Answers
Answer:
Step-by-step explanation:
You might see this a bit easier if you change the 5/4 * pi into degrees.
pi/180 = 5/4*pi / x This is the proportion. Change 5/4 into a decimal
pi/180 = 1.25 *pi / x Cross multiply
x * pi = 1.25 pi * 180 Divide by pi
x = 1.25 * 180
x = 225 degrees.
The fraction of the area of the sector is angle/360
The fraction of the area of the sector is 225/360
The fraction of the area area of the sector is 5/8 Reduced.
225: 3*3*5*5
360 = 2*2*2*5*3 *3
Cancel out the common factors
3 * 3 * 5
which leaves 5/8
Two
-3x^2 + 5x - 2 - 2x^2 + 4x + 2
- 5x^2 + 9x (the 2's cancel)
a = - 5
b = 9
c = 0
Related Questions
which function has real zeros at x=-8 and x=5?
Answers
Answer: The required function would be [tex]x^2+3x-40[/tex]
Step-by-step explanation:
Since we have given that
There are two real zeroes :
x = -8 and x = 5
So, we need to find the function satisfying the above two zeroes:
Let α = -8 and β = 5
So, it means it is a quadratic equation :
[tex]x^2-(\alpha +\beta)x+\alpha \beta \\\\=x^2-(-8+5)x+-8\times 5\\\\=x^2+3x-40[/tex]
Hence, the required function would be [tex]x^2+3x-40[/tex]
Answer:
The answer is A
Step-by-step explanation:
A school attendance clerk wants to determine if there is a relationship between the number of times a student arrives to school late and the distance the student lives from the school. The clerk gathered data for the month of October and made the graph shown below.
Which statement BEST describes the data?
There is no clear relationship between the number of times students arrive late and the distances they live from school.
Students who arrived late more than six times live the shortest distances from the school.
Students who arrived late more than six times live more than one mile from the school.
Students who arrived late more than six times live the farthest distances from the school.
Answers
Answer:
There is no clear relationship between the number of times students arrive late and the distances they live from school.
Step-by-step explanation:
By looking at the graph, there is no clear direction or association that the graph has. Therefore, there is no clear relationship between the variables being compared.
Answer:
looking at the graph, there is no clear direction or association
Step-by-step explanation:
Amber obtained a 30-year, $260,000 loan for her new home. The interest rate is 3.8% and her monthly payment is $1,211.49. How much of the first payment is for principal?
Answers
Answer:
$388.16
Step-by-step explanation:
Her monthly interest rate is 3.8%/12, so the amount of interest due on the first payment is ...
$260,000 × 0.038/12 ≈ $823.33
Then the amount applied to the principal is ...
$1211.49 -823.33 = $388.16
Kendra sold 200 shares through her broker on June 8. The price per share was $22.10. The broker charged her a 0.5% commission on the total value. What was Kendra’s return on the trade?
A. $4,397.90
B. $4,420.00
C. $4,596.90
D. $4,620.00
Answers
Answer:
A. $4397.9
Explanation:
We are given that Kendra sold 200 shares and that the price per share was $22.1
This means that:
Total value = 200 * 22.1 = $4420
Now, we know that the broker charged 0.5% commission on the total value
This means that:
Broker's charge = 0.5% * 4420 = 0.005 * 4420 = $22.1
Therefore,
Kendra's return = Total value - broker's charge
Kendra's return = 4420 - 22.1 = $4397.9
Hope this helps :)
Answer:
$4,397.90
Step-by-step explanation:
Simplify the expression. sine of x to the second power minus one divided by cosine of negative x
Answers
Answer:
the answer is the letter a) -sin x
Step-by-step explanation:
Simplify the expression.
sine of x to the second power minus one divided by cosine of negative x
(1−sin2(x))/(sin(x)−csc(x))
sin2x+cos2x=11−sin2x=cos2x
cos2(x)/(sin(x)−csc(x))csc(x)=1/sin(x)cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x))sin2(x)− 1=-cos2(x)cos2(x)/(( -cos2(x))/sin(x))
=-sin(x)
Answer:
[tex]-cos \ x[/tex]
Step-by-step explanation:
First of all, we must have to understand what is the described expression in the paragraph
"sine of x to the second power minus one divided by cosine of negative x"
In this sentence, we need to identify what are the elements and operations involved in the expression.
