The 12th term of the sequence 3, -9, 27, -81, 243, ... is 177,147.
Explanation:The given sequence is: 3, -9, 27, -81, 243, ...
To find the 12th term, we can observe that the sequence alternates between positive and negative, and each term is obtained by multiplying the previous term by -3. Starting with 3 as the first term, we can find the 12th term using the formula:
an = a1 * (-3)n-1
Substituting the values, we have:
a12 = 3 * (-3)12-1a12 = 3 * (-3)11a12 = 3 * (-32)5a12 = 3 * 95a12 = 3 * 59049a12 = 177,147Final answer:
The 12th term of the geometric sequence is -531441, found by using the formula for the nth term of a geometric series with a first term of 3 and a common ratio of -3.
Explanation:
The sequence given is geometric with each term being multiplied by -3 to obtain the next term. To find the 12th term of the sequence, we can use the formula for the nth term of a geometric sequence: Tn = a * rn-1, where a is the first term, r is the common ratio, and n is the term number.
For the given sequence, the first term a is 3 and the common ratio r is -3. The 12th term is found by placing these values into the formula:
T12 = 3 * (-3)12-1
T12 = 3 * (-3)11
T12 = 3 * (-177147)
T12 = -531441
Therefore, the 12th term of the sequence is -531441.
Bob bought 3 packs of model cars. He gave 4 cars to Ann.Bob has 11 model cars left how many model cars were in each pack.
Please help math question
The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
(3, 4)
(3, 5)
(30, 401)
(30, 501)
Factor this expression completely and then place the factors in the proper location. Note: Place factors alphabetically!
mn - 4m - 5n + 20
To solve this problem you must apply the proccedure shown below:
1. You have the following expression given in the problem above:
[tex] mn - 4m - 5n + 20 [/tex]
2. The first thing you must do to factor the expression is to group the terms, as following:
[tex] (mn-4m)+(-5n+20) [/tex]
3. Now, choose the greatest common factor of each group:
[tex] m(n-4)-5(n-4) [/tex]
4. Now, you need to factor the expression by factoring out the [tex] n-4 [/tex]
[tex] (m-5)(n-4) [/tex]
The answer is: [tex] (m-5)(n-4) [/tex]
Tomas can do a job in 4 hours. julia can do the same job in 6 hours. how many hours will it take the two of them to do the job if they work together?
Benson has a bankruptcy on his credit report, so he pays higher interest rates on his current loans. He calculates that the extra money he pays in additional interest each year, if invested at the rate of 2% for one year, could earn him simple interest totaling $180. How much does Benson pay in additional interest each month? a. $360 b. $750 c. $900 d. $1,000
Answer:
The correct answer is letter b, $750
Step-by-step explanation:
Which of the following is a solution of x2 + 6x = −18?
The correct option are a. [tex]\(x = -3 + 3i\)[/tex] and b. [tex]\(x = -3 - 3i\)[/tex].The solutions are complex numbers [tex]\(x = -3 + 3i\)[/tex] and [tex]\(x = -3 - 3i\)[/tex].
To find the solution of the quadratic equation [tex]\(x^2 + 6x = -18\)[/tex], we need to solve it for [tex]x[/tex].
Starting with the given equation:
[tex]\[x^2 + 6x = -18\][/tex]
Rearranging it to the standard form of a quadratic equation:
[tex]\[x^2 + 6x + 18 = 0\][/tex]
Now, to find the solutions, we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 1\), \(b = 6\)[/tex], and [tex]\(c = 18\).[/tex]
Substituting the values:
[tex]\[x = \frac{{-6 \pm \sqrt{{6^2 - 4 \cdot 1 \cdot 18}}}}{{2 \cdot 1}}\]\[x = \frac{{-6 \pm \sqrt{{36 - 72}}}}{2}\]\[x = \frac{{-6 \pm \sqrt{{-36}}}}{2}\]\[x = \frac{{-6 \pm 6i}}{{2}}\]\[x = -3 \pm 3i\][/tex]
So, the solutions are complex numbers [tex]\(x = -3 + 3i\)[/tex] and [tex]\(x = -3 - 3i\)[/tex].
The complete question is:
Which of the following is a solution of [tex]\(x^2 + 6x = -18\)[/tex]?
a) [tex]\(x = -3 + 3i\)[/tex]
b) [tex]\(x = -3 - 3i\)[/tex]
c) [tex]\(x = -3\)[/tex]
d) [tex]\(x = 3\)[/tex]
Researchers randomly choose two groups from 15 volunteers. Over a period of 9 weeks, one group watches television before going to sleep, and the other does not. Volunteers wear monitoring devices while sleeping, and researchers record dream activity. Which type of study method is described in each situation?
A. not enough information given
B. survey
C. observational study
D. controlled experiment
Match the y-coordinate with the given x-coordinate for the equation y = log10x.
1. 1/100 -2
2. 1/10 0
3. 1 2
4. 10 1
5. 100 -1
Answer:
Match the y-coordinate with the given x-coordinate for the equation y = log10x.
1. 1/100
3
0
2. 1/10
1
-2
3. 100
2
-1
4. 1
5
2
5. 10
4
1
In how many ways can 3 identical emeralds 2 identical diamonds and 2 different opals be arranged in a row in a display case
They can be arranged in 210 ways.
We have given that, 3 identical emeralds 2 identical diamonds and 2 different opals
What is the arrangement of n object where n₁ is one kind, n₂ is a second kind, and n₃ is a third kind?The arrangement of n objects where n₁ is one kind, n₂ is a second kind, and n₃ is a third kind is given by
[tex]\frac{n!}{n_1!*n_2!*n_3!}[/tex]
The total number of gems =7
3 of the first kind, 2 of the second kind and 2 of the third kind
Therefore, we get
[tex]\frac{7!}{2!*2!*3!}=210[/tex]
Therefore ,they can be arranged in 210 ways.
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What is the value of x?
a. 7
b. 7√2
c. 14
d. 14√2
p(x)= x^3+4x^2-8x-6
a= -2
Solve 3/10 n-3 1/5 = -1 1/5
Answers-
A.n =-12 2/3
B.n = 6 2/3
C.n = 8
D.n = -6/25
Answer: B. n = 6 2/3
Hope this helps!
How do I solve for X?
Determine the values of x on which the function f(x)=2x^2-x-15/4x^2-12x is discontinuous and verify the type of discontinuity at each point.
A.There is a vertical asymptote at 0 and a hole at 3.
B.There are vertical asymptotes at -5/2 & 0 and a hole at 3.
C.There is a vertical asymptote at 3 and a hole at 0.
D.There are vertical asymptotes at 0 & 3.
There is a vertical asymptote at x = 0 (because the denominator becomes 0). We need to further analyze the behavior at x = 3 to see if it's a hole (cancellation) or the function is continuous there (Option A or B might be the answer).
Step 1: Identify Potential Discontinuities
A rational function (like f(x)) is discontinuous when its denominator is zero. So, we need to find the values of x that make the denominator 0:
Denominator = 4x^2 - 12x = 0
Factor the denominator: 4x(x - 3) = 0
This gives us two possible values for x: x = 0 and x = 3.
Step 2: Verify Discontinuity Type at Each Point
Check if the function is defined (has a value) at these points.
x = 0: If we plug x = 0 in the original function, we get 0/0, which is indeterminate. This suggests a potential vertical asymptote at x = 0.
x = 3: If we plug x = 3 in the original function, the expression doesn't become 0/0. The function might have a hole or be continuous at x = 3.
Step 3: Analyze for Holes (Optional):
To further investigate x = 3, we can try to simplify the function by factoring the numerator (possible because the denominator is already factored). If the simplification gets rid of the term that causes the 0/0 at x = 3, it creates a hole.
realtor makes 3% commission. What is the commission on a $200,000 house?
How many combinations of four books can be made from eight different books? 24 70 1,680?
Answer:
70
Step-by-step explanation:
four books can be made from eight different books
4 books to be chosen from 8 books
The order does not matters so we use Combination.
four books can be made from eight different books, so we find 8C4
[tex]nCr= \frac{n!}{r!(n-r)!}[/tex]
[tex]8C4= \frac{8!}{4!(8-4)!}[/tex]
[tex]8C4= \frac{8!}{4!(4)!}[/tex]
[tex]8C4= \frac{8*7*6*5*4!}{4!(4)!}=70[/tex]
Answer:
70
Step-by-step explanation:
For an investment of $26,245, a quarterly statement reports that the account balance is $26,292. The statement also reports that for the same quarter, the rate of return on the investment was -0.02%. Given the information regarding the investment's current balance, does the reported rate of return seem reasonable? Use complete sentences to explain your answer.
