Consider the following sequence of numbers.
The common ratio of the sequence is =?
The sum of the first five terms of the sequence is=?
Blank 1 options: -1/3,-3,1/3,3
Blank 2 options: -303,183,-60,363
Answers
Answer:
Blank 1 is -3
Blank 2 is 183
Step-by-step explanation:
Let r be common ratio
[tex]r = \frac{ - 9}{3} \\ r = - 3[/tex]
Sum of first 5 terms
[tex]s = \frac{a( {r}^{n} - 1)}{r - 1} \\ s = \frac{ 3( {( - 3)}^{5} - 1) }{ - 3 - 1} \\ s = 183[/tex]
Answer:
1) Second option: -3
2) Second option: 183
Step-by-step explanation:
1) You can use any two consecutive terms to find the common ratio. This is given by:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
You can choose these consecutive terms:
[tex]a_n=-9\\a_{n-1}=3[/tex]
Then the common ratio "r" is:
[tex]r=\frac{-9}{3}=-3[/tex]
2) The sum of the first "n" terms can be found with this formula:
[tex]S_n=\frac{a_1(r^n-1)}{r-1}[/tex]
Since ther first term is 3 and you need to find the sum of the first 5 terms, then:
[tex]a_1=3\\n=5[/tex]
Substituting into [tex]Sn=\frac{a_1(r^n-1)}{r-1}[/tex], you get:
[tex]S_{(5)}=\frac{3((-3)^5-1)}{-3-1}=183[/tex]
Related Questions
I will mark Brainliest The radius of a sphere is 7 feet. Which formula can be used to find the surface area of the sphere? A = 4?(7)3 A = 3?(7)2 A = 3?(7)3 A = 4?(7)2
Answers
Answer:
A = 4π(7)^2
Step-by-step explanation:
The formula for the area of a sphere is ...
A = 4πr^2 . . . . . . for radius r
When the radius is 7 feet, the value 7 goes where r is in the formula:
A = 4π·7^2 . . . . . square feet
What is the probability of either outcome b or d?
a. .28
c. .19
b. .38
d. .33 please select the best answer from the choices provided a b c d?
Answers
Answer:
B.38
Step-by-step explanation:
Use function notation to write a recursive formula to represent the sequence: 4, 8, 12, …
A.f(n) = f(n − 1) + 4
B.f(n) = f(n − 1) + 2
C.f(n) = f(n − 1) ⋅ 4
D.f(n) = f(n − 1) ⋅ 2
Answers
Answer:
A.f(n) = f(n − 1) + 4
Step-by-step explanation:
4+4 = 8
8+4 = 12
We are adding 4 to the term before it
f(n) = f(n-1) +4
Answer: A.f(n) = f(n − 1) + 4 Hope this helps :)
How do you solve x^4 - 3x^3 - 3x^2 - 75x - 700
Answers
Answer:
= (x +4)(x -7)(x^2 +25)
roots are -4, 7, ±5i
Step-by-step explanation:
You have not said what "solve" means in this context. An expression by itself doesn't have a solution. We have assumed you want to find the factoring and/or roots of it.
I like to use a graphing calculator to find the real roots. For this expression, there are two of them, one positive and one negative. (You know there will be one positive real root, and at least one negative real root, from Descartes's rule of signs.)
Then those roots can be factored out and the solution to the remaining quadratic determined. That factoring can occur by polynomial long division, synthetic division, or other means.
I like to see what happens when I plot the graph of the function divided by the known factors. (We expect a parabola that doesn't cross the x-axis.) The vertex of that parabola can be used to find the remaining roots.
The x-intercepts of the given expression are -4 and +7, so two of the factors are (x+4) and (x-7). Dividing these from the given expression (by synthetic division or other means) gives (x^2 +25). This only has imaginary roots (±5i).
____
If you're constrained to doing this "by hand" with only a scientific calculator, Descartes's rule of signs tells you there is one positive real root. (Only one sign change in the sequence of coefficient signs: +----.)
