The average rate of change of the sequence from n = 2 to n = 4 is 1.5, which is determined by calculating the difference in sequence values for these n values and dividing by the difference in n.
The average rate of change of a function between two points reflects the function's slope between those points. To find the average rate of change of the sequence [tex]a_n = \frac{1}{2} (2)^{n - 1}[/tex]from n = 2 to n = 4, we calculate the differences in the sequence values corresponding to these n values and divide by the difference in n itself.
The value of a_n when n = 2 is [tex]a_2 = \frac{1}{2} (2)^{2 - 1}= 1.[/tex]The value of a_n when n = 4 is [tex]a_4 = \frac{1}{2} (2)^{4 - 1}[/tex]= 4.To find the average rate of change, use the formula: rate of change = [tex](a_4 - a_2)[/tex] / (4 - 2) = (4 - 1) / (4 - 2) = 3/2 = 1.5.Therefore, the average rate of change between n = 2 and n = 4 for this sequence is 1.5.
In one city, 3,546 people attended a concert but in another city, 9,238 people attended the same band's concert. Estimate how many more people attended the concert in the second city by rounding to the nearest hundred and then subtracting.
Approximately 5,700 more people attended the concert in the second city.
To estimate how many more people attended the concert in the second city, we can round the attendance numbers to the nearest hundred and then subtract the smaller number from the larger one. For the first city, 3,546 people rounds off to 3,500 people, and for the second city, 9,238 people rounds off to 9,200 people. Now we subtract the rounded number of the first city from the rounded number of the second city.
So, 9,200 (rounded attendance in the second city) minus 3,500 (rounded attendance in the first city) equals 5,700.
Therefore, approximately 5,700 more people attended the concert in the second city.
help help help!!!ill return
If c=3k+4 and d=7+9k^2, what is d in terms of c?
Answer:
d = (c -4)² +7 = c² -8c +23
Step-by-step explanation:
Both 'c' and 'd' are expressed in terms of the variable k. In general, that variable is eliminated by writing k in terms of 'c' or 'd', then substituting for k in the other equation.
Eliminating kWe recognize that the 9k² term in the expression for 'd' is the square of the 3k term in the expression for 'c'. That means we don't have to solve for k; we only need to solve for 3k. The equation for 'c' gives an easy way to do that.
c = 3k +4
c -4 = 3k . . . . . . . subtract 4 to get an expression for 3k
Substituting into the equation for 'd', we have ...
d =7 +9k²
d = 7 +(3k)² . . . . . writing 9k² in terms of 3k
d = 7 +(c -4)² . . . . substituting for 3k. This is d in terms of c.
This can be simplified to ...
d = c² -8c +23 . . . . another form of d in terms of c.
To express 'd' in terms of 'c', solve the first equation for 'k' and substitute this value into the second equation. This yields: d=7+((c-4)^2)/3.
Explanation:To express d in terms of c, we first need to make k the subject of c=3k+4. We do this by subtracting 4 from both sides, getting c-4=3k, and then dividing both sides by 3, which gives us k=(c-4)/3. Next, we substitute this value of k into the second equation: d=7+9k^2. Substituting, we get d=7+9*((c-4)/3)^2, which, when simplified, gives the result d=7+((c-4)^2)/3. This is the expression for d in terms of c.
Learn more about Equation substitution here:https://brainly.com/question/10852714
#SPJ12
EMERGENCY PLEASE HELP REALLY HARD!
The first and fourth terms of a geometric sequence are shown.
−2,___ , ___, 128
What are the second and third terms of this geometric sequence?
mario earns money mowing his neighbors lawns the revenue for mowing x lawns is r(x)=25x marios cost for gas and the mower rental is c(x)=6x+15 his profit from mowing x lawns is p(x)=(r-c)(x) what is p(x)
Answer:
p(x) = 19+15
Step-by-step explanation:
Last one give me the best answer
A spherical balloon is inflated until its diameter is 24 in. Air is then released from the balloon until its diameter is 18 in. Approximately many cubic inches of air were released from the balloon?
formula: V =4π(r^3)/3 **make sure you use the radius and not the diameter**
Answer:
4182 is ur answer
Step-by-step explanation:
A box of candy contains 6 lemon, 3 orange, and 4 cherry pieces. If you select a piece of candy at random, what is the probability that you select an orange OR a cherry piece?
A high-speed elevator can rise 480 feet in 30 seconds. Which expression represents the rate, in feet per minute, of the elevator?
a- 480 × 30
b- 480 ÷ 30
c- 480 × 0.2
d- 480 ÷ 1/2
16x-10y=10
-8x-6y=6
can someone help me understand this question?
Suppose two fractions are both less than 1. Can their sum be greater than 1? greater than 2?
