The common difference in the arithmetic sequence is 2.5
What is arithmetic sequence ?
Arithmetic sequence is a sequence in which the differences between consecutive terms are always same.
Example : 2, 5, 8, 11, ..... is an arithmetic sequence where the common difference is 3.
What is the formula of arithmetic sequence ?Formula of arithmetic sequence is [tex]a_{n} =a_{1}+(n-1)d[/tex] ,
where [tex]a_{n}[/tex]= [tex]n^{th}[/tex] term in the sequence,
[tex]a_{1}[/tex]= [tex]1^{st}[/tex] term in the sequence,
d = common difference between terms
How to find required common difference ?Given, [tex]a_{1}[/tex] = 16 and [tex]a_{9}[/tex] = 36
Let, d be the common difference.
∴ From the formula of arithmetic sequence,
[tex]a_{9} =a_{1}+(9-1)d[/tex]
⇒ 36 = 16+8d
⇒ 36-16=8d
⇒ 20=8d
⇒ d = 20/8
⇒ d = 5/2 = 2.5
Hence, The common difference is 2.5
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Three geometric sequences are given below.
Sequence A: 160, 40, 10, 2.5, ...
Sequence B: -21, 63, -189, 567, ...
Sequence C: 8, 12, 18, 27, ...
Order the sequences from least common ratio to greatest common ratio.
Sequence A
Sequence C
Sequence B
Answer:
B, A, C
Step-by-step explanation:
Calculating the common ratio for each sequence
A → r = [tex]\frac{40}{160}[/tex] = [tex]\frac{1}{4}[/tex] = 0.25
B → r = [tex]\frac{63}{-21}[/tex] = - 3
C → r = [tex]\frac{12}{8}[/tex] = 1.5
B, A, C ← from least to greatest common ratio
Find the surface area of the cereal box.
cm
20 cm
3 cm
10 cm
Answer:
580 cm squared
Step-by-step explanation:
surface area = 2LW + 2LH + 2HW
or 2(20)(3) + 2(20)(10) + 2(3)(10)
What is the solution to the equation 5 x = 32?
a. x = 6
b. x = 6.4
c. x = 27
d. x = 160
Answer
x = 32/5 = 6.400
Answer is B
Step-by-step explanation:
1: Rearrange
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
Solving a Single Variable Equation
Solve : 5x-32 = 0
Add 32 to both sides of the equation :
5x = 32
Divide both sides of the equation by 5:
x = 32/5 = 6.400
The correct answer is B.
Answer: x = 32/5 = 6.400
Hope this helps.
Answer:
B
Step-by-step explanation:
5x=32 move the 5 over by dividing
x=5/32. 5 divided by 32 equals 6.4
so x=6.4
Suppose an investment of $500 doubles in value every 15 years. How much is the investment worth after 30 years? After 45 years?Write an equation and solve
Answer:
Step-by-step explanation:
well all you have to do is 500 dollars times two, because it times each 15 years right and 30/15=2. So you do $500*2 which is $1000. And you get $1500 in 45 yrs.
So the equations are for each 15 yrs you add 500 dollars to the amount.
Kent multiplies both sides of the equation below by an expression. k + StartFraction 12 Over k EndFraction = 8 Then he moves all the terms to one side of the equal sign in the resulting equation. Which equation must he solve now? k squared minus 8 k minus 12 = 0 k squared + 8 k + 12 = 0 k squared minus 8 + 12 = 0 k squared minus 8 k + 12 = 0
Answer:
k^2-8k+12=0D
Step-by-step explanation:
Explanation:
1) Given equation:
k+12/k=8
2) Multiplication property of equality:
k(k+12/k)=8k
3) Distributive property:
k^2+12k/k=8k
4) Simplification:
k^2+12=8k
5) Subtraction property of equality:
k^2-8k+12=0
Answer:
k^2-8k+12=0D is correct
Step-by-step explanation:
If the cost to fill the pool is $2.55 per cubic foot, how much will it cost to fill the pool?
Can someone help me with this please, I need to get this thing done?
Answer:
The answer is B (9)
Step-by-step explanation:
Count the distance.
The point (0, 5) lies on a circle that is centered at the origin. Does (–3, –4) also lie on the circle? Identify the radius from the graph. r = units Determine the distance from the center to (–3, –4) using the distance formula. distance = units Compare the radius to the distance. Does the point (–3, –4) also lie on the circle?
Answer:
The point (0, 5) lies on a circle that is centered at the origin. Does (–3, –4) also lie on the circle?
