To indirectly measure the distance across a river, Sebastian stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Sebastian draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
Answers
Sebastian uses the method of similar triangles to find the distance across the river, and the distance across the river is 372 foot.
What is a Triangle?A triangle is a polygon with three sides and three vertices.
The triangle's total number of angles comes to 180°.
The distances between the formed the sight-lines are;
RB = 210 feet
OC = 275 feet
The distance between the point close to the river and the next point further from the river = 115 feet
In triangles ΔPRB and ΔPOC,
we have;
∠PRE = ∠POC = 90°
Given;
∠PER ≅ ∠PCO
By corresponding angle formed between two parallel lines and a common transversal.
Using angle-angle similarity theorem;
∴ ΔPRE is similar to ΔPOC Which gives;
PR / PO = RE / OC
Let x represent the distance across the river,
we have;
PR = x
PO = 115 + x
Which gives;
x / (115+x) = 210 / 275
275x = 210 × (115 + x)
275x = 24150 + 210x
275x - 210x = 24150
65x = 24150
x = 371. 54
Therefore, the distance across the river is 372 foot.
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Related Questions
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student chosen randomly from the class has a cat or a dog?
Has a cat Does not have a cat
Has a dog 9 2
Does not have a dog 4 5
Answers
Answer:
0 students have a cat and 92 students have a dog
The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
The class has a cat and a dog = 9
Has a dog and does not have a cat = 2
Does not have a dog and has a cat = 4
Does not have dog and cat = 5
The total strength of the class is 20
The probability that a student is chosen randomly from the class has a cat or a dog = Number of favorable outcomes / total number of outcomes
P(E) = 15 /20
Hence, The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.
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2 1/4 yd x 1/4 yd
stuck, please help
Answers
Answer:
9/16 yd^2
Step-by-step explanation:
2 1/4 as an improper fraction is 9/4, 9/4 * 1/4 = 9/16, and since you are multiplying two yards, thats yard^2, so 9/16 yd^2
A toy manufacturer wants to know how many new toys children buy each year. A sample of 305 children was taken to study their purchasing habits. Construct the 80% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 7.6. Assume that the population standard deviation is 1.5. Round your answers to one decimal place.
Answers
Answer:
The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.1 = 0.9[/tex], so Z = 1.28.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.28\frac{1.5}{\sqrt{305}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 7.6 - 0.1 = 7.5
The upper end of the interval is the sample mean added to M. So it is 7.6 + 0.1 = 7.7
The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.
Luis solved the following equation below: - x ^ 2 + 10x - 21 = y Line Line Line 1x = (- (10) plus/minus sqrt((10) ^ 2 - 4(- 1) * (- 21)))/(2(- 1)) 2x = (- 10 plus/minus sqrt(100 - 84))/- 2 3x = (- 10 plus/minus sqrt(16))/- 2 Line 4 x= -10 pm sqrt 4 -2 5x = (- 10 plus/minus 2)/- 2 Linedx = (- 10 + 2)/- 2 x = (- 10 - 2)/- 2 x = - 8/- 2 x = - 12/- 2 Line Line 7 Line 8 x = 4 x = 6 Did Luis solve the above function properly ? Justify why or why not and be specific (use the line numbers as reference
Answers
Answer:
Sorry try using the math tool.... it looks like a square root sign with a x inside of it! :)
[tex]\sqrt{x}[/tex] <-- pretty much like this one and is at the bottom of your brainly tab :)
It makes things clearer when it comes to these sort of things and eliminates things like, " plus/minus, sqrt, Linedx, 2 Line Line 7 Line 8x = 4x =6
Hope this helps :)
Step-by-step explanation:
Answer:
x = 7, x = 3Steps:
-x²+10x-21 = 0
x = (-10±√(10²-4×(-1)×(-21)))/2×(-1)
x = (-10±√(100-84))/-2
x = (-10±√16)/-2
x = (-10±4)/-2
x = (-10-4)/-2 , x = (-10+4)/-2
x = -14/-2 , x = -6/-2
x = 7 , x = 3
Luis did not solve the equation properly!
A nurse administers 25 milligrams of a drug to a patient. The amount of the drug, A, in milligrams, left in the patient after thours can be modeled by the function A(t) = 25e 0.354
How many hours will it take for the amount of the drug left in the patient to drop to 0.25 milligrams? Round your answer to the nearest tenth of an hour.
hours
Pls helppp
Answers
Answer:
heyy guyss how r u all I'm Aditya from. India I've changed my server to Ireland is this Ireland
Step-by-step explanation:
and plss guyss fo llo w me
the graph shows the height y, in feet, of a balloon that is launched from a platform 13.5 feet high, as a quadratic function of x, the time in seconds. What is the domain of this function in this situation?
