Use the following sequence to complete the parts: 8, 5, 2, -1,...
Is this arithmetic or geometric? (Type A or G)
What are the NEXT 3 terms?
What is the equation? t(n) =
What would be the 100th term?
n+
Is-345 a part of the sequence? (Type Y or N)
Answers
The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289.
What is a sequence?
A sequence is a function from natural numbers to the set of real numbers. it maps the set of number numbers on the set of real numbers.
We are given a sequence 8, 5,2, -1,.....
Now the first term of the sequence is 8 and common difference is -3.
As the difference between 2 consecutive terms is same, the given sequence is arithmetic.
now substituting this in the standard equation
we get,
t(n) = a+ (n-1)d
t(n)= 8+(n-1)(-3)
t(n) = 8-3n+3
t(n) = 11-3n (1)
Now we have to find the 5th, 6th, 7th term of the sequence
We substitute n=5, n=6, n=6 in equation 1
We get
t(5) = 11-3(5)
t(5) = 11-15
t(5) = -4
And,
t(6) = 11-3(6)
t(6) = 11-18
t(6) = -7
And,
t(7) = 11-3(7)
t(7) = 11-21
t(7) = -10
Hence the next three terms are -4, -7, -10.
The equation is t(n) = 11-3n
The 100th term would be given as
t(100) = 11-3(100)
t(100) = 11-300
t(100) = -289
Hence, The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289
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Related Questions
The top of a 15-foot ladder is 3 feet farther up a wall than the foot of the ladder is from the bottom of the wall. How far up is the foot of the ladder from the bottom of the wall?
The answer is 9 but I don’t know how to get there.
Answers
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]
let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.
write a congruence statement for the pair of triangles
Answers
The concurrency statement for the given triangles is that (D) △RGB ≅ △DCS under ASA condition.
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.If two triangles satisfy one of the following conditions, they are congruent: The three corresponding side pairings are all equal. The comparable angles between two pairs of corresponding sides are equal. The corresponding sides between two pairs of corresponding angles are equal.So, the congruence statement of the given 2 triangles is as follows:
△RGB ≅ △DCS
∠G = ∠CGB = CS∠B = ∠SHence, △RGB ≅ △DCS under ASA condition.
Therefore, the concurrency statement for the given triangles is that (D) △RGB ≅ △DCS under ASA condition.
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X
Work out the mean for the data set
below:
6.8, 5.7, 0.8, 4.7, 1.3
Give your answer as a decimal.
Answers
Average = Sum / Count
= 19.3 / 5
= 3.86
a square matrix is nilpotent if for some positive integer . let be the vector space of all matrices with real entries. let be the set of all nilpotent matrices with real entries. is a subspace of the vector space ?
Answers
An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
What is nilpotent matrix?A nilpotent matrix in linear algebra is a square matrix N such thatfor some positive integer kk. The index of occasionally the degree of the smallest such k A nilpotent transformation, more generally speaking, It is a linear transformation of a vector space such that Lk=0 for some positive integer. Both of these ideas are specific examples of the more basic idea of nilpotence, which is applicable to rings' constituent parts.acc to our question-
When n=1, the only 1×1 nilpotent matrix is (0). Thus U={(0)} and it is a subspace of VIn this case, we prove that the set U of all 2×2 nilpotent matrices is not a subspace of V.The set U is not a subspace because it is not closed under addition as the following example shows.Hence,An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
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the number of cars that go through the drive-in window at a local bank each hour is an example of a continuous random variable.
Answers
The first statement is false and the second statement is true.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. There are two types of random variables.
Discrete random variablesContinuous random variablesA random variable that takes a finite number of possible values can be defined as a Discrete random variable. A random variable that takes an infinite number of possible values can be defined as a Continuous random variable. A continuous random variable consists of only continuous values.
Continuous random variables are defined at intervals of values. Continuous random variables are represented by the area under a curve.
⇒ The number of cars that go through the drive-in window at a local bank each hour.
The number of cars can be counted and can be an integer like 10, 20,100 etc.
∵ The number of cars is countable it is not an example of a continuous random variable
⇒ The high daily temperature in Anchorage.
High daily temperature can be an integer or function like 60°, 120° etc
∵ The high daily temperature is an example of a continuous random variable.
Therefore, The number of cars that go through the drive-in window at a local bank each hour is not an example of a continuous random variable and The high daily temperature in Anchorage is an example of a continuous random variable.
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The complete question is
A line with a slope of –
5 passes through the points (7,–
2) and (8,q). What is the value of q?
Answers
The line with a slope of –5 that passes through the points (7,–2) and (8,q) has q as -7.
How to find the value of q with the slope?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (7, –2) and (8, q) with a slope of - 5.
