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
Sorry the pic looks like that but help me pleasee
Researcher were testing out a new antibiotic on a certain bacteria. They started with 38,000 bacteria. After one treatment with antibiotics, 33,820 were left. After a second treatment, 30,100 bacteria were left. How many bacteria will be left on day 27
Answer:
1836 bacteria
Step-by-step explanation:
Now the data is a progression; 38,000, 33,820, 30,100 .........
We can find out what type of progression it is, in this case, we can see that it is a geometric progression because;
r= 33,820/38,000 = 30,100/33,820 = 0.89
So, for a geometric progression;
Un = ar^n-1
Where;
a = 38,000
r = 0.89
n = 27 days
Un = ???
Un = 38,000 * (0.89)^27 - 1
Un = 1836 bacteria
What is the 10th term of 300, 150, 75
Answer:
So the pattern is dividing in half
So 300, 150, 75
We have the first 3 terms
The 4th term: 37.5, 18.75,
So we get the 10th term: 0.58
A football team moved -8 yards on one play, then lost another 4 yards on the next play. How many total yards did the football team move on those two plays?
Answer:
12 yards
Step-by-step explanation:
you subtract negative 8 and 4 and it gives you twelve yards of the play
Helpppppp meee please
Answer:
7.25 and 7.20
Step-by-step explanation:
I calculated and got it correct
Answer:
a) $14.45 b) 1.45x+1.2y
Step-by-step explanation:
5*1.45+6*1.2=14.45
Use the number line below, where RS = 6y + 3, ST = 4y + 7, and RT = 60.
Answer:
Step-by-step explanation:
RS + ST = RT
6y + 3 + 4y + 7 = 60
6y + 4y + 3 + 7 = 60
10y + 10 = 60
10y = 60 - 10
10y = 50
y = 50/10
y = 5
RS = 6*5 + 3 = 30 +3 = 33
ST = 4*5 + 7 = 20 + 7 = 27
Step-by-step explanation:
[Diagram in image attached]
RS + ST = RT
(6y +3) + (4y + 7) = 60
6y + 3 + 4y + 7 = 60
10y + 10 = 60
10y = 60 - 10
10y = 50
y = 50/10
y = 5
RS = 6y +3 = 6(5) + 3 = 30 + 3 = 33
ST = 4y +7 = 4(5) + 7 = 20 + 7 = 27
RT = 60
{RS + ST = RT
33 + 27 = 60}
HOPE THIS HELPS YOU
MARK AS BRAINLIEST
what's the gcf of 3x and 12x
Answer: GCF- is 3x
Step-by-step explanation:
So first you will ignore the X.
You will then find the GCF of 3 and 12.
The calculated value of the gcf of 3x and 12x is 3x
Calculating the gcf of 3x and 12xFrom the question, we have the following parameters that can be used in our computation:
Expressions = 3x and 12x
Expand both expressions
So, we have
3x = 3 * x
12x = 2 * 2 * 3 * x
Multiply the common factors
GCF = 3 * x
Evaluate
GCF = 3x
Hence, the gcf of 3x and 12x is 3x
Read more about GCF at
https://brainly.com/question/17067741
#SPJ4
A boat is on the same horizontal level as the foot of a cliff and the angle of depression of the boat 30 degree. If the boat is 120m away from the foot of the Cliff, find the height of the Cliff to 3 significant figures
Answer:
69.282 m
Step-by-step explanation:
We can use the trigonometry of right triangles to solve this, since we are in the presence of a right triangle with acute angle 30 degrees, opposite side unknown (the vertical height of the cliff), and adjacent side equal to 120 m.
we use the tangent function to solve for the unknown, as shown below:
tan(30) = x/120
x = 120 * tan(30) = 69.282 m
1. The solution to a system of equations is (6,-3). Choose two equations that might
make up the system.
A. y = -2r+6
B. y = 2x - 9
C. y = -5x + 27
D. y = 2x - 15
E. y = -4x + 27
please help will give brainly
Graph the system of linear inequalities.
y > x + 2
y ≥ x − 2
Answer:
I hope this helps sorry if I'm wrong
Answer:
y = 1x
Step-by-step explanation:
y
[tex]y \geqslant 1x + 2[/tex]
cancel out the +2 by using the opposite sign and add a 1 in front of the x
I need some help 6(4x-3)-9x
Answer:
3(5x-6)
Step-by-step explanation:
I hope this helps you out, let me know if you need to know how it's solved.
Answer:
15x-18
Step-by-step explanation:
[tex]6(4x-3)-9x\\24x-18-9x\\15x-18[/tex]
In which point of the graph is the water increasing?
Answer:
2
Step-by-step explanation:
I need to know the graph points and how to graph it ASAP
Answer: for the first one it's the first picture and the second equation is the second picture
Step-by-step explanation: the pictures
the first one's coordinates are : (-0.4, -1)
the second one's coordinates are: (2,-6)
they are both dotted lines
HELP ASAP
1.Which number or symbol is a variable in the following algebraic expression?
5 + 4y x 32
a 5
b 4
c y
d 2
2.Convert the following word phrase to an algebraic expression:
9 less than a number.
a x - 9
b 9 -x
c 9 ÷ x
d x ÷ 9
Answer: 1.C 2.B
Step-by-step explanation:
Can you help me with question number 10, please?
Answer:
(1) 8.3
Step-by-step explanation:
Answer:
1) 8.3
Step-by-step explanation:
get rid of the (), which u will get 4x-28=0.3x+0.6+2.11
combine like terms, which u will get 4x-28=0.3x+2.71
move variable to one side and numbers to the other, which you will get
3.7x=30.71
divide both sides by 3.7 which u will get 8.3
how do I solve this question ?
Answer:
x=37 CD=20
Step-by-step explanation:
We know this becuase the two triangles are congruent.
You have performed very well on your new job. Without even requesting it your boss gave you a $2.50 raise. If your previous wage was $6.25, what was the percent increase of your raise?
Answer:
40%
Step-by-step explanation:
$6.25/100=0.0625
$2.50/0.0625=40
so your wage increased by 40%
PLEASE help mee. Explain and show work plsss.
6. yes, if line was originally in the top right quadrant you could lower y intercept so that it no longer goes through top right
Hrozmarly needs to evaluate the following expression y^2-x^2 when y=9 and x=2. Her answer should be?
i am in 6 grade
Answer:
Step-by-step explanation:
y^2 -x^2=
y^2=9^2=81
x^2=2^2=4
81-4=77
Your friend has $80 when he goes to the fair. He spends $4 to enter the fair and $12 on food. Rides at the fair cost $1 25 per ride. Which function can be used to determine how much money he has left over after x rides?
Answer:
80m - (12+4) = x
Step-by-step explanation:
Hope this helps! I mean its self explanatory
Answer:
$38.75
Step-by-step explanation:
We can add up the amount he spent before he started riding and we'll get $16. Subtract 16 from 80 which is 64. $64 dollars divided by $1.25 would be 51.2. We round down because he can't ride more then 50 rides. He would be able to ride 51 rides with the money he has. Let's say he rode 20 rides and then left the fair. We would subtract 20 from 51 and get 31. After that we would multiply 31 by 1.25 and get $38.75. So he would have $38.75 dollars after he left the fair.
17c+7c-6c^6+2c^8 the polynomial standard form is _
7.0 x 10^3 + 2.0 x 10^2
Answer:
7200
Step-by-step explanation:
Find the exponents first.
10^3 = 1000
10^2 = 100
So..
7 x 1000 + 2 x 100
Do the multiplication first (BEDMAS - Brackets Exponents Division Multiplication Addition Subtraction).
7000 + 200 = 7200
Problem
Jun used 56\,\text{cm}56cm56, start text, c, m, end text of ribbon to go around the edge of a rectangular lid. The lid was 13\,\text{cm}13cm13, start text, c, m, end text long.
What is the width of the lid?
Answer:
The width of the lid is 15 cm
Step-by-step explanation:
The Perimeter of a Rectangle
Given a rectangle of width W and height H, the perimeter is calculated as:
P = 2(W + L)
Jon used 56 cm of ribbon to go around the edge of a rectangular lid. This means the perimeter is:
2(W + L) = 56
Dividing by 2:
W + L = 28
Since the lid was L=13 cm long, the width is:
W = 28 - 13 = 15
The width of the lid is 15 cm
3(2x+5)-x=__x+__
put 2 numbers in the blanks to make no solutions
Answer:
5x + 15
Step-by-step explanation:
3(2x + 5)-x
6x + 15 - x
5x + 15
Hope this Helps!!!
Write the exponent for the expression.
15 × 15
The exponent for the expression is ___
Answer:
2. i think. correct me if im wrong.
Answer: The answer is 2
Step-by-step explanation:
help me plz i dum reeee
Answer:
The mean absolute deviation of the data set is 2.5
Step-by-step explanation:
We need to find mean absolute deviation of the data set:
10,8,10,6,6,2,10,4
First we will find mean of the given data set.
The formula used is: [tex]Mean=\frac{Sum\:of\:all\:data}{Number\:of\:data}[/tex]
Sum of all data = 10+8+10+6+6+2+10+4 = 56
Number of data = 8
So, mean will be:
[tex]Mean=\frac{Sum\:of\:all\:data}{Number\:of\:data}\\Mean=\frac{56}{8}\\Mean=7[/tex]
Now, we will calculate the absolute difference between mean and each data value.
|10-7| = 3
|8-7| = 1
|10-7| = 3
|6-7| = |-1| = 1
|6-7| = |-1| = 1
|2-7| = |-5| = 5
|10-7| = 3
|4-7| = |-3| = 3
Now, we will find mean of 3,1,3,1,1,5,3,3
Sum of all data = 3+1+3+1+1+5+3+3 = 20
Number of data = 8
So, mean will be:
[tex]Mean=\frac{Sum\:of\:all\:data}{Number\:of\:data}\\Mean=\frac{20}{8}\\Mean=2.5[/tex]
So, the mean absolute deviation of the data set is 2.5
A man is 5 feet 9 inches tall. To find the height of a tree, the shadow of the man and the shadow of the tree were measured. The length of the man's shadow was 3 feet 6 inches. The length of the tree's shadow was 10 feet 6 inches. What is the height of the tree?
Answer:
17 feets 3 inches
Step-by-step explanation:
Given :
Converting the parameters to inches only:
Recall:
1 feets = 12 inches
Man's height : 5 feets 9 inches = (12 *5) + 9 = 69 inches
Man's shadow : 3 feets 6 inches = (12 * 3) + 6 = 42 inches
Tree's shadow : 10 feets 6 inches = (12 * 10) + 6 = 126 inches
(Tree's height / tree's shadow) = (man's height / man's shadow)
Let tree's height = x
x / 126 = 69 / 42
Solve for x
42x = 126 * 69
42x = 8694
x = 8694 / 42
x = 207 inches
207 / 12 = 17 feets 3 inches
Answer:
17.25 ft
Step-by-step explanation:
The figure shows two triangles X Y Z and H R Q. Side X Y has a length of h units, side Y Z has a length of 10 feet 6 inches, angle Y is a right angle. Side H R has a length of 5 feet 9 inches, side R Q has a length of 3 feet 6 inches. Angle R is a right angle.
Let h be the height of the tree.
Convert all measurements to a single unit, inches, using the fact that 1 foot is equal to 12 inches.
ZY=(10⋅12) in.+6 in.
Simplify.
ZY=126 in.
QR=(3⋅12) in.+6 in.
Simplify.
QR=42 in.
HR=(5⋅12) in.+9 in.
Simplify.
HR=69 in.
ZX¯¯¯¯¯ and QH¯¯¯¯¯¯ are parallel because the rays of the Sun that form them are parallel. Therefore, the angles they form with the ground are congruent: ∠Z≅∠Q.
∠Y≅∠R by the Right Angle Congruence Theorem.
Therefore, by the Angle-Angle Similarity △ZXY~△QHR.
Find XY. Set up a proportion with the lengths of the known sides and the unknown length (height of the tree).
ZY/QR = XY/HR
Substitute the values.
126/42=h/69
Cross multiply.
42h=69(126)
Simplify.
42h=8694
Divide both sides by 42.
h=207 in.
Therefore, the height of the tree is 207 in., or 17.25 ft.
In 7th grade, the ratio of boys to girls is 6 to 7. If there are 143 students in 7th grade, how many are girls? Do NOT write a label. Just write the number.
Answer:
123 if your going to the nearest whole number
Step-by-step explanation:
Since
6 : 7 = X : 143
Then we know
6/7 = X/143
Multiplying both sides by 143 cancels on the right
143 × (6/7) = (X/143) × 143
143 × (6/7) = X
Then solving for X
X = 143 × (6/7)
X = 122.57142857143
Therefore
6 : 7 = 122.57142857143 : 143
Pls help and show workings
Due ASAP
Answer: B
Step-by-step explanation:
The equation [tex]y+2=\frac{3}{4} x-8[/tex] is not yet in slope-intercept form([tex]y=mx+b[/tex]). Simply subtract 2 from both sides to turn the equation into slope intercept form as [tex]y=\frac{3}{4}x-10[/tex]. For a line to be perpendicular to another, it must have an opposite reciprocal slope. A reciprocal is the fraction reversed, where the numerator is the denominator and vice versa. Thus, 3/4 would become 4/3. The opposite reciprocal of 3/4 would be -4/3.
The slope of the line given is 3/4. Thus, simply plug in the opposite reciprocal of 3/4 for the slope to get: [tex]y=-\frac{4}{3} x+b[/tex]. Then, because the line passes through -12, 1, plug those values in for x and y, respectively.
[tex]1=-\frac{4}{3}*-12+b[/tex]
[tex]1=16+b[/tex]
[tex]-15=b[/tex]
Thus, the equation of the line is [tex]y=-\frac{4}{3} x-15[/tex], or B.
Hope it helps :D
1. Calculate the volume of the following shapes.
I
a)
9m
8m
5m
It’s a rectangle
Answer:The answer is 360 cubic meter.
Step-by-step explanation:
Answer:
It's 360 cubic meter.
Step-by-step explanation:
Volume of rectangle=length*width*height
= 9×8×5
= 360m³