Given:
The geometric sequence is:
25.5, 5.1, 1.02, 0.204, ...
To find:
The explicit rule for the given geometric sequence.
Solution:
We have,
25.5, 5.1, 1.02, 0.204, ...
Here, the first term is 25.5 and the common ratio is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{5.1}{25.5}[/tex]
[tex]r=\dfrac{1}{5}[/tex]
The explicit rule for a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]a=25.5,\ r=\dfrac{1}{5}[/tex] in the above formula, we get
[tex]a_n=25.5(\dfrac{1}{5})^{n-1}[/tex]
Therefore, the correct option is B.
How
many solutions exist for the mixed-degree system graphed below?
Answer:
There is one solution
(2, 2)
Step-by-step explanation:
The solutions are where the line and curve intersect.
The isone point of intersection and therefor one solution (2, 2)
Answer:
answer is b.) one
Step-by-step explanation:
edge 2021
Select the correct answer.
Which graph models the function f(x) = 2(x – 4)^2 + 3
Answer:
the graph is going to be facing up not down
The table and boxplots below shows summary statistics for
two distributions of calories in 10 brands of beef hot dogs
and 10 brands of turkey hot dogs.
Answer:
Step-by-step explanation:
Write a variable expression for this amount.
fourteen times x
Type the correct answer.
Answer:
14x
Step-by-step explanation:
14x = 14 x (x) = 14(x)
GIVING OUT BRAINLIEST ANSWER PLSS HELP!
Answer:
It should be c
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The answer is A
Very few circles are congruent. Certainly if a circle has a radius of 8 and another one 2 city blocks away also has a radius of 8, both are congruent. But if one of them has a radius of 4 and the other a radius of 10, they are not congruent.
A does not have to be true.
simplify : sqrt(25-10sqrt(3) +3)
Answer:
3.26794919243
Step-by-step explanation:
The temperature at 12 p.m. wa
34. The temperature at 12 a m
was-16. What was the difference
in the temperatures?
An elevator was at the 4floor
It traveled up 18 floors, down 7
floors, up 6 floors and down 2
floors. What floor did the elevator
end up on?
submarine was traveling at 62
feet below sea level. It rose 17
feet, dropped 250 feet, then rose 25
feet. What was the submarines
Final position?
Answer:
first is 52°C
Step-by-step explanation:
A class spends 1 hour 15 minutes on
English Language each school day. If
the total time spent in school each day
is 5 hour. What fraction of the time is
spent on English Language
Answer:
1/4
this is fraction of time spent on English language...
Which fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)?
Answer:
Step-by-step explanation:
slope=y2-y1/x2-x1
here x1=2 , y1=-4 , x2=-6 , y2=1
=1-(-4)/2-(-6)
=1+4/2+6
=5/8
-5/8 fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
the slope formula for the line containing (2, -4) and (-6, 1) we calculate by plugging the values to the slope formula.
m=1-(-4)/-6-2
m=1+4/-8
m=-5/8
Hence, -5/8 fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ2
Practice polynomials
solve and show your work
3x^2-14x-5
Answer:
( − 5 ) ( 3 + 1 )
Step-by-step explanation:
Use the sum-product pattern: 3 2 − 1 4 − 5
3 2 + − 1 5 − 5
Common factor from the two pairs: 3 2 + − 1 5 − 5
( 3 + 1 ) − 5 ( 3 + 1 )
Rewrite in factored form
Answer:
Step-by-step explanation:
Standard form:
3x2 − 14x − 5 = 0
Factorization:
(x − 5)(3x + 1) = 0
Solutions based on factorization:
x − 5 = 0 ⇒ x1 = 5
3x + 1 = 0 ⇒ x2 = −1
3
≈ −0.333333
Extrema:
Min = (2.333333, −21.333333)
Answer:
(3 x + 1 ) ( x − 5 )
Find a polynomial f(x) of degree 4 that has the following zeros. 7 (multiplicity 2), 0,-4. Leave your answer in factored form
Answer:
see below
Step-by-step explanation: 5 30 9 50
This is what I think they are asking for....
the zeroes are x = 0 x = -4 x = 7 twice ?? so
x(x+4)(x-7)² = 0
when I graphed the function it looked to be correct
Heston Wagons reported in June that 20 out of 500 wagons failed inspection. In July, they reported that 25 out of 625 wagons failed inspection. Which proportion can be used to represent the wagon failures? StartFraction 25 over 20 EndFraction = StartFraction 500 over 625 EndFraction StartFraction 20 over 25 EndFraction = StartFraction 625 over 500 EndFraction StartFraction 20 over 500 EndFraction = StartFraction 625 over 25 EndFraction StartFraction 20 over 500 EndFraction = StartFraction 25 over 625 EndFraction
Answer:
20/500 and 25/625
Step-by-step explanation:
1. 20 of 500 failed, which is 20/500
2. 25 of 625 failed, which is 25/625
Answer:
its d
Step-by-step explanation:
i did the test
The graph shows the function f(x) = 2*
What is the value of x when f(x) = 4?
A. 3
B. 1
C. 2
D 0
Answer:
Step-by-step explanation:
2
A ladder is leaning against the side of a 10cm house. If the base of the ladder is a 3cm away from the house, how tall is the Ladder
Answer:
10.44cm lon
Step-by-step explanation:
Given data
Height of house= 10cm
Distance of ladder from wall= 3cm
We can apply the Pythagoras theorem to get the length of the ladder
Also, the length of the ladder is the hypothenuse
z^2= x^2+y^2
z^2= 10^2+ 3^2
z^2= 100+9
z^2= 109
square both sides
z= √109
z= 10.44cm
Hence the ladder is 10.44cm long
Use a table of values to find the solution to the equation f(x)=h(x) where
f (x) = 2/3-x and
h(x)= 3- 2x
Show your work
9514 1404 393
Answer:
x = 2 1/3
Step-by-step explanation:
We can examine the equations to see where the solution lies.
f(x) = (2/3) -x
This has an x-intercept where y=0, at x=2/3. It has a y-intercept where x=0, at y=2/3. Its slope is -1.
h(x) = 3 -2x
This has an x-intercept where y=0, at x=3/2. It has a y-intercept where x=0, at y=3. Its slope is -2.
__
In the first quadrant, the graph of h(x) is farther from the origin and steeper than the graph of f(x). The lines must cross in the 4th quadrant at some value of x that is greater than 3/2. The fraction in the definition of f(x) suggests that the solution will be a multiple of 1/3.
The attached table shows a couple of guesses at values of x that would make f(x) = h(x). We find that x = 7/3 is the solution we're looking for.
_____
Additional comment
Repetitive function evaluations are done conveniently and with fewer errors by a calculator or spreadsheet that can work with tables of values. Here, we have used a graphing calculator. These tools are readily available for free on almost any phone, tablet, or desktop computer platform.
Each question Sandra answers incorrectly changes her overall score by -3/4 points. Sandras overall score was -4 1/2 points , and then she answered the last question incorrectly. What was Sandras final score
Find the area of the shape shown below...
Please help-
Answer:
[tex]A=32~sq~units[/tex]------------------
[tex]A=A_1+A_2+A_3+A_4[/tex][tex]A=1/2(4)(10)+1/2(2)(2)+(2)(2)+1/2(2)(6)[/tex][tex]A=20+2+4+6[/tex][tex]A=32[/tex]-------------------------
hope it helps...
have a great day!!
Which triangle isn't similar to QRS?
Answer:
∆ RPQ
Step-by-step explanation:
__________________
[tex] \bf \pink{Define \: the \: decimal \: number \: system \: in \: your \: own \: words. }[/tex]
Answer:
The decimal number system comprises digits from 0-9 that are 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9. Some of the decimal number system examples are: ... 34110, 5610, 678910, 7810. Now as we know to write decimal numbers till 10 let us use the 3 rules on a decimal system,to write further numbers.
[tex] \bf \pink{Define \: the \: decimal \: number \: system \: in \: your \: own \: words. }[/tex]
Decimal system, also called Hindu-Arabic number system or Arabic number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. ... It also requires a dot (decimal point) to represent decimal fractions.
Factor 2x^2 c^2 + 3xc^2- 35c^2
Josh's bill for lunch at a restaurant was $49.59. He left an 18% tip. What was the amount
of the tip?
Round your answer to the nearest cent: $
Help besties please flip the picture to see better
Answer:
E. C= 80+ 12n
Step-by-step explanation:
____________
The mean number of rushing yards for one NFL team was less than 105 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis
Answer:
Null hypothesis rejected means that there is significant evidence to conclude that the team's mean rushing yards per game is less than 105 yards.
Step-by-step explanation:
The mean number of rushing yards for one NFL team was less than 105 yards per game.
At the null hypothesis, we test if the mean number of rushing yards for the team was the league's mean, which is close to 105 yards per game, that is:
[tex]H_0: \mu = 105[/tex].
At the alternate hypothesis, we test if there is significant evident to conclude that this team average is less than 105 yards per game, that is:
[tex]H_1: \mu < 105[/tex]
How should you interpret a decision that rejects the null hypothesis?
Null hypothesis rejected means that there is significant evidence to conclude that the team's mean rushing yards per game is less than 105 yards.
56+ ? +11=94
Help me
Answer:
? = 27
Step-by-step explanation:
56 + ? + 11 = 94
? + 67 = 94
? = 27
According to a study, 50 % of adult smokers started smoking before 21 years old. 5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded. a) The probability that at least 2 of them started smoking before 21 years of age is b) The probability that at most 4 of them started smoking before 21 years of age is c) The probability that exactly 3 of them started smoking before 21 years of age is
Answer:
a) The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.
b) The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.
c) The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.
Step-by-step explanation:
For each smoker, there are only two possible outcomes. Either they started smoking before 21 years old, or they did not. Smokers are independent, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
50% of adult smokers started smoking before 21 years old.
This means that [tex]p = 0.5[/tex]
5 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.
This means that [tex]n = 5[/tex].
a) The probability that at least 2 of them started smoking before 21 years of age is
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]
[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.03125 + 0.15625 = 0.1875[/tex]
The probability that at least 2 of them started smoking before 21 years of age is 0.1875 = 18.75%.
b) The probability that at most 4 of them started smoking before 21 years of age is
This is:
[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.03125 = 0.96875[/tex]
The probability that at most 4 of them started smoking before 21 years of age is 0.96875 = 96.875%.
c) The probability that exactly 3 of them started smoking before 21 years of age is
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]
The probability that exactly 3 of them started smoking before 21 years of age is 0.3125 = 31.25%.
PLEASE HELP! 30 POINT!!!
What is the value of y when x = 3 in this equation
Y = 2x + 2
Answer:
5
7
8
12
Answer:
Step-by-step explanation:
8
Please help and hurry!
Answer:
25.13
C=2πr
C=2(3.14)4
Relationship in Figures
What are the first eight numbers in a Fibonacci sequence when N is equal to 1?
a. 1,2,3,4,5,6,7,8
b. 1,1,2,3,5,8,13,21
c. 3,0,2,3,2,5,5,7
d. 1,1,2,2,3,4,5,7
Please select the best answer from choices provided
Answer:
B. 1,1,2,3,5,8,13,21
Step-by-step explanation:
I calculated it logically
Following are the three types of data sets: a. Vehicle speeds on highway I-5 (9 vehicles) 74, 82, 67, 73, 65, 41, 74, 49, 85 b. Sodium grams in canned soup (8 varieties) 4.22, 3.60, 2.68, 2.75, 2.70, 4.17, 2.72, 4.29 c. Campus health center visits (12 students) 1, 5, 6, 13, 2, 3, 1, 3, 3, 1, 4, 3 For each data set, find the median, midrange, and geometric mean. (Round your answers to 2 decimal places. Leave no cells blank. Enter 0 as an answer if undefined.)
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
A.)
Vehicle speeds on highway (9 vehicles) 74, 82, 67, 73, 65, 41, 74, 49, 85
Ordered data :
41, 49, 65, 67, 73, 74, 74, 82, 85
Sample size, n = 9
Median = 1/2 * (n +1) th term
Median = 1/2 * 10 = 5th term
Median value = 73
Midrange = (Maximum + minimum) / 2
Midrange = (85 + 41) / 2 = 126 / 2 = 63
Geometric mean : √(x1*x2*.. xn)^1/n
Geometric Mean:
(41*49*65*67*73*74*74*82*85)^1/n
= 66.19
B.)
Sodium grams in canned soup (8 varieties)
X = 4.22, 3.60, 2.68, 2.75, 2.70, 4.17, 2.72, 4.29
Ordered data:
2.68, 2.70, 2.72, 2.75, 3.60, 4.17, 4.22, 4.29
Sample size, n = 8
Median = 1/2 * (n +1) th term
Median = 1/2 * 9 = 4.5th term
Median value = (2.75+ 3.6) / 2 = 3.175
Midrange = (Maximum + minimum) / 2
Midrange = (4.29 + 2.68) / 2 = 3.485
Geometric mean : √(x1*x2*.. xn)^1/n
Geometric Mean:
(2.68*2.70*2.72*2.75*3.60*4.17*4.22*4.29)^1/8
= 3.32
C.)
Campus health center visits (12 students)
X : 1, 5, 6, 13, 2, 3, 1, 3, 3, 1, 4, 3
Ordered data :
1, 1, 1, 2, 3, 3, 3, 3, 4, 5, 6, 13
Sample size, n = 12
Median = 1/2 * (n +1) th term
Median = 1/2 * 13 = 6.5th term
Median value = 3
Midrange = (Maximum + minimum) / 2
Midrange = (1 + 13) / 2 = 7
Geometric mean : √(x1*x2*.. xn)^1/n
Geometric Mean:
(1*1*1*2* 3*3*3*3*4* 5*6*13)^1/12
= 2.82
llll answer this an i will mark u brainliest
Answer: yeah the other person is right
Step-by-step explanation: