Answer:
Sequence: ordered list of numbers
Series: sum of the terms of a sequence
Arithmetic sequence: the difference between the terms is constant
Geometric Sequence: the ratio between the terms is constant
Step-by-step explanation:
The difference between a series and a sequence is that a sequence is a list of numbers that follow a pattern or rule.
For example
1, 3, 5, 7, 9...
[tex]a_n = 1 +2(n-1)[/tex]
On the other hand, a series is the sum of the terms of a sequence.
1 + 3 + 5 + 7 + 9 + ...+ n
[tex]\sum_{n=1}1 +2 (n-1)[/tex]
----------------------------------------------------------------------------------
The difference between an arithmetic sequence and a geometric sequence is that:
for the arithmetic sequences the subtraction of:
[tex]a_n - a_{n-1} = d[/tex]
Where d is a constant called difference..
In the Arithmetic sequence the difference between the terms is constant
For the geometric sequences, it is satisfied that the quotient between two consecutive terms is:
[tex]\frac{a_{n-1}}{a_n} = r[/tex]
Where r is a constant value called common ratio
In geometric Sequence the ratio between the terms is constant
Final answer:
A sequence is an ordered list of numbers, while a series is the sum of the terms of a sequence. An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio.
Explanation:
Difference Between Sequence and Series
A sequence is an ordered list of numbers following a specific pattern, while a series is the sum of the terms of a sequence. For example, in the sequence 2, 4, 6, 8, ..., each term is 2 more than the previous term. However, when these terms are added together, for instance, 2 + 4 + 6 + 8, we get a series.
Difference Between Geometric and Arithmetic Sequences
An arithmetic sequence is characterized by a constant difference between consecutive terms. For example, the sequence 3, 7, 11, 15, ... has a common difference of 4. On the other hand, a geometric sequence has a common ratio between consecutive terms, such as the sequence 2, 6, 18, 54, ... where each term is 3 times the previous term.
please help and look at the picture
ANSWER
A.
[tex] \frac{1}{64} [/tex]
EXPLANATION
The given expression is:
[tex] {4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } [/tex]
Recall that:
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
We apply this property to obtain:
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - \frac{11}{3} - - \frac{2}{3} } [/tex]
Collect LCM
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 11 + 3}{3}} [/tex]
Simplify;
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ \frac{ - 9}{3}} [/tex]
.
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = {4}^{ - 3} [/tex]
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{ {4}^{3} } [/tex]
[tex]{4}^{ - \frac{11}{3} } \div {4}^{ - \frac{2}{3} } = \frac{1}{64} [/tex]
The first choice is correct
Shannon and Leslie want to carpet a 16 1/2ft by 16 1/2ft square room. They can't put carpet under an entertainment system that juts out.
A. In square feet what is the area of the space with no carpet?
B. how many square feet of carpet will Shannon and Leslie need to buy?
A. 272 1/4 ft
B. 68 5/8 ft
Hope this helps!
Shannon and Leslie need to carpet 272.25 square feet in a room with an entertainment system that takes up 12.25 square feet. Therefore, they need to buy 12.25 square feet of carpet.
Shannon and Leslie are planning to carpet a square room that measures 16.5 feet by 16.5 feet. However, they need to account for an entertainment system that juts out into the room, taking up 3.5 feet by 3.5 feet of space.
A. Area of the space with no carpet:
To determine the area of the space with no carpet, we first calculate the area of the entertainment system:
Area of entertainment system = 3.5 feet * 3.5 feet = 12.25 square feet
Next, we subtract the area of the entertainment system from the total area of the room:
Total area of room - area of entertainment system = area of space with no carpet
272.25 square feet - 12.25 square feet = 260 square feet
Therefore, the area of the space with no carpet is 260 square feet.
B. Carpet needed for the room:
To calculate the amount of carpet Shannon and Leslie need to buy, we simply subtract the area of the space with no carpet from the total area of the room:
Total area of room - area of space with no carpet = area of carpet needed
272.25 square feet - 260 square feet = 12.25 square feet
Shannon and Leslie need to buy 12.25 square feet of carpet.
Please help and thank you
Answer:
C. or D. I would say D though.
Step-by-step explanation:
All you have to do is look at the total with both children and adults, then you can take that and divide it by the total of either children or adults and then you would get the answer D.
Answer: B
Step-by-step explanation:
One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared
Answer:
29119.66666...+14561.3333...=43681, 209ft^2, not square feet.
Step-by-step explanation:
"One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared"
Ok, so this is a tricky one- 209 feet squared, not 209 square feet, therefore the area is 209^2, or 43,681.
Next, let's define our variables-
x= the "other side"
z= 3 feet shorter than twice side
We can now make these (useful) equations
z=2x-3
43681= (2x-3)+x
We will focus on the latter for now-
Simplify
43681= (2x-3)+x
43681= 2x-3+x
43681= 3x-3
+3
43684=3x
/3
14561.3333...=x
z=2x-3
z=2*(14561.3333)-3
z=29119.66666....
29119.66666...+14561.3333...=43681
Anybody understand this I am really confused..
Answer:
Step-by-step explanation:
The volume of a cone is
V = (1/3) * pi * r^2 * h
pi = 3.14
r = 3
h = 8
V = 1/3 * 3.14 * 3^2 * 8
V = 1/3 * 3.14 * 9 * 8
V = 75.36
V = 75.4
what is the square root of m to the power of 6
Step-by-step explanation:
[tex]\sqrt{m^6}=\sqrt{m^{3\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt{a^2}=|a|\\\\=|m^3|\\\\\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3\\\\\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3[/tex]
What percent of a dozen is 3
Answer:
25%
Step-by-step explanation:
Percentages are one of several ways of describing quantities' relationships to one another. Specifying one number as a percentage of another means specifying the fraction of the second quantity the first comprises. The percentage value is the number that, divided by 100, equals that fraction. To express the percentage as a whole number, round it accordingly. Some applications, however, don't require percentages as exact whole figures.
Divide the first number the second. For instance, if you want to find what percentage 43 is out of 57, divide 43 by 57 to get 0.754386.
the radius of a regular pentagon measures 7ft. which of the following would be an acceptable equation to use to solve for the measure of the side, s?
(the selected answer is just randomly selected)
Answer:
Option D. [tex]cos(54\°)=\frac{0.5s}{7}[/tex]
Step-by-step explanation:
we know that
A regular pentagon can be divided into 5 isosceles triangles
The length side of the legs of one isosceles triangle is equal to the radius
The vertex angle of one isosceles triangle is equal to 360/5=72 degrees
The base angle of one isosceles triangle is equal to 54 degrees
Let
s------> the length side of the regular pentagon
so
[tex]cos(54\°)=\frac{(s/2)}{r}[/tex]
substitute the given value
[tex]cos(54\°)=\frac{(s/2)}{7}[/tex]
[tex]cos(54\°)=\frac{0.5s}{7}[/tex]
The average battery life of 2800 manufactured cell phones is recorded And normally distributed. The mean battery life is 14 hours with a standard deviation of .5 hours. Find the number of phones who have a battery life in the 13 to 14 range.
Answer:
1336 phones
Step-by-step explanation:
The average battery life of 2800 manufactured cell phones has a normal distribution.
The mean battery life is 14 hours, therefore: μ = 14 hours.
The standard deviation is 0.5 hours, therefore: σ = 0.5 hours.
To find the number of phones who have a battery life in the 13 to 14 range, we're going to ask for the help of a calculator. The probability of finding phones who have a battery life in the 13 to 14 range is: 0.4772. (See attached picture)
Therefore, the number of phones who have a battery life in the 13 to 14 range is: 0.4772×2800 = 1336,16 ≈ 1336 phones.
Final answer:
To find the number of phones with a battery life between 13 and 14 hours, calculate the z-scores, find the corresponding percentage using the standard normal distribution, and then multiply by the total number of phones, resulting in approximately 1336 phones.
Explanation:
The question asks for the number of cell phones with a battery life in the 13 to 14 hour range out of 2800 phones where the mean battery life is 14 hours with a standard deviation of 0.5 hours. The battery life is normally distributed.
To find this number, we need to calculate the z-scores for 13 and 14 hours and then determine the percentage of phones between those z-scores. The z-score for 13 hours is (13 - 14)/0.5 = -2 and for 14 hours is (14 - 14)/0.5 = 0. Using the standard normal distribution table, the area under the curve from -2 to 0 is approximately 47.7%. Therefore, the number of phones with battery life between 13 and 14 hours is 0.477 * 2800 ≈ 1336 phones.
