(a) There are 665280 ways of selection if the order of the choices matters.
(b) There are 924 ways of selection if the order of the choices does not matters.
(a) If the order of the choices matters, then we must use the permutation formula that is
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
Here n is the total no. of objects and r is chosen objects
We have n = 12
r = 6
After we substitute the value we get
[tex]^{12}P_6 = \frac{12!}{(12 - 6)!}[/tex]
[tex]^{12}P_6 = \frac{12!}{6!}[/tex]
[tex]^{12}P_6[/tex] = 665280
Thus, there are 665280 ways of selection if the order of the choices matters
(b) If the order of the choices does not matter, then we must use the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n - r)!}[/tex]
After we substitute the value we get
[tex]^{12}C_6 = \frac{12!}{6!(12 - 6)!}[/tex]
[tex]^{12}C_6 = \frac{12!}{6! 6!}[/tex]
[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7×6! / 6!×6!
[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7/ 6!
[tex]^{12}C_6 =[/tex] 665280/ 720
[tex]^{12}C_6 =[/tex] 924
Thus, there are 924 ways of selection if the order of the choices does not matters.
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Patricia wishes to have a rectangular garden in her backyard. She has 88 ft of fencing with which to enclose her garden. Letting x denote the width of the garden, find a function f in the variable x giving the area of the garden.
The area of the rectangular garden in terms of a function in x is given by 44x - x²sq. ft.
What is the area of a rectangle?
A rectangle is a closed geometric figure with opposite sides equal to each other. The area of this rectangle is given by the product of its length and width.
Calculating the area of a rectangular garden in terms of a function in x
Let us consider a variable x that denotes the length of a rectangular garden
Given perimeter of a rectangular garden is 88 ft with y as the width of a rectangular garden
Perimeter = 2×(length + breadth)
88 = 2(x + y)
44 = x + y
y = 44 - x
Area of a rectangular garden = xy
= x(44 - x)
= 44x - x² sq. ft
Hence, the area of a rectangular garden in terms of a function in x is given by 44x - x² sq. ft.
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Please show me how you got the answer. Will give brainliest.
Answer: 410 possible points
To solve for the possible points in the course, use a proportion and cross multiply.
What is a proportion?
A proportion is two fractions that are equal to each other. For the fractions to be equal, they are proportionate. In our math problem, percentage is proportionate the the number of points.
The fractions represent information you have, and one variable will represent what you are solving for.
GivenYour points = 361
Points to get an 'A' = your points + 8
'A' = 90% of possible points
Find the points needed for an 'A' at 90%Points to get an 'A' = your points + 8
= 361 + 8
= 369
State variableslet x be the amount of possible points
Write a proportionWe know the number of points for 90% is 369 points. Remember that 90% is the same as 90/100.
Keep the information with the same units inside the same fraction. Here, percentage is represented by the first fraction. Points is represented by the second fraction.
[tex]\displaystyle{\frac{90}{100}=\frac{369}{x}}[/tex]
SolveWe can solve using cross multiplication. This is when we multiply each numerator by the denominator from the other fraction.
[tex]90x = 369*100[/tex] Simplify by multiplying.
[tex]90x = 36,900[/tex] Isolate the variable x.
[tex]\displaystyle{\frac{90x}{90} = \frac{36,900}{90}}[/tex] Divide both sides by 90 to cancel out 90 on the left.
[tex]\displaystyle{x = \frac{36,900}{90}}[/tex] Divide.
[tex]x = 410[/tex] Solved for x, representing the possible points.
∴ The possible points in the art course is 410.
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Answer:
410 possible points
Step-by-step explanation:
PLEASE GEKO ME EHFND
Answer: 164 degrees
Step-by-step explanation:
IHG=JHG+IHJ
19x-7=84+7x+17
19x-7=101+7x
12x-7=101
12x=108
x=9
IHG=19x-7
IHG=19(9)-7
IHG=171-7
IHG=164 degrees
the sum of nine consecutive natural numbers, the first of which is n?
Answer:
What is the sum equal to?
Step-by-step explanation:
( 1/2 x 1/3) x 1/4 = 1/2 x (1/3 x 1/4)
A. Reflexive
B. Commutative
C. Associative
D. Distributive
Answer:
The answer is commutitve
Guys can you help me with this FAST!!
Answer:
1/6
Step-by-step explanation:
30+20= 50
200+100= 300
you divide 50÷300 and you get 1/6
PLEASE HELP!!!!!
