Determine if it is an arithmetic or geometric sequence:72, 48, 24…Also find the 12th term of the sequence
Answers
Given
Determine if it is an arithmetic or geometric sequence:
72, 48, 24…
Solution
Arithmetic Sequence is described as a list of numbers, in which each new term differs from a preceding term by a constant quantity.
Geometric Sequence is a set of numbers wherein each element after the first is obtained by multiplying the preceding number by a constant factor.
\(72,48,24\)-24 is the constant quantity, therefore it is an arithmetic sequence
Find the 12th term
formula
\(a_n=a_1+(n-1)d\)\(\begin{gathered} n=12 \\ a_1=72 \\ d=-24 \end{gathered}\)We can plug in to the formula
\(\begin{gathered} a_{12}=72+(12-1)-24 \\ a_{12}=72+(11)-24 \\ a_{12}=72+(-264) \\ a_{12}=72-264 \\ a_{12}=-192 \end{gathered}\)The 12th term of the sequence is -192
Related Questions
A rectangle has an area of 18 square centimeters.
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
B
C
1 cm and 18 cm
2 cm and 9 cm
3 cm and 6 cm
4 cm and 5 cm
Answers
Answer:
1 cm and 18 cm
2 cm and 9 cm
3 cm and 6 cm
Step-by-step explanation:
We need to find the factors of 18
which are; 1,18; 2,9; 3,6
So therefore we'd pick:
1 cm and 18 cm
2 cm and 9 cm
3 cm and 6 cm
Write the polynomial in factored form PICK A B C D
Answers
Factorization of Polynomials
We'll use different techniques to factorize the following polynomial:
\(6x^3-60x^2+144x\)First, we factor out the greatest possible number with the greatest possible power of the variable. This is called the GCF or the greatest common factor.
All the numbers are multiples of 6 and all of the terms have the variable x. The GCF of the three terms is 6x, thus:
\(6x^3-60x^2+144x=6x(x^2-10x+24)\)Now we need to factorize the polynomial in parentheses. The inspection method requires us to find two numbers that add up to -10 and their product is 24. These numbers are -4 and -6. Thus the polynomial can be factored as:
\(6x^3-60x^2+144x=6x(x-4)(x-6)\)This corresponds to option d
hello can you help me with this question
Answers
Answer:
B. x is less than or equal to 5
Step-by-step explanation:
The dot is on 5 and is also a solid dot which means it is less than or equal to or greater than or equal to
In this case it is less than or equal to because the line goes to the left
Hope this helped!
What is the standard form for 4x10,000+8x1,000+2x100+3x10+6x1+7x1/10
choices
48,237.07
48,236.7
4,830.07
none of these
:)
Answers
Answer:
48,236.7
Step-by-step explanation:
40,000 + 8,000 + 200 + 30 + 6 + 7/10
7/10 can also be written .7
Homework part2 need help asap
Answers
The key features of the given quadratic functions are listed below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.
For the quadratic function y = 3x² - 5, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, -5).
Domain: [-∞, ∞]
Range: [-5, ∞]
For the quadratic function y = -2x² + 12x - 15, the key features are as follows;
Axis of symmetry: x = 3.
Vertex: (3, 3).
Domain: [-∞, ∞]
Range: [-∞, 3]
For the quadratic function y = -x² + 1, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, 1).
Domain: [-∞, ∞]
Range: [-∞, 1]
For the quadratic function y = 2x² - 16x + 30, the key features are as follows;
Axis of symmetry: x = 4.
Vertex: (4, -2).
Domain: [-∞, ∞]
Range: [-2, ∞]
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Solve 8a-15-6a=85-3a
Answers
Answer:
a= 20
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helps.
Answer:
the value of a is 20
Step-by-step explanation:
8a-15-6a = 85-3a
or, 2a-15 = 85-3a
or, 2a+3a = 85+15
or, 5a = 100
or, a = 100/5
or, a = 20
therefore, a = 20
I hope it helped u. plz mark brainliest!
14 points!! PLEASE HELP MARKING BRAINLIST
Answers
Answer:
x = 58.03°
Step-by-step explanation:
Given:
17 cm is the length of the hypotenuse9 cm is the length of the adjacent sideSolve for x:
cos x = adjacent / hypotenusex = \(cos^{-1}(\frac{adjacent}{hypotenuse})\)1. \(x=cos^{-1}(\frac{9}{17})=58.03\)
Answer:
So, the measure of angle x is equal to 58.03.
What is the common difference for the arithmetic sequence?
3.2, 5, 6.8, 8.6, 10.4, ...
Answers
which is T1= 3.2 and T2= 5
so substitute :
d= 5-3.2
d= 1.8
The common difference(d) for the arithmetic sequence 3.2, 5, 6.8, 8.6, 10.4,... is 1.8.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, An arithmetic sequence 3.2, 5, 6.8, 8.6, 10.4,...
Now, to obtain the common difference we'll subtract any previous term from its next term which is d = aₙ - aₙ₋₁.
So, d = 5 - 3.2 = 1.8.
To confirm let's take another two terms d = 10.4 - 8.6 = 1.8.
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A total of 96 pints of blood were collected at the blood drive. How many quarts were collected?
Answers
Answer: 48 qt
Step-by-step explanation:
The conversion factor between pints and quarts is two which means there are 2 pints in every quart. divide the number of pints by two to find the number of quarts.
96/2 = 48
EX: 24 pints = 12 quarts
24/2 =12
EX 8 quarts = 16 pints
The same rule works in reverse but instead of dividing you multiply.
8x2 = 16
Can someone help me with this please?
Answers
Answer:
The triangles are similar.
Explanation:
Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.
Jorge is hiking a trail that is 2½ miles long. He hikes 13 miles before resting.
How much farther does he have to hike?
O A.
mile
OB.
B. mile
O C.3 mile
OD. mile
Answers
By taking a difference between mixed numbers, we can conclude that the distance left is 5/8 of a mile.
How much farther does he have to hike?We know that the total length of the trail is 2½ miles, and Jorge hikes 1⁷/₈ miles before resting.
So the distance that he has left is equal to the difference between 2½ miles and 1⁷/₈ miles.
Remember that the mixed numbers can be rewritten as:
2½ = 2 + 1/2
1⁷/₈ = 1 + 7/8
So we need to find the difference:
(2 + 1/2) - (1 + 7/8) = ( 2 - 1) + (1/2 - 7/8)
= 1 + (4/8 - 7/8) = 1 - 3/8
Now we can simplify this so we get a single fraction:
1 - 3/8 = 8/8 - 3/8 = 5/8
From this, we can conclude that the distance left is 5/8 of a mile.
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Let A =(3, 2) and B = (7, -10). What is the displacement vector that moves point A onto point B? What vector moves B onto A? Draw a diagram.
Answers
Given:
The coordinates of point A,( x1, y1)=(3, 2)
The coordinates of point B, (x2, y2)=(7, -10).
The displacement vector that moves from point A onto B can be found as,
\(\begin{gathered} \vec{BA}=(x2-x1)\hat{i}+(y2-y1)\hat{j} \\ =(7-3)\hat{i}+(-10-2)\hat{j} \\ =4\hat{i}-12\hat{j} \end{gathered}\)Hence, the displacement vector tha moves point A onto B is,
\(4\hat{i}-12\hat{j}\)The displacement vector that moves point B onto A can be found as,
\(\begin{gathered} \vec{AB}=(x1-x2)\hat{i}+(y1-y2)\hat{j} \\ =(3-7)\hat{i}+(2-(-10)\hat{j} \\ =-4i+12\hat{j} \end{gathered}\)The displacement vector BA can be drawn as,
The displacement vector AB can be drawn as,
The displacement vector from point A onto B can be found as,
\(\begin{gathered} \vec{BA}=\begin{bmatrix}{x2-x1} & {} & {} \\ {y2-y1} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{7-3} & {} & {} \\ {-10-2} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{4} & {} & {} \\ {-12} & {} & {} \\ {} & {} & \end{bmatrix} \end{gathered}\)The displacement vector from point B onto A can be found as,
\(\begin{gathered} \vec{AB}=\begin{bmatrix}{x1-x2} & {} & {} \\ {y1-y2} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{3-7} & {} & {} \\ {2-(-10)} & {} & {} \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{-4} & {} & {} \\ {12} & {} & {} \\ {} & {} & \end{bmatrix} \end{gathered}\)
In October of 2019, Gallup asked a random sample of 1,506 Americans which of two approaches to punishing murder they thought was better, the death penalty or life without possibility of parole. For the first time since Gallup began asking the question in 1985, a majority of Americans now say life imprisonment is a better approach for punishing murder than is the death penalty. According to the 2019 Gallup death-penalty poll, 60% percent of Americans asked to choose whether the death penalty or life without possibility of parole "is the better penalty for murder" chose the life-sentencing option. 36% favored the death penalty.
Required:
a. Find a 95% confidence interval for the proportion adults in the US that now believe life imprisonment is a better approach for punishing murder.
b. Interpret your interval above in the context of this problem.
c. Use your interval to find the margin of error associated with this confidence interval.
d. If we increase the level of confidence to 98%, will the interval be wider or narrower?
Answers
Answer:
a
The 95% confidence interval is \(0.5753< p <0.62474\)
b
This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval
c
The margin of error is \(E = 0.02474 \)
d
The confidence interval becomes wider
Step-by-step explanation:
From the question we are told that
The sample size is n = 1506
The sample proportion is \(\^ p = 0.60\)
From the question we are told the confidence level is 95% , hence the level of significance is
\(\alpha = (100 - 95 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)
=> \(E = 1.96 * \sqrt{\frac{0.60 (1- 0.60)}{1506} } \)
=> \(E = 0.02474 \)
Generally 95% confidence interval is mathematically represented as
\(\^ p -E < p < \^ p +E\)
=> \(0.60 - 0.02474 < p <0.60 + 0.02474\)
=> \(0.5753< p <0.62474\)
This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval
Generally the level of confidence varies directly with the critical value of \(\frac{\alpha }{2}\) and this in turn varies directly with the margin of error which when sample proportion is constant it determines the width of the confidence interval so when the level of confidence increases the confidence interval becomes wider
$200 at 6% for 10 years find the interest and find the balance of the account
Answers
Answer:
358
Stefffffffffffffffffffffffffffp-by-step explanation:
Determine which translations would map Figure
W onto Figure X
Answers
The sequence of steps that translates figure W to figure X are -
It is first shifted by the rule (x, y) → (x, y - 3)The image is then reflected across the y - axis.The image is then reflected across the x - axis.Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -
It is first shifted by the rule (x, y) → (x, y - 3)The image is then reflected across the y - axis.The image is then reflected across the x - axis.To solve more questions on translations, visit the link-
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Find the value of x in each figure
Please help
Answers
Applying the definition of complementary angles, the value of x in the given figure is: x = 18.
What are Complementary Angles?Complementary angles are a pair of angles that add up to 90 degrees. In other words, when two angles are complementary, the sum of their measures is 90 degrees.
3x and 2x are complementary angles, therefore:
3x + 2x = 90
Solve for the value of x:
5x = 90
5x/5 = 90/5
x = 18
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V=T+ab How do you Solve for A
Answers
a = (V-T)/b
Diaz Company owns a machine that cost $126,900 and has accumulated depreciation of $94,800. Prepare the entry to record the disposal of the machine on January 1 in each separate situation. 1. The machine needed extensive repairs and was not worth repairing. Diaz disposed of the machine, receiving nothing in return. 2. Diaz sold the machine for $15,800 cash. 3. Diaz sold the machine for $32,100 cash. 4. Diaz sold the machine for $40,600 cash.
Answers
Answer:
32100 is the right answer
If f(x) = (2x^3 − 4)^6, then what is f '(x)?
21x^2(x^3 − 4)^5
21x^8
6(2x^3 − 4)^5
6(2x^3 − 4)^5(6x^2)
Answers
6(2x^3-4)^5(6x^2)
Explanation:
That is the derivative after you differentiate using the Chain Rule.
expressions that have 2\3 as a product.
Answers
The expression that have 2\3 as a product are 4/5 × 5/6 and 6/7 × 7/9 which is option (a) and (e) .
An expression in maths could be a sentence with a minimum of 2 numbers/variables and a minimum of one maths operation in it.An expression could be a combination of terms that are combined by victimization mathematical operations like subtraction, addition, multiplication, and division.(a) 4/5 × 5/6 = 20/30
= 2 /3
(b) 7/8 × 9/10 = 63 / 80
(c) 1/3 × 2/3 = 2 /9
(d) 3/4 × 7/12 = 21 / 48
= 7 / 16
(e) 6/7 × 7/9 = 42 /63
= 6 / 9
= 2 / 3
Only the expression (a) and (e) have 2\3 as a product.
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The complete question is given below :
Choose all the expressions that have 2\3 as a product.
(a) 4/5 × 5/6
(b) 7/8 × 9/10
(c) 1/3 × 2/3
(d) 3/4 × 7/12
(e) 6/7 × 7/9
3(x+5)-2(-3x+1)
PLZ Answer
Answers
It should look like...
3x +15-6x-2
Then you would combine light terms.
And your final answer should be
-3x+13
the point halfway between two endpoints of a line segment
Answers
The midpoint of a line segment is the point that is halfway between the two ends of the line segment. A midway separates a line segment into two equal parts.
This is further explained below.
What is a line segment?Generally, In the field of geometry, a line segment is defined as the portion of a line that is enclosed by two unique points on the line.
Alternatively, we may say that a line segment is the portion of a line that is between two points. A line does not have any endpoints and may stretch endlessly in any direction, however, a line segment has two endpoints that are fixed or definite in some way.
In conclusion, The term "midpoint" refers to the point along a line segment that is situated exactly midway between the beginning and ending points. A midway separates a line segment into two equal parts.
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The gas tank in Phil’s car was 1/8 full. He put more gasoline in the cars gas tank.the number line below shows how full the cars gas tank was before and after Phil put in more gasoline.
Answers
Answer:
The answer is 1/8+5/8=3/4
Step-by-step explanation:
Integrate :-
\(\displaystyle \int \dfrac{\sqrt{x}}{1+x}\:dx\)
\( \: \: \: \: \)
Answers
Explanation :
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ \int \frac{2 \: {t}^{2} }{1 + {t}^{2} } \: dt }} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \times \int \frac{ {t}^{2} }{1 + {t}^{2} } \: dt}} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \times \int \frac{ {t}^{2} + 1 - 1}{1 + {t}^{2} } \: dt}} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \times \int \frac{ {t}^{2} + 1 }{1 + {t}^{2} } - \frac{1}{1 + {t}^{2} } \: dt}} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \bigg( \int \frac{ {t}^{2} + 1 }{1 + {t}^{2} } \: dt - \int\frac{1}{1 + {t}^{2} } \: dt} \bigg)} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \bigg( t - \int \frac{ 1 }{1 + {t}^{2} } \: dt \bigg)}} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \bigg(t - arctan(t) \bigg)}} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\( \begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \bigg( \sqrt{x} - arctan( \sqrt{x} ) \bigg)}} \\ \\ \end{gathered}\end{gathered} \end{gathered} \)
\(\begin{gathered}\begin{gathered}\begin{gathered}\\ : \implies{ \bold{ 2 \sqrt{x} - 2 \: arctan( \sqrt{x} \: ) }} \\ \\ \end{gathered}\end{gathered} \end{gathered}\\ \\ \begin{gathered}\begin{gathered}\begin{gathered}\\ :\implies\large{ \boxed{ \bold{ 2\sqrt{x} - 2 \: arctan( \sqrt{x} \: ) + C}}} \\\end{gathered} \\ \\\end{gathered}\end{gathered}\)
Find APR (rounded to the nearest tenth of a percent) for the loan. Purchase a living room set for $3,600 at 8% add-on interest for 3 years.
Answers
Answer:
The APR for the loan 15.6%
Step-by-step explanation:
From the given information:
The annual percentage can be calculated by using the formula:
\(APR = \dfrac{2 \ Nr}{N +1}\)
where;
N = number of payments = 3 years = 12 × 3 = 36 months
r = add-on interest rate = 8% = 0.08
Replacing our value to calculate the APR, we get:
\(APR = \dfrac{2 \times 36 \times 0.08}{36 +1}\)
\(APR = \dfrac{5.76}{37}\)
APR = 0.155675
APR ≅ 15.6%
A marching band needs to raise $13,500 for a trip to the Rose Bowl. The director told the band members that one-third of the amount that has been raised so far is equal to half of the amount that is still needed. How much more money needs to be raised for the trip?
Answers
Answer: $5400
Step-by-step explanation:
x = amount raised so far
13500 - x = amt. still needed
x/3 = (13500 - x)/2
2x = 3(13500 - x)
2x = 40500 - 3x
5x = 40500
x = 40500/5 = 8100 (amt. raised so far)
13500 - 8100 = 5400 (amt. still needed)
Find the sum of the first 40 terms of the series (-59)+(-56)+(-53)+…..
Answers
Given:
\((-59)+(-56)+(-53)+\text{.}\ldots\ldots\text{.}\)The given series is in arithmetic progression with a common difference of 3.
The sum of the first n terms in the arithmetic progression is given as,
\(\begin{gathered} S_n=\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ a=-59,d=3 \\ S_{40}=\frac{40}{2}\lbrack2(-59)+(40-1)3\rbrack \\ =20\lbrack-118+117\rbrack \\ =-20 \end{gathered}\)Answer: the sum of the first 40 terms in the given series is -20.
Sam and Paul started a business. Their investments were in the ratio 6 : 7, respectively. How much did Paul invest if Sam's investment was $828?
Answers
Answer:
$966
Step-by-step explanation:
6/7 = 828/x
Write a proportion.
6x = 7(828) Use cross products.
6x = 5796 Multiply.
x = 966 Divide both sides by 6.
Paul's investment was $966.
I NEED HELPP Solve for PMR please
Answers
The angle PMR in the quadrilateral is 32 degrees.
How to find the angle PMR?The angle PMR can be found as follows;
The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.
∠RPM ≅ ∠WPM
Hence,
∠RPM ≅ ∠WPM = 58 degrees
Therefore,
∠WPM = 58 degrees
∠PWM = 90 degrees
Let's find ∠PMR as follows
∠PMR = 180 - 90 - 58
∠PMR = 90 - 58
∠PMR = 32 degrees
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Refer to a deck of fifty-two playing cards (jokers not allowed).
(a) How many five-card poker hands consisting of all hearts are possible?
(b) How many five-card poker hands consisting of all cards of the same suit are possible?
Answers
a) 1287 five-card poker hands consisting of all hearts possible.
(b) 5148 five-card poker hands consisting of all cards of the same suit are possible?
What are the combination formulae?\(_{n} C_{r} = \frac{n!}{(n-r)!r!} \\\\\)
consider a deck of fifty-two playing cards (jokers not allowed).
(a) To calculate five-card poker hands consisting of all hearts possible we can use the combination formulae
\(_{n} C_{r} = \frac{n!}{(n-r)!r!} \\\\_{13}C_{5} = \frac{n!}{(n-r)!r!} \\_{13}C_{5} = \frac{13! }{(13-5)!5!} \\\\_{13}C_{5} = \frac{13*12*11*10*9*8!}{8!*(5*4*3*2*1)} \\\\_{13}C_{5} = 1287\)
b) To calculate five-card poker hands consisting of all cards of the same suit possible by using combination formulae
A deck of cards contains four different suits. After selecting one of them, we must then select five cards from that deck. The total number of five-card poker hands with identical-suited cards is thus:
\(_{n} C_{r} = \frac{n!}{(n-r)!r!} \\\\4 * _{13}C_{5} =4 * \frac{n!}{(n-r)!r!} \\4 * _{13}C_{5} = 4 * \frac{13! }{(13-5)!5!} \\\\4 * _{13}C_{5} = 4 * \frac{13*12*11*10*9*8!}{8!*(5*4*3*2*1)} \\\\4 * _{13}C_{5} = 4 *1287\\\\4 * _{13}C_{5} = 5148\)
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