Let A, B, and C denote the sets of students that have taken calculus, sociology, and Spanish, respectively.
We're given that [tex]A\cup B\cup C[/tex] consists of 187 students.
We want to find the size of [tex]A\cap B\cap C[/tex], given that
• A has 61 students;
• B has 78;
• C has 72;
• [tex]A\cap B[/tex] has 15;
• [tex]A\cap C[/tex] has 20; and
• [tex]B\cap C[/tex] has 13.
Using the inclusion/exclusion principle, we have
[tex]|A\cup B\cup C|=|A|+|B|+|C|-(|A\cap B|+|A\cap C|+|B\cap C|)+|A\cap B\cap C|[/tex]
where |X| denotes the size of the set X. Plug in all the known sizes:
[tex]187=61+78+72-(15+20+13)+|A\cap B\cap C|[/tex]
[tex]\implies|A\cap B\cap C|=24[/tex]
so 24 students have taken all three classes.
Max is trying to prove to his friend that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. His friend Josiah is trying to prove that a reflection across the x-axis followed by a reflection across the y-axis will result in a reflection across the line y = x for a pre-image in quadrant II. Which student is correct, and which statements below will help him prove his conjecture? Check all that apply.
Max is correct.
Josiah is correct.
If one reflects a figure across the x-axis from quadrant II, the image will end up in quadrant III.
If one reflects a figure across the y-axis from quadrant III, the image will end up in quadrant IV.
A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x.
If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) Right-arrow (x, –y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-arrow (–x, y).
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line y = x should give.
Answer:
The correct option is;
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-arrow (x, -y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-Arrow (-x, y).
Taking the result from the first reflection (x, -y) and applying the second mapping rule will result in (-x, -y), not (y, x), which reflection across the line y = x should give
Step-by-step explanation:
We have that for reflection across the x-axis, (x, y) → (x, -y)
For reflection across the y-axis, (x, y) → (-x, y)
Therefore, given that the pre-image before the reflection across the y-axis is (x, -y), we have;
For reflection across the y-axis, (x, -y) → (-x, -y)
For reflection across the line, y = x, gives (x, y) → (y, x) which is not the same as (-x, -y)
Answer:
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-arrow (x, -y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-Arrow (-x, y).
Taking the result from the first reflection (x, -y) and applying the second mapping rule will result in (-x, -y), not (y, x), which reflection across the line y = x should give
Step-by-step explanation:
Explain PLEASE:
The legs of a right triangle are lengths x and x√3. The cosine of the smallest angle of the triangle is _____.
a. 1/2
b. √3
c. √3/2
d. 2√3
Answer:
[tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
The quickest way to solve this is to recognize this as a 30-60-90 triangle. The smallest angle is 30 degrees, and the answer is simply cos 30º.
You can also use the pythagorean theorem to find the length of the hypotenuse, then use SOH-CAH-TOA to get the answer.
Divide. Plssssss I forgot how
Answer:
1/21
Step-by-step explanation:
=> [tex]\frac{1}{7} / 3[/tex]
=> [tex]\frac{1}{7} * \frac{1}{3}[/tex]
=> [tex]\frac{1*1}{7*3}[/tex]
=> 1/21
Please help me.. tysvm if you do
Answer:
D.Step-by-step explanation:
"or" means sum, that is all x≤-2 plus all x≥3
≤-2 mens all numbers less than -2 and the -2
≥3 mens all numbers greater than 3 and the 3
how to do this question plz
Answer:
Depth of the milk = 4 cm
Step-by-step explanation:
In the figure attached,
Milk carton is in the shape of a cuboid having length = 8 cm, Width = 5 cm and Height = 15 cm
Depth of the milk in the carton = 12 cm
Milk inside the carton will have the same shape of cuboid, having same length and width but a different height.
Volume of the milk = volume of the cuboid shape of the milk
= Length × width × height
= 8 × 5 × 12
= 480 cm³
Now the carton is turned with its base on the shaded region.