Answers
Answer:
B) 0<=x<=54
Step-by-step explanation:
The domain of the function is,
0 ≤ x ≤ 54.
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
Given:
The graph is given in the attached image.
The graph shows the height y, in feet, of a balloon that is launched from a platform 13.5 feet high, as a quadratic function of x, the time in seconds.
The domain of the function is those value where the function is defined.
The domain of the function is,
0 ≤ x ≤ 54.
Therefore, 0 ≤ x ≤ 54 is the domain.
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Lesson 18: Exponentials Unit Test Algebra 1 B Unit 5: Exponentials
What is the value of the function? f(x)=(−2)3(3)0(4)−2
−3/2
0
−3/4
−1/2
Simplify the expression (45y5y744y9)2
This is a 17 question test those are the first 2 please try and find all 17 you have the title first to give all 17 will get brainlist
Answers
Answer:
search mo po sa goggle
Answer:
id k the first one
Simplify the expression (45y5y744y9)2 =
90[tex]y^{758}[/tex]
Aziza has a triangle with two sides measuring 11 in. and 15 in. She claims that the third side can be any length as long as
it is greater than 4 in. Which statement about Aziza's claim is correct?
O Aziza's claim is not correct. The third side must be between 4 in. and 26 in.
O Aziza's claim is not correct. The third side can be any length less than 26 in.
O Aziza's claim is not correct. The third side can be any length.
O Aziza's claim is not correct. The third side must create a scalene triangle.
Answers
The 4th one? i think im not sure tho
Step-by-step explanation: The correct answer is A: O Aziza's claim is not correct. The third side must be between 4 in. and 26 in.
help me please i’ll give you brainliest
Answers
Answer:
He should have canceled x
AB is the mindset of the trapezoid. Find the value of X.
Answers
Answer:
AB has a bad mindset :(
X is valued a lot bc he helps out AB
My question... please answer asap
Answers
Answer:
slope=1/4
y-intercept=3
y=.25x+3
Step-by-step explanation:
slope=rise over run so
slope=1/4
y-intercept is the value of y where the line crosses the y axis..
y-intercept=3
In y=mx+b form m is slope and b is y-intercept so...
y=.25x+3
Please help I will give brainlist thanks
Answers
Answer:
still need help?
Step-by-step explanation:
damon buyd a rose bush priced at $10. if the sales tax ix 10% how much tax will damon pay
Answers
Answer:
Before Tax Price: $10.00
Sale Tax: 10.00% or $1.00
After Tax Price: $11.00
please heart or brainlyiest
Please help I need it soon
Answers
Answer:
[tex](3 \times 12) + (3 \times 3 \times 0.5)[/tex]
Step-by-step explanation:
answer is 40.5 . please like my answer and brainliest me HSHSSHSHS
A gardener made a scale drawing of a lawn with a scale
factor of 1:4. The dimensions of her drawing are 15 inches
long by 10 inches wide. Her partner plans to make another
scale drawing of the lawn, but with a scale factor of 1:20.
What are the dimensions of her scale drawing?
A. The length is 3 inches and the width is 2 inches.
B. The length is 50 inches and the width is 75 inches.
O c. The length is 2 inches and the width is 3 inches.
O D. The length is 75 inches and the width is 50 inches.
Answers
Answer: A.
Step-by-step explanation:
I just took the exam
can i get brainlyiest?
Help a brother out pls
I have a f because of this assignment pls help
Answers
Answer:
error: "I was a newly caged animal that rushed about"
correction: "I was like a newly caged animal that rushed about"
This is hard please help
Answers
Answer:
SA = 208 in²
Step-by-step explanation:
SA = 2(2)(7) + 2(2)(10) + 2(10)(7) = 208 in²
Answer:
208 in^2
Step-by-step explanation:
SA: 2(w · l + h · l + h · w) formula
SA: 2(2 · 7 + 10 · 7 + 10 · 2) plug the numbers in- w: width, l: length, h: height
SA: 2(14 + 70 + 20) find area of 3 sides with different areas
SA: 28 + 140 + 40 doubling
SA: 208 final answer
A computer generates a two-digit number random number. It can be any number from 00 to 99.
