Consider the following data for 120 mathematics students at a college concerning the languages French, German, and Russian:
65 study French, 45 study German,
42 study Russian , 20 study French and German,
25 study French and Russian,
15 study German and Russian.
8 study all three languages.
Determine how many students study exactly 1 subject and fill the correct numbers of students in each eight region of Venn diagram shown in figure.
Answers
Answer:
check online for more information
The Venn diagram for given situation is as shown below.
The number of students who study exactly one subject = 56
What is set?"It is a collection of well-defined elements"
What is Venn diagram?"It is a pictorial representation that uses circles to show the relationships among sets."
For given example,
We have been given the data for 120 mathematics students at a college concerning the languages French, German, and Russian
Let set A, B and C represents the number of students who study French, German and Russian respectively.
⇒ n(A) = 65
⇒ n(B) = 45
⇒ n(C) = 42
20 study French and German
⇒ n(A ∩ B) = 20
25 study French and Russian,
⇒ n (A ∩ C) = 25
15 study German and Russian.
⇒ n(B ∩ C) = 15
8 study all three languages.
⇒ n(A ∩ B ∩ C) = 8
So, the Venn diagram for given situation is shown below.
Now, we find the number of students who study exactly one subject.
28 students study French only, 18 students study German only and 10 students study Russian only.
So, the total number of students who study exactly one subject is,
28 + 18 + 10 = 56
Therefore, 56 students study exactly one subject
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Related Questions
the sum of three terms in a GP is 14 and the sum of their squares is 84, find the terms
Answers
Answer:
The terms are 2, 4, and 8
Step-by-step explanation:
a+b+c=14
a^2+b^2+c^2=84
Plug in numbers.
3+6+5=14
3^2+6^2+5^2=70
This is too little, meaning the some of the terms have to be larger.
1+7+6=14
1^2+7^2+6^2=86
This is too much, meaning smaller terms are needed.
2+8+4=14
2^2+8^2+4^2=84
This is perfect.
A vase held flowers 1/2 is the flowers were roses and 1/4 of those flowers were red what fraction where red roses?
Answers
1/2 x 1/4 means 1/8 were red roses
To prepare for a wedding, Aiden bught 60 candles. He paid $0.37 for each candle. His sister bought 170 candles at a sale where she paid $0.05 less for each candle than Aiden did. How much did Aiden spend on candles, how much did his sister spend on candles, and who spent more on candles (how much more when you answer this question).
Answers
Answer:
Aiden spent $22.20. His sister spent $54.40. His sister spent $32.20 more than Aiden.
Step-by-step explanation:
Please help solve for a in the equation in the photo
Answers
[tex]\huge\bf Question:—[/tex]
[tex] \sf \longmapsto \: g=a(4− {d}^{2} )[/tex]
[tex]\huge\bf Solution:—[/tex]
[tex] \underline{\bf \: Flip \: the \: equation:—}[/tex]
[tex] \sf \longmapsto \: −a {d}^{2} +4a=g[/tex]
[tex] \underline{\bf \: Factor \: out \: variable \: (a):—}[/tex]
[tex] \sf \longmapsto \: a(− {d}^{2} +4)=g[/tex]
[tex]\underline{ \bf \: Divide \: both \: sides \: by -d^2+4 :—} [/tex]
[tex]\sf \longmapsto \: \dfrac{a( - {d}^{2} + 4) }{ { - d ^2+ 4}^{} } = \dfrac{g}{{ - d ^2+ 4}^{}} [/tex]
[tex]\sf \longmapsto \:1 a = \dfrac{g}{{ - d^2 + 4}^{}} [/tex]
[tex]\underline{\bf Answer:—}[/tex]
[tex]\boxed{ \bf \: a = \dfrac{g}{ - d^2 + {4}^{} } }[/tex]
Answer:
[tex]\boxed{\boxed{\sf a=\cfrac{G}{4-d^2} }}[/tex]
Step-by-step explanation:
[tex]\sf G=a(4-d^2)[/tex]
Use the Distributive Property to multiply a by (4-d^2):
[tex]\sf G=4a-ad^2[/tex]
Now, we'll swap sides so that all variable terms are on the left hand side.