By changing the base, dimensions of the milk inside the carton will change but the volume of the milk will remain the same.
New dimensions of the milk inside the carton will be,
Length = 15 cm
Width = 8 cm
Height = d cm (unknown side)
By using the formula of volume again,
V = l × b × h
480 = 15 × 8 × d
480 = 120d
d = [tex]\frac{480}{120}[/tex]
d = 4 cm
Therefore, depth of the milk in the carton will be 4 cm.
A circular table top has a radius of 24 inches.
What is the area of the table top, to the nearest square inch? Use 3.14 for n.
75 in.2
151 in.
1809 in.2
7235 in.2
Answer:
(C) 1809 in.2
Step-by-step explanation:
Took the test on edg :3
PLZ HELP ASAP!!! Will give brainliest if answered correctly with explanation!!!
Answer: Given.
Step-by-step explanation: The last sentence of the directions, Begin. . .
ends with: Construct line RS a bisector of ∠PQR
Please answer the question in the image below ASAP
Answer:
Option A.
Step-by-step explanation:
See attachment.
Basically, the reason why I left it at cm(3) was because that's the standard unit for volume, any length of measurement to the third power.
What is the slope of a line that contains the points (4, -2) and (-1, 4)
Answer:
-6/5
Step-by-step explanation:
The slope is (4 - (-2)) / (-1 - 4) = (4 + 2) / (-5) = 6 / -5 = -6/5.
Answer:
-6/5
Step-by-step explanation:
We can find the slope by using the slope formula
m = (y2-y1)/(x2-x1)
= (4 - -2)/(-1 -4)
= (4+2)/ ( -1-4)
=-6/5
Janine wants to build a model using 1/2-inch cubes. How many 1/2-inch cubes would she use to build a solid, cube-shaped model with side lengths of 4 inches? Show your work.
An aircraft carrier can travel 450 km in the same time a container ship travels 300 km. If the aircraft carrier was travelling 5 km/h faster what was the speed of the container ship? (answer is a rational expression)
Answer:
10 km/hr
Step-by-step explanation:
The aircraft carrier and the container ship both took 30 hours to travel their respective distances. If you divide both numbers by 30, you find that their differences is 5. We can tell that the aircraft carrier traveled 450 ÷ 30 = 15 km/hr and the container ship traveled at a speed of 300 ÷ 30 = 10 km/hr. The aircraft carrier traveled 5 km/hr faster. So, we can tell the container ship traveled at 10 km/hr.
Hope this helps! Plz give me brainliest, it will help me achieve my next rank.
Solve the system of equations algebraically.
{Y=(x-2)^2+2
{Y+4=3x
Answer:
(5, 11) and (2, 2)
Step-by-step explanation:
y = (x-2)² + 2
y + 4 = 3x
(x-2)² + 2 + 4 = 3x
x² - 4x + 4 + 6 = 3x
x² - 7x + 10 = 0
(x - 5)(x - 2) = 0
x - 5 = 0, x = 5
x - 2 = 0, x = 2
y = (5-2)² + 2 = 11
(5, 11)
y = (2-2)² + 2 = 2
(2, 2)
Answer:
[tex]\large \boxed{\sf \bf \ \text{ The solutions are } x=2, y=2 \text{ and } x=5, y=11.} \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We want to solve this system of equations.
[tex]\begin{cases}&y=(x-2)^2+2\\&y+4=3x\end{cases}[/tex]
This is equivalent to (subtract 4 from the second equation).
