Answer:
The sequence's fifth term is equal to 7.5.
Step-by-step explanation:
It is given in the question that A sequence is defined recursively using the formula f(n+1)=-0.5f(n) and we need to calculate f(5) if the first term of the sequence is 120.
Firstly,
The definition of a series is given by the formula f (n + 1) = -0.5 f. (n).
Now, what will be f(5) if the sequence's initial term is 120, let's calculate;
Recursively, a series is defined as follows;
=> f(n) = 120 if n = 1, otherwise.
Otherwise,
=> f(n) =-0.5f(n-1) if n > 1.
Now,
=> f(1) = 120
=> f(2) = -0.5f(1) = -0.5(120) = -60
=> f(3) = -0.5f(2) = -0.5(-60) = 30
=> f(4) = -0.5f(3) = -0.5(30) = -15
=> f(5) = -0.5f(4) = -0.5(-15) = 7.5
So, For n > 1, f(n) = (-0.5)(n-1) × 120
Therefore, the sequence's fifth term is equal to 7.5.
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help me pleaseeeeeeeeeeeeeeeeeeeeeee
Use the picture to answer the following question.
Which of the following statements BEST proves that lines k and m are parallel?
A. Angle 2 is congruent to angle 6 because corresponding angles are congruent if two parallel lines are cut by a transversal.
B. Angle 3 is congruent to angle 4 because supplementary angles are congruent if two parallel lines are cut by a transversal.
C. Angle 1 is congruent to angle 6 because alternate exterior angles are congruent if two parallel lines are cut by a transversal.
D. Angle 4 is congruent to angle 5 because alternate interior angles are congruent if two parallel lines are cut by a transversal.
The statement which best proves that lines k and m are parallel is: C. Angle 1 is congruent to angle 6 because alternate exterior angles are congruent if two parallel lines are cut by a transversal.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure.
In this context, we can reasonably infer and logically deduce that the statement which best proves that lines k and m are parallel is angle 1 is congruent to angle 6 because by definition all alternate exterior angles are congruent, if two parallel lines are cut by a transversal.
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Jaydan uses 3/4 water and 1/5 lime juice and reese uses 2/3 water and 1/6 lime juice which one is weaker
Answer:
1/6 lime juice
Step-by-step explanation:
1/6 is less than 1/5,3/4,and 2/3
How to multiply 2*3*5*7 (I need explanation)
Answer:
Look the answer is simple...just multiply one by one
Step-by-step explanation:
For example;
2*3*5*7
2x3=6
6x5=30
30x7=210
please help meee. ..
Answer:
4
Step-by-step explanation:
How to Round each decimal to the nearest whole number. 6.7
Answer:
6.7 ≈ 7
Step-by-step explanation:
Rounding rule x is supposed to be the decimal for this example
[tex]\mathrm{.x < 0.5}[/tex] round down[tex]\mathrm{.x = 0.5}[/tex] round up(or keep the same)[tex]\mathrm{.x > 0.5}[/tex] round upI hope that example helps you understand. If you have any concerns, ask me, but otherwise, have a great day!
what is the best answer that can add 500divdied by 1010 but also as a fraction
Write the equation of the line in slope-intercept form for each question below.
7. slope = 3, y-intercept = 2
holow
Answer:
General linear equation;
[tex]{ \tt{y = mx + c}} \\ [/tex]
Where m is the gradientWhere c is the y-intercept[tex]{ \boxed{ \tt{y = 3x + 2}}}[/tex]
Math on the Spot Suppose there are 3 groups of
4 trumpet players. In front of the trumpet players are
9 saxophone players. How many students play the
trumpet or saxophone?
The number of students who play the trumpet or saxophone will be 21 students.
How to illustrate the information?From the information, there are 3 groups of
4 trumpet players. In front of the trumpet players are 9 saxophone players.
Therefore, the number of students who play the trumpet or saxophone will be the addition of both values given. This will be:
= (3 × 4) + 9
= 12 + 9
= 21
Consequently, there will be 21 students who play the trumpet or saxophone.
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In how many ways can the digits in the number 7,444,000 be arranged?
The digits of 7,444,000 can be only be arranged in 140 ways
What are combinations?Combinations are used to determine the number of selections of an item within another
How to determine the number of arrangement?The arrangements of the digits is an illustration of factorials
The number is given as: 7,444,000
From the given number, we have the following parameters:
Total (n) = 7 i.e. number of digits
n(4) = 3 i.e. number of digit-4
n(0) = 3 i.e. number of digit-0
So, the number (N) of arrangements is:
N = n!/(n(4)! * n(0)!)
Substitute known values in the above equation
So, we have
N = 7!/(3! * 3!)
Evaluate the factorials in the above equation
So, we have
N = 5040/(6 * 6)
Evaluate the quotients in the above equation
N = 140
Hence, the digits of 7,444,000 can be arranged in 140 ways
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Area of a Field A rectangular field is 364 yards in length and 433 yards in width. Find the area of the field in ACRES (1 acre = 43,560 square feet). Round to the nearest tenth of an acre
The area of the yard is 32.56 acres.
What is the area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given,
the length of the field = 364 yards
width of the field = 433 yard
area of the field = length × breadth
area = 157612 sq. yards
1 sq. yard = 0.000207 acres
area in acres = 32.56 acres
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= 1
2
3
= 4
= 5
4
A line passes through point (-9, -6) and has a slope of 4/3
Write an equation in Ax+By=C form for this line.
Use integers for A, B, and C.
Answer:
4x-3y=-18.
Step-by-step explanation:
1) common form of slope-interception form: y=slope*x+interception;
2) if according to the condition slope=4/3, thenthe slope-interception form is y=4/3*x+interception;
3) it is possible to calculate the interception if to substitute given coordinates (-9;-6) into the slope-interception form:
-6=4/3*(-9)+interception; ⇒ interception=6, then
4) the slope-interception form is y=4/3*x+6;
5) finally, 3y=4x+18, ⇔ 4x-3y= -18 (A=4, B=-3, C=-18).
A woman can bicycle 21 miles in the same time as it takes her to walk 5 miles. She can ride 8 mph faster than she can walk. How fast can she walk?
She can walk __________________ mph
Answer:4
Step-by-step explanation:
im pretty sure its right
A sky diver descended 132 meters in 12 seconds. How far did he fall in one second? how many meters?
Answer:
he fell 11 meters
Step-by-step explanation:
132 divided by 12 is 11.
Cuántos kilogramos pesan 11 metros de alambre, si 154 metros de alambre del mismo grueso pesan 7 kilogramos?
Answer:
0,5 Kg
Step-by-step explanation:
Whats the unit value of the 6 in 261
The unit value of 6 in the number 261 is: tens.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.In this scenario, the unit value of each digit in the number 261 are as follows:
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Convert 8.67 into fraction
8.67 as a mixed fraction is
8 and 67/100
you could also say 867/100
Solve the equation. If the equation is an identity, choose identity. If it has no solution, choose no solution.
4y + 2 =-1/3
(8-12y)
[tex]\displaystyle\\Answer: y=-\frac{7}{12}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\4y+2=-\frac{1}{3}\\\\[/tex]
Multiply both parts of the equation by 3:
[tex]\displaystyle\\(3)(4y+2)=(-\frac{1}{3} )(3)\\12y+6=-1\\12y+6-6=-1-6\\12y=-7[/tex]
Divide both parts of the equation by 12:
[tex]\displaystyle\\y=-\frac{7}{12}[/tex]
The annual interest on a $9000 investment exceeds the interest earned on a $6000 investment by $135. The $9000 is invested at a 0.5% higher rate of interest than the $6000. What is the interest rate of each investment?
The interest rate of $9000 and $6000 investment are 3.5% and 3% respectively.
let's assume the interest rates X and Y on $9,000 and $6,000 investments.
The $9000 is invested at an interest rate that is 0.5% higher than the $6000.
Therefore,
9000(X) = 6000(Y) + 135
X = Y + 0.005
In canonical form:
9000X - 6000Y = 135
X - Y = 0.005
or X = 0.005 + Y
Then,
9000( 0.005 + Y) - 6000Y = 135
Then Y = 0.3 , therefore X = 0.3
So, X = 3.5% (the rate on $9,000 investment) and;
Y = 3% (the rate on $6,000 investment).
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R 2x+21 Q 12 x + 24 P
The value of function R+Q is 14x+45.
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.
Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
An output variable and one or more input variables are the minimum number of variables in a function. An equation can have any number of variables and declares that two expressions are equal (none, one, or more).
Disclaimer:
If the value of R = 2x+21, Q= 12 x + 24, P =2x-9, then find the value of R+Q ,where R and Q are functions.
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Xochitl is buying tacos and sodas for her friends. Each taco, t, costs $1.50 and each soda, s,
costs $2.00. Xochitl spends $39.00 total. Write an equations that models the situation.
The equations that model the situation is 1.50t + 2s = $39
What is the equation that models the situation?The total amount spent is the sum of the total cost of the tacos and the total cost of soda. The total cost of tacos is the product of the cost of one taco and the number of tacos bought. The total cost of sodas is the product of the cost of one soda and the number of sodas bought.
The mathematical operations that would be used is multiplication and addition. Addition is the process of determining the sum of two or more numbers. The sign used to represent addition is +.
Multiplication is the process of determining the product of two or more numbers. The sign used to represent multiplication is x.
Total amount Xochitl spends = total cost of tacos + total cost of sodas
Total amount Xochitl spends = (1.50 x t) + (2 x s)
39 = 1.50t + 2s
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Amy, bill and cara each played a game. amy's score was ten times bill's score. cara's score was half of amy's score. write down the ration of amy's score to bill's score to cara's score. give your answer in its simplest form
Answer:
2:1:1
Step-by-step explanation:
A:B:C
10:1:5
÷5. ÷5
=2:1:1
help me help me pleasee
Answer:
g = -11
Step-by-step explanation:
The question is giving you the answer of (x)
1) Plug in -2, into x so it will look like this:
g(-2) = 4x^3 -x^2 +2x -2
2) Plug the -2 into the x, it will look like this:
g(-2) = -4(-2)^3 - (-2)^2 +2(-2) -2
3) Solve!
g(-2) = 8^3 - 4 - 4 -2
g(-2) = 32 - 4 - 4 - 2
g(-2) = 32
-2g/-2 = 22/-2
g = -11
I hope this helped! If you need more help with understanding, let me know! :)
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continues.
