Answers
Solution:
Given:
[tex]108,105,102,...,15[/tex]This is an arithmetic sequence because it has a common difference.
From the nth term of an arithmetic sequence,
[tex]\begin{gathered} a_n=a+(n-1)d \\ a=108 \\ d=105-108=102-105=-3 \\ a_n=15 \\ \\ Hence,\text{ the number of terms in the sequence is;} \\ 15=108+(n-1)-3 \\ 15-108=-3(n-1) \\ -93=-3(n-1) \\ \frac{-93}{-3}=n-1 \\ 31=n-1 \\ 31+1=n \\ 32=n \\ n=32 \end{gathered}[/tex]The sum of an arithmetic sequence is given by;
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ \\ where: \\ first\text{ term, }a=108 \\ last\text{ term, }l=15 \\ n=32 \\ \\ Hence, \\ S_n=\frac{32}{2}(108+15) \\ S_n=16(123) \\ S_n=16\times123 \\ S_n=1968 \end{gathered}[/tex]herefore, the sum oft the sequence is 1968
Related Questions
What is (-5,2); m=2/5 in standard form?
Answers
The standard form of the straight line is given by 5y - 2x = 20 .
Ax + By = C is the standard form for two-variable linear equations.
Standard form is used, for instance, in the linear equation 6x+5y=11. This method makes finding an equation's two intercepts very simple (x and y) .Y = mx + c is the cartesian equation for a straight line, where m denotes the gradient of the line and c denotes the location of its y-axis intersection.An infinitely long object without any width, depth, or curvature is a line. Since they can exist in two, three, or higher dimensions, lines are one-dimensional objects.We know that when a straight line passes through (a,b) with slope m then the equation of the line is given by:
y - b = m ( x - a )
putting the values in the respective places we get:
y - 2 = 2/5 × ( x + 5 )
or, 5y - 10 = 2x + 10
or , 5y - 2x = 20
Hence the standard form of the straight line is given by
5y - 2x = 20 .
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If y = 2cos(lnx). + 3sin(Inx) then Select one: 0 dy a 22 dy +r +y = 0 dx dx2 d'y x2 dy +2 dr2 dr y=0 o x2d²y dy dx + y To dx2 day 22 dy dr -y=0 dr2
Answers
Solution
Given
[tex]y=2\cos(\ln x)+3\sin(\ln x)[/tex][tex]\begin{gathered} \frac{dy}{dx}=\frac{-2}{x}\sin(\ln x)+\frac{3}{x}\cos(\ln x) \\ \\ \end{gathered}[/tex]Hello, I need some assistance with this homework question please for precalculusHW Q37
Answers
Given the function, we are asked to find a graph that is symmetric about the y-axis.
Explanation
Functions can be symmetrical about the y-axis, which means that if we reflect their graph, about the y-axis we will get the same graph. In the above question, the answer is
Answer:
[tex]y=|x|[/tex]Simplify the following expressions (10)
Answers
The given expression is,
[tex](3y^2-1)(2y^2-5y+8)[/tex]Using distributive property( A (B+C)=AB+BC),
[tex](3y^2-1)(2y^2-5y+8)=3y^2(2y^2-5y+8)-1(2y^2-5y+8)[/tex]Again using distributive property in RHS of above equation,
[tex]\begin{gathered} (3y^2-1)(2y^2-5y+8)=3y^2\times2y^2+3y^2\times(-5y)+3y^2\times8)-2y^2+5y-8 \\ (As\text{ }x^ax^b=x^{a+b}) \\ =6y^4-15y^3+24y^2-2y^2+5y-8 \\ =6y^4-15y^3+22y^2+5y-8 \end{gathered}[/tex]Therefore, the simplified expression is,
[tex]6y^4-15y^3+22y^2+5y-8[/tex]1&4/5 on a number line
Answers
Question in file need this ASAP for homework
Answers
The calculation of the value 3/4 - 2/6 is 5/12.
How to calculate the fraction?It should be noted that the question relates to the subtraction of fraction. This will be illustrated as:
= 3/4 - 2/6
It should be noted that the lowest common multiple of 4 and 6 is 12. This will be illustrated as:
= 3/4 - 2/6
= 9/12 - 4/12
= 5/12
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Need help answering this
Answers
Let's multiply the following polynomial:
[tex]\text{ \lparen5x}^2\text{ + y\rparen\lparen x}^2\text{ -2y\rparen}[/tex]We get,
[tex]\text{ \lparen5x}^2\text{ + y\rparen\lparen x}^2\text{ - 2y\rparen= \lparen5x}^2)(\text{x}^2)\text{ + \lparen5x}^2)(-\text{2y\rparen+ \lparen y\rparen\lparen x}^2)\text{ + \lparen y\rparen\lparen-2y\rparen}[/tex][tex]\text{ = 5x}^4\text{ - 10x}^2y\text{ + x}^2y\text{ - 2y}^2[/tex][tex]\text{ = 5x}^4\text{ - 9x}^2y\text{ - 2y}^2[/tex]Harry puts money into an account which pays 6% compound interest per year. If he puts £23000 in the account for 5 years how much more interest will he earn altogether?
