How do I find n in the the permutation equation of nP3 = 990
Answer:
n=11
Step-by-step explanation:
Permutations
The formula to calculate permutations is:
[tex]\displaystyle nPm=\frac{n!}{(n-m)!}[/tex]
We know nP3=990. Substituting:
[tex]\displaystyle nP3=\frac{n!}{(n-3)!}=990[/tex]
Expanding the factorial in the numerator:
[tex]\displaystyle \frac{n(n-1)(n-2)(n-3)!}{(n-3)!}=990[/tex]
Simplifying:
[tex]n(n-1)(n-2)=990[/tex]
This equation can be easily solved by inspection. The product of three consecutive numbers resulting 990. Starting from greatest to smallest, those numbers are 11,10, and 9, thus:
[tex]n(n-1)(n-2)=11*10*9[/tex]
It follows that n=11
jazmines dog weights 63 pounds. Her vet told her that a healthy weight for her dog would be less than or equal to 47 pounds. Jazmines dog can lose an average of 6 pounds every week. Write the solution to an inequality that describes all posible number of weeks x for which her dog can be at a healthy weight
Answer:
2 weeks and 4 days
Step-by-step explanation:
she is 63 pounds and she needs to get to 47 so 63-47=16 then if she loses 6 pounds every week then 6+6=12 which make 2 weeks cause we used two 6's so now we have a remainder which makes days 12-16=4 so their ya go
2 weeks and 4 days
What's the unit rate for 15 plates in 3 stacks?
A: 3 Plates Per Stack
B: 4 Plates Per Stack
C: 5 Plates Per Stack
D: 6 Plates Per Stack
Answer:
My pretty sure its 5
(don’t count on it too much, this is my first answer)
Step-by-step explanation:
The question is in the picture.
Answer:
2
Step-by-step explanation:
when you combine all the terms (7 - 14 + 8+ 10 - 4+ 5) and divide by the number of terms (6) you get 2
Answer:
43.83...
Step-by-step explanation:
you add up all the numbers then divide by the numbers that are listed... :)
Here is a scale drawing of a garden.
Kim wants to plant a tree in the garden according to the following rules:
It must be 7 m from A and 4 m from C.
Place a cross where Kim can plant the tree.
1 cm represents 2 m
D
2.5 cm
А A
B.
4 cm
View One Minute Version
Answer:
The coordinates of the cross on the scale drawing which locates where Kim can plant the tree is (3.45 cm, 0.58 cm)
Step-by-step explanation:
The question relates to coordinates geometry and the solution can be obtained graphically by construction as shown in the attached drawing
The given parameters of the scale drawing are;
The scale of the drawing is 1 cm = 2 m
The dimensions of the rectangle representing the garden in the scale drawing is given as follows;
The width of the rectangle = 2.5 cm
The length of the rectangle = 4 cm
The required location where the tree is to be planted = 7 m from A and 4 m from point C
Therefore, the location where Kim can plant the tree on the scale drawing is 3.5 cm from point A and 2 cm from point C
Taking the coordinate of point A as the origin, we have;
The coordinates of point A = (0, 0)
∴ The coordinates of point C = (4, 2.5)
The general equation of a circle is (x - h)² + (y - k)² = r²
Where, (h, k) is the coordinate of the center of the circle
The location of the point is on a radius 3.5 cm from point A and a radius 2 cm from point C
Therefore, for point A, we have;
(x - 0)² + (y - 0)² = 3.5²
x² + y² = 12.25...(1)
For point C, we have;
(x - 4)² + (y - 2.5)² = 2² = 4
Which gives;
x² - 8·x + 16 + y² - 5·y + 6.25 = 4
x² + y² - 8·x - 5·y + 22.25 = 4
We have x² + y² = 12.25 from equation (1), therefore, we have;
12.25 - 8·x - 5·y + 22.25 = 4
- 8·x - 5·y = 4 - 22.25 - 12.25 = -30.5
∴ 8·x + 5·y = 30.5
y = (30.5 - 8·x)/5
Therefore, we have;
x² + y² = 12.25 = x² + ((30.5 - 8·x)/5)² = 12.25
Using a graphing calculator we get;
356·x² - 1952·x + 2496 = 0
Which gives;
x = (1952 ± √((-1952)² - 4×356×2496))/(2 × 356)
x = 3.452197227 or 2.03094884081
To two decimal places, we have the coordinates of the points where the tree can be planted given as follows;
Therefore, y = (30.5 - 8×3.452197227)/5 = 0.5764844368
or y = (30.5 - 8×2.03094884081)/5 = 2.8504818547
y = 0.5764844368 or 2.8504818547
To two decimal places, we have the coordinates of the places where Kim can plant the tree are given as follows;
(3.45, 0.58) or (2.03, 2.85)
We note that the point (2.03, 2.85) is at the outside the drawing the area as 2.85 cm is more than 2.5 cm which is the width (height) of the rectangle as shown in the attached drawing created with Microsoft Word.
Therefore, the coordinates of the cross where Kim can plant the tree is (3.45, 0.58)
Answer:
Step-by-step explanation:
Make sure to use protractor and cross tools to get full marks
Thank you
Answers the question please
Answer:
I would say (B) 14,55
Step-by-step explanation:
Sushil and Fiona win some money and share it in the ratio 4:1. Sushil gets £33 more than
Fiona. How much did they get altogether?
Mateo found a sale on skateboards.The skateboard he would like to purchase is 179.99. The sales tax is 6.5%. How much will Mateo spend in all after the discount and tax are applied?
Answer:
$191.69
Step-by-step explanation:
0.065 x 179.99 = 11.70
179.99 +11.70
what is x given circle Z? please help !!
Answer:
x=6
Step-by-step explanation:
because of vertical angles, 9x-4=12x-22
3x=18
x=6
plz give thx and brainliest!
Enter the range of values for x:
[?]
Answer:
2<x<7
Step-by-step explanation:
Answer:
2<x<7
Step-by-step explanation:
10+x=21 ?
What’s the answer
Answer:
x=11
Step-by-step explanation:
first you flip the X and the 10, then subtract the 10 on both sides and you should be left with x=11
Ashley purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost s that Ashley paid.
Answer:
5n=s
Step-by-step explanation:
5*n notebooks
5n=s
Anybody know how to do # 14, 15, and 16? Would also be nice if yall told me if any of these were wrong
Step-by-step explanation:
1. Right
2. Right
3. Right
4. Right
5. Right
6. Right
7. Its not properly visible sorry for this.
8. Its wrong
[tex] (\frac{1}{3} ) {}^{2} = \frac{1}{9} [/tex]
9. Right
10. Its wrong
[tex]0.5 {}^{3} = 0.125[/tex]
11. Right
12. Its wrong.... Bcz square of minus is plus
[tex] - 9 {}^{2} = 81[/tex]
13. Right
14. According to the BODMAS rule..
[tex]15 - 7 \times 2 + {2}^{3} [/tex]
[tex]15 - 14 + 8[/tex]
[tex]1 + 8 = 9[/tex]
15.
[tex](11 - 8) {}^{2} - 2 \times 6[/tex]
[tex]3 {}^{2} - 12[/tex]
[tex]9 - 12 = - 3[/tex]
16.
[tex]12 + \frac{ {9}^{2} }{3} [/tex]
[tex]12 + \frac{81}{3} [/tex]
[tex]12 + 27 = 39[/tex]
Hope this helps u... ✌️❤️
Use the distributive property to simplify the expression: -5(4W - 3s + 1)
Answer:
-20w+15s-5
Step-by-step explanation:
-5*4w= -20w
-5*-3s= 15s
-5*1= -5
Distribute : 2(2x-6)
He he please
Answer:
4x -12
Step-by-step explanation:
is that what u needed lol
Step-by-step explanation:
-24 ==== ( 2×-6=-12___-12×2= -24)
if MP= 6x-5, QR = 3x+1 ,and RN = 6, what is QN
Answer:
19 units.
Step-by-step explanation:
Consider the below figure attached with this question.
From the below figure it is given that MN=PQ.
It is given that MP = 6x – 5, QR = 3x + 1, and RN = 6.
Since non parallel sides are equal, therefore it is an isosceles trapezoid.
The diagonals of an isosceles trapezoid are equal.
Substitute the given values.
The value of x is 4.
Hence, the measure of QN is 19 units.
What is the radius of a sphere with a volume of 3026 cm ^3, to the nearest tenth of a centimeter?
Answer:
[tex]r=9.0\:\mathrm{cm}[/tex]
Step-by-step explanation:
The volume of a sphere is given as [tex]\frac{4}{3}r^3\pi[/tex]. Therefore we have the following equation:
[tex]\frac{4}{3}r^3\pi=3026,\\r^3=\frac{3}{4}\cdot\frac{3026}{\pi},\\r^3=722.40428,\\r=\sqrt[3]{722.40428},\\r\approx \fbox{$9.0\:\mathrm{cm}$}[/tex].
Rounding this to the nearest tenth of a centimeter, the radius of the sphere is approximately 14.0 cm.
What is volume?Volume refers to the amount of space occupied by an object or substance. In mathematics, it is usually measured in cubic units (e.g. cubic meters, cubic centimeters).
The volume of an object can be calculated using its dimensions and specific formulas that depend on the shape of the object.
For example, the volume of a cube is calculated by multiplying its length, width, and height, while the volume of a sphere is calculated using the formula [tex](4/3)\pi r^3[/tex], where r is the radius of the sphere.
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere and π (pi) is a mathematical constant approximately equal to 3.14159.
We can rearrange this formula to solve for r:
r = [tex](3V/4\pi)^{(1/3)[/tex]
Substituting the given volume V = 3026 [tex]cm^3[/tex], we get:
r = [tex](3(3026)/(4\pi))^{(1/3)[/tex] ≈ 14.0 cm
Thus, the radius of the sphere is approximately 14.0 cm, rounded to the nearest tenth of a centimetre.
For more details regarding volume, visit:
https://brainly.com/question/1578538
#SPJ3
Mr Paul bought 2 bags of fertilizer at $75 a bag,a wheelbarrow for $350 and 3 spades at $130 a spade.he paid $1000 to the cashier how much change did he receive plz explain
Answer:
$110
Step-by-step explanation:
1000-75-75-350-130-130-130=$110 in change
Madison was given a large box of 42 chocolates for her birthday. If she eats exactly 5
chocolates each day, how many chocolates would Madison have remaining 5 days
after her birthday?
Answer:25
Step-by-step explanation: bc 5 x 5 =25
Answer:17 chocolates left
Step-by-step explanation:
5x5= 25
42 - 25 = 17
hopefully this helps
Comparing Methods to solving systems.
x -y =-2
7x +2y =-5
Solve it by graphing method
Answer:
[tex]x = - 1 \\ y = 1[/tex]
Step-by-step explanation:
[tex]x - y = - 2 [/tex]
[tex]x = y - 2[/tex]
[tex]7x + 2y = - 5[/tex]
[tex]7(y - 2) + 2y = - 5 \\ [/tex]
[tex]7y - 14 + 2y = - 5[/tex]
[tex]9y = 14 - 5[/tex]
[tex]9y = 9[/tex]
[tex]y = \frac{9}{9} = 1[/tex]
[tex]x = y - 2 = 1 - 2 = - 1[/tex]
the difference of 18 and m is equal to the product of m and 7
Answer:
M = 11/2
Step-by-step explanation:
first set up the problem
18-m = m+7
subtract m to both sides
18 -2m = 7
then subtract 18
-2m = -11
divide by negative 2
m = 11/2
what is the value halp me
Answer- This is a fairly simple calculation, I got a -1/5,
Step-by-step explanation:
This is the way solved it, just substitute the x value for 1, and just solve. Hope it helps.
helpppppppppppppppppppppppppppppppppppppppppppp
Answer:
I can help
Step-by-step explanation:
Answer:
Step-by-step explanation:
the first one- 40
the second one- 2.5
This should be correct if I did my math correctly
6. Which number is equal to 7(3.5x104) written in scientific notation?
A.245x70
B.2.45x105
C.24.5x104
C.1.05x10
Answer:
C
Step-by-step explanation:
This is basically:
7 x 3.5 x 104 = 24.5 x 104
An electrician charges a flat fee for each job, plus an hourly rate for each hour he takes to complete the job. The total cost of the job can be modeled by the equations y = 50 + 65x. What does the independent variable represent in this situation?
Answer: The independent variable = x which represent the the number of hours taken to complete the job.
Step-by-step explanation:
Independent variable is the variable on which dependent variable is dependent.In the given function: y = 50 + 65x, x = Number of hours, y = Total cost of the job.
Here, total cost of the job depends on the number of hours.
So the independent variable = x which represent the the number of hours taken to complete the job.
Vhat is the value of x in the equation 3x - 2y = 18, when y= 27?
Answer:
x = 24
Step-by-step explanation:
3x - 2y = 18
y = 27
3x - 2(27) = 18
3x - 54 = 18
3x = 72
x = 24
Answer:
x=24
Step-by-step explanation:
3x-2y=18
Put the y value where it belongs...
3x-2(27)=18
3x-54=18 Separate the x
+54 +54
3x=72 Divide
x=24
You open a drink stand where you sell coffee and hot chocolate. You sell coffee for $1.80 and hot chocolate for $3.15. At the end of the day, you sold 120 cups and the total money you earned was $284.40. How many of each type of drink did you sell?
Answer:
c = 69 and h = 51
Step-by-step explanation:
You will need two different equations here
use variable c as coffee and variable h as hot chocolate
c + h = 120
1.80c + 3.15h = 284.40
By moving variables, you can alter the first equation
h = 120 - c
Now insert this into the second equation
1.80c + 3.15(120 - c) = 284.40
Multiply
1.80c + 378 - 3.15c = 284.40
Subtract the c
-1.35c + 378 = 284.40
Subtract 378 from both sides
-1.35c = -93.6
Divide both sides by -1.35
c = 69
Then plug into the first equation
69 + h = 120
Subtract 69
h = 51
Geometry work pls help
Answer:
true
Step-by-step explanation:
Answer:
TRUE
Step-by-step explanation:
THE FIGURE HAS PARALLEL LINES.
i need the answer to this asap, plzz
Answer:
[tex]\mathrm{D.\:}\sqrt{126}[/tex]
Step-by-step explanation:
All three triangles in the figure are similar. Therefore, we can set up the following proportion:
[tex]\frac{18}{m}=\frac{m}{7}[/tex]
Cross-multiply to solve:
[tex]m^2=18\cdot 7 = 126, \\\\m=\fbox{$\sqrt{126}$}[/tex].
Plz help find each circle measure !!!!!
Answer:
for the first one it is
ED= 26
CF= 13
mED= 136
mHD= 68
mCE= dont know this one but the other ones im positive their right
Step-by-step explanation:
9514 1404 393
Answer:
ED = 26; CF = 13; arc ED = 136°; arc HD = 68°; arc CE = 88°
QU = 8; QR= 16; arc ST = 114°; arc QR = 114°; arc XT = 57°
Step-by-step explanation:
Chords the same distance from the center of the circle are the same length. Chords of the same length intercept arcs of the same angle measure. A radius perpendicular to a chord bisects it and the arc it subtends. The sum of arcs in a circle is 360°. These facts are used to solve the problems here.
__
Circle J
ED = 2×GD = 26
CF = GD = 13
arc ED = arc CD = 136°
arc HD = 1/2 arc CD = 68°
arc CE = 360° - 2×136° = 88°
__
Circle Y
QU = 1/2×ST = 8
QR = ST = 16
arc ST = arc QR = 1/2(360° -34° -98°) = 114°
arc XT = 1/2 arc ST = 57°