Answer:
1: 16
2: 4940
3: 24
4: 25
5: 9
Step-by-step explanation:
A permutation is a method of calculating the number of possible outcomes. It follows the following general formula;
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
There (n) is the number of objects, and (r) is the number of objects selected.
1. Arranging 4 pots with different plants in a row
In order to solve this, one needs two pieces of information, the number of objects, and the number of objects selected. One is given the number of objects; (4), but when the problem states "in a row" it never specifies how many plants are in a row. Thus, let one assume that a "row" can have an infinite amount of space, but in this case, only (4) space will be used. Therefore there are (4) objects with (4) objects selected. However, the drawback is that the combination formula doesn't work when the two parameters (n) and (r) are the same. Hence, to solve this special case, one simply multiplies the two numbers to get the answers:
[tex]n*r\\\\=4*4\\\\=16[/tex]
2. Forming a four-digit ATM pin
One is given that there are (4) digits in the ATM pin, this is the number of objects selected. One is also given that number of objects, there are (10) digits including (0). Set up the permutation and solve;
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
[tex]_1_0P_4=\frac{10!}{(10-4)!}\\\\=\frac{10!}{6!}\\\\=\frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}\\\\=10*9*8*7\\\\=4940[/tex]
3. Securing a motorcycle with a three-digit combination lock using the numbers (1), (2), (3), and (6).
There are (4) digits to choose from on the lock. But there are (3) numbers that can be selected.
[tex]_4P_3=\frac{4!}{(4-3)!}\\\\=\frac{4!}{1!}\\\\=\frac{4*3*2*1}{1}\\\\=4*3*2*1\\\\=24[/tex]
4. Displaying 3 identical small vases, 1 figure, and a photo frame in a row.
There are (5) objects, and (5) spaces (read problem (1) for an explanation for the objects being put in a row). Thus, this is a special case; multiply the two numbers to get the result;
[tex]n*r\\=5*5\\=25[/tex]
5. 3 girls sitting around a circular table
There are (3) subjects, and (3) spaces in this problem. Apply the same logic applies to a row in this problem. Therefore, this is another special case; multiply the two numbers to get the result;
[tex]n*r\\=3*3\\=9[/tex]
11. The student government is selling flowers for homecoming. The project costs them $20 for advertising and
$3 for each flower sold.
a. Evaluate the expressions 3n+20 and 3(n+20) when n = 4.
b. Which expression shows their total cost? How do you know?
Answer:
32
Step-by-step explanation:
3(n+20) = 3(4+20) = 3(24) = 723n+20 = 3(4)+20= 12+20=32If n represents the amount of flowers they sold, then the correct answer should be 32. The cost for each flower they sold would be 3 x 4 and then add $20 for advertising.
19. PLEASE HELP ME
Order the group of quadratic functions from widest to narrowest graph.
y=, y=, y=
A. y= -7x2, y= -1/3x2, y= -1/5x2
B. y= -1/5x2, y= -7x2, y= -1/3x2
C. y= -1/3x2, y= -1/5x2, y= -7x2
D. y= -1/5x2, y= -1/3x2, y= -7x2
Answer:
D. y= -1/5x2, y= -1/3x2, y= -7x2
Step-by-step explanation:
A5cm x 11 cm rectangle sits inside a circle with radius of 12 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
5 cm
12 cm
11 cm
cm?
PLS HELP ME FOR 17 POINTS
Answer:
397.16 cm²
Step-by-step explanation:
Area of the circle = πr²
3.14 * 144 = 452.16
452.16 - (11 x 5 ) = area shaded region
452.16 - 55 = 397.16
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Ivana wants to give books from her store to the local library. She needs to place 8 books in each box. If she has 1,125 books to give away, how many boxes will she need
Answer:
140.625
Step-by-step explanation:
1125 books, placed into 8 per boxes, 1125/8=140.625
Pls only answer if you know the correct answer! Thanks! :))
Answer:
(3,5)
Step-by-step explanation:
The y axis is the vertical line
Reflection means it is reflected off of. So if the point was ink, and you folded the paper in half vertically, you would have another dot of ink at the points (3,5)
Solve for x:
( x - 6 ) ^ 2 = 7
Answer: x= 6 +/- root of 7
Step-by-step explanation:
1. Expand the left hand side: e.g, 3^2 = 3×3 =9
(x-6)(x-6) = 7
2. Multiply the brackets first by "separating" one of them, and take 7 to the left hand side:
x(x-6) - 6(x-6) =7
x^2 - 6x -6x +36-7=0
Simplify by adding like terms
x^2 -12x +29=0
3.Now your equation is in the form ax^2+bx + c =0, it means you can use the quadratic formula which is x= [-b +/- root of (b^2 - 4ac)]÷ 2a
Then SUBSTITUTE where:
a=1
b= -12
c=29
Therefore, x should be 6+ root of 7 OR 6- root of 7
Answer:
uhhhh okay thank you for removing my answer
Step-by-step explanation:
^^^ refer to the photo
Hello,
Answer: 2.5 (rad)
[tex]L=\theta*R\ \\\\\Longrightarrow\ \theta=\dfrac{L}{R} =\dfrac{30}{12} =2.5 (rad)\\[/tex]
Water is leaking out of an inverted conical tank at a rate of 6800 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 21 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Answer:
1508527.582 cm³/min
Step-by-step explanation:
The net rate of flow dV/dt = flow rate in - flow rate out
Let flow rate in = k. Since flow rate out = 6800 cm³/min,
dV/dt = k - 6800
Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone
dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)
So, dV/dt = (πr²dh/dt)/3
Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min
Now, by similar triangles, h/r = h'/r'
r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm
Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.
