[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Let's see if the sequence is Arithmetic or Geometric :} [/tex]
[tex] \textsf{If the difference between successive terms is } [/tex] [tex] \textsf{equal then, the terms are in AP} [/tex]
[tex] \sf{ \dfrac{14}{3}- \dfrac{13}{3} = \dfrac{1}{3}} [/tex][tex] \sf{ {5}{}- \dfrac{14}{3} = \dfrac{15-14}{3} =\dfrac{1}{3}} [/tex][tex] \textsf{Since the common difference is same, } [/tex] [tex] \textsf{we can infer that it's an Arithmetic progression} [/tex] [tex] \textsf{with common difference of } \sf \dfrac{1}{3} [/tex]
Answer:
Arithmetic with common difference of [tex]\sf \frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\textsf{Given sequence}=4, \dfrac{13}{3}, \dfrac{14}{3}, 5, \dfrac{16}{3},...[/tex]
If a sequence is arithmetic, the difference between consecutive terms is the same (this is called the common difference).
If a sequence is geometric, the ratio between consecutive terms is the same (this is called the common ratio).
[tex]\sf 4\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad\dfrac{13}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{14}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad 5\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{16}{3}[/tex]
As the difference between consecutive terms is [tex]\sf \frac{1}{3}[/tex] then the sequence is arithmetic with common difference of [tex]\sf \frac{1}{3}[/tex]
General form of an arithmetic sequence: [tex]\sf a_n=a+(n-1)d[/tex]
where:
[tex]\sf a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven:
a = 4[tex]\sf d=\dfrac{1}{3}[/tex]So the formula for the nth term of this sequence is:
[tex]\implies \sf a_n=4+(n-1)\dfrac{1}{3}[/tex]
[tex]\implies \sf a_n=\dfrac{1}{3}n+\dfrac{11}{3}[/tex]
Bombarding plutonium-239 with an alpha particle creates an isotope of curium. balance the equation. 239 94 pu 4 2 he → a b cm c d n identify the values for the unknown letters. a is b is c is d is
Since mass is neither created nor destroyed, the missing items are;
a = 242b = 96c = 1d = 0What is nuclear reaction?The term nuclear reaction has to do with the transformation of one nucleus to another. On this case, we are going to transform P u to c m.
Since mass is neither created nor destroyed, the missing items are;
a = 242b = 96c = 1d = 0Learn more about nuclear reaction: https://brainly.com/question/25455333?
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Answer:
A: 242
B: 96
C: 1
D: 0
Step-by-step explanation:
Solve the following
A) multiply by 2 both sides, canceling the ÷ by 2
4x - 1 = 2x + 14
+1
4x = 2x +15
-2x
2x. = 15
÷2
x = 7.5
B) mutiply 3 both sides
9x + 6 = 2x + 13
-6
9x. = 2x + 7
-2x
7x. = 7
÷1
x = 1
Hope this helps!
Divide. Write your answer as a fraction or a mixed number in simplest form. 4 3/4 / 5/6
Answer:
57/10 is the simplest form
Step-by-step explanation:
To divide fractions you need to do the reciprocal rules.
You also need to convert any mixed numbers to improper to make them easier to divide.
4 3/4 and 5/6 are your fractions.
4 3/4 converted into an improper fraction is 19/4
This is because the rule with this is that you take your whole number multiply it by the denominator and take the product and add it to the numerator.
19/4 divided by 5/6.
You need to flip 5/6 to 6/5 due to the reciprocal rules and also change the division sign to a multiplication sign.
19/4 x 6/5
You can multiply straight across!
19 x 6 and 4 x 5
19 x 6 = 114
4 x 5 = 20
Our answer: 114/20
We still need to simplify this answer
We can divide this result into 2/2.
114/20 = 57/10
57/10 is the simplest form. If you were to divide more, you will get involved with decimals.
Answer: 57/10 is the simplest form
Step-by-step explanation:
To divide fractions you need to do the reciprocal rules.You also need to convert any mixed numbers to improper to make them easier to divide.
4 3/4 and 5/6 are your fractions.
4 3/4 conerted into an improper fraction is 19/4
This is because the rule with this is that you take your whole number multiply it by the denominator and take the product and add it to the numerator.
19/4 divided by 5/6.
You need to flip 5/6 to 6/5 due to the reciprocal rules and also change the division sign to a multiplication sign.
19/4 x 6/5
You can multiply straight across!19 x 6 and 4 x 5
19 x 6 = 114
4 x 5 = 20
Our answer: 114/20
We still need to simplify this answer
We can divide this result into 2/2.
114/20 = 57/10
57/10 is the simplest form. If you were to divide more, you will get involved with decimals.
EP6. Abby works at a job that starts out paying $15 per hour. Each year she continues
at the job, she will get a 5% raise. How much will Abby make per hour if she stays at that
job for 30 years?
Answer:
$64.83.
Step-by-step explanation:
Each year the multiplier fffor her new rate will be 1.05.
So after 30 years her hourly rate will be 15 * 1.05^30
= $64.83
What is the volume of the cylinder below?
8
• A. 96r units3
•
B. 2257 units*
• C. 1927 units3
D. 5767 units3
Answer:
192π
Step-by-step explanation:
cylinder volume is base times height
2πr^2 = base = 64π
height = 3
64π*3 = 192π
The volume of the given cylinder is 192π cubic units. Therefore, option C is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
From the given figure, radius of a cylinder = 8 units and radius of a cylinder = 3 units.
We know that, volume of a cylinder is πr²h.
Now, volume = π×8²×3
= π×64×3
= 192π cubic units.
Therefore, option C is the correct answer.
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The area of a circle is 36.43cm2.
Find the length of the radius rounded to 2 DP.
Answer:
3.40 cmStep-by-step explanation:
It is given that the area of a circle is 36.43cm² and we have to find the length of the radius.
So, first of we must know this formula :
⇒ πr² = Area(Circle)
We will take the value of π as 3.14Now, Substituting the given values in the formula :
⇒ 3.14 × r² = 36.43
⇒ r² = 36.43/3.14
⇒ r² = 11.60
⇒ r = √11.60
⇒ r = 3.40
Therefore,
The radius of the circle is 3.40 cmHey ! there
Answer:
Radius of circle = 3.40 cmStep-by-step explanation:
In this question we are given with area of circle that is 36.43 cm² . And we are asked to find the length of radius of circle rounded to two decimal points .
We know that ,
[tex] \qquad \quad \frak{Area_{(Circle)} = \pi r {}^{2} } \quad \bigstar[/tex]
Where ,
π = 3.14r = radius of circleSolution : -
According to question , area of Circle is equal to 36.43 . So ,
[tex] \longrightarrow \qquad \: \pi r {}^{2} = 36.43[/tex]
Step 1 : Substituting value of π :
[tex] \longrightarrow \qquad \:3.14 \times r {}^{2} = 36.43[/tex]
Step 2 : Transposing 3.14 to right side :
[tex] \longrightarrow \qquad \: r {}^{2} = \cancel{\dfrac{36.43}{3.14} }[/tex]
On dividing 36.43 by 3.14 , We get :
[tex] \longrightarrow \qquad \: r {}^{2} = 11.60[/tex]
Step 3 : For removing square from r , We are applying root on both sides :
[tex] \longrightarrow \qquad \: \sqrt{r {}^{ 2 }} = \sqrt{ 11.60}[/tex]
We get :
[tex] \longrightarrow \qquad \:r = \sqrt{11.60} [/tex]
Step 4 : Finding square root of 11.60 , We get :
[tex] \longrightarrow \qquad \: \purple{\underline{\boxed{\frak{r = 3.40 \: cm}}}} [/tex]
Therefore, radius of circle is 3.40 cm#Keep LearningWhat is 4,255 rounded to the nearest THOUSAND?
Answer:
4,000
Step-by-step explanation:
To round a number, take the place next to the one you wish to round and look to see if it is four or under, or five or up. In this case, 2 is less than 5 so we will be rounding down towards the nearest integer, which is 4. Also, all places after the place value you round will become zero. So, 4,000 rounded to the thousands place is 4,000.
hope this helps :)
Answer:
The answer would be 4,000
Step-by-step explanation:
even if you round it up the the nearest hundred, it would still be 4,000.
High School Geometry Khan Academy help. Need to pass this class!
What subset, a, of the sample space represents the complement of the event in which camille is the final swimmer? a = {cba, cab, bca, acb} a = {abc, bac} a = {cba, cab, bac, bca, acb, abc} a = {ab, ba}
Answer:
the first choice :)
Step-by-step explanation:
Answer:
Option A: A = {CBA, CAB, BCA, ACB}
find the vol of this prism
Answer:
V = 396 cm³
Step-by-step explanation:
the volume (V) of the prism is calculated as
V = Ah ( A is the area of the triangular face and h the height of prism )
A = [tex]\frac{1}{2}[/tex] bh ( b is base and h perpendicular height )
here b = 9, h = 8 , then
A = [tex]\frac{1}{2}[/tex] × 9 × 8 = 4.5 × 8 = 36 cm² , so
V = 36 × 11 = 396 cm³
x+1=5 wat is this pls answer bozo
Answer:
x = 4
Step-by-step explanation:
x + 1 = 5
- 1 -1
5 - 1 = 4
x = 4
A__________ has a regular polygon base and a vertex over the center of the base.
A. regular pyramid
B. pyramid
C. prism
D. right prism
help me put these numbers from least to greatest 1 1/3, -5/6, 0, -2/3, -1 from least to greatest.
Answer:
-5,6,-2/3,1 1/3,0
Step-by-step explanation:
I think this how it goes try it out or not i need help to
solve the equastion for x + 2 1/2 =10
Answer:
x= 7 1/2
Step-by-step explanation:
Subtract the 1/2 to get it out of the way (whatever you do on one side of the = sign you have to do to the other)
So 10- 1/2= 9 1/2
Subtract the 2 to get it out of the way
9 1/2-2=
7 1/2
Hope it helped :)
If a=2, b=-3, c=4
ab - bc =
After being involved in a car accident last month, ralph’s insurance company has increased his annual premium by $105.38. approximately what change will ralph see on his future monthly statements as a result of the change? a. ralph’s monthly insurance payment will not change. b. ralph’s monthly insurance payment will increase by $8.78. c. ralph’s monthly insurance payment will increase by $17.56. d. ralph’s monthly insurance payment will increase $105.38.
Answer:
B. if it says that the insurence company has increased the price of the plan by a certian amount, then the montly price will increase by a few dollars.
Step-by-step explanation:
Find the length of the third side. If necessary, round to the nearest tenth.
15
13
Pythagorean theorm
Answer:
third side ≈ 19.8
Step-by-step explanation:
using Pyjthagoras' identity in the right triangle.
the square on the hypotenuse x is equal to the sum of the squares on the other 2 sides, that is
x² = 13² + 15² = 169 + 225 = 394 ( take square root of both sides )
x = [tex]\sqrt{394}[/tex] ≈ 19.8 ( to the nearest tenth )
1 ) Old Navy is offering a 20 % discount on all sweaters. If the regular price of a sweater is $45,what is the sale price?
Answer:
Sale Price = $36
Step-by-step explanation:
To find the sale price, you need to find what 10% of the original price is. 10% of $45 is $4.50. Now we need to find what 20% is, 20% is double 10% so we multiply the answer we got by 2. This equals to $9. The question is asking for the sale price, to find it you have to subtract $9 (the discount) from $45 (regular price). The answer you should get is $36.
Equation:
$45 ÷ 10 = $4.50
$4.50 × 2 = $9
$45 - $9 = $36
PLEASE I NEED HELP I HAVE NO IDEA WHAT THE ANSWERS ARE
Answer:
Sector AOB: 3.87
Sector BOC: 7.74
Sector COD: 5.16
Sector DOE: 3.01
Sector AOE: 11.19
Explanation:
Equation used: [tex]S=\frac{r^2*a}{2}[/tex]
What would be the correlation coefficient (r) of the following scatter plot?
Look at the picture down below to answer the question
options:
-.15
.92
-.89
.45
Answer:
-0.89 (i think)
Step-by-step explanation:
Since the graph seems to be going downwards from the right, it has a negative correlation. And since the data seems to be pretty close together, the correlation must be strong. That narrows the answer down to -0.89
If its wrong then i'm not a smart person, and it's -0.15
Use the long division method to find the result when x^3+9x² +21x +9 is divided
by x+3
Answer:
x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0
Step-by-step explanation:
Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:
| | | x^2 | | | |
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
| -(x^3 | + | 3 x^2) | | | |
| | | 6 x^2 | + | 21 x | + | 9
To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:
| | | x^2 | + | 6 x | |
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
| -(x^3 | + | 3 x^2) | | | |
| | | 6 x^2 | + | 21 x | + | 9
| | | -(6 x^2 | + | 18 x) | |
| | | | | 3 x | + | 9
To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:
| | | x^2 | + | 6 x | + | 3
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
| -(x^3 | + | 3 x^2) | | | |
| | | 6 x^2 | + | 21 x | + | 9
| | | -(6 x^2 | + | 18 x) | |
| | | | | 3 x | + | 9
| | | | | -(3 x | + | 9)
| | | | | | | 0
The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.
| | | x^2 | + | 6 x | + | 3 | (quotient)
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |
| -(x^3 | + | 3 x^2) | | | | |
| | | 6 x^2 | + | 21 x | + | 9 |
| | | -(6 x^2 | + | 18 x) | | |
| | | | | 3 x | + | 9 |
| | | | | -(3 x | + | 9) |
| | | | | | | 0 | (remainder) invisible comma
(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0
Write the result in quotient and remainder form:
Answer: Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:
| | | x^2 | | | |
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
| -(x^3 | + | 3 x^2) | | | |
| | | 6 x^2 | + | 21 x | + | 9
To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:
| | | x^2 | + | 6 x | |
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
| -(x^3 | + | 3 x^2) | | | |
| | | 6 x^2 | + | 21 x | + | 9
| | | -(6 x^2 | + | 18 x) | |
| | | | | 3 x | + | 9
To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:
| | | x^2 | + | 6 x | + | 3
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9
| -(x^3 | + | 3 x^2) | | | |
| | | 6 x^2 | + | 21 x | + | 9
| | | -(6 x^2 | + | 18 x) | |
| | | | | 3 x | + | 9
| | | | | -(3 x | + | 9)
| | | | | | | 0
The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.
| | | x^2 | + | 6 x | + | 3 | (quotient)
x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |
| -(x^3 | + | 3 x^2) | | | | |
| | | 6 x^2 | + | 21 x | + | 9 |
| | | -(6 x^2 | + | 18 x) | | |
| | | | | 3 x | + | 9 |
| | | | | -(3 x | + | 9) |
| | | | | | | 0 | (remainder) invisible comma
(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0
Write the result in quotient and remainder form:
Answer: x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0
What is the solution of log subscript 3 baseline (3 x 2) = log subscript 3 baseline (4 x minus 6)?
The solution tothe logarithmic function log₃([3x+2] = log₃(4x - 6) is 8
Law of logarithmGiven the logarithm expression
log(3)[[3x+2] = log(3)[4x - 6]
The logarithm on both sides of the equation will cancel out to have:
3x + 2 = 4x - 6
Collect the like terms
3x - 4x = -6 - 2
-x = -8
x =8
Hence the solution tothe logarithmic function log₃([3x+2] = log₃(4x - 6) is 8
Learn more on logarithm here: https://brainly.com/question/13473114
Answer:
8
Step-by-step explanation:
Which story problem can be answered using the equation below?
2/3x4=8/3
A.
A group of eight friends share 4 pounds of ice cream equally among themselves. How many pounds of ice cream do 3 of them get?
B.
Jason has 2 pounds of berries to share with 3 friends. He divides the berries into 4 equal servings. How many pounds of berries does each person get?
C.
Jessica cuts 4 meters of ribbon into 3 equal parts and uses 2 of these parts to decorate a poster. How many meters of ribbon does she use on her poster?
D.
Adam is hosting a graduation party. He pours 4 cans of juice into 8 glasses equally. How many cans of juice will 3 of these glasses have?
Answer: C
Step-by-step explanation:
4/8 ×3/1
the ribbon or each doll is divided into 3 equal pieces.What is the length in yards of each piece
Answer:
1 yard
Step-by-step explanation:
If the ribbon to begin with is 3 yards then if cut in to 3 pieces each peace would be 1 yard.
Question Five: Rates, Ratios, and proportion
simplify = $450/40 hours
Answer:
$45/4hrs
Step-by-step explanation:
450/40 divide both sides with 10
Candice and Phoebe are traveling on the same
highway in the same direction. Candice is
traveling at 45 mph and is exactly 40 miles
ahead of Phoebe who is traveling at 55 mph.
How many hours will it take Phoebe to catch
Candice?
Using proportions, it is found that it will take 4 hours for Phoebe to catch Candice.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Given their velocities, and the fact that they travel in the same direction, each hour, Phoebe gets 10 mph closer to Candice.
The initial distance is of 40 miles, 40/10 = 4, hence it will take 4 hours for Phoebe to catch Candice.
More can be learned about proportions at https://brainly.com/question/24372153
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PLS PLS HELP ME
76. In five successive hours, a car travels 40 km, 45
km, 50 km, 35 km and 55 km. In the next five
hours, it travels with an average speed of 50 km
per hour. Find the total distance the car traveled
in 10 hours.
a. 425 km
b. 450 km
c. 475 km
d. 500 km
Answer:
475 km
Step-by-step explanation:
(40 + 45 + 50 + 35 + 55 km + 50 *5 km)
mr richey bought 20 organizer books and 20 staplers for students. each stapler costs 3$. mr richey spent in total of 200$ for the organizer books and staplers. what is the cost, in dollars of 1$ organizer book
Answer: $7
Step-by-step explanation: if a stapler cost $3, then 20staplers will cost $60
Amount left will be $200-60=$140
Cost of one organiser will be $140/20
That will be $7
PLEASE HELP IM TIMES
Answer:
k = 60°
Step-by-step explanation:
y and z are parallel with each other against x line.
So we can make (2k+11)° = 131° and then solve for k.
2k + 11 = 131°
2k = 131° - 11°
2k = 120°
k = 60°
X+2/3x=180
What is the value of x?
Answer:
[tex]x = \frac{2}{539} [/tex]
Step-by-step explanation:
[tex] \frac{x + 2}{3x} = 180[/tex]
[tex]180(3x) = x + 2[/tex]
[tex]540x = x + 2[/tex]
[tex]540x - x = 2[/tex]
[tex]539x = 2[/tex]
[tex] \frac{539x}{539} = \frac{2}{539} [/tex]
[tex]x = \frac{2}{539} [/tex]