Answers
The interest that Harry will earn altogether if he puts £23000 in the account for 5 years is £386,538,000.
Compound interest refers to the interest added to a loan or deposit. It is the concept that we use every day the most regularly. For an amount, compound interest is computed using both the principal and accrued interest. This is the primary difference between compound and simple interest.
Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.
In mathematics, compound interest is frequently referred to as C.I.
It is possible to compute interest using both the initial principle and interest that has accumulated over time.
Compound interest is calculated mathematically as Amount - Principal, where
Amount = Principal*(1 + (r/n))t, where r is the rate of interest, n is the number of times interest is compounded annually, and t is the number of years, and Principal is the initial amount deposited.
Given, Principal = £23000
Rate of interest = 6%
Number of times interest is compounded per year = 1
Number of years = 5
Using above literature, Amount = 23000(1 + (6/1))^5 = 23000*16807 = £ 386,561,000.
Thus, Compound Interest = £386,561,000 - £23000 = £386,538,000.
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Which function, g or h, is the inverse function for function f? CHECK PHOTO
Answers
Answer: The function g because the graphs of f and g are symmetrical about the line y=x.
Answer:
A. The function g because the graphs of f and g are symmetrical about the line y=x.
Step-by-step explanation:
If the inequality y < 3x – 4 is graphed in the xy - plane above, which quadrant contains no solutions to the inequality? (A) Quadrant I (B) Quadrant II (C) Quadrant III (D) Q8uadrant IV
Answers
Answer:
T
(B) Quadrant II
xplanation:
Firstly, let us plot the graph of the inequality;
[tex]y<3x-4[/tex]We can plot the graph as:
From the graph of the inequality, we can see that the solution to the inequality are only contained in the Quadrant I, Quadrant III and Quadrant IV. So, And the is no solution in the Quadrant II.
Therefore, the Quadrant that contains no solutions to the inequality is Quadrant II
In a lottery game, a player picks six numbers from 1 to 21. if the player matches all six numbers they win 50,000 dollars otherwise they lose $1
Answers
Your best option is to simply choose six distinct numbers, in any sequence. You would win if those six numbers matched the six that the lottery officials chose (again, in any sequence).
The likelihood of selecting the correct six numbers is one in
[tex]\frac{23}{6}[/tex] = [tex]\frac{23}{6(23-6)}[/tex] = [tex]\frac{23.22.21.20.19.18}{1.2.3.4.5.6}[/tex] = 100974
Therefore, 100946/100947, or a probability of losing, is very near to 1.
The total of your payouts multiplied by the probability that each scenario will occur is the anticipated value of the game. which is
(50,000) [tex]\frac{1}{100947}[/tex] + (-1) [tex]\frac{100946}{100947}[/tex] = [tex]\frac{50000-100946}{100947}[/tex] = -0.5046
You will typically break even if its value is 0. You should play the game if it is more than zero because you will typically win, and you shouldn't play it if it is less than zero because you will typically lose. The payoff is decently substantial for this, however the typical player loses just over 70 cents per round. Almost every player loses a complete dollar.
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How is climate change altering the approach to sustainability and sustainable development?
Answers
Climate change is altering the approach to sustainability and sustainable development as a result in the disruption of the economy of the countries which are affected.
What is Climate change?This is referred to as the long-term shifts in temperatures and weather patterns and are influenced by factors such as greenhouse gas emissions, solar cycle etc which affects the different factors.
Climate change will make people become poor due to the unfavorable working environment being it causes and therefore brings about a disruption in the economy as there will be a shift in focus which makes it the correct choice.
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If 1 x 10^a + 2 x 10^b + 3 x 10^c + 4 x 10^d = 24130 and a≠b≠c≠d, then what does a/2 + b/4 + c/8 + d/16 equal?
Answers
Question 1
Using scientific notation, we know a=2, b=4, c=1, and d=3. So,
[tex]\frac{a}{2}+\frac{b}{4}+\frac{c}{8}+\frac{d}{16}=1+1+\frac{1}{8}+\frac{3}{16}=37/16[/tex]
Question 2
[tex]a+13b=3(3a-b)\\\\a+13b=9a-3b\\\\16b=8a\\\\a=2b\\\\\therefore \frac{a^3}{b^3}=\frac{(2b)^3}{b^3}=\frac{8b^3}{b^3}=8[/tex]
A passbook savings account has a rate of 10% Find the effective annual yield if the interest is compounded daily.