The net rate of increase of water is dV/dt = (πr'²dh/dt)/3
dV/dt = (π(262.5 cm)² × 21 cm/min)/3
dV/dt = (π(68906.25 cm²) × 21 cm/min)/3
dV/dt = 1447031.25π/3 cm³
dV/dt = 4545982.745/3 cm³
dV/dt = 1515327.582 cm³/min
Since dV/dt = k - 6800 cm³/min
k = dV/dt - 6800 cm³/min
k = 1515327.582 cm³/min - 6800 cm³/min
k = 1508527.582 cm³/min
So, the rate at which water is pumped in is 1508527.582 cm³/min
black pencils cost 75 naira each and colour pencils cost 105 naira each if 24 mixed pencils cost 2010 naira how many of them were black hint let there be x black pencils thus there are (24-x) coloured pencils.
Answer:
number of black pencils is 17
In the diagram, the measure of angle 3 is 105°
Which angle must also measure 105°
1
4
6
8
Answer:
the answer will be 1 on the basis of the option
Step-by-step explanation:
and other are 7 5
the legs of a 45 45 90 triangle have a length of 8 units what is the length of the hypotenous
Answer:
11.31 units
Step-by-step explanation:
a^2 + b^2 = c^2
8^2 + 8^2 = c^2
64 + 64 = c^2
128 = c^2
Opposite of exponents is square roots, and we need to get rid of that exponent in c^2, meaning we find the square root.
[tex]\sqrt{128\\} \\\\[/tex] = c
c = 11.31 units
Which of the following is a solution of y + x < -5?
(-2, -3)
(-4, -2)
(-3, -2)
(-1, -3)
i need help ASAP. troll answers WILL be deleted.
(-2, -3) || -3 + -2 < -5 || -5 < -5 || FALSE
(-4, -2) || -2 + -4 < -5 || -6 < -5 || TRUE
(-3, -2) || -2 + -3 < -5 || -5 < -5 || FALSE
(-1, -3) || -3 + -1 < -5 || -4 < -5 || FALSE
Correct Answer: (-4, -2)
Hope this helps!
Answer:
(-1,-3)
Step-by-step explanation:
(x,y)
it's not hard just plug in the coordinates for x and y ;-;
-2 is x, -3 is y
-3+-2<-5
-5<-5? false.
-4 is x, -2 is y
-2+-4<-5
-6<-5? false.
-3 is x, -2 is y
-3+-2<-5
-5<-5? false
-1 is x, -3 is y
-1+-3<-5
-4<-5? true
hopefully you found out the pattern in how to do this if you did not know. or if you simply were too l a z y to do it urself I understand that as well. have a great day!
Your brother tells you that he went to a baseball game and spent $19 on hot dogs and a soda. If hot dogs cost $4 and his one soda was $3, how many hot dogs did he eat? Write a two-step equation for this scenario then solve for the number of hot dogs.
Answer:
he ate 4 hot dogs
Step-by-step explanation:
$19-$3=$16
$16÷4=4
5×12÷[-12÷{15+(4-3)}]
Answer: -80
Step-by-step explanation:
2( 5 1 m− 5 2 )+ 5 3 2, left parenthesis, start fraction, 1, divided by, 5, end fraction, m, minus, start fraction, 2, divided by, 5, end fraction, right parenthesis, plus, start fraction, 3, divided by, 5, end fraction
Answer:
2/5m - 1/5
Step-by-step explanation:
Given the equation :
2(1/5m - 2/5) + 3/5
First step:
Open the bracket by multiplying values in the bracket by 2
2/5m - 4/5 + 3/5
-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5
Hence,
2/5m - 4/5 + 3/5 = 2/5m - 1/5
= 2/5m - 1/5
The mean length of a group of fish is 14.2 inches. A fish that is 41 inches long
joins the group. How does this fish's length affect the mean?
A. The new mean length will be less than 14.2 inches.
B. The new mean length will still be 14.2 inches.
C. The new mean length will be 41 inches.
D. The new mean length will be greater than 14.2 inches.
The fish's length will affect the mean because the new mean length will be less than 14.2 inches. That is option A.
What is mean?Mean is defined as the sum of all the data values divided by the count of values in a data set.
What a new value is added to a data set such as the group of fishes, it will affect the fish mean by reducing it to less than its former mean value which is 14.2 inches.
Therefore, the fish's length will affect the mean because the new mean length will be less than 14.2 inches.
Learn more about mean here:
https://brainly.com/question/1136789
#SPJ1
which of the statement is true
Answer:
c
Step-by-step explanation:
Profit = 4.5 (240)-1080 = 0
the maximum profit would occur when u sell all 350 tickets,
profit = 4.5(350)-1080 = 495 (not a nor b)
Answer:
The statement that is true is C
x2 +15-8x entre 3-x ayuda pliz
*HELP*
calculate the pay for the following day of a weekly time card given a wage of $12 an hour
Answer:
96 dollars and 50 cents
Step-by-step explanation:
a) 61°
b) 29°
C) 40°
d) 50°
Answer:
29 degrees (~0.506 rad)
What is the domain of G
Answer:
D: {-6, 6}
Step-by-step explanation:
The domain are all the possible values for x. For this graph in the x-position, it starts from -6 to +6. Therefore, the domain will be {-6,6}.
Answer:
[tex]-6\leq x\leq 6[/tex]
[tex]x[/tex] ∈ [tex][-6, 6][/tex]
Step-by-step explanation:
The domain is the set of all numbers for which a function is defined. As one can see on the given graph, the function spans between the numbers (-6) and (6). Therefore, the function is defined between the numbers (-6) and (6). The closed dots on either end of the function signify that the function includes these values. Thus, the domain of the function is as follows:
([tex]-6\leq x\leq 6[/tex])
In set notation,
([tex]x[/tex] ∈ [tex][-6, 6][/tex])
Cedric and Insha solved the same equation using the calculations below.
Cedric’s Work
Insha’s Work
z minus 4.5 = negative 1.5. z minus 4.5 + 4.5 = negative 1.5 + 4.5. z = 3.
z minus 4.5 = negative 1.5. z minus 4.5 + (negative 4.5) = negative 1.5 + (negative 4.5). z = negative 6.
Which statement is true about their work?
The first working out is correct, z = 3
What is the area of this figure?
Answer:
answer of this qn is 15in^2
are there any inputs that cannot be evaluated by the function 6/x-3?
Answer:
as written
[tex]\frac{6}{x} -3[/tex] zero would not be allowed....
BUT !!! I think that your question
is ......
[tex]\frac{6}{x-3}[/tex] then the answer is "3"
Step-by-step explanation:
There were some people no a boat 26 people got off the boat at the first dock 22 people got off the boat now there ate 74 people on the boat how many people were on the boat?
Answer:
Step-by-step explanation:
Let the initial number of people on the boat be x:
x - 26 - 22 = 74
x -48 = 74
x = 74 + 48
x = 122
Answered by G a u t h m a t h
calculate w reasons the size of the unknown angles
Answer:
a= 75°
β= 30°
Step-by-step explanation:
α = 75° This is because triangle PQR isosceles. Thus two of its angles are equal and these two are angle α and the one labelled 75.
β = 30° This is because angles in a triangle sum up to 180°. We already know two of these angles. To find β you say 180 - ( 75 × 2)
The answer becomes 30°.
HOPE THIS HELPED
1. Find the probability of picking a yellow marble and an orange
marble when 2 marbles are picked (without replacement)
from a bag containing 2 yellow and 4 orange marbles
Answer:
4/15
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that the bag contains 2 yellow and 4 orange marbles, the probability of picking a
Yellow marble = 2/(2+4) = 2/6
Orange marble = 4/(2+4) = 4/6
The probability of picking a yellow marble and an orange marble without replacement
= 2/6 * 4/5
= 8/30
= 4/15
How much is 3a²-5ab+7b²+3 greater than 2a²+2ab+5?
Answer:
a²-7ab+7b²-2
Step-by-step explanation:
3a²-5ab+7b²+3 - ( 2a²+2ab+5 ) = 3a²-5ab+7b²+3 - 2a²-2ab-5 = a²-7ab+7b²-2
Express an angle of square into grade.
Answer:
please solve my questiob check my profile
Lúc 6 giờ, một ô tô xuất phát từ A đến B với vận tốc trung bình 40km/h. Khi đến B,
người lái xe làm nhiệm vụ giao nhận hàng trong 30 phút rồi cho xe quay trở về A với vận
tốc trung bình 30km/h. Tính quãng đường AB, biết rằng ô tô về đến A lúc 10 giờ cùng
ngày.
Answer:
Đáp án:
60km
Step-by-step explanation:
30 phút
=
1
2
giờ
Ô tô đi từ A đến B rồi từ B về A mất số thời gian là:
10
−
6
−
1
2
=
3
,
5
giờ (không tính thời gian nhận hàng)
Gọi độ dài quãng đường AB là
x
(km)
Ta có:
Thời gian đi từ A đến B là
x
40
(quãng đường chia vận tốc)
Thời gian đi từ B đến A là
x
30
Ta có phương trình:
x
40
+
x
30
=
3
,
5
⇔
x
=
60
(km)
Vậy quãng đường AB là 60km.
