Answers
Solution:
We can see that each term when subtracted by 4, gives the next term.
This means that:
n₁ - 4(2) + 4(1) = n₂Let's substitute the values to check:
=> n₁ - 4(2) + 4(1) = n₂ => n₁ - 8 + 4 = n₂ => n₁ - 4 = n₂ => 18 - 4 = 14=> 14 = 14 (Proved)Now, we can find the nth term aₙ by using the formula:
18 - 4(nth term) + 4(1) = Value of nth termTo check that the formula is correct, let's substitute the value of nth as the fifth term of the sequence.
18 - 4(nth term) + 4(1) = Value of nth term=> 18 - 4(5) + 4(1) = Value of 5th term=> 18 - 4(5) + 4(1) = Value of 5th term=> 18 - 20 + 4 = Value of 5th term=> 18 - 16 = Value of 5th term=> 2 = Value of 5th termNow, let's find the fifth term mentally. Keep subtracting 4 until you reach the fifth term.
=> 18 - 4 = Second term of sequence=> 14 = Second term of sequence=> 14 - 4 = Third term of sequence=> 10 = Third term of sequence=> 10 - 4 = Fourth term of sequence=> 6 = Fourth term of sequence=> 6 - 4 = Fifth term of sequence=> 2 = Fifth term of sequenceWe are getting the same result from both ways.
In conclusion, our formula to find the nth term is "18 - 4(nth term) + 4(1)".
Related Questions
Simplify:w^30/(w^3)^2
Answers
Answer:
Step-by-step explanation:
[tex](a^{m})^{n} = a^{m*n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\frac{w^{30}}{(w^{3})^{2}} = \frac{w^{30}}{w^{3*2}}[/tex]
[tex]= \frac{w^{30}}{w^{6}}\\\\=w^{30-6}\\\\= w^{24}[/tex]
Answer:
w^24
You would simplify the expression by first finding the product of (w^3)^2 which is w^6. Next you would divide w^30 and w^6 which would get you your answer which is w^24. Hope this helps!
3. The difference of the squares of two positive consecutive odd integers is 32. Find the
integers.
Answers
Answer:
7,9
Step-by-step explanation:
Let two consecutive odd integer=X and (X+1)
The difference of the squares of two positive consecutive odd integers is 32.
So(X+2)^2-x^2=32
(x^2+4+4x)-x^2=32
x^2+4+4x-x^2=32
4x=32-4
4x=28
X=28/4
X=7
So first integer=7
Second integer=7+2
=9.
Suppose a constellation of stars is plotted on a coordinate plane. The coordinates of one star are (0,-8). The
point representing the star is then translated left 3 units. What are its new coordinates?
1. (0,-5)
2. (-3,-8)
3. (3.-8)
4. (0.-11)
Answers
Answer:
4
Step-by-step explanation:
One base of a trapezoid is decreasing at a rate of 888 kilometers per second and the height of the trapezoid is increasing at a rate of 555 kilometers per second. The other base of the trapezoid is fixed at 444 kilometers. At a certain instant, the decreasing base is 121212 kilometers and the height is 222 kilometers. What is the rate of change of the area of the trapezoid at that instant (in square kilometers per second)
Answers
The rate of change of the area of the trapezoid at that instant is 5 square kilometers per second and this can be determined by differentiating the area of the trapezoid with respect to time 't'.
Given :
One base of a trapezoid is decreasing at a rate of 8 kilometers per second and the height of the trapezoid is increasing at a rate of 5 kilometers per second. The other base of the trapezoid is fixed at 4 kilometers. At a certain instant, the decreasing base is 12 kilometers and the height is 2 kilometers.First, determine the area of a trapezoid, that is:
[tex]\rm A = \dfrac{b_1+b_2}{2}\times h[/tex]
[tex]\rm \dfrac{2A}{h}=b_1+b_2[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}-b_1[/tex]
Now, differentiate the above expression with respect to 't'.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2A}{h^2}\dfrac{dh}{dt}-\dfrac{db_1}{dt}[/tex]
Now. substitute the values of the known terms in the above formula.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2\times (16)}{2^2}\times (5)-(-8)[/tex]
[tex]\rm \dfrac{db_2}{dt} = -32\;km/sec[/tex]
So, the area is decreasing at the rate of 5.