In the sentence appears ""to the second power", "minus" and "divided by" (highlighted)
"sine of x to the second power minus one divided by cosine of negative x"
Therefore, the expression must has three operations:
"to the second power": refers to exponentiation"minus": refers to a substraction"divided by": refers to a divisionNow, we can identify what are the elements: "sine of x", "one" and "cosine of negative x"
"sine of x": refers to [tex]sin\ x[/tex]"one": refers to the number one (1)"cosine of negative x": refers to [tex]cos (-x)[/tex]Therefore, the expression is:
[tex]\frac{(sin\ x)^{2}-1}{cos(-x)}[/tex]
In order to find the simplified expression, we must have to apply these trigonometric identities:
[tex](sin\ x)^{2} = sin^{2}x[/tex][tex]sen\x^{2}x \ +\ cos\x^{2}x=1[/tex][tex]cos(-x)=cos\ x[/tex]Applying the first and third identities, we have:
[tex]\frac{(sin\ x)^{2}-1}{cos(-x)}=\frac{sin\x^{2}x-1}{cos\ x}[/tex]
From the second trigonometric identity, we have:
[tex]cos\x^{2}x=\ 1-sin\x^{2}x[/tex]
Now, multiplying by -1 in both sides:
[tex](-1)(cos\x^{2}x)=(-1)(1-\ sin\x^{2}x)[/tex]
In the left side, multiplying by -1 the sign of the expression changes:
[tex](-1)(cos\x^{2}x)=-cos\x^{2}x[/tex]
In the right side, multiplying by -1 changes the order of the substraction:
[tex](-1)(1-\ sin\x^{2}x)=\ sin\x^{2}x-1[/tex]
Putting all together:
[tex]-cos\x^{2}x=\ sin\x^{2}x-1[/tex]
Now, replacing values we have:
[tex]\frac{sin\x^{2}x-1}{cos\ x}=\frac{-cos\x^{2}x}{cos\ x}=-\frac{cos\x^{2}x}{cos\ x}[/tex]
Finally, the property of the first trigonometric identity (property of exponentiation) can be apply in this case:
[tex]-\frac{cos\x^{2}x}{cos\ x}=-\frac{(cos\ x)^{2}}{cos\ x}=-cos\ x[/tex]
[Trigonometric Graphs]
Use the following information to write an equation of the graph described:
7. sin; Amp = 2, per = π, vertical shift = down 3.
8. cos; Amp = 1; per = π/4, phase shift = left π.
Explain.
Answers
Answer: 7. y = 2 sin (2x) - 3
[tex]\bold{8.\quad y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)}[/tex]
Step-by-step explanation:
The general form of a sine equation is: y = A sin (Bx - C) + D where
Amplitude = |A|Period (P) = [tex]\dfrac{2\pi}{B}[/tex]Phase Shift = [tex]\dfrac{C}{B}[/tex]Vertical Shift = D (positive is up, negative is down)7. Given:
A = 2P = π = [tex]\dfrac{2\pi}{B}[/tex] → B = 2C = 0 (none)D = -3--> y = 2 sin (2x) - 3
8. Given:
A = 1P = [tex]\dfrac{\pi}{4}[/tex] = [tex]\dfrac{2\pi}{B}[/tex] → B = 8[tex]\text{Phase Shift = }-\pi = \dfrac{C}{8}\implies C = -8\pi[/tex]D = 0 (none)[tex]\implies y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)[/tex]
show work please.
solve system of equations using matrices.
Answers
Answer:
(t, t -1, t)
Step-by-step explanation:
You have three unknowns but only 2 equations, so you can't really SOLVE this...you can get a solution with a variable still in it (I forget what this is called. I think it refers to infinite many solutions). Here's how it works:
Set up your matrix:
[tex]\left[\begin{array}{ccc}1&-2&1\\2&-1&-1\\\end{array}\right] \left[\begin{array}{ccc}2\\1\\\end{array}\right][/tex]
You want to change the number in position 21 (the 2 in the scond row) to a 0 so you have y and z left. Do this by multiplying the top row by -2 then adding it to the second row to get that 2 to become a 0. Multiplying in a -2 to the top row gives you:
[tex]\left[\begin{array}{ccc}-2&4&-2\\2&-1&-1\\\end{array}\right]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]
Then add, keeping the first row the same and changing the second to reflect the addition:
[tex]\left[\begin{array}{ccc}-2&4&-2\\0&3&-3\\\end{array}\right] \left[\begin{array}{ccc}-4\\-3\\\end{array}\right][/tex]
The second equation is this now:
3y - 3z = -3. Solving for y gives you y = z - 1. Let's let z = t (some random real number that will make the system true. Any number will work. I'll show you at the end. Just bear with me...)
lf z = t, and if y = z - 1, then y = t - 1. So far we have that y = t - 1 and z = t. Now we solve for x:
From the first equation in the original system,
x - 2y + z = 2. Subbing in t - 1 for y and t for z:
x - 2(t - 1) + t = 2. Simplify to get
x - 2t + 2 + t = 2 and x - t = 0, and x = t. So the solution set is (t, t - 1, t). Picking a random value for t of, let's say 2, sub that in and make sure it works. If:
x - 2y + z = 2, then t - 2(t - 1) + t = 2 becomes t - 2t + 2 + t = 2, and with t = 2, 2 - 2(2) + 2 + 2 = 2. Check it: 2 - 4 + 4 = 2 and 2 = 2. You could pick any value for t and it will work.
Find the area. (Geometry)
Answers
Answer: 12800m^2
This shape is made up of a rectangle and a triangle.
Rectangle
= 120 x 60
= 7200
Triangle
= (200 - 60) x (120 - 40) x 0.5
= 140 x 80 x 0.5
= 5600
Total Shape
= 7200 + 5600
= 12800m^2
Of all the baseball caps in a store. 2/3 of the caps are blue. Of all the blue baseball caps. 4/7 are on sale. What fraction of the baseball caps in the store are blue and on sale
Answers
19/50 of the baseball caps in the store are blue and on sale.
Let's say there are a total of 100 baseball caps in the store. Then, 2/3 of them are blue, which is:
2/3 x 100 = 66.67 (approximately 67)
So, there are approximately 67 blue baseball caps in the store. Out of these, 4/7 are on sale, which is:
4/7 x 67 = 38 (rounded to the nearest whole number)
Therefore, there are approximately 38 blue baseball caps that are on sale in the store.
The fraction of baseball caps in the store that are blue and on sale is:
38/100 = 19/50
So, 19/50 of the baseball caps in the store are blue and on sale.
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To find the fraction of baseball caps in the store that are blue and on sale, multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.
Explanation:To find the fraction of baseball caps in the store that are blue and on sale, we need to multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.
Given that 2/3 of the caps are blue and 4/7 of the blue caps are on sale, we can calculate the fraction of blue caps that are on sale by multiplying 2/3 and 4/7:
2/3 * 4/7 = 8/21
Therefore, 8/21 of the baseball caps in the store are blue and on sale.
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A polynomial has been factored, as shown below:
f(x) = (x - 3)(x + 8)(x - 11)
What are the zeros of the polynomial?
3, 8, 11
3,-8, 11
-3, 8, -11
-3,3, -8,8, -11, 11
Answers
Answer:
3, -8, 11
Step-by-step explanation:
The first factor is zero when x=3.
The second factor is zero when x=-8.
The third factor is zero when x=11.
Whenever any factor is zero, the polynomial is zero.
The zeros are 3, -8, 11.
PLEASE HELP!!!
9/10 divided by (-3/5)
Write the answer as a mixed number
Answers
[tex]
\frac{\frac{9}{10}}{\frac{-3}{5}}=\frac{45}{-30}=-\frac{9}{6}=\boxed{\frac{3}{2}}
[/tex]
Hope this helps.
r3t40
James bought two T-shirts and one pair of jeans at an online store and paid $40, not including taxes, for his purchase. A month later, the same store sold the T-shirts and jeans at a 50% discount from their original prices. James bought two T-shirts and five pairs of jeans for $60, not including taxes.
