A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).
A geometric series is the sum of an infinite number of terms of a geometric sequence.
A geometric series is convergers if |r| < 1.
A geometric series is diveres if |r| > 1.
Calculate the common ratio:
[tex]r=\dfrac{18}{27}=\dfrac{18:9}{27:9}=\dfrac{2}{3}\\\\r=\dfrac{12}{18}=\dfrac{12:6}{18:6}=\dfrac{2}{3}\\\\r=\dfrac{8}{12}=\dfrac{8:24}{12:4}=\dfrac{2}{3}[/tex]
[tex]\left|\dfrac{2}{3}\right| < 1[/tex]
The geometric series is converges.Therefore exist the sum.
Formula of a sum of a geometric series:
[tex]S=\dfrac{a_1}{1-r},\qquad|r| < 1[/tex]
Substitute:
[tex]a_1=27,\ r=\dfrac{2}{3}[/tex]
[tex]S=\dfrac{27}{1-\frac{2}{3}}=\dfrac{27}{\frac{1}{3}}=27\cdot\dfrac{3}{1}=81[/tex]
[tex]\huge\boxed{S=81}[/tex]
His friends all drive more expensive cars, and Tony is now starting to desire these same expensive products. Which factor is Tony experiencing
When doing his homework, a student uses the addition property of equality to solve for c below. Which statement BEST applies to the sample? 6 + c = 10 6 + (–6) + c = 10 + (–6) c = 4 A. The student failed to keep both sides of the equation balanced. B. The student’s final answer does not have the variable c isolated. C. The use of the addition property of equality is sound, and the answer is correct. D. The student should have used the subtraction property of equality.
Answer:
The answer would be C
Lily is 22 years old. Monica is 3 years older than Lily and 2 years younger than Christine. How old is Christine
Answer:
she would be 20 years old if lily is 22
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
Using the triangle midsegment theorem, x = 5; BC = 10 units.
What is the Triangle Midsegment Theorem?According to the triangle midsegment theorem, ED = 1/2(BA).
Given the following:
ED = x + 2
BA = 4x - 6
x + 2 = 1/2(4x - 6)
2(x + 2) = 4x - 6
2x + 4 = 4x - 6
2x - 4x = -4 - 6
-2x = -10
x = 5
BC = 2(BE)
BC = 2(x)
BC = 2(5)
BC = 10 units
Learn more about the triangle midsegment theorem on:
https://brainly.com/question/12234706
#SPJ1
Answer:
D
Triangle Midsegment
5
10
Step-by-step explanation:
E2020 Geometry B!!:3
Which of the following represents a function
Answer:
(2,3),(4,3),(-2,-3),(-4,-3)
Step-by-step explanation:
A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).
This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.
The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.
A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.
In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:
(5,1),(5,2),(5,3),(5,4)
Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.
Consider the function f(x)=1/3(6)x. What is the value of the growth factor of the function?
Answer:
F = 2
Step-by-step explanation:
Answer:6
Step-by-step explanation:i did the quiz
E
What is the solution to the system of equations?
y = 0x + 3
x = −2
O [--]
O
[22]
[2
O
[-2]
Answer:
-2
Step-by-step explanation:
The solution to the system of equations is (x, y) = (-2, 1).
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The second equation tells us that x = -2.
Substituting this value into the first equation, we get:
y = -2 + 3
Simplifying, we get:
y = 1
Therefore,
The solution to the system of equations is (x, y) = (-2, 1).
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ5
M angle A=
M angle B=
M angle C=
Help me please Stuck on this question thanks
m<A = 28
m<B = 96
m<C = 56
One-quarter of the counters in a tub are red. The rest of the counters are green. If there are 48 green counters, how many red counters are there?
There are 16 red counters there.
Fractions and proportionsIf one-quarter of the counters in a tub are red and the rest are green, then there are three-quarter of the counter in the tub.
Let the total counter be x such that
3/4x = 48
3x = 4 * 48
x = 4 * 16
x = 64
Determine the amount of red counter
Red counter = 64 - 48
Red counter = 16
Hence there are 16 red counters there.
Learn more on proportion here; https://brainly.com/question/1496357
#SPJ1
A rectangle is four times as long as it is wide. If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square. What are the rectangle’s dimensions?