[tex]\sf 4a-ad^2=G[/tex]
Combine like terms:
[tex]\sf (4-d^2)\:a =G[/tex]
Divide both sides by 4-d^2:
[tex]\sf \cfrac{(4-d^2)a}{4-d^2} =\cfrac{G}{4-d^2}[/tex]
Dividing by 4-d^2 undoes the multiplication by 4-d^2.
[tex]\sf a=\cfrac{G}{4-d^2}[/tex]
_______________________________________
Sally can paint a room in 4 hours while it takes Steve 7 hours to paint the same room. How long would it take them to paint the room if they worked together?
Answers
Answer:
3 hours
Step-by-step explanation:
7hours - 4hours
hope it helped
pls give me brainliest
Is it possible to have a bounded feasible region that does not optimize an objective function?
Answers
It is not possible to have a bounded feasible region that does not optimize an objective function.
What is the feasible region?The viable zone is the common area that the linear programming problem's constraints all dictate.
There is an optimum value of the objective function if the feasible region is bounded and the function attains its optimum values at the extremes of the feasible region.
Hence, it is not possible to have a bounded feasible region that does not optimize an objective function.
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In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more than 4.8. . A builder needs to install a ramp to reach a door that is 2.5 feet off the ground.Is 20 feet long enough for the straight line distance of the ramp to meet the requirements? What angle of elevation will this ramp have?
Answers
Answer:
Yes, 35 feet is enough
The angle of elevation is 4.1º
How do I divide using "partial remainders"?
Answers
Step-by-step explanation:
When the modulus is ∞, the result is equal to the value in ST(0). Otherwise, C2 is set, and the result in ST(0) is called the partial remainder. The exponent of the partial remainder will be less than the exponent of the original dividend by at least 32. Using partial remainders, dividing multiples of 4 from 46 until you can't divide anymore. You can't divide anymore because 2 is less than 4. So, 2 is the remainder.
PLZ HURRY IT'S URGENT!!!
What is the value of x? Leave answer in **simplest radical form.***
options:
4
4√3
8
8√3
Answers
Three-fourths of the 8th graders at Kingston
Middle School went on the class trip. If 252
students went on the trip, how many 8th
graders are there?
Answers
sAnswer:189 students
Step-by-step explanation:
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the quadratic formula to solve the equation.
X^2 - 7x – 6 = 0
Answers
Step-by-step explanation:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a=1.
b=-7
c=-6
x=
[tex] \frac{ - ( - 7) + \sqrt{ (- 7)^{2} - 4(1)( - 6)} }{2(1)} [/tex]
OR
[tex] \frac{ - ( - 7) - \sqrt{ (- 7) ^{2} - 4(1)( - 6)} }{2(1)} [/tex]
Therefore x= 7,772
OR
x=-0,772
[6x(5-3)+9]-5 with step by step
Answers
Answer: 10
Step-by-step explanation: [30-24+9]=15-5=10
The answer after calculation the given expression using PEDMAS rule: [6x(5-3)+9]-5 is 16.
What is the answer using PEDMAS?The given expression, [6x(5-3)+9]-5, can be simplified using the order of operations, also known as PEDMAS P – Parenthesis First: B – Brackets First
E – Exponents
D – Division
M – Multiplication
A – Addition
S – Subtraction
First, we evaluate the expression inside the bracket: 5-3, which equals 2. Substituting this result back into the expression, we have [6x2+9]-5.
For the next step, we perform the multiplication operation. Multiplying 6 by 2 gives us 12. Now our expression becomes [12+9]-5.
Moving on to addition, we add 12 and 9, resulting in 21. Our expression now becomes [21]-5.
Finally, we subtract 5 from 21, which gives us 16. Thus, the value of the expression [6x(5-3)+9]-5 is 16.
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joey’s town voted on a new speed limit . 40 % of the 25 votes were in favor of the new speed limit . How many votes were in favor ?