Answers
Answer:
The T-shirts cost $10 and the jeans cost $20.
Step-by-step explanation:
I guess you want to find the cost of the T-shirts and jeans at his first buy,
Let the cost be $t and $j for T-shirts and jeans respectively.
Then we have the system:
2t + j = 40...................(1)
and a month later:
0.5*2t + 0.5*5j = 60
t + 2.5j = 60................(2)
Multiply by - 2:
-2t - 5j = -120.............(3)
Adding equations (1) and (3):
-4j = -80
j = -80 / -4
j = $20.
Substituting j = 20 into equation (2):
t + 2.5(20) = 60
t = 60 - 50
t = $10.
t = $55
Miguel has a piece of string that is 3 m 25cm long he cut a piece off and used it to tie Around his sleeping bag now his oringinol piece is only 1 m 46 cm long how long is the piece of string Miguel cut off
Answers
Answer:
1 m 79 cm
Step-by-step explanation:
Subtract 1.46 m from 3.25 cm: 1.79 cm, or 1 m 79 cm
Margaret is making strawberry milkshakes for the kids party. The recipe calls for of a cup of strawberry syrup to make 8 milkshakes. How many cups of strawberry syrup are needed to make 96 milkshakes.?
Answers
Answer:
12
Step-by-step explanation:
96 / 8
Answer:
12 Cups are needed!
Step-by-step explanation:
You find the answer by dividing 96 milkshakes by 8 Milkshakes and find that 12 cups are needed.
:)
Please help!!!!!!!!!!!!!!!!!!
Answers
A = 0.5 x 10.4 x 16.9
A = 87.88
The area of the triangle is 87.88 ft²
Kyle volunteered 5.5 hours at the library this week. He needs to volunteer a total of 12 hours. Which equation can be used to find the number of hours, h, Kyle still needs to volunteer this week?
Answers
Answer:
12-5.5=h
12-5.5=6.5
Kyle needs to volunteer 6.5 more hours.
Step-by-step explanation:
Answer:
5.5 + h = 12
Step-by-step explanation:
Here, h represents the number of hours, Kyle still needs to volunteer this week,
Given,
He volunteered 5.5 hours at the library this week.
Since, the total number of hours he needs to volunteer = 5.5 + h
According to the question,
5.5 + h = 12
Which is the required equation.
What is the inverse of the function below? f(x) = 5x - 2
A. f -1(x) = x - 2/ 5
B. f -1(x) = x + 2 / 5
C. f -1(x) = -2 + 5x
D. f -1(x) = -5x + 2
Answers
Answer:
B. f -1(x) = x + 2 / 5
[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]
Step-by-step explanation:
To find the inverse of a function we need to interchange x and y an solve for y.
Since [tex]f(x)=y[/tex], then
[tex]f(x)=5x-2[/tex]
[tex]y=5x-2[/tex]
[tex]x=5y-2[/tex]
Add 2 to both sides
[tex]x+2=5y-2+2[/tex]
[tex]x+2=5y[/tex]
Divide both sides by 5
[tex]\frac{x+2}{5}=\frac{5y}{5}[/tex]
[tex]\frac{x+2}{5}=y[/tex]
[tex]y=\frac{x+2}{5}[/tex]
[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]
We can conclude that the correct answer is B. f -1(x) = x + 2 / 5
Determine if the Mean Value Theorem for Integrals applies to the function f of x equals 2 times the square root of x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem.
No, the theorem does not apply.
Yes, x = 1.
Yes, x equals 8 over 3.
Yes, x equals sixteen divided by 9.
Answers
[tex]f(x)=2\sqrt x[/tex] is continuous on [0, 4] and differentiable on (0, 4), so the MVT holds. We have
[tex]f'(x)=\dfrac1{\sqrt x}[/tex]
so that by the MVT, there is some [tex]c\in(0,4)[/tex] such that
[tex]f'(c)=\dfrac{f(4)-f(0)}{4-0}\implies\dfrac1{\sqrt c}=\dfrac{2\sqrt4}4=1[/tex]
[tex]\implies1=\sqrt c\implies \boxed{c=1}[/tex]
Answer:
x= 16/9
Step-by-step explanation:
[tex]f(x) = 2\sqrt{x}[/tex] is differentiable on [0,4] so the Mean Value Theorem For Integrals applies.
Average Value of the Integral:
[tex]\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx = \frac{1}{4-0} \int\limits^4_0 {2\sqrt{x} } \, dx[/tex]
After evaluating you will get [tex]\frac{8}{3}[/tex]
Now, this is the average value so you still need to find the x-value using the original equation:
[tex]\frac{8}{3} =2\sqrt{x}\\\\\frac{4}{3} = \sqrt{x}\\\\\frac{16}{9} =x[/tex]
A function is graphed on the coordinate plane.
what is the value of the function when x = 4
Answers
Answer:
1
Step-by-step explanation:
y = mx + b
y = 1/2 x - 1
y = 1/2 (4) - 1
y = 2 - 1
y = 1
When x = 4, the function y = (1/2)x - 1 evaluates to y = 1. This linear equation has a slope of 1/2 and a y-intercept of -1.
To find the value of the function y = (1/2)x - 1 when x = 4, you simply need to substitute x = 4 into the equation and solve for y:
y = (1/2)(4) - 1
y = 2 - 1
y = 1
So, when x = 4, the value of the function y is 1.
In a more general sense, this equation represents a linear function with a slope of 1/2 and a y-intercept of -1. The slope (1/2) represents the rate of change, meaning that for every unit increase in x, y increases by 1/2. The y-intercept (-1) is the value of y when x is 0.
When x = 4, as calculated above, y is 1. This means that if you were to plot this function on a coordinate plane, the point (4, 1) would lie on the graph.
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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
If f(x) = -3x^4 - 2x^3 + 3x^2, and g(x) = 3x^4 - 4x^3 + x^2 then f(x) + g(x) =
Answers
Answer: B) -6x³ + 4x²
Step-by-step explanation:
f(x): -3x⁴ - 2x³ + 3x²
+ g(x): 3x⁴ - 4x³ + x²
f(x) + g(x): - 6x³ + 4x²
Alberto has 92 stamps in one large álbum and 38 stamps in anotaré small álbum. How can he use mental math to find how many more stamps are in the large album use drawings to show your answer
Answers
Answer:
The answer would be the large album has 54 more stamps than the small album.
Step-by-step explanation:
... 92 - 38 = 54
Do you need a drawing done though?
the plot line shows the number of miles the individual members in a group of runners run each day
How many runners run at most 2 miles per day?
Answers
The number of runners run at most 2 miles per day is 13.
The calculation is as follows;2 miles = 6
3 miles = 4
4 miles = 2
5 miles = 1
Now if we add this,
So,
= 6 + 4 + 2 + 1
= 13
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Answer:
13
Step-by-step explanation:
Its easy, but its a trick question into getting you to click 6
This beach toy is a square pyramid. It has a height of 4 inches and the base has side lengths of 4 inches. What is the volume?
Answers
Check the picture below.
[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{4\times 4}{16}\\ h=&4 \end{cases}\implies V=\cfrac{1}{3}(16)(4)\implies V=\cfrac{64}{3}\implies V=21.\overline{3}[/tex]
Answer:
21.03^3 this is the answer.
Brainliest and lots of points
The function P(x)=2x2+3x+4, is dilated by the function I(x)=P(13x).
Which function rule represents I(x)?
Answers
Answer:
Step-by-step explanation:
I(x)=P(13x) = 2(13x)²+3(13x) +4
I(x)=P(13x).= 338x²+39x+4
A series of steps designed to help you solve problems and answer questions
A) observation
B) scientific method
C) experiment
D) hypothesis
Answers
Answer: B Scientific Method
Factor completely x³ - 7x² + 2x + 40 given x = -2 is a root.
Answers
Answer:
(x +2)(x -4)(x -5)
Step-by-step explanation:
When you divide the cubic by (x +2), the factor that has -2 as a root, you get a quadratic with roots 4 and 5. Thus the factors are ...
