The limit of the nth term of a sequence does not exist option (D) is correct.
What is the limit?A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have an expression:
[tex]= \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
Applying limit:
[tex]= \lim_{n \to \infty} \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
[tex]=\lim _{n\to \infty \:} n \left(\dfrac{2+\dfrac{25}{n^3}+\dfrac{32}{n^4}-\dfrac{15}{n^5}}{6+\dfrac{2}{n}-\dfrac{11}{n^2}-\dfrac{2}{n^3}+\dfrac{17}{n^4}}\right)[/tex]
= ∞ = The limit does not exist
Thus, the limit of the nth term of a sequence does not exist option (D) is correct.
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Could someone help me on this?
Find all solutions to the equation x3 + 100x + 8x2 = –800. –10, –8, 10 –10, 8, 10 8, –10i, 10i –8, –10i, 10i
All the solution of the equation x³ + 8x² + 100x + 800 = 0 will be 10i, -10i, and -8. Then the correct option is D.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The equation is given below.
x³ + 8x² + 100x = -800
x³ + 8x² + 100x + 800 = 0
Then the factor of the equation will be
x³ + 8x² + 100x + 800 = 0
x² (x + 8) + 100(x + 8) = 0
(x² + 100)(x + 8) = 0
Then all the solution of the equation will be
x = 10i, -10i, and -8.
Then the correct option is D.
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Answer:
d
Step-by-step explanation:
The area of a square is given by and the perimeter is given by , where s is the side length of the square.
If the side length of a square is 4 inches, its area is
square inches and its perimeter is
inches.
The area of the square is 16 square inches and its perimeter is 16 inches.
What is Area of square ?
A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.
The area of a square is given by the formula:
A = s²
where A is the area and s is the length of a side.
If the side length of the square is 4 inches, the area can be calculated as:
A = 4² = 16 square inches.
The perimeter of a square is given by the formula:
P = 4s
where P is the perimeter and s is the length of a side.
If the side length of the square is 4 inches, the perimeter can be calculated as:
P = 4 x 4 = 16 inches.
Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.
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The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔA'B'C' is right because it is the image of ΔABC.
ΔADC is right because AA' intersects AC at A.
ΔBCC' is right because B lies of the line of reflection.
ΔBGC is right because Line E G is perpendicular-to CC'.
Δ DGC is right angled triangle because Line E G is perpendicular-to CC', Option D is the correct answer.
What is Triangle ?Triangle is a polygon with three sides , angles and vertices.
It is given that the there are two Triangles , ABC and A'B'C' as an image of the ABC
* Line segment AA' has a midpoint at point F
*D is the mid point of the line joining BB' .*
The figure is attached with the answer.
the line of reflection of the object is always perpendicular to the object and the image.
it is also given that CGF is a right angle.
Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) , Line E G is perpendicular-to CC'.
Option D is the correct answer.
Please Refer to the image for correct coordinates.
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if the formula for number of people in bus is p=50b, where k= 50 people per bus show me the formula for number of buses per person ?
The formula for number of buses per person is b = p/50
This is a way of using a variable to represent other variables in a function.
Given the expression
p = kb
If k = 50, then;
p = 50b
Make b the subject of the formula
p/50 = 50b/50
b = p/50
Hence the formula for number of buses per person is b = p/50
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Select the correct answer.
Which graph best models the inequality?
y ≤ -2/5x + 2
Answer:
it would look like this
Step-by-step explanation:
what is b when the slope is 7/6 and the points are (10, -9)
Answer:
y = 7/6x - 62/3
Step-by-step explanation:
The equation for slope:
y = mx + b
m is the slope and b is the y-intercept
y = 7/6x + b
-9 = 7/6(10) + b
-9 = 35/3 + b
-62/3 = b
Select the correct answer.
One tactor of the polynomial 253 - 352 - 35 + 2 is (x - 2). Which expression represents the other factor, or factors, of the polynomial?
OA. (2:2 + 1)
OB. (252 - 5 + 1)
OC. (25 - 1 (s+1)
OD. (25 + 1) (5 - 1)
The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.
Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)
We have to find second factor of given equation
First we will be rational root theorem to given expression so will get following expression:
[tex]\left(x+1\right)\frac{2x^3-3x^2-3x+2}{x+1}[/tex]
So one factor is (x-1) and now simplifying [tex]\frac{2x^3-3x^2-3x+2}{x+1}[/tex] we get 2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)
Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
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Solve the equations for the given variable. Then place the equations in the table under the correct solution
Placing the equations under the correct solution, we get
x = 3 x ≠ 3
-14x = -42 -5 + x = -9
[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex] [tex]\frac{x}{3} =9[/tex]
[tex]\frac{x}{4} =\frac{6}{8}[/tex]
x -5 = -2
Solving Linear EquationsFrom the question, we are to place the equations under the correct solution
To do this, we will solve the equations one after the other
-14x = -42x = -42/-14
x = 3
-5 + x = -9x = -9 + 5
x = -4
∴ x ≠ 3
[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex][tex]x = \frac{12}{5} +\frac{3}{5}[/tex]
[tex]x = \frac{12+3}{5}[/tex]
[tex]x = \frac{15}{5}[/tex]
x = 3
[tex]\frac{x}{4} =\frac{6}{8}[/tex][tex]x=\frac{6\times 4}{8}[/tex]
[tex]x=\frac{24}{8}[/tex]
x = 3
[tex]\frac{x}{3} =9[/tex]x = 3 × 9
x = 27
∴ x ≠ 3
x -5 = -2x = -2 + 5
x = 3
Hence, placing the equations under the correct solution, we get
x = 3 x ≠ 3
-14x = -42 -5 + x = -9
[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex] [tex]\frac{x}{3} =9[/tex]
[tex]\frac{x}{4} =\frac{6}{8}[/tex]
x -5 = -2
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angle A and angle B are a linear pair. If measure of angle A = 4x-10 and measure of angle B = 3x+43, find the measure of angle A and measure of angle B
Answer:
See below ~
Step-by-step explanation:
Linear pairs add up to 180 degrees.
⇒ 4x - 10 + 3x + 43 = 180
⇒ 7x + 33 = 180
⇒ 7x = 147
⇒ x = 21
∠A = 4(21) - 10
∠A = 84 - 10
∠A = 74°
∠B = 3(21) + 43
∠B = 63 + 43
∠B = 106°
Can anyone explain how to do mathematical induction. The question is below. Brainliest awarded for the right answer. Thanks.
The sum of the triangular numbers is [tex]\frac{n(n+1)(n+2)}{6}[/tex]
According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n
triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of series of equilateral triangle.
given series in the figure
1, 3, 6, 10, 15, . . . . . . ., n
each number represents the number of dots containing in triangle
now the series can be given by
[tex]S = \frac{n(n+1)}{2}[/tex] for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒ ∑S
⇒ ∑[tex]\frac{n^2+n}{2}[/tex]
⇒ [tex]\frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}[/tex]
Thus, the sum of the triangular number is given by [tex]\frac{n(n+1)(n+2)}{6}[/tex]
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Which statements describe a triangular prism? Select three options. It has one base. It has two bases. It has three lateral faces. It has four lateral faces. Its lateral faces are rectangular.
The statements that describe a triangular prism are:
It has one base. It has three lateral faces. Its lateral faces are rectangular.What is a triangular prism?A triangular prism is a three-dimensional object that is made up of one base that has the shape of a triangle and three lateral sides that have the shape of a rectangle. A triangular prism has 5 faces, 9 edges and 6 vertices.
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What is x^3-2x^2-4x-1 divided by X+1?
Answer:
x^2-3x-1
Step-by-step explanation:
So we have the equation:
x^3-2x^2-4x-1/x+1
First factor the equation:
(x+1)(x^2-3x-1)/x+1
Then cancel the common factor: x+1 to solve the equation:
x^2-3x-1
2.) The quotient of 3 and y
Answer:
3 ÷ y
Step-by-step explanation:
Quotient refers to the division of two values, in this case 3 and y.