Answers
Step-by-step explanation:
I don't know the answer really
[tex]\sf 3x+6y=12[/tex]
Answers
Answer:
[tex]3x + 6y = 12[/tex]
[tex]3x + 6y - 6y = 12 - 6y[/tex]
[tex]3x = 12 - 6y[/tex]
[tex] \frac{3x}{3} = \frac{12}{3} - \frac{6y}{3} [/tex]
[tex] \frac{3x}{3} = 1 = x[/tex]
[tex] \frac{12}{3} - \frac{6y}{3} [/tex]
[tex] = \frac{12 - 6y}{3} [/tex]
[tex] = \frac{6(2 - y)}{3} [/tex]
[tex] \frac{6}{3} = 2[/tex]
[tex] = 2( - y + 2)[/tex]
[tex]x = 2( - y + 2)[/tex]
Answer:
x=2(3-y)
Step-by-step explanation:
3x+6y=12
x+2y=4
x=4-2y
=2(2-y)
0.03249 in standard form to 3 significant figures is
(A) 3.24 × 10−1
(B) 3.24 × 10−2
(C) 3.25 × 10−2
(D) 3.25 × 10−3
Answers
can someone please tell me whether the answer is a, or b? or if it’s none of those. ty :)
Answers
1.) If you are dividing 1.7 by 8.5, how many places to the right will you need to move the decimal point in the divisor and dividend? a.) 1 b.) 2 c.) 3 d.) 0 2.) Find the quotient of 50 divided by 0.1. a.) 0.5 b.) 5 c.) 50 d.) 500 3.) In the division problem 0.86 ÷ 0.02, What would be the new dividend once you move the decimal as needed? a.) 8.6 b.86 c.) 43 d.) .2 4.) 6.9 divided by .3 is . a.) 2.3 b.) 23 c.) .23 d.) 123 5.) When 75.64 is divided by 0.61, the quotient is . a.) 124 b.) 125 c.) 134 d.) 126 6.) 7.26 ÷ 0.22 = N a.) 33 b.) 0.33 c.) 0.31 d.) 0.35 7.) 5.12 ÷ 0.10=n a.) 51.2 b.) 5.12 c.) 512 8.) Glen bought 0.75 meter of pink ribbon, which she will cut into 0.25meter strips for her Project in EPP. How many pieces did she make? a.) 3 b.) 4 c.) 5 d.) 6 9.) A bottle of medicine contains 27.5 ounces. I take 1.65 ounces each dose. How many doses are in th bottle? a.) 16.67 doses b.) 16 doses c.) 61 doses d.) 66 doses 10.) If Pathy earns Php256.25 for gardening. If she worked 20.5 hours this month, then how much did she earn per hour? a.) Php 12.5 b.) Php 125.00 c.) Php 25.00 d.) Php1.25 11.) 5.26 times 10 is . 12.) a.) 52.6 b.) 5.26 c.) .526 Divide 59 ÷ 7. Round off the answer to two places of decimals. d.) 5,260 a.) 8.44 b.) 8.53 c.) 8.43 d.) 8.42 13.) Which of the following mathematical equation has a quotient of 6.78? a.) 61÷ 7 b.) 61÷9 c.) 6.1÷ 9 d.) 9 ÷ 61 14.) How many 7 does 86 has? a.) 12 b.) 13 c.) 11 d.) 10 15.) What would be the remainder if you divide 59 by 9? a.) 3 b.) 5 c.) 6 d.) 1 16.) When the divisor is bigger than the dividend,the quotient is . a.) decimal in form b.) whole number c.) zero d. one 17.) 4÷9 = n a.) 0.4 b.) 0.5 c.) 0.6 d.) 07 18.) Which mathematical sentence below has a quotient of never ending decimal? a.) 24 ÷ 27 b.) 25 ÷ 25 c.) 1 ÷ 5 d.) 100 ÷ 500
Answers
All the answers to the given fraction problems are;
1) A; 1
2) D: 500
3) B: 86
4) B: 23
5) A: 124
6) A: 33
7) A: 51.2
8) A: 3
9) A: 16.67 doses
10) A: Php 12.5
11) A: 52.6
12) C: 8.43
13) B: 61 ÷ 9
14) A: 12
15) B: 5
16) A: decimal form
17) A: 0.44
18) A: 24 ÷ 27
1) 1.7 ÷ 8.5
We need to change them to whole numbers by shifting the decimal points one place to the right to get; (17/85)
2) 50 ÷ 0.1
Shift decimal one place to the right to get;
500/1
Quotient = 500
3) 0.86 ÷ 0.02
The dividend is usually the numerator. Let us shift both numerator and denominator by two decimal places to the right to get; 86 ÷ 2
Thus, new dividend = 86
4) 6.9 ÷ 0.3
Move decimal points one place to the right to get;
69 ÷ 3 = 23
5) 75.64 ÷ 0.61
Move decimal points two places to the right to get;
7564 ÷ 61
Numerator written as a factor of denominator gives;
(124 × 61)/61
Quotient = 124
6) 7.26 ÷ 0.22
Move decimal points two places to the right to get;
726/22
Numerator written as a factor of denominator gives;
(33 × 22)/22 = 33
7) 5.12 ÷ 0.10
Move decimal points two places to the right to get;
512/10 = 51.2
8) A 0.75 m pink ribbon was cut into 0.25 m strips. Thus;
Number of pieces = 0.75/0.25
Move both decimals 2 places to the right to get;
75/25 = 3 pieces
9) A bottle contains 27.5 ounces
You take 1.65 ounces for each dose.