Answers
The effective annual yield if the interest is compounded daily is 10.5155 %.
The annual interest rate or rate of return that an investor is entitled to over a particular time period is known as effective annual yield.
In the case of daily, there are 360 days in a year.
Therefore, making n = 360.
Therefore, the effective annual yield if the interest of 10% is compounded daily when r = 10 % and n = 360 will be:
Y = ( 1 + r/n )ⁿ - 1
Y = ( 1 + 0.1 / 360 )³⁶⁰ - 1
Y = ( 1 + 0.000277 )³⁶⁰ - 1
y = 1.105155 - 1
Y = 0.105155
However, since it is in decimal form, we must first multiply it by 100 before adding the symbol "%" after the last digit of the value.
Therefore,
Y = 0.105155 × 100%
Y = 10.5155 %
Therefore, the effective Annual Yield is 10.5155 %
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Let u = (1, −1, 3, 5) and v = (2, 1, 0, −3). Find scalars a and
b so that au + bv = (1, −4, 9, 18).
Answers
The value of the scalars a = 3 , and b = -1 .
In the question ,
it is given that
u = (1, −1, 3, 5) and v = (2, 1, 0, −3)
and the equation au + bv = (1, −4, 9, 18)
Substituting the first value of u that is u=1 and substituting the first value of v that is v=2 ,
we get a+2b=1 ....(i)
Now , Substituting the second value of u that is u= -1 and substituting the second value of v that is v=1 ,
we get -a+b= -4 ...(ii)
Solving the equations (i) and (ii)
Adding both the equations we get
a-a+2b+b=1-4
3b= -3
b= -1
a+2b=1
put b= -1
a+2(-1)=1
a-2=1
a=3.
Therefore , the value of the scalars a = 3 , and b = -1 .
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answer the unknown Angles
Answers
Answer:
p=45°, q=45°, s=112.5°
Step-by-step explanation:
Because the triangle is an isosceles right triangle, [tex]p=q=45^{\circ}[/tex].
In the top triangle, because of the isosceles triangle, the other two angles are each 67.5°.
Therefore, because angles that add to form a straight angle add to 180°, s=112.5°.
Simplify the expression: −(1/5)^−2.
Answers
Answer:
-(1/5)^-2
-5²
-25
Step-by-step explanation:
.....
4 = 4(k − 15) hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answers
Answer:
distribute the 4 to the k and -15 so you get 4=4k-60 then add the 60 to the other 4 so its 64=4k then divide 4 to 64 and your answer is 16
Step-by-step explanation:
[tex]4=4k-60\\4k-60=4\\4k=4+60\\4k=64\\\frac{4k}{4} =\frac{64}{4} \\k=16[/tex]
As solved above k=16
The house that David bills for his cat cat is a cube with an edge length of 4 ft to how to use the volume formula V equals x exponent 3 find the volume of the house
Answers
The volume of house built by David for cat is 64 ft³.
Firstly representing the mentioned statement about volume as mathematical expression. Exponent is the power of variable or constant. So, volume = x³, where x is the edge length.
As the edge length of house of car is given, we will keep the value in formula to find the volume of house.
V = 4³
Taking cube of the value on Right Hand Side of the equation
V = 4×4×4
Performing multiplication on Right Hand Side of the equation
V = 64 ft³
Thus, the volume of the house of cat is 64 ft³.
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5. Solve: x² – 3x – 18 = 0a. x= -6, x= 3b. X = 6, X = -3c. X = -9, x = 2d. x = 9, X = -2
Answers
Write out the equation
[tex]undefined[/tex]Information is given about a polynomial f(x)
whose coefficients are real numbers. Find the
remaining zeros of f.
Degree 4; zeros: i, - 6+ i
The remaining zero(s) of fis(are)
(Use a comma to separate answers
as needed.)
Answers
Answer:
Step-by-step explanation:
What is the solution of 2 + 2 =
Answers
Set up a proportion and solve.
If 4 containers of yogurt cost $2.00, find the cost of 5 containers of yogurt.
Five containers of yogurt will cost what?
Answers
Answer: $2.5 for 5 containers of yogurt
Step-by-step explanation:
To set up a proportion for this problem, we will have the 4 containers on the left with the 5 containers on the right and the container amount in the numerator with the dollar amount in the denominator. Let x be the unknown amount that we are solving for.
[tex]\dispalystyle \frac{4\text{ containers}}{\$2} =\frac{5\text{ containers}}{\$x}[/tex]
Now, we will cross-multiply and isolate the variable using inverse operations.
4 * x = 2 * 5
4x = 10
x = $2.5
What is the value of the expression? (−52)2+3^3/4
Answers
Answer:
If [tex]3^\frac{3}{4}[/tex] , ≈ -101.7205
If [tex]\frac{3^3}{4}[/tex] , = -389/4
Step-by-step explanation:
If [tex]3^\frac{3}{4}[/tex] :
[tex](-52)2+3^{\frac{3}{4} } =[/tex]
[tex]-104+\sqrt[4]{3^{3} }=-104+\sqrt[4]{27}=-101.7205[/tex]
If [tex]\frac{3^3}{4}[/tex] :
[tex](-52)2+ \frac{3^3}{4} =[/tex]
[tex]-104+\frac{27}{4} =-\frac{416}{4}+\frac{27}{4} =-\frac{389}{4}[/tex]
Given m/8= 86° and m/4= (4x + 2)°, what is the value of x ?
X =
Answers
Bring the variable to the left and the remaining values to the right to define the value of x. If m/8 = 86° and m/4 = (4x + 2)° then value of x = 21.
How to find the value of x?Any of the algebraic expressions, including addition, subtraction, multiplication, and division, should be used. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
Let the m/8 = 86° and m/4 = (4x + 2)°
m ∠4 = m ∠8 (Corresponding angles are equal)
To estimate the value of x
4x + 2 = 86
Substracting both sides of the equation by 2, we get
4x + 2 - 2 = 86 - 2
simplifying the above equation,
4x = 86 - 2
4x = 84
Dividing both sides of the equation by 4, we get
4x / 4 = 84 / 4
x = 21
Therefore, the value of x = 21.
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Question 5 (5 points)
What is the value of b?
3(b + 4) + 5b = 44
11
4
2
9
Answers
Answer:
4
Step-by-step explanation:
[tex]3(b+4)+5b=44 \\ \\ 3b+12+5b=44 \\ \\ 8b+12=44 \\ \\ 8b=32 \\ \\ b=4[/tex]
4.
908 ÷ 10 Power of 5
0.908
90.800,000
9.08
0.00908
Answers
Answer:
0.00908 is the answer...
Can you please help me, I'm not really good at geometry, please and thank you!
Answers
Circle and Point
Option B and D are the correct answers.
Graph the polynomial function. Note x- and y-intercepts, multiplicity, and end behavior.h(x) = (x − 1)3(x + 2)2
Answers
Given:
[tex]h\left(x\right)=\left(x-1\right)^3\left(x+2\right)^2[/tex]To graph the given polynomial function, we can plug in any values of x to find values of h(x). The graph is shown below:
We also note that the x-intercept is the point on the x-axis, while the y-intercept is the point on the y-axis. Hence,
x-intercepts: (1,0), (-2,0)
y-intercept: (0,-4)
Tt can also be noted that (x − 1) occurs 3 times while (x+2) occurs 2 times. Hence, x=1 has a multiplicity 3, while x=-2 has a multiplicity 2.
aased on the graph, the end behavior would be:
[tex]as\text{ x}\rightarrow+\infty,h(x)\rightarrow+\infty,\text{ and as x}\rightarrow-\infty,h(x)\rightarrow-\infty[/tex]3. Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven,
respectively.
Answers
A numeral exists a sign, combination of symbols, or figure that represents a number.
142 in base 5 means [tex]$1\left(5^2\right)+4\left(5^1\right)+2\left(5^0\right)[/tex] = 25 + 20 + 2 = 47
11011 in base 2 means [tex]$1\left(2^4\right)+1\left(2^3\right)+0\left(2^2\right)+1\left(2^1\right)+1\left(2^0\right)[/tex]= 27π
39 T in base 12 means [tex]$3\left(12^2\right)+9\left(12^1\right)+10\left(12^0\right)[/tex] = 550
What is meant by numeral?A numeral is a sign, combination of symbols, or figure that represents a number. It can be a mathematical numbering system.
A numeral's value is determined by the number it represents. All modern numbers cannot be represented by all number systems; Roman numerals, for instance, do not have a zero. A numeral system should, in theory, be able to: Represent a useful set of numbers (e.g. all integers, or rational numbers).
The correct answer is as follows:
142 in base 5 means [tex]$1\left(5^2\right)+4\left(5^1\right)+2\left(5^0\right)[/tex] = 25 + 20 + 2 = 47
11011 in base 2 means [tex]$1\left(2^4\right)+1\left(2^3\right)+0\left(2^2\right)+1\left(2^1\right)+1\left(2^0\right)[/tex]= 27π
39 T in base 12 means [tex]$3\left(12^2\right)+9\left(12^1\right)+10\left(12^0\right)[/tex] = 550
The complete question is:
Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respectively.
Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten andeleven, respectively.
a. 142five
b. 11011two
c. 39Ttwelth
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