the solution.

Step-by-step explanation:

The first thing to do is to treat the given positions in space as position vectors which gives us room to perform vector manipulations on them. Next we calculate the magnitude of the position vector which is the square root of the sun of the square of the positions of the vectors along the three respective axes). Then we calculate the dot product. After this is calculated the angle can then be found easily using formula for the dot product.

Thank you for reading this and I hope it is helpful to you.

4 0
3 years ago
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