Answer:
3/y
Step-by-step explanation:
Here is a list of ages (years) of children in a room:
8
,
8
,
9
,
5
,
10
,
4
,
9
State the median.
Answer:
5
Step-by-step explanation:
median basically means the number which is in the middle so 8,8,9, 5 ,10,4,9
the median is 5 because left and right middle is 5 that's why it is median
Use the periodic compound interest formula to solve.
Suppose that $11,000 is invested at 5.8% compounded quarterly. Find the total amount of this investment after 6 years.
Answer:
$15,539.67
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $11,000r = 5.8% = 0.058n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}[/tex]
[tex]\implies \sf A=11000(1.0145)^{24}[/tex]
[tex]\implies \sf A=15539.67451...[/tex]
Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.
A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A. 5/18
B. 4/9
C. 1/2
D. 5/9
The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.The total sample will have 9 numbers
S = { 1,2,3,4,5,6,7,8,9} = 9
Even Number = { 2,4,6,8} = 4
Odd Number = { 1,3,5,7,9} = 5
P ( A ) = ( 4 / 9 )
P ( B ) = ( 5 / 9 )
The probability will be calculated as:-
P( A:B ) = [tex]\dfrac{P(A)\times P(B)}{P(B)}[/tex]
P( A:B ) =[tex]\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }[/tex]
P( A:B ) = 4 / 9
Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).
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a triangle is obtuse provided all the angles have a measure greater then 90 degrees
Answer:
An obtuse triangle can not have more than one angle measured greater than 90.
Step-by-step explanation:
Obtuse triangles have 2 acute angles (less than 90 degrees) and 1 obtuse angle (greater than 90).
Expand & simplify 6 ( p + 6 ) + 2 ( p + 4 )
Solution: 8p+44
Detailed explanation:
First we can "expand" by multiplying 6 times the parentheses and then 2 times the other set of parentheses.
[tex]--\mapsto\boldsymbol{6(p+6)+2(p+4)}\\\\---\mapsto\boldsymbol{6p+36+2p+8}[/tex]
To make life easier let's just put the p's next to each other.
[tex]--\mapsto\boldsymbol{6p+2p+36+8}[/tex]
Now let's add the p's
[tex]---\mapsto\boldsymbol{8p+44}[/tex]
Voila! There's our answer!
Cheers! ^-^__________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
____________________
⚜The dot plots below show the ages of students belonging to two groups of painting classes:
A dot plot shows two divisions labeled Group A and Group B. The horizontal axis is labeled as Age of Painting Students in years. Group A shows 1 dot at 9, 7 dots at 10, 8 dots at 15, 8 dots at 17, and 6 dots at 19. Group B shows 6 dots at 10, 5 dots at 14, 6 dots at 18, 5 dots at 25, 4 dots at 28, and 4 dots at 29.
Based on visual inspection, which group most likely has a lower mean age of painting students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.
Answer:
The group that is most likely able to have a lower mean age of painting students is Group A
Step-by-step explanation:
mean = sum of all terms divided by total number of terms
Looking at the graph data you have provided you can see that group A's students are a younger than students in Group B.
Which means when you calculate the mean the group which would give you the lower ratio with the same denominator of K (let there is K number of students in the class) will have lower mean age
here group A students are younger therefore their ratio will be lower
hence lower mean age
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SOS help please ignore the answers I put they are wrong
The conversion to logarithm function will be that log3 27 = 3.
How to calculate the log?From the information given, we are to convert the exponential equation to logarithm function. This will be:
log 3 27
This will be log 3 3³
= 3 × log 3^3
= 3 × 1
= 3
Therefore, x = 3.
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The question is:
Jason has 20 gallons of a 12% alcohol solution. How many gallons, to the nearest tenth, must be replaced by a 36% alcohol solution to give 20% gallons of 15% alcohol solution.
I need and explanation on how to set it up and do it. I have a test today and I don’t understand it.
Answer:
2.5 gallons of the 20% solution must be replaced by the 36% solution.