Hence, let's find q.
y = - 5x + b
Let's find y-intercept
-2 = -5(7) + b
b = -2 + 35
b = 33
Therefore,
y = -5x + 33
Hence, let's find q.
y = -5(8) + 33
q = -40 + 33
q = -7
Therefore, q = - 7
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Write the following values in ascending order (smallest to largest):
0.1, 0.09, 2%,7/10,19/100
Answers
In this case put all the numbers over 100
10/100 (0.1),
9/100 (0.09),
20/100 (2%),
70/100 (7/10),
19/100 (19/100).
Then order them using the base 10 system
9/100, 10/100, 19/100, 20/100, 70/100
Answer: 0.09, 0.1, 19/100, 2%, 7/10
Reflect the figure over the line y=1/3x+1
Answers
Answer:
see the attachment
Step-by-step explanation:
You want a graph of the given figure reflected over the line y = 1/3x +1.
Line of reflectionThe given line of reflection can be written in general form as ...
y = 1/3x +1
3y = x +3 . . . . . . multiply by 3
x -3y +3 = 0 . . . . subtract 3y
This is in the general form ...
ax +by +c = 0
where a=1, b=-3, c=3.
The line of reflection is the perpendicular bisector of the segment joining a point (x, y) with its reflection (x', y').
Reflected pointUsing the formula in the second attachment, we find the reflection
(x1, y1) ⇒ (x, y)
satisfies ...
(x -x1)/a = (y -y1)/b = -2(ax1 +by1 +c)/(a² +b²)
or ...
x = -2a/(a²+b²)·(ax1 +by1 +c) +x1
y = -2b/(a²+b²)·(ax1 +by1 +c) +y1
Using the known values for a, b, c, we have ...
x = -2(1)/(1² +(-3)²)·(x1 -3y1 +3) +x1 = (1/5)(4x1 +3y1 -3)
y = -2(-3)/10·(x1 -3y1 +3) +y1 = (1/5)(3x1 -4y1 +9)
Rewriting the mapping in more conventional terms, we have ...
(x, y) ⇒ ((4x +3y -3)/5, (3x -4y +9)/5)
It is convenient to let a spreadsheet do the repetitive tedious math. The third attachment shows the application of this mapping to the coordinates of the figure's vertices (clockwise from bottom).
__
Additional comment
The figure showing the reflected polygon was created by a geometry program using its "reflect over a line" feature.
a simple random sample of 25 observations is dervied from a normally distributed population with a population standard deviation of 8.2. compute the margin of error with 80% confidence.
Answers
The margin of error with 80% confidence interval is 2.099
Given that,
A straightforward random sample of 25 observations is taken from a population that is normally distributed and has a standard deviation of 8.2.
To find : The margin of error with 80% confidence
Margin of Error : The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
Here we have
n=25,σ=8.2
For 80% confidence interval, the critical value of z is 1.28. So requried margin of error is
ME=[tex]Z_{c}\cdot \frac{\sigma}{\sqrt{n}}[/tex]=1.28[tex]\cdot \frac{8.2}{\sqrt{25}}[/tex]=2.0992
Thus, with 80% confidence, the error margin is 2.099.
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p(x) = (x² - 9) (x² + x - 2)
factor for zeros to plot on a graph
pls help :(
Answers
Answer:
P(x) = (x - 3)(x + 3)(x + 2)(x - 1)
Answer:
Step-by-step explanation:
Solution:To write a polynomial in standard form, simplify and then arrange the terms in descending order.Expand ( x2 − 9 )( x + 2 ) using the FOIL Method.Simplify each term.
nine out of ten student prefer math class over lunch. how many student do not prefer math if 200student were asked
Answers
20 x 1 = 20 (1 out of ten)
20 students do not prefer math
Answer:
Step-by-step explanation:
20? lol
4. Which of the following statements is true?
A. -8> -7
B.9<3
C.0> -3
D. 0> 4
Answers
Answer:
C
Step-by-step explanation:
If you look at a number line, you can see that numbers with greater values are to the right of numbers with smaller values.
-8 is to the left of -7 on a number line so it is not greater
9 is to the right of 3 on a number line so it is not smaller
0 is to the right of -3 on a number line so it is greater
And lastly, 0 is to the left of 4 on a number line so it is not greater
a banana weighs 140 g a pineapple weighs 345 g bag a contains 8 bananas and bag b contains 3 pineapples which bag weighs more and by how much show your working
Answers
Answer:
Bag a, by 85 grams!
Step-by-step explanation:
1) Work out the weight of bag a
1 banana is 140 grams so to find out 8 you have to multiply them
140 x 8 = 1120
Bag a = 1120 grams
2) Work out the weight of bag b
1 pineapple weight 345 grams so to find out 3 you have to multiply them just like above
345 x 3 = 1035
Bag b = 1035
3) Find the difference
Bag a is 1120 grams and bag b is 1035
To find out out by how much you just have to subtract them
1120 - 1035 = 85
Hope this helps, have a great day!
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
the shorter leg = 9mm
the longer leg = 12mm
the hypotenuse is 15mm
Step-by-step explanation:
x^2 +(x+3)^2 =(x+6)^2
x^2 + x^2 + 6x +9=x^2 + 12x +36
x^2-6x-27=0
(x+3)(3-9)=0
x=-3 (impossible) ... or x=9
average temperatures were measured at five randomly selected soups. the x-bar and r-bar were found 45.25 degree and 1.05 degree, respectively. the uclr and lclr are:
Answers
The UCLR (Upper Control Limit) and LCLR(Lower Control Limit) are 2.22 and 0 respectively.
Given that,
At five soups that were chosen at random, average temperatures were recorded. X-bar and r-bar positions were 45.25 degree and 1.05 degree, respectively.
To find : UCLR (Upper Control Limit) and LCLR (Lower Control Limit)
R-bar = 1.05 Degrees
X-bar = 45.25 Degrees
Sample Size , n=5
D3=0
D4=2.114
3 Sigma control limits of Range Chart
LCLR = D3*R-bar = 0*1.05 =0
UCLR =D4*R-bar = 2.114*1.05 = 2.22
The UCLR (Upper Control Limit) and LCLR (Lower Control Limit) are therefore 2.22 and 0, respectively.
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An account now contains $12,680 and has been accumulating interest at a 8% annual rate, compounded continuously, for 7 years. find the initial deposit. (round your answer to the nearest cent.)
Answers
The initial amount of the deposit is $7234.23
Compound interest is calculated on a deposit's or a loan's initial principal as well as the accrued interest from earlier periods. Compound interest's impact is frequency-dependent. The most frequent compounding occurs with continuously compounded rewards. The mathematical maximum that compound interest can achieve is continuous compounding. Since most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.
For compound continuous problems, we use the formula [tex]A = Pe^{rt}[/tex]
where A = final amount
P = principal amount invested
e = exponent
r = rate of interest
t = time period in years
[tex]12680 = Pe^{.08(7)} \\12680 = Pe^{0.56}\\ 12680 = P*1.7506\\[/tex]
P = $7243.23
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Método de igualación. {x-2y=11
x+5y=−17
Answers
The value of x and y is 7 and -2 respectively.
The equations to solve are -
x - 2y = 11 ....[1]x + 5y =−17 ....[2]On adding equations 1 and 2 we get ,
3y = -6
y = -2
Putting the value of y in equation 1,
⇒ x - 2(-2) = 11
⇒ x + 4 = 11
⇒ x = 7
Hence ,the value of x and y is 7 and -2 respectively.
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easy trig please heeelp me
Answers
Answer:
9
Step-by-step explanation:
Pythagorean triples. 3, 4, 5. Multiply by 3 and get 9.
daysha loves the caramel macchiato at the coffee shop. the 16 oz. medium size has 260 calories. how many calories will she get if she drinks the larger 20 oz. size?
Answers
After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.
What is proportion?
Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.
Here 16 oz medium size has 260 calories.
Then
=> [tex]\frac{size of coffee}{ calories}[/tex]
=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]
=>x=[tex]\frac{20*260}{16}[/tex]
=> x = 325
Hence 325 calories will she get if she drinks the larger 20 oz. size.
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What is the equation of the line that passes through the points (-7.
-5) and (2, 3)? Write your answer in slope-intercept form.
Show your work here
Answers
The equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
The first point = (-7, -5)
The second point = (2, 3)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (3- (-5) / (2 - (-7))
= (3 + 5) / (2 + 7)
= 8 / 9
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point = (2,3)
Substitute the values in the equation
y - 3 = (8/9)(x - 2)
y - 3 = (8/9)x - 16/9
y = (8/9)x - 16/9 + 3
y = (8/9)x - 11/9
Hence, the equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
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A survey of the worlds nation in 2004 shows a strong positive correlation between percentage of the country using cell phones and life expectancy and years at birth
Answers
1. No This survey does not mean that cell phones are good for your health.
2. The factor that can be used as the best explanation for the strong correlation would be the general economic conditions of the people.
What is meant by a strong correlation?When one variable's value rises, the other variable's value also rises in a similar way. For instance, a student's exam score tends to be greater the more hours they study. Exam results and study time have a significant positive link.
A strong correlation, also known as a high correlation, indicates that two or more variables have a significant relationship with one another, whereas a weak or low correlation indicates that the variables are rarely associated.
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complete question
A survey of the world's nations in 2004 shows a strong positive correlation (hence, a positive association) between percentage of the country using cell phones and life expectancy in years at birth.
a. Does this mean that cell phones are good for your health? select one: ____ yes ____ no
b. What might best explain the strong correlation (as a lurking variable)?
Select one:
_____ Percent of young people
____ General economic conditions of the country
____ Percent of pop. living in cities
HELPPPPPPPPPPPpp
Robert pays for his family to go to the arcade. He pays an entrance fee for his group and an additional amount per game that his family plays as shown in the graph. Use the graph to answer.
Find the slope and interpret its meaning.
Answers
Answer:
3/4,. it's means for every 4 games there's a $3 fee
Step-by-step explanation:
3/4
it's means for every 4 games there's a $3 fee
Given
a = -4, b = -4 and c = -5
work out
b² - 2ac
Answers
Answer:
-24
Step-by-step explanation:
b²-2ac
(-4)²-2(-4)(-5)16-40-24⇒Plug in the values given in places and simplify.
[tex]=(-4)^{2} -2(-4)(-5)\\=16-2(20)\\=16-40\\=-24[/tex]
-24 is the answer after substitution of the known values.
a recipe calls for 15oz of flour every 8oz of milk, if you use 150z of milk how much flour should you use
Answers
The required weight of the flour is 28.125 ounces.
A recipe calls for 15 ounces of flour for every 8 ounces of milk. It is given that we use 15 ounces of milk. Then we need to calculate the weight of flour we need to use.
The ratios of the ingredients must remain in equal proportions. The fraction of one divided by the other is referred to as the ratio. A proportion is an equation that equates two ratios. We will use the unitary method. Let the weight of the flour required be denoted by the variable "w". A variable is a quantity that can change in a mathematical problem or experiment.
w = (15/8)*15
w = 28.125
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Find the slope on the line going through the points (36, -21) and (-14, -21)
Answers
Answer:
0
Step-by-step explanation:
[tex]m=\frac{-21-(-21)}{-14-36}[/tex]
Answer: slope = 0
Step-by-step explanation:
slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0
It's a horizontal line
P(A and B)
P(B)
Find P (Junior | Girl) Hint:
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5
7 12
Junior 2
3 5
Senior 1 4 5
12 18
[?]
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
Answers
Probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
As given in the question,
From the given table we have,
Total number of girls and boys in the class = 30
Total number of boys in class = 12
Total number of girls in class = 18
As per given Hint: P(A/B) = P(A and B) / P(B)
A is the Junior
B is the girl
Probability as per given condition is:
P(Junior / Girl) = P(Junior and girl) / P(girl)
= (3/30) / (18/30)
= 3/18
= 1/6 ( lowest term of fraction)
Therefore, probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
The complete question is:
Find P(Junior / Girl) Hint: P(A/B) = P(A and B) / P(B) .
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5 7 12
Junior 2 3 5
Senior 1 4 5
12 18
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
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students deliver newspapers and magazines to houses.
one day,they have to deliver 875 newspapers and 1200 magazines.
each student can deliver 35 newspapers or 50 magazines in 1 hour.
each student can only work for 8 hours
work out the minimum number of students needed
Answers
Answer:
4 students for newspapers & 3 students for magazines are needed for the deliveries to be made in a day.
Step-by-step explanation:
According to the question,
875 newspapers & 1200 magazines are to be delivered in a day by students.In an hour each student can deliver 35 newspapers or 50 magazines & each student can only work for 8 hoursSo, In 8 hours each student can deliver:
35 × 8 = 280 newspapers
50 × 8 = 400 magazines
To find out minimum number of students needed to work we need to divide work done by each student in 8 hours by total deliveries to be made.
[tex] \therefore[/tex]
For Newspapers:
875/280 = 3.125
So, by rounding of the figure we will need 4 students to deliver newspapers as each student can work only for 8 hours.
For magazines:
1200/400 = 3
3 students are needed to deliver magazines.
directions: use the given information to find the desired measurement. a ferris wheel has a diameter of 50 feet. how far has a person traveled when they have moved 270 degrees?
Answers
Based on the information, the person traveled 117.8 feet by the Ferris wheel.
Circumference = π×diameter
Keep the values in formula and perform multiplication to find the circumference of the wheel
Circumference = 50π
On 1 complete revolution of 360 degrees, the distance covered = 50π
So, revolution of 270 degrees, the distance covered will be = (50π/360) × 270
Performing multiplication and division on Right Hand Side of the equation
The distance traveled = 117.8 feet
Hence, the person travelled 117.8 feet.
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Which function represents the i shown in the graph below
A. G(x)=-x+2
B. G(x)=2^x-1
C. G(x)=(x+2)^2
D. -2x
Answers
Directions: Write an equation passing through the point and PARALLEL to the given line.
1. (4, 7); y = 3x+6
Answers
Answer: y=3x-5
Step-by-step explanation:
This was the answer i got after solving
Hope that helped :)
Screenshot is the proof of the answer btw :)