The rational root theorem tells you it will be a divisor of 700. Various estimates of the maximum magnitude of it will tell you it is probably less than 14 (easily checked). So, the numbers you can test as roots would be 1, 2, 4, 5, 7, 10, 14. You will find that 7 is a root, and then you can reduce the problem to the cubic x^3 +4x^2 +25x +100.
When odd-degree term signs are changed, there will be 3 sign changes (-+-+), hence at least one negative real root. The rational root theorem tells you it is a divisor of 100, so possible choices are -1, -2, -4, -5. By trial and error or other means, you can find the root to be -4. Then the problem reduces to the quadratic x^2 +25.
Roots of that are ±√(-25) = ±5i.
This process generally entails a fair amount of trial-and-error work, which is why I prefer one that makes some use of technology.
_____
We have presumed you have some familiarity with ...
Descartes's rule of signsRational Root Theoremsynthetic divisionThis will usually be the case when you're presented with problems like this. If you need additional information on any of these, it is readily available on the internet (and probably also in your reference material).
PLEASE HELP!
Point A is located at (-2, 2), and D is located at (4, -2). Find the coordinates of the point that lies halfway between A and D.
1) (0, 1)
2) (-1, 1)
3) (1, 0)
4) (1, 1)
Answers
Answer:
3) (1, 0)
Step-by-step explanation:
The midpoint can be computed as the average of the coordinates.
M = (A + D)/2 = ((-2, 2) +(4, -2))/2 = ((-2+4)/2, (2-2)/2) = (1, 0)
The midpoint is (1, 0).
___
This is also easily seen on a graph of the points.
Shayla has 6 1/2 pounds of potato salad into containers each of which holds 1 5/8 pounds. How many containers does she need?
Answers
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}}~\hfill \stackrel{mixed}{1\frac{5}{8}\implies \cfrac{1\cdot 8+5}{8}}\implies \stackrel{improper}{\cfrac{13}{8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{total salad}}{\cfrac{13}{2}}\div \stackrel{\stackrel{\textit{conainer's}}{\textit{capacity}}}{\cfrac{13}{8}}\implies \cfrac{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\underset{1}{\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\cdot \cfrac{\stackrel{4}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies 4[/tex]
Camilla borrows a book from the library for ddd days. The library charges a late fee of 0.100.100, point, 10 dollars per day that the book is late.
If Camilla returns the book more than 212121 days after she borrowed it, the expression 0.10(d-21)0.10(d−21)0, point, 10, left parenthesis, d, minus, 21, right parenthesis represents the total late fee Camilla owes.
What does (d-21)(d−21)left parenthesis, d, minus, 21, right parenthesis represent in this context?
Answers
Answer:
(d -21) is the number of days the book is late
Step-by-step explanation:
There is no fee if the book is returned within 21 days, so d-21 represents the number of "late days" for which a fee is charged.
Answer:
(d -21) is the number of days the book is late
Step-by-step explanation:
How to tell if a function is even or odd from a graph
Answers
Answer:
if u can divide it to two
Step-by-step explanation:
Need help with this math question
Answers
Answer:
x = 3.1 ft
Step-by-step explanation:
Use Pythagoras' Theorem to find the base of the triangle. The base of the triangle is half of 'x'. Let's call the base 'y' for now.
To find 'y' we must use this formula,
[tex]y^{2} = c^{2} -b^{2}[/tex]
'c' is the hypotenuse, the longer side, and 'b' is the other short side.
Sub in the numbers for 'c' and 'b',
[tex]y^{2} = 2.1^{2} -1.4^{2}[/tex]
= 2.45
Square root both sides to get 'y' by itself,
y = 1.5652.....
Remember that 'y' is half of x? Simply multiply 'y' by 2 to get an answer for 'x',
x = 1.5652.... x 2
= 3.1 ft (1 d.p. nearest tenth)
Hope this helped!!
BRAINLIEST !!!!!
ms.wolf earns a salary of $50,000 per year plus a 4% commission on her sales. the average price of a share she sells is $50.
write an inequality to describe how many shares ms. wolf must sell to make an annual income of at least $70,000.
Answers
Answer:
[tex]2x + 50,000 \ge 70,000[/tex].
[tex]x \ge 10,000[/tex].
Step-by-step explanation:
What's the total income of Ms. Wolf in a year?