Number of doses per bottle = 27.5/1.65
Move decimal points two places to the right; 2750/165
Number of doses per bottle = 16.67 doses
10) She earned Php256.25 for gardening.
She worked 20.5 hours the month.
Amount earned per hour = 256.25/20.5
move decimal places two points to the right to get;
Amount earned per hour = Php 12.5
11) 5.26 times 10
move decimal place two points to the right to get;
(526 × 1/100) × 10 = 52.6
12) 59 ÷ 7
Nearest multiple of 7 to 59 is 8.
Thus, 59 ÷ 7 = 8³/₇
⇒ 8.43
13) The one that gives a quotient of 6.78 is;
61 ÷ 9
14) How many 7 does 86 have?
This is; 86 ÷ 7
Nearest multiple of 7 to 86 is 84 which is 12 × 7
Thus, there are 12 numbers of 7 in 86.
15) Remainder if you divide 59 by 9
Nearest multiple of 9 to 59 is 54 which is 9 × 6.
Remainder = 59 - 54 = 5
16) When divisor is bigger than the dividend, it means the denominator is bigger than the numerator and so the quotient is an improper fraction which is a decimal.
17) 4 ÷ 9 = 0.444
Approximating to one decimal place = 0.4
18) The correct mathematical sentence with never ending decimal is;
24 ÷ 27
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. Solve the rational equation x+6 / 3 − x+8 / 5 = 0.
Answers
Answer:
x= -3
Step-by-step explanation:
[tex] \frac{x + 6}{3} - \frac{x + 8}{5} = 0[/tex]
Multiply both sides by 15 (LCM of 3 and 5):
[tex] \frac{15(x + 6)}{3} - \frac{15(x + 8)}{5} = 0[/tex]
5(x +6) -3(x +8)= 0
Expand:
5x +30 -3x -24= 0
2x +6= 0
-6 on both sides:
2x= -6
x= -6 ÷2
x= -3
Stuck on this, need help on this.
Answers
Answer:
Domain: (-∞ , ∞)
Range: y <= 8 [8 , -∞)
Step-by-step explanation:
x = 2
f(x) = 8
x<=2
f(x) <=8
What is equivalent to 56 − 7 + ( 26 − 4 ) ÷ 2
Answers
Answer:
60
Step-by-step explanation:
56-7+22÷2
56-7+11
67-7=60
hope it helps thanks
I NEED HELP WITH PRECALC PLEASE
Answers
Answer: First question: D, Second question: A
Step-by-step explanation:
Note: I'm not so good at expanding so I'll just solve it :)
So this leaves either C or D
Apply the sum rule:
8-70=-62
The only one that gives a negative sum is D
For the second picture, the one you have chosen is correct
a1 = 3 and r = -5 so:
an = 3/5 * (-5)^n
Plugging in 8 for n (the first choice) we get the given term: -234,375
Answer:
(d) 2 +(-5) +(-12) +... (a) a8Step-by-step explanation:
1.Putting n = 0 and n = 1 into the expression being summed will show you which series is correct.
2 -7n for n=0 is 2 -7·0 = 2
2 -7n for n=1 is 2 -7·1 = -5
The series of the last choice (d) is correct.
__
2.The given sequence is exponential with a first term of 3 and a common ratio if -5. Then the n-th term is ...
an = 3(-5)^(n -1)
We want to find n for an = -234,375.
-234375 = 3(-5)^(n-1)
-78125 = (-5)^(n-1)
For n to be a real number, we must have n even. In that case, the value of n is equivalent to the value that is the solution to ...
