Answer:
630 distinct possible collections of letters could be put in the bag.
Step-by-step explanation:
Since on the refrigerator, MATHCOUNTS is spelled out with 10 magnets, one letter per magnet, and two vowels and three consonants fall off and are put away in a bag, if the Ts are indistinguishable, to determine how many distinct possible collections of letters could be put in the bag, the following calculation must be performed:
Vowels: 3
(AO, AU, OU)
Consonants: 7
3 x 7 x 6 x 5 = X
3 x 210 = X
630 = X
Therefore, 630 distinct possible collections of letters could be put in the bag.
Answer: 75 distinct possible collections
Step-by-step explanation:
2 vowels = 3C2 = 3
3 vowels = 25 ways
25 * 3 = 75 total ways
Suppose you plan to go out for a picnic during spring break. You plan to bring sandwiches, fruits, and drinks. But you only have one picnic basket that can only hold a certain capacity. Each of the items has a value and a size, and you cannot hold all your items in the basket. The picnic basket can hold a total size of 17. Given that the size and the value of items are as follows, how many of each item should you bring to maximize the total value?
Size Value
Sandwich 9 6
Fruit 3 4
Drink 4 6
a) List and explain carefully what the decision variables are.
b) Write out the objective function.
c) Write out the constraints.
d) Write the linear program.
e) Solve the Linear Programming problem using excel. Show your results.
Answer:
e) z (max) = 24
x₁ = x₂ = 0 x₃ = 4
Step-by-step explanation:
a) The problem requires maximizing the total value from sandwich fruits and drink, therefore the objective function is associated to the sum of the values of each value.
We have three variables xi ( x₁, x₂, x₃ ) the values of sandwich, fruits and drink, and we have to maximize such quantities subject to the constraint of size (the capacity of the basket)
b) z = 6*x₁ + 4*x₂ + 6*x₃ Objective Function
Constraint :
basket capacity 17
9*x₁ + 3*x₂ + 4*x₃ ≤ 17
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
e) z (max) = 24
x₁ = x₂ = 0 x₃ = 4
NOTE: Without the information about fractional or decimal feasible solution we decided to use integers solution
The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 6. Find the probability that less than 3 road construction projects are currently taking place in this city.a) 0.050409b) 0.089235c) 0.301168d) 0.014936
Answer:
The probability that less than 3 road construction projects are currently taking place in this city is 0.06197
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Poisson distribution with a mean of 6.
This means that [tex]\mu = 6[/tex]
Find the probability that less than 3 road construction projects are currently taking place in this city.
This is:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.00248[/tex]
[tex]P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.01487[/tex]
[tex]P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.04462[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00248 + 0.01487 + 0.04462 = 0.06197[/tex]
The probability that less than 3 road construction projects are currently taking place in this city is 0.06197
The measure of angle NOP is 140
Which of the equations could be used to find the measure of angle NOQ?
Answer:
a) 23 + x = 140
Step-by-step explanation:
140 - 23 = 117
the angle x = 117°
HELP DUE RIGHT NOW
will mark brainliest!
10 points
Pls write answer as soon as possible
Answer:
Step-by-step explanation:
11.-3(2x-8)=-12
-6x+24=-12
-6x=-12-24
x=-36/-6
x=6
12.4(6+2x)=0
24+8x=0
8x=0-24
x=-24/8
x=-3
13.3x+2x+6=-15
5x+6=-15
5x=-15-6
x=-21/5
14.4=-2(x+3)
4=-2x-6
4+6=-2x
10/-2=x
-5=x
15.27=46+2x-x
27=46+x
27-46=x
-19=x
Answer:
11. -6
12. -3
13. 4.2
14. -5
15. -19
Step-by-step explanation:
Check the pictures. Would take too long for me to type it all out.
Write the equation of the line that has a slope of 2 and passes through the point (-5, 1).
y = 2x - 5
y = 2x + 11
y = 2x + 1
y = 2x + 9
Step-by-step explanation:
= 2x +b
Use the given point (2, 5)
5 = 2(2) +b
b = 5 -4 = 1
The equation of the line is
y = 2x +1
Note general form of the slope-intercept form of a line is y = mx +b, where m is the slope and b is the y-axis intercept
help if you can! no links please :)
Answer:5/12
Step-by-step explanation:
Enter the correct answer in the box.
Replace the values of m and n to show the solutions of this equation.
X^2 + 6x-5=0
Answer:
x= -3 + [tex]\sqrt{14}[/tex]
Step-by-step explanation:
Which type of function is shown in the table below?
x f(x)
1 8
2 15
3 24
4 35
5 48
Answer:
2 15 sorry po kung mali
Step-by-step explanation:
Wala pong step by step
i will give brainliest please i need help its a middle school question
9514 1404 393
Answer:
33 pounds per weekW = 33t + 42Step-by-step explanation:
The pumpkin gained 372 -141 = 231 pounds in 7 weeks, or an average of ...
(231 lb)/(7 wk) = 33 lb/wk
The pumpkin gained 33 pounds per week.
__
In the 3 weeks after the pumpkin plant was chosen, it would have gained 3×33 = 99 pounds. It weighed 141 pounds at that point, so must have had an initial weight of 141 -99 = 42 pounds at t=0. The weight of the pumpkin can be modeled as ...
W = 33t +42
Please help! Image attached!
Number 1 is 5y = 50
Number 2 is h = 7
Number 3 is multiplication
Number 4 is addition
help please ............
Answer:
A is the Far Left
B is the Base
C is the Hypotenuse
Step-by-step explanation:
Interpretation
Open with Angles p and q are complementary, p is four times the size of q. What is the size of q ?
Answer:
p = 72
q = 18
Step-by-step explanation:
Complementary means they add to 90o
p + q = 90
p = 4*q
Substitute 4q for p
4q + q = 90 Combine
5q = 90 Divide by 5
5q/5 =90/5
q = 18
p = 4q
p = 4*18
p = 72
lim (x->0) ((x^3 - 2x) ln(1+sinx))/ ln(cos 3x)
Answer:
qijejejsllaoajvrjaoaq
Classify each triangle as right triangle or not right triangle
Answer:
Step-by-step explanation:
pythagoras theorem
a^2+b^2=c^2
21^2+20^2=29^2
441+400=841
841=841
since the sum of square of two smaller sides is equal to the square of longest side .The given triangle can form right angle.
someone knows thiss?
how do you find volume of sphere, cylinder, cone ? ... explaining please
Answer:
Step-by-step explanation:
The formula for the volume of a sphere is given by :
[tex]V_s=\dfrac{4}{3}\pi r^3[/tex]
Where
r is the radius of the sphere
The formula for the volume of a cylinder is given by :
[tex]V_c=\pi r^2 h[/tex]
Where
r and h is the radius and height of the cylinder
The formula for the volume of a cone is given by :
[tex]V_C=\dfrac{1}{3}\pi r^2 h[/tex]
Where
r and h is the radius and height of the cone
Definition: Another unit of measurement for angles. This one can be measured on the x-y coordinate
plane. The number of these in an angle equals the number of radii it takes to measure a circular arc
described by that angle.
Answer:
radians
Step-by-step explanation:
Another unit of measure for angles others then degrees are radians.
Answer:
radians
Step-by-step explanation:
Help me (pre algebra by the way)
Answer:
A, D, & F
Step-by-step explanation:
When you distribute, you get 6a + 5a + 5 - 3a + 21.
After combining like terms, you get 8a + 26.
Lastly, all you have to do is figure out which expressions are equivalent to
8a + 26.
A) 8a + 26 = 8a + 26
D) 6a + 5a + 5 - 3a + 21 (combine like terms) = 8a + 26
F) 2(4a + 13) - Simple distribution
2 x 4a = 8a
2 x 13 = 26
2(4a + 13) = 8a + 26
if I choose two cards, one of the time, from a standard deck of cards, what’s my probability that I choose A red card, then without putting it back to a black card
Answer:
P(Red) = 26/52, P(Black) = 26/51
Step-by-step explanation:
There are 26 red cards and 26 black cards in a standard deck of 52 cards.
This means the probability of picking a red card from the deck is 26/52.
Now, since we are taking out the red card after drawing from the deck, we only have 51 cards. Therefore, the probability of picking a black card from the deck is 26/51.
13 Calculate the area of a circle with radius 14 cm.
Answer:
[tex]{ \tt{formular : {area = \pi {r}^{2} }}} \\ area = 3.14 \times {14}^{2} \\ \\ { \bf{answer : { \tt{area = 615.75 \: {cm}^{2} }}}} \\ \\ { \underline{ \blue{ \tt{⚜becker \: jnr}}}}[/tex]
Answer:
A≈ 615.75 [tex]cm^{2}[/tex]
Step-by-step explanation:
A= [tex]\pi[/tex][tex]r^{2}[/tex]
A= [tex]\pi[/tex]·[tex]14^{2}[/tex]
A≈ 615.75216 [tex]cm^{2}[/tex]
Find the distance between the two points. Round to the nearest tenth if necessary. (0, 7), (–12, –2)
Answer:
Distance = 15 units
Step-by-step explanation:
[tex]Let \ (x_1 , y_ 1 ) = ( 0 , 7 ) \ , \ (x _ 2 , y _ 2 ) \ = ( -12 , -2 ) \\\\Dsitance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1 )^2} \\\\[/tex]
[tex]= \sqrt{(-12 - 0)^2 + ( -2 - 7)^2} \\\\=\sqrt{12^2 + 9^2 }\\\\=\sqrt{144 + 8 1} \\\\= \sqrt {225 } \\\\= 15[/tex]
Answer:
( 12 , - 10 )
Step-by-step explanation:
Difference between the x points : 0 - ( - 12 ) = 12
Difference between the y points : - 12 - ( - 2 ) = -10
There fore the difference ( 12 , - 10 )
Hopefully this is what you mean
Have a nice day !
if a student is selected at random, find the probability the student is a junior. round to the nearest whole percent! i’m not good at probability so an explaination would be appreciated!!!
Answer:
the answer is 40%.
Step-by-step explanation:
probability= total number of juniors all over total number.
that is , 8
20
2
5
rounding it the nearest whole percent is
2 × 100
5
40%.
The probability that the selected student is a junior is 27%.
What is the probability of an event?The probability of an event is the ratio of the number of outcomes favorable to the event to the total number of outcomes for the event. This represents the chance for the event to take place.
If A is the event, n is the number of outcomes favorable to the event and S is the total number of outcomes, then the probability of the event A is given as:
P(A) = n/S.
How do we solve the given question?We are given a two-way table showing the number of freshmen, sophomores, juniors, and seniors in the class with respect to their gender.
We are asked to find the probability of selecting a junior student while picking a random student from the class.
Let the event of selecting a junior student from the class be A.
Number of favorable outcomes to event A (n) = 2 + 6 = 8 (junior males + junior females)
Total number of outcomes (students in the class) (S) = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30.
∴ The probability that the selected student is a junior is given by:
P(A) = n/S = 8/30
or, P(A) = (8/30)*100% = 26.67% = 27% (rounding to the nearest whole percent).
∴ The probability that the selected student is a junior is 27%.
Learn more about the probability of an event at
https://brainly.com/question/7965468
#SPJ2
Factor 21a–27.
........................................
Answer:
3(7a - 9)
Step-by-step explanation:
21a–27
3*7*a - 3*9
Factor out 3
3(7a - 9)
Answer:
3(7a-9)
Step-by-step explanation:
The greatest common factor between 21a and 27 is 3. Hope this helps!
you can play one game for free. Which game has a higher expected value:
a. a 0% chance of winning $1,000
b. a 10% chance of winning $50
c. a 100% chance of winning $1
d. a 25% chance of winning $100
If you know how to solve this, Please answer it. Thank You
Please show your work and the steps.
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
Answer:
Step-by-step explanation:
Work done by Kayla in 1 hour = 1/15
Work done by Jennifer in 1 hour = 1/16
Work done by both Kayla and Jennifer = [tex]\frac{1}{15}+\frac{1}{16}[/tex]
[tex]= \frac{1*16}{15*16}+\frac{1*15}{16*15}\\\\=\frac{16}{240}+\frac{15}{240}\\\\=\frac{31}{240}\\[/tex]
Hours taken by both = 240/31 = 7 23/31 hours
A = {5, 6, 7, 8, 9, 10} and B = {2, 3, 4, 5, 11, 12, 13}. What is A∪B? What is A∩B?
Step-by-step explanation:
A U B= {2,3,4,5,6,7,8,9,10,11,12,13}
A n B= {5}
In a class of 35 students 1/5
of total students like to play cricket, 2/5 of students like to play football, remaining students like to play volleyball
i) How many students like to play cricket
ii) How many students like to play football?
iii) How many students like to play volleyball?
if you answer correctly you wil get brainliest plus 10 points
if you give wrong answer your wrong answer will be reported
only people who know maths well can give correct answer.
Good luck
Answer:
7 play cricket
14 play football
21 play volleyball
Step-by-step explanation:
1. Find the slope of a line passing through the given points
(-4,2) and (5,6)
2. Find the slope of a line passing through the given points
(5,-5) and (7,3)
Step-by-step explanation:
m=differences in y value over differences in x values .
i.e y²-y¹ over x²-x¹
so 1. 6-2/5--4
which will be 4/9
the slope is 4/9 or 0.4
2. 3--5/7-5
which will be 8/2
the slope is 4
Question 4 of 25 There are 6 brooms and 4 mops in a janitor's closet. What is the ratio of the number of brooms to the number of mops? 3/5
Answer:the ratio of brooms to mops is 3:2
Step-by-step explanation:
6:4 can be simplified to 3:2
Answer:
6:4
Step-by-step explanation:
also can be simplified 3:2