The annual income of Ms. Wolf comes in two parts:
The fixed salary of $50,000, andThe 4% commission on shares she sold.How many commission does Ms. Wolf receive for each share she sold? [tex]\$\;50 \times 4\% = \$\;50 \times 0.04 = \$\;2[/tex].
Let the number of shares that Ms. Wolf sold be [tex]x[/tex]. Ms. Wolf will receive a commission of [tex]\$\;2x[/tex].
Total annual income of Ms. Wolf: [tex]\$\; (50,000 + 2x)[/tex].
The phrase "at least" indicates that [tex]\$\; (50,000 + 2x)[/tex] shall be greater than or equal to $70,000. That is:
[tex]\$\; (50,000 + 2x)\ge \$\;70,000[/tex].
[tex]2x + 50,000 \ge 70,000[/tex].
[tex]x \ge 20,000[/tex].
Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on a random sample of 34 days, and the average (mean) value is 126.5 volts. Choose the correct answer below. A. The given value is a parameter for the year because the data collected represent a sample. B. The given value is a statistic for the year because the data collected represent a population. C. The given value is a statistic for the year because the data collected represent a sample. D. The given value is a parameter for the year because the data collected represent a population
Answers
Answer:
5 but its probaly not right bc im just looking for pointsStep-by-step explanation:
4 yards of woolen fabric costs $30.00 more than 6 yards of silk fabric. How much does the silk cost if the cost of the silk is $25.00 less than the cost of the wool?
Answers
Answer:
Cost of yard silk fabric : $35
Cost of yard of woolen fabric: $60
Step-by-step explanation:
This problem must be represented as a linear system of equations
Let
x = the cost of 1 yard of woolen fabric
y = the cost of 1 yard of silk fabric
The problem tells us
4 yards of woolen fabric costs $30.00 more than 6 yards of silk fabric.
4.x = 6.y + 30
cost of the silk is $25.00 less than the cost of the wool
y = x - 25
The system of equations is
4x - 6y = 30
x - y = 25
If we solve this system of equations using a calculator or computational tool, we get the following values
x = $60
y = $35
PLS HELP SHOW ALL YOUR WORKING OUT BRAINLIEST
Answers
Area of a triangle = height x base ÷ 2
When ever you have an isosceles triangle, remember that you can split it in half to form two right angled triangles - which allow you to use Pythagoras' Theorem.
So we split 10cm in half to get 5cm.
We can then use 13cm and 5cm to work out the height:
Height = √(13² - 5²) (Note: you subtract because you are using the
= √144 (hypotenuse)
= 12
---------------------------------------------------------
Now to get the area, we just multiply the base (which is 10) by the height (which is 12) and divide by 2:
Area = 12 x 10 ÷ 2
= 6 x 10 (note: 12 ÷ 2 = 6 )
= 60 cm²
_____________________________________
Answer:
60 cm²
the sum of two numbers is 68.the smaller number is 8 less than the larger number what are the numbers
Answers
Answer:
30 and 38
Step-by-step explanation:
If x is the smaller number and y is the larger number:
x + y = 68
x = y - 8
Solve with substitution:
y - 8 + y = 68
2y = 76
y = 38
x = 30
So the two numbers are 30 and 38.
Answer:
Smaller number = 30
Larger number = 38
Step-by-step explanation:
68 = (x+8) + x
68 = 2x - 8
60 = 2x
30 = x
and
68 = (x-8) + x
68 = 2x - 8
76 = 2x
38 = x
Need help with a math question
Answers
Answer:
[tex]x =26\°[/tex]
Step-by-step explanation:
For this case we have 2 secant lines and an exterior angle x.
Then by definition the measure of the outer angle is equal to half the difference of the arcs formed by the sides.
This means that the angle x is equal to:
[tex]x =\frac{66\°-14\°}{2}\\\\x =26\°[/tex]
the answer is:
[tex]x =26\°[/tex]
add 5/9 and 5/6, then subtract 2/3 from the sum. please show work
Answers
Answer:
13/18
Step-by-step explanation:
We need to get a common denominator for 9,6,3
That would be 18
5/9 *2/2 = 10/18
5/6 * 3/3 = 15/18
2/3 *6/6 = 12/18
5/9+5/6 = 10/18 +15/18 = 25/18
Then
25/18 - 2/3 = 25/18 - 12/18 = 13/18
The length of a parking Lot is 5 yards more than the width. If the area of the parking lot is 66 square yards, find the dimensions of the parking lot.
