The first five terms of a complex sequence are 4, 7, 10, 16, and 28.
Let's consider a non-trivial sequence.
Let's say the first term of our sequence, a1, is 4.
From then on, the sequence increases by 3 times the previous term, but instead of simply multiplying by 3, we will multiply by 3 raised to the power of one less than the term's position in the sequence. However, we are given that the general expression for the nth term is 4 + 3 x 2(n-2), except for the first term which remains 4.
This gives us a starting point for both our formulas.
To find the first five terms of this sequence, we can manually calculate them using the explicit formula given:
a1 = 4 (by definition)a2 = 4 + 3 x 2(2-2) = 4 + 3 x 1 = 7a3 = 4 + 3 x 2(3-2) = 4 + 3 x 2 = 10a4 = 4 + 3 x 2(4-2) = 4 + 3 x 4 = 16a5 = 4 + 3 x2(5-2) = 4 + 3 x 8 = 28Therefore, the first five terms are 4, 7, 10, 16, and 28.
Explicit Formula:
The explicit formula for any term an in the sequence is:
an = 4 + 3 x 2(n-2) for n > 1, with a1 = 4.
Recursive Formula:
The recursive formula builds each term based on the preceding term. For n > 1, the recursive formula is an = an-1 + 3 imes 2(n-2), with a1 still equal to 4.
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Factor the quadratic equations W^2-W-12
Jacqueline's piggy bank contains $6.20 in dimes and quarters. There are 32 coins in all. How many of each kind are there?
In the two triangles below, all angles equal 60 degrees and ab = ef. are the two triangles congruent?
Which answer represents the series in sigma notation?
[tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.
What is sigma notation?The symbol Σ (sigma) is generally used to denote a sum of multiple terms. This symbol is generally accompanied by an index that varies to encompass all terms that must be considered in the sum.
Given is a series (-7 + (-2) + 3 + 8 + 13), we need to define it in sigma notation,
Therefore,
For j = 1 up to j = 5
j = 1
(5j - 12) = (5(1) - 12) = 5 - 12 = - 7
j = 2
(5j - 12) = (5(2) - 12) = 10 - 12 = - 2
j = 3
(5j - 12) = (5(3) - 12) = 15 - 12 = 3
j = 4
(5j - 12) = (5(4) - 12) = 20 - 12 = 8
j = 5
(5j - 12) = (5(5) - 12) = 25 - 12 = 13
This gives us the given series,
(-7 + (-2) + 3 + 8 + 13)
Hence, [tex]\sum^5_{j=1} (5j-12)[/tex] represents the series in sigma notation.
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Write and solve an equation to find the value of each variable
can someone answer this?
What is the total number of rectangles and triangles used for the net of this solid?
a. 3
b. 4
c. 5
d. 6
The total number of rectangles and triangles used for the net of this solid is 4.
Explanation:To find the total number of rectangles and triangles used for the net of a solid, we need to examine the shape of the solid. If the given solid has 4 faces, like a regular tetrahedron or a pyramid, then it will have 3 triangles and 1 rectangle. Hence, the total number of rectangles and triangles used for the net of this solid is 4, so the answer is option b.
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Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition?
A. 2 + x + 3y
B. (2 + x) + 3y
C. 2x + (3 + y)
D. x + (2 + 3y)
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 5 7.5 15 7.5 11 13.8 6.4
HS 16 0 9.5 14.5 5 13 . 10.7 5.3
Which of the choices below best describes how to measure the spread of this data? (Hint: Use the minimum and maximum values to check for outliers.) (2 points) A:Both spreads are best described with the IQR.
B:Both spreads are best described with the standard deviation.
C:The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D:The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answer:
Option A is correct
Step-by-step explanation:
Given is a table which shows data from a survey about the amount of time students spend doing homework each week.
College HS
High 50 16
Low 5 0
Q1 7.5 9.5
Q3 15 14.5
IQR 7.5 5
Median 11 13
Mean 13.8 10.7
Std dev 6.4 5.3
1.5IQR 11.25 7.5
Q1-1.5IQR -9.38 -12
Q3+1.5IQR 37.5 29.5
WE find that there is only one outlier in college with 50 as high.