Answer:
Length equals 16 and Width equals 4
Step-by-step explanation:
First let us create an equation. We can use L and W for length and width.
If the length is 4 times the width, then we end up with: L = 4W
It then says, " If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square."
Since a square has an equal length and width then we end up with:
L - 6 = W + 6
Knowing this we can just substitute the first equation into the second one leaving us with: 4W - 6 = W + 6
We then remove a W from both sides so that the right side is left with a 6, and add 6 to both sides to remove the -6 from the left one.
This leaves us with 3W = 12
W = 4, and if we put that into our first equation, L = 4W, then Length equals 16, and Width equals 4. We can check this by putting it into the 2nd equation. 16 - 6 = 4 + 6.
Find the area of a triangle with points (-8,8) , (10,-2), and (-8,-8)
Answer:
144
Step-by-step explanation:
Base:16
Height: 18
Triangle area formula: (bxh)/2
16x18=288
288/2=144
There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three gardens in square feet.
65
60
62
64
Answer:
62
Step-by-step explanation:
1. To find the total area, we must find the area of the three individual gardens and sum them together
2. Since the gardens are square, the area is equal to the side length squared
3. Therefore, square the sides and sum:
3^2 = 9
7^2 = 49
2^2 = 4
4+9+49 = 62
A 2012 survey of 2,254 American adults indicates that 17% of cell phone owners do their browsing on their phone rather than a computer or other device. (a) According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones. Conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%. The hypotheses for this test are:
The hypothesis which can be used to show whether data provide strong evidence or not are: [tex]H_{0}:p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1}:p_{1}=p_{2}[/tex] where [tex]p_{1} and p_{2}[/tex] are the proportions of Americans and chinese people who use mobile phones to access internet.
Given proportion of Americans uses mobile phones is 17%. Proportion of chinese uses mobile phones is 38%.
Hypothesis are the statements which can be tested through its validity. There can be null hypothesis and alternate hypothesis.
The hypothesis which can be used are as under:
[tex]H_{0} :[/tex][tex]p_{1}[/tex]≠[tex]p_{2}[/tex]
[tex]H_{1}:p_{1} =p_{2}[/tex]
We have used equal to signs because we have to check whether they are different or not.
We cannot check hypothesis as we don't have standard deviation.
Hence the hypothesis for this test are: [tex]H_{0} :p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1} :p_{1} =p_{2}[/tex].
Learn more about hypothesis at https://brainly.com/question/11555274
#SPJ4
HELP GEOMETRY) Fill in the blanks:
How many degrees is angle LKZ?
How many degrees is angle LMZ?
How many degrees is arc LKZ?
Answer:
Step-by-step explanation:
Use the box-and-whisker plots to determine which statements are true.
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers and a box. The whiskers represents the minimum and maximum scores. The difference between the minimum and maximum scores is the range.
On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
To learn more about box plots, please check: brainly.com/question/27215146
#SPJ1
Which equation correctly describes the relationship between the measure of the inscribed angle and the measure of the intercepted arc in the figure? m∠PQR=360°−mPR⏜ m∠PQR=12mPR⏜ m∠PQR=2(mPR⏜) m∠PQR=mPR⏜ Circle with two chords. Point Q at 10 o clock, point P at 3 o clock, and point R at 6 o clock are on the circle. Segment Q R and Q P share a common end-point at point Q.
Answer:
Your answer is ∠PQR=(1/2)* m arc PR.
Step-by-step explanation:
The Angle Described is one that has its vertex in the circumference. The inscribed angle measures half of the arc it comprises.
So, in this problem, The inscribed angle=∠PQR
The arc it comprises=m arc PR too.
So therefore:
∠PQR=(1/2)* m arc PR is the answer
0.65 more than -4.35
Answer:
-3.7
Step-by-step explanation:
1. More = Addition
2. 0.65 + -4.35 = -3.7
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
0.65 more than -4.35
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The word more means addition, thus
-4.35+0.65=
[tex]\bf{-3.7}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=-3.7}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
For the following exercises, solve each inequality and write the solution in interval notation.
