Answer:
cosec A = [tex]\frac{17}{15}[/tex]
Step-by-step explanation:
We have,
15 cot A = 8
[tex]\implies cotA = \frac{8}{15}[/tex]
We know that,
cosec²A - cot²A = 1
⇒cosec²A = 1 + cot²A
Taking square root both sides, we get
[tex]\sqrt{cosec^2A} = \sqrt{1+cot^2A[/tex]
[tex]\implies cosec A = \sqrt{1+cot^2A}[/tex]
[tex]\implies cosec A = \sqrt{1+(\frac{8}{15})^2}[/tex]
[tex]\implies cosec A=\sqrt{1+\frac{64}{225}}=\sqrt{\frac{289}{225}}=\frac{17}{15}[/tex]
So, the value of cosec A is [tex]\frac{17}{15}[/tex].
The midpoint of AB is (3,-5).
A = (9,4)
What are the coordinates of point B?
Give your answer in the form (x,y).
Answer:
(-3, -14)
Step-by-step explanation:
the difference between 9 and 3 is 6 so subtract 6 from 3 to get negative 3. the difference between 4 and - 5 is 9 so subtract 9 from -5
a line with a slope of 10 passes through the point 0,2. what is the equation in slope intercept form
Answer:
y=10x+2
Step-by-step explanation:
y-y1=m(x-x1)
y-2=10(x-0)
y-2=10(x)
y-2=10x
y=10x+2
Write a two column proof.
Step-by-step explanation:
AC ≅ EF, given
AB ≅ ED, given
∠C ≅ ∠F, right angles are congruent
ΔABC ≅ ΔEDF, SSA congruence
BC ≅ DF, corresponding parts of congruent triangles are congruent
If g (x) = StartFraction x + 1 Over x minus 2 EndFraction and h(x) = 4 – x, what is the value of (g circle h) (negative 3)?
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Given that [tex]g(x) = \frac{x + 1}{x - 2}[/tex] and h(x) = 4 - x
Now, if y = f(x) and y = g(x) then the composite function (f∘g)(x) is given by f[g(x)].
Hence, (g∘h)(x) = [tex]g[h(x)] = \frac{(4 - x) + 1}{(4 - x) - 2} = \frac{5 - x}{2 - x}[/tex] .......... (1)
Now, from equation (1) we get,
(g∘h)(x) = [tex] \frac{5 - x}{2 - x}[/tex]
⇒ (g∘h)(- 3) = [tex]\frac{5 - ( - 3)}{2 - ( - 3)} = \frac{8}{5}[/tex] (Answer)
Answer:
The answer is 8/5
Step-by-step explanation:
ALGEBRA 24 POINTS
simplify?
Answer:
1200
Step-by-step explanation:
its just common sense that 2*2=4 and 10*4=40 so now all you have to do is 40*30 which its just common knowledge that 4*3=12 now just add the zeros 1200
Mandy has a 10.2-ounce container of mustard. She uses 130 of the mustard to put on her hot dog each time. How many ounces of mustard are left after she has eaten 6 hot dogs?
Answer:
fevervrv
Step-by-step explanation:
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As per question, Mandy has a 10.02-ounce container of mustard. The required Amount of Mustard left after she has eaten 6 hot dogs is 8.16 ounce.
Given:
Mandy has a 10.2-ounce container of mustard.
She uses 1/30 of the mustard to put on her hot dog each time.
According to question, Mandy has a 10.2-ounce container of mustard.
Now, 1/30 of the mustard to put on her hot dog each time to 6 hot dogs, so weight of mustard used is calculated as,
[tex]\frac{1}{30}\times10.2\times 6=2.04\;\rm{ounce}[/tex]
So, Amount of Mustard left after eating 6 hot dogs is,
[tex]10.2-2.04=8.16\;\rm{ounce[/tex]
Therefore, the required amount of mustard left after eating 6 hot dogs is 8.16 ounce.
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Kara and Lindsey both hike in separate directions from their campsite, with Kara hiking straight to the east and Lindsey hiking straight north. At
2:00 p.m., Kara hiked twice as far to the east as Lindsey hiked to the north. At 2:30 p.m., Kara had covered another mile, while Lindsey had
covered another half of a mile. If x represents Lindsey's distance, in miles, from the campsite at 2:00p.m., what function could be used to
represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m.?
Answer:
A. f(x)=x^2+x+0.25
Step-by-step explanation:
If x represents Lindsey's distance at 2:00 PM, then 2x represents Kara's distance at 2:00 PM because she walked twice as far as Lindsey. Then adding on the values we got for 2:30 PM, we get that Kara walked a distance of 2x+1 and Lindsey walked a distance of x+0.5 at the time of 2:30 PM. Now, we know that they have formed a right triangle because we are given the directions they walked in; east and north. This allows us to use a formula for the area of a right triangle: 1/2(L x W). Plugging in our values, we get...
1/2(2x+1)(x+0.5)
which simplifies to...
1/2(2x^2+2x+0.5)
which further simplifies to...
x^2+x+0.25
which is our answer.
Answer:
A. f(x) = x^2 + x + 0.25
Step-by-step explanation:
Factor completely: 2x4 − 32.
a 2(x2 − 4)(x2 + 4)
b 2(x − 2)(x + 2)(x2 + 4)
c 2(x − 2)(x + 2)(x + 2)(x + 2)
d 2(x − 2)(x + 2)(x2 − 4)
Answer:
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Step-by-step explanation:
Given expression is [tex]2x^4-32[/tex]
To find the completed factor for the given expression:
[tex]2x^4-32[/tex]:
Taking the common number "2" outside to the above expression we get
[tex]2x^4-32=2(x^4-16)[/tex]
Now rewritting the above expression as below
[tex]=2(x^4-2^4)[/tex] (since 16 can be written as the number 2 to the power of 4)
[tex]=2((x^2)^2-(2^2)^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x^2[/tex] and [tex]b=2^2[/tex]
Therefore it becomes
[tex]=2(x^2+2^2)(x^2-2^2)[/tex]
[tex]=2(x^2+4)(x^2-2^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x[/tex] and [tex]b=2[/tex]
Therefore it becomes
[tex]=2(x^2+4)(x+2)(x-2)[/tex]
[tex]=2(x+2)(x-2)(x^2+4)[/tex]
Therefore [tex]=2(x+2)(x-2)(x^2+4)[/tex]
[tex]2x^4-32=2(x-2)(x+2)(x^2+4)[/tex]
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Answer:
b
Step-by-step explanation:
On a recent survey, 40% of those surveyed indicated that they preferred walking to running. If 540 people preferred walking, how many people were surveyed
Answer:
The Total number of people were surveyed is 1,350 people.
Step-by-step explanation:
Given as :
The total number of people who preferred walking = 540 people
The percentage of people who preferred walking to running = 40% of the total people
Let The Total number of people were surveyed = n people
Now, According to question
The total number of people who preferred walking = 40% of the total number of people were surveyed
Or, 40% of n = 540
Or, [tex]\dfrac{40}{100}[/tex] × n = 540
Or, n = [tex]\frac{540\times 100}{40}[/tex]
∴ n = 1350
So,Total number of people were surveyed = n = 1350 people
Hence,The Total number of people were surveyed is 1,350 people. Answer
Which statement is true about the function f(x)= -√-x?
Answer:
Never mind, but your question makes no sense.
Step-by-step explanation:
List the rest of the question.
Two step equations
-5n+8=-7
Arc are subtends a central angle measuring 3pi/5 radians . What fraction of the circumference is this arc?
Answer:
The arc is 3/10 of the circumference
Step-by-step explanation:
we know that
The complete circumference subtends a central angle of 2π radians
so
using proportion
Find out what fraction of the circumference represent an arc with a central angle of 3pi/5 radians
[tex]\frac{1}{2\pi}=\frac{x}{(3\pi/5)}\\\\x=\frac{(3\pi/5)}{2\pi}\\\\x=\frac{3}{10}[/tex]
a games room charges a $13 entrance fee, plus $2.35 per hour of play time. Annie Marie has $29.45. how long can she play in the games room? a) Choose a variable and write an inequality for this problem
Answer:
a) The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].
b) Annie Marie can play maximum of 7 hours.
Step-by-step explanation:
Given:
Entry fee charge of game room = $13
Cost of hourly playtime = $2.35 per hour
Total Money Annie Marie has = $29.45
We need to find number of hours she can play with this amount.
Let number of hours she will play be 'x'.
No we know that Total Money she has should be less than or equal to sum of Entry fee charge of game room and Cost of hourly playtime multiplied by number of hours she can play.
Framing in equation form we get;
[tex]13+2.35x\leq 29.45[/tex]
Hence The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].
On Solving this equation we get;
Subtracting both side by 13 we get;
[tex]13+2.35x-13\leq 29.45-13\\\\2.35x\leq 16.45[/tex]
Now dividing both side by 2.35 using division property of Inequality we get;
[tex]\frac{2.35x}{2.35}\leq \frac{16.45}{2.35}\\\\x\leq 7 \ hrs.[/tex]
Hence Annie Marie can play maximum of 7 hours.
Find the minimum or maximum value off
x^2 + 6x +11
Answer:
The minimum is the point (-3,2)
Step-by-step explanation:
we have
[tex]x^{2} +6x+11[/tex]
This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
Convert the equation in vertex form
Complete the square
[tex]f(x)=(x^{2} +6x+3^2)+11-3^2[/tex]
[tex]f(x)=(x^{2} +6x+9)+11-9[/tex]
[tex]f(x)=(x^{2} +6x+9)+2[/tex]
Rewrite as perfect squares
[tex]f(x)=(x+3)^{2}+2[/tex] ----> equation in vertex form
The vertex is the point (-3,2)
therefore
The minimum is the point (-3,2)
What are the domain and range of the function f(x)=(√x-7)+9?
Answer:
the domain of the function f(x) is [tex]x\ge 7[/tex]
the range of the function f(x) is [tex]f(x)\ge 9[/tex]
Step-by-step explanation:
Consider the parent function [tex]y=\sqrt{x}.[/tex]
The domain og this function is [tex]x\ge 0,[/tex] the range of this function is [tex]y\ge 0.[/tex]
The function [tex]f(x)=\sqrt{x-7}+9[/tex] is translated function [tex]y=\sqrt{x}[/tex] 7 units to the right and 9 units up, so
the domain of the function f(x) is [tex]x\ge 7[/tex]
the range of the function f(x) is [tex]f(x)\ge 9[/tex]
Answer:
C
Step-by-step explanation:
Just took quiz
Which of the following could be a solution to a system of linear equations including the line graphed below?
Select one:
A. (-2, 3)
B. (1,4)
OC. (3,0)
D.(-5,-4)
Correct answer:
D. (-5,-4)
Explanation:In order to solve this problem, let's plot each point. So, see the attached file below and keep in mind the following:
Point (-2, 3) is the red one.Point (1, 4) is the blue one.Point (3, 0) is the orange one.Point (-5, 4) is the yellow one.As you can see on the graph, only point (-5, -4) lies on the given line. Therefore, the conclusion is that this point could be a solution to a system of linear equations including the line graphed below.
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Times the sum of a number and two is less than seven times the number
Answer:
[tex]x >\frac{3}{2}[/tex]
Step-by-step explanation:
The complete question is
Three times the sum of a number and two is less than seven times the number. Find the number
Let
x -----> the number
we know that
The linear equation that represent this problem is
[tex]3(x+2) < 7x[/tex]
Solve for x
Apply distributive property left side
[tex]3x+6 < 7x[/tex]
Subtract 3x both sides
[tex]6 < 7x-3x[/tex]
[tex]6 < 4x[/tex]
Divide by 4 both sides
[tex]\frac{6}{4}< x[/tex]
Simplify
[tex]\frac{3}{2}< x[/tex]
Rewrite
[tex]x >\frac{3}{2}[/tex]
Which expression can be used to check the answer to 56 divided by negative 14=n
Answer:
n=-4
Step-by-step explanation:
56/-14=n
n=-4
Is the product of square root of 16 and 4/7 rational or irrational
The square root of 16 is rational 4.
The ratio of 4 and 7 is rational 0.5714285714285
The product is hence rational.
The product of the square root of 16 and 4/7 (which equals 16/7) is rational.
What are rational and irrational numbers?Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
The square root of 16 is 4, and 4/7 is a rational number. When you multiply a rational number (4/7) by an integer (4), the result remains rational.
Calculation: √16 * 4/7 = 4 * 4/7
= 16/7
16/7 is the product which is a rational number.
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You worked the following hours this week: Monday 8 AM to PM, Tuesday 9 AM to 3 PM, Thursday 8:30 AM to 2:15 PM.
You get a 30-minute unpaid lunch break every work day. How many hours will you be paid for this week?
To calculate the total hours you will be paid for this week, subtract the total lunch break time from the total working hours. Therefore, the total hours you will be paid for this week is 19 hours and 45 minutes.
Explanation:To calculate the number of hours you will be paid for this week, you need to subtract the total lunch break time from the total working hours.
On Monday, you worked from 8 AM to PM, which is 10 hours.
On Tuesday, you worked from 9 AM to 3 PM, which is 6 hours.
On Thursday, you worked from 8:30 AM to 2:15 PM, which is 5 hours and 45 minutes.
Overall, your total working hours for the week are 10 + 6 + 5 hours and 45 minutes.
Each day you have a 30-minute unpaid lunch break, so for the entire week you would have 4 lunch breaks x 30 minutes = 2 hours taken for lunch breaks.
Therefore, the total hours you will be paid for this week are 10 + 6 + 5 hours and 45 minutes - 2 hours = 19 hours and 45 minutes.
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What is the solution to the equation 5a^2 - 44 = 81
A. Plus minus 25
B. -5
C. Plus minus 5
D. Plus minus 125
Answer:
Step-by-step explanation:
5a^2 - 44 = 81
5a^2 = 81 + 44 {add 44 both the sides}
5a^2 = 125
a^2 = 125/5 {divide both sides by 5}
a^2 = 25
a^2 = 5*5
a = ±5
Answer:
Option c) is correct
ie, a=plus minus 5 or [tex]a=\pm 5[/tex]
Step-by-step explanation:
Given equation is [tex]5a^2-44=81[/tex]
To find the solution of the given equation we have to solve the equation
[tex]5a^2-44=81[/tex]
[tex]5a^2=81+44[/tex]
Now applying the algebraic sum to the terms on the right hand side of the equation
[tex]5a^2=125[/tex]
[tex]a^2=\frac{125}{5}[/tex]
Now applying the division rule
[tex]a^2=25[/tex]
Therefore [tex]a=\pm 5[/tex]
Therefore option c) is correct
ie, [tex]a=\pm 5[/tex].
Mr. Babe used to work at a local furniture store.
This is what my answers were for these questions(If it is correct, just write a comment. But if it is incorrect, explain why in the answers box)
A. While he worked there, Mr. Babe earned 3% on how much he sells. If he sold $495 couch, how much commission did he make?
What I did:
495 x 3 = 1485
1485/100 = 14.85
B. On top of his commission, Mr. Babe made $15 per hour. He eventually got a raise with an increase of 5% per hour. After the raise, how much did he make per hour?
What I did:
495 x 5 = 2475
2475/100 = 24.75
A. Mr. Babe made a commission of $14.85
B. He makes $15.75 per hour after the raise.
Step-by-step explanation:
A. While he worked there, Mr. Babe earned 3% on how much he sells. If he sold $495 couch, how much commission did he make?
Worth of sold couch = $495
Commission = 3%
Amount of commission = 3% of total worth sold
Amount of commission = [tex]\frac{3}{100}*495[/tex]
Amount of commission = [tex]\frac{1485}{100}=\$14.85[/tex]
Mr. Babe made a commission of $14.85
B. On top of his commission, Mr. Babe made $15 per hour. He eventually got a raise with an increase of 5% per hour. After the raise, how much did he make per hour?
Amount earned per hour = $15
Increase = 5%
As the increment is on per hour amount, therefore,
Amount of increase = 5% of per hour amount
Amount of increase = [tex]\frac{5}{100}*15=\frac{75}{100} = \$0.75[/tex]
New amount per hour = Per hour amount + amount of increase
New amount per hour = 15+0.75 = $15.75
He makes $15.75 per hour after the raise.
Keywords: percent, addition
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Jennifer wants to rent a car for 5 days, and she's interested in the loss
damage waiver but not the collision damage waiver. If the daily rate is $45
and LDW is $65, what is her total rental cost?
Answer:
290
Step-by-step explanation:
is √ 4/9 a rational number
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
Recall that a rational number is a number that results from dividing 2 integers
I'm not sure if your question refers to (√4) / 9 or √(4/9), but either way both are rational numbers:
If (√4) / 9, Then,
(√4) / 9
= 2/9
Since both 2 and 9 are integers, then 2/9 is a rational number
If √(4 / 9), Then,
√(4 / 9)
= √4 / √9
= 2/3
Since both 2 and 3 are integers, then 2/3 is also a rational number
Paul is looking at two vacation packages while planning a trip to Cancun, Mexico. In the first vacation package, round-trip airfare costs $799, and it costs $139 per night to stay at the resort. In the second vacation package, it costs $587 per night to stay in the resort and $285 for round-trip airfare. Let x represent the number of nights spent at the resort, and let y represent the total cost of the trip. Which system of equations could be used to find how many nights Paul needs to stay at either resort so that both vacation packages have the same cost? A. B. C. D.
Answer:
y = 139x + $ 799
y = 587x + $ 285
Step-by-step explanation:
Let x represent the number of days spent at the resort and y represent the total cost.
for the first option
y = 139x + $799 since $ 139 is the amount per night at the resort, $139x must be the cost for x number of days
y = 587x + $285 similarly x number of days should equal $587x
If d , e, and f are midpoints of the sides of ABC, find the perimeter of ABC.
The perimeter of a triangle with midpoints d, e, and f on each side is twice the sum of segments d, e, and f. However, without specific numerical values for d, e, and f, the exact numerical measurement for the perimeter of triangle ABC cannot be determined.
Explanation:The question is referring to a specific characteristic of geometry known as the midpoint. The midpoints, in this case d, e, and f, divide each side of the triangle into two equal parts. The side length of ABC is equal to double the sum of segments d, e, and f since they represent the half lengths of the sides.
However, please note that without any additional information or numeric representation, we cannot compute the exact numerical measurement of the perimeter of triangle ABC.
To illustrate, if we were given that the lengths d, e, and f were respectively 5 units, 6 units, and 7 units, we would calculate the perimeter of triangle ABC by adding the lengths of d, e, and f and multiplying the sum by 2.
In such a scenario: Perimeter of ABC = 2 * (d + e + f) = 2 * (5 units + 6 units + 7 units) = 2 * 18 units = 36 units.
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Identify the equation of the linear function through the points (- 2,- 7) and (1,2). Then state the rate of change of the function. What is the equation of the linear function?
A. y = 3x - 1
B. y = - 3x - 1
C. y = 3x + 1
D. y = -3x + 1
The rate of change is ( ? ).
Answer:
The equation of line is y = 3 x - 1 , i.e option A .
The rate of change = m = 3
Step-by-step explanation:
Given as :
The points are
([tex]x_1[/tex],[tex]y_1[/tex] ) = (- 2, -7)
([tex]x_2[/tex],[tex]y_2[/tex] ) = (1 , 2)
Let The slope = m
Now, The slope is calculated in points form
So, Slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
I.e m = [tex]\dfrac{2-(-7)}{1-(-2)}[/tex]
or, m = [tex]\dfrac{9}{3}[/tex]
I.e m = 3
So, The slope of points = m = 3
I,e Rate of change = m = 3
Now, the equation of line in slope - point form can be written as
y -[tex]y_1[/tex] = m ( x - [tex]x_1[/tex])
where m is the slope of line
i.e y - (-7) = ( 3 ) × ( x - (-2) )
or, y + 7 = 3 × (x + 2)
∴ y + 7 = 3 x + 6
Or, y = 3 x + 6 - 7
Or, y = 3 x - 1
So, The equation of line is y = 3 x - 1
Hence, The equation of line is y = 3 x - 1 , i.e option A .
And The rate of change = m = 3 Answer
Last Sunday, the average temperature was 8%, percent higher than the average temperature two Sundays ago. The average temperature two Sundays ago was T
degrees Celsius.
Which of the following expressions could represent the average temperature last Sunday?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
\left(1+\dfrac{8}{100}\right)T(1+
100
8
)Tleft parenthesis, 1, plus, start fraction, 8, divided by, 100, end fraction, right parenthesis, T
(Choice B)
B
T+8T+8T, plus, 8
(Choice C)
C
1.08T1.08T1, point, 08, T
(Choice D)
D
1.8T1.8T1, point, 8, T
(Choice E)
E
T+0.08T+0.08
Final answer:
The expressions that correctly represent an 8% increase from T are (1 + 8/100)T, which simplifies to 1.08T, and 1.08T directly. So, choices (A) 1.08T and (C) 1.08T are correct.
Explanation:
The student is asked to determine which expression represents the average temperature last Sunday when it was 8% higher than the temperature two Sundays ago, given as T degrees Celsius. To find 8% of T, the student would multiply T by 0.08. To calculate the total average temperature last Sunday, the student would then add this to T.
The correct expressions that represent this situation are:
(Choice A) A: [tex](1 + \dfrac{8}{100})T[/tex]or 1.08T. This is because multiplying T by the fraction 8/100 gives us 8% of T, and adding T to that gives the increased temperature.(Choice C) C: 1.08T. This is a direct calculation, as multiplying by 1.08 is the equivalent of increasing a number by 8%.Expressions (Choice B) B: T + 8 and (Choice D) D: 1.8T incorrectly represent an absolute increase of 8 degrees and an 80% increase, respectively, not an 8% increase. Expression (Choice E) E: T + 0.08T is equivalent to 1.08T and is also correct.
Therefore, the correct answers are (Choice A) and (Choice C).
Convert to standard form 25x^2 + 4y^2 - 50x -75 = 0
Answer:
[tex]\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1[/tex]
Step-by-step explanation:
we have
[tex]25x^{2}+4y^{2}-50x-75=0[/tex]
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](25x^{2}-50x)+4y^{2}=75[/tex]
Factor the leading coefficient of each expression
[tex]25(x^{2}-2x)+4y^{2}=75[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]25(x^{2}-2x+1)+4y^{2}=75+25[/tex]
[tex]25(x^{2}-2x+1)+4y^{2}=100[/tex]
Rewrite as perfect squares
[tex]25(x-1)^{2}+4y^{2}=100[/tex]
Divide both sides by the constant term to place the equation in standard form
[tex]\frac{25(x-1)^{2}}{100}+\frac{4y^{2}}{100}=\frac{100}{100}[/tex]
Simplify
[tex]\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1[/tex]
Katy makes 48 cookies an hour. If she has 24 alr, how long would it take her to make 120?
Question:
Katy makes 48 cookies an hour. If she has 24 already, how long would it take her to make 120?
Answer:
It takes 2.5 hours for Katy to make 120 cookies
Step-by-step explanation:
Given:
Time taken to make 48 cookies = 1 hour
To Find:
Time taken to make 120 cookies = ?
Solution:
Time taken to make 48 cookies = i hour
So now time taken to make 1 cookie = [tex]\frac{1}{48} hour[/tex]
So time taken to make 120 cookies
= Number of cookies X time taken to make one cookie
=>[tex]120 \times \frac{1}{48}[/tex]
=>[tex] \frac{120}{48}[/tex]
=> 2.5 hours