2,
an
22 2
-
3'9' 27' 81
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Assume the first term is a₁.
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The general term for the sequences 2, 2/3, 2/9, 2/27, and 2/81 .. is Tₙ = 2/3ⁿ⁻¹.
Given sequence is 2, 2/3, 2/9, 2/27, 2/81 .....
Geometric Progression is also known as a geometric sequence in which each term after the first term is obtained by multiplying the previous one by a constant, non-zero number called the common ratio.
We know that a given sequence is a Geometric progression. So we need to find the common ratio
Here the first term is a = 2
common ratio r = 2/3/2 = 1/3
Now the formula for a geometric sequence for n terms is
Tₙ = a * rⁿ⁻¹
Tₙ = 2 * (1/3)ⁿ⁻¹
Tₙ = 2/3ⁿ⁻¹
Therefore the general term for the sequences 2, 2/3, 2/9, 2/27, and 2/81 .. is Tₙ = 2/3ⁿ⁻¹.
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5. A rugby team scores the following number of points in 12 matches: 21, 18, 3, 12, 15, 21, 42, 24, 31, 3, 12, 21 a) The mean score: b) The mode: c) The range:
PLEASEE HELPP ME
The mean score is 18.5833 , Mode is 21 and Range is 39 of the given scores.
Mean is the average value of all the given numbers
To calculate the mean we have to add all the values and divide the sum by the numbers of values.
Total of all value = 21+18+3+12+15+21+42+24+31+3+12+21 = 223
No of values = 12
Mean = [tex]\frac{223}{12} =18.58333[/tex]
Mode is the value which comes frequently in data set
In the given data 21 is come three times which is most frequently so Mode is 21.
Range is the difference between the largest number and the smallest number of the given data set.
Largest number of the data set is 42 and smallest number is 3 so the range is 42-3 = 39.
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The distance from Earth to the Sun is approximately 9 x 10^7 miles. The distance from Earth to the moon is approximately 2 x 10^5 miles. Approximately how many times the distance from the Earth to the Moon is the distance from Earth to the Sun?
A:18
b:45
C:222
D:450
its 8th grade math
Answer:
D
Step-by-step explanation:
[tex]\frac{9x10^{7} }{2x10^{5} }[/tex] = 9/2 is 4.5 The quotient property principle tells us that when the bases are the same and we are dividing powers, we subtract the exponents. 7-5 = 2
4.5 x [tex]10^{2}[/tex] In standard notation, this is 450
Write the fraction below as a sum or difference.
7-9x/3
Answer:The answer is -2 over 3
Step-by-step explanation:
Is 4.635 larger than 4.6135
Answer:
Yes.
Step-by-step explanation:
4.635 is larger that 4.6135.
two streets are parallel in a map, chestnut street and walnut street. the map is put on a coordinate plane and the equation for chestnut is y=2x-6. walnut street goes through the coordinates (1,3) on the map. write an equation for the line for walnut street
An equation for the line for walnut street is: y = 2x + 1.
What is defined as the slope intercept form?An intercept is a y-axis point whereby the slope of a line passes. It is the y-coordinate of a point on the y-axis where a straight line or a curve intersects.The slope intercept form for line is given by;
y = mx + c
where
m = slope
c = y-intercept
As, the two streets chestnut street and walnut street are parallel in a map, their slopes are also equal.
The equation of chestnut is y = 2x-6; comparing with general form;
m = 2.
The coordinates of walnut street is (1, 3) = (x₁, y₁)
Thus, equation is;
(y - y₁) = m(x - x₁)
Put the values.
(y - 3) = 2( x - 1)
simplify,
y - 3 = 2x - 1
y = 2x + 1
Thus, the equation for the walnut street is found as; y = 2x + 1.
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Using the image below, find the x value for the point that divides the line segment AB into a ratio of 2:3.
A. -1
B. -0.4
C. 0
D. 0.5
Answer:
The value of x for the point that divides the line segment AB into a ratio of 2:3 is (B) -0.4
Step-by-step explanation:
It is given that we need to find the x value for the point that divides the line segment AB into a ratio of 2:3 from the option given in the question.
Now, let us find the difference between the values of x of point A and of point B;
=> 5 - (-4)
=> 5 + 4
=> 9
Now, let us divide 9 by 5 so that we get the ratio 2:3;
=> 9/5
=> 1.8
Further, for getting the segments as 2 + 3;
=> 1.8 × 2
=> 3.6
and
=> -4 + 3.6
=> -0.4
Therefore, the value of x for the point that divides the line segment AB into a ratio of 2:3 is (B) -0.4
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