Pythagoras and True Love
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Pythagoras is a "Mr. Lonelyhearts" columnist for a popular newspaper. He recently
received the following letters. How would you solve these lovebirds' problems?
15a6=c
c=24.4
1. Dear Pythagoras: My girlfriend Roma and I want to elope. But we have a
problem. She lives in a third-floor apartment. There is a 14-foot-wide moat
around the apartment, and Roma's window is 20 feet above the moat. If I
throw a rope up to Roma, she could slide down it and escape. How long a
rope should I buy?
Longingly, Jules
149+
142.c
796=02
Let us find the length of rope Jules will need using the pythagoras theorem .
Width of the moat ( let the moat be the base of this triangle ) = 14 foot
Distance from Roma's window to the boat ( let this be the side of the triangle where the right angle is present ) =20 feet
Then the length of rope needed ( hypotenuse ) =
= Let us name the triangle that is formed as △ ABC . Then ;
In △ ABC :
AB = the width of moat ( leg of triangle ) = 14 foot
BC = The distance from the window to the moat ( base ) = 20 feet
AC = Length of rope needed ( hypotenuse ) =
= AB ² + BC² = AC² ( according to the pythagoras theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )
= 14² + 20² = AC²
= 196 + 400 = AC²
= 596 = AC²
= 24 × 24 = AC × AC
= 24 foot = AC = length of rope needed by jules .
Therefore , Jules will need a 24 foot rope so that his girlfriend can slide down and escape from her apartment .
The following are a list of variables that will almost certainly vary across students in a large undergraduate introductory statistics course.
(a) Favorite beverage
(b) Year of birth
(c) Typing speed
(d) Handedness (e.g., left or right handed)
(e) Age
(f) Occupation
(g) Self-report of Assertiveness
For questions 1a to 1d that follow choose the variable or variables that best represent the level of measurement.
a) Which variables would typically be measured on a nominal scale of measurement?
b) Which variable would likely be measured on an interval, but not a ratio scale?c) Which two variables are most likely to be measured on a ratio scale?d) As typically measured, which variable represents at least an ordinal scale of measurement, but probably not a true interval scale?
Step-by-step explanation:
a. nominal scales
occupation
Favorite beverage
b. Interval but not ratio.
Typing speed
c. ratio scale.
age
Handedness (e.g., left or right handed)
d. Ordinal scale of measurement but not a true interval scale.
Self-report of Assertiveness
year of birth
Restless Leg Syndrome and Fibromyalgia
People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent study indicates that people with fibromyalgia are much more likely to have restless leg syndrome than people without the disease. The study indicates that, for people with fibromyalgia, the probability is 0.33 of having restless leg syndrome, while for people without fibromyalgia, the probability is 0.03. About 2% of the population has fibromyalgia. Create a tree diagram from this information and use it to find the probability that a person with restless leg syndrome has fibromyalgia.
Answer:
The probability that a person with restless leg syndrome has fibromyalgia is 0.1833.
Step-by-step explanation:
Denote the events as follows:
F = a person with fibromyalgia
R = a person having restless leg syndrome
The information provided is as follows:
P (R | F) = 0.33
P (R | F') = 0.03
P (F) = 0.02
Consider the tree diagram attached below.
Compute the probability that a person with restless leg syndrome has fibromyalgia as follows:
[tex]P(F|R)=\frac{P(R|F)P(F)}{P(R|F)P(F)+P(R|F')P(F')}\\\\=\frac{(0.33\times 0.02)}{(0.33\times 0.02)+(0.03\times 0.98)}\\\\=0.183333\\\\\approx 0.1833[/tex]
Thus, the probability that a person with restless leg syndrome has fibromyalgia is 0.1833.
Evaluate the expression
3n - x =
if n = 5 and x = 3
Answer:
12
Step-by-step explanation:
Answer:
she's a 100% correct its 12
Step-by-step explanation:
Give her brainliest!!!!!!
a spring of original length 25 cm was stretched to a new length of 28 cm when a force of 12 n was applied. what would its new length be if the applied force is doubled?
a. 31 cm
b. 35 cm
c. 50 cm
d. 45 cm
Answer:
A. 31 cm
Step-by-step explanation:
Hopefully its right :)
Store B sells a set for $27.00 and offers a 20% discount
Answer:
22.50
and you can pleasent do 22.50
Step-by-step explanation:
A building lot in a city is shaped as a 30°-60°-90° triangle, like the figure shown. The side opposite the 30° angle measures 41 feet.
a. Find the length of the side of the lot opposite the 60° angle.
Show how you know.
b. Find the length of the hypotenuse of the triangular lot.
Show how you know.
Answer: a) 71.01408311ft
b)82ft
Step-by-step explanation: Definition of 30-60-90 degree triangle, "a right triangle in which the angle measure 30-60-90 degrees. The hypotenuse is twice the shorted leg and the longer leg is square root of 3 times longer than the shorter."
a) x √3 = 41 √3 = 71.01408311
b) 2x = 2(41) = 82 ft
A survey showed that 82% of kids play video games at home. What fraction of kids play video games at home?
Answer:
8.2/10
Step-by-step explanation:
Answer:
42/50
Step-by-step explanation:
Estimate the average time spent picking one's nose in minutes per day
Answer: 2 minutes
Step-by-step explanation:
According to the book, ''Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin'', on average, everyone picks their noses for 2 minutes each day.
This figure is simply a reasonable compromise between the least and highest amount of time that people can spend picking their nose in a day as well as the assumption that everyone does it.
85 miles on 8 gallons of gas
Answer:
11.6 miles per gallon
Step-by-step explanation:
Answer:
11.6 miles per gallon
Step-by-step explanation:
just divide
Y=3x+10 slope and y intercept
Answer:
The slope is 3 and the y-intercept is 10
Step-by-step explanation:
Answer:
Slope: 3
y-intercept: ( 0 , 10)
Step-by-step explanation:
y=mx+b
y=3x+10
Hope this Helps!!!
Need answers to this geometry assignment similarity and similarity transformations
Answer:
the awnser is c then pust reset and it will give you the awnser
x+12x-13 = 0 and azo, what
is the value x+lo?
which number is the additve inverse of -5
Answer:
Additive inverses add to 0. The additive inverse of a number is the opposite of the number.
What is 5/8 divided by 1/4?
Answer: 2.5
Step-by-step explanation: If you do 5/8 divided by 1/4 in the calculator it is 2.5.
help me please i’ll give u a cookie
Answer:
the answer is B
Step-by-step explanation:
i just did this.
amanda owes $20,000 in student loans for college. The simple interest rate in 6.25% and the loan will be paid off over 6 years. Including interest how much will Jodi pay for her loan? HURRYY!! i will mark brainliest!!
Answer:
$12,500
Step-by-step explanation:
Answer:
27,500.00
Step-by-step explanation:
8 mice.
There are _ mice.
All the mice run away.
_ mice are left.
Please answer correctly
Answer:
0 because if all the mice ran away then they would be gone
4x-8 = 12
4x - 8 + 8 = 12 + 8
4x= 20
4/4x=20/4 x=
Answer:
x=5
i just got it right on my quiz
Answer:
x5
Step-by-step explanation:
can someone tell me what to write of how i found the answer please ?!
Answer:
108
Step-by-step explanation:
4−22+135−9
=−18+135−9
=117−9
=108
The Walt Disney Company, the production studio behind the Marvel Cinematic Universe, is trying to find the best release date for their new super hero movie. They are hesitating between the summer and winter holiday release, and they want to know if there is any difference between the earning potential during those seasons. The analytics division in the company examined a random sample of box-office data for movies released during the past 5 years in the USA and Canada and found that 52 out of 1258 movies with summer release date earned over 400 million dollars. They also counted that out of 545 movies released in the winter, 8 earned over 400 million dollars.
Over 4 million USD Under 4 million USD
Summer release 57 1251
Winter release 11 544
Total
1. We want to investigate whether there is a difference in the proportion of movies that eam over 400 million dollars for the two release seasons. Which hypotheses should we use?
2. Calculate the difference in the proportions of movies that eamed over 400 million dollars.
3. The paragraph below describes the set up for a randomization test, if we were to conduct a hypothesis test without using software. Fill in the blanks with a number.