Answer:
Rate of return is 0.2% positive according to given data. The given rate of return is inconsistent with the given data.
Step-by-step explanation:
The rate of return on the statement is inconsistent with the information given.
As per given data
Investment = $26,245
Account balance = $26,292
Return on the investment
Difference = $26,292 - $26,245 = $47
Investment is increase by $47
Now calculate the percentage of rate of return.
Percentage change = ($47 / $26,245) x 100 = 0.2%
Rate of return is 0.2% positive according to given data. Hence proved that, the given rate of return is inconsistent.
shadesha invests $24,000 at age 27. at the age 31 jerome invests $2000 annually until retirement both invest at 7% compounded annually to plan to retire at 65 who has more money for retirement
what is the sum of 2 2/3 and 1 5/6?
Deon worked 16 hours last week at the grocery store and earned $124.00. If he continues to earn the same hourly pay, how many additional hours must he work to earn another $186.00? A. 20 hours B. 24 hours C. 32 hours D. 62 hours
Celeste wants to have her hair cut and permed and also go to lunch she knows she will need $95. the perm costs twice as much as her haircut and she needs 5$ for lunch. how much does the perm cost
What is the slope of the line shown on the graph?
1) If the endpoints of the diameter of a circle are (9, 4) and (5, 2), what is the standard form equation of the circle?
In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 8 in.?
8√ in.
88√ in.
28√ in.
82√ in.
Yo! For anyone who comes across this..answer is D; 8√2in.
Hope this helps!!
The length of the hypotenuse when the length of one of the legs is 8 in. is 8√2 in option (D) is correct.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given:
In a 45-45-90 triangle
The length of one side = 8 in
The length of other side = 8 in (because 45-45-90)
Using Pythagoras theorem:
Hypotenuse = √8² + 8²
= 8√2
Thus, the length of the hypotenuse when the length of one of the legs is 8 in. is 8√2 in option (D) is correct.
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Rovide an appropriate response.4) assume that adults have iq scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the wechsler test). find the iq score separating the top 14% from the others. 4)
What is the solution to the following system? 3x+3y+6z=9 x+3y+2z=5 3x+12y+12z=18
(3, 1, 0)
(0, 1, 0)
(2, 1, 0)
(–2, 1, 0)
Answer:
C. (2, 1, 0)
Step-by-step explanation:
Hope this helps!! Have a great day!! : )
I'm so glad to have been able to helps 6,000 of y'all!!
Today Jan put a necklace on layaway by making a down payment of $75 and agreeing to pay $15 per month, starting next month, for 18 months. When will Jan receive the necklace?
Answer:
The answer is 18 months.
Step-by-step explanation:
Today Jan put a necklace on layaway by making a down payment of $75 and agreeing to pay $15 per month, starting next month, for 18 months.
So, she will receive the necklace in 18 months.
Layaway is a system of paying a deposit for your product to secure it for later purchase. When all your payments are done, the product is given to you.
What is the range of the function y = -x2 + 1?
Final answer:
The range of the function y = -x^2 + 1 is all real numbers less than or equal to 1, represented as ]-∞, 1].
Explanation:
The range of the function y = -x^2 + 1 refers to the set of all possible values that y can take as x varies over all real numbers. Since the function is a downward-opening parabola (due to the negative coefficient of x^2), the maximum value of y is at the vertex of the parabola. The vertex, in this case, occurs at x=0, which gives us the maximum y value of y = 1. As x moves away from zero in either direction, the value of y decreases and approaches negative infinity. Hence, the range of this function is ]-∞, 1], or all real numbers less than or equal to 1.
There are 750 toothpicks in a regular sized box. If a jumbo box is made by doubling all the dimensions of the regular sized box, how many toothpicks will the jumbo box hold? (With work pls)
To answer this, let the 3 sides of the regular sized rectangular box be x, y, and z.
When we double all the sides, the new sides have lengths 2x, 2y, and 2z, respectively.
Since the regular box (with dimensions x,y, and z) have 750 toothpicks, we can write
[tex]xyz=750[/tex]
Similarly we can write for the jumbo box as,
[tex](2x)(2y)(2z)[/tex]
which is equal to [tex]8(xyz)[/tex]
So this is 8 times the original of [tex]xyz[/tex]. Hence the jumbo box will have 8 times 750 number of toothpicks.
ANSWER: [tex]8*750=6000[/tex] toothpicks
Answer:
6000
Step-by-step explanation: