Consider we need to find f(n).
Given:
Achilles ordered a pizza with 16 slices.
Every hour, he ate half of the remaining slices.
To find:
The function f(n) that is the number of slices Achilles ate in the hour since he got home.
Solution:
Initial number of slices = 16
Every hour, he ate half of the remaining slices. So, the number slices Achilles ate in the hour since he got home are:
8, 4, 2, 1, ...
It is a geometric sequence with first term 8 and common ratio [tex]\dfrac{1}{2}[/tex].
The explicit formula for a geometric sequence is:
[tex]f(n)=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Substituting [tex]a=8,r=\dfrac{1}{2}[/tex], we get
[tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex]
Therefore, the function f(n) that is the number of slices Achilles ate in the hour since he got home is [tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex].
all the angles in the angles in the figure are right angles and lengths are measured in centimeters. what is the area , in square centimeters, of the figure?
58
62
66
70
Answer:
62 square cm
Step-by-step explanation:
The whole rectangle 12X10 = 120
Now subtract 2 restangles:
5x8 =40
6x3 =18
30+18= 58
120-58 =62
Answer: 62
Step-by-step explanation:
help me out, thank you !
help me pls
5x^2-45=0
Step-by-step explanation:
5x²-45=05x²=45x²=9x=√9x=3hope it helps.
Answer:
x=±√9 or x= 3, x=-3
Step-by-step explanation:
The problem requires us to find the x.
So we must isolate the variable, as so-
[tex]5x^2-45=0\\5x^2=45[/tex] (add 45 to both sides)
Now we can divide both sides by -
[tex]5x^2=45\\x^2=9[/tex]
Now we must square root both sides to find the root of x.
[tex]\sqrt{x^2} =\sqrt{9}[/tex]
x=±√9
or x= 3, x=-3
(2N/6N+4) (3N+2/3N-2
A line with a slope of -5 passes through the point (-3, 1). Write the
equation of the line in slope-intercept form.
Answer:
1/2
Step-by-step explanation:
Pleas help grade depends on it
Answer:
C. 62x+239=672
Step-by-step explanation:
X represents hours , which means 62 miles per hours equals 62x. Since Ed has already traveled 239 miles the opposite would be to add in order to subtract in the equation. 672 would be the equivalent of traveling 672 miles in x hours.
The chance of randomly selecting a red marble from a bag is 3/10. What is the probability of not selecting a red marble.
PLEASE HELP
NO LINKS
Answer:
The first blank is $640.30
The second blank is 670
Step-by-step explanation:
PLEASEEEE HELPPP SOMEONEEE
The number of texts Lee and John received each day for 8 days is shown. Lee's Text messages: (36, 31, 33, 35, 40, 29, 34, 34)
John's Text messages: (20, 15,45,5,23,22, 12, 18)
Lee's mean number of texts per day is 34 and John's mean number of texts per day is 20.
What statement involving MAD (mean absolute deviation) is true?
A. Lee has less variation in the number of text messages per day than John because Lee's MAD of texts per day is less than John's.
B. Lee has less variation in the number of text messages per day than John because Lee's MAD of texts per day is greater than John's.
C. Lee has greater variation in the number of text messages per day than John because Lee's MAD of texts per day is less than John's.
D. Lee has greater variation in the number of text messages per day than John because Lee's MAD of texts per day is greater than
John's
Answer:
a
Step-by-step explanation:
We in the same boat sis
someone help me i don’t understand this !
Answer: put it in the calculator with the () and they will give it to you right like you need it
Step-by-step explanation: :)
Answer:
I help you
Step-by-step explanation:
I help you _GUTI_ discord
Cual es la potencia de base 3 que corresponde al producto 3 elevado a 3,3elevao a menos 2y 9 elevado a menos
PLSS HELP IMMEDIATELY!!!! ILL MARK BRAINIEST IF U DONT LEAVE A LINK OR GUESS!!!!
Answer:19
Step-by-step explanation:
7x3=21
21-2=19
Answer:
total of 7 fabric needed but 2 are given so:total fabric minus 2 is; 7 minus 2 is 5 needed
Need help with algebra fast plz it’s due in 2 hours and can work be included if not that fine I just want the answer
[tex] \binom{ 1/3}{-2/3} \binom{1/3}{-1/6} [/tex]
Rewrite the logarithmic equation: log4x = 5 in exponential form.
Answer:
4^5=x
x= 1045
Step-by-step explanation:
4 to the power of 5 is 1045:)
Answer:
The base of the log is the same as the base of the exponential form and in our case the base is 4. The value of the exponent is what the log is equal too and in our case it is 5. We already know the base is 4 and we want to raise it to the exponent of 5 so we get
x=45 *five on top*
x=1024
Step-by-step explanation:
How do you do this pls I need help
Answer:
416 cm2
Step-by-step explanation:
The formula for surface area of prism.
2Ab+ Pb*h
2(1/2)(12)(8)+ 32*10
= 96+320
= 416 cm2
if my answer helps please mark as brainliest.
1) ABC is a right-angled triangle.
AB = 50 cm.
Angle ABC= 24°
Work out the length of BC.
Give your answer correct to 1 decimal place.
Answer:
112.3
Step-by-step explanation:
What is the correct angle measure 42° 38° 142° 158°
Answer:
142°
Step-by-step explanation:
If it's goes from right to left, you read bottom numbers.
if it goes from left to right, you read the top numbers.
what is the missing number for the problem bottom left cornerd
I WILL GIVE BRAINLIEST
Answer:
length = 10
Step-by-step explanation:
Volune = L W H
H=40
W=8
L=X
40*8*X = 3200
320 X = 3200
X = 10
Volume : 40 x 8 x10 = 3200
Can anyone solve for x? Please.
Answer:
[tex] \frac{20}{24} = \frac{22}{x + 22} \\ 24 \times 22 = 20x + 20 \times 22 \\ 20x = 4 \times 22 \\ x = 88 \div 20 = 4.4[/tex]
In the figure above, ABCD is a cyclic quadrilateral. What ja the value of x in degrees?
Answer:
Step-by-step explanation:
Remark
The diagram makes the line AB look like it is tilted a bit to the right. I'm going to assume that isn't right. AB extended is a straight line. ADC is supplementary to the 80o angle.
Solution
<ADC + 80o = 180 They are on the same straight line
<ADC = 180 - 80 Subtract 80 from both sides
<ADC = 100o
Opposite angles of a cyclic quadrilatral are supplementary
<ADC + <ABC = 180 Property of cyclic quadrilaterals
100 + <ABC = 180 Subtract 100 from both sides
<ABC = 80 degrees.
<x + <ABC = 180
<x + 80 = 180
<x = 100 degrees
Discussion
I cannot be sure what the arc at B is equal to. Is the arc = 80 o or is <ABC = 80. And it is unresolvable. My suggestion is that you ask your teacher.
Can someone please help me
Answer:
1/6
Step-by-step explanation:
he has 1 chance to roll 6 different numbers
answer dis or somethinggg
Answer:
ok just did now give be brainlyest
Step-by-step explanation:
Answer:
ur mom ur mom ur mom ur mom ur mom ur mom ur mom
Step-by-step explanation:
Find the variable in the figure. The diagram is not to scale.
Volume=16π
r = 2
The volume of a cone can be found using the following equation
[tex]V = r^2\frac{h}{3} \pi[/tex]
After putting in the information that we already know we get
[tex]16\pi = r^2\frac{12}{3} \pi \\16\pi = r^2(4) \pi \\4 = r^2\\ r = 2\\[/tex]
For proof's sake, we can try the equation again with the information we know
[tex]V = r^2\frac{h}{3} \pi \\V = 2^2\frac{12}{3} \pi \\V =4(4) \pi \\V = 16\pi[/tex]
Please answer this question correctly
Answer: 44
EC is basically EF times 2
Answer: EC=44
Step-by-step explanation:
can you guys help me with this
Answer:
BD = 3.2.
CD = 2.4.
Step-by-step explanation:
By Pythagoras:
AB^2 = 3^2 + 4^2 = 25
AB = 5.
Triangles ADC and ACB are similar, so
AC / AB = AD / AC
3 / 5 = AD / 3
AD = 3*3/5
AD = 9/5 = 1.8
So BD = 5 - 1.8
= 3.2.
CD^2 = AC^2 - AD^2 (Pythagoras)
CD^2 = 3^2 - 1.8^2 = 5.76
CD = 2.4.
A magazine mailed a survey to 3,975 subscribers. Twenty-six percent of the subscribers answered the survey. About how many people answered the survey?
The area of this shape is
Answer:
Step-by-step explanation:
Answer:
169.4ft^2
Step-by-step explanation:
Area of right triangle= base x height /2
Area of right triangle= 24.2x (7x2) /2
Area of right triangle= 24.2x (14) /2
Area of right triangle= 24.2x (14) /2
Area of right triangle= 169.4ft^2
please help tysm ! Giving brainliest to best answer
Step-by-step explanation:
here is your answerrrrrrrrrrr
Need help take your time and thx
Answer:
if you factor it the answer is (x−5)(x−9)
write the number in word form .0001
Answer:
0.0001 in word form is ten thousandth