The amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.
What is an arithmetic sequence?The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms. Let us recall what is a sequence. A sequence is a collection of numbers that follow a pattern. The general form of an arithmetic sequence is an=a+(n-1)d.
If Takuya's parents gave him $100 as a birthday gift and she spent $20 each month on board games until his money ran out, this means he keeps spending $20 every month and his money keeps reducing by the same amount each month until his money ran out, the following can be inferred;
initial amount = $100
If he spends $20 each month,
Balance at the end of 1st month = $100-$20 = $80
Balance at the end of 2nd month = $80-$20 = $60
Balance at the end of 3rd month = $60-$20 = $40 and so on
Since the amount keeps reducing by the same value i.e $20, then the sequence formed is an arithmetic sequence.
a is the first term of the sequence = 100
d is the common difference = 80-100 = 60-80 = 40-60 = -20
n is the number of terms
Substituting the given values in the formula we have; an=100+(n-1)(-20)
⇒an=100+(-20n+20)
⇒an=100-20n+20
⇒an=120-20n
Therefore, the amount of money that remained from Takuya's presence during month n is expressed as an=120-20n and the sequence is an arithmetic sequence.
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1) Option (A) arithmetic sequence.
2) The recursive formula is f(n) = f(n-1) - 20 with an initial condition of f(1) = 100.
3) The explicit formula is f(n) = 120 - 20n.
Let's address Takuya's birthday gift scenario step by step.
1. Type of Sequence
The sequence described is an arithmetic sequence because the same amount of money, $20, is spent each month, leading to a consistent decrease in the balance.
2. Recursive Formula
Initially, he had $100. So,
f(1) = 100
Given the monthly spending of $20, the recursive formula is: f(n) = f(n-1) - 20
3. Explicit Formula
To find the explicit formula of the arithmetic sequence, we use the initial value and the common difference:
f(n) = 100 - 20(n-1)
Simplifying gives us:
f(n) = 120 - 20n
Thus, the balance remaining after n months can be calculated using this explicit formula.
Complete question:
Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $ 20 dollars out of his present on board games at the end of each month until his money ran out. Let f(n) be the amount of money that remained from Takuya's present during month n, where n=1 represents the month he received his present.
1) f is a sequence. What kind of sequence is it?
Choose 1 answer:
A ) Arithmetic sequence
B) Geometric sequence
2) Complete the recursive formula for f(n).
f(1) = □
f(n) = □
3) Find the explicit formula.
Find the MAD for both citys and then round your answer to the nearest tenth
City A: 3.5, 4, 4, 2, 5.5, 5
City B: 5, 6, 3.5, 4, 5.5, 6
Answer:
A. 4 city b 6
B. City a, 8, when rounded 10
City b, 12, when rounded 10
C. City A. 2, 3.5, 4, 4, 5.5, 5..... so it's 4
City B. 3.5, 4, 5, 5.5, 6, 6..... so it's 5.25
Step-by-step explanation:
Answer:
A: ⅚
B: ⅚
Step-by-step explanation:
City A: 4, 3.5, 5, 5.5, 4, 2
Mean: sum/n
= 24/6 = 4
|x - mean|: 0, 0.5, 1, 1.5, 0 , 2
MAD = sum|x - mean|/n
5/6 = 0.833
City B: 5, 6, 3.5, 5.5, 4, 6
Mean: 30/6 = 5
|x - mean|: 0, 1, 1.5, 0.5, 1, 1
MAD = sum|x - mean|/n
5/6 = 0.833
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 1 < x < 5.
Answer:
180
Step-by-step explanation:
The average rate of change, in simplest form, of the function over the interval 1 < x < 5 is 18.
Find the average rate of change?The average rate of change is the change in the slope of the function, it is given by the formula,
[tex]\text{Average rate of change} = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Given to us
y₂ = f(x₂) = 27
x₂ = 3
y₁ = f(x₁) = 9
x₁ = 2
Substitute the values in the formula,
[tex]\text{Average rate of change} = \dfrac{27-9}{3-2} = 18[/tex]
Hence, the average rate of change, in simplest form, of the function over the interval 1 < x < 5 is 18.
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Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?
