The relationship between the number of students that are good at a given subject is an illustration of sets.
26 students are good at Mathematics only.28 students are not good at all.We use the following representations:
[tex]M \to[/tex] Mathematics
[tex]E \to[/tex] English
[tex]P \to[/tex] Psychology
From the question, we have the following parameters
[tex]M = 45[/tex] -- Mathematics
[tex]M\ n\ E =15[/tex] -- Mathematics and English
[tex]M\ n\ P =13[/tex] -- Mathematics and Psychology
[tex]E\ n\ P =16[/tex] -- English and Psychology
[tex]P=20[/tex] -- Psychology
[tex]All = 9[/tex] -- All 3 subjects
[tex]Total = 80[/tex] -- All students
The number of students that are good at mathematics only is as follows:
First, we calculate those that are good at mathematics and English only
[tex](M\ n\ E)' = M\ n\ E - All[/tex]
[tex](M\ n\ E)' = 15 - 9 = 6[/tex]
Then those that are good at mathematics and psychology only
[tex](M\ n\ P)' = M\ n\ P - All[/tex]
[tex](M\ n\ P)' = 13 - 9 = 4[/tex]
So, the students that are good at mathematics only are:
[tex]M' = M - (M\ n\ E)' -(M\ n\ P)' - All[/tex]
[tex]M' = 45 - 6 -4 -9[/tex]
[tex]M' = 26[/tex]
Hence, 26 students are good at Mathematics only.
To calculate the number of students that are not good in any of the subjects, we make use of the complement rule
[tex]A + A' = Total[/tex]
Where:
[tex]A \to[/tex] Students that are not good in any
[tex]A' \to[/tex] Students that are good in at least one
So, we have:
[tex]A' =M' + (M\ n\ E)' + (M\ n\ P)' + (E\ n\ P)' + All[/tex]
Where:
[tex](E\ n\ P) = (E\ n\ P)' - All[/tex]
[tex](E\ n\ P) = 16-9 = 7[/tex]
The equation becomes:
[tex]A' =26 + 6 + 4+7+9[/tex]
[tex]A' =52[/tex]
Recall that:
[tex]A + A' = Total[/tex]
[tex]A = Total - A'[/tex]
[tex]A = 80 - 52[/tex]
[tex]A = 28[/tex]
Hence, 28 students are not good at all.
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Your average bi-weekly net pay is $489.00. What is 15% of your average monthly net pay? (1 point)
$146.70
$158.93
$160.13
Bi weekly means you get paid every 2 weeks so you would get two paychecks per month.
Monthly net pay = 489.00 x 2 = $968.00
Multiply monthly by 15%
968 x 0.15 = $146.70
Answer: $146.70
If Your average bi-weekly net pay is $489.00. Your average monthly net pay is:$146.70.
Average monthly net payFirst step
Monthly net pay=$489.00×2
Monthly net pay=$968
Second step
Average monthly net pay:
Average monthly net pay=$968×15%
Average monthly net pay=$146.70
Therefore your average monthly net pay is:$146.70.
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WILL GIVE BRAINLIEST IF FAST!!!!
The store for select the poi was coming in 2010, the population was tot 30 million people in the
tering this feat
Trechts by trong this time
Enter your soxandre
Get More Help
Cear
CA
Help Me Shive This
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Answer:
can you please type that question
Use exponents to rewrite 27.
A. 93
B. 39
C. 9 + 9 + 9
D. 23
E. 33
Answer:
3³ = 27
Step-by-step explanation:
I'm guessing you need answer E
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! LOOK IMAGE FOR OPTIONS
Which table represents a direct variation function?
Find the area of a square with sides 11 feet long.
Answer:
the area of square is
the area of square is side*side
therefore ,area= 11*11= 121 feet square
Write the equation of the line in fully simplified slope- intercept form .
Anyone know how to solve it?
Answer:
[4 -2 -19]
[-1 1 8]
Step-by-step explanation:
[ 2 5] * [a b c] = [3 1 2]
[ 1 3] ld e f] [1 1 5]
[2a+5d 2b+5e 2c+ 5f] = [3 1 2]
[a+3d b + 3e c + 3f] [1 1 5]
Solving systems of equations:
2a + 5d = 3
a + 3d = 1
2a + 6d = 2
Subtract -d = 1 so d = -1
and a = 1 - 3d = 1 - 3(-1) = 4
So d = -1 and a = -4.
In the same way we find that b = -2, e = 1, c = -19, f = 8.
Which expressions are equivalent? Check all that apply. 39 34 –92 99 Which expressions are equivalent? Check all that apply. 39 34 –92 99 811
Answer:
3 to the fourth power and 81 to the first power.
Step-by-step explanation:
i took he quiz
The equivalent expressions are 3^4 and -9^2
How to determine the equivalent expressions?To determine the equivalent expressions, we simply solve the options.
So, we have:
3^9 = 19683
3^4 = 81
-9^2 = 81
9^9 = 387420489
From the above computation, we have:
3^4 = 81 and -9^2 = 81
Hence, the equivalent expressions are 3^4 and -9^2
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A bakery sells 12 gourmet orange-zest cupcakes for $36.00. Select all the statements that are true.
Answer:
wut are the statements?
Step-by-step explanation:
in class of 80 student debre berhan university ,45 are good in mathematics,15 are good in both mathematics and in english,13 are good in both mathematics and psychology,16 are good in both english and psychology only,20 are good in psychology and 9 are good in both of three courses.how many students are not good in any of three courses ?
We want to find the number of students that are not good in any of the courses.
There are 80 students.
45 are good in mathematics
15 are good in both, mathematics and in English
13 are good in both, mathematics and psychology
16 are good in both English and psychology
20 are good in psychology
9 are good in all of the courses.
First, we know that we have:
45 good in math + 20 good in psychology = 65 students good in something.
But we know that:
13 are good in both, mathematics and psychology
This means that there are 13 students that are being counted twice, so we need to subtract 13.
45 + 20 - 13 = 52 students good in something.
Now we know that:
15 are good in both, mathematics and in English
16 are good in both English and psychology
9 are good in all of the courses.
So one would want to also count these students, but notice that these are already good in mathematics or in psychology, so these are already counted.
And we can't see the number of students that are only good with English, so we can conclude that
52 students are good in something.
then 28 students are not good at any of the 3 courses.
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solve for c
ad + bc = 2
Answer:
c = (2 - ad) / b
Step-by-step explanation:
Subtract both sides by ad
bc = 2 - ad
Divide both sides by b
c = (2 - ad) / b
Roast beef has 25 g of protein and 11 g of calcium per serving. A serving of mashed potatoes has 2 g of protein and 25 g of calcium. Set up and solve a system to show how many servings of each are needed to supply exactly 29g of protein and 61 g of calcium.
Step-by-step explanation:
your answer
mark me a brainlistWhat is the surface area of the rectangular prism formed from this net?
O A. 10.5 in.2
B. 16 in.2
C. 16.5 in.2
Ο Ο Ο
OD. 18 in.2
E 32.5 in.2
Find the greatest common factor of these two expressions.
28xy8v7 and 14x6v3
9514 1404 393
Answer:
14xv^3
Step-by-step explanation:
Coefficients are 28 and 14, which have a GCF of 14.
x exponents are 1 and 6, so the GCF is x^1 = x
y exponents are 8 and 0, so the GCF is y^0 = 1
v exponents are 7 and 3, so the GCF is v^3
The GCF of the two terms is the product of the factors just found:
14xv^3
What value of x makes the equation 3(x-6) – 8x = -2 + 5(2x + 1) true? Show your work.
9514 1404 393
Answer:
x = -1.4
Step-by-step explanation:
3(x-6) -8x = -2 + 5(2x + 1)
3x -18 -8x = -2 +10x +5 . . . . . . . eliminate parentheses
-21 = 15x . . . . . . . . . . . . . . add 5x -3 and collect terms
x = -21/15 = -7/5
x = -1.4
__
Check
3(-1.4 -6) -8(-1.4) = -2 +5(2(-1.4) +1) . . . substitute for x
3(-7.4) +11.2 = -2 +5(-2.8 +1)
-22.2 +11.2 = -2 +5(-1.8)
-11 = -2 -9 . . . . . true
Someone please help!
-it is a 4 digit number.
-the vaule of the digit in the thousands place is 10 times greater than the value of the digit in the hundreds place.
-the least digit is in the tens place.
-the sun of the digits is 19. -the digit in the ones place is 4 more than the digit in the hundreds place.
-whats the mystery number?
Answer:
5539
Step-by-step explanation:
You should conclude that the number in the thousands place and the one in the 100s place are the same.
x * 1000 + x * 100 + y + x + 4
So you could sum the digits as
3x + y + 4 = 19 Subtract 4 from both sides
3x + y = 15
x can be six That means y = 1 which is OK
x can be five That means y = 3 which is OK
Now we run into a little grief. Can x be 4? No
x cannot be 4 that would mean that y = 19 - 12 = 7 The tens digit is too big.
Come to think of it, x cannot be 6 because then the units digit will be 10 -- not possible.
So the answer is
1000*5 + 100*5 + 10*3 + 9
5539 is the answer.
Thanks for posting.
We want to find a 4-digit number that meets some given conditions. We will find two, which are:
4438 and 5509
A general 4-digit number can be written as:
a*1000 + b*100 + c*10 + d
Where a, b, c, and d are single-digit numbers.
a is the thousands digit
b is the hundreds digit
c is the tens digit
d is the units digit.
Here we know that:
"the value of the digit in the thousands place is 10 times greater than the value of the digit in the hundreds place."
So the first term is 10 times the second term, this means that:
(a*1000) = 10*(b*100)
a*1000 = b*1000
a = b
-the least (the smaller one) digit is in the tens place.
so:
c < a, b, d
- The sun of the digits is 19.
So:
a + b + c+ d = 19
-The digit in the ones place is 4 more than the digit in the hundreds place.
so:
d = b + 4
Now we can rewrite all of these conditions as:
b = ac < b, a, da + b + c + d = 19d = b + 4Using the first one, we can replace all the b's by a's in the other conditions, so we have:
c < a, d2a + c + d = 19d = a + 4Now we can use the third equation and replace it in the second one to get:
2a + c + d = 19
2a + c + (a + 4) = 19
3a + c + 4 = 19
3a + c = 19 - 4
3a + c = 15
Now we need to remember that:
c < a.
So we can try with different values of a.
For example, if a = 3, then:
3*3 + c = 15
9 + c = 15
c = 15 - 9 = 6
here we have c > a, so we can discard this.
If a = 4, then:
3*4 + c = 15
12 + c = 15
c = 15 - 12 = 3
c < a
From this we can construct our number:
a = b = 4
c = 3
d = b + 4 = 4 + 4 = 8
Then the number is:
4438
If a = 5, then:
3*5 + c = 15
15 + c = 15
c = 15 - 15 = 0
c < a
So we also can have:
a = b = 5
c = 0
d = b + 4 = 9
Such that the number is:
5509
And if a is equal to or larger than 6 we have problems, because
3*6 + c = 15
18 + c =15
c = 15 -18 = -3
And c can't be a be a negative number.
So we can conclude that we found two 4-digit numbers that meet all the conditions, and these are:
4438 and 5509
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No link answers please solve honestly
Answer:
y = 78
Step-by-step explanation:
66 + 4 = 70 + 4 = 74 + 4 = 78
-12 + 3 = -9 + 3 = -6 + 3 = -3
x = -3
y = 78
Help me with the e or how many you can
Please afsp
Answer:
(a)
sin²A×cos²A+sin⁴A
we will take sin²A as an common factor
so it become
sin²A×(cos²A+sin²A)
sin²A+cos²A=1
sin²A×1=sin²A
(c)
sinA×cotA
cotA= cosA/sinA
sinA×cosA/sinA=cosA
(e)
(1+sinA)²-(1-sinA)²
(a+b)²=a²+b²+2×a×b
(a-b)²=a²+b²-2×a×b
1²+sin²A+2×1×sinA-(1²+sin²A-2×1×sinA)
1+sin²A+2sinA-1-sin²A+2sinA=4sinA
(g)
(cosec²A-1)/cosec²A
cosecA=1/sinA
1/sin²A-1/1/sin²A
(1/sin²A-1)×sin²A
1-sin²A
1=sin²A+cos²A
sin²A+cos²A-sin²A=cos²A
(i)
sqrt(1+tan²A)×sqrt(1-cos²A)
1+tan²A=
1+sin²A/cos²A=
sin²A+cos²A/cos²A
sin²A+cos²A=1
=1/cos²A
1-cos²A
1=sin²A+cos²A
sin²A+cos²A-cos²=sin²A
sqrt(1/cos²A)×sqrt(sin²A)
1/cosA×sinA=sinA/cosA=tanA
have a great day
Name prime numbers 1-30
Answer:
2,3,5,7,11,13,17,19,23 and 29
Step-by-step explanation:
hope this helps
find the radius of a circle which has a sector of area 9 square meters determined by a central angle 1/3 radian
Answer:
L = length of arc , R = radius
radian angle = L / R
L = R* radian angle
L = R * 1/3
L = R/3 #1
Area of sector = 1/2 L*R
By substitution using #1
Area of sector = 1/2 * R/3 * R
9 = R^2 /6
R^2= 6*9
R^2= 36
R =✓36
R = 6
Fred and Gina are playing tennis. The first player to win 2 sets wins their match. Fred has a 3/5 chance to win each set while Gina has a 2/5 chance. What is the probability that the match goes three sets until someone wins?
Answer:
60/125 which can be reduced to 12/25
Step-by-step explanation:
Gina wins
2/5 * 2/5 = 4/25
3/5 * 2*5 * 2/5 = 12 /125
2/5 * 3/5 * 2/5 = 12/125
Fred Wins
3/5 * 3/5 = 9/25
2/5 * 3/5 * 3/5 = 18/125
3/5 * 2/5 * 3/5 = 18/125
P(3 sets) = (18 + 18 + 12 + 12)/125 = 60/125
P(2 sets) = (20 + 45)/125 = 65/125
I found the probability of 2 sets so I could add the results together to see if the probability totals 1. It does. This question is done correctly.
Juan Carlos grew 2.79 inches last year. Which shows a way to represent the value of the 9 in this number?
Answer:
0.09
Step-by-step explanation:
hope it helps!!!!!!
I need help ASAP!!! Thanks
Express the following as the sum of two odd primes
a) 36
b)68
c)24
d)42
Answer:
b)68
Step-by-step explanation:
i think helping you...say correct or no...
Write the decimal expansion for 5/6 Choose the correct decimal notation. A. 0.83 B. 0.8 C. 0.6 D. 0.83
Answer: Choice A
Explanation:
If you use a calculator or long division, you should find that
5/6 = 0.8333333...
where the '3's go on forever. We shorten this down to [tex]0.8\overline{3}[/tex], the horizontal bar tells us which item goes on forever (just the 3 only).
The answer is A. I don't know how to explain.
Which is the graph of f(x) = 100(0.7)?
Answer:
70; The following graph is simply a horizontal line at the value 70.
Step-by-step explanation:
Answer:
Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).
Step-by-step explanation:
Edge
Evaluate (solve) the expression 4x + 8 when x = 2
Hi ;-)
[tex]x=2\\\\4x+8=4\cdot2+8=8+8=\boxed{16}[/tex]
Step-by-step explanation:
4x + 8
4 × 2 + 8
8 + 8
16
Therefore its 16.
Find the simple interest.
Principal
Rate 11% principle 9000 time1 1/2 years what's the amount of simple interest earned is
Answer:
Here is your answer. Hope this helps you!
Answer:
Rate(R)= 11%
Times(T)=11/2
Principle(P)= 9000
We know that,
SI = P×T×R÷100
= 9000×11/2×11÷100
=9000×5.5×11÷100
= 544500÷100
=5445
Hence, the required simple interest is 5445.
Ans
Please Help! I am so confused. I will give you the brainiest and a lot of points.
Please show work
Read each number from top to bottom. Each digit is in base 20, and as I pointed out in another question of yours, 1 bar = 5, 1 dot = 1, and disk = 0.
(47) Only 1 digit here, with 2 bars and 4 dots. So this is 14.
(49) 3 digits, in order from top to bottom: 19, 0, 6. So this number is
[19]06₂₀ = 19×20² + 0×20¹ + 6×20⁰ = 7606
(51) 3 digits: 8, 8, 8.
888₂₀ = 8×20² + 8×20¹ + 8×20⁰ = 3368
(53) 4 digits: 2, 0, 0, 11.
200[11]₂₀ = 2×20³ + 0×20² + 0×20¹ + 11×20⁰ = 16011
(55) 4 digits: 10, 10, 0, 10.
[10][10]0[10]₂₀ = 10×20³ + 10×20² + 0×20¹ + 10×20⁰ = 84010
(57) 6 digits: 5, 10, 0, 6, 2, 3.
5[10]0623₂₀ = 5×20⁵ + 10×20⁴ + 0×20³ + 6×20² + 2×20¹ + 3×20⁰ = 17602443
(59) 6 digits: 10, 5, 0, 0, 11, 4.
[10]500[11]4₂₀ = 10×20⁵ + 5×20⁴ + 0×20³ + 0×20² + 11×20¹ + 4×20⁰ = 32800224
2x-3y=6 and x+3y=3
help me I cannot understand it please in substitution method
Answer:
[tex]thank \: you[/tex]
Answer:
Take 2x- 3y= 6 as equation 1
And
x+ 3y= 3 as equation 2
Now add both equation
2x - 3y = 6
x + 3y = 3
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
3x 0 = 9
We can also write 3x 0= 9 as 3x = 9
Now we have to solve 3x =9
3x = 9
x = 9/3
x= 3
I hope this will help you