How did convenience store there is a 25% chance as customer enters the store within one minute of closing time describe the complementary and find this probability
2x+3(x-4)=8
Solve the equation
Find the AREA of this triangle
I need the answer for B! whoever answers first will get a brainliest, a thanks, and 50 points! also plz tell me how you got the answer
i need really need help please
what is 9.03×10^2 in standard form
The value of the exponent number in standard from is A = 903
What is Exponential Form?The exponential form is an easier way of writing repeated multiplication involving base and exponents. It has a base and a power
The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1.
It is often used in mathematics and science to represent large or small numbers more efficiently. It can also be used to simplify certain mathematical operations, such as multiplication and division, by using the properties of exponents.
Given data ,
Let the exponential form of the number be A
Now , the value of A = 9.03×10²
To convert 9.03×10² to standard form, we need to multiply the number by the appropriate power of 10 so that it is expressed as a number between 1 and 10.
Starting with 9.03×10² , we can move the decimal point two places to the right to get:
9.03×10^2 = 903
So the standard form of 9.03×10² is simply 903
Hence , the standard form is A = 903
To learn more about exponential form click :
https://brainly.com/question/29337692
#SPJ2
MATH HELP PLEASE WILL GIVE BRAINLIEST!!
What is the trigonometric ratio for cosN ?
Enter your answer, as a simplified fraction, in the boxes.
Given is a Right triangle LMN with right angle at M i.e. angle M = 90 degrees.
Given are the sides LM = 15, MN = 36, and LN = 39.
It says to find cos(N) = ?
So opposite side would be LM, adjacent side would be MN, and LN is the hypotenuse.
We know about the "Soh-Cah-Toa" rule in which cosine ratio is given by :-
[tex] cos(N) = \frac{Adjacent}{Hypotenuse} \\\\
cos(N) = \frac{MN}{LN} \\\\
cos(N) = \frac{36}{39} \\\\
cos(N) = \frac{12}{13} [/tex]
Hence, final answer is [tex] cos(N) = \frac{12}{13} [/tex].
Are these correct please help
rectangle abcd is similar to rectangle pqrs. given ab=14 cm, BC=8cm and pq=21cm, calculate the length of QR
The length of QR in rectangle PQRS is 12 cm, found by setting up the proportional relationship 14/21 = 8/QR, where 14 cm and 8 cm are the lengths of sides AB and BC of rectangle ABCD, respectively, and 21 cm is the length of side PQ of rectangle PQRS.
Since rectangle ABCD is similar to rectangle PQRS, their corresponding sides are proportional. To find the length of QR, we will set up a proportion using the given lengths:
AB/PQ = BC/QR
Substituting the given lengths:
14/21 = 8/QR
Now, solve for QR:
QR = (21 * 8) / 14
QR = 168 / 14
QR = 12 cm
So, the length of QR in rectangle PQRS is 12 cm.
find the diameter of a circle with an area of 226.98
A student solved this problem by working backward. Janice went shopping with her mom and at the end of the day she had $59.50 left over. She spent $13.65 on a T-shirt, $22.99 on some new sandals, and $40.75 on a new skirt. How much money did Janice have at the beginning? Student's solution - Janice had $59.50 left. Add up all the amounts she spent ($13.65 + $22.99 + $40.75) and add to the amount she has left over ($77.39 + $59.50). So Janice had $136.89 to begin with. Solve this problem. Dale was fixing his fence. At the end of the day, he had 12.5 feet of wood left over. During the day he had used one 3.5 foot long piece of wood, two 5.9 foot long pieces of wood, and one 10 foot long piece of wood. How many feet of wood did Dale have at the beginning of the day? feet
Need this answered today also explain the answers please
Julia measured the high temperature in her town for one week. Using the chart below, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth. Be sure to show your work for finding:
the mean of the set of data
the distance of each number from the mean
the mean absolute deviation
the triangle in the diagram are similar. how long will the footbridge be
I NEED HELP ASAP!
A metal rod is
7/8
meters long. It will be cut into pieces that are each
1/56
meters long. How many pieces will be made from the rod?
Write your answer in simplest form.
7y+4x=3; (-4,-7) write the equation in slope intercept form
help please thanks
Which trinomials are perfect square trinomials?
Select each correct answer.
a2+15a+75
a2+26a+169
a2+14a+49
a2+4a+16
Which expressions are differences of squares?
Select each correct answer.
t2−4
h2−20
x2−169
a2+1
PLZ HELP, GRAPH IT THEN FOR BRAINLIEST
graph the quadratic function f(x)=x^2−12x+27.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
There are 20 children at a library. Six of the children have an average age of 5 years. The remaining children have an average age of 8 years. What is the average age of the children at the library? Enter your answer in the box. WILL GIVE BARINLIYEST
How do u solve g/12=-10