[tex]\begin{cases}&y=(x-2)^2+2\\&y=3x-4\end{cases}[/tex]
Then, we can write y = y, meaning:
[tex](x-2)^2+2=3x-4\\\\\text{*** We develop the left side. ***}\\\\x^2-4x+4+2=3x-4 \\\\\text{*** We simplify. *** }\\\\x^2-4x+6=3x-4\\\\\text{*** We subtract 3x-4 from both sides. ***}\\\\x^2-4x+6-3x+4=0\\\\\text{*** We simplify. *** }\\\\x^2-7x+10=0[/tex]
[tex]\text{*** The sum of the zeroes is 7 and the product 10 = 5 x 2 ***}\\\\\text{*** We can factorise. ***}\\\\x^2-5x-2x+10=x(x-5)-2(x-5)=(x-2)(x-5)=0\\\\x-2 = 0 \ \ or \ \ x-5 = 0\\\\x= 2 \ \ or \ \ x=5[/tex]
For x = 2, y =0+2=2 (from the first equation) and for x = 5 y=3*5-4=15-4=11 (from the second equation)
So the solutions are (2,2) and (5,11)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Jacob and issac decided to run to the basketball court after school the basketball court is 5 1/4 Miles from school the boys run at a pace 3 3/8 miles per hour
Answer: [tex]1\dfrac{5}{9}\text{ minutes}[/tex]
Step-by-step explanation:
Complete question is provided in the attachment below.
Given: Jacob and Issac decided to run to the basketball court
Distance between basketball court and school = [tex]5\dfrac{1}{4}[/tex] miles
[tex]=\dfrac{21}{4}[/tex] miles
Speed = [tex]3\dfrac{3}{8}[/tex] miles per hour
[tex]=\dfrac{27}{8}[/tex] miles per hour
Since, time = (distance) ÷ ( speed)
Now, the time taken by boys to arrive at the basketball court = [tex]\dfrac{21}{4}\div\dfrac{27}{8}[/tex] hours
[tex]=\dfrac{21}{4}\times\dfrac{8}{27}\\\\=\dfrac{7\times2}{9}=\dfrac{14}{9}\\\\=1\dfrac{5}{9}\text{ minutes}[/tex]
Hence, the required length of time = [tex]1\dfrac{5}{9}\text{ minutes}[/tex]
The boat is 130 m from the base of a cliff. The cliff is 80m high. Determine, to the nearest degree, the angle of depression of the boat from the top of the cliff.
Answer:
32 degrees (rounded to nearest angle)
Step-by-step explanation:
Using trigonometric ratios:
Please refer to the picture of my explanation below.
tan^-1 means inverse, so on calculator remember to use the inverse function, by shifting.
Ajay said to Ragu, “If you lend one five rupees, both of us will have equal amount”. Ragu said to Vijay, “If you lend me five rupees, I will have 5 times the amount as you”. What amount does each of them have now?
Answer:
Ajay has 10 rupees and Ragu has 20 rupees.
Step-by-step explanation:
Let's say Ajay has a rupees, and Ragu has r rupees.
Ragu lends 5 rupees to Ajay.
r - 5 = a + 5
r = a + 10
Ajay lends 5 rupees to Ragu.
5(a - 5) = r + 5
5a - 25 = r + 5
r + 5 = 5a - 25
r = 5a - 30
5a - 30 = a + 10
4a = 40
a = 10 rupees
r = 5 * 10 - 30
r = 50 - 30
r = 20 rupees
Hope this helps!
Answer:
Ajay has 15 Rupees while Ragu has 45 Rupees
Step-by-step explanation:
I believe by " one five", you mean fifteen
Let the original amount that Ajay has be "a"
Let the original amount that Ragu has be "r"
If Ragu lends Ajay 15 rupees, Ragu will now have, (r - 15) while Ajay will have (a + 15)
Since both of them will have equal amount, r - 15 = a + 15
r = a + 30.............(1)
If Ajay lends Ragu 5 rupees, Ajay will have a - 5 while Ragu will have r + 5.
Since Ragu will now have 5 times the amount Ajay has, r + 5 = 5(a - 5)
r + 5 = 5a - 25
r = 5a - 30.............(2)
Equating equations (1) and (2):
a + 30 = 5a - 30
4a = 60
a = 15
Substitute a = 15 into equation (2)
r = 5(15) - 30
r = 75 - 30
r = 45
Ajay has 15 Rupees while Ragu has 45 Rupees
Dmitri needs 6 liters of a 16% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 12% solution and the other an unlimited supply of the 24% solution. How many liters of each solution should Dmitri use?
Answer:
4 litres of 12% solution
2 litre of 24% solution
Step-by-step explanation:
Let the 12% solution = l
Let the 24% solution = h
Dimitri needs a total of 6 litres of both :
l + h = 6 - - - - - - - - (1)
He needs a mixture of both volumes of both to give a 16% volume
12%l + 24%h = 16% * 6
0.12l + 0.24h = 0.96 ----(2)
From (1)
l + h = 6;
l = 6 - h
Substitute l =6-h into (2)
0.12(6 - h) + 0.24h = 0.96
0.72 - 0.12h + 0.24h = 0.96
0.72 + 0.12h = 0.96
0.12h = 0.96 - 0.72
0.12h = 0.24
h = 0.24 / 0.12
h = 2
From ;
l = 6 - h
l = 6 - 2
l = 4
Can anyone help quickly.. explanation is not necessary but would be appreciated, I struggle with this topic and would like to understand it a little bit.
Answer:
38.68 degrees
Step-by-step explanation:
In this equation you are trying to find the degrees using the hypotenuse and opposite. So you have to use the function sin^-1(5/8). Because when using Sin it is opposote ove hypotenuse.
a^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.
Answer:
[tex]2a - 3b + 4c = 1[/tex]
Step-by-step explanation:
Given
[tex]a^2 + b^2 + c^2 = 2(a - b - c) - 3[/tex]
Required
Determine [tex]2a - 3b + 4c[/tex]
[tex]a^2 + b^2 + c^2 = 2(a - b - c) - 3[/tex]
Open bracket
[tex]a^2 + b^2 + c^2 = 2a - 2b - 2c - 3[/tex]
Equate the equation to 0
[tex]a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0[/tex]
Express 3 as 1 + 1 + 1
[tex]a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0[/tex]
Collect like terms
[tex]a^2 - 2a + 1 + b^2 + 2b + 1 + c^2 + 2c + 1 = 0[/tex]
Group each terms
[tex](a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
Factorize (starting with the first bracket)
[tex](a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex](a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + (b^2 + b+b + 1) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)(b + 1)) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + (c^2 + 2c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + (c^2 + c+c + 1) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + (c(c + 1)+1(c + 1)) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + ((c + 1)(c + 1)) = 0[/tex]
[tex]((a - 1)^2) + ((b + 1)^2) + ((c + 1)^2) = 0[/tex]
Express 0 as 0 + 0 + 0
[tex](a - 1)^2 + (b + 1)^2 + (c + 1)^2 = 0 + 0+ 0[/tex]
By comparison
[tex](a - 1)^2 = 0[/tex]
[tex](b + 1)^2 = 0[/tex]
[tex](c + 1)^2 = 0[/tex]
Solving for [tex](a - 1)^2 = 0[/tex]
Take square root of both sides
[tex]a - 1 = 0[/tex]
Add 1 to both sides
[tex]a - 1 + 1 = 0 + 1[/tex]
[tex]a = 1[/tex]
Solving for [tex](b + 1)^2 = 0[/tex]
Take square root of both sides
[tex]b + 1 = 0[/tex]
Subtract 1 from both sides
[tex]b + 1 - 1 = 0 - 1[/tex]
[tex]b = -1[/tex]
Solving for [tex](c + 1)^2 = 0[/tex]
Take square root of both sides
[tex]c + 1 = 0[/tex]
Subtract 1 from both sides
[tex]c + 1 - 1 = 0 - 1[/tex]
[tex]c = -1[/tex]
Substitute the values of a, b and c in [tex]2a - 3b + 4c[/tex]
[tex]2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)[/tex]
[tex]2a - 3b + 4c = 2 +3 -4[/tex]
[tex]2a - 3b + 4c = 1[/tex]
What is the sum of 3x to the second power +2x-1
Answer:
[tex]3x^2+2x+1[/tex]
Step-by-step explanation:
Sum means to add and second power means that the exponent is "2". So, the expression is:
=> [tex]3x^2+2x+1[/tex]
It cannot be simplified further.