Find the probability that it is 99
Answers
Answer:
1/99
Step-by-step explanation:
total is 99 and there is only one 99 between 0-99 so the probability is 1/99
Study each equation, then solve.
18) 5 + r = 6 - r
Answers
Answer:
5+r=6-r
-5 -5
r=1-r
+r +r
2r=1
÷2 ÷2
r=1/2
Please help will give brainliest
Answers
Answer:
Should be 70 since <B is also 70
Step-by-step explanation:
Going by the diagram, you just read the value of x. The value of y requires a little bit of calculation. x=70 degree
Step-by-step explanation: Step One
Find x
You just read the value.
x is the same as the 70 degree angle. That comes about from parallel lines.
x = 70 degrees. <<<< answer
Step Two
Find y
All triangles have 180 degrees.
So ABC has 180 degrees.
70 + 50 + <ACB = 180 Combine like terms
120 + <ACB = 180 Subtract 120 from both sides
<ACB = 180 - 120
<ACB = 60
y = <ACB
y = 60 degrees. <<<< Answer.
hoped this helped :)
I don’t get this I need help if you get it right I will mark you as brainlest
Answers
Answer:
Step-by-step explanation:
2. Rosa made a mosaic wall mural using 15 black tiles, 60 blue tiles, and 25 red tiles. Write a percent to represent the number of red tiles that were used in the mural.
Answers
9514 1404 393
Answer:
25%
Step-by-step explanation:
The ratio of red tiles to all tiles is ...
25/(15 +60 +25) = 25/100 = 25%
25% of the tiles were red tiles.
_____
Additional comment
It is often useful to think of the % symbol as being equivalent to /100, and vice versa.
Complete the sentence.
9 is 36% of
Answers
Answer:
3.24
Step-by-step explanation:
9 takes up 3.24 of 36%
Answer:
9 is 36% of 25
Step-by-step explanation:
36%×x=9
36/100×x=9
x=9×100/36
x=25
You pick a card at random.
2 3 4 5
6 7 8 9
What is P(5)
Write your answer as a percentage.
Answers
Step-by-step explanation:
There are a total of 8 cards, you are picking only one card,
therefore P(5) =
[tex] \frac{1}{8} \times 100 \\ = \frac{100}{8} \\ = 12.5percent[/tex]
56. The zip code of a location consists of five digits chosen from the set Z shown below.
Z= {0, 1, 2, 3, 4, 5, 6, 7, 8,9}
The set L represents the digits in the zip code for Key Largo.
L = {3,3,0,3,7)
The set K represents the digits in the zip code for Killarney.
K= {3,4,7,4,0}
How many odd numbers are in the set "(L UK)?
Answers
Answer:
2 I.e 3 and 7
Step-by-step explanation:
(L U K)={0,3,4,7} [ elements are not repeated in set ]
odd numbers = 3 & 7
Of the population of all fruit flies we wish to give a 90% confidence interval for the fraction which possess a gene which gives immunity to fungal infections. To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene. Give the margin of error for the 90% confidence interval. Round your answer to 3 decimal
Answers
Answer:
The margin of error for the 90% confidence interval is of 0.038.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene.
This means that [tex]n = 400, \pi = \frac{280}{400} = 0.7[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Give the margin of error for the 90% confidence interval.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.645\sqrt{\frac{0.7*0.3}{400}}[/tex]
[tex]M = 0.038[/tex]
The margin of error for the 90% confidence interval is of 0.038.
Isaac's finish 7 heavy cleans every 5 minutes Ryan finish heavy 8 clean every 4 minutes how many more cleans did Isaac complete than
Ryan
Answers
Answer:
12 more cleans
Step-by-step explanation:
You need to make each person have done work the same amount of time that is a multiple of 4 and 5. The closest is 20. So multiply 5 to 8 cleans for Ryan and 4 to 7 cleans for Issac. 40 cleans for Ryan - 28 cleans for Issac = 12 more cleans for RYAN, not Issac.
Find the x and y intercept of this equation: -2x + 8y =4 write your solutions as a point in the form (x,y)
Answers
Answer:
8y=4
Step-by-step explanation:
Trigonometric ratios can be used with any type of triangle.
O
True
O
False
Answers
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Line u has a slope of Line v is parallel to line u. What is the slope of line v? v יל Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
I have no idea what the answer is because I am in 6th grade but good luck
Step-by-step explanation:
I don't know