6 + 2(x + 4) = 6 plus 2 left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis 3 minus x right-parenthesis.(3 – x)
6 + 2(x + 4) = 6 plus 2 left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
(6 + 2)(x + 4) = left-parenthesis 6 plus 2 right-parenthesis left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis 3 minus x right-parenthesis.(3 – x)
(6 + 2)(x + 4) = left-parenthesis 6 plus 2 right-parenthesis left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
Answer:
A) 6+2 (x+4) = 1/2 (3-x)It's correct on ed2020 :)
Final answer:
The equation that represents the given verbal statement is 6 + 2(x + 4) = ½(3 − x), which translates the words into algebraic expressions and sets them equal as per the statement.
Explanation:
The correct equation to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number" is:
6 + 2(x + 4) = ½(3 − x)
Let's break down the statement and turn it into an equation step by step:
Six added to indicates we start with a six and add something to it.Twice the sum of a number (x) and four is written as 2(x + 4).Finally, is equal to one-half of the difference of three and the number translates to ½(3 − x).Putting it all together, we get the equation above, which correctly represents the given verbal statement.
Solve the system of equations using the substitution method y=2 and 2x+y=8
Answer:
x=3 y=2
Step-by-step explanation:
y=2
2x+y=8
Substitute y=2 into the second equation
2x+2=8
Subtract 2 from each side
2x+2-2=8-2
2x=6
Divide each side by 2
2x/2 =6/2
x=3
x=3 y=2
If the Circumfernce of a circle is 25.1, please find: -The radius -The diameter -The area
Answer:
Radius = 1.997
Diameter = 3.993
Area = 12.549
Find the area of the shape shown below
Answer:
10
Step-by-step explanation:
one of them is 2
one of them is 4
one of them is 4
add them and it equals
Answer:
10
Step-by-step explanation:
formula for triangle 1: 2x2 divided by 2 (the area is 2)
formula for square: 2x2 (area is 4)
formula for triangle 2: 2x4 divided by 2(area is 4)
then you add everything
2+4+4= 10
What is x in the equation please help.
Answer:
6
Step-by-step explanation:
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A circle's circumference is approximately 44 cm.
Complete each statement using one of these values: 7, 11, 14, 22, 88, 138, 154, 196, 380, 616.
The circle's diameter is approximately cm.
The circle's radius is approximately cm.
The circle's area is approximately cm2.
these are all approximate
======================================
Explanation:
C = pi*d is the formula for the circumference. We know that C = 44 approximately, so,
C = pi*d
d = C/pi
d = 44/3.14
d = 14.01 approximately
d = 14 also approximate
take half of this to get the radius
r = d/2 = 14/2 = 7
Then use this radius to find the circle's area
A = pi*r^2
A = 3.14*7^2
A = 153.86
A = 154 rounding to the nearest whole number
Answer:
Circle's radius
[tex]r=7.00\rm cm[/tex]
Circle's diameter
[tex]d=2r=2\times7=14\rm cm[/tex]
Circle's area
[tex]a=\pi \times r^2=3.14\times 7^2=154\rm cm^2[/tex]
Step-by-step explanation:
Given information:
Circle's circumference is = [tex]44\rm cm[/tex]
We know,
Circumference of circle [tex]=2\times\pi\times r[/tex]
On substitution,
[tex]2\times3.14\times r=44\rm cm[/tex]
Circle's radius
[tex]r=7.00\rm cm[/tex]
Circle's diameter
[tex]d=2r=2\times7=14\rm cm[/tex]
Circle's area
[tex]a=\pi \times r^2=3.14\times 7^2=154\rm cm^2[/tex]
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Beth buys a flute for $400 and pays 6% sales tax. What is the total price she pays for the flute?
Answer:
457.95
Step-by-step explanation:
430 + 6.5% (27.95) = 457.95
Hope this helps you!
Answer:
$424
Step-by-step explanation:
Multiply 400 by .06 and get 24
add 24 to 400 and you get 424
A function is shown in the table. Which of the following is a true statement for this function? (5 points) The function is decreasing from x = 0 to x = 1. The function is decreasing from x = −1 to x = 0. The function is increasing from x = 0 to x = 1. The function is increasing from x = −2 to x = −1.
Answer:
Im pretty sure the function is increasing from x = -2 to x = -1
Step-by-step explanation:
True or false a circle could be circumscribed about the quadrilateral below
Answer: a: true
Step-by-step explanation:
Yes, a circle can be circumscribed in quadrilateral.
What is cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.
we know, If opposite angles of a quadrilateral add to 180 then it is called a cyclic quadrilateral and a circle can be inscribed in it.
In this case the opposite angles add upto 180 which shows that is it is a cyclic quadrilateral.
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A TV has a rectangular picture with an area of 6 square feet. The picture has a length of 3 feet. What is the perimeter of
the picture?
9 feet
12 feet
10 feet
11 feet
Answer:
C. 10 ft.
Step-by-step explanation:
Area of 6 sq. ft. which is rectangular. The length is 3 ft and perimeter is l+l+w+w=perimeter. A rectangular shape has 2 sides of the same length and the other two are the same but, a different length the the other two sides.
Equation:
3+3+2+2=10
Select the correct answers.
What was Manifest Destiny?
a. the idea that the United States was meant to stretch from the Atlantic Ocean to the Pacific Ocean
b. the idea that the United States was meant to go to war to control Canada
c. the idea that the United States was meant to become a democracy
d. the idea that the United States was meant to bring an end to slavery in its western territories
Answer:
A- Be sure to check.
Explanation:
I found this online, I hope it helps you!
The Coining of 'Manifest Destiny'
By the time Texas was admitted to the Union as a state in December 1845, the idea that the United States must inevitably expand westward all the way to the Pacific Ocean had taken firm hold among people from different regions, classes and political persuasions.
My Answer: Manifest Destiny is the idea that the US was meant to rule from here to here.
Good Luck!
Write the equation of the circle graphed below
Answer:
[tex](x-1)^2+(y+1)^2=0.25[/tex]
Step-by-step explanation:
From the given graph it is clear that the center of the circle is (1,-1) and the circle passing through the point (0.5,-1).
So, radius of the circle is
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]r=\sqrt{(0.5-1)^2+(-1-(-1))^2}[/tex]
[tex]r=\sqrt{(-0.5)^2}[/tex]
[tex]r=\sqrt{(0.5)^2}[/tex]
[tex]r=0.5[/tex]
The radius of the circle is 0.5 units.
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, (h,k) is center and r is radius.
The center of given circle is (1,-1) and radius is 0.5. So, the equation of circle is
[tex](x-(1))^2+(y-(-1))^2=(0.5)^2[/tex]
[tex](x-1)^2+(y+1)^2=0.25[/tex]
Therefore, the required equation is [tex](x-1)^2+(y+1)^2=0.25[/tex].
which is more 8 tons or 16,002 pounds
Answer:
16,002
Step-by-step explanation:
Answer: none
Step-by-step explanation: because they are equivalent
Select the exclusion that fits best with this problem.
Answer:
[tex]\frac{1}{2y-2y^2}, y\neq 1[/tex]
Step-by-step explanation:
observe by factorization and cancelation
[tex]\frac{y^2+y+1}{-2y(y^3-1)}=\frac{y^2+y+1}{-2y(y-1)(y^2+y+1)}
\\=\frac{1}{-2y(y-1)}
\\=\frac{1}{2y-y^2}[/tex]
Given two circles whose radio are 3” and 2”, the ratio of their areas is....what?
(Will mark as Brainliest)
Answer:
28.27 and 12.60
Step-by-step explanation:
Answer:
28.27 and 12.60
Step-by-step explanation:
pls help if good at math
Using a 16-sided number cube, what is the probability that you will roll a multiple of 4 or an odd prime number? The number 1 isn't an odd prime. Round to three decimals.
A. 0.625
B. 0.250
C. 0.563
D. 0.688
Answer:
C
Step-by-step explanation:
All odd prime numbers up to 16:
3, 5, 7, 11, 13
All multiples of four up to 16:
4, 8, 12, 16
All of those in a list:
3, 4, 5, 7, 8, 11, 12, 13, 16
There are 9 things on that list. The probability is equal to:
[tex]\frac{9}{16}=c) 0.563[/tex]
Please mark brainliest. Have a nice day!
In 2007, a census counted 2815 of a certain animal. This was 315 fewer than the number counted in 2006. What was the population of the animal in 2006?
The population of the animal in 2006 was
(Simplify your answer.)
Answer: 3,130
Step-by-step explanation: 2,815 + 315 = 3,130
The population of the animal in 2006 was 2500.
What is subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Given that, in 2007, a census counted 2815 of a certain animal. This was 315 fewer than the number counted in 2006.
So, the population of the animal in 2006 is
2815-315
= 2500
Therefore, the population of the animal in 2006 was 2500.
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find the value of y
Answer:
y ≈ 4.3 cm
Step-by-step explanation:
Given 2 secants from an external point to the circle.
The the product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
3(3 + y) = 2(2 + 6 + 3) = 2(11) = 22, that is
9 + 3y = 22 ( subtract 9 from both parts )
3y = 13 ( divide both sides by 3 )
y ≈ 4. 3 cm ( to the nearest tenth )
can i please know the asnwer
Answer:
[tex]volume = 10m^3[/tex]
Step-by-step explanation:
This shape is called a rectangular prism. The formula for finding the volume of this prism is: [tex]volume = L * W * H[/tex]
All you do is plug the values into the formula.
The length is 2m
The width is 1m
the height is 5m
Volume = (2m)(1m)(5m)
Volume = [tex]10m^3[/tex]
Calculate Line AC showing working to 1dp
Answer:
18.1 cm
Step-by-step explanation:
Consider a segment parallel to CD and passing through B.
This segment will form a right-angle triangle with A
It's length would be equal to the length of CD (the missing length)
Height of that triangle:
11 - 4 = 7
CD² = 16² - 7²
CD² = 207
CD = sqrt(207)
AC² = AD² + CD²
AC² = 11² + 207
AC² = 328
AC = 2sqrt(82)
Which is roughly 18.1 cm
If the time has a 8 in
it, it has to be
8 o'clock
Answer:
No
Step-by-step explain:
It does not have to be 8 o'clock for the time to have an 8.
Please somone helppppp
Answer:
its an open circle on -2 and the line is to the right
Step-by-step explanation:
-2x=4
x=4/-2=-2
and the sign is the same and its an open dot because its not greater too or equal to
Answer:
the answer is 8
I cant graph it for you sorry
Step-by-step explanation:
-2x>4
*2 *2
x = 8
its side of the length of the rectangle is x 1/3 describe the change in the area justify your answer
Answer:
the area will change by 1/9
Step-by-step explanation:
from linear to area scale factor you have to square the value
Answer:
It would be 1:9 of the old rectangle area to the new rectangle area.
Step-by-step explanation:
because it's area, you would do [tex](1/3)^{2}[/tex]. Which is 1/9 because you do 1*1 and 3*3.
THANK YOU! :D
I HOPE THIS HELPED AND STAY SAFE!
please help :) it’s math
Answer:
Step-by-step explanation:
brand B
Answer:
Brand A
Step-by-step explanation:
Volume of brand A cone is about 251.33
Volume of brand B cone is about 314.16
Find the distance of line segment AB with endpoints A(8 -3) and B(6 1) express your answer in simplest form or as a decimal correctly rounded to the nearest tenth.
(Example:3 times the square root of 2)
Answer:
Step-by-step explanation:
Answer:
The answer would be 4.47 or 4.5.
Step-by-step explanation:
explain if you can please and thank you
Given:
Given that the angles of the kite.
The opposite angles of the kite measures (3y + 14)° and (y + 50)°
We need to determine the value of y.
Value of y:
We know the property that the opposite angles are equal.
Thus, applying the property, we have;
[tex]3y+14=y+50[/tex]
Subtracting both sides of the equation by y, we have;
[tex]2y+14=50[/tex]
Subtracting both sides of the equation by 14, we get;
[tex]2y=36[/tex]
Dividing both sides of the equation by 2, we get;
[tex]y=18[/tex]
Thus, the value of y is 18.
2. Raquiem needs to know if the triangle shown is a right triangle. Which equation could he use to help? A.36+25=49 B.25+36-49 C.25 (to the power of two)+36(to the power of two)=40(to the power of two)
Answer:
C
Step-by-step explanation:
Because it uses the Pythagorean Theorem. (a squared plus b squared equals c squared)
Three runners are jogging from North Augusta to Beech Island. Runner 1 runs 14 miles in 3 hours while .Runner 2 runs 16 miles in 4 hours. Runner 3 runs 15 miles in 6 hours. What is the average speed of each runner?
Answer:
Runner 1,2 and 3 ran at a average speed of 4.67 , 4 and 2.5 miles per hour respectively
Step-by-step explanation:
We can all agree that speed equals distance divided by time and we are asked to find out the average speed of this 3 people.
---Average speed of runner 1
Speed = distance / time
Since he ran 14 miles within 3 hours
S = 14/3
The average speed was 4.67 miles pet hour
---For runner 2,
Speed = distance / time
Since he ran 16 miles in 4 hours,
Average speed = 16/4
= 4 miles per hour
---For runner 3,
Speed = distance / time
Since he ran 15 miles under 6 hours,
Average speed = 15/6
= 2.5 miles per hour