Answers
First note that [tex]A_n[/tex] means the nth term in the sequence.
1. First one is a simple arithmetic progression/sequence as the common differences between each two numbers are 1
So the sequence will be
1.) 2,3,4,5,6,7...
And the rule since its +1 each time will be
[tex]A_n=2+1*(n-1)[/tex]
For the nth term of the sequence.
2.This one can be seen as a simple geometric sequence as the common ratio between the number and the number after it is 1:2
So the sequence will be
2.)2,4,8,16,32,64
And the rule since it is *2 each time is a simple exponential function
[tex]A_n=2*2^{n-1}\\or\\A_n=2^n[/tex]
3.This one is tricky but it can be seen that the term is double the term before subtract 1
So the sequence will be
3.)5,9,17,33,65,129
And the rule based on this sequence will be
[tex]A_n=A_{n-1}*2-1[/tex]
**Please note that this rule specifically is written in recursive form as it is a lot more difficult otherwise.
4 This one is similar to problem 1 which is an arithmetic sequence this one just have a common differences of 3 instead of 1.
So the sequence will be
4.)25,28,31,34,37
And the rule based on the sequence will be
[tex]A_n=25+3*(n-1)[/tex]
I hope this helps and if you don't understand any part of my explanation I would gladly help!
Related Questions
Decreasing 3/4 times a number by 18 is equal to increasing 1/2 times the number by 5 give an equation and solution to the situation.
Please help me out on this problem thank you!!!!!!
Answers
Answer:
solved below.Explanation:
[tex]\sf \frac{3}{4} x-18 = \frac{1}{2} x +5[/tex]collect variables:
[tex]\sf \frac{3}{4} x - \frac{1}{2} x = + \ 5 + 18[/tex]simplify:
[tex]\sf \frac{1}{4} x = 23[/tex]final answer:
[tex]\sf x = 92[/tex]Add 2/10 +36/100 =
Write each sum as fraction with a denominator of 100 and as a decimal
Answers
Answer:
56/100 or 0.56
Step-by-step explanation:
you first need the dinominators to be the same so to figure that at you can do 100 divided by 10 which is 10. so to make the doniomators even you need to multipy the 2/10 by 10. so 2x10=20 and 10x10=100 so that makes the fraction 20/100. now you have 20/100 + 36/100 =? which makes it a lot easier. so now all you do is add ONLY THE NUMERATOR so you do 20+36 which is 56 and you keep the 100 and that 56/100.
To make it into a decimal, this one is easy because the denominater is 100 so you just take 56.0 and move the decimal two place values so its 0.56. :)
simplify 2 2/5 x 1 2/5
A. 8/25
B. 84/25
C. 2 4/25
D. 3 9/25
please hurry due in 11 min!!!
Answers
Answer:
84/25
Step-by-step explanation:
3.
What is the value of the expression below when a = 3 and b = 5?
8a^2– 6b + 10
Answers
Answer: 52
Step-by-step explanation:
We can plug in the values for a and b.
= 8*3^2 - 6*5 + 10
= 72 - 30 + 10
= 42 + 10
= 52
Answer:
52
Step-by-step explanation:
Start by substituting the given values into the expression:
[tex]8a^2-6b+10\\8(3^2)-6(5)+10\\\text{Solve the expression}\\8(9)-30+10\\72-30+10\\42+10\\52[/tex]
Remember Order of Operations:
Parentheses
Exponents
Multiplication/Division (Whichever comes first)
Addition/Subtraction (Whichever comes first)
Only 12 people can ride a trolley at one time. This is 20% of the people waiting to ride. How many people are waiting to ride?
Answers
Answer:
2 people are waiting if you want a whole number
explanation:
12=20%(x)
reverse operations
12/.20=x
x=60
An employee works as a teacher at an online school making $38,900 per year. However, the school is hiring a principal at a salary of $59,500 per year.
The employee went back to school to become a principal.
How much more money could the employee make working as a principal instead of a teacher over 5 years?
Enter your answer in the box
Answers
Answer:
$103,000
Step-by-step explanation:
teacher : 38,900 x 5 = 194,500
principal : 59,500 x 5 = 297,500
$297,500 - $194,500 = $103,000 more
What values of x make 3 - 4x > 17 true?
Answers
Answer: x < -3.5
Step-by-step explanation:
Subtract 3 from both sides and we get
-4x > 14
We divide -4 on both sides, but be careful because we have to flip the sign since it's a negative number.
x < -3.5
Ms. Ashley planned to stay at a hotel that charges $88 per night for a room and $20 per night in fees and taxes. She used this expression to calculate the total cost of staying in the hotel for n nights. 88n 20n
Answers
Step-by-step explanation:
Since 88 is for one night and 20 per night in fees and taxes.
Step 1 : Calculate for $88
[tex] \frac{88n}{88} \\ [/tex]make N the subject of formula
[tex]n = \frac{88}{88} \\ [/tex]
N= 1
Step 2: Calculate for $20
[tex] \frac{20n}{20} \\ [/tex]
make N the subject of formula
[tex]n = \frac{20}{20} [/tex]
N = 1
Which is a better deal? Three packs of gum for 5 dollars or 9 packs of gum for 14 dollars? HOW DO YOU KNOW?
Answers
Answer:
9 for 14 is slightly less expensive, but for convenience 3 for 5 is better
Step-by-step explanation:
5/3=1.(6)
14/9=1.(5)
1. what is the y-intercept of this line?
2. what is the slope of this line?
3. what is the equation for this line?
Answers
Step-by-step explanation:
1. The y-intercept is the value for y when x = 0.
When x = 0, y equals 7.
Represented as:
(0, 7)
2. How to find the Slope?
Find 2 points on the graph then use the slope formula.
[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]
m = slope
2 points:
(0, 7)
(2, 3)
Substitute the points into the formula:
[tex] \frac{3}{2} - \frac{7}{0} = m[/tex]
Subtract:
[tex] \frac{ - 4}{2} = m[/tex]
[tex] \frac{ - 4}{2} = m[/tex]Simplify:
[tex] \frac{ - 4 \div 2}{2 \div 2} = - \frac{2}{1} [/tex]
The slope is -2.
Forming an equation:
Use the slope-intercept format.
[tex]y = mx + b[/tex]
m = slope
b = y-intercept
Substitute 7 for b, and -2 for m.
[tex]y = - 2x + 7[/tex]
Finding Circumference The radius is cm. v cm OZ The circumference in terms of ais Using 3.14 for A, the approximate circumference of the circle is cm. d=2cm
Answers
Answer:7picm Circumference = pi x d Diameter = 7 C = pi x 7 C = 7pi cm.
Step-by-step explanation:
The circumference of the circle with diameter 2 cm is 6.28 cm.
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given that a circle has a diameter of 2 cm we need to find its circumference,
The circumference of a circle is given by, π × diameter
Therefore, the circumference of the circle with diameter 2 cm =
= π × diameter
= π × 2
= 3.14 × 2
= 6.28 cm
Hence, the circumference of the circle with diameter 2 cm is 6.28 cm
Learn more about circles, click;
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What is the missing numbers in the synthetic division problem below?
Answers
Answer:
A. 9
Explanation:
2×4=8 and 8+1=9 so that's it.
Write and solve a word problem that requires multiplying two mixed numbers.
Answers
Answer:
Jack ate two and a half pieces of a pie. Amy ate one and three fourth pieces of a pie. How much pie did they eat altogether?
Step-by-step explanation:
Jack ate 2 1/2 pie
Amy ate 1 3/4 pie
2 1/2 + 1 3/4 = 4 1/4
They ate four and one-fourth pieces of pie altogether.
Madison is buying a laptop for $586. He paid for the laptop
using four $100 bills, fifteen $10 bills and forty-six $1 bills. How
much did Madison pay?
Answers
Small batteries are sold in packs of 8. Mr. Winn bought 4 packs and Mrs. Winn bought 6 packs. Which expressions show how many batteries the Winn family purchased? Select all that apply.
a. 8(4) + 8(6)
b. 8(4) ⋅ 6
c. 6(4 + 8)
d. 8(4) + 6(4)
e. 8(4 + 6)
Answers
There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.How many kids own their own instruments?
Answers
Answer:
18 kids
Step-by-step explanation:
because you multiply 0.2 by 90 and it equals 18
The sum of two numbers is 16. One number is 2 less than the other. Find the numbers
Answers
Answer:
9+7=16
Step-by-step explanation:
An open box with a square base is constructed so that it has a volume of 64in^3. The base needs to be made out of a material that costs twice as much as the sides. What are the dimensions of the box, what are the dimensions of the box x and y (x being the width and depth of the square dimensions, and y being the height of the box) which will minimize the cost of the box?
Answers
The volume of a box is the amount of space in the box
The dimensions that minimize the cost of the box is 4 in by 4 in by 4 in
How to determine the dimensions that minimize the costThe dimensions of the box are:
Width = x
Depth = y
So, the volume (V) is:
[tex]V = x^2y[/tex]
The volume is given as 64 cubic inches.
So, we have:
[tex]x^2y = 64[/tex]
Make y the subject
[tex]y = \frac{64}{x^2}[/tex]
The surface area of the box is calculated as:
[tex]A =x^2 + 4xy[/tex]
The cost is:
[tex]C = 2x^2 + 4xy[/tex] --- the base is twice as expensive as the sides
Substitute [tex]y = \frac{64}{x^2}[/tex]
[tex]C = 2x^2 + 4x * \frac{64}{x^2}[/tex]
[tex]C =2x^2 + \frac{256}{x}[/tex]
Differentiate
[tex]C' =4x - \frac{256}{x^2}[/tex]
Set to 0
[tex]4x - \frac{256}{x^2} = 0[/tex]
Multiply through by x^2
[tex]4x^3 - 256= 0[/tex]
Divide through by 4
[tex]x^3 - 64= 0[/tex]
Add 64 to both sides
[tex]x^3 = 64[/tex]
Take the cube roots of both sides
[tex]x = 4[/tex]
Recall that:
[tex]y = \frac{64}{x^2}[/tex]
So, we have:
[tex]y = \frac{64}{4^2}[/tex]
[tex]y = 4[/tex]
Hence, the dimensions that minimize the cost of the box is 4 in by 4 in by 4 in
Read more about volume at:
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Answer the following
Answers
Answer:
14
sorry if i need any.
Step-by-step explanation:
9-8=1 + 13 = 14
what is the Estimate 26% of 84.
Answers
Answer: 26% of 84 is 21.84
Step-by-step explanation:
0.26 * 84 = 21.84
Answer:
26%
of
84
=
21
Step-by-step explanation:
nwhsk sgswke dydownegsownsgsos isbstwkw
4
3
С
2
1
In the similarity
transformation of AABC
to ADEF, AABC was dilated by
a scale factor of [?], reflected
across the [ ], and moved
through the translation [ ].
B.
A
-7
-6
-5
-4
-2
-1 0
1
2
3
+
E
D
-2
-3
F
A. 2
B. 1/2
C. 3
D. 1/3
Answers
Answer: A
Step-by-step explanation:
Since DE=4 and AB=2, we know the scale factor of the dilation was 4/2 = 2.
new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.
a Find the probability that the employee is idle.
Answers
The probability that the employee is idle in the shopping mall based on the information given will be 0.33.
How to calculate probability?From the information given, it is believed that people will arrive at the desk at a rate of 20 per hour and that it takes an average of 2 minutes to answer a question.
Therefore, the probability that the employee is idle will be:
= 1 - (20/30)
= 1 - 0.67
= 0.33
Therefore, probability that the employee is idle is 0.33.
Learn more about probability on:
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Solve the follow inequality. ∣3x−4∣≥8
Answers
Hello.
Let's solve the absolute value inequality.
In order to do that, let's imagine that |3x-4| is positive.
Since the absolute value of |3x-4| is 3x-4, we write 3x-4 and solve:
[tex]\mathrm{3x-4\geq 8}[/tex]
Now, move -4 to the right, using the opposite operation:
[tex]\mathrm{3x\geq 8+4}[/tex]
Add:
[tex]\mathrm{3x\geq 12}[/tex]
Divide both sides by 3:
[tex]\mathrm{x\geq 4}[/tex]
However, this is only 1 solution.
Let's imagine that |3x-4| is a negative number.
So, the inequality looks like so:
[tex]\mathrm{-3x+4\geq 8}[/tex]
Move 4 to the right:
[tex]\mathrm{-3x\geq 8-4}[/tex]
[tex]\mathrm{-3x\geq 4}[/tex]
Divide both sides by -3:
[tex]\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
Therefore, the solutions are
[tex]\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
[tex]\bigstar[/tex] Note:
If we divide both sides of an inequality by a negative number, we flip the inequality sign.
I hope this helps you.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
First step- Add 4 to both sides
Simply-3x>=12
Divide both sides by 3- 3x/3 12/3
X>=4 is final answer
Hank is painting houses this summer. He can paint 7 houses in 5 weeks. At this rate, how many houses did he paint in 18 weeks?
Answers
[tex]\begin{array}{ccll} houses&weeks\\ \cline{1-2} 7&5\\ x&18 \end{array}\implies \cfrac{7}{x}=\cfrac{5}{18}\implies 126=5x \\\\\\ \cfrac{126}{5}=x\implies 25\frac{1}{5}=x[/tex]
Pls help me and thanks rounding
Answers
Answer:
Step-by-step explanation:
1399 rounds to 1400 so A is not the answer
1449 rounds to 1400 so B is not the answer
1589 rounds to 1600 so D is not the answer
The hundreds place is second from the left. Third from the left determines what happens to second from the left. 5 and over round up. Less than 5 just use the first 2 digits left and 2 zeros.
The answer is C
1457 rounds to 1500
1547 rounds to 1500
What is the exact volume of the cone
Answers
Answer:
V = [tex]\frac{400}{3}[/tex][tex]\pi[/tex]
Step-by-step explanation:
Volume of a cone is:
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
Substitute values given:
[tex]V = \pi (5^{2} )(\frac{16}{3})[/tex]
[tex]V = \pi (25)(\frac{16}{3} )[/tex]
V = [tex]\pi \frac{400}{3}[/tex]
V = [tex]\frac{400}{3}[/tex][tex]\pi[/tex]
What is the surface area?
32 cm
11 cm
15 cm
Answers
Answer:
(rectangular prism) Opposite sides are equal;
Area of bottom base:-
11 x 15 = 165
Above base, (165 x 2) = 330
Area of front:-
15 x 32 = 480
Area of back, (480 x 2) = 960
Area of left side:-
11 x 32 = 352
Area of right side, (352 x 2 ) = 704
Add the sums of all the areas;
330 + 960 + 704 = 1,994 square cm
3x - 2 + x + 8 = -(9x + 7
=
- 2(9x + 7 - x + 5)
1 (8x + 12)
4x + 6 =
2
4x + 6 = 4x + 6
4x + 6 = 4x - 6 = 4x + 6 - 4x - 6
0=0
Is this correct?
Answers
Answer:
no
Step-by-step explanation:
3x−2+x+8=−9x−7
4x+6=−9x−7
4x+6+9x=−7
13x+6=−7
13x=−13
x=−1
Round 385,497 to the nearest thousand.
Answers
Answer:
385,000
Step-by-step explanation:
As an apprentice to a chef you are preparing a recipe that says to bake the dish for 3/4 of a hour how many minutes should you bake the dish?
Answers
You should bake the dish for 45 minutes.
Explanation:
So you have 60 minutes in an hour and if you divide that in 4 you get 15. And for the last step you add 15 three times or just multiply 15*3 and get 45.
Hope this helps :D
