Answer:
f(n) = 120 * (1/2)^n
Step-by-step explanation:
First the first number is 120, so we get y = 120, then 60/120 = 1/2
So we no the r, or constant rate is 1/2.
After that, we can finish our equation by doing
f(n) = 120 * (1/2)^n
or
y = 120*(1/2)^x
The explicit formula for the given geometric sequence is:
[tex]a_n = 120 \times 0.5^{n-1}[/tex]
We have,
To find an explicit formula for the geometric sequence 120, 60, 30, 15, ...,
we need to determine the common ratio, denoted by 'r'.
To find the common ratio, we divide any term in the sequence by its preceding term.
Let's choose the second and first terms:
r = 60 / 120 = 0.5
Now that we have the common ratio 'r', we can express the nth term of the geometric sequence using the explicit formula:
[tex]a_n = a_1 r^{n-1}[/tex]
where '[tex]a_n[/tex]' represents the nth term of the sequence, '[tex]a_1[/tex]' is the first term, 'r' is the common ratio, and 'n' is the position of the term we want to find.
Using the given sequence, '[tex]a_1[/tex]' is 120, and 'r' is 0.5.
Plugging these values into the formula, we have:
[tex]a_n = 120 \times0.5^{n-1}[/tex]
Therefore,
The explicit formula for the given geometric sequence is:
[tex]a_n = 120 \times 0.5^{n-1}[/tex]
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A cylinder has a diameter of 40 feet and a height of 32 feet. What is the surface area of the cylinder? Express the answer in terms of Pi. Recall the formula S A = 2 pi r squared + 2 pi r h. 1,320 pi feet squared 1,792 pi feet squared 2,080 pi feet squared 2,640 pi feet squared
Answer:
2080
Step-by-step explanation:
The surface area of the cylinder is 2080π square feet. Answer: 2,080 pi feet squared.
What is a cylinder?A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).
Since the diameter is given as 40 feet, the radius is half of that, or 20 feet.
So, substituting the values into the formula, we get:
SA = 2π(20)² + 2π(20)(32)
SA = 2π(400) + 2π(640)
SA = 800π + 1280π
SA = 2080π
Therefore, SA = 2080π.
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40 POINTS!!!!!!!!! Given the following system of equations and their graph below, what can be determined about the slopes and y-intercepts of the system of equations? A line includes points 6 comma 1 and 4 comma 0. 3x − 6y = 12 9x − 18y = 36 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.
Answer:
The slopes are the same and the y-intercepts are the same.
Step-by-step explanation:
Looking at the two systems of equations:
3x - 6y = 12
and
9x - 18y = 36
We can see that the two equations have a GCF, that GCF would be 3.
Since, 3 ( 3x - 6y = 12) = 9x - 18y = 36
or vice versa: (9x - 18y = 36)/3 = 3x - 6y = 12
Therefore, both the slopes and the y-intercepts are the same just dilated by a factor of 3.
Answer:
The slopes are the same and the y-intercepts are the same.
Step-by-step explanation:
Find the exact value of sec30°.
Decimal Form:
1.15470053
…
Step-by-step explanation:
The exact value of sec(30°) is 2√3 / 3.
We have,
To find the exact value of sec(30°), use the trigonometric identity:
sec(θ) = 1 / cos(θ)
Now,
cos(30°) = √3 / 2
Now, substitute this value into the formula for sec(θ):
sec(30°) = 1 / cos(30°) = 1 / (√3 / 2)
sec(30°) = 2 / √3
To rationalize the denominator, multiply the numerator and denominator by √3:
sec(30°) = 2 / √3 * √3 / √3
= 2√3 / 3
Therefore,
The exact value of sec(30°) is 2√3 / 3.
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Please I been struggling so much and need help please help me out and it is due today this geometry math assignment and I try and nothing. Works I need it by today and I willl mark Brainly
Answer:
9a) corresponding
9b) Congruent
9c) x=5
10) x=4
11=9
Step-by-step explanation:
9a. The angles are corresponding, as, if you look at the 8 angles as 2 groups of 4, they would be in the same spot.
b. Corresponding angles are congruent (by corresponding angles are congruent theorem)
c. Because the angles are congruent, we know that
23x-5=21x+5
23x-21x=5+5
2x=10
x=5
10. We know that (see attached photo) angle a is equal to angle b through the vertical angle theorem. Then, we know that angle b is equal to angle c through corresponding angles. So, we know that a=b, and b=c, so through the transitivity property, a=c, and c=90 degrees (it is a right angle)
Therefore, a=90 degrees
a=21x+6, so 21x+6=90
21x=84
x=4
11) This is almost the exact same problem as 10. We know that (see attached photo) a=b through vertical angles, and b=c through corresponding angles. Therefore, a=c
When you substitute the values of the two angles, we get:
-1+14x=12x+17
14x-12x=17+1
2x=18
x=9
Ginny Jones receives $624 gross salary biweekly. Her income tax rate is 14%. Her group health plan contribution is $4.25 per pay period. She belongs to the company retirement plan, to which she contributes 6% of her earnings. She is also covered under Social Security benefits. Her current contribution is 6.05%. If these items are all her deductions, what is her take-home pay per period? Ginny gets a $35 raise per pay period. If her health plan is unchanged, how much of the raise will she have to take home?
Answer:
take home pay $457.20
$30.78 from the raise
Step-by-step explanation:
Which ordered pair cannot be a solution of h(t)=-16^2+80t If h is the height of a ball above ground after t seconds?
Answer:
NON of them can be a solution.
Step-by-step explanation:
When I plugged them in to the equation they all came out false.
Answer:
It seems that this question would make more sense if it were: Which ordered pair can be a solution of [tex]h(t)=-16^2+80t[/tex]
All alternatives but B) cannot be a solution for the function.
Step-by-step explanation:
Here we have [tex]t=x[/tex]
So, we may write the funtion as: [tex]h(x)=-16^2+80x[/tex]
[tex]h(x)=y[/tex]
Let's test all the points:
A)[tex](1, 64)[/tex]
[tex]h(1)=-16^2+80(1)\\h(1)=-256+80\\h(1)=-176[/tex]
B)[tex](2, 96)[/tex]
[tex]h(2)=-16^2+80(2)\\h(2)=-256+160\\h(2)=96[/tex]
C) [tex](-4, 256)[/tex]
[tex]h(-4)=-16^2+80(-4)\\h(-4)=-256-320\\h(-4)=-576[/tex]
D)[tex](5, 0)[/tex]
[tex]h(5)=-16^2+80(5)\\h(5)=144[/tex]
PLEASE HELP WILL MARK BRAINLIEST!
Prove graphically and algebraically that a clockwise rotation of 270 degrees about the origin has an equivalent counterclockwise rotation. In your final answer, name the equivalent counterclockwise rotation and show all of your work.
On your graph, label the following:
1. parallelogram PARK and the coordinates of all four of its vertices
2. parallelogram P'A'R'K and the coordinates of all four of its vertices
3. center of rotation and its coordinate
4. the invisible circle of rotation, its radius and the length of the radius
5. use arrows to show the clockwise movement of the parallelogram
Answer:
Make a coordinate plane and you have to solve around the origin say 4,4 and 4,1.
Step-by-step explanation:
Answer:
Make a coordinate plane and you have to solve around the origin say 4,4 and 4,1.
Step-by-step explanation:
Drag the tiles to the boxes to form correct pairs. Match each function to the equation of the tangent line to its graph at x = 2.
Step-by-step explanation:
the picture includes the answer and work
I plugged in 2 for x
the equations that got the same answer, I put together
Answer:
Step-by-step explanation:
Find the arc length of a semi circle of 12
Answer:
Step-by-step explanation:
The arc length would be around 37.7, because the central angle would be 80 degrees, the radius is 12, and the diameter is 24.