A. What is 4.186 rounded to the nearest tenth?
B. What is 2.758 rounded to the nearest tenth?
C. What is 72.05 rounded to the nearest tenth?
D. What is 45.64 rounded to the nearest tenth?
E. What is 82.156 rounded to the nearest tenth?
F. What is 41.31 rounded to the nearest tenth?
G. What is 29.16 rounded to the nearest tenth?
H. What is 17.054 rounded to the nearest tenth?
I. What is 11.65 rounded to the nearest tenth?
J. What is 0.83 rounded to the nearest tenth?
K. What is 29.16 rounded to the nearest tenth?
L. What is 12.48 rounded to the nearest tenth?
M. What is 0.91 rounded to the nearest tenth?
_______________________________________________________
N. What is 20.5 rounded to the nearest whole number?
O. What is 13.71 rounded to the nearest whole number?
P. What is 71.23 rounded to the nearest whole number?
Q. What is 36.57 rounded to the nearest whole number?
R. What is 17.89 rounded to the nearest whole number?
S. What is 50.147 rounded to the nearest whole number?
T. What is 19.05 rounded to the nearest whole number?
U. What is 7.61 rounded to the nearest whole number?
V. What is 92.38 rounded to the nearest whole number?
W. What is 57.25 rounded to the nearest whole number?
X. What is 16.3 rounded to the nearest whole number?
Y. What is 44.08 rounded to the nearest whole number?
Z. What is 17.9 rounded to the nearest whole number?
1. What is 9.06 rounded to the nearest whole number?
Check all relationships between 1 and 22.
Answer:
adjacent , linear pair ,
Step-by-step explanation:
and i don't think there is something else
Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha 3 bought is of the number of red balloons. The number of green 5
balloons is also 2 3 of the number of yellow balloons.
How many balloons did Masha buy for the party?
Answer:
its 100 ez bro
Step-by-step explanation:
Answer: 100 balloons
Step-by-step explanation:
because it is 100 balloons
147 divided by 7
(Explanation needed please)
Answer: 21
Step-by-step explanation:
Use a calculator
Which is an illustration of the associative
property?
a. (b.c) = (b.c).a
α · b = α
a (b.c) = (a.b).c
a.b=b.a
6) What is 1.333... in fraction form?
Answer:
It would be 1333/1000.
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 2 small boxes has a total weight of 117 kilograms. A delivery of 3 large boxes and 8 small boxes has a total weight of 164 kilograms. How much does each type of box weigh?
THIS ANSWER WAS DELETED DUE TO NOT BEING TRUE.
Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of $13.50 each, but later decreased the price of each by $4.00. If they sold all 91 pieces and took in $972.50, find how many they sold at the original price and how many they sold at the reduced price.
The number sold at the original price is 27 and they sold 64 at the reduced price.
How to calculate the value?Let x = number of pieces sold at 13.50
Let y = number of pieces sold at 9.50
The equation will be:
x + y = 91. ..... i
13.50x + 9.50y = 972.50 ..... ii
From equation i x = 91 - y
13.50x + 9.50y = 972.50
13.50(91 - y) + 9.50y = 972.50
1228.50 - 13.50y + 9.50y = 972.50
1228.50 - 4y = 972.50
4y = 1228.50 - 972.50
4y = 256
y = 256/4
y = 64
Since x + y = 91
x = 91 - 64 = 27
Therefore, the number sold at the original price is 27 and they sold 64 at the reduced price.
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Find all integer solutions of each system of inequalities.
a) 6-4b>0
3b-1>0
b) 3-18x<0
0.2-0.1x>0
Answer:
A: [tex]b < \frac{3}{2}[/tex] and the second equation is: [tex]b > \frac{1}{3}[/tex]
B: [tex]x > \frac{1}{6}[/tex] and the second equation is: [tex]x < 2[/tex]
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Hope this helps!
Have a great day and God bless! :)
A blueprint of a house shows a dining room wi an area of 7 square inches. If the blueprint' scale is 1 inch : 6 feet, what would be the act area of the dining room? 1
The Actual area of the dining room is: 252 square feet.
How to Find the Actual Area Using Scale?Given that the area of the house on a blue print = 7 square inches.
Scale of the blue print = 1 inch : 6 feet.
Therefore, we would have the following proportion:
Area on blue print/actual area = square of the scale
7/actual area = 1²/6²
7/actual area = 1/36
Actual area = (7)(36)
Actual area = 252 square feet.
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Answer: Actual area (252 square feet).
Explanation:
How to Find the Actual Area Using Scale?
Given that the area of the house on a blueprint = is 7 square inches.
The scale of the blueprint = is 1 inch: 6 feet.
Therefore, we would have the following proportion:
The area on the blueprint/actual area = square of the scale
7/actual area = 1²/6²
7/actual area = 1/36
Actual area = (7)(36)
Actual area = 252 square feet.
Hope it helps!The table shows some values of x and y that satisfy the equation y = acosx + b
180
120
150
4 -3V3
-2
0
30
60
10
4 + 3V3
7
Find the value of y when x = 45
X
90
4
II. What are the coordinates
of A' using the rule
(x, y) (x-3, y+7)?
A(2, 5)
Need help
Answer:
so xtime sy ,fe fwvnvf nfdv bregbrrsikrwnknrhvnk vnf vknvns;;abjwrjkgwnkgwjknnnxnfnfsvmsr
K
What is 0.514 written as a power of 10??
Answer:
To write this is true scientific notation the decimal point needs to be moved 1 place to the right so the exponent for the 10s term will be negative:
0.514=5.14×10
−1
Answer:5.14
Step-by-step explanation:
Write an equation in slope- intercept form for the line described.
parallel to y = -3x + 4, x- intercept at 4
Answer:
y = -3x + 12
Step-by-step explanation:
If two lines are parallel, their slopes are equal, then m = -3
x intercept is 4 then y = 0
y = mx + b
0 = -3(4) + b
b = 12
y = -3x + 12
(3x-5) + (x+1) = 180
The value of 'x' for the given expression is calculated as (x = 48).
What is defined as the linear equation in one variable?A linear equation in one variable is an equation that has only one solution.
It is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. The numbers a' and b' are real numbers.'a' and 'b' are both greater than zero.2x+3=8, for example, is a linear equation with a single variable.Now, for the given expression;
(3x-5) + (x+1) = 180
Open the brackets.
3x-5 + x+1 = 180
Add the similar parts;
4x - 4 = 180
Further simplifying;
4x = 180 + 4
4x = 184
x = 184/4
x = 48
Therefore, the value of 'x' is estimated as 48.
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Please help with this question I will give you brainliest
Answer:
89.50 = 7.75 + 27.25p
subtract 7.75 from both sides
89.50 - 7.75 = 27.25p
81.75 = 27.25p
divide both sides by 27.25
p = 81.75 / 27.25
p = 3
Step-by-step explanation:
The number of people who can go to the amusement park is 3 people
Answer: p=3
Hence, the Linear Equation in two variables is used to determine the total number of people who go to the park is - y=7.75+27.25p
Step-by-step explanation:
89.50=7.75+27.25p
89.50-7.75+27.25p
81.75=27.25
81.75/27.25
p=3
The distance between City A and City B is 2700 miles. On a certain wall map, this distance is represented by 9 inches. The actual distance between City C and City D is 4100 miles. How far apart are they on the same map?
The distance between City C and City D is represented by 13.67 inches on a certain wall map.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Let x inches would be far apart are they on the same map
We can write this as a ratio as
As per the given information,
9 inches : 2700 miles = x inches : 4100 miles
⇒ 9/2700 = x/4100
⇒ x = (4100×9)/2700
⇒ x = 13.67 inches
Therefore, on a certain wall map, the distance between City C and City D is represented by 13.67 inches.
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Bill's school is selling tickets to a fall musical.
On the first day of ticket sales the school sold 1 adult ticket
and 6 child tickets for a total of $52.
The school took in $66 on the second day by selling 1 adult
ticket and 8 child tickets.
Find the price of an adult ticket.
•$3
•$10
•$7
•$9
By solving a system of equations, we can see that the adult ticket costs $10.
How to find the price of the adult ticket?
Let's define the two variables:
x = price of the adult ticket.y = price of the child ticket.With the given information, we can write a system of equations:
1*x + 6*y = $52
1*x + 8*y = $66
By taking the difference between the two equations we get:
(1*x + 8*y) - (1*x + 6*y) = $66 - $52
2y = $14
y = $14/2 = $7
Now that we know the value of y, we can find the value of x.
Replacing the value of y in the first equation we get:
1*x + 6*$7 = $52
x = $52 - 6*$7 = $10
With this, we know that the adult ticket costs $10.
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The area of a rectangular garden is 7584 ft squared If the width of the garden is 79 feet, what is its length?
Answer: 96
Step-by-step explanation:
Length = Area/Width
7584/79 = 96 feet
96 x 79 = 7584 ft²
Check all relationships
Complementary
Linear pair
Adjacent
Vertical
Supplementary
[tex]\implies[/tex]The answer is Adjacent and Complementary.
Step-by-step explanation:The two corners are complementary and adjacent to each other.So select Adjacent and Complementary.7th-grade question
5. Sara used 4 1/2 packs of pencils in the first 1/4 of the year. At what rate
is Sara using pencils?
A. 1 1/8 packs per year
B. 6 packs per year
C. 16 1/8 packs per year
D. 18 packs per year
the inequality always, sometimes, or never true
4x8> 1 + 4(x + 3)
The given inequality is never true which means it has no solutions. If an inequality has no actual solution, then there aren't any numbers that might be used to solve it and make the statement true. An inequality can be made true by substituting any real number into it if the solution to the inequality is all real numbers.
Given the expression is 4x ₋ 8 > 1 ₊ 4(x₊3)
first apply the distributive property.
4x ₋ 8 > 1 ₊ 4x ₊ 12
now combine the like terms.
4x ₋ 8 > 4x ₊ 13
Variables should be moved to the equation's left side.
4x ₋ 4x > 13 ₊ 8
combine like terms.
0 > 13 ₊ 8
calculate the sum.
0>21
This is the solution of inequality which has no solutions.
Hence the inequality of the expression is never true.
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
The probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be D. (0.27 + 0.49)³ = 0.4390
How to calculate the probability?It should be noted that probability simply means the chance that a particular event will occur.
In this case, the probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be:
= (27% + 49%)³
= (0.27 + 0.49)³
= 0.4390
The probability is 0.4390.
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Given mn, find the value of x
118%
x=62 bec 180-118=62.
Step-by-step explanation:
180=118-x
180-118=x
x=62