1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
hram777 [196]
2 years ago
11

addison and kelsey are running on a path modeled by x^2+y^2-10x-18y-378=0, where the distance is in meters. what is the maximum

distance between the runners at any given time
Mathematics
1 answer:
bulgar [2K]2 years ago
7 0

The maximum distance is the <u>diameter of the circle</u>, which is of 44 units.

The equation of a circle of <u>radius r and center</u> (x_0,y_0) is given by:

(x - x_0)^2 + (y - y_0)^2 = r^2

  • The diameter is <u>twice the radius</u>, and is the <u>maximum distance</u> between two points inside a circle.

In this problem, the circular path is modeled by:

x^2 + y^2 - 10x - 18y - 378 = 0

We complete the squares to place it in the standard format, thus:

x^2 - 10x + y^2 - 18y = 378

(x - 5)^2 + (y - 9)^2 = 378 + 25 + 81

(x - 5)^2 + (y - 9)^2 = 484

Thus, the radius is:

r^2 = 484 \rightarrow r = \sqrt{484} = 22

Then, the diameter is:

d = 2r = 2(22) = 44

The maximum distance is the <u>diameter of the circle</u>, which is of 44 units.

A similar problem is given at brainly.com/question/24992361

You might be interested in
Write your answer in simplest radical form.​
pantera1 [17]

9514 1404 393

Answer:

  √3

Step-by-step explanation:

The ratio of the short sides to the hypotenuse in an isosceles right triangle is ...

  1 : 1 : √2

This means ...

  p·√2 = √6

  p = (√6)/(√2) = √(6/2)

  p = √3

6 0
3 years ago
A 2003 study of dreaming found that out of a random sample of 106 ​people, 80 reported dreaming in color.​ However, the rate of
Vlad [161]

Answer:

Step-by-step explanation:

Hello!

You have the following experiment, a random sample of 106 people was made and they were asked if they dreamed in color. 80 persons of the sample reported dreaming in color.

The historical data from the 1940s informs that the population proportion of people that dreams in color is 0.21(usually when historical data is given unless said otherwise, is considered population information)

Your study variable is a discrete variable, you can define as:

X: Amount of people that reported dreaming in colors in a sample of 106.

Binomial criteria:

1. The number of observation of the trial is fixed (In this case n = 106)

2. Each observation in the trial is independent, this means that none of the trials will have an effect on the probability of the next trial (In this case, the fact that one person dreams in color doesn't affect or modify the probability of the next one dreaming in color)

3. The probability of success in the same from one trial to another (Or success is dreaming in color and the probability is 0.21)

So X~Bi(n;ρ)

In order to be able to run a proportion Z-test you have to apply the Central Limit Theorem to approximate the distribution of the sample proportion to normal:

^ρ ≈ N(ρ; (ρ(1-ρ))/n)

With this approximation, you can use the Z-test to run the hypothesis.

Now what the investigators want to know is if the proportion of people that dreams in color has change since the 1940s, so the hypothesis is:

H₀: ρ = 0.21

H₁: ρ ≠ 0.21

α: 0.10

The test is two-tailed,

Left critical value: Z_{\alpha/2} = Z_{0.95} = -1.64

Right critical value: Z_{1-\alpha /2} = Z_{0.95} = 1.64

If the calculated Z-value ≤ -1.64 or ≥ 1.64, the decision is to reject the null hypothesis.

If -1.64 < Z-value < 1.64, then you do not reject the null hypothesis.

The sample proportion is ^ρ= x/n = 80/106 = 0.75

Z= <u>     0.75 - 0.21    </u> = 12.83

    √[(0.75*0.25)/106]

⇒Decision: Reject the null hypothesis.

p-value < 0.00001 is less than 0.10

If you were to conduct a one-tailed upper test (H₀: ρ = 0.21 vs H₁: ρ > 0.21) with the information of this sample, at the same level 10%, the critical value would be Z_{0.90}1.28 against the 12.83 from the Z-value, the decision would be to reject the null hypothesis (meaning that the proportion of people that dreams in colors has increased.)

I hope this helps!

4 0
3 years ago
Find the product: (-8)(-6) =
larisa86 [58]

Answer:

48, since the numbers are next to each other with no sign, they need to be multiplied, and a negative times a negative is a positive

Step-by-step explanation:

hope this helps

4 0
3 years ago
Read 2 more answers
An inscribed angle in a semicircle is always
DIA [1.3K]
An inscribed angle in a semicircle is always90 degrees
5 0
3 years ago
Which term best describes a proof in which you assume the opposite of what u want to prove​
ANTONII [103]

Answer:

The Latin phrase is "reduction ad absurd um", meaning reduction to absurdity. You assume the opposite and show that logically it leads to a contradiction and therefore cannot be true.

Hope this helps.

8 0
3 years ago
Other questions:
  • Peter has 18 oranges, 27 pears, and 12 bananas. He wants t o make fruit baskets with the same number of each fruit in each baske
    14·2 answers
  • mary says then pen for her horse is a acute right angle. is this possible? explain clearly and explain everthing
    12·1 answer
  • Which expression represents the product of 83 and x
    7·2 answers
  • Which of the binomials below is a factor of this trinomial x^2+4x+4
    14·1 answer
  • HELP PICTURE IS SHOWN
    5·1 answer
  • The temperature is -2 if the temperature rises by 15 what is the new temperature​
    13·1 answer
  • What multiplication fact could you use to find a number that can be divided equally by 8 and 9
    7·2 answers
  • I want to take a trip to California. I need to choose if I want to fly, drive, or take a train. Once I am there, I can stay at a
    9·1 answer
  • Select all ratios equivalent to 20:18.<br> 3:2<br> 18:9<br> 30:27
    15·1 answer
  • 6sacks of potatoes weigh 122.4 kg and 4 sacks of onions weigh 50 kg. What is the total amount of 1 sack of potatoes and 1 sack o
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!