For more information, refer to the link given below:
https://brainly.com/question/1083374
Randomly selected 150 student cars have ages with a mean of 7.3 years and a standard deviation of 3.6 years, while randomly selected 65 faculty cars have ages with a mean of 5.9 years and a standard deviation of 3.5 years.
1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars.
The test statistic is
Is there sufficient evidence to support the claim that student cars are older than faculty cars?
A. Yes
B. No
2. Construct a 99% confidence interval estimate of the difference μ1−μ2, where μ1 is the mean age of student cars and μ2 is the mean age of faculty cars. <(μ1−μ2)
Answers
Answer:
1) B. NO
2) -0.049 < (μ1 − μ2) > 2.751
Step-by-step explanation:
Data of student cars;
Sample size; n1 = 150
Sample mean; x1¯ = 7.3
Sample standard deviation; s1 = 3.6
Faculty cars data;
Sample size; n2 = 65
Sample mean; x2¯ = 5.9
Sample standard deviation; s2 = 3.5
The hypotheses is defined as;
Null hypothesis; H0: μ1 = μ2
Alternative hypothesis; Ha: μ1 > μ2
1) Formula for test statistic for 2 sample test is;
z = (x1¯ - x2¯)/√[((S1)²/n1) + ((S2)²/n2)
z = (7.3 - 5.9)/√[((3.6)²/150) + ((3.5)²/65)
z = 1.4/√((12.96/150) + (12.25/65))
z = 1.4/√0.2749
z = 1.4/0.5243
z = 2.67
From online p-value from z-score calculator attached, using z = 2.67, one tailed test, significance level = 0.01,we have;
P-value = 0.003793
This is less than the significance level, thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that student cars are older than faculty cars.
2) Formula for the confidence interval is;
CI = μ1−μ2 = (x1¯ - x¯2) ± z√[((S1)²/n1) + ((S2)²/n2)
At significance level of 99%, z-score value is 2.576
Thus;
μ1−μ2 = (7.3 - 5.9) ± 2.576√[((3.6)²/150) + ((3.5)²/65)
μ1 − μ2 = 1.4 ± 2.576(0.5243)
-0.049 < (μ1 − μ2) > 2.751
Leslie invests $2500 in a savings account for 10 years. The account accrues interest at a rate
of 6% compounded semi-annually. How much money will be in the account at the end of the
10 years?
Answers
Answer:
You make $32,000 a year and want to save 10% of your income every year. How much should you put into savings every month?
$32$,000 x 0.10 = 3,200
You want to save $3200 a year.
You should be saving $266.67 a month or $133.33 a paycheck if you are paid
Step-by-step explanation:
13, 11, 9, 7 what is the recursive rule
Answers
Answer:
it is -2
Step-by-step explanation:
because 13-2=11-2=9-2=7-2=5-2=3-2=1
Fine the distance between (-8, 4) and (-8, -2)
Answers
Answer:
The distance between the two points is six units.
Step-by-step explanation:
We are given two coordinate pairs:
(-8, 4)(-8, -2)With these, we can find the distance between the two using the distance formula. The distance formula is:
[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, \ \text{where d is the distance.}[/tex]
Additionally, we need to label our coordinates. In math, coordinates are labeled as (x₁, y₁) and (x₂, y₂).
Therefore, our coordinate pairs can be labeled in this format.
(-8, 4)
x₁ = -8y₁ = 4(-8, -2)
x₂ = -8y₂ = -2Now, we can substitute these values into the formula and solve for d.
[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d = \sqrt{(-8 - -8)^2 + (-2 - 4)^2}\\\\d = \sqrt{(0)^2+(-6)^2}\\\\d = \sqrt{0 + 36}\\\\d = \sqrt{36}\\\\d = 6[/tex]
Therefore, the distance between the two points is six units.
The current of a river is 2 miles per hour. A boat travels to a point 3 miles upstream and back in 2 hours. What is the speed of the boat in still water? The speed of the boat in still water is.
Answers
Answer:
1.5 miles per hour
Step-by-step explanation:
3 miles divided by 2 hours
What is the cost of a $40 after a 15% mark-up?
Answers
Answer:
Revenue: $46
Profit: $6
60 POINTS PLEASE HELP! If the parent function f (x) =log (x+1) were replaced by g (x)= -log(x-1) , how would the graph be affected? SEE PHOTO FOR ANSWER OPTIONS
Answers
Answer:
C is the correct awnser
Step-by-step explanation:
if cade shoots 359 free throws shoot in 4 hours, how many can he shoot in 6 hours
Answers
Explanation
You divide 359 by 4 and then you multiply the answer by 6
Hurry help me pls
1/2 (6a + 8)=14
Answers
Answer:
a= 10/3
Step-by-step explanation:
multiply both sides by 2
get 6a +8 =28
subtract 8 from both sides
you get 6a=20
divide 6 both sides and 10/3.
Arianna runs up 4 flights of stairs and then runs down 4 flights of stairs.
Does this situation represent additive inverses? Explain.
A
Yes; The numbers combine to eight.
B
Yes; The numbers combine to zero.
No; The numbers are both represented by the same integer.
D
No; The numbers cannot be added together.
Answers
Answer:
Yes this represents additive inverse,
Step-by-step explanation:
Since you are subtracting the same number 4 to get to zero.
Find the unit rate in decimal representation $150 for 22 ft.²
Answers
Answer:
$6.82 per foot
Step-by-step explanation:
To find the unit rate, divide.
150 / 22 ≈ 6.82
Best of Luck!
Word problem: Jen wants to rent a car. There is a one-time fee of 50 dollars plus 40 dollars per day. Write an algebraic expression for the total cost for “d” days.
A. 90d
B. 50d + 40
C. 50 + 40d
D. 50d + 40d
Please help me!
Answers
Answer:
50+40d C
Step-by-step explanation:
Michael went on a hike and recorded his elevation. In total, he went up 14.26 kilometers and went down 11.86 kilometers. His friend Andre did a different hike, and his net elevation gain was 2.5 times Michael’s. What was Andre’s net elevation gain?
Answers
Answer:
I don't know
Step-by-step explanation:
LOL XDDDDd
Andre is writing a paper for science class. He can type 30 words per minute.
What is the ratio of words to minutes? Write the ratio three ways.
Answers
Answer:
30/1, 30:1, 30 to 1
Step-by-step explanation:
Which statement about|-8 is true?
|-8| represents a negative number.
|-8| represents the distance from -8 to 0 on a number line.
|-8|represents the opposite of 8.
|-8| represents the negative distance from 8 to 0 on a number line.
J
Answers
Answer:
Your second listed answer choice would be your answer.
Consider an ANOVA procedure to compare five population means. In this case, the total number of pairs to be considered in multiple comparisons is ten. If the probability that the null hypothesis is falsely rejected at least once in all six pairs needs to be 0.05, the probability that the null hypothesis is falsely rejected in each pair should be:________. (Give your answer to 4 decimal places.)
Answers
Answer:
The right response is "0.0085". A further explanation is given below.
Step-by-step explanation:
Let,
P (across each pair, this same null hypothesis would be wrongly rejected) be "a".
Therefore,
⇒ [tex]P=1-P(no \ time \ rejected)[/tex]
⇒ [tex]1-(1-a)^6 =0.05[/tex]
⇒ [tex]1-a=0.95^{(\frac{1}{6} )}[/tex]
⇒ [tex]a=1-0.95^{(\frac{1}{6} )}[/tex]
⇒ [tex]0.0085[/tex]
You deposit $2000 in an account earning 7% interest compounded continuously. How much will you have in
the account in 15 years?
Answers
Answer:
$3,715.30
Step-by-step explanation:
Total P+I (A): $3,715.30
Principal (P): $2,000
Compound (n): Continuously
Time (t in years): 15 years
By plugging this into an interest rate calculator, the amount settles to be approximently $3,715.30
Hope this helps!
The table shows how much money a grocery store receives for selling different amounts of asparagus.
ASPARAGUS SALES
NUMBER OF POUNDS
TOTAL SALES
4 lb=
$10
6 lb=
$15
8 lb=
$20
10 lb=
?
12 lb=
?
If the unit rate is constant what are the total sales for 12 pounds of asparagus?
A. $32.50
B. $25.00
C. $22.50
Answers
Answer:
The answer is 32.50
Step-by-step explanation:
You would just keep counting up by fives and then you would also have to add tax because it is food -- I am happy to help! :)
An automobile costs $22,750 after a 30% discount. What was the original price of the automobile? (Do not enter the $ sign in your answer.)
Answers
Answer:
32,500
Step-by-step explanation:
22,750 = .70x. (Paid 70% since it was 30% discount)
divide both sides by .70
x = 32,500
Tell whether the other pair (8,2) is a solution of the system of linear equations.
x - y = 6
2x - 10y = 4
The ordered pair ______ a solution.
Answers
Is
Is not
The answer is not a solution
Answers
8 - 2 = 6
Yes the ordered pair is a solution
2(8) - 10(2) = 4
16 - 20 = 4
No the ordered pair is not a solution
By direct evaluation, we will see that the pair (8,2) is not a solution of the system of equations.
Evaluating a system of equations.
A given point is a solution of a system of equations if and only if it is a solution for both equations, then to see if (8, 2) is a solution of the given system, we need to replace the values in both equations and see if it is a solution of each one.
For the first one we have:
x - y = 6
8 - 2 = 6
6 = 6
So (8, 2) is a solution of the first equation.
For the second one we have:
2x - 10y = 4
2*8 - 10*2 = 4
16 - 20 = 4
-4 = 4
Note that this equation is false, then the point (8, 2) is not a solution for the second equation, then the point is not a solution for the system of equations.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/14323743
Which equation is y = –6x2 + 3x + 2 rewritten in vertex form
Answers
Answer:
14 + 3x
Step-by-step explanation:
6x2= 12
12 + 3x + 2
=14 + 3x
Answer:
y =-6(x-1/4)^2+19/8
Step-by-step explanation:
I hope this helps I don't have an explanation I just got it right on EDG 2021
God Bless You!!!!!
A sporting goods store is having a 15% off sale on all items. Which functions can be used to find the sale price of an
item that has an original price of X? You may choose more than one correct answer.
y=.85 x
Of(x) = 1.15
Sale = Original - 15
Of(x) = x - 15
Sale = Original - 15(Original)
Answers
Answer:
The function is:
[tex]f(x) = x - 0.15x[/tex]
Can also be written as:
[tex]Sale = Original - 0.15(Original)[/tex]
Step-by-step explanation:
Given that the sale percentage is 15%
In general, the sale price is calculated by finding the discount according to discount percentage and then subtracting the discount from original price.
Given that x is the original price
Then the discount will be:
[tex]Discount = Original Price * 0.15\\Discount = 0.15x[/tex]
The sale price will be:
[tex]Sale Price = Original\ Price - 0.15(Original\ Price)\\[/tex]
As x is the original price
[tex]f(x) = x - 0.15x[/tex]
Can also be written as:
[tex]Sale = Original - 0.15(Original)[/tex]
Describe a situation that could be modeled with the ratio 3: 1.
Answers
Answer:
three boys to 1 girl
Step-by-step explanation:
a
Given f(x) = - 3x + 1 , solve for a when f(x) = - 5 .
Answers
Answer:
x=2
Step-by-step explanation:
-5=-3x+1
-1 -1
-6=-3x
divide both sides by -3
x=2
The value of x when f(x) = - 5, In the function f(x) = - 3x + 1 is 2.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f(x) = - 3x + 1.
Now, when f(x) = - 5 the equation would be,
- 5 = - 3x + 1.
- 5 - 1 = - 3x.
- 6 = - 3x.
3x = 6.
x = 2.
learn more about functions here :
https://brainly.com/question/12431044
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4) Gas mileage is the number of miles you can drive on a a gallon of gasoline.
A test of a new car results in 450 miles on 20 gallons of gas. How far could
you drive on 40 gallons of gas? What is the car's gas mileage?
Answers
Answer:
900 miles
Step-by-step explanation:
Simply multiply 450 by 2.
40 ÷ 20 = 2
450 x 2 = 900
OR
Based on Proportion:
[tex]\frac{450}{20}[/tex] x [tex]\frac{x}{40}[/tex]
Cross multiply:
450 x 40 = 18,000
20 x X = 20x
20x = 18,000
Divide by 20:
x = 18,000 ÷ 20
Solve:
x = 900
Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas.a. -1.45, 1.45
b. -1.39, 1.39
c. -1.53, 1.53
d. -1.46, 1.46