Step-by-step explanation:
[tex].12(20 - x) + .36x = 20(.15)[/tex]
[tex]2.4 - .12x + .36x = 3[/tex]
[tex]2.4 - .24x = 3[/tex]
[tex] - .24x = - .6[/tex]
[tex].24x = .6[/tex]
[tex]x = 2.5[/tex]
Compare the quantity in Column A with the quantity in Column B.
Column A Column B
slope of y = 3 slope of x = 3
The quantity in Column A is greater.
The quantity in Column B is greater.
The two quantities are equal.
The relationship cannot be determined on the basis of the information supplied.
Keep in mind that one is talking about the slope of y and one is about the slope of x. One has no slope and one has an undefined slope. So is it D? Does anyone know the answer to this question?
Compare the quantity in Column A with the quantity in Column B.
Column A Column B, The two quantities are equal.
What is the slope?Generally, the surface that has one end or side that is higher than the other (or vice versa); is a surface that slopes up or down.
In conclusion, Compare the number in Column A with the number in Column B.
The two amounts are identical in Columns A and B.
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hey god its me again
The statement D is false that No irrational number is rational.
What are real numbers?The set of real numbers includes integers, rational numbers, and irrational numbers.
This implies that all irrational numbers and integers are also real numbers.
Thus, statements A and B are correct.
Rational numbers are numbers that can be written as the division of two integers, which thus also include all integers.
The set of irrational numbers then contains all real numbers that are NOT rational numbers
Therefore, the set of irrational numbers does not include integers, which implies that statement D is false.
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Select the correct answer.
A petri dish contains cells of a certain strain of bacteria. Each bacterial cell in the dish divides in half approximately every 6 minutes. The curve of best fit that models the number of bacterial cells in the dish is given by the equation f(x) = 4.2 • 1.1x, where x represents the number of minutes and y represents the number of cells. Which value most likely represents the initial number of bacterial cells in the petri dish?
A.
10 cells
B.
5 cells
C.
2 cells
D.
1 cell
Answer:
the answer to that is B. 5 cells
What is the range of possible sizes for side x?
If x is the largest side :
x < 4.1 + 1.3x < 5.4If 4.1 is the greatest side :
4.1 < x + 1.3x > 2.8Range of possible sizes for side 'x' :
2.8 < x < 5.4What is 108+259+301+405
Answer:
1073
Step-by-step explanation:
it's simple addition
can someone help me with these answers please
since we were given the key ( how it should be sort out or used )
then we get all the numbers out which are:
21, 23, 30, 32, 32, 35, 43, 44, 46, 48, 49, 49, 50, 52, 52, 53, 55
then we go ahead to answer the questions:
a) Range = highest number minus Lowest number
55 - 21 = 34
b) 17 (by counting all individual ages ).
c) Median = the middle age
(but before that, we must arrange the ages either a cording to their sizes either from biggest to smallest (descending order) or from smallest to biggest (ascending order)
so we arrange in ascending order but the numbers are already arranged so we don't have to stress ourselves:
Median = 46 (the number in the middle ).
Hope you ace your tests, Good luck ✅.
if you are examining a triangle with given measurements for one leg and the hypotnuse,how will you determine the measure of the unknown leg?
We will apply the Pythagoras theorem to find the measure of the unknown leg in a triangle when one leg and the hypotenuse are provided dimensions.
What is the definition of a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.
According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.
[tex]\rm h^2 = p^2+ b^2[/tex]
Where,
h is the hypotenuse
p is the perpendicular
b is the base
If any of the two is given the third side will be obtained using the Pythagoras theorem.
In a triangle with given measurements for one leg and the hypotenuse, we will determine the measure of the unknown leg by the Pythagoras theorem.
Hence we willl apply the pythogorous theorem for finding the unknown side.
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18
1 point
The scatter plot shown below would best be modeled by a line of best fit.
True
False
G
0
The statement about using the line of best fit for the given scatter plot is; False
How to interpret a scatter plot?When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.
Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.
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