Answers
Answer:
6 yards by 11 yards
Step-by-step explanation:
Factors of 66 are ...
66 = 1·66 = 2·33 = 3·22 = 6·11
The last pair of factors differ by 5, so represent the solution to the problem.
The width of the parking lot is 6 yards; the length is 11 yards.
Final answer:
The parking lot's dimensions are found by setting a quadratic equation w × (w + 5) = 66 based on its area. Solving for w, the width is 6 yards, hence the length is 11 yards, making the dimensions 6 yards by 11 yards.
Explanation:
To find the dimensions of the parking lot when the length is 5 yards more than the width and the area is 66 square yards, we can set up an equation based on the area of a rectangle (area = length × width). We can define the width as w and the length as w + 5 since the length is 5 yards more than the width.
The equation representing the area will then be:
w × (w + 5) = 66
Solving this quadratic equation (w^2 + 5w - 66 = 0) by factoring or using the quadratic formula, we find that w = 6 or w = -11. We discard the negative value since a width cannot be negative, so the width is 6 yards and the length is 11 yards (since it's 5 yards more than the width).
Therefore, the dimensions of the parking lot are 6 yards by 11 yards.
If w represents the width of a rectangle with a length of 12 centimeters and an area of 590 square centimeters, what is the best algebraic equation?
a) 590=12w
b) 590=2w+24
c)590=12+w
Answers
The formula for the area of a rectangle is...
Area = length x width
A = L x W
What we know so far...
Area is 590 cm^2
length is 12 cm
width is unknown
Plug all of these into the equation for area of a rectangle:
590 = 12 * w
or
590 = 12w
Letter A is the correct answer
Hope this helped!
~Just a girl in love with Shawn Mendes
PLEASE HELP
4. The table shows the probabilities of a response chocolate or vanilla when asking a child or adult. Use the formula for conditional probability to determine independence.
Chocolate | Vanilla | Total
Adults 0.21 0.39 0.60
Children 0.14 0.26 0.40
Total 0.35 0.65 1.00
a. Are the events “Chocolate” and “Adults” independent? Why or why not?
b. Are the events “Children” and “Chocolate” independent? Why or why not?
c. Are the events “Vanilla” and “Children” independent? Why or why not?
Answers
Answer:
All events are independent
Step-by-step explanation:
You are given the table
[tex]\begin{array}{cccc}&\text{Chocolate}&\text{Vanilla}&\text{Total}\\\text{Adults}&0.21&0.39&0.60\\\text{Children}&0.14&0.26&0.40\\\text{Total}&0.35&0.65&1.00\end{array}[/tex]
Two events A and B are independent when
[tex]Pr(A\cap B)=Pr(A)\cdot Pr(B)[/tex]
a) A="Chocolate"
B="Adults"
A and B="Chocolate and Adults"
[tex]Pr(A)=0.35\\ \\Pr(B)=0.60\\ \\Pr(A\cap B)=0.21[/tex]
Since [tex]0.35\cdot 0.60=0.21[/tex] events are independent
b) A="Children"
B="Chocolate"
A and B="Children and Chocolate"
[tex]Pr(A)=0.40\\ \\Pr(B)=0.35\\ \\Pr(A\cap B)=0.14[/tex]
Since [tex]0.40\cdot 0.35=0.14[/tex] events are independent
c) A="Vanilla"
B="Children"
A and B="Vanilla and Children"
[tex]Pr(A)=0.65\\ \\Pr(B)=0.40\\ \\Pr(A\cap B)=0.26[/tex]
Since [tex]0.65\cdot 0.40=0.26[/tex] events are independent
What is the value of x when y is 21
Answers
Answer:
7
Step-by-step explanation:
7 x 3 = 21
Which function is quadratic function? a(x) = –2x^3 + 2x – 6 b(x) = 5x^3 + 8x^2 + 3 c(x) = –8x^2 + 3x – 5 d(x) = 6x^4 + 2x – 3
Answers
Answer:
c(x) = –8x^2 + 3x – 5 is a quadratic function.
Step-by-step explanation:
At first, we will define what a quadratic function is.
A quadratic function is a polynomial with one or more variables with degree 2.
So, from the given functions
a(x) = -2x^3+ 2x – 6 has highest degree 3. So it is not a quadratic function.
b(x)=5x^3 + 8x^2 + 3 has highest degree 3. So it is not a quadratic function.
c(x) = –8x^2 + 3x – 5 has highest degree 2. So it is a quadratic function.
d(x) = 6x^4 + 2x – 3 has highest degree 4. So it is not a quadratic function.
Answer:
Step-by-step explanation:
I need help ASAP!!
Consider the equation below.
x^2-10x-11=0
Determine which equation has the same solutions as the given equation.
A. (x-10)^2=36
B. (x-5)^2=21
C. (x-10)^2=21
D. (x-5)^2=36
Answers
Answer:
D. (x-5)^2 = 36
Step-by-step explanation:
If you add 11 to the given equation, you get ...
x^2 -10x = 11
Then you can add the square of half the x-coefficient to complete the square.
x^2 -10x +25 = 11 +25
(x -5)^2 = 36 . . . . simplify to the appropriate form
Find the radius and center of the circle given by the equation below. (x – 6)2 + (y + 4)2 = 7 r = 7 and center at (-6, 4) r = 7 and center at (6, -4) r = √7 and center at (-4, 6) r = √7 and (6, -4)
Answers
Answer:
center at (6, -4) r = √7
Step-by-step explanation:
(x – 6)^2 + (y + 4)^2 = 7
This is in the form
(x – h)^2 + (y - k)^2 = r^2
Where (h,k) is the center of the circle and r is the radius of the circle
Rearranging the equation to match this form
(x – 6)^2 + (y -- 4)^2 = sqrt(7) ^2
The center is at (6, -4) and the radius is the sqrt(7)
Answer:
center at (6, -4) r = √7
Step-by-step explanation:
(x – 6)^2 + (y + 4)^2 = 7 This is in the form (x – h)^2 + (y - k)^2 = r^2 Where (h,k) is the center of the circle and r is the radius of the circle Rearranging the equation to match this form (x – 6)^2 + (y -- 4)^2 = sqrt(7) ^2 The center is at (6, -4) and the radius is the sqrt(7)
Nia has $19.50 to ride the subway around New York. It will cost her $0.75 every time she rides. Identify the dependent variable and independent variable in this scenario.
A.) The number of rides and the total cost are both independent variables.
B.) The number of rides and the total cost are both dependent variables.
C.) The number of rides is the independent variable, and the total cost is the dependent variable.
D.) The total cost is the independent variable, and the number of rides is the dependent variable.
Answers
Answer:
The correct answer is B. The number of rides and the total cost are both dependent variables, as both depend on the amount of money that Nia has.
Step-by-step explanation:
Both the number of rides and the total cost are variables that depend on the amount of money that Nia has. This is so because the passage has a cost, and that cost can not exceed the amount of money that Nia has, because if she exceeds her $ 19.50 she won't be able to pay the ticket. Then, Nia has a possible amount of 26 rides as maximum (19.5 / 0.75 = 26), and the maximum total cost that can be paid is $ 19.50.
Final answer:
The correct answer is: C) The number of rides is the independent variable, and the total cost is the dependent variable.
Explanation:
In the scenario where Nia has $19.50 to ride the subway around New York, at a cost of $0.75 per ride, the correct identification of the dependent and independent variables is crucial for understanding the relationship between these quantities.
The independent variable is the number of rides Nia can take. This is because it is the variable over which we have control or can set at different levels; in other words, Nia decides how many trips she takes.
The dependent variable is the total cost of these rides. The cost depends on how many rides she takes, changing accordingly with that number.
Therefore, the correct answer is: C) The number of rides is the independent variable, and the total cost is the dependent variable.
help me, anyone???...
Answers
Answer:
x = 34
Step-by-step explanation:
The 3 given angles form a straight angle and sum to 180°, hence
x + 12 + 100 + x = 180
2x + 112 = 180 ( subtract 112 from both sides )
2x = 68 ( divide both sides by 2 )
x = 34
Answer:
x=34
Step-by-step explanation:
Alright.
x+12+100+x=180
2x+112=180
2x=68
x=34
Duane is filing his federal income tax return with the 1040EZ form using the Single filing status, and nobody can claim him as a dependent. If he had wages, salaries, and tips of $37,400, taxable interest of $160, and no unemployment compensation, what should he enter on line 6 of the Income section below?
Answers
Answer:
$27410
Step-by-step explanation:
Duane is filing his federal income tax return with the 1040EZ form using the Single filing status, and nobody can claim him as a dependent. If he had wages, salaries, and tips of $37,400, taxable interest of $160, and no unemployment compensation, what should he enter on line 6 of the Income section below?
form 1040EZ is the form used for paying tax by the Inland Revenue Services(IRS)
Line 6 of the 1040EZ from will contain taxable income
so he will fill
$27410
His taxable income is when standard deductions and deductions for exemption is subtracted from the total income
37,400+160-(6200+3950)
$27410
1040EZ form
Filing status and income:,
Filing status: Single
Are you someone's dependent?: No
Wages, salaries, tips, etc:
$37,400
Taxable interest:
$160
Unemployment compensation:
$0
Standard deduction:
$6,200
Deduction for exemptions:
$3,950
Taxable income:
$27,410
Federal income tax withheld:
$0
Answer:
28,210
Step-by-step explanation:
just answered it
What is the domain of the function y=2 VX-6?
Answers
Answer:
The answer in the procedure
Step-by-step explanation:
case 1) If the function is
[tex]y=2\sqrt{x-6}[/tex]
we know that
The term in the radicand must be positive
so
[tex]x-6\geq 0\\ \\x\geq 6[/tex]
therefore
The domain of the function is the interval -----> [6,∞)
All real numbers greater than or equal to 6
case 2) If the function is
[tex]y=2\sqrt{x}-6[/tex]
we know that
The term in the radicand must be positive
so
[tex]x\geq 0[/tex]
therefore
The domain of the function is the interval -----> [0,∞)
All real numbers greater than or equal to 0
50 POINTS SIMPLIFY RADICAL EXPRESSION! + BRAINLIEST TO RIGHT/BEST ANSWER
PLEASE only answer if you are POSITIVE!!
Answers
0.125 is the cube of 0.5 and b3 is the cube of b.
Answer:
.5b
Step-by-step explanation:
( .125 b^3) ^ 1/3
We know that ( xy) ^c = x^c * y ^c
( .125) ^ 1/3 (b^3) ^ 1/3
Rewriting .125 as .5^3
( .5^3) ^1/3 ( b^3) ^ 1/3
We know that a^c^d = a^(c*d)
.5 ^ (3*1/3) b ^ (3*1/3)
.5 b
which of the va;ues of P and Q result in an equation with no solutions? Qx+P=33x+25
Answers
Answer:
Step-by-step explanation:
No solution means that the 2 lines will never intersect in a coordinate plane. The only kinds of lines that can exist within the same coordinate plane and never intersect are lines that are parallel. The slopes have to be the same for lines to be parallel. The y-intercept, or where they go through the y axis, won't be the same, but the value of the slope has to be. The slope of the equation on the right is 33, so if these lines are parallel, then Q has to equal 33. P can then be any real number NOT equal to 25.
Need help with a math question PLEASE HELP
Answers
Answer:
18%
Step-by-step explanation:
From the table you can state that:
the total number of students is 10,730the number of students receiving Finincial Aid and is Graduate is 1,879Use the definition of the probability
[tex]Pr=\dfrac{\text{The number of favorable outcomes}}{\text{The number of all possible outcomes}}[/tex]
So,
the number of favorable outcomes = 1,879the number of all possible outcomes = 10,730Hence, the probability is
[tex]Pr=\dfrac{1,879}{10,730}\approx 0.1751\approx 18\%[/tex]