The student's final moment of inertia is 18.18 kgm².
What is moment of inertia?The moment of inertia of an objecr is the property of an object which shows its ability to rotate.
How to find the final moment of inertia?Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.
What is the law of conservation of angular momentum?The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.
So, Iω = constant where
I = moment of inertia and ω = angular speed.So, Iω = I'ω' where
I = initial moment of inertia of student = 25kgm²ω = initial angular speed of student = 1.6 rev/s I' = final moment of inertia of student ω' = final angular speed of student = 2.2 rev/sMaking I' subject of the formula, we have that
I' = Iω/ω'
So, substituting the values of the variables into the equation, we have that
I' = Iω/ω'
I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s
= 40 kgm²rev/s ÷ 2.2 rev/s
= 18.18 kgm²
So, the final moment of inertia is 18.18 kgm².
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the sales tax rate is 7.8%.kiara buys a box of dirt priced at $150.24 what is the tax amount,round your number to the nearest penny
With a sales tax rate of 7.8%, the tax amount is $11.72.
How to determine the tax amount?A sales tax rate is the percentage of the sale price of a good or service that is added on as a tax. It is usually applied to the final purchase price of a product or service and is paid by the consumer at the time of purchase.
Since the sales tax rate is 7.8% and Kiara buys a box of dirt priced at $150.24. Thus, the tax amount can be determined as follows:
Tax amount = 7.8/100 × $150.24
Tax amount = $11.72
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at Freddy's, three steak burgers zzz and two orders of fries cost $18. Two steak burgers and three orders of fries cost $15.75. What is the cost for one steak burger? What is the cost of one order of feries
The cost of one steak burger is $4.5 and the cost of one order of fries is $2.25.
How to find a cost using equation?To find a cost using an equation, you need to first identify the variables involved in the equation.
Variables are values that can change, such as the price of an item or the quantity of an item. Next, you must determine the value of each variable.
Once you have all the values, plug them into the equation and solve for the cost. For example, if you have an equation where x is the cost, y is the quantity, and z is the price per item, you would plug in the values of y and z and solve for x.
The answer you get would be the cost of the item. Additionally, you can use the equation to find the cost of multiple items by changing the value of the variable y to represent the amount of items you need.
After plugging in the new values into the equation, you can solve for the cost of all the items.
Let x be the fries and y be the steak burgers.
From the following information, the equation are as follows:
2x + 3y = 18 ---------equation 1
3x + 2y = 15.75 -------equation 2
To find cost of one steak burger and cost of one order of fries,
Multiply by 3 in equation 1 and 2 in equation 2,
6x + 9y = 54 -------3
6x + 4y = 31.5 -----4
Subtracting the equation 3 and 4, we get
5y = 22.5
y = 22.5/5
y = 4.5
Substitute y=4.5 in eq 1,
2x + 3(4.5) = 18
2x = 4.5
x = 2.25
∴ The cost of one steak burger is $4.5
∴The cost of one order of fries is $2.25.
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How to find proportional parts in triangles and parallel lines?
If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.
If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.
The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.
Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.
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A radar gun meaured the peed of a baeball at 5 mile per hour. If the baeball wa going 4.2 mile per hour, what wa the percent error in thi meaurement?
The percent error in this measurement would be 16%.
1. Calculate the difference between the measured speed and the actual speed: 5 mph - 4.2 mph = 0.8 mph
2. Calculate the percent error: (0.8 mph / 4.2 mph) x 100 = 19.05%
3. Round to the nearest whole number: 19.05% = 19%
The percent error in this measurement is 19%, which means that the measured speed was 19% higher than the actual speed.
This can be caused by a variety of factors, including the radar gun being set to an incorrect sensitivity, the speed of the ball being too high for the radar gun to accurately measure, or the radar gun not being able to accurately detect the speed of the ball due to environmental factors such as wind or lighting.
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PLSSS HELP IF YOU TURLY KNOW THISSSS
Answer:
x = 15
Step-by-step explanation:
Because the first part is division.... x/5, you'd want to multiply by that same number to get X alone. So you'd multiply by 5
Because of that
x = (3)(5)
x = 15
[tex]\dfrac{x}{5} =3[/tex]
Multiply both sides by 5:
[tex](\dfrac{x}{5} )\times5=(3)\times5[/tex]
[tex]\fbox{x = 15}[/tex]
at the time of this writing 1 u.s. dollar is worth 1.28 canadian dollars. an automobile in toronto sells for 25,500 canadian dollars. the same car sells in detroit for 21,000 u.s. dollars. what is 25,500 canadian dollars equivalent to in u.s. dollars?
