We will investigate the evaluation of recursive sequences.
A iterative sequences are categorized by two values i.e one value preceding and the current value. The current value is evaluated on the basis of the previous value. In other words the current value is a function of preceeding value or depends on it.
All iterative relations of a sequence are expressed mathematically by two values as follows:
[tex]\begin{gathered} f\text{ ( n ): Current nth term value} \\ f\text{ ( n - 1 ): preceeding/ previous value} \end{gathered}[/tex]A iterative relation is a unique mathematical relationship between the current term f ( n ) and the previous value given as follows:
[tex]\textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( n ) = f ( n - 1 ) + 3}}[/tex]For this particular relationship the first term value is given as follows:
[tex]\textcolor{#FF7968}{n}\text{\textcolor{#FF7968}{ = 1, f ( 1 ) = 10}}[/tex]We will now start determining the terms in the sequence by plugging the respective term numbers ( n ) and use the mathematical relationship for the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 2,}} \\ f\text{ ( 2 ) = f ( 1 ) + 3} \\ f\text{ ( 2 ) = 10 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 2 ) = 13}} \end{gathered}[/tex]We have evaluated the 2nd term in the sequence as 13. We will repeat the above steps for all term numbers ( n = 3 , 4 , 5 , 6 ).
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 3,}} \\ f\text{ ( 3 ) = f ( 2 ) + 3} \\ f\text{ ( 3 ) = 13 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 3 ) = 16}} \\ \\ \text{\textcolor{#FF7968}{For n = 4,}} \\ f\text{ ( 4 ) = f ( 3 ) + 3} \\ \text{f ( 4 ) = 16 + 3} \\ \text{\textcolor{#FF7968}{f ( 4 ) = 19 }} \\ \\ \text{\textcolor{#FF7968}{For n = 5,}} \\ f\text{ ( 5 ) = f ( 4 ) + 3} \\ f\text{ ( 5 ) = 19 + 3} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( 5 ) = 22}} \end{gathered}[/tex]And them lastly for the 6th term in the sequence as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 6,}} \\ f\text{ ( 6 ) = f ( 5 ) + 3} \\ f\text{ ( 6 ) = 22 + 3} \\ \text{\textcolor{#FF7968}{f ( 6 ) = 25}} \end{gathered}[/tex]Hence, the answer to the 6th term number is:
[tex]\textcolor{#FF7968}{25}[/tex]
Dm³ + n = rwhat does D equal?
Which symbol correctly compares these fractions? -13\15 and -5\6 a: = b: > c:
Answer:
B
Step-by-step explanation:
None
Emily and Andy each go to a hardware store to buy a wire. the table shows the relationship between the cost and the length of wire. Part A: Emily needs 24 ft of wire. how much will she spend on wire.Part B: Andy needs 13 yards of wire. how much will he spend on wire
Part A
If Emily needs 24 feet of wire, then she has to spend $14.4
Part B
If Andy needs 13 yards of wire, then he has to spend $23.4
From the given graph choose one option
The length of the wire = 120 inches
The cost of 120 inches of wire = $6
Cost of 1 inch of wire = 6/120
= $0.05
Part A
The length of the wire = 24 feet
Convert the feet to inches
24 feet = 288 inches
The cost of 288 inches of wire = 0.05×288
= $14.4
Part B
The length of the wire = 13 yards
Convert the yards to inches
13 yards = 468 inches
The cost of 468 inches of wire = 0.05×468
= $23.4
Hence,
Part A
If Emily needs 24 feet of wire, then she has to spend $14.4
Part B
If Andy needs 13 yards of wire, then he has to spend $23.4
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HELPDetermine the equation of the line shown in the graph:y = −1y = 0x = −1x = 0
in this problem we have a vertical line
The equation of a vertical line is equal to the x-coordinate of the point that passes through it
so
in this case
the equation of the line is
x=-1
. Suppose that in this process, 20% of the available raw sugar is changed to a refined sugar every 5 hrs. If a process begins with 1,000 pounds of raw sugar, write an exponential equation for the amount A of raw sugar (in pounds) t hrs after the process begins.
The exponential equation which represents the amount of raw sugar t hours after the process begins is; A = 1,000 (0.8)^(t/5).
Which equation represents the amount of raw sugar left t hours after the process begins?It follows from the task content that the amount of raw sugar left after the process begins is to be determined according to the information given.
Since, 20% of the available raw sugar is changed to a refined sugar every 5 hrs, it follows that only 80% of the raw sugar is left after each successive time interval period.
Hence, the exponential model of the situation is such that;
A = 1,000(0.8)^(t/5).
Where t = number of hours after the process begins.
Therefore, the required equation is; A = 1,000(0.8)^(t/5).
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A store sells cat food in 4-pound bags. The cat food cost 2 dollars per pound.
Here is the completed table:
Number of bags purchased Total weight Total Cost
1 4 8
2 8 16
3 12 24
4 16 32
5 20 40
What is the total weight and the total cost?One bag of cat food weighs 4 pounds. This means that as the bag increases by 1, the weight of the bag increases by 4.
Weight of 1 bag of cat food = 4
Weight of 2 bags of cat food = 4 x 2 = 8
Weight of 3 bags of cat food = 4 x 3 = 12
Weight of 4 bags of cat food = 4 x 4 = 16
Weight of 5 bags of cat food = 4 x 5 = 20
The cost of cat food is $2 per pound.
Cost of a bag of cat food = number of bags bought x weight of one bag x cost per pound
Cost of 1 bag of cat food = 1 x 4 x 2 = 8
Cost of 2 bags of cat food = 2 x 4 x 2 = 16
Cost of 3 bags of cat food = 3 x 4 x 2 = 24
Cost of 4 bags of cat food = 4 x 4 x 2 = 32
Cost of 5 bags of cat food = 5 x 4 x 2 = 40
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joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles assuming she runs at the same pace how far can she run in 40 minutes? round to the nearest hundredth how far can she run in m minutes
In a case whereby joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles the distance she can she run in 40 minutes is 4.31 miles.
How can the number of miles be calculated?This can be solved by the cross multiplication using the rate that given in the question.
We were told that joeita took 58 minutes of her time to run 6.25 hours miles , then to know the distance she can cover within 40 minutes is
58 minutes = 6.25 miles
40 minutes = X miles
Let X be the number of miles she want to cover in 40 minutes
we ca cross multiply the expression above as :
( 40 minutes * 6.25 miles ) = (58 minutes * X miles)
the X = 4.31 miles
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ERROR ANALYSIS In Exercise 30, describe and correct the error in finding the inverse of the functionf(x)=1/7x^2, x>=0y=1/7x^2x=1/7y^27x=y^2+-√7x=y
Given the function
[tex]\begin{gathered} f(x)=\frac{1}{7}x^2 \\ x\ge0 \end{gathered}[/tex]To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.
We are already given the domain of f, all the real numbers equal or greater than zero.
The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.
Once we find the inverse function, we'll use this concept.
Step 1: Substitute f(x) for y:
[tex]y=\frac{1}{7}x^2[/tex]Step 2: Swap the variables:
[tex]x=\frac{1}{7}y^2[/tex]Step 3: Solve for y:
[tex]y=\pm\sqrt[]{7x}[/tex]But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:
[tex]f^{-1}(x)=\sqrt[]{7x}[/tex]help me please......
There is the required value would be 6 in the box.
What is the Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
If you are in the partition XY in the ratio 3 to 4 from point X to point Y
To determine multiply the length of XY.
XY = 14 units then 3/7 of 14
= 3/7 × 14
Apply the multiplication operation,
= 42/7
Apply the division operation,
= 6
Hence, the required value would be 6 in the box.
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In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $49 and standard deviation of $2. Find the margin of error at a 80% confidence level.
Give your answer to two decimal places
Given the data that we have here where the number of people in the survey is 10, s = 2 and mean = 49, the margin of error is given as 0.76
How to solve for the margin of errorThe margin of error can be used to provide the data that has to do with the amount of sampling error that would be in a given data statistic.
We would have to calculate the amount of error using the data that we have below.
We have the following values
number n = 10
mean u = 49
standard deviation sd = 2
The level of confidence c i = 80% = 0.80
we have to find the critical value
degree of freedom = 1 - 0.80
= 0.20
zα/2
= 0.20 / 2 = 0.10
= 1.383
The margin of error
= zα / 2 * s / √n
= 1.383 * 2/√10
= 1.383 x 2 / 3.623
= 1.383 x 0.552028
= 0.7634
The calculated margin of error is given as 0.7634
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A simple random sample of 5 months of sales data provided the following information:
Month: 1 2 3 4 5
Units Sold: 97 110 89 97 92
a. Develop a point estimate of the population mean number of units sold per month.
b. Develop a point estimate of the population standard deviation (to decimals).
Using it's concepts, the point estimates for the population are given as follows:
a) Mean: 97 units sold per month.
b) Standard deviation: 16.06 units sold per month.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of observations in the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality(number of observations) of the data-set.In the context of this problem, the 5 observations are given as follows:
97, 110, 89, 97, 92.
Hence the mean is given by:
M = (97 + 110 + 89 + 97 + 92)/5 = 97.
Considering the mean of 97 found above, the standard deviation is given as follows:
[tex]S(X) = \sqrt{\frac{(97 - 97)^2 + (110 - 97)^2 + (89 - 97)^2 + (97 - 97)^2 + (92 - 97)^2}{5}} = 16.06[/tex]
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Complete the instructions to move from one point to another along the line
y = 2/3x + 1
___ ___ unit(s), then right 9 units.
Answer:
Step-by-step explanation:
the equation is written in slope intercept form
y= mx + b with m= slope and b= y-intercept
so in your equation
y=2/3x + 1,
the slope is 2/3 and the y-intercept is (0,1)
slope is also known as rise/run
so to move from one point to another, starting at (0,1) (since you know that point is on the line) you would move up 2 units and to the left 3 units.
hope this helped!
What is the value of x?
4x=5x-12
Enter your answer in the box.
X=
Answer:
12
Step-by-step explanation:
First, get all of the x values to one side of the equation so that we can solve for x. One way to do this is subtract 5x from both sides.
Now we have this:
4x - 5x = -12.
Simplify:
-x = -12.
We need positive x, so divide both sides by -1.
x = 12.
Hope this helps! :)
The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?A)21B)24C)20D)19
SOLUTION:
Step 1:
In this question, we are given the following:
The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?
Step 2:
The details of the solution are as follows:
Since side DE = 45, side HI = 36, and side DF = 30.
Then, the length of side HJ =
[tex]\begin{gathered} Using\text{ Similar triangles, we have that:} \\ \frac{DF}{DE}=\frac{HJ}{HI} \\ Then,\text{ we have that:} \\ \frac{30}{45}=\frac{HJ}{36} \\ cross-multiply,\text{ we have that:} \\ 30\text{ x 36 = 45 x HJ} \\ Divide\text{ both sides by 45, we have that:} \end{gathered}[/tex][tex]HJ=\frac{30\text{ x 36}}{45}[/tex][tex]HJ\text{ = }\frac{1080}{45}[/tex][tex]HJ\text{ = 24 \lparen OPTION B \rparen}[/tex]The two triangles in the figure below are similar triangles. Solve for x.128846O 810O not enough information
Solution
step 1
Explain similarity
Both triangles are similar therefore the ratio of their corresponding sides must be equal.
Step2
State the corresponding sides
[tex]\frac{12}{x}=\frac{8}{4}[/tex]Step 3
Find x
[tex]\begin{gathered} 8x\text{ = 12}\times4 \\ x\text{ =}\frac{48}{8} \\ x=6 \end{gathered}[/tex]Hence option A
Using standard normal table if the area is 0.125 what would the probability be ?