Jerry's team has played 8 games of basketball. During those 8 games his team scored 59, 66, 56, 63, 42, 55, 62 and 51. What is the range in the number of points scored for each game?
A) 20
B) 22
C) 24
D) 26
Answer:
To calculate the mean of a set of data, you have to work out the sum of the data (in this case, you need to work out the sum of all the points) and divide it by the number of data points there are (in this case, number of games played).
So you have to do:
(67 + 45 + 84 + 55 + 73 + 36 + 80 + 62 + 38)/9 = 60
The mean number of points is 60.
Step-by-step explanation:
please mark as brainiest
Answer:
Your Answer here is C)24
Step-by-step explanation:
First order the scores from lowest to highest.
42,51,55,56,59,62,63,66
The highest number would be 66 and the lowest would be 42.
Subtracting 42 from 66 you would get 24 so the Range is the 24
When you multiply by an even number the product is even. true or false And why
can anybody correct me on this right away if you got any time? click/tap in here for the image
Answer:
Yep, they all match:
1. Correct
2. Correct
3. Correct
4. Correct
Step-by-step explanation:
1.
√2 • √3 • √3 = 4.242640687119285
3√2 = 4.242640687119285
2.
√2 • √3 • √-3 = 4.24264069i
3i√2 = 4.24264069i
3.
√-2 • √-3 • √-3 = -4.24264069i
-3√2 = -4.24264069i
4.
√2 • √-3 • √-3 = -4.24264069i
-3i√2 = -4.24264069i
isaac noticed 15 jeeps and motorcycles in the Walmart parking lot when he went to work . He saw 44 wheels . How many of each did he see ?
steps ?
Answer:
7 cars and 8 motorcycles
Step-by-step explanation:
15 cars and motorcycles total, with 44 wheels total.
cars = 4 wheels
motorcycles = 2 wheels
(7 * 4) + (8 * 2)
(28) + (16) = 44
Hope this helped!
(・∀・(・∀・(・∀・*)
Which ordered pair is generated from the equation shown below?
y = 3x + 2
A) (3, 11)
B) (3, 9)
C) (5, 15)
D) (2, 4)
Answer:
(3, 11)
Step-by-step explanation:
To check the ordered pair from given option .
lets plug in the value of x from the choices given .
If value of y is same a sin ordered pair then that pair is correct answer else it can be concluded that pair is not generated from equation given.
equation: y = 3x + 2
_____________________________________
A) (3, 11)
If we put value of X=3 in equation y = 3x + 2,
then y should be 11
y = 3x + 2
=> y = 3*3+2 = 9+2 = 11 . (This is as expected for ordered pair)
Hence this pair (3, 11) is generated from given equation.
_____________________________________
A) (3, 9)
If we put value of X=3 in equation y = 3x + 2,
then y should be 9
y = 3x + 2
=> y = 3*3+2 = 9+2 = 11 . (This is not as expected for ordered pair(3,9)
Hence this pair is not generated from given equation.
_____________________________________
A) (5, 15)
If we put value of X=5 in equation y = 3x + 2,
then y should be 15
y = 3x + 2
=> y = 3*5+2 = 15+2 = 17 . (This is not as expected for ordered pair(5,15)
Hence this pair is not generated from given equation.
_____________________________________
A) (2, 4)
If we put value of X=3 in equation y = 3x + 2,
then y should be 9
y = 3x + 2
=> y = 3*2+2 = 6+2 = 8. (This is not as expected for ordered pair(2, 4)
Hence this pair is not generated from given equation.
_________________________________________________
Thus, only A) (3, 11) is generated from the equation y = 3x + 2
Answer:
A I did quiz on time4learning ^-^
Step-by-step explanation:
Last Saturday, the average temperature was 8% higher than the average temperature, 2 Sundays ago, the average temperature 2 Sundays ago with T degrees Celsius, which of the following expressions could represent the average temperature last Sunday.
choose 2 answers.
A) 1.8T
B) T+8
C) T+0.08
D) 1.08T
E) (1 + 8/100) T
Answer: 1.08T and (1+8/100)T
Step-by-step explanation:
Given: The average temperature two Sundays ago was T degrees Celsius.
Since, last Sunday, the average temperature was 8% higher than the average temperature two Sundays ago.
⇒ The average temperature last Sunday
Since 8%=0.08
Therefore, The average temperature last Sunday
⇒ The average temperature last Sunday
⇒ The average temperature last Sunday
⇒ The average temperature last Sunday
Thus, the right option is 1.08T and (1+8/100)T
For which equation would x = 8 not be a solution?
a. 8 x = 64
b. 4 x = 48
c. 10 x = 80
d. 9 x = 72
Answer:
b. 4x = 48
Step-by-step explanation:
If you look closely an multiply 4 x 8, it equals 32, not 48
The other equations:
8 x 8 does equal 64
10 x 8 does equal 80
9 x 8 does equal 72
It's pretty simple once you try each problem first
Hope this helps!
Answer:
4x = 48
Step-by-step explanation:
Since x = 8,
4x = 48
4 * 8 = 32
So 32 is the LHS and 48 is the RHS.
Since the LHS is not equal to the RHS, x=8 is not a solution to the equation 4x = 48
Hope this answer is helpful!!
You buy a movie ticket for $5.25 and popcorn for $2.98. You pay with a 10-dollar bill.
How much change will you get back?
Answer:
$1.77
Step-by-step explanation:
Add the Movie Ticket and Popcorn together
$5.25 + $2.98
Simplify
$8.23
Subtract the total from your 10 dollar bill
$10 - $8.23
Simplify
$1.77
Answer:
$1.77
Step-by-step explanation:
$5.25 + $2.98 to find the total (I am not including tax, as there is not a mentioned rate) = $8.23
10.00 - 8.23 = 1.77 so, $1.77 is the change.
A faucet leaks water at a constant rate of quart every 15 minutes.
I
How many quarts does the faucet leak per hour?
Answer:
4 quarts per hour.
Step-by-step explanation:
60/15 = 4
The reason why i did 60 is because there is 60 min in a hour. then i divided it by 15 and got 4
hope this helps : )
The required quart that leaks is 4 quart, faucet leak per hours.
A faucet leaks water at constant rate of quat every 15 minutes. How many quarts does the faucet leak per hour to be determined.
Rate of change is defined as the change in value with rest to the time is called rate of change.
1 quart = 60 units
Every 15 minutes, 1 quart has been leaked from the faucet.
1 quart will be leaked fully = 15 minutes
Divide by 15 into both sides
1 / 15 quart will be leak fully = 1 minute
multiply both sides by 60
60 / 15 quart will be leak fully = 60 minute
4 quart will be leaked fully = 1 hour (60 min = 1 hour)
Thus, 4 quarts does the faucet leak per hours.
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What’s the range of the function fix)=4x+9, given the domain D={-4,-2,0,2}?
Answer:
The range is all real numbers.
Step-by-step explanation:
I graphed the equation on the graph below to find the range. The range is all real numbers because the line never stops and it touches all possible y-values.
If this answer is correct, please make me Brainliest!
A sector with an area of 140 pie cm^2 has a radius of 20 cm.
r = 20 cm
A = 140 pie cm^2
What is the central angle measure of the sector in degrees?
Answer:
Central angle = 126°
Step-by-step explanation:
Area of the sector = 140π cm²
Radius of the given circle = 20 cm
Since area of the sector = [tex]\frac{\theta}{360}\times (\pi r^{2})[/tex]
[where θ is the central angle formed by the sector at the center]
140π = [tex]\frac{\theta}{360}(\pi)(20)^{2}[/tex]
θ = [tex]\frac{(140\pi)\times 360}{400\pi }[/tex]
θ = 126°
Therefore, central angle of the sector will be 126°.
Answer:
cm 32
Step-by-step explanation:
somebody can you please help me?!?!?!?!?
Answer:
C
Step-by-step explanation:
180-133=47
180-108=72
180-119=61
Which ratio would help find the
height of the kite?
200 feet
50°
tan 50
sin 50
COS 50
cot 50
Answer:
Cos 50
Step-by-step explanation:
Liz was testing Jane on solving with equations. She gave Jane the
following problem:
“I am a number such that when you divide me by 7, and then, add 13
you get 32. What number am I?”
Write and solve an equation to determine Liz's number.
Answer:
x/7+13=32
Step-by-step explanation:
work backward so subtract 13 from 32 and get 19 multiply it by 7 and get 133, to make sure your answers right just substitute 133 back into the equation
If you had 1,100 blue berry's and 3 people took 61 each how many would you have left?
Answer:
917.
Step-by-step explanation:
I'm 100% sure because 1,00-61-61-61=917.
Hope this helped lots and lots,
sincerely, me
HELP ME ASAP!!!!!!! IT IS QUICK PROMISE JST ANSWER TWO SIMPLE QUESTIONS
Answer:
3.6 for tomatoes and 8.4 for lettuce
Step-by-step explanation:
70% of 12=8.4
30% of 12=3.6
check: 3.6+8.4=12
Question 3 of 10
2 Points
What is the volume of the sphere below?
5
A.
100
3
7 units 3
O
B.
ni units 3
3
C.
125
3
units 3
D.
500
3
7 units 3
Answer:
D
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius ), thus
V = [tex]\frac{4}{3}[/tex]π × 5³
= [tex]\frac{4}{3}[/tex]π × 125 = [tex]\frac{4(125)}{3}[/tex]π = [tex]\frac{500}{3}[/tex]π units³ → D
The volume of the sphere of the given figure is [tex]\frac{500}{3} \pi units^{3}[/tex] .Option D is correct.
It is given that the radius(r) of the sphere is 5 unit.
It is required to find the volume of the sphere of the given figure.
What is the volume of the sphere below?As we know the volume of the sphere is:
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
Where, r represents the radius of the sphere.
Now putting the value of 'r' in the formula,
V = [tex]\frac{4}{3}\pi (5)^{3}[/tex]
V = [tex]\frac{4}{3} \pi[/tex]×(125)
V = [tex]\frac{4 (125)}{3}\pi[/tex]
V = [tex]\frac{500}{3} \pi[/tex] [tex]unit^{3}[/tex]
Thus, the volume of the sphere of the given figure is [tex]\frac{500}{3} \pi units^{3}[/tex] .
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Money that is collecting interest in a bank account doubles in value every 10 years.
When the account was opened, it had 16, or 2 to the power of 4, dollars in it. After 50 years, the account balance has doubled 5 times, increasing by a factor of 2 to the 5th power.
It now has a balance of 2 to the 4th power x 2 to the 5th power. Expressed as a power, how much money, in dollars, is in the account after 50 years?
A. 4 to the power of 9
B. 2 to the power of 20
C. 2 to the power of 9
D. 2 to the power of 5
What is -1 and 3/5 divided by -2/3? As a fraction.
Answer=
mixed form=2 2/5
decimal form=2.4
exact form= 12/5
What is the mode of the following numbers?
67, 76, 67, 76, 67, 23, 32, 23, 32
0
Answer:
67
Step-by-step explanation:
67, 76, 67, 76, 67, 23, 32, 23, 32 ,0
Put the numbers in order from smallest to largest
0,23, 23, 32,32, 67, 67, 67, 76, 76,
The mode is the number that appears most often
67 appears 3 times so it is the mode
Easy Question About Area
Answer:
Option C.
Step-by-step explanation:
In the figure attached, a triangle has been given with angles.
m∠F = 73°
m∠D = 48°
And m∠E = 180° - (73 + 48)° = 59°
∠D < ∠E < ∠F
Since opposite sides of the largest angle in a triangle is longest and opposite side of the smallest angle is shortest,
Hence, d < e < f
Therefore, order given in Option C will be the answer.
Answer:
d, e, f
Step-by-step explanation:
Hope this helps:)