78125 = 5^(n -1)
Taking logs of both sides, we get ...
log(78125) = (n -1)·log(5)
log(78125)/log(5) = n -1 . . . . . . . . . . . . divide by log(5)
n = 1 +log(78125)/log(5) = 1 +7 = 8 . . . add 1 and evaluate
-234,375 is the 8th term of the sequence.
Which statement is true about point Y?
Point Y is the center of the circle that passes through points D, F, and N.
Point Y is the center of the circle that passes through points M, N, and E.
Point Y is the center of the circle that passes through points L, M, and N.
Point Y is the center of the circle that passes through points D, E, and F.
Answers
Answer:
D, E and F
Step-by-step explanation:
Beause y is a point. It is a prime example physics.
Sheila is making accessories for the soccer team. She uses 559.24 inches of fabric on headbands for 28 players and 3 coaches. She also uses 271.04 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answers
Answer:
27.72 inches of fabric
Step-by-step explanation:
28+3=31
Fabric used on each player:559.24÷31=18.04
271.04÷28=9.68
18.04+9.68=27.72
How do u solve this?
Answers
Answer:
first you need a problem to solve.
Step-by-step explanation:
what is the question here?
CAN SOMEONE TELL ME IF I CLICKED THE RIGHT AWNSER PLEASE
Answers
Answer:
yes your absolutely right
Step-by-step explanation:
you just are
Select all equations that do NOT have a solution.
A 8x + 4x = 0
B 6x + 2 = 4x + 2 + 2x
C 4x – 8x – 3 = 6 – 4x
D 5x + 1 = 1 – 5x
E 12x – 3 – 5x = 9 + 7x – 6
Answers
Answer:
C and E are the answers:)
Step-by-step explanation:
Hope this helps!
Answer- C,D, and E
If you plug in any number for those proplems you will get a different number a each side
Marisol has 5 times as many books as jerry. Jerry has 15 books. How many more books does marisol have
Answers
Answer:
5 times more books
Step-by-step explanation:
In total Marisol has 75 books. She has 5 times as many books and Jerry has 15. 5*15=75
Answer each part. If necessary, round your answers to the nearest hundredth. (a) A color printer prints 9 pages in 3 minutes. How many pages does it print per minute? | pages per minute (b) At Hoffman's Bike Rentals, it costs $37 to rent a bike for 7 hours. How many hours of bike use does a customer get per dollar? hours per dollar
Answers
Answer:
Q1: 3 pages per minute
Step-by-step explanation:
time = 3 minutes
pages = 9 pages
answer = 9 divided by 3 = 3
Answer:
3 pages per minute
1 hour per $5.29
Step-by-step explanation:
9÷3= 3
37÷7= 5.29
Jason stands in the corner of a very large field. He walks, on a bearing of 030°,
a distance of d metres. Jason then changes direction and walks twice as far on a new
bearing of 120°. At the end of the walk Jason calculates both the distance he must
walk and the bearing required to return to his original position. Given that the total
distance walked is 120 metres, what answers will Jason get if he is correct?
Answers
Answer:
Step-by-step explanation:
d + 2d = 120
3d = 120
d = 40 m
east distance was 40cos30 + 80cos120 = -5.35898 m
north distance was 40sin30 + 80sin120 = 89.282032
as 30° and 120° bearings are 90° apart, Jason needs to walk
D = √(d² + (2d)²) = d√5 or 40√5 meters or about 89.44 m to return to his original position.
we could also use √(-5.35898² + 89.282032²) = 89.44 m
direction will be
θ = arctan -89.28/5.359 = -86.565° or a bearing of 273.4°
The length of the opposite side of a right triangle is 2cm longer than the length of the adjacent side. The hypotenuse is 4cm longer than the adjacent side. Use a quadratic equation to determine the perimeter of the triangle.
PLEASE HELP
Answers
Answer:
Step-by-step explanation:
Let x be the adjacent side length in cm
opposite side is x + 2 cm
hypotenuse is x + 4 cm
x² + (x + 2)² = (x + 4)²
x² + (x² + 4x + 4) = (x² + 8x + 16)
x² - 4x - 12 = 0
(x - 6)(x + 2) = 0
so either
x - 6 = 0 x = 6
or
x + 2 = 0 x = -2
positive answer is x = 6 as negative length does not make sense
opposite side is 6 + 2 = 8
hypotenuse is 6 + 4 = 10
perimeter is 6 + 8 + 10 = 24 cm