George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 9 feet per second. Paula takes 50 seconds to run a lap of the track. George and Paula pass each other after 14 seconds.
After running for 4 minutes, how far east of his starting point is George?
Answers
Answer:
George is 43.20 ft East of his starting point.
Step-by-step explanation:
Let Paula's speed be x ft/s
George's speed = 9 ft/s
Note that speed = (distance)/(time)
Distance = (speed) × (time)
George takes 50 s to run a lap of the track at a speed of y ft/s
Meaning that the length of the circular track = y × 50 = 50y ft
George and Paula meet 14 seconds after the start of the run.
Distance covered by George in 14 seconds = 9 × 14 = 126 ft
Distance covered by Paula in 14 seconds = y × 14 = 14y ft
But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track
That is,
126 + 14y = 50y
50y - 14y = 126
36y = 126
y = (126/36) = 3.5 ft/s.
Hence, Paula's speed = 3.5 ft/s
Length of the circular track = 50y = 50 × 3.5 = 175 ft
So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of
9 × 240 = 2160 ft.
2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.
Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft
So, 60 ft along a circular track subtends an angle θ at the centre of the circle.
Length of an arc = (θ/360°) × 2πr
2πr = total length of the circular track = 175
r = (175/2π) = 27.85 ft
Length of an arc = (θ/360) × 2πr
60 = (θ/360°) × 175
(θ/360°) = (60/175) = 0.343
θ = 0.343 × 360° = 123.45°
The image of this incomplete lap is shown in the attached image,
The distance of George from his starting point along the centre of the circular track = (r + a)
But, a can be obtained using trigonometric relations.
Cos 56.55° = (a/r) = (a/27.85)
a = 27.85 cos 56.55° = 15.35 ft
r + a = 27.85 + 15.35 = 43.20 ft.
Hence, George is 43.20 ft East of his starting point.
Hope this Helps!!!
Related Questions
What’s the correct answer for this question?
Answers
Answer:
C.
Step-by-step explanation:
Central angle = 360-52=308°
In radians
308° = 308π/180
Now
S = r∅
S = 3×308π/180
S = 924π /180
S = 77π/15 in.
Answer:
answer is 13π/15
Step-by-step explanation:
correct answer is 13π/15.
Write down the definition of a random sample.
Answers
Answer:
Step-by-step explanation:
Random sampling is a procedure for sampling from a population in which (a) the selection of a sample unit is based on chance and (b) every element of the population has a known, non-zero probability of being selected.
Answer:
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
I hope this helped...
What Ln(z) is answer????!!
Answers
Write z in exponential form:
[tex]z=1-i=\sqrt2 e^{-i\frac\pi4}[/tex]
Then taking the logarithm, we get
[tex]\mathrm{Ln}(z)=\ln(\sqrt2) + \ln e^{-i\frac\pi4} = \boxed{\ln(\sqrt2)-\dfrac\pi4i}[/tex]
so a is the correct answer.
theo started to solve the quadratic equation (x+2)2 - 9 = -5
Answers
Answer:2x−5=−5
Add 5
to both sides of the equation.
2x=−5+5
Add −5
and 5
.
2x=0
Divide each term by 2
and simplify.
Divide each term in 2x=0
by 2
.
2x2=02
Cancel the common factor of 2
.
Cancel the common factor.
2
x2=02
Step-by-step explanation:
Apply the distributive property.
x⋅2+2⋅2−9=−5
Move 2
to the left of x
.
2⋅x+2⋅2−9=−5
Multiply 2
by 2
.
2x+4−9=−5
Subtract 9
from 4
.
A driver and a passenger are in a car accident. Each of them independently has probability 0.3 of being hospitalized. When a hospitalization occurs, the loss is uniformly distributed on [0, 1]. When two hospitalizations occur, the losses are independent. Calculate the expected number of people in the car who are hospitalized, given that the total loss due to hospitalizations from the accident is less than 1.