1.21 Canadian dollars is equivalent to 1 US dollar
What is 25,500 Canadian dollars equivalent to in US dollars?A monetary exchange rate, also known as a foreign exchange rate, is the rate at which one currency can be exchanged for another. Exchange rates are determined by the foreign exchange market and can fluctuate based on supply and demand.
Since an automobile in Toronto sells for 25,500 Canadian dollars and the same car sells in Detroit for 21,000 US dollars.
Thus, 25,500 Canadian dollars equivalent in US dollars will be:
25,500 Canadian dollar /21,000 US dollars = 1.21
Thus, 1.21 Canadian dollar is equivalent to 1 US dollar dollars
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if JKLM is a parallelogram, what is m
m is the angle formed by the two parallelogram sides that are next to each other. Because all angles in a parallelogram are equal, m is equal to all other angles in the parallelogram.
What is a parallelogram?A parallelogram is a four-sided form having two parallel sides and four right angles on each side. Both sides are straight and opposite sides are equal in length. A parallelogram's opposing angles are also equal.
M is the angle subtended by the parallelogram JKLM. A parallelogram is a four-sided form with parallel and equal-length opposing sides. A parallelogram's angles are also equal in size. As a result, m is an angle of the parallelogram JKLM and is proportional to the other angles of the parallelogram JKLM.
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Write 7.67 times 10 -² in standard notation.
7.67 times 10^-² in standard notation can be written as 0.0767.
To convert scientific notation to standard notation, you can simply move the decimal point to the left or right as many times as indicated by the exponent of the power of 10. In this case, the exponent is -2, so you move the decimal point 2 places to the left. The result is 0.0767.
In the triangle below, what is the tangent of 30°?
O A.
OB.
-IN
B. √3
OC. 2
O D. 1
60°
2
13
30°
Answer:
B
Step-by-step explanation:
tangent formula is the line facing the angle divided by the shorter one. so 1/root3
Answer:
Option B.
[tex]tan(30)=\frac{1}{\sqrt{3} }[/tex]
Step-by-step explanation:
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse.
TOA is for tangent.
So we can say the tangent of angle x is the opposite side divided by the adjacent side.
[tex]tan(x)=\frac{O}{A}[/tex]
In this triangle we are given
[tex]O=1\\A=\sqrt{3} \\H=2[/tex]
Therefore
[tex]tan(30)=\frac{1}{\sqrt{3} }[/tex]
If f(x) =-2x^2 +5 then find ( - 5)
Answer:
-45
Step-by-step explanation:
f(x) = -2x² + 5
f(-5) = -2(-5)² + 5
= -2(25) + 5
= -2 × 25 + 5
= -50 + 5
= -45
Both lines on the graph represent proportional relationships. What is the constant of proportionality for each line? Choose one option from each drop-down menu to answer the question. Line passes through the point Choose.. . The constant of proportionality between and for line is Chooss.. Choose.. The constant Line passes through the point of proportionality between and for line is Chooss.. pls help soon
Line a which passes (1, 4) has a constant of proportionality of 4.
Line b runs through (5, 2), with a constant of proportionality of 2/5.
What is the Constant of Proportionality?The constant of proportionality is often represented by the letter "k" and it is used in a mathematical relationship known as a proportionality relationship. The proportionality relationship can be written as y = kx, where y and x are the two variables and k is the constant of proportionality.
This means that the value of y is directly proportional to the value of x and is equal to k times the value of x. The value of k can be found by dividing the value of y by the value of x, when the two variables are in proportion.
Line a passes through the (1, 4), therefore:
constant of proportionality = y/x = 4/1 = 4.
Line b passes through the (5, 2), therefore:
constant of proportionality = y/x = 2/5.
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Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of 24 cubic centimeters and base lengths of 9 cm and 7 cm.
The height of the trapezoid with an area of 24cm² and base lengths of 9 cm and 7 cm is 3cm.
What is the height of the trapezoid?A trapezoid is simply a quadrilateral with at least one pair of parallel sides.
The area of a trapezoid is expressed as;
A = 1/2(a+b)h
Given that;
Area A = 24 cmBase side a = 9cmBase side b = 7cmHeight h = ?Plug in the values into the above formula and solve for h.
A = 1/2(a+b)h
A = 1/2(a+b)h
2A = (a+b)h
2A/(a+b) = h
h = 2A/(a+b)
h = ( 2 × 24cm² ) / ( 9cm + 7cm )
h = 48cm² / 16cm
h = 3cm
Therefore, the value of height h is 3cm.
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PLEASE HELP??!!
What is the end behavior of the function f(z)
2c2
1?
O As approaches infinity, f(r) approaches negative infinity. As I approaches
negative infinity, f(x) approaches infinity.
O As I approaches infinity, f(x) approaches infinity. As approaches negative
infinity, f(x) approaches negative infinity.
As I approaches infinity, f(x) approaches negative infinity. As I approaches
negative infinity, f(x) approaches negative infinity.
As I
approaches infinity. f(a) approaches infinity. As 2 approaches negative infinity, f(x) approaches infinity.
Answer:
d
Step-by-step explanation:
Martina made 3 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 3 necklaces was $11.10 . If the beads cost $1.80 for each necklace, how much did each pendant cost?
Answer:
1.9
Step-by-step explanation:
11.1 /3 =3.7 for beads + pendants per necklace
pendant =3.7-1.8 =1.9
Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)
The length of the north side of the house is 2x^2 + 9x - 32
The length of the north side of the house.From the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have
North side = 5x - 4 + x^2 - 23 + x^2 + 4x - 5
Evaluate
North side = 2x^2 + 9x - 32
The area of the kitchenHere, we have
Length = 2x + 1
Width = x^2 + 4x - 5
So, we have
Area = (2x + 1) * (x^2 + 4x - 5)
Area = 2x^3 + 8x^2 -10x + x^2 + 4x - 5
Area = 2x^3 + 9x^2 - 6x - 5
The area of the bedroomHere, we have
Length = 5x - 4
Width = 5x + 4
So, we have
Area = (5x - 4) * (5x + 4)
Area = 25x^2 - 16
Dimension of the bathroomFrom the figure, we have
Dimensjon = 5x - 4 by (2x + 1 + x + 6 - 5x - 4)
Dimensjon = 5x - 4 by - 2x + 3
Hence, the dimension of the bathroom is 5x - 4 by - 2x + 3
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Yusuf drove 156 miles in 3 hours. If he continued at the same rate, how far would he travel in 2 hours?
The distance travelled by Yusuf in 2 hours is 104 miles.
What is the distance travelled by Yusuf?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given that, Yusuf drove 156 miles in 3 hours.
We determine the speed of Yusuf.
Speed = Distance / time
Speed = 156 miles / 3 hours
Speed = 52 miles per hour
Now, the distance travelled in 2 hours will be;
Speed = Distance / time
Distance = Speed × time
Distance = 52 miles per hour × 2 hours
Distance = 104 miles.
Therefore, the distance covered is 104 miles.
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Evaluate the expression.
4×(7×5)
=
Answer:
4x(7x5) = 4x(35)
To evaluate the expression, we must first perform the operations inside the parentheses. In this case, 7x5 = 35. Then we can multiply 4 with that result, which gives us 4x35 = 140. So the final value of the expression is 140.
Answer: 140
Step-by-step explanation:
4 x (7 x 5)
7 x 5 = 35
4 x 35
= 140
Help me pls it’s due tomorrow and pls have a explanation!!
Answer: 16/24
Step-by-step explanation: You should convert 7/8 and 2/3 to get a common denominator, in this situation the common denominator is 24. You multiply 2/3 by 8 on both sides of the fraction and the same with 7/8 except with 3. When you convert it 7/8 becomes 21/24 which is the total amount of grapes she bought, the amount she used comes out to be 16/24.
The table shows the change in the annual sales turnover of a company in millions of dollars, S(x), where x represents the years since the company was founded. X 1 3 5 7 9 S(x) $495 $598. 95 $724. 73 $876. 92 $1,061. 08 What is the predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11]? A. $111. 42 per year B. $184. 15 per year C. $92. 08 per year D. $222. 83 per year
The predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is $92.08 per year.
To find the predicted average rate of change of the company's sales turnover over the interval [9, 11], we need to find the slope of the line that best fits the data points provided.
The slope of the line can be calculated using the formula:
(change in y) / (change in x) = (S(x2) - S(x1)) / (x2 - x1)
We can use any two of the provided data points to find the slope. Using the data points (9, $1,061.08) and (7, $876.92), we get:
(change in y) / (change in x) = ($1,061.08 - $876.92) / (9 - 7) = $184.15 / 2 = $92.08 per year
This is the average rate of change of the company's sales turnover over the interval [9, 11]. So the answer is C. $92.08 per year.
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Awnse choice cAnswer:
Step-by-step explanation:
Over 40% of
Belorussian territory
is covered in forests,
this is why they have
a green stripe on
their flag is Belarus
is 80,153 mi? what
percentage is NOT
forests?
If 40% of Belorussian territory is covered in forests , and the total area is 80153 mi² , then the percent that is not covered in forests is 60% and land area is 48,091.8mi² .
the total land area of Belorussian territory is = 80153 mi² ;
the percent of land area covered in forest is = 40% ;
So , the percent that is not covered in Forest is = 100 - 40 = 60% ;
and the land area not covered in forest is = 60% of 80153 ;
= 0.6 × 80153 ;
= 48,091.8 .
Therefore , the percentage that is NOT forests is 60% .
The given question is incomplete , the complete question is
Over 40% of Belorussian territory is covered in forests, this is why they have a green stripe on their flag is Belarus total area is 80153 mi² , What percentage is NOT forests ?
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what is 5/8Y + 7 = 3/4Y - 3
Answer:
y = 1/80
Step-by-step explanation:
[tex] \sf\frac {5}{8y} + 7 = \frac{3}{4y}- 3[/tex]
Substract 7 from both sides
[tex] \sf\frac {5}{8y} + 7 - 7 = \frac{3}{4y}- 3 - 7[/tex]
Calculate
[tex] \sf\frac {5}{8y} = \frac{3}{4y}-10[/tex]
Substract 3/4y from both sides
[tex] \sf\frac {5}{8y} - \frac{3}{4y} = \frac{3}{4y} - \frac{3}{4y} -10[/tex]
Calculate
[tex] \sf\frac {5}{8y} -\frac{3}{4y}= -10[/tex]
L.C.M = 32y²
[tex] \sf \frac{−4y}{ {32y}^{2} } = -10[/tex]
-4y/32y² Divide further
[tex] \sf \frac{ - 4}{ 32y } = -10[/tex]
Divide further
[tex] \sf \frac{ - 1}{ 8y } = -10[/tex]
Cross - multiply
[tex] \sf \: 8y \times - 10 = - 1[/tex]
Multiply
[tex] \sf \: - 80y = - 1[/tex]
Divide both sides by -80y
[tex] \sf \: \frac{ - 80y}{ - 80} = - \frac{ - 1}{ - 80} [/tex]
Calculate
[tex] \sf \: y = \frac{1}{80} [/tex]
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How do you solve this type of problem?
Answer:
(3x+4)+55°+85°=180°
(3x+4)+140°=180°
(3x+4)=180°-140°
(3x+4)=40°
3x+4=40
3x=40-4
3x=36
x=12
(3x+4)
(3×12)+4
=40°
Copy the problem, and write a Statement/Reason proof.
The problem is given as follows:
Prove: ΔLUZ ≅ ΔIDA
The triangles above can be said to be congruent because:
[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)
[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides)
[tex]\overline{UZ}[/tex] ≅ [tex]\overline{AD}[/tex] (Corresponding sides)
It is also given that:
m ∠ ULZ ≅ m ∠ ADI
since
[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)
[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides) and
m ∠ ULZ ≅ m ∠ ADI ;
We can thus conclude that the ΔLUZ ≅ ΔIDA
What is the meaning of congruent triangles?When two triangles are congruent, one can be moved (through one or more stiff movements) to coincide with the other. All congruent sides and angles will be found.
The triangles are congruent if two sides and the included angle of one triangle are congruent to the corresponding sections of another triangle. [Side - Angle - Side]
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5,000 books in the town's library of this 4,600are fiction. To find the percent of the books that are fiction, first set up the percent equation. Then find the percent.
please answer this it is done in a few minutes
The set up percent equation is:
4600 = m . 5000
The percent of books that are fiction will be:
m = 92%.
Now, According to the question:
A relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Number of books in the town's library = 5,000
Number of books that are fiction= 4,600
The set up percent equation is:
4600 = m . 5000
where, m is the books' fiction
The percent of books that are fiction will be:
m = 4600/5000 × 100
m = 92%.
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I need help! ……………….
Answer:
x = 140 degrees
Step-by-step explanation:
this polygon has 6 sides
to find the number of degrees of the six interior angles you can use this formula:
(n-2)*180 where 'n' equals the number of sides
(6-2)*180 = 4(180) = 720 degrees
starting with the 'x' angle and going clockwise, we have the following:
x + 90 + 104 + 123 + 155 + 108 = 720
x + 580 = 720
x = 720 - 580
x = 140
What is the answer for 2 x 2 x 11 in exponential?
Answer: Your answer would be 2x ⋅ (2x) ⋅ 11
Step-by-step explanation: I hope this helps!
Help!!
I’m really bad at this
For Figure 2, Triangles are congruent by SSS (side side side).
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now ,
As in given figure for triangles
2 sides of both are parallel and one is common for both
Hence,
These are congruent by SSS theorem.
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Please help I dont know where to start
the standard deviation of a simple random sample of 40 calling times on a payphone is found to be 2. 6 minutes. Find the test statistic to test a claim that the standard deviation of all phone calls on a payphone is less than 2. 9 minutes. Use a 0. 05 significance level
32. 152
31. 348
48. 519
34. 966
Here we have to compare a standard deviation of test statistic with the expected standard deviation of the population. So a chi square test is used. The chi square value got after the calculations is 31.348.
It is a hypothesis testing method. Significance level is 0.05.
The equation for chi square is
Χ² = (n-1)s²/ σ₀²
Lets look into what each term means
n is the sample size which is 40
s² is the sample variance = 2.6²
σ² is the population variance =2.9²
X² = (40-1)×2.6²/ 2.9²
= 39× 6.76/ 8.41
= 31.3483947681
= 31.348
So the X² value is 31.348
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The Nelson family drank 1/4 of a gallon of orange juice on Saturday morning and 2/5 of a gallon of orange juice on Sunday morning. How much orange juice did they drink in all?
Answer: 13/20
Step-by-step explanation: First to find the first part, we need to find a common denominator. So we must ask ourselves, which number is a multiple that both 5 and 4 have in common? The answer then would be 20. So, it would look like this:
[tex]\frac{1}{4} = \frac{?}{20}[/tex]
[tex]\frac{2}{5} = \frac{?}{20}[/tex]
So to find what "?" equals for both fractions, we must use this formula:
Amount = Right denominator / Left denominator (1st part)
So, now we do 20 / 5 and 20 / 4
20 / 5 = 4
20 / 4 = 5
So, the 2nd part is taking the quotient from that and multiplying it by the left numerators. This would look like this:
5 * 1 = 5
4 * 2 = 8
So your "?" should look like this:
[tex]\frac{1}{4} = \frac{5}{20}[/tex]
[tex]\frac{2}{5} = \frac{8}{20}[/tex]
Then, you'd just add! So, 8 + 5 = 13 and 20 + 20 would stay that same ; 20. So your result is [tex]\frac{13}{20}[/tex]
I hope this helped!
emmanuel weighs 150 pounds. about how many hours will it take him to metabolize one standard drink?
Emmanuel weighs 150 pounds. about 2 hours will it take him to metabolize one standard drink
Every hour, the body processes one normal drink. If you have 5 standard drinks, your body will take 5 hours to absorb the alcohol.
In general, the liver can digest one ounce of liquor (or one standard drink) in one hour. If you consume more than this amount of alcohol, your system will get saturated, and the excess alcohol will accumulate in your blood and physiological tissues until it can be metabolized.
It takes your liver around an hour to break down the amount of alcohol in a standard alcoholic drink (one beer, one glass of wine, or one shot).
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