Identify the radius from the graph.
r = 5 units
Determine the distance from the center to
(–3, –4) using the distance formula.
distance = 5 units
Compare the radius to the distance. Does the point (–3, –4) also lie on the circle? yes
i hope this helps :) i got it from e2020
Answer:
5
5
yes
Step-by-step explanation:
The point (0, 5) lies on a circle that is centered at the origin. Does (–3, –4) also lie on the circle?
Identify the radius from the graph.
r = ✔ 5 units
Determine the distance from the center to
(–3, –4) using the distance formula.
distance = ✔ 5 units
Compare the radius to the distance. Does the point (–3, –4) also lie on the circle?
✔ yes
An angle in standard position has a terminal side that passes through (-1, -1). Choose all of the functions that will be negative for the angle.
tan
csc
sin
sec
cot
cos
Answer:
Tan
Step-by-step explanation:
find the area of each figure . only 3 questions !
Answer:
(1) 391, (2)663, (3)12
Step-by-step explanation:
1. rectangle area formula = height * width
17 * 23 = 391
2. parallelogram area formula = height * base(or width)
17 * 39 = 663
3. parallelogram area again
8 * 1.5 = 12
If 24 pencils cost $1.20 then how much does one pencil cost?
Answer:
$0.05
Step-by-step explanation:
1.20 divided by 24
Answer:
The cost is $.05 or 5 cents per pencil
Step-by-step explanation:
Take the cost and divide by the number of pencils
1.20 /24
.05
The cost is $.05 or 5 cents per pencil
A right triangle has a height of 20 cm and a base of 10 cm. What is the area of the triangle? (A = 1/2 bh)
Answer:
100 because its way too ez
Answer:
A = 100
Step-by-step explanation:
A = bh/2
A = 20(10)/2
A = 200/2
A = 100
PLSSS HELP ME PLS GET THE RIGHT ANSWER
Answer:
hey you single lmf.aoooooo
help asap thank youu
Answer:
Yes
Step-by-step explanation
Linear means no exponents i believe i hope this is right and i help if its not im soooooo sorry :)
What is the answer? Please help!
Answer:
It is the second answer!
Step-by-step explanation:
6+24-6854+21=????????
Answer:
-6803
Step-by-step explanation:
Answer:
6 + 24 - 6854 + 21 = -6803
Step-by-step explanation:
hi ryan
Savings: It is important to pay yourself first in the form of putting money into your savings account. Each paycheck, deposit 10% of your take home pay into your savings account.
Amount deposited every week into savings: __________________
How much will then go into your checking account: ______________
Answer:
10%of the savings
Step-by-step explanation:
have a great day :)
What is the probability that a blue marble is selected, given that it is large?
Answer:
P(blue given large)=1/2
Step-by-step explanation:
Marble being blue=1/4
Large Marble=2/5
Both blue and large=1/5
2/5x=1/5
x=1/5*5/2
x=1/2
Therefore, 1/2
Braniest and Extra Points will be given!!!!! Choose an option from both parenthesis!!!
In order to use the Pythagorean Theorem, you must know the length or lengths of (all three sides/any 2 sides/any side) of the triangle and know that the measure of one of the angles is (greater than 90°/exactly 90°/less than 90°) .
Answer:
a) Any 2 sides
b) exactly 90°
Step-by-step explanation:
The point of the Pythagorean Theorem is to find the length of the hypotenuse using 2 sides.
This only works for right triangles.
Hope this helps!
-MoCKEry
Answer:
1) any two sides
2)exactly 90 degrees
Step-by-step explanation:
1) The pythagorean theorem only applies to right angle triangles
since right angle triangles measure 90 degrees exactly we will choose exactly 90 as an option.
2) so the formula for pythagorean theorem is a^2+b^2=c^2 where
a=side 1
b= side 2
c=hypotenuse(biggest side)
to find the hypotenuse you need to know both the values of a and b hence we will take the option "any two sides"
Each cube in this figure measures 1 foot on each side.
What is the volume of this figure?
45 ft³
80 ft³
200 ft³
300 ft³
A rectangular prism made up of unit cubes. There are 8 layers, and each layer is 5 units long and 5 units wide.
A total of 426 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the
number of adult tickets sold. How many adult tickets were sold?
I hope this helps you
a bag is filled with 4 red marbles, 3 blue marbles,3 yellow marbles, and 2 green marbles. you randomly choose one marble from the bag. (a) find the number of ways the event can occur. (b) find the favorable outcomes of the event
Answer:
a. 12
b. it depends on the color of the marble.
Step-by-step explanation:
In this case the number of ways would be the number of events, in this case the events would be the total number of marbles since any of them can come out. so:
4 + 3 + 3 + 2 = 12
Therefore, the number of ways the event can occur is 12 ways.
Now, in the favorable outcomes of the event, it would come depending on what color the marble would be, whether it be red, blue, yellow or green.
In each color, the number of the favorable outcomes of the event would be the quantity of each marble, that is, 4 for red, 3 for blue, 3 for yellow and 2 for green.
A point is selected at random inside the given figure. What is the probability the point will be in the region labeled B? Enter your answer, as a fraction in simplest form, in the box. The figure is a rectangle that is made up of three rectangles and one square. The rectangles are labeled A, B, and D, and the square is labeled C. Rectangle A is in the upper left portion of the large rectangle. The left side of rectangle A is labeled 5 inches and it is part of the left side of the large rectangle. Rectangle B is in the lower left portion of the large rectangle below rectangle A. The lower side of rectangle B is labeled 3 inches and makes up a part of the lower side of the large rectangle. Rectangle D makes up the right side of the large rectangle and is to the right of rectangle A. The upper side of rectangle D is labeled 3 inches and makes up a part of the upper side of the large rectangle. The right side of rectangle D makes up the entire right side of the large rectangle. Square C lies below rectangle A and between rectangles B and D. The lower side of square C is labeled 4 inches and makes up part of the lower side of the big rectangle. The right side of square C is also labeled 4 inches.
Answer:. 12/90. Or about 13.3%
Step-by-step explanation: If I interpreted your description correctly, and put the dimensions in the correct places, the large rectangle has an overall width of 10 inches and length of 9 inches. The Total Area is 90 sq in.
The rectangle Region B is 3 (given) by 4 (assumed from shared side with the given square) . So the Area of region B is 12 sq in.
The chance of randomly selecting a point is the ratio of the Area of the selected region to the Total Area. In this example, it's 12/90, simplified to 2/15 or about 13.3%
Select the correct answer from each drop-down menu.
Which system of equations is represented by this graph?
Answer:
2 for first answer
-1/2 for second
Step-by-step explanation:
First line starts on positive 3 then goes down 2 left 1 -2/-1=2
what is the zero of the function below?
f(x)=3x-15
A. -15
B. 0
C. 5
D. 3
Answer:
x = 5 (Answer C)
Step-by-step explanation:
Set f(x) = 3x - 15 = to 0 and solve for x:
3x - 15 = 0
Adding 15 to both sides isolates 3x:
3x = 15
Dividing both sides by 3 yields x = 5 (Answer C)
Find the mean absolute deviation (MAD) of the data in the pictograph
Answer:
1.5
Step-by-step explanation:
First, find the mean (average) of the data set.
mean = (x1 + x2 + ...)/N
where x1, x2, ... are the data points, and N the total amount of data points.
mean = (7 + 2 + 4 + 3)/4 = 4
Then, mean absolute deviation is computed as follows:
MAD = (|x1 - mean| + |x2 - mean| + ...)/N
MAD = (|7 - 4| + |2 - 4| + |4 - 4| + |3 - 4|)/4
MAD = (3 + 2 + 1)/4 = 1.5
Answer:
1.5
Step-by-step explanation:
your welcome
What is |a| + |b + c| when a = - 4 , b = 2 , and c = - 7 ?
Answer:
9
Step-by-step explanation:
Rule => if ''a'' is negative, |a| = -a|0| = 0absolute value means how far a number from 0if we don't know anything about x,and x equals to a. We can say |x| = a and |-x| = a....So , x or -x equals a . But both of x aren't equals a, one of them is same|a| + |b + c| = |-4| + |2 + (-7)|
|-4| = -(-4) = +4
|2 + (-7)| = |-5|
|-5| = -(-5) = +5
4 + 5 = 9
Hope this helps ^-^
help!!!!!!!
I will make you brainliest
Answer:
Step-by-step explanation:
(a) The appropriate formula is C = 2πr. Here r = 14 cm, so
C = 2π)14 cm = 28π cm, or (if we take π to be 22/7), C = 88 cm²
(b) We use the same circumference formula: C = 2πr and solve it for r before inserting numeric values:
C 132 m 7(132 m)
r = -------- and in this case, r = ------------------- = ------------- = 21 m
2π [ 2 * (22/7) ] 44
what is the volume of the cylinder
Answer:
Step-by-step explanation:
volume =πr²h=π×4²×8=128π in³
What is an easy way to remember what a dot plot is?
Answer:
Its a place where you can park your dot.
Step-by-step explanation: