Answer:
(a) Total No. of Subsets = 128
(b) Total No. of Proper Subsets = 127
Step-by-step explanation:
First we need to define the set of days of the week.
Set of Days of Week = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
It is evident from the set of days of the week, that it contains 7 elements.
(a)
The total no. of subsets of a given set is given by the following formula:
Total No. of Subsets = 2^n
where,
n = no. of elements of the set = 7
Therefore,
Total No. of Subsets = 2^n
Total No. of Subsets = 2^7
Total No. of Subsets = 128
(b)
The total no. of proper subsets of a given set is given by the following formula:
Total No. of Proper Subsets = (2^n) - 1
where,
n = no. of elements of the set = 7
Therefore,
Total No. of Proper Subsets = (2^n) - 1
Total No. of Proper Subsets = (2^7) - 1 = 128 - 1
Total No. of Proper Subsets = 127
The total number of subsets is 128 and the total number of proper subsets is 127 and this can be determined by using the given data.
Given :
The set of days of the week.
The following steps can be used in order to determine the number of subsets and the number of proper subsets:
Step 1 - According to the given data, the set is given below:
S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Step 2 - Now, the total number of subsets is given by the formula [tex]2^n[/tex] where 'n' is the number of elements of the set.
[tex]{\rm Total\;Subsets} = 2^7\\{\rm Total\;Subsets} = 128[/tex]
Step 3 - Now, the total number of proper subsets is given by the formula [tex](2^n-1)[/tex] where 'n' is the number of elements of the set.
[tex]{\rm Total\; Proper\; Subsets}=2^7-1\\{\rm Total\; Proper\; Subsets}=127[/tex]
a) The total number of subsets is 128.
b) The total number of proper subsets is 127.
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Sally is shopping for diapers and sees a box with 216 diapers for \$39.98 and a box with 88 diapers for \$24.99 . Which option has the better deal the diapers?
Answer:
For me I think 216 diapers for 39.98 is the best option
Step-by-step explanation:
Get the price of one diaper in each offer
216 = $39.98
1= ?
1×39.98÷216=0.19
Option 2
88=24.99
1 =?
1×24.99÷88=0.28
So I prefer buying 1 diaper for$0.19 and get 216 of them for $39.98 rather than buying 1 diaper for $0.28 and get 88 of them for $24.99
Exams are approaching and Helen is allocating time to studying for exams. She feels that with the appropriate amount of studying, she has an 80% chance of getting an A in Marketing. She also feels that she has a 60% chance of getting an A in Spanish with the appropriate amount of studying. Given the demands on her time, she feels that she has only a 45% chance of getting an A in both classes. What is the probability that Helen does not get an A in either class?
Answer: 0.05
Step-by-step explanation:
Let M = Event of getting an A in Marketing class.
S = Event of getting an A in Spanish class,
i.e. P(M) = 0.80 , P(S) = 0.60 and P(M∩S)=0.45
Required probability = P(neither M nor S)
= P(M'∩S')
= P(M∪S)' [∵P(A'∩B')=P(A∪B)']
=1- P(M∪S) [∵P(A')=1-P(A)]
= 1- (P(M)+P(S)- P(M∩S)) [∵P(A∪B)=P(A)+P(B)-P(A∩B)]
= 1- (0.80+0.60-0.45)
= 1- 0.95
= 0.05
hence, the probability that Helen does not get an A in either class= 0.05
Cristina held a raffle in which each ticket had a cost of 500 pesos. She sold all the tickets but 5 of her friends didn't pay for them immediately, they will pay for them later. How much money do her friends owe Cristina?
Answer:
$100 each.
Step-by-step explanation:
500 divided by 5 = 100
The formula for the volume of a cone is V = 1/3 bh
Solve v = 1/3 bh for b, the base of the cone.
A. b= 3h/v
B. b= v/3h
C. b= h/3v
D. b= 3v/h
Answer:
D. B=3v/h
Step-by-step explanation:
V = bh
multiply both sides by 3 to eliminate the fraction
3V = bh ( divide both sides by h )
B= 3v/h
The expression for the b is b = 3V/h if the formula for the volume of a cone is V = (1/3)bh option (D) is correct.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
It is given that:
The formula for the volume of a cone is:
V = (1/3)bh
To solve for b:
The expression can be defined as the combination of constants and variables with mathematical operators.
Make the subject as b:
V = (1/3)bh
On cross multiplication:
3V = bh
Divide by h on both the sides:
3V/h = bh/h
b = 3V/h
Thus, the expression for the b is b = 3V/h if the formula for the volume of a cone is V = (1/3)bh option (D) is correct.
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A brick is shaped like a rectangular prism. The length is 8 inches. The height is 4 inches. The width is 4 inches. What is rhe surface area of the brick?
Answer:
160
Step-by-step explanation:
8(4)(2)= 64
4(4)(2)= +32
8(4)(2)= 64
______
160
Answer:
Step-by-step explanation:
Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. She spends StartFraction 1 Over 15 EndFractionof her paycheck on dinner with friends. If she had not earned the bonus, the amount she spent on dinner would have been StartFraction 1 Over 10 EndFraction of her paycheck. Which equation can be used to find h, the number of hours Lindsay worked last week? StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis(10h + 60) = StartFraction 1 Over 10 EndFraction(10h) StartFraction 1 Over 15 EndFraction(10h + 60h) = StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 h right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis(10h) StartFraction 1 Over 15 EndFractionh(10 + 60) = StartFraction 1 Over 15 EndFraction h left-parenthesis 10 plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction h left-parenthesis 10 right-parenthesish(10) StartFraction 1 Over 15 EndFraction left-parenthesis 10 plus 60 h right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis(10 + 60h) = StartFraction 1 Over 10 EndFraction(10h)
Answer:
StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis
Step-by-step explanation:
The desired equation equates 1/15 of the amount Lindsay earned with 1/10 the amount without the bonus:
StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis
_____
Comment on the form of the answer
If you don't like answers in this form, please do not post questions in this form. Ordinary math symbols are much appreciated.
Answer:
A
Step-by-step explanation:
edge 23
uiuuiukiuiuiiuiuiuiuijkyfyi
Answer:
rawrrrrrr mannnnnn
Step-by-step explanation:
Answer:
Boo!
Step-by-step explanation:
What is the solution of the equation 16-17+ Vb=1?
b = 3
O b = 9
O b = 81
no solution
Sixty three hundred thousandth in standard form what is it?
Answer:
63(10)^4
Step-by-step explanation:
630 000= [tex]63(10)^4[/tex]
Jane's penny bank is 1/3 full. After she adds 480 pennies, it is 7/9 full. How many pennies can Jane's bank hold?
answer
980
Step-by-step explanation:
7/9-1/3=480
4/9=480
9/9=?
9/9×9/4×4809/1×120= 980Answer:
1080
Step-by-step explanation:
We take x to be the number of pennies in the bank at first which filled the bank by a ¹/3
¹/3=×
⁷/9=×+480
⅓ multiply by 3 with both the numerator and denominator to get 3/9
7/9-3/9=4/9
4/9=480
If 4/9=480 what of 9/9
9/9×480÷4/9
Reciprocate 4/9
9/9×480×9/4=1080
what is one way you can easily tell that 3/6 is not a simplified fraction
Answer:
3/6 can be simplified
Step-by-step explanation:
3 divided by 3
6 divided by 3
it comes out to be 1/2
A woman has a total of $ 12 , 000 to invest. She invests part of the money in an account that pays 7 % per year and the rest in an account that pays 9 % per year. If the interest earned in the first year is $ 920 , how much did she invest in each account?
Emerson is cutting boards that are 3/4 foot long to make bird houses. How many pieces can he cut from a board that is 9 feet
4 boxes of candy costs $ 10. How much
would 14 boxes of candy cost?
Answer:
14 boxes of candy would cost $35
Step-by-step explanation:
First find the unit price. It is $2.50 per box. Next multiply it by 14. It is $35 for 14 boxes of candy.
I hope this helped and have a great day.
(Please vote this the brainliest)
use the pictures or words to explain how you could find the sum of 7+7
If the odds against Deborah's winning first prize in a chess tournament are 1 to 7, what is the probability of the event that she will win first prize?
Answer:
7/8
Step-by-step explanation:
Odds against are the ratio between losses and wins.
odds against = L / W
Probability of winning is the ratio between wins and all games.
probability = W / games
probability = W / (W + L)
The odds against are 1 to 7.
1/7 = L / W
W = 7 L
The probability is therefore:
P = (7 L) / (7 L + L)
P = 7/8
A car is advertised as $288/month for 72 months. What is the cost of the car?
To
$14,400
$20,736
O
$28,800
O $17,280
Answer:
$20,736
Step-by-step explanation:
When these kind of advertisements are displayed,, it means the EMI cost per month shall be $288.
Since it provides the time period, that is 72 months,
Total cost of car in this case shall be $288 [tex]\times[/tex] 72 months = $20,736
Also, these include an interest factor, but overall it is = $20,736 only,
If one down payment for full price of the car is made the cost shall reduce by the interest amount, but since no interest rate is provided it shall be ignored.
For which values of a the system has at least one solution: 1.x≤7 ,x≥a
Given:
The system of inequalities
[tex]x\leq 7[/tex]
[tex]x\geq a[/tex]
To find:
The values of a for which the system has at least one solution.
Solution:
We have,
[tex]x\leq 7[/tex] ...(i)
It means all real values of x which are less than or equal to 0.
[tex]x\geq a[/tex] ...(ii)
It means all real values of x which are greater than or equal to a.
Using (i) and (ii), we get
[tex]a\leq x\leq 7[/tex]
The value of x is lies in the interval [a,7].
It means, if the value of a is less than or equal to 7, then system has at least one solution.
But if a is more than 7, then the system of inequalities have to solution.
Therefore, the value of a must be less than or equal to 7.
Si x2 = 3 a que es igual x6
Answer:
x2=3
x= 3/2
x= 1.5
x•6= 1.5•6
x=9
A study by a group of cardiologists determined that maximal heart rate in humans, a parameter used as a basis for prescribing exercise programs, depends on age. Maximal heart rate is around 201 beats per minute for a 10-year-old, and decreases at a constant rate of 7 every 10 years. Which of the following inequalities best describes the ages, for which maximal heart rate is less than 180, a is >or equal to 10.. HELP
Answer:
208 - 0.7a < 180
Step-by-step explanation:
What is the equation of this line?
Answer:
y=4/3x-1
Step-by-step explanation:
Answer:
Yes.
because yea
-V35 is it an irrational number
Death Valley headquarters in California is 190 feet below sea level. Badwater, America's lowest point, is 92 feet lower than Death Valley headquarters. How far below sea level is Badwater?
Answer: 282 Feet.
Step-by-step explanation:
given data:
sea level of Death Valley California = 190 feet
Sea level of Badwater America lowest point = 92 Feet lower than Dead valley.
Solution:
if Badwater is 92 feet lower than Death Valley,
Therefore; Badwater is 282 feet above sea level.
One side of triangle is 3x -5.. the other side is 19-x and the base is 2x. What is the perimeter of the triangle
Answer:
4x+14
Step-by-step explanation:
In order to find the perimeter of an triangle you need to add up all the sides of the triangle.
3x-5+19-x+2x ---> 3x+14-x+2x --> 4x+14
rx - sx + y = b solve for y
Answer:
y = b-rx+sx
Step-by-step explanation:
rx - sx + y = b
Subtract rx from each side
rx-rx - sx + y = b-rx
-sx +y = b-rx
Add sx to each side
sx - sx + y = b-rx+sx
y = b-rx+sx
[
When a submarine starts at sea level, goes down
250 feet, rises 80 feet, and descends another 18
feet, how would this be shown mathematically?
Answer:
This should be shown as:
-250 + 80 - 18 = - 118
Step-by-step explanation:
Going down 250 feet will mean going down feet 250 so it will be -250. Rising 80 feet will mean going up 80 feet so it will be adding 80. Finally, descending 18 feet will mean going down 18 feet, so it will be -18. If you put them all together as one equation, you will get -250 + 80 - 18 which is -118.
Hope this helps!
The required mathematical expression would be shown as:
-250 + 80 - 18 = - 118
What is algebra?Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.
When a submarine starts at sea level, goes down 250 feet, rises 80 feet, and descends another 18 feet which are given in the question.
Going down 250 feet means going down 250 feet, thus it will be -250. Rising 80 feet will result in an increase of 80 feet. Finally, descending 18 feet means going down 18 feet, therefore the result is -18. When you add them all together, you get -250 + 80 - 18, which equals -118.
Therefore, the required mathematical expression would be shown as:
-250 + 80 - 18 = - 118
To learn more about the Algebra link is given below.
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9) Gabriel took three math tests last semester. He scored a 91 on the first test, a
72 on the second test, and he couldn't remember what he scored on the third
test. When he saw his progress report, he saw that the average score for his
three tests was an 80. What did Carlos score on his third test?
PLEASE ANSWER ASAP I GOT UNTIL 6:30 AND I DONT GET IT
The average of anything can be calculated by adding up all the terms and dividing by the number of terms.
In this case,
the number of terms = 3
x = the missing test score.
(91 + 72 + x) / 3 = 80
Let's multiply both sides by 3
91 + 72 + x = 240
Combine like terms.
163 + x = 240
Subtract 163 from both sides
x = 77
Carlos scored a 77 on his third test.
Solve each equation. Check your solutions.
5 - 3|2 + 2w|= -7
Answer:
[tex]w=1\text{ or } w=-3[/tex]
Step-by-step explanation:
So we have the equation:
[tex]5-3|2+2w|=-7[/tex]
First, subtract 5 from both sides:
[tex]-3|2+2w|=-12[/tex]
Divide both sides by -3:
[tex]|2+2w|=4[/tex]
Definition of Absolute Value:
[tex]2+2w=4\text{ or } 2+2w=-4[/tex]
Divide both sides of the equation by 2 for both equations:
[tex]1+w=2\text{ or } 1+w=-2[/tex]
Subtract 1 from both sides:
[tex]w=1\text{ or } w=-3[/tex]
And we're done!
To check:
[tex]5-3|2+2(1)|=-7[/tex]
Multiply:
[tex]5-3|2+2|=-7[/tex]
Add:
[tex]5-3|4|=-7[/tex]
Multiply:
[tex]5-12=-7[/tex]
Subtract:
[tex]-7\stackrel{\checkmark}{=}-7[/tex]
And:
[tex]5-3|2+2(-3)|=-7[/tex]
Multiply:
[tex]5-3|2-6|=-7[/tex]
Subtract:
[tex]5-3|-4|=-7[/tex]
Absolute Value:
[tex]5-3(4)=-7[/tex]
Multiply:
[tex]5-12=-7[/tex]
Subtract:
[tex]-7\stackrel{\checkmark}{=}-7[/tex]
5x2x_=90
A-9 B-10. C-80. D-83
1/5 X B = 40 what is b
Answer:B = 200
Step-by-step explanation:multiply both sides by 5
5*1/5 = 5*40
B = 200