What is the meaning of Zero on a number line
The definition of a number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.
simplify polynomial 2x^2+6x-7x+8-3x^2+1
Answer: [tex]-x^2-x+9[/tex]
Step-by-step explanation:
To simplify the given polynomial [tex]2x^2+6x-7x+8-3x^2+1[/tex] we need to add the like terms. Then we get:
[tex]2x^2+6x-7x+8-3x^2+1=(2x^2-3x^2)+(6x-7x)+(8+1)=-x^2-x+9[/tex]
Therefore, we get that the polynomial simplified is:
[tex]-x^2-x+9[/tex]
Which is a trinomial ( A polynomial that has three terms) of degree 2 (Because the highest exponent is 2).
Answer:
Final answer is [tex]-x^2-x+9[/tex].
Step-by-step explanation:
Given polynomial is [tex]2x^2+6x-7x+8-3x^2+1[/tex].
Now we need to simplify the given polynomial so we can begin with combining like terms.
[tex]2x^2+6x-7x+8-3x^2+1[/tex]
[tex]=2x^2-3x^2+6x-7x+8+1[/tex]
[tex]=(2-3)x^2+(6-7)x+(8+1)[/tex]
[tex]=(-1)x^2+(-1)x+(9)[/tex]
[tex]=-x^2-x+9[/tex]
Hence final answer is [tex]-x^2-x+9[/tex].
There is 1 red gumdrop and 4 green gumdrops in a small jar. Also, 1 piece of butterscotch candy and 4 pieces of cinnamon candy are in another jar. If Craig draws one piece of candy from each jar without looking, what's the probability that he will get a green gumdrop and a piece of butterscotch candy?
A. 4 / 25
B. 1 / 5
C. 1 / 2
D. 8 / 25
The probability that Craig will get a green gumdrop and a piece of butterscotch candy is 4/25.
To find the probability that Craig will get a green gumdrop and a piece of butterscotch candy, we need to calculate the probability of each event happening separately and then multiply those probabilities together.
There are 5 gumdrops in the first jar with 4 being green, so the probability of choosing a green gumdrop is 4/5. In the other jar, there are 5 pieces of candy with 1 being butterscotch, so the probability of choosing a butterscotch candy is 1/5. Multiplying these probabilities together gives us 4/5 × 1/5 = 4/25.
In exercises 18 and 19 determine which solution if any is an extraneous solution 18.sprt(3x-2)=x; x=1,x=2. 19. Sprt(x+6=x; x=3,x=-2
ANSWER
18. No extraneous solution.
19. The extraneous solution is x=-2
EXPLANATION
18. The given radical equation is:
[tex] \sqrt{3x - 2} = x[/tex]
Solving this radical equation yields
[tex]x=1,x=2[/tex]
We check for an extraneous solution by substituting each value into the equation.
Checking for x=1,
[tex] \sqrt{3 \times 1 - 2} = 1[/tex]
[tex]\sqrt{3- 2} = 1[/tex]
[tex]\sqrt{1} = 1[/tex]
[tex]1 = 1[/tex]
This is true.
Checking for x=2
[tex]\sqrt{3 \times 2- 2} = 2[/tex]
[tex]\sqrt{6- 2} = 2[/tex]
[tex]\sqrt{4} = 2[/tex]
[tex]2 = 2[/tex]
This is also true. Hence there is no extraneous solution.
19. The given radical equation is:
[tex] \sqrt{x + 6} = x[/tex]
Solving this equation yields,
[tex]x=3,x=-2[/tex]
Checking for x=3,.
[tex]\sqrt{3+ 6} = 3[/tex]
[tex] \sqrt{9} = 3[/tex]
3=3.
This is a true solution.
Checking for x=-2.
[tex]\sqrt{ - 2 + 6} = - 2[/tex]
[tex] \sqrt{4} = - 2[/tex]
[tex]2 \ne - 2[/tex]
Hence x=-2 is an extraneous solution.
can someone please help me with these two questions pleasee
Answer:
7. 62.8 sq.in.8. 21.2 sq.in.Step-by-step explanation:
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{1}{2}ab\sin\theta[/tex]
a, b - adjacent sides
θ - included angle
=============================================
7.
a = 9in, b = 14in, θ = 85°
sin85° ≈ 0.9962
Substitute:
[tex]A_\triangle=\dfrac{1}{2}(9)(14)\sin85^o=\dfrac{1}{2}(126)(0.9962)\approx62.8 in^2[/tex]
8.