29. | x − 2 | > 10
Answer:
The solution to the inequality |x-2|>10 in interval notation is given by -8<x<12
Step-by-step explanation:
An absolute value inequality |x-2|>10 is given.
It is required to solve the inequality and write the solution in interval form.
To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.
Step 1 of 2
The given absolute value inequality is $|x-2|>10$.
The inequality can be written as
x-2<10 and x-2>-10
First solve the inequality, x-2<10.
Add 2 on both sides,
x-2<10
x-2+2<10+2
x<12
Step 2 of 2
Solve the inequality x-2>-10.
Add 2 on both sides,
x-2>-10
x-2+2>-10+2
x>-8
The solution of the inequality in interval notation is given by -8<x<12.
Quinn wants to save $300 this year. She saves $25 after her first dog-sitting job. How much more money does Quinn need to reach her goal for the year?
Quinn needs to save another $275.
How much more money does Quinn need to reach her goal for the year?
The money that she needs will be equal to the difference between the amount that she wants to save, and the amount that she already has.
She wants to save $300.She already has $25The difference is:
D = $300 - $25 = $275
This means that, to reach her goal this year, Quinn needs to save another $275.
If you want to learn more about differences:
https://brainly.com/question/5342576
#SPJ1
PLS HELP I REALLY NEED HELP
Answer:
a) AB = 10 unitsb) Midpoint is (2, 6)===================
GivenPoints A( - 1, 10) and B(5, 2)To finda) The length of ABb) The midpoint of ABSolutiona) Use the distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the coordinates and calculate:
[tex]d=\sqrt{(5-(-1))^2+(2-10)^2} =\sqrt{6^2+(-8)^2} =\sqrt{36+64} =\sqrt{100} =10[/tex]
The distance is AB = 10 units
b) Use midpoint formula and find x and y- coordinates of this point:
[tex]x= \cfrac{x_1+x_2}{2}[/tex] and [tex]y= \cfrac{y_1+y_2}{2}[/tex]
Substitute coordinates and find the midpoint:
[tex]x= \cfrac{-1+5}{2} =2[/tex] and [tex]y= \cfrac{10+2}{2}=6[/tex]
The midpoint is (2, 6)
Answer:
Length of line segment AB = 10 units
Midpoint of line segment AB = (2, 6)
Step-by-step explanation:
To find length, apply the distance formula :
AB = √(5 - (-1))² + (2 - 10)²AB = √36 + 64 = √100[tex]\fbox {AB = 10 units}[/tex]To find the midpoint :
M = (-1 + 5 / 2, 10 + 2 / 2)[tex]\fbox {Midpoint = (2, 6)}[/tex]73. Real-World Applications
A city's population in the year 1960 was 287,500 . In 1989 the population was 275,900 . Compute the rate of growth of the population and make a statement about the population rate of change in people per year.
Answer:
The rate of growth of the population is -400, this means the growth of the population from year 1960 to 1989 has dropped by 400 per city.
Step-by-step explanation:
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
It is required to compute the rate of growth of population and make a statement about the population rate of 1989 with the year 1989 and the time taken to change the population.
Step 1 of 1
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
To find the rate of growth of population and make a statement about the population rate of change in people per year.
Now let f(x) be the number of population and x be the year and use formula of rate of change to find the change in population,
[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$[/tex]
Now substitute, 275900 for [tex]$f\left(x_{2}\right)[/tex], 287500 for then,
[tex]$$\begin{aligned}m &=\frac{275900-287500}{1989-1960} \\&=\frac{-11600}{29} \\&=-400\end{aligned}$$[/tex]
The rate of growth of population -400, so there is a drop in the population by 400 per city.
A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of Plot A can be represented by 3x^2 +7x - 5, and the area of Plot B can be represented by 5x^2 - 4x + 11. Write a polynomial that represents the total area of both plots of land.
Step-by-step explanation:
Combine common terms
(3x²+5x²)+(7x-4x)+(-5+11)
8x²+3x+6
The polynomial that represents the total area of both plots of land will be; 8x²+3x+6
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We are given that ;
The area of Plot A can be represented by 3x² +7x - 5, and the area of Plot B can be represented by 5x² - 4x + 11.