Answers
Answer:
0.534
Step-by-step explanation:
p(0 losses) = 0.7² = 0.49
p(1 loss) = 2 x 0.3 x 0.7 = 0.42
p(2 losses) = 0.09
This is a conditional probability problem. If the number of people hospitalized is 0 or 1, then the total loss will be less than 1. However, if two people are hospitalized, the probability that the total loss will be less than 1 is 0.5. we need to exclude the 50% x 0.09 chance of a double loss costing more than 1. So
P(Cost < 1)
= 0.49 + 0.42 +0.045
= 0.955
P(0 losses | Cost < 1)
= P(0 losses and Cost < 1) / P(Cost < 1)
= 0.49 / 0.955 = 0.513
P(1 loss | Cost < 1)
= 0.42 / 0.955 = 0.440
P(2 losses | Cost < 1) = 0.045 / 0.955 = 0.047
Now take the expectation:
E[X] = (0)(0.513) + (1)(0.440) + (2)(0.047)
= 0.440 + 0.094
= 0.534
Mario’s Restaurant is planning to tile the floor of their outdoor dining area, represented by the composite figure below. The tile costs $1.50 per square foot. How much should the restaurant plan to spend on tile to complete the job?
Answers
Answer:
Cost of tiling the floor of the restaurant = $346.5
Step-by-step explanation:
Since Mario's restaurant is in the shape of a composite figure.
Area of the composite figure = Area of the rectangle + Area of trapezoid
Area of the rectangle = 3 × 9
= 27 square feet
Area of the trapezoid = [tex]\frac{1}{2}(b_{1}+b_{2}).h[/tex]
Here [tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the parallel sides of the trapezoid and 'h' is the distance between these sides.
Area of the trapezoid = [tex]\frac{1}{2}[12+(31-9)]\times 12[/tex]
= 17 × 12
= 204 square feet
Total area of the floor = 27 + 204
= 231 square feet
Cost of the tiles = $1.5 per square feet
Total Cost of tiling the floor of Mario's restaurant will be,
= per square feet cost × Area of the floor
= 1.50 × 231
= $346.5
Answer:
THE ANSWER IS .B 346.50
Step-by-step explanation:
linear function for f(-11)=5, slope of f= -2/3
Answers
Answer:
f(x) = -2/3(x +11) +5
Step-by-step explanation:
The point-slope form of the equation of a line will give you the desired linear function:
y = m(x -h) +k . . . . . for slope m through point (h, k)
You are give point (x, f(x)) = (-11, 5) = (h, k), and you are given slope m = -2/3. Putting these values into the function form gives ...
f(x) = -2/3(x +11) +5
Thw sum of 12x^2+9x^2
Answers
Answer:
21 x^2
Step-by-step explanation:
12x^2+9x^2
Combine like terms
x^2(12+9)
x^2(21)
21 x^2
An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 4 novels, 6 plays, 8 poetry books, and 4 nonfiction books. Step 1 of 2 : If she wants to include no more than 3 poetry books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.
Answers
Answer:
the number of possible reading schedules is 1.064301638 × 10¹²
Step-by-step explanation:
Given that :
The English teacher needs to pick 10 books to put on her reading list for the next school year.
If the English teacher picks at most 3 poetry books i.e no more than 3 poetry books from 8 books. and other books are picked from (6+4+4 ) = 14 books
Thus; the number of ways to pick the books are :
[tex]\left[\begin{array}{c}8\\0\\ \end{array}\right] \ \left[\begin{array}{c}14\\10\\ \end{array}\right]+ \left[\begin{array}{c}8\\1\\ \end{array}\right] \left[\begin{array}{c}14\\9\\ \end{array}\right] + \left[\begin{array}{c}8\\2\\ \end{array}\right] \left[\begin{array}{c}14\\8\\ \end{array}\right] + \left[\begin{array}{c}8\\3\\ \end{array}\right] \left[\begin{array}{c}14\\7 \\ \end{array}\right][/tex]
[tex]= [ \dfrac{8!}{0!(8-0)!}* \dfrac{14!}{10!(14-10!)} ] + [ \dfrac{8!}{1!(8-1)!}* \dfrac{14!}{9!(14-9)!}]+ [ \dfrac{8!}{2!(8-2)!}* \dfrac{14!}{8!(14-8)!}] + [ \dfrac{8!}{3!(8-3)!}* \dfrac{14!}{7!(14-7)!}][/tex]
[tex]= [ 1*1001]+[8*2002]+[28*3003]+[56*3432][/tex]
[tex]\mathbf{= 293293}[/tex]
However, to determine how many reading schedules that are possible we use the relation:
Number of ways to pick a book × [tex]^{10}P_{10}[/tex]
[tex]= 293293* \dfrac{10!}{(10-10)!}[/tex]
= 293293 × 10!
= 1.064301638 × 10¹²
Thus , the number of possible reading schedules is 1.064301638 × 10¹²
figure ABCD is a parallelogram what is the perimeter of ABCD
Answers
Help asap giving branlist!!
Answers
Answer: Thr amount spent to manufacture each radio.
Step-by-step explanation: I put two and two together...lol...plz brainlest.
Answer:
The amount spent to manufacture each radio.
Step-by-step explanation:
125 is the start up cost and each radio costs 5.25 to make.
Quadrilateral BCDE is a kite. What is BF?
B
20
С
12
E
F
D
Answers
Answer:
32
Step-by-step explanation:
if u do pythagoras, sq root of 20^2-12^2=16
16x2=32
Find the volume of the cone.
Please help
Answers
Answer:1232m^3
Step-by-step explanation:
1/3 *22/7*7^2*24
1232m^3
Identify the domain of the function shown in the graph.
A
B
C
D
Answers
Answer:
D. x is all real numbers
Step-by-step explanation:
The graph only goes from -11 to +11 in the horizontal direction, but that domain is not a choice. Apparently, we're to assume the graph extends to infinity both to the left and the right.
The domain is the horizontal extent of the function, so is ...
x is all real numbers
Please answer number 3 I will give brainliest thank you!
Answers
Answer:
Skewed to right
Step-by-step explanation:
there is no explanation, it just is, just like how 1+1 is 2
Brainleist! as you promised!
Answer:
Yeah no skewed right, like the guy said.
These items are taken from the financial statements of Sean McCann, CPA for 2019. Sean McCann, capital 1/1/19 $106,000 Sean McCann, Drawing 10,000 Equipment 130,000 Accumulated depreciation (equip) 32,000 Accounts payable 10,600 Cash 33,800 Supplies 7,000 Salaries payable 6,000 Fees earned 136,000 Salaries expense 66,000 Rent expense 14,200 Supplies expense 1,600 Depreciation expense 4,000 Utilities expense 2,400 Accounts receivable 28,000 Mortgage payable (due 12/31/35) 6,400 Instructions: 1. Prepare the journal entries to close your temporary accounts. (Hint: The temporary accounts are revenues, expenses and the drawing account) Date Description Debit Credit 2. Prepare an income statement and a statement of owner’s equity for the year ended December 31, 2019 and a classified balance sheet as of December 31, 2019. Sean McCann, CPA Income Statement For year ended 12/30/19 Sean McCann, CPA Statement of Owner’s Equity For Period Ended 12/31/19 Sean McCann, CPA Balance Sheet For Period Ended 12/30/19
Answers
Answer:
1. Prepare the journal entries to close your temporary accounts.
the journal entries required to close the temporary accounts are:
December 31, 2019, closing of temporary revenue accounts
Dr Fees earned 136,000
Cr Income summary 136,000
December 31, 2019, closing of temporary expense accounts
Dr Income summary 88,200
Cr Salaries expense 66,000
Cr Rent expense 14,200
Cr Supplies expense 1,600
Cr Depreciation expense 4,000
Cr Utilities expense 2,400
December 31, 2019, closing of temporary income summary account
Dr Income summary 88,200
Cr Retained earnings 88,200
December 31, 2019, closing of drawings account
Dr Retained earnings 10,000
Cr Sean McCann, Drawing 10,000
2. Prepare an income statement and a statement of owner’s equity for the year ended December 31, 2019 and a classified balance sheet as of December 31, 2019.