We write Summer on_____cards and cards representing the movies with summer release date, and Winter on_____cards. Then, we shuffle these cards and split them into two groups one group of size_____representing the movies with box-office over 400 million dollars, and another group of size_____representing the rest of the movies. We calculate the difference in the proportions of movies that eaned over 400 million dollars during the two release seasons to get PSmmer PWinter. Finally, we build a histogram of these simulated dfterences.
Answer:
Step-by-step explanation:
Over 4 million USD Under 4 million USD Total
Summer release 57 1195 1251
Winter release 11 533 544
1)Let [tex]P_1[/tex] be the proportion of movies that earn over 400 million in summer and [tex]P_2[/tex] be the proportion of movies that earn over 400 million in winter.
Null hypothesis:[tex]H_0:P_1= P_2[/tex]
Alternate hypothesis : [tex]H_a: P_1 \neq P_2[/tex]
2)Calculate the difference in the proportions of movies that earned over 400 million dollars.
[tex]P_1=\frac{57}{1251}=0.045[/tex]
[tex]P_2=\frac{11}{544}=0.0202[/tex]
3)
[tex]P_{(Summer)}-P_{(winter)}=0.045-0.0202=0.0248[/tex]
We write Summer on 1251 cards and cards representing the movies with summer release date, and Winter on 544 cards. Then, we shuffle these cards and split them into two groups one group of size 68 representing the movies with box-office over 400 million dollars, and another group of size representing 1728 the rest of the movies.
Please Solve as Fast as You Can
The coordinates of Point A are (-1, 4). If Point A is reflected across the x-axis AND then across the y-axis, what are the coordinates of Point A now?
Answer:
(1,-4)
Step-by-step explanation:
If you reflect it over the x it would equal (-1,-4), then if you reflect it over the y it would equal (1,-4)
Solve the following equation: 7a-5=2a-15
Answer:
7a-5=2a -15
7a-2a=-15+5
5a=-10
5a/5=-10/5
a=-2
Review the graph.
Which function is represented in the graph?
y = tanx
y = cosx
y = tan-1x
y = cos-1x
Answer:
D)
Step-by-step explanation:
I used a graphing calculator and typed in every equation and D matched the graph.
The graph given in the figure represents cos^-1(x). The correct option is (D).
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The graph for the given question shows that for the given function the range and domain are as follows,
Domain = [-1, 1]
Range = [0, π]
The value of the function at 0 is π/2.
Since only the inverse of sinusoids have their range as [-1, 1] and the value of cos(x) at x = π/2 is 0. It implies that the given function is inverse of cos(x).
Hence, the given function represents inverse function of cos(x) which is cos^-1(x).
To know more about trigonometric ratio click on,
https://brainly.com/question/25122825
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Use a system of linear equations with two variables and two equations to solve.
175 students enrolled in a freshman-level chemistry class. By the end of the semester, 4 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
Answer:
35 failed and 140 passed
Step-by-step explanation:
Let p = number who passed
f = number who failed
p+f = 175
4 times the number of students passed as failed, so we need to balance this to set it equal
4f = p
Substitute this into the first equation
4r+f = 175
5f = 175
5f/5 =175/5
f = 35
Now find the number who passed
p = 4f
p = 4*35
p =140
a hill rises 10 meters over horizontal distance of 8 meters
calculate the slope
Answer:
Slope = 5/4
Step-by-step explanation:
GCF of 10 and 8 is 2, divide both values by two and have the 10 as the rise and 8 as the run.
6. The admission fee to an amusement park is $20. It
costs an additional p dollars to rent a locker to hold
your belongings. The total cost for 3 people to
enter the amusement park and each rent a locker is
$87. How much does it cost for one person to rent a
locker?
A. $9
B. $29
C. $10
D. $1
Plz help :( I need the negative if y plz show steps 6X plus 6Y equal 83/9 upper 2N
Answer:
x=8
Step-by-step explanation:
Simplifying
Combine like terms
Solving
if a part is 3 cm long how long is it in inches
Answer:
1.1811
Step-by-step explanation:
googloo will help lol it's just your search browser
hope this helps :)
Answer:
3 cm to inches is 1.1811
Step-by-step explanation:
divide the length (3) by 2.54 to get covert cm to in
Brainllist if this helped plx
HELPP ！I'm stucked at question b. can somebody help me? I'm not sure when should I change the sign thank you!
Answer:
dang
Step-by-step explanation:
that looks hard