(x +2)(x -4)(x -5)
___
In the attachment, we have done the division using a graphing calculator. You can also do it by polynomial long division or by synthetic division. The resulting quadratic is ...
x^2 -9x +20 = (x -4)(x -5) . . . . . factor the quadratic
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A politician wants to see what people in her district think about tax cuts. Which procedure would be a good way of conducting a survey?
Answers
Answer:
D
Step-by-step explanation:
C is also possible but it is not purely random and it is not mentioned the mall is in her district.
Answer: D) Mail a questionnaire to random households.
Step-by-step explanation:
A) You are limited to only listeners of the radio show
B) You are limited to only those that are wiling and able to attend the meeting.
C) You are limited to only shoppers at that particular mall.
D) Randomly selecting households is the least biased method of responses from the district.
The frequency table was made using a deck of cards in which each card is numbered 1, 2, 3, or 4.
Create a bar graph by dragging the sliders on the horizontal axis to represent the probability distribution.
Answers
Answer:
Step-by-step explanation:
So the table means that there are 20 1's, 120 2's, 40 3's, and 20 4's.
The total number is 20+120+40+20 = 200.
So the probability of each is:
1: 20/200 = 0.10
2: 120/200 = 0.60
3: 40/200 = 0.20
4: 20/200 = 0.10
A bar graph that represents the probability distribution of each card is shown in the image below.
In Mathematics and Statistics, a frequency table can be used for the graphical representation of the frequencies or relative frequencies that are associated with a categorical variable or data set.
Based on the frequency, the total number of deck of cards can be calculated as follows;
Total number of deck of cards = 20 + 120 + 40 + 20
Total number of deck of cards = 200 cards.
Next, we would determine the probability distribution of each card as follows:
P(X = 1) = 20/200 = 0.10.
P(X = 2) = 120/200 = 0.60.
P(X = 3) = 40/200 = 0.20.
P(X = 4) = 20/200 = 0.10.
Identify the value of x and the length of each secant segment. HELP ASAP!!
Answers
Answer:
[tex]x=10, NL=8, NP=12[/tex]
Step-by-step explanation:
we know that
Applying the Intersecting secant Theorem
[tex]NL*NM=NP*NO[/tex]
substitute the given values and solve for x
[tex](3+5)*3=(2+x)*2[/tex]
[tex](8)*3=(2+x)*2[/tex]
[tex]24=(2+x)*2[/tex]
[tex]12=(2+x)[/tex]
[tex]x=12-2=10[/tex]
Find the value of NP
[tex]NP=(2+x)=2+10=12[/tex]
therefore
[tex]x=10, NL=8, NP=12[/tex]
Answer:
x = 7; NL = 12; NP = 20
Step-by-step explanation:
ur welcome
A man who weighs approximately 140 pounds has two 12 ounce beers and 1.5 ounce shot of liquor in two hours. How many standard drinks did the man consume
Answers
The answer is:
The man did consume two standard drinks in two hours.
Why?According to the standard drink conversion, we know that each 12 ounce beer we have one (1) standard drink, and each 1.5 ounce shot of liquor, we have another standar drink.
Calculating we have:
[tex]DrinksConsumed=12Oz(Beer)+1.5Oz(Liquor)=1StandardDrink+1StandardDrink\\\\DrinksConsumed=1StandardDrink+1StandardDrink=2StandardDrinks[/tex]
We have that the man did consume two standard drinks in two hours.
Have a nice day!
A man who consumed two 12 ounce beers and a 1.5 ounce shot of liquor has consumed three standard drinks according to the National Institute on Alcohol Abuse and Alcoholism's definition of a standard drink in the United States.
Explanation:According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), a standard alcoholic drink in the United States is equivalent to 14 grams (0.6 ounces) of pure alcohol. This typically is found in a 12-ounce beer, a 5-ounce glass of wine, or a 1.5 ounce shot of distilled spirits or liquor. The man in the question consumed two 12 ounce beers and one 1.5 ounce shot of liquor. Given that both the beer and the shot each lay within the standard drink size, we can conclude that the man consumed three standard drinks in total. Alcohol consumption and understanding standard drinks is important to monitor one's drinking habits for overall health.
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