Answer:
- 13
Step-by-step explanation:
f(1) = 7
f(n) = f(n − 1) – 4
f(₂) = f(1) – 4 = 7 - 4 = 3
f(₃) = f(₂) – 4 = 3 - 4 = -1
f(₄) = f(3) – 4 = (-1) - 4 = - 5
f(₅) = f(₄) – 4 = (- 5) - 4 = - 9
f(₆) = f(₅) – 4 = (- 9) - 4 = - 13
The value of f(6) is -13, calculated based on the provided recursive formula where each term is four less than the previous.
Explanation:We are given that f(1) = 7, and the recursive equation for n is f(n) = f(n − 1) – 4. Since the equation shows that each next term is four less than the previous one, we can calculate the following iterations:
f(2) = f(2-1) - 4 = f(1) - 4 = 7 - 4 = 3f(3) = f(3-1) - 4 = f(2) - 4 = 3 - 4 = -1f(4) = f(4-1) - 4 = f(3) - 4 = -1 - 4 = -5f(5) = f(5-1) - 4 = f(4) - 4 = -5 - 4 = -9f(6) = f(6-1) - 4 = f(5) - 4 = -9 - 4 = -13So, the value of f(6) is -13.
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claire%20deposited%20$2,500%20into%20an%20account%20that%20accrues%20interest%20monthly.%20she%20made%20no%20additional%20deposits%20or%20withdrawals.%20after%202%20years,%20claire%20had%20$2,762.35%20in%20the%20account.%20what%20is%20the%20annual%20interest%20rate%20of%20the%20account?%20compound%20interest%20formula:%20t%20=%20years%20since%20initial%20deposit%20n%20=%20number%20of%20times%20compounded%20per%20year%20r%20=%20annual%20interest%20rate%20(as%20a%20decimal)%20p%20=%20initial%20(principal)%20investment%20v(t)%20=%20value%20of%20investment%20after%20t%20years%205%%2011%%2026%%2031%
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Answer:
The annual interest rate is 5.247%.
Step-by-step explanation:
Question
Claire deposited $2,500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had $2,762.35 in the account. what is the annual interest rate of the account?
Subtract $2,500.00 from $2,762.35 and you get 262.35- the 2-year interest. To get the annual interest, divide 262.35 by 2, which equals 131.75. Then, divide 131.75 by 2,500 (original amount) and you get 0.05247. Lastly, multiply 0.05247 by 100 to get the answer (5.247%).
To find the annual interest rate, use the compound interest formula and set it equal to the final amount in the account. After performing the necessary computations, 'r' comes out to approximately 5%.
Explanation:To find the annual interest rate of Claire's account, you'll need to use the compound interest formula: v(t) = p * (1 + r/n)^(nt), where:
'p' is the initial (principal) investment, in this case $2,500;'r' is the annual interest rate, which is what we're solving for;'n' is the number of times the interest is compounded per year, which, since it's compounded monthly, is 12; and't' is the number of years since the initial deposit, which is 2 in this case.Claire's account had $2,762.35 in it after 2 years. Therefore, you would set $2,762.35 equal to the formula and solve for 'r'.
Doing so yields $2,762.35 = $2,500 * (1 + r/12)^(12*2) which simplifies, after some mathematical computations, to an annual interest rate (r) of roughly 5%.
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Please help with probability
Step-by-step explanation:
2. The total number of calculators is 6 + 9 + 2 = 17.
When she hands out the first calculator, the probability that it is blue is 2/17.
When she hands out the second calculator, there is one less calculator total, so the probability that it is yellow is 9/16.
The probability of both is therefore:
P = 2/17 × 9/16
P = 9/136
3. There are 13 clubs in a standard deck of 52 cards.
The probability that the first card is clubs is 13/52 = 1/4.
Since you replace the card, there are still 52 cards in the deck. So the probability that the second card is clubs is 13/52 = 1/4.
The probability that both cards are clubs is:
P = 1/4 × 1/4
P = 1/16
4. The total number of pieces of gum is 6 + 9 + 5 = 20.
When you pick the first piece, the probability that it is grape is 6/20.
When you pick the second piece, there's one less piece of gum, and one less grape flavor, so the probability is 5/19.
The probability that both pieces are grape is:
P = 6/20 × 5/19
P = 3/38
5. The total number of drinks is 6 + 3 + 4 = 13.
Since the coach replaces the first drink, the second selection will be independent of the first. So the probability is still P = 6/13.
6. A die has six sides. They are numbered 1 through 6. Three of the numbers are even. Each roll is independent, so the probability of a previous roll does not affect the probability of future rolls.
The probability that you get 3 even numbers, followed by a one, is:
P = (3/6) (3/6) (3/6) (1/6)
P = 1/48
If the ratio of a circle's sector to its total area is 3/11, what is the measure of
its sector's arc?
Answer:
6πr/11.
Step-by-step explanation:
The length of the arc = rC where C is the central angle of the sector in radians and r = the radius.
C = (3/11) * 2π
= 6π/11 radians.
So the measure of the arc = 6πr/11.
A circular mirror is surrounded by a square metal frame. The radius of the mirror is 3x. The side length of the metal frame is 15x. What is the area of the metal frame?
The area of the metal frame surrounding a circular mirror can be calculated by figuring the expression 225x² - 9πx², which represents the area of the square minus the area of the circle.
Explanation:The subject of this question is based in mathematics, specifically the area of geometry. The area of the metal frame surrounding the mirror can be found by calculating the difference between the area of the square frame and the area of the circular mirror.
The area of the square frame is given by the formula A = s² where 's' is the length of a side of the square. In this case, each side of the square is 15x so the area of the square frame would be (15x)² = 225x².
The area of the circular mirror is given by the formula A = πr² where 'r' is the radius of the circle. For this mirror, the radius is 3x, so the area of the mirror would be π*(3x)² = 9πx².
So, the area of the metal frame is the difference between the area of the square and the area of the circle. Thus, the area of the frame = 225x² - 9πx².
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Final answer:
To find the area of the metal frame, calculate the area of the square then subtract the area of the circle. The area of the frame is the difference between the square's area, (15x)², and the circle's area, π(3x)².
Explanation:
The question asks for the area of the metal frame surrounding a circular mirror with the mirror's radius being 3x and the frame's side length being 15x.
To find the area of the frame, first calculate the area of the square and then subtract the area of the circle (mirror). The area of the square is given by the formula A = side², so:
Area of the square (Frame + Mirror): A = (15x)²Next, calculate the area of the circle using the formula A = πr²:
Area of the circle (Mirror): A = π(3x)²Finally, subtract the mirror's area from the frame's area to find the area of the metal frame alone:
Area of the metal frame: Aframe = (15x)² - π(3x)²It takes Esther 12 minutes to ride a roller
coaster four times. Write an equation to represent
the proportional relationship between the number
of rides and the total amount of time.
Final answer:
The proportional relationship between the number of rides and time is represented by the equation t = 3n where t is the total time in minutes and n is the number of rides.
Explanation:
Since it takes Esther 12 minutes to ride a roller coaster four times, we can find the time taken for one ride by dividing the total time by the number of rides.
Time for one ride = Total Time / Number of Rides = 12 minutes / 4 rides = 3 minutes per ride.
The proportional relationship between the number of rides (n) and the total amount of time (t) can be represented by the equation t = 3n. This indicates that for every ride, 3 minutes are added to the total time.
carter needs to wrap 7 presents. he lays the ribbon out flat and says ,if i nake 6 equally spaced cuts i'll have just enough pieces i can use 1 piece for each packages and i won't have any pieces left over .does he have enough pieces to wrap all the presents
Express 2.41 x 10^4 in a standard form
Step-by-step explanation:
[tex]2.41 \times {10}^{4} \\ = 2.41 \times 10000 \\ = 24100 \\ [/tex]
what is the value of c so that -12 and 12 are both solutions of x^2-c=108?
Answer:
c=36
Step-by-step explanation:
Because [tex]x^2-c=108[/tex] can be rewritten as [tex]x^2-c-108=0[/tex], finding the value of c so that x=(+-)12 solves this equation it means to find the value of c so that [tex](+-)12^2-c-108=0[/tex].Because [tex]12^2=(-12)^2=144[/tex], we must find c so that [tex]144-c-108=0[/tex].Because [tex]144-108=36[/tex], c=36.To check, replace c=36 in the initial equation, and check it is a solution for x=(+-)12.45 percent of a group of people have blue eyes. How many people are in the group if 180 people have blue eyes
Answer:
81
Step-by-step explanation:
Madison went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 700 mg of sodium. Madison purchased 2 more frozen dinners than cans of soup and they all collectively contain 7400 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
Madison purchased 5 cans of soup and 7 frozen dinners.