I don't understand the British system of colonization
Answer:
Which of the following numbers is a composite number that is divisible by 3? A. 49 B. 103 C. 163 D. 261 Answer: B) 245
Step-by-step explanation:
The Department of Health in the United Kingdom wants to know whether the healthcare system is achieving its goals in Scotland. Much information about healthcare comes from patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the Department of Health conducted the Scotland Health Survey, which was used to interview a random sample of 34,572 people who live in Scotland.
Part A: What is the population for this sample survey? What is the sample? (4 points)
Part B: The survey found that 70% of males and 87% of females in the sample had visited a general practitioner at least once during the past year. Do you think these estimates are close to the truth about the entire population? Explain. (6 points)
Answer:
A. the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population.
Step-by-step explanation:
A. According to the given data we have that it was used to interview a random sample of 34,572 people who live in Scotland, therefore, the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population becuase a large sample was conducted, hence we can make an aproximation that represents the population parameter.
Consider the function represented by the table.
What is f(0)?
04
O 5
06
O 7
Answer:
6
Step-by-step explanation:
From the table given defining a function, the values of "x" on the table represents the input of the function, which gives us an output, f(x), which can be labelled as "y" in some instances.
Thus, the value of f(0), is simply the output value we would get, given an input value of "0".
So therefore, f(0) = 6. That is, at x = 0, f(x) = 6.
Answer: 6
Step-by-step explanation:
After getting 10% discount a customer paid RS 2034 with 13% VAT to buy a bag from a retailer. If the retailer made a profit of 20%, by how many percent did he mark the price of the bag above the cost price?
Answer:
33.33%
Step-by-step explanation:
We are told that the customer paid Rs. 2034 after getting 10% discount with 13% vat on marked price (m.p.)
hence:-
2034 = m.p. × 90/100 × 113/100
m.p = (2034 × 100 × 100)/(90 × 113)
m.p. = Rs.2000
Now, due to the fact that VAT (which in this question is given to be 13%) is not the profit of the retailer, thus the selling price (s.p.) of the bag would be given by;
s.p = m.p. × 90/100
s.p = 2000 × 90/100
s.p = Rs. 1800
We are told that the retailer made a profit of 20%
Thus:-
c.p. × 120/100 = s.p.
c.p.= s.p. × 100/120
c.p.= 1800 × 100/120
c.p. = Rs.1500
Therefore, the percentage with which he marked above the c.p is;
% mark up = (m.p - c.p)/c.p) × 100
Plugging in the relevant values, we have;
(2000 - 1500)/1500) × 100
(500/1500) × 100 = 33.33%
Question 5. The area of square A is 144 square feet. The side length of square B is 6 feet less than the side length of square A. How many times greater is the area of square A than the area of square B? *
Answer:
Square A is 4 times greater than Square B
Step-by-step explanation:
Square A is 12 feet x 12 feet = 144
Square B is 6 feet x 6 feet = 36
144 ÷ 36 = 4
Andrew's bicycle has tires with a radius of 7 inches. What is the area of one of the bicycle tires, in terms of π?
Answer:
49π
Step-by-step explanation:
The formula for the area of a circle is,
[tex]\pi r^2[/tex]
If the radius is 7 inches we need to plug that in for r in the formula.
π(7)^2
7*7 = 49
Thus,
the area in terms of pi is 49π.
