The explicit formula for this geometric sequence is: a_n = 3 (-2)^{n-1}. he common ratio is negative, so the domain is all odd positive integers.
Explicit formula:
The explicit formula for a geometric sequence is of the form: a_n = a_1 r^{n-1}
In this case, the first term is 3 and the common ratio is −2. Therefore, the explicit formula for this geometric sequence is:
a_n = 3 (-2)^{n-1}
Restrictions to the domain:
The domain of a geometric sequence is all positive integers, unless the common ratio is negative. In this case, the common ratio is negative, so the domain is all odd positive integers.
Example:
Using the explicit formula, we can find the fourth term of the sequence as follows:
a_4 = 3 (-2)^{4-1} = 3 (-2)^3 = -24
We can also verify that the domain of the sequence is all odd positive integers by checking the first few terms:
n | a_n
1 | 3
2 | -6
3 | 12
4 | -24
5 | 48
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Calculate the upper and lower limit for a 95% confidence interval about this mean.
A family needs a new car, but isn't sure they can fit the payment into their budget. A sample of 36 months of grocery bills yields a mean of $94 with a standard deviation of $10. If the upper limit of a 95% confidence level is below $100, the family can afford to buy the car.
Standard error = (standard deviation)/(square root of sample size)
Upper limit (dollars and cents)
Lower limit (dollars and cents)
Answer:Upper limit ⇒ 94+(1.96)(10÷√36) = 94+(1.96)(10/6) = $97.27
Lower limit ⇒ 94 - (1.96)(10÷√36) = 94 - (1.96)(10/6) = $90.73
Which of the following equations has the solution x = all real numbers? Select one: a. 4(3 - x) + 6x = 3x + 12 - x b. 4(3 - x) + 6x = 3x + 10 - x c. 4(3 - x) + 6x = 3x + 12 + 2x d. 4(3 - x) + 6x = x + 12 - 3x
The equation that has the solution x = all real numbers is given by option a) (4(3 - x) + 6x = 3x + 12 - x) and this can be determined by using the arithmetic operations.
Check all the options in order to determine which of the following equations has the solution x = all real numbers.
A) 4(3 - x) + 6x = 3x + 12 - x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 3x + 12 - x
= 2x + 12
LHS = RHS means there is an infinite number of solutions.
B) 4(3 - x) + 6x = 3x + 10 - x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 2x + 10
LHS [tex]\neq[/tex] RHS means that there are no solutions.
C) 4(3 - x) + 6x = 3x + 12 + 2x
Simplify the above equation separately that is:
LHS = 12 - 4x + 6x
= 12 + 2x
RHS = 5x + 12
LHS [tex]\neq[/tex] RHS means that there are no solutions.
D) 4(3 - x) + 6x = x + 12 - 3x
Simplify the above equation separately that is:
LHS = 12 + 2x
RHS = 12 - 2x
LHS [tex]\neq[/tex] RHS means that there are no solutions.
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Assuming that n 1 , rewrite the compound interest equation B t 900 1.185 t in the general form.
You invest a total of $5800 in two investments earning 3.5% and 5.5% simple interest. Your goal is to have a total annual interest income of $283. Write a system of linear equations that represents this situation where x represents the amount invested in the 3.5% fund and y represents the amount invested in the 5.5% fund. Solve this system to determine the smallest amount that you can invest at 5.5% in order to meet your objective.
Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)
Enter the degree of the polynomial below
7x^7+10x^4+4x^3-5x^11-10x^6-6x^7
A. 11
B. 10
C. 6
D. 7
HELP! Algebra!
The following two-way table shows the number of students of a school who have a cell phone and/or have a part-time job:
Based on the table, how many students have both a cell phone and a part-time job?
Answers:
A- 10
B- 40
C- 50
D- 100
The number of students have both a cell phone and a part-time job is 40.
The correct option is (B)
What is algebra?
Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.
Given table shows that,
The students having whether having cell phones or not and whether the students are having part time job or not.
As we can see from the Column I shows students having cellphones and the first row shows students having part time job. which is 40.
Hence, the students have both a cell phone and a part-time job is 40.
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What is the sum of the two vectors (2,-1) and (3,3)?
Carlos graphs the equations y = 0.5x^2 + 3 and y = –4x^2 + 24x – 35 and generates the graph below. Which conclusion is supported by the graph?
A. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has no solutions.
B. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has one solution.
C. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has two solutions.
D. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has three solutions.
Answer: The correct option is A. The equation 0.5x2 + 3 = –4x2 + 24x – 35 has no solutions.
Explanation:
The given equations are,
[tex]y=0.5x^2+3[/tex]
[tex]y=-4x^2+24x-35[/tex]
Since the above equations are quadratic equations, therefore they area parabola.
The coefficient of first equation is a positive therefore it is an upward parabola. The coefficient of second equation is a negative therefore it is an downward parabola.
From given figure it is noticed that the vertex of first parabola is (0,3) and the vertex of second parabola is (3,1).
The vertex is the extreme point of the parabola. So for first equation [tex]y\geq 3[/tex] and for second equation [tex]y\leq 1[/tex]. Therefore the parabolas will never intersect each other.
Since there is no intersection between parabolas therefore the equation
[tex]0.5x^2+3=-4x^2+24x-35[/tex] has no solution and the correct option is A.
What is the following product
If g is the variable, which mathematical sentence expresses the information below? "The number of gallons of gas in the tank plus 7 more adds up to 12 gallons."