Step-by-step explanation:
Given,
Quantity of sodium in each soup can = 500 mg
Quantity of sodium in each frozen dinner = 700 mg
Total quantity = 7400
Let,
Number of soup cans purchased = x
Number of frozen dinners purchased = y
According to given statement;
500x+700y=7400 Eqn 1
y = x+2 Eqn 2
Putting value of y from Eqn 2 in Eqn 1
[tex]500x+700(x+2)=7400\\500x+700x+1400=7400\\1200x=7400-1400\\1200x=6000[/tex]
Dividing both sides by 1200
[tex]\frac{1200x}{1200}=\frac{6000}{1200}\\x=5[/tex]
Putting x=5 in Eqn 2
[tex]y=5+2\\y=7[/tex]
Madison purchased 5 cans of soup and 7 frozen dinners.
Keywords: linear equation, substitution method
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Answer:
Madison purchased 5 cans of soup and 7 frozen dinners
Step-by-step explanation:
If a^2 + b^2=c^2 then the triangle is a right triangle.
A triangle with side lengths of 15m, 30m and 34m is a right triangle.
True or False
***Important... Even though the question says 15m, the question owner says he meant to put 16m***
[tex]a^2+b^2=c^2\\\\16^2+30^2=34^2\\\\256+900=1156\\\\1156=1156[/tex]
True!
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
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3.14*16.8*16.8*16.9
Find answer then round to the nearest hundredths
[Mark Brainliest if correct]
Answer: 3.14 *16.8*16.8*16.9=14977.3478
14977.3478= 14,977.35
6. Rectangle GHIJ is enlarged to form
rectangle KLMN.
G 5cm H
2.5 cm
20 cm
10cml
Scale Factor:
Answer:
Scale Factor=2
Step-by-step explanation:
As the rectangle is enlarging from GHIJ to KLMN
then
Sacle Factor = Larger length / Smaller Length
Scale Factor = 5 cm / 2 cm = 2
Scale Factor = 20 cm / 10 cm = 2
Find an equation for the line with the given properties.
Parallel to the line x = -5; containing the point (6, 2)
Given that the surface of the area cube is given by the formula SA equals 6S2 what is the value of essay if S equals 1/2 cm
Answer:
[tex]SA=1.5\ cm^2[/tex]
Step-by-step explanation:
we know that
The surface area of a cube is equal to
[tex]SA=6s^2[/tex]
where
s is the length side of a cube
we have
[tex]s=\frac{1}{2}\ cm[/tex]
substitute
[tex]SA=6(\frac{1}{2})^2[/tex]
[tex]SA=(\frac{6}{4})=1.5\ cm^2[/tex]
A bank is offering you an introductory credit card promotion. Your interest for the first year is 8%. But, at the beginning
of the 2nd year your interest rate will go up to 23%. If you have an $1,800 balance on your card throughout both years, what will be the
difference in the monthly interest owed during year 1 and year 2?
O a) $10.80
Ob) $15.66
O c) $22.50
O d) $34.50
Answer:
c) $22.50
Explanation:
1. Calculate the monthly interest owed during year 1
Interest for first year: 8%The monthly rate is the yearly rate divided by 12: 8% / 12 = 0.08/12The monthly interest owed is the monthly rate times the balance: (0.08/12)×$1,800 = $12.002. Calculate the monthly interest owed during year 2
Interest for second year: 23%The montly rate is the yearly rate divided by 12: 23% / 12 = 0.23/12The monthly interest owed is the monthly rate times the balance: (0.23/12)×$1,800 = $34.50
3. Calculate the difference
Difference in the monthly interest owed during year 1 and year 2 = $34.50 - $12.00 = $22.50Hence, the answer is the option c) $22.50
Marcy has $20 she wants to buy a book that is marked down 30% from its original price of $28. If the sales tax is 2.5 does she have enough money
Answer:
no
Step-by-step explanation:
thirty percent of $28 is $8.4, so you would subtract the two leaving you with $19.6
2.5 sales tax of $19.6 is $0.49
Adding those two, the total comes to 20.09 which is just over budget
The amount of the book is more than $20. Then she does not have enough money.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let 'x' be the markdown price. Then the equation is given as,
30% = [(28 - x) / 28] × 100
0.30 = [(28 - x) / 28]
8.4 = 28 - x
x = $19.6
Then the amount of book after tax is given as,
⇒ $19.6 x 1.025
⇒ $20.09
The amount of the book is more than $20. Then she does not have enough money.
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help please I'm stuck once again?
Answer:
The probe's final position is -143m
Step-by-step explanation:
Note that the words 'lowered' and 'below' mean subtract; while the word 'raised' means add. Thus, interpreting the statement to mathematical expression is done below.
[tex] - 90m + 50m - 138m + 35m[/tex]
[tex] = - 143m[/tex]
Therefore, the probe's final position is -143m. Hence, the sensor is 143m below the sea level.
solve 1/8 + 6a/5 = 3/8 + 2a/5 + 7/8
Answer:
no6666//7
Step-by-step explanation:
88../6
* 14 * x=2 * 28 . What x equal ?
Answer:
answer is 4
Step-by-step explanation:
look at picture
Answer:
x = 1
Step-by-step explanation:
14 x 2x = 28
2 x 1 = 2
14 x 2(1) = 28
14 x 2 = 28
What is the slope of the line with the equation 0 = -15x + 6y
Answer:
15/6
Step-by-step explanation:
if ax^2+bc+c=0 is given equation then slope of this equation will be
m=-a/b
tan 116° =
A) tan 64°
B) -tan 64
C) tan 26
D) -tan 26
Answer:
B)
Step-by-step explanation:
All three trigonometric functions are positive in Quadrant I
Sine only is positive in Quadrant II
Tangent only is positive in Quadrant III
Cosine only is positive in Quadrant IV
Now
tan 116° tan 116° means that the angle 116° lies in the second quadrant.
sin is positive while cos and tan are negative in the second quadrant
tan 116° = -tan(180°-116)
= -tan(64°)
The sum of two numbers is a hundred one number is at least 16 more than the other number. What are the numbers? Please help
Answer:
42 and 58
Step-by-step explanation:
Let the two numbers be represented by A And B
A + B = 100
A = B + 16
Substitute B + 16 in place of A in equation 1
We have,
B + 16 + B = 100
It can also be written as
B + B + 16 = 100
2B + 16 = 100
Subtract 16 from both sides
2B + 16 - 16 = 100 - 16
2B = 84
Divide both sides by 2
2B/2 = 84/2
B = 42
Now substitute 42 for B in any of the equations to get A.
Using equation 1
A + B = 100
A + 42 = 100
Subtract 42 from both sides
A + 42 - 42 = 100 - 42
A = 58
Therefore the two numbers are 42 and 58
The measures of two angles in a triangle are 48° and 71°. What is the measure of the third angle?
The sum of the 3 angles needs to be 180.
To find the third angle subtract to the known angles from 180.
180 - 48 - 71 = 61
The third angle is 61 degrees.
Solving for t?
[tex]6t - 2 = 5t[/tex]
[tex]8t + 6 = 7t + 6[/tex]
Answer:
Step-by-step explanation:
6t-2=5t
8t+6=7t+6
A container holds sugar shape of a cylinder that radius of the containers 3 inches in the height of the container is 10.5 inches which measurement is closest to the volume of the container cubic inches
Answer:94.5pie
Step-by-step explanation:
Final answer:
To calculate the volume of a cylindrical sugar container with a radius of 3 inches and a height of 10.5 inches, use the formula V = πr²h, which yields approximately 296.78 cubic inches.
Explanation:
The question asks for the volume of the container that has the shape of a cylinder. The given dimensions are a radius of 3 inches and a height of 10.5 inches. To find the volume of a cylinder, we use the formula:
V = πr²h
Where V is the volume, π (pi) is a constant approximately equal to 3.14159, r is the radius, and h is the height of the cylinder.
We calculate the volume as follows:
V = π × (3 inches)² × 10.5 inches
V = π × 9 in² × 10.5 in
V = π × 94.5 in³
V ≈ 296.78 in³
Thus, the volume of the cylinder is approximately 296.78 cubic inches
m×n, when m=13 and n=12
Answer:
156
Step-by-step explanation:
13 × 12
13
×
12
=
26
130
=
156
Answer:
Step-by-step explanation:
m*n
m=13
n=12
13 * 12
156
bob shot the basketball 32 times and made 23 baskets. What percent of his shots did get in?
Question in the picture, please give the answer and how you got it
Area of the circle is 78.5 sq. units.
Step-by-step explanation:
Circumference of the circle = 31.4 units
2 π r = 31.4 units
2 × 3.14 ×r = 31. 4 units
r = 31.4 / (2×3.14)
= 5 units.
Area of the circle = π r² = 3.14 × 5 × 5 = 78.5 sq. units.
A triangle with no equal sides is called a scalene triangle, right? or no
Answer: Yes a scalene triangle is a triangle with 3 sides that all have different lengths.
Answer:
Correct
Step-by-step explanation:
Scalene means it has no equal side.