Hope this helps :)
Answer:
49πStep-by-step explanation:
[tex]r = 7\\A = ?\\A =\pi r^2\\A =\pi7^2\\A = 49\pi[/tex]
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
20x-8 ...last option
Step-by-step explanation:
PLEASE HELP MEEEE
I need help finding x a b and c
Answer:
x=15
angle b=7*15=105
angle a=180-105=75
angle c=2x=30
Step-by-step explanation:
b=7x
sum of straight angle :=180
isoceles traingle = 2 sides are equal, and two angles are equal
b+a=180
7x+a=180
sum of traingle =180
2a+c=180
2a+2x=180 first equation
7x+a=180 second equation
solve by elimination ( multiply second equation by 2)
2a+2x=180
2a+14x=360 ( subtract)
2a+2x-2a-14x=180-360
-12x=-180
x=-180/12=
x=15
angle b=7*15=105
angle a=180-105=75
angle c=2x=30
Examine circle C, with inscribed angle ∠EQD, central angle ∠ECD, and intercept ED⌢. Central angle ECD is labeled with a measure of 104∘. What is m∠EQD, in degrees? Enter your answer as a number, rounded to the nearest tenth, if necessary, like this: 42.5
Answer:
∠EQD = 72°Step-by-step explanation:
From the circle it can be seen that the angle ∠EQD lies on the circumference of the circle. A circumference of a circle is known to be any point on the circle. Also we have central angle ∠ECD of 104°
In circle geometry, there is a theorem that states; Angle at the center of a circle is twice the angle at the circumference. Applying this theorem to the given question we can say, ∠ECD = 2∠EQD
Substituting the given value;
104° = 2∠EQD
Dividing both sides by 2
104/2 = 2∠EQD/2
∠EQD = 104/2
∠EQD = 72°
Answer: The answer is 52.
Step-by-step explanation:
Suppose the mean height for adult males in the U.S. is about 70 inches and the standard deviation is about 3 inches. Assume men’s heights follow a normal curve. Using the Empirical Rule, 95% of adult males should fall into what height range?
Question options :
a. They should be between 64 and 76 inches tall.
b. They should be close to the height that is 95% of the mean. That is, 66.5 inches, plus or minus 2 standard deviations.
c. They should be at or below the 95th percentile, which is 74.92 inches.
d. None of the above.
Answer: a. They should be between 64 and 76 inches tall.
Step-by-step explanation:
Given the following :
Assume men's height follow a normal curve ; and :
Mean height = 70 inches
Standard deviation= 3 inches
According to the empirical rule ;
Assuming a normal distribution with x being random variables ;
About 68% of x-values lie between -1 to 1 standard deviation of the mean. With about 95% of the x values lying between - 2 and +2 standard deviation of mean. With 99.7% falling between - 3 to 3 standard deviations from the mean.
Using the empirical rule :
95% will fall between + or - 2 standard deviation of the mean.
Lower limit = - 2(3) = - 6
Upper limit = 2(3) = 6
(-6+mean) and (+6+ mean)
(-6 + 70) and (6+70)
64 and 76
The range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches
According to the given data
The mean height for adult males in the U.S. is about 70 inches
The standard deviation of heights is about 3 inches.
Considering the data to be normally distributed
According to the empirical rule for normal distribution we can write that
95.45% of the data lies with in the range of
[tex]\rm \mu - 2\sigma \; to \; \mu +2\sigma\\\\where \\\mu = Mean\\\sigma = Standard \; deviation[/tex]
We have to to determine that using the Empirical Rule 95% of adult males should fall into what height range
According to the given data
[tex]\rm \mu = 70\\\rm \sigma = 3 \\[/tex]
[tex]\rm Lower \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 - 2(3) = 64[/tex]
[tex]\rm Upper \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 +2(3) = 76[/tex]
So we can conclude that the range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches
For more information please refer to the link given below
https://brainly.com/question/25394084
My state's lottery has 30 white balls numbered from 1 through 30 and 20 red balls numbered from 1 through 20. In each lottery drawing, 3 of the white balls and 2 of the red balls are drawn. To win, you must match all 3 white balls and both red balls, without regard to the order in which they were drawn. How many possible different combinations may be drawn?
Answer:
I dont give you the answer right away so you will read what i write and fully understand :D
Step-by-step explanation:
We are picking 3 balls from 30 balls, so its C(30,3) because the order of picking the balls doesnt matter. We also need to pick 2 balls from 20 balls, which is C(20,2). So the answer is C(30,3) * C(20,2).