Sean McCann, CPA
Income Statement
For the Year Ended December 31, 2019
Fees earned $136,000
Salaries expense ($66,000)
Rent expense ($14,200)
Supplies expense ($1,600)
Depreciation expense ($4,000)
Utilities expense ($2,400)
Net income $47,800
retained earnings = net income - drawings = $47,800 - $10,000 = $37,800
Sean McCann, CPA
Balance Sheet
For the Year Ended December 31, 2019
Assets
Current assets:
Cash $33,800
Accounts receivable $28,000
Supplies $7,000
Total current assets $68,800
Non-current assets:
Equipment $130,000
Accumulated dep. (equip)-$32,000
Total non-current assets $98,000
Total assets $166,800
Liabilities and equity
Current liabilities:
Accounts payable $10,600
Salaries payable $6,000
Total current liabilities $16,600
Long term liabilities:
Mortgage payable $6,400
Total long term liabilities: $6,400
Equity
Sean McCann, capital $106,000
Retained earnings $37,800
Total equity $143,800
Total liabilities and equity $166,800
Sean McCann, CPA
Statement of Owner’s Equity
For the Year Ended December 31, 2019
Sean McCann, capital 1/1/19 $106,000
Net income $47,800
Subtotal $153,800
Drawings during the year -$10,000
Sean McCann, capital 1/1/19 $143,800
A toy manufacturer wants to know how many new toys children buy each year. Assume a previous study found the standard deviation to be 1.8. She thinks the mean is 5.8 toys per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.12 at the 80% level of confidence
Answers
Answer:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]
So the answer for this case would be n=369 rounded up to the nearest integer
Step-by-step explanation:
We know the following info given:
[tex] \sigma = 1.8[/tex] represent the standard deviation
[tex]\mu = 5.8[/tex] the true mean that she believes
[tex] ME = 0.12[/tex] represent the margin of error
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =+0.12 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 80% of confidence interval now can be founded using the normal distribution the significance level would be 20% and the critical value [tex]z_{\alpha/2}=1.28[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.28(1.8)}{0.12})^2 =368.64 \approx 369[/tex]
So the answer for this case would be n=369 rounded up to the nearest integer
8b-ab=7a, .subtracted from 3a-9ab+b
Answers
Answer: You can't. Read explanation.
Step-by-step explanation:
You can't subtract an expression from an equation. If you said something like subtract 8b-ab+7a from 3a-9ab+b that would work, but not here.
Let's just assume You mean it as 8b-ab-7a, then (3a-9ab+b)-(8b-ab-7a) = -8ab + 10a - 7b.
Hope that helped,
-sirswagger21
on solving x/2 +5/3=_1/2 we get x=
Answers
Step-by-step explanation:
I hope it's correct... Hope this is what you want
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answers
Answer:
y = [tex]\frac{1}{2}[/tex]x - 5
Step-by-step explanation:
Use rise over run to find the slope, which will get you 1/2 as the slope
The y-intercept is at (0, -5) so put -5 in the equation
Answer: y= 1/2x + -5
Step-by-step explanation: slope is 1/2 because the line is going up one and over 2 (rise over run), the y intercept is -5 because that is where the line hits on the y axis
Formula to find the number of subsets of a set that has "n" number of elements. 2 raise 1)to the nth power 2)n squared 3)2 times n 4)All of these
Answers
Answer:
(A)[tex]2^n[/tex]
Step-by-step explanation:
Given a set with "n" number of elements, the collection of all subsets of the set is referred to as the Power set of the given set.
To find the number of possible subsets of any set, we use the formula: [tex]2^n[/tex]
Take for example the set: A={2,3,4)
A has 3 elements, therefore n=3
The number of possible subsets of A is: [tex]2^3=8$ subsets[/tex]
Please answer this correctly
Answers
Answer:
Set the height of the bar to 5
Step-by-step explanation:
Since there are 5 quantities between 20-29, So set the height up to 5
Distance between (-6,8) and (-3,9)
Answers
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
substitute
[tex]d = \sqrt{((-3) - (-6))^2 + ((9)-(8))^2}[/tex]
[tex]\sqrt{10}[/tex]
IWhat is the equation of a line that passes through the points (3, 6) and (8, 4)?
Answers
Answer:
[tex] (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)[/tex]
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{4-6}{8-3}= -\frac{2}{5}[/tex]
And for this case we can use the first point to find the intercept like this:
[tex] 6 = -\frac{2}{5}(3) +b[/tex]
And solving we got:
[tex] b = 6 +\frac{6}{5}= \frac{36}{5}[/tex]
And then the line equation would be given by:
[tex] y = -\frac{2}{5}x +\frac{36}{5}[/tex]
Step-by-step explanation:
For this case we have the following two points given:
[tex] (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)[/tex]
And for this case we want an equation for a line with the two points given by:
[tex] y = mx+b[/tex]
Wher m is the slope and b the y intercept. We can find the slope with this formula:
[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{4-6}{8-3}= -\frac{2}{5}[/tex]
And for this case we can use the first point to find the intercept like this:
[tex] 6 = -\frac{2}{5}(3) +b[/tex]
And solving we got:
[tex] b = 6 +\frac{6}{5}= \frac{36}{5}[/tex]
And then the line equation would be given by:
[tex] y = -\frac{2}{5}x +\frac{36}{5}[/tex]
The probability of randomly selecting a white flower from a garden that has green, pink, yellow, and white flowers is 6%.
Which of the following describes the likelihood of selecting a white flower?
A.
likely
B.
unlikely
C.
neither unlikely nor likely
Answers
Answer:
b. unlikely
Step-by-step explanation:
I don't really know a step by step explanation :( sry
When estimating the minimum sample size for proportion, it is indicated to keep a 50/50 split between the probabilities of success (p) and failure (q), even if we know from previous studies where the split has been in the past.
a.True
b. False .
c. That's a tricky
Answers
Answer:
b) False
Explanation:
It is not needed to keep 50/50 split.
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The p-value is
Answers
What is the value of the trig ratio cos x ? Help ASAP
Answers
Answer:
14/50 or 7/25
Step-by-step explanation:
cos x = adj/hyp
adj = 14
hyp = 50
---------
you ca learn more about trig
sin x = opp/hyp
tan x = opp/adj
The value of the trigonometric ratio, cos x in a right angle triangle XYZ is [tex]\dfrac{14}{50}[/tex].
Trigonometric ratios – The relation between the angles and the sides of a right-angle triangle is called Trigonometric ratios.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given figure a right-angle triangle XYZ we know that
ZY is the length of the perpendicular. XY is the base of the triangle and ZX is the hypotenuse.
By trigonometric ratio, we know that
[tex]Cos \Theta = \dfrac{adjacent}{hypotenuse}[/tex]
Where [tex]\Theta[/tex] is the acute angle between the base and the Hypotenuse
On substituting value,
[tex]Cos \Theta = \dfrac{14}{50}[/tex]
The value of the trigonometric ratio, cos x in a right angle triangle XYZ [tex]\dfrac{14}{50}[/tex].
Learn more about Trigonometric ratios here:
https://brainly.com/question/25122825
#SPJ2
Which of the following is the solution to 1 x1 +9 $7?
A XS -2
B. All values are solutions
C. 3-2 and 2-16
D. No solution
Answers
Answer:
d. no solution
Explanation:
Step 1 - Subtract nine from both sides of the equation
[tex]|x| + 9 \leqslant 7 \\ |x| + 9 - 9 \leqslant 7 - 9 \\ |x| \leqslant - 2[/tex]
Step 2 - Remove the absolute value
[tex] |x| \leqslant - 2 \\ 2 \leqslant x \leqslant - 2 \\ 2 \leqslant - 2[/tex]
Therefore, since positive two is not less than or equal to negative two, there is no solution.
Vlad tried to solve an equation step by step.
-8p 14 = 42
-8p = 28 step 1
p= -3.5 step 2
Find Vlad's mistake.
Choose 1 answer:
A)Step 1
B)Step 2
C)Vlad did not make a mistake
Answers
Answer:
C
Step-by-step explanation:
-8 14 = 42 (He subtracted 14 from 42)
-8p = 28 (Which is how he got 28)
p = -3.5 (He took 28 divide by -8 which got him -3.5)
Answer:
C
Step-by-step explanation:
C