The area under a standard normal distribution, which we get on a standard normal table, is the same as the probability on that area.
Thus if the area is 0.125, the probability is 0.125, that is, 12.5%.
Gerard compares the offers at two different banks to decide where he should open a savings account. A. Draw a representation to show how much would be in the first savings account if Gerard's initial deposit were d dollars.
Explanations:
Given the following parameters
An initial deposit of Gerard is "d" dollars
For the savings with 5% interest, the interest on "d" dollars will be expressed as;
[tex]\begin{gathered} \text{Interest = 5\% of d} \\ \text{Interest = 0.05d} \end{gathered}[/tex]Get the total savings plus interest in the first account
[tex]\begin{gathered} \text{Balance}=\text{Initial deposit + Interest} \\ \text{Balance=d+0.05d} \\ \text{Balance=1.05d} \end{gathered}[/tex]Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars
For the other account:
Initial deposit = "d" dollars
Interest = $100
Since the interest will be added to the first deposit, hence;
[tex]\text{Balance=(d+100)dollars}[/tex]In Tabulated form:
Can you please help me out with a question
Answer:
P = 80 units
Explanation:
Let's label some points in the triangle as:
Since the sides of the triangles are tangent to the circumference, we can write the following relationships:
XC = YC
AZ = AY
BX = ZB
So, the length of the missing side XC is equal to:
XC = YC = 14
On the other hand, the length of AB is the sum of the length of AZ and ZB, so we can calculate ZB as:
AB = AZ + ZB
26 = AY + ZB
26 = 18 + ZB
26 - 18 = ZB
8 = ZB
Because AZ and AY have the same length.
Finally, the measure of BX is equal to:
BX = ZB
BX = 8
Therefore, the perimeter of the triangle is:
Perimeter = AY + YC + AZ + ZB + BX + XC
Perimeter = 18 + 14 + 18 + 8 + 8 + 14
Perimeter = 80
So, the answer is 80 units.
Sebastian bought cookies from his sister's scout troop. He bought 4 boxes of shortbread cookies and 3 boxes of peanut butter cookies. There are 20 shortbread cookies in each box but only 18 peanut butter cookies in each box. How many cookies did Sebastian buy in all?
Sebastian buy 134 cookies.
Given,
He bought 4 boxes of shortbread cookies
and, 3 boxes of peanut butter cookies.
There are 20 shortbread cookies in each box.
but only 18 peanut butter cookies in each box.
To find the how many cookies did Sebastian buy in all?
Now, According to the question:
Formulate the above conditions:
18 x 3 + 20 x 4
Calculate the product or quotient
54 + 20 x 4
54 + 80
= 134
Hence, Sebastian buy 134 cookies.
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A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.
Answer:
75?
Step-by-step explanation:
Answer:
75
Step-by-step explanation:
3 divided by 5
0.6x125
An architect designs a house that is 10 m wide. The rafters holding up the roof are equal length and meet at an angle of 65°. The rafters extend 0.4 m beyond the supporting wall. How long are the rafters?
The length of the rafter when the architect design a house is 12.778m.
How to calculate the length?The information illustrates that the architect designs a house that is 10 m wide and that the rafters holding up the roof are equal length and meet at an angle of 65°.
The rafters extend 0.4 m beyond the supporting wall. Then, the length will be:
cos65° = BC / AC
cos 65° = (5 + 0.4)/x
cos 65° = 5.4/x
x = 5.4 / 0.4226
x = 12.778m
The length is 12.778m
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usBelow, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female3463TotalIf a student is selected at random, find theprobability the student is a female given that it'sa junior. Round to the nearest whole percent.[?]%
Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30
The probability that a student is female given that it is a junior is computed as follows:
[tex]\text{ P(}female|junior\text{)=}\frac{P(female\cap junior)}{P(junior)}[/tex]The probability that a student is female and junior is:
[tex]P(female\cap junior)=\frac{6}{30}=\frac{1}{5}[/tex]The probability that a student is a junior is:
[tex]P(junior)=\frac{2+6}{30}=\frac{8}{30}=\frac{4}{15}[/tex]Finally, The probability that a student is female given that it is a junior is:
[tex]P(female|junior)=\frac{\frac{1}{5}}{\frac{4}{15}}=\frac{1}{5}\cdot\frac{15}{4}=\frac{3}{4}=0.75\text{ or 75\%}[/tex]624 students in a class took an algebra test.If 18 students passed the test, what percent passed?Answer:
The answer is 75%
the sequence has 100 term and the listing of number were as follow x, 7, 11, 15.......... 399 find the value of x
Answer:
x = 3
Step-by-step explanation:
Given the sequence x, 7, 11, 15, ... 399, where 399 is the 100th term, you want to know the first term, x.
Arithmetic sequenceThe differences of the first few terms are ...
11 -7 = 4
15 -11 = 4
This suggests an arithmetic sequence with a common difference of 4.
The first term, x, will be 4 less than the second term:
x +4 = 7
x = 7 -4 = 3
The value of x is 3.
__
Check
The n-th term of an arithmetic sequence with first term a1 = 3 and common difference d = 4 is ...
an = a1 +d(n -1)
an = 3 +4(n -1) = 4n -1
Then the 100th term is ...
a100 = 4(100) -1 = 399 . . . . consistent with the given information
An architect is designing a gazebo which base is a regular dodecagon. At what angle should he cut to frame the base?
Answer:
15
Explanation:
Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.
So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;
[tex]\begin{gathered} \frac{360^{\circ}}{12}=30^{\circ}\text{ (degre}e\text{ per corner)} \\ \frac{30^{\circ}}{2}=15^{\circ\text{ }}(angle\text{ to be cut)} \end{gathered}[/tex]The angle that the architect should cut to frame the base is 15 degrees
Fill in the blank to make the two fractions equivalent. 4 = $ U A 30 ?
Given:
[tex]\frac{x}{30}=\frac{4}{5}[/tex]To find: The value of x (box)
Explanation:
Multiplying 30 on both sides. We get,
[tex]\frac{x}{30}\times30=\frac{4}{5}\times30[/tex]Solving we get,
[tex]\begin{gathered} x=4\times6 \\ x=24 \end{gathered}[/tex]Thus, the value of x is 24.
Final answer: The missing value is 24.
y= 3x - 5 y= -6x + 4
The given system of equation:
y = 3x - 5 (1)
y = -6x + 4 (2)
We can solve the system of equation by using elimination method :
Elimination Method: In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
Subtract the equation (1) & (2)
[tex]\begin{gathered} y-y=3x-5-(-6x+4) \\ 0=3x-5+6x-4 \\ 0=9x-9 \\ 9x=9 \\ x=\frac{9}{9} \\ x=1 \end{gathered}[/tex]So, we get x = 1
Substitute the value of x in the equation (1)
[tex]\begin{gathered} y=3x-5 \\ y=3(1)-5 \\ y=3-5 \\ y=(-2) \end{gathered}[/tex]y = (-2)
So, the solution of the system of equations are : (x,y) = (1,-2)
Answer: (x,y) = (1,-2)
Write and solve an equation. Do not forget to label your variable or your units
Mr. Thompson weighs 260 pounds and he loses 4 pounds each month.
The equation will be :
w = 260 - 4m
where w is the weight after m months
when w = 220 pounds, the number of months will be :
220 = 260 - 4m
4m = 260 - 220
4m = 40
m = 40/4
m = 10
The answer is 10 months
Please help I am so bad at geometry
The cafeteria prepares 80 meals a day for students if 3/8 of the meals are vegetarian, how many meals are are not vegetarian?
Meal prepared a day = 80 meals
Vegetarian meals will be
[tex]\text{vegetarian}=\frac{3}{8}\times80=\frac{240}{8}=30[/tex]Non vegetarian meals = 80 - 30 = 50 meals