a = 12 in, b = 5 in, θ = 135°
sin135° = sin(180° - 45°) = sin45° ≈ 0.7071 used sin(180° - x) = sin(x)
Substitute:
[tex]A_\triangle=\dfrac{1}{2}(12)(5)\sin135^o=\dfrac{1}{2}(60)(0.7071)\approx21.2\ in^2[/tex]
Give the polynomial function below find f(-4) f(x) =2x^2 - x+ 9
Answer:
f(-4) = 45Step-by-step explanation:
Put x = -4 to f(x) = 2x² - x + 9:
f(-4) = 2(-4)² - (-4) + 9 = 2(16) + 4 + 9 = 32 + 4 + 9 = 45
Which of the following is the order of magnitude for the number feet in a mile A.4
B.3
C.1
D.2
Answer:
b
Step-by-step explanation:
The vertex of this parabola is at (-1,3) Which of the following could be its equation
Answer:
y - 3 = a(x + 1)^2
Step-by-step explanation:
The vertex equation of a vertical parabola is:
y - k = a(x - h)^2.
If the vertex is at (-1, 3), then the equation becomes:
y - 3 = a(x + 1)^2, where a is a constant.
Next time, would you please share the answer choices. Thank you.
Answer:
Step-by-step explanation:
all parabola have equation : y = a(x +1)²+3 a in R
Please need help
Find area of shaded region.
Round to the nearest tenth
Answer:
818.4 in²
Step-by-step explanation:
The area (A) of the shaded region is
A = area of circle - ( area of white sector + area of triangle )
= ( π × 27.8²) - (π × 27.8² × [tex]\frac{210}{360}[/tex] +(0.5 × 27.8 ×27.8 × sin150°)
= 2427.95 - (1416.30 + 193.21 )
= 2427.95 - 1609.51 ≈ 818.4 in²
Calculate the exact value of ( 4 1/3 - 1 2/5 ) ÷ 4/15
the answer is 11.
use BEDMAS, and calculate the equation inside the brackets (answer to that is 44/15)
then divide it by 4/15 and you get 11
let's firstly convert the mixed fractions to improper fractions and proceed.
[tex]\bf \stackrel{mixed}{4\frac{1}{3}}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}}~\hfill \stackrel{mixed}{1\frac{2}{5}}\implies \cfrac{1\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{7}{5}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{recall that by PEMDAS, parenthesis first}~\hfill }{\left(\cfrac{13}{3}-\cfrac{7}{5} \right)\div \cfrac{4}{15}\implies \left(\stackrel{\textit{using an LCD of 15}}{\cfrac{(5)13-(3)7}{15}} \right)\div \cfrac{4}{15}\implies \left(\cfrac{65-21}{15} \right)\div \cfrac{4}{15}} \\\\\\ \left(\cfrac{44}{15}\right)\div \cfrac{4}{15}\implies \cfrac{44}{15}\times \cfrac{15}{4}\implies \cfrac{44}{4}\cdot \cfrac{15}{15}\implies 11\cdot 1\implies 11[/tex]
What is 5482.7+6978+h=12434.7
solve for h please
Answer: 26
Step-by-step explanation:
Add all together and the subtract by 12434.7 and you get 26 hope this helps!
Determine if the binomial is a perfect square binomial. If so, show the original monomial squared.
5. x2+ 16
6. x4 + 12x2+ 36
Answer:
Step-by-step explanation:
(5) x^2 + 16 is a perfect square binomial only if imaginary roots are allowed.
x^2 + 16 = (x + 4i)(x - 4i)
(6) x^4 + 12x^2 + 36 is a perfect square trinomial.
The square root of x^4 is x^2 and the square root of 36 is 6.
Experimenting, we find that x^4 + 12x^2 + 36 = (x² + 6)²
so we can conclude that x^4 + 12x^2 + 36 = (x² + 6)(x² + 6) = (x² + 6)².
Which geometric series converges ???
Answer:
C
Step-by-step explanation:
A geometric series will only converge if - 1 < r < 1
sum to infinity = [tex]\frac{a}{1-r}[/tex]
The nth term formula for a geometric series is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
The only summation with - 1 < r < 1 is C where r = - 0.2
Answer: The correct option is
(C) [tex]\sum_{n=1}^{\infty}4(-0.2)^{n-1}.[/tex]
Step-by-step explanation: We are give to select the geometric series that converges.
We know that
the general (n-th) term of a common geometric series is given by
[tex]a_n=ar^{n-1}.[/tex]
And the series converges if the modulus of the common ratio is less than 1, .e., |r| < 1.
Now, for the first infinite geometric series, we have
[tex]a_n=\dfrac{2}{3}(-3)^{n-1}.[/tex]
So, the common ratio will be
[tex]r=-3~~~\Rightarrow |r|=3>1.[/tex]
That is, the series will not converge. Option (A) is incorrect.
For the second geometric series, we have
[tex]a_n=5(-1)^{n-1}.[/tex]
So, the common ratio will be
[tex]r=-1~~~\Rightarrow |r|=1.[/tex]
That is, the series will not converge. Option (B) is incorrect.
For the third geometric series, we have
[tex]a_n=4(-0.2)^{n-1}.[/tex]
So, the common ratio will be
[tex]r=-0.2~~~\Rightarrow |r|=0.2<1.[/tex]
That is, the series will CONVERGE. Option (C) is correct.
For the fourth geometric series, we have
[tex]a_n=0.6(-2)^{n-1}.[/tex]
So, the common ratio will be
[tex]r=-2~~~\Rightarrow |r|=2>1.[/tex]
That is, the series will not converge. Option (D) is incorrect.
Thus, (C) is the correct option.
1. What is the value of x? Show all of your work.
Answer:
The value of x is x
Step-by-step explanation:
Answer: x = 5
Step-by-step explanation:
whats the y intercept to x g(x) 0 2 1 6 2 10
Answer:
y-intercept = (0,2).
Step-by-step explanation:
We have been given a table of the function g(x) as shown below:
x g(x)
0 2
1 6
2 10
Using that table we need to find about what is the y-intercept of the given function g(x).
By definition of y-intercept, we know that, y-intercept is the y-value or function value of g(x) value when x=0.
From table we see that g(x)=2 when x=0.
So the y-intercept = 2.
In point form we can write y-intercept as (0,2).
please help with this thank you
Answer:
(4, - 2 )
Step-by-step explanation:
To find the x- coordinate substitute y = - 2 into the equation
y + 2 = - 3(x - 4), thus
- 2 + 2 = - 3x + 12
0 = - 3x + 12 ( subtract 12 from both sides )
- 12 = - 3x ( divide both sides by - 3)
4 = x
What is the range for this set of data? 38, 17, 55, 40
Answer:
38.
Step-by-step explanation:
range is taking the highest number subtracting it by the smallest
Answer:
the answer is 38
Step-by-step explanation:
you subtract the biggest number with smallest number
If a drug's recommended dose is 5 mg/kg, and a solution contains a concentration of 2 mg/mL of the drug, what volume of the solution should be given to a cat that weighs 8 lb.?
A. 20 mL
B. 90 mL
C. 2 mL
D. 9 mL
The answer would be....:B.90 ML
The volume of the solution should be given to a cat that weighs 8 lbs. is 9 ml. Thus, the correct option is D.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
The weight of the cat is 8 lbs. Therefore, the weight of the cat in kg will be,
Weight of cat = 8 lbs = (8×0.454) kgs = 3.632 kgs
Since for one kg, the recommended dose is 5 mg, therefore, the recommended dose for the cat will be,
Recommended dose for cat = 3.632kg × 5 = 18.16 mg
Now, as given that one ml of solution contains 2mg of drugs, therefore,
1 ml = 2mg
1 mg = 1/2 ml
18.16 mg = 18.16 × 1/2 = 9.08ml ≈ 9 ml
Hence, the volume of the solution should be given to a cat that weighs 8 lbs. is 9 ml. Thus, the correct option is D.
Learn more about Units conversion:
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what the hell is a rotation?
Answer:
A rotation is when a shape rotates across the x or y axis on a coordinate plane :)
Step-by-step explanation:
i am a number. If the area of each square below is 25 square units, i am the perimeter of the figure. i am ___________
Answer: 20
Step-by-step explanation:
The area= 25
The square root of 25=5
So we know that 2 sides are 5
5×4=20
Multiply 5 by 4 because squares have all sides of the same length, so the remaining 2 sides are 5.
8x-6y=54 in slope intercept form please!!
Answer: y= 4/3x-9
Step-by-step explanation:
The equation 8x - 6y = 54 can be converted to slope-intercept form (y = mx + b) by isolating y. The steps involve rearranging terms and simplifying to yield the equation: y = (4/3)x - 9.
Explanation:First, you want to manipulate your equation: 8x - 6y = 54 into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Here are the steps:
Add 6y to both sides to isolate variables on one side. Now, the equation is 8x = 6y + 54. Divide everything by 6 to solve for y. The equation becomes y = (8x/6) - (54/6). Simplify the equation: y = (4/3)x - 9.
Therefore, the equation 8x - 6y = 54 in slope intercept form is y = (4/3)x - 9.
Learn more about Slope-Intercept Form here:
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