Except that all others are well within IQR range. Hence outliers are minimum
So option A is right.
Final answer:
To determine the spread of data on student homework hours, IQR and standard deviation are used. The college data's spread is best described by IQR, while the high school data's spread is best described by standard deviation, making Option C the most suitable choice.
Explanation:
To measure the spread of the data for the amount of time students spend doing homework each week, we have two primary measures: the Interquartile Range (IQR) and the standard deviation (σ). IQR represents the difference between the third quartile (Q3) and the first quartile (Q1) and describes the spread of the middle 50% of the data. The standard deviation indicates how much the values in the dataset deviate from the mean, which can help in understanding the overall spread including potential outliers.
When dealing with outliers, it's important to consider that potential outliers are typically identified as values that are more than 1.5 × IQR above Q3 or below Q1. We would use the minimum (Low) and maximum (High) values provided alongside the IQR to check for outliers. For the college data, with a High of 50 and a Low of 5, the range is 45. For high school, the range is 16. Outliers could potentially affect the standard deviation significantly, making IQR a better measure for the middle spread of data.
Based on this, the college data with a wider range may be more affected by outliers, whereas the high school data with a smaller range may not. Therefore, the spread for the college data can be better described by the IQR, while the standard deviation can be a good measure for the high school data. This suggests that Option C: "The college spread is best described by the IQR. The high school spread is best described by the standard deviation." is the most suitable choice.
The expression below is the factorization of what trinomial?
(2x + 7)(4x - 3)
A. 8x2 + 22x + 4
B. 8x2 + 28x - 21
C. 8x2 + 28x + 4
D. 8x2 + 22x - 21
The three angle bisectors of ΔABC meet at P. Drag the vertices around to form different triangles, and then make a conjecture. Which segments appear to be equal in length? Check all that apply. XP = YP for an acute triangle XP = ZP for an acute triangle YP = ZP for an obtuse triangle ZP = XP for a right triangle XP = YP for an obtuse triangle
find the inverse of y=x2-10x
y = x^2 - 10x + 25 - 25
y = (x-5)^2 - 25
y+25 = (x-5)^2
x-5 = +/-sqrt(y+25)
And you get TWO inverses:
x = 5 + sqrt(y+25), for x>=5
x = 5 - sqrt(y+25), for x<=5
Answer:
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Step-by-step explanation:
We are asked to find the inverse for the function [tex]y=x^2-10x[/tex].
We know that to find inverse, we interchange x and y values and then solve for y.
After interchanging x and y values, we will get:
[tex]x=y^2-10y[/tex]
Switch sides:
[tex]y^2-10y=x[/tex]
[tex]y^2-10y-x=x-x[/tex]
[tex]y^2-10y-x=0[/tex]
Now, we will use quadratic formula to solve for y.
[tex]y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}[/tex]
[tex]y=\frac{10\pm \sqrt{100+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4*25+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4(25+x)}}{2}[/tex]
[tex]y=\frac{10\pm 2\sqrt{(25+x)}}{2}[/tex]
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Therefore, the inverse function for our given function would be [tex]y=5\pm \sqrt{(25+x)}[/tex].
Consider the polynomial: x/4– 2x^5 + x^3/2 + 1 Which polynomial represents the standard form of the original polynomial?
a.x^3/2 – 2x^5 + x/4 + 1
b.–2x^5 + x^3/2 + x/4 + 1
c. –2x^5 + x/4 + x^3/2 + 1
d. 1 – 2x^5 + x^3/2 + x/4
Answer:
b. –2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
In the given expression, the degrees of the terms, in the order given, are ...
1, 5, 3, 0
When the terms are properly arranged in standard form, they will be ...
5, 3, 1, 0 . . . . descending order
The standard form of this expression is ...
-2x^5 +x^3/2 +x/4 +1 . . . . . . matches choice B
Answer: b.–2x^5 + x^3/2 + x/4 + 1
Step-by-step explanation:
7. What is the angle measure that is vertical to an 83° angle?
Eric borrowed $1,800 for 9 months at 13.5% simple interest under an
add-on plan. What was his monthly payment?
a. $15.63
b. $220.25
c. $187.50
d. $1,982.25
ANSWER IS NOT C
If f is differentiable at x = c, then f is continuous at x = c.
True
False
Answer:
This is true!
Step-by-step explanation:
P.S: keep in mind that the opposite is not true! If f is continuous at x = c, then f is NOT differentiable at x = c.
:)))
If f is differentiable at x = c, then f is continuous at x = c is not true.
What is differentiable?Any point inside the range of a function's purview has a derivative, making it a computable function of one real variable. In these other phrases, each interior site in the domain of an invertible method's graph does indeed have a non-vertical line segment.
F is NOT differentiable at x = c if it is continuous at x = c.
When working with units, this quality is highly helpful since, if a curve is discrete, we automatically infer that it is indeed continuous.
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30 POINTS!!! WILL MARK BRAINLIEST! : )
1. Name the property the equation illustrates.
8 x 1/8 = 1
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
2. Name the property the equation illustrates.
–5 + (8 + 10) = (–5 + 8) + 10
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
3. Name the property the equation illustrates.
-4 x -1/4 = 1
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
4. Name the property the equation illustrates.
(ab)3 = a(b3)
A) Multiplication Property of –1
B) Inverse Property of Addition
C) Inverse Property of Multiplication
D) Identity Property of Division
Answer:
1. C) Inverse Property of Multiplication
2. None of these. The answer is Associative property of Addition
3. C) Inverse Property of Multiplication
4. None of these. The answer is Associative property of Multiplication
Step-by-step explanation:
1.
Given a number a , the inverse property of multiplication states that
a * 1/a = 1
and 1/a is called the multiplicative inverse of a.
So 8 * 1/8 = 1 features the inverse property of multiplication where a = 8.
2.
Given three numbers a,b,c , the associative property of addition states that a + (b + c) = (a + b) + c
In this case, a = -5, b = 8 and c = 10
3.
-4 x -1/4 = 1 features the inverse property of multiplication where a = -4.
4.
Given three numbers a,b,c , the associative property of multiplication states that (a * b) * c = a * (b * c)
In this case, a = a, b = b and c = 3
how would I solve for x?
solve the right triangle shown in the figure BC = 1.6in< A=48.8 C =90
I think your answer is A
Someone pleaser help me !
Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row, and Lorraine has gotten 13. How many more jumps (j) do they need to match the record? Show your work!
A right triangle has legs that are 15 feet and 25 feet long.
What is the length of the hypotenuse?
15^2 + 25^2 = X62
225 + 625 = x^2
850 = x^2
x = 5sqrt(34)
if you need it as a decimal = 29.1547
Answer: The length of the hypotenuse is 5√34 units.
Step-by-step explanation: Given that a right-angled triangle has legs of length 15 ft and 25 ft.
We are to find the length of the hypotenuse.
As shown in the attached figure, AB and BC are the legs of the right-angled triangle ABC. AC is the hypotenuse of the triangle.
Also, AB = 15 ft and BC = 25 ft.
From Pythagoras theorem, we have
[tex]AC^2=AB^2+BC^2\\\\\Rightarrow AC^2=(15)^2+(25)^2\\\\\Rightarrow AC^2=225+625\\\\\Rightarrow AC^2=850\\\\\Rightarrow AC=\sqrt{850}\\\\\Rightarrow AC=5\sqrt{34}.[/tex]
Thus, the length of the hypotenuse is 5√34 units.
For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.
{-4, 12, -36, ...}
A sidewalk forms the diagonal of a square park. The sidewalk is 30 meters long. To the nearest tenth of a meter, how long are the sides of the park ?
The sum of the roots of the equation 1/2x^2-5/4x-3=0
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. y = 2.5 when x = 9 answer asap plaese
Answer:
k = 22.5; xy = 22.5
your welcome
XD
Ginny has a sheet of plywood that is 4 feet by 8 feet. She wants to saw the plywood into pieces 1 foot high and 2 feet long for signs. How many signs can she make with the sheet of plywood?
Answer: 16 signs
Step-by-step explanation: i not saying this cause the other person said it i am saying it because i tookthe question
Write an expression for the following situation and solve it. Mr. Simms bought 20 pencils. He used 1/4 of the pencils and then gave 4 to his students.
What is 4 equal parts