Answer: [tex]g+7=12[/tex]
Step-by-step explanation:
The given statement : The number of gallons of gas in the tank plus 7 more adds up to 12 gallons.
Given variable : 'g'
if g represents the number of gallons of gas in the tank, then for the given statement we have the following expression:-
[tex]g+7=12[/tex]
Hence, the mathematical sentence expresses the given information :-
[tex]g+7=12[/tex]
three consecutive even numbers have a sum where one half of the sum is between 84 and 96
86 *2 = 172
172/3 = 57.33
54 + 56 +58 =168
168/2 =84
56 + 58 +60 = 174
174/2 =87
58 +60 +62 = 180
180/2 = 90
60 +62 +64 = 186
186/2 = 93
62 +64+66 = 192
192/2 = 96
there are 3 sets of numbers that fall between 84 & 96
1 set equals 84 and 1 set equals 96
so if you are counting those there are 5 sets
The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?
Please just help me understand, do not give me the answer! thank you
A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation?
Let u = <-9,4>, v = <8, -5>. Find u - v.
To find the difference between vectors u and v, subtract corresponding components.
Given vectors u = <-9,4> and v = <8, -5>, to find the difference u - v, subtract corresponding components:
Subtract the x-components: -9 - 8 = -17
Subtract the y-components: 4 - (-5) = 9
Therefore, u - v = <-17, 9>.
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Evaluate 5x + (-2x 2) for x = 3.
Which expression can be used to determine the average rate of change in f(x) over the interval [2,9]
a) f(9-2)
b) f(9)-f(2)
c) f(9-2)/9-2
c) f(9)-f(2)/9-2
Answer:
D. f(9-2)/9-2 on Edg2020
Step-by-step explanation:
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The curve y = x/(1 + x2) is called a serpentine. find an equation of the tangent line to this curve at the point (2, 0.40). (round the slope and y-intercept to two decimal places.) y =
The equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is given by y = -0.24x + 0.88, rounded to two decimal places.
Explanation:The subject of the question refers to calculus, specifically the concept of finding the equation of a tangent line to a curve. This process typically involves finding the derivative of the function (which gives the slope of the tangent), and then using the point-slope form of the line equation.
The derivative of y = x/(1 + x2) can be found using the quotient rule for differentiation and is given by y' = (1 - x2)/(1 + x2)2. Evaluating this at x = 2 gives a slope of about -0.24 (rounded to two decimal places).
The equation of the line is usually written in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Since we know that the line passes through the point (2, 0.40), we can substitute these values into the equation and solve for b. This yields a y-intercept of about 0.88 (rounded to two decimal places).
Therefore, the equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is approximately y = -0.24x + 0.88.
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(06.01)Which point on the scatter plot is an outlier?
Point H
Point I
Point J
Point K
A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 5 seats in business class.
13 +5 =18
360/18=20
13*20 = 260
5*20 =100
260 economy & 100 business
Do as follows:
13 +5 =18
360/18=20
13*20 = 260
5*20 =100
260 economy & 100 business
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = –3 + (n – 1)(–2.2)
The arithmetic sequence A(n) = –3 + (n – 1)(–2.2) yields the first, fourth, and tenth terms as -3, -9.6, and -22.8 respectively when n is substituted with the corresponding term number.
Explanation:The arithmetic sequence described by the rule A(n) = –3 + (n – 1)(–2.2) can be used to find specific terms of the sequence. To find the first term, plug in n = 1 into the formula to get A(1) = -3 + (1 - 1)(-2.2) = -3. The fourth term can be found by plugging in n = 4 which yields A(4) = -3 + (4 - 1)(-2.2) = -9.6. The tenth term is calculated as A(10) = -3 + (10 - 1)(-2.2) = -22.8. Therefore, the first, fourth, and tenth terms are -3, -9.6, and -22.8 respectively.
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Solve and check the inequality
|8m+4|<12
The football team has 30 more members than the basketball teams. If each group had 10 more members, the ratio of their membership would be 3.2. How many members are in each group? Write your answer as football x basketball y
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if the lines a and b in the diagram below are parallel why do angles 1 nd 8 measure 120 degree angles
A) Because they are alternate interior angles.
B) Because they are corresponding angles.
C) Because they are alternate exterior angles.
D) Because they are same-side interior angles.
how many cookies will tony have if he bakes 5 more batches y=90+ 14 (x)
replace x with 5
y=90+14(5)
14*5 =70
90+70 =160
y=160
he will have 160 cookies
Answer:
Given the equation:
[tex]y = 90+14x[/tex] .....[1]
where,
y represents the total number of cookies and
x represents the number of batches bake.
From the statement:
we have;
x = 5
Substitute in [1] we have;
[tex]y = 90+14 \cdot 5 = 90+70 = 160[/tex]
Therefore, 160 cookies will tony have if he bakes 5 more batches
Of the 30 girls who tried out for lacrosse team 12 were selected. Of the 40 boys that tried out 16 were selected. Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls? Explain.
The population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the approximate population of the town in 2005?
A. 578,813
B. 587,712
C. 499,354
D. 512,945
What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1?
f(x) = − one fourth (x − 1)2 + 1
f(x) = − one fourth (x − 1)2
f(x) = one fourth (x − 1)2 + 1
f(x) = one fourth (x − 1)2
If x and y are both negative when is x-y positive