So the polynomial that represents the total area of both plots of land
Now Combine common terms;
(3x²+5x²)+(7x-4x)+(-5+11)
Then we get;
8x²+3x+6
Learn more about polynomials here:
https://brainly.com/question/27343162
#SPJ2
can someone help me solve this problem?
Answer:
13
Step-by-step explanation:
cos17 = x/14
x = 14cos17
x= 13.38826658
to the nearest hundredth
x=13
GUYS CAN SOMEONE PLEASE HELP ASAP?
THANKS SO MUCH ULL GIVE 40POINTS AND BRAINLIEST
Answer:
1136/295 cm
Step-by-step explanation:
Corresponding lengths of similar figures are proportional.
If we let the radius of the second cylinder be x,
x/6.4 = 7.1/11.8
x = 6.4(7.1/11.8) = 1136/295 cm
what are the possible numbers of positive, negative, and complex zeros of f(x)=x^6+x^5+x^4+4x^3-12x^2+12?
The number of zeros are; Positive; 2 or 0; Negative: 4 or 2 or 0; Complex; 0, 2, 4, 6
How to find the zeros of a Polynomial?We are given the polynomial function as;
f(x) = x⁶ + x⁵ + x⁴ + 4x³ - 12x² + 12
Use Descartes Rule rule of signs allows us to determine the possible number of positive, negative, and complex roots.
For the function f(x), the number of sign changes that occur from term to term will give us the number of positive possible roots.
For the function f(-x), the number of sign changes that occur from term to term will give us the number of negative possible roots.
The numbers of complex roots is the difference between the degree of function and total number of positive and negative roots.
For f(x), the signs change 2 times. Thus, there can only be a possibility of 2 positive roots
For f(-x), we have;
x⁶ - x⁵ + x⁴ - 4x³ - 12x² + 12
Thus, the sign changes 4 times and so we have a possibility of 4 negative roots.
Read more about Descartes rule of polynomials at; https://brainly.com/question/12006853
#SPJ1
HELPP!!!
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction
if needed.
Answer:
15/17
Step-by-step explanation:
Write pqqqqrr in exponential form.
p^1
q^4
r^2
Is this what your asking for and also can you please mark me as brainlist. Thank you
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O A is 3. The length of A A prime is 9.
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation.
What is the scale factor of the dilation?
1/3
3
4
1/4
Answer:
3
Step-by-step explanation:
9 divided by 3 is 3...
hope this helped
Answer:
its 3
Step-by-step explanation:
im doing summer school rn lol
this is timed, much help is appreciated:)
The value of the angle m∠4 is 105 degrees.
How to find angles in a quadrilateral?The sum of angles in a quadrilateral is 360 degrees.
Therefore,
m∠1 + m∠2 + m∠3 + m∠4 = 360°
Hence,
x + x + 10 + x + 20 + x + 30 = 360
4x + 60 = 360
4x = 360 - 60
4x = 300
x = 360 / 4
x = 75
Therefore,
m∠4 = 75 + 30 = 105°
learn more on quadrilaterals here: https://brainly.com/question/17178852
#SPJ1
A solid right pyramid has a square base with an edge length of s units and a height of h units.
Which expression represents the volume of the pyramid?
One-fourth s^2h units^3
One-third s^2h units^3
s^2h units^3
3^s2h units^3
The volume of the square pyramid is: B. One-third s^2h units^3.
What is the Volume of a Square Pyramid?An example of a square pyramid is given in the image attached below. It has a square base and 4 triangular faces.
A right pyramid that has a square base has a volume that can be calculated using the following volume formula, given as: 1/3(a² × h), where "a" is the length of the edge of the square base, and "h" is the height of the square pyramid.
Given the following parameters for a square pyramid:
The length of the edge of the square base (a) = s units
The height of the square pyramid = h units.
Plug in the values into 1/3(a² × h) to find the expression that represents the volume of the pyramid:
Volume of the square pyramid = 1/3(a² × h) = 1/3(s² × h)
Volume of the square pyramid = 1/3s²h units ³.
The expression that represents the volume of the square pyramid is: B. One-third s^2h units^3.
Learn more about square pyramid on:
https://brainly.com/question/3688277
#SPJ1