Write a conjecture for the pattern of the sequence
To conjecture a sequence, one must identify and extend the observable pattern, much like the quark hypothesis predicted unseen particles, or like recognizing the vowel sounds in specific linguistic patterns.
Explanation:In mathematics, creating a conjecture for a sequence involves analyzing the given numbers or patterns and predicting the next element based on the identified pattern. The process comparable to what the developers of the quark hypothesis did, working to predict unknown elements based on established patterns, can aid us in formulating a conjecture for the sequence in question.
For instance, if we refer to the resonance frequencies of a closed tube which form a pattern represented by the formula An = L / (4n) where n is an odd number, we can conjecture that the next frequency in the sequence would be determined by the next odd integer following the last one used.
Similarly, the binomial theorem expansion shows a pattern of coefficients that can be used to conjecture future terms in a binomial expansion. Analyzing patterns like VCC and VCle that determine whether the vowel sound should be long or short in English offer a linguistic parallel to mathematical pattern predictions.
To create a conjecture for a sequence, examine the values and look for a consistent relationship or rule. An example is adding 3 to the previous term in the sequence.
Explanation:A conjecture for the pattern of a sequence can be created by examining the values in the sequence and looking for a consistent relationship or rule. For example, if the sequence is 1, 4, 7, 10, 13, the conjecture may be that each term is obtained by adding 3 to the previous term. This can be represented mathematically as An = A(n-1) + 3, where An represents the nth term in the sequence.
Tony is training to run a marathon. He has already run 2 miles today and is running additional miles at 6 miles per hour. Write an equation that represents the miles, M, that Tony runs, where h represents the number of hours
For which pair of numbers is the greatest common factor 8
What is the answer to this.
2 1/3 + 3 1/4
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
Answer:
(4 square root 2, 315°), (-4 square root 2, 135°)
Step-by-step explanation:
(1-sec x)/(1-cos x) = -sec x
I got up to this:
(cos x - 1)/ (cos x(1 - cos x)
Can you help me verify the following identity?
We are given the trigonometric equation:
(1 - sec x) / (1 - cos x) = - sec x
Since the left side has more terms, then let us work on that side to make it exactly like the right side.
We know that sec = 1 / cos, therefore:
(1 – 1 / cos x) / (1 – cos x) = - sec x
[(cos x – 1) / cos x] / (1 – cos x) = - sec x
[- (1 – cos x) / cos x] / (1 – cos x) = - sec x
Cancelling out the term (1 – cos x):
- 1 / cos x = - sec x
- sec x = - sec x
PROVEN!
Write the equivalent decimal and fraction for each percent.
Percent: 15%
Percent:120%
Percent:36%
Percent:22%
Percent:54%
Percent:205%
_______________________________________________________________
For each fraction or decimal, write the equivalent percent.
3/25 =
4.06 =
0.01 =
1/8 =
2/5 =
0.6%
__________________________________________________________
90% or 120 is:___
3.6 or 5% of:___
37 1/2 or 64 is:____
39 is __% of 52
110% or 55 is____
18 is 40% of ____
27 is ___ % of 108
35 is 25% of ___
28 is __% of 20
82 is ___% of 40
Answer:
15% = 0.15
120% = 1.2
36% = 0.36
:22% = 0.22
54% = 0.54
205% = 2.05
3/25 = 12%
4.06 = 406%
0.01 = 1%
1/8 = 12.5%
2/5 = 40%
0.6% = 60%
Hope this helps :)
An item has a listed price of $80. If the sales tax rate is 6% , how much is the sales tax (in dollars)?
6% = 0.06
80 x 0.06 = 4.80
the tax is $4.80
Of the 8760 hours in a year, one television was on for
1752 hours. What percent is this?
the lines shown below are perpendicular. if the green line has a slope of 1/7, what is the slope of the red line?
Answer: it's -7
Step-by-step explanation:
Answer:
Therefore, the slope of the red line must be -7
Step-by-step explanation:
If the two lines are said to be perpendicular each other, then the multiplicative of their slope is -1.
Let "m1" be the slope a line and "m2" be the slope of the perpendicular line.
So, m1*m2 = -1
Here, let's take "m1" be the slope of the green line and "m2" be the slope of the red line.
They said to be perpendicular to each other.
So, m1*m2 = -1
Given: m1 = 1/7
NOw plug in m1 = 1/7 in the above statement, we get
1/7 *m2 = -1
Let's find the value of m2, multiply both sides by the reciprocal of 1/7
The reciprocal of 1/7 is 7.
7*1/7*m2 = -1*7
7/7.m2 = -7
m2 = -7
Therefore, the slope of the red line must be -7
a whole number is a perfect square if its square root is an integer true or false
209,767 rounded to the nearest 10,000
What is the relationship between 8.76 x 10^6 and 8.76 x 10^2
Starting at home, Jessica traveled uphill to the grocery store for 18 minutes at just 20 mph. She then traveled back home along the same path downhill at a speed of 60 mph.
What is her average speed for the entire trip from home to the grocery store and back?
During low tide, the beachfront in some places is about 350 from the ocean to the homes . High tide can change the width of a beach at a rate of -17 feet each hour . It takes 6 hours for the ocean to move from low to high tide . What is the change in the width of the beachfront from low to high tide ?
the change in width would be -17 * 6 = -102 feet
distance from the ocean to the houses would be 350-102= 248 feet
Find the GFC of 56 and 84. A factor tree for 84 is given below. The GCF of 84 and 56 is .
The greatest common factor of the given numbers is 4.
The given numbers are 56 and 84.
The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers.
Here, the factors of given numbers are
56 = 2×2×2×7
84 = 2×2×3×7
Now, the common factors from the above factorization is 2×2
= 4
Therefore, the greatest common factor of the given numbers is 4.
To learn more about the greatest common factor visit:
brainly.com/question/11221202.
#SPJ6
Find the value of the expression m4 - m3 - 2m2 + 10m + 15 when m = -3.
Rewrite 256 in exponential form using 2 as the base
Find the product of 0.094 ×0.367
A cheetah runs at a speed of 54 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?
A.) d = 54t
B.) t = 54d
C.) d = 54 + t
D.) t = 54 + d
you would multiply the number of hours (t) by the speed (54) to find the distance (d)
so A) d=54t
Stumped on how to solve this one! The numbers just aren't making sense to me
30=3/5
so 10 miles = 1/5 on the map
there re 5/5 per inch, so 4 inches = 4*5 = 20/5
20*10 = 200
so they are 200 miles apart
Help pleasee i am beggin
Holly earns $30 for babysitting 5 hours. She earns $28 when she does chores for 4 hours. Which compares the unit rates?
The rate of earning money for both activities will be calculated by dividing the amount earned by the total time spent for each of the activity.
Babysitting: rate = ($30 / 5 hours ) = $6 / hour
Doing chores: rate = ($28 / 4 hours) = $7 / hour
Thus, Holly is able to earn money faster when doing the chores compared to when she do the babysitting if she work for the same amount of time for each.
Answer:
The unit rate for doing chores is $1 more than the unit rate for babysitting.
Step-by-step explanation:
30 divided by 5=6 So that means it was six dollars for babysitting.
28 divided by four=7 So that means it was seven dollars for babysitting.
Sarah is making flower arrangements. She has 15 roses and 10 daisies. If she wants to make all identical arrangements, with no flowers leftover, what is the greatest number of arrangements she can make? And how much of each flower will be in each arrangement
given that there are eight ounces in a cup and four cups in a quart, which quantity below is equal to 128 ounces
256 ounces 64 ounces 18 cups 4 quarts
Answer:
4 quarts i had this question on a test and got it right
Step-by-step explanation:
128 ounces is equal to 4 quarts.
To solve this, we need to convert the amount given in ounces to quarts.
Step-by-Step Solution:
There are 8 ounces in a cup.There are 4 cups in a quart.Therefore, there are 8 ounces/cup × 4 cups/quart = 32 ounces in a quart.To find out how many quarts are in 128 ounces, divide 128 by 32: 128 ounces / 32 ounces per quart = 4 quarts.So, the quantity equal to 128 ounces is 4 quarts.
The other options: 256 ounces and 64 ounces are obviously not equal to 128 ounces since 256≠ 128≠ 64
and, 18 cups =18×8= 144 ounces ≠ 128 ounces.
Another struggle.... Helppp
-4(2x-6)=-(4x-9)-2x+3
s the work shown below correct? Explain your answer. (11 + 2i ) – (3 – 10i ) = 11 + 2i – 3 – 10i = (11 – 3) + (2i – 10i) = 8 – 8i
Answer:
Given that: [tex](11+2i)-(3-10i)[/tex]
Remove the parentheses, we have;
[tex]11+2i-3+10i[/tex]
Like terms are those terms which have same variables to the same power.
Combine like terms of a constant variable;
[tex](11-3) +2i+10i[/tex]
Similarly, combine like terms of imaginary part, we have;
[tex](11-3) +(2i+10i)[/tex]
Simplify:
[tex]8 +(12i)[/tex]
or
[tex]8+12i[/tex]
Therefore, the correct solution of [tex](11+2i)-(3-10i)[/tex] = [tex]8+12i[/tex]
What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?
a. 1 and 3
b. 0 and 2
c. 0
d. 3
HURRY IM BEING TIMED!!
Answer:
Step-by-step explanation:
Given: –x² + 2x + 3 = x² – 2x + 3 .
To find: What are the solution(s) .
Solution: we have given that
–x² + 2x + 3 = x² – 2x + 3 .
On subtracting both side by x² .
-2x² + 2x + 3 = x² - x² - 2x + 3
-2x² + 2x + 3 = -2x +3
On Addition both side by 2x .
-2x² + 2x + 2x + 3 =-2x +2x +3
-2x² + 4x + 3 = 3
On subtracting both side by -3 .
-2x² + 4x + 3 -3 = 3 - 3
-2x² + 4x = 0
Taking common 2x .
2x (- x +2 ) =0 .
On grouping .
2x= 0
so x= 0
Now , -x +2 =0 .
-x = -2 .
On dividing by -1
x= 2
Therefore , option B is 0 and 2 .
The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:
F = 9 over 5 C + 32
Which of the following formulas correctly solves for C?
A) C = 5F − 32 over 9
B) C = 5 F over 9 − 32
C) C = 9 over 5 (F − 32)
D) C = 5 over 9 (F − 32)
it is the last option C=5/9(F-32)
Answer:
option (D) is correct.
formula that solves for C is [tex]C=\frac{5(F-32)}{9}[/tex]
Step-by-step explanation:
Given : the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F as , [tex]F=\frac{9}{5}C+32[/tex]
We have to find the correct formula that solve for C,
Consider the given formula,
[tex]F=\frac{9}{5}C+32[/tex]
We have to find formula for C,
Thus, first subtract 32 both side, we get,
[tex]F-32=\frac{9}{5}C[/tex]
Now, multiply 5 both side, we get,
[tex]5(F-32)={9}C[/tex]
Now , divide both side by 9, we get,
[tex]\frac{5(F-32)}{9}=C[/tex]
Thus, formula that solves for C is [tex]C=\frac{5(F-32)}{9}[/tex]
Thus, option (D) is correct.