Answer: 18, 10, 6, 4
The first four terms of an arithmetic sequence are 18, 10, 6, 4 if the first term and the relationship between the a(n) and a(n+1) terms.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have given the first term and the relationship between the a(n) and a(n+1) terms.
The first term:
a(1) = 18
The relationship:
a(n+1) = [2 + a(n)]/2
Plug n = 1
a(1+1) = [2 + a(1)]/2
a(2) = [2 + 18]/2
a(2) = 20/2
a(2) = 10
Plug n = 2 in the expression:
a(2+1) = [2 + a(2)]/2
a(3) = [2 + 10]/2
a(3) = 6
Plug n = 3 in the expression:
a(3+1) = [2 + a(3)]/2
a(3) = [2 + 6]/2
a(3) = 4
Thus, the first four terms of an arithmetic sequence are 18, 10, 6, 4 if the first term and the relationship between the a(n) and a(n+1) terms.
Learn more about the sequence here:
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On a normally distributed anxiety test with mean 48 and standard deviation 4, approximately what anxiety test score would put someone in the top 5 percent? Group of answer choices
Answer:
Anxiety score close to 54.58.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 48, \sigma = 4[/tex]
Approximately what anxiety test score would put someone in the top 5 percent?
We have to find the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 48}{4}[/tex]
[tex]X - 48 = 1.645*4[/tex]
[tex]X = 54.58[/tex]
Anxiety score close to 54.58.
A graph is given to the right. a. Explain why the graph has at least one Euler path. b. Use trial and error or Fleury's Algorithm to find one such path starting at Upper A, with Upper D as the fourth and seventh vertex, and with Upper B as the fifth vertex. A C B D E A graph has 5 vertices labeled A through E and 7 edges. The edges are as follows: Upper A Upper C, Upper A Upper B, Upper A Upper D, Upper C Upper D, Upper C Upper E, Upper B Upper D, Upper D Upper E. a. Choose the correct explanation below. A. It has exactly two odd vertices. Your answer is correct.B. It has exactly two even vertices. C. It has more than two odd vertices. D. All graphs have at least one Euler path. b. Drag the letters representing the vertices given above to form the Euler path.
Answer:
a. It has exactly two odd vertices
b. A C E D B A D C
Step-by-step explanation:
(a) There will not be an Euler path if the number of odd vertices is not 0 or 2. Here, the graph has exactly two odd vertices: A and C.
__
(b) We are required to produce a path of the form {A, _, _, D, B, _, D, _}.
Starting at A, there is only one way to get to node D as the 4th node on the path: via C and E. Node B must follow. From B, there is exactly one way to cover the remaining three edges that have not been traversed so far.
The Euler path meeting the requirements is ...
A C E D B A D C
It is shown by the arrows on the edges in the graph of the attachment.
A company dyes two sixes of rugs. Which of the following inequalities can be paired with x+y>22 to create a system that represents this situation?
Let x=small rugs and y=medium rugs. It takes 8 hours to dye a small rug, so you would write 8x. It takes 12 hours to dye a small rug, so you would write 12y. Those two would need to be added together. The dyer needs to dye at least 22 rugs in 240 hours, so you would need a less than or = to sign.
I'm not sure which choice has the line beneath, indicating that the sign is a "less than or equal to" sign, but the answer is gonna be either C or D.
8x+12y≤240, or 12y+8x≤240
Answer:
Step-by-step explanation:
hello there i will give you an explanation of how this works so let go to it
so the question that you are asking me is to create a system that represent
this situation so what we can do is that let just imagine that x equals to small rugs and z equals medium rugs. so it takes 8 hours to dye a small rug so this suggest that you would right it as 8x. so its take 12 hours to dye a medium rug so we do the same thing as we do to the small rug so you already know that is would be 12z ok so those needed to be added together.
the dyer needs to dye at least 22 rugs in 240 hrs so you would need a less than or a equal to sign.
so with all of this we can tell what the answer already is so i will give a a minute to get the answer time is up here is the answer down below :
8x+12y≤240, or 12y+8x≤240
If a hexagon is distorted into a curve, what happens to the order of points around the curve?
Answer:
the order of points remains the same
Step-by-step explanation:
Assuming the distortion is isomorphic, the order of points on any line or other continuous curve will remain the same.
Verify the continuity type C° and C1 between curve(l) and curve(2).
Curve 1: (0,0), (1,1), (4,1), and (6,0)
Curve 2: (6,0), (7,-1), (10,-1), and (12,0)
Step-by-step explanation:
to be honest I'm not sure how to do
Comment
by which number -7 /25 should be divided to get -1/15?
Answer:
21/5
Step-by-step explanation:
if a/b = c, then b=a/c
in other words:
divide -7/25 by -1/15 to get the answer
It also helps to use the fact that a/b / c/d = a/b * d/c
-7/25 / -1/15 = -7/25 * -15/1
= 105 / 25
= 21 / 5
Answer:
[tex]4 \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] \frac{ - 7}{25} \div x = \frac{ - 1}{15} [/tex]
[tex]x = \frac{ - 7}{25} \div \frac{ - 1}{15} [/tex]
[tex] = \frac{7}{25} \times \frac{15}{1} [/tex]
[tex] = \frac{21}{5} = 4 \frac{1}{5} [/tex]
A child is playing games with empty soda cups. There are three sizes: small, medium, and large. After some experimentation
she discovered she was able to measure out 160 ounces in the following ways:
1) 2 small, 2 medium, 4 large
2) 2 small, 6 medium, 1 large
3) 5 small, 1 medium, 3 large
Determine the size of the cups.
Answer:
S is the volume of the small cup, M the volume of the medium cup and L the volume of the large cup:
2*S + 2*M + 4*L = 160oz
2*S + 6*M + 1*L = 160oz
5*S + 1*M + 3*L = 160oz.
First, we must isolate one of the variables, for this we can use the first two equations and get:
2*S + 2*M + 4*L = 160oz = 2*S + 6*M + 1*L
We can cancel 2*S in both sides:
2*M + 4*L = 6*M + 1*L
now each side must have only one variable:
4*L - 1*L = 6*M - 2*M
3*L = 4*M
L = (4/3)*M.
now we can replace it in the equations and get :
2*S + 2*M + 4*(4/3)*M = 160oz
2*S + 6*M + (4/3)*M = 160oz
5*S + 1*M + 4M = 160oz.
simplifing them we have:
2*S + (22/3)*M + = 160oz
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
(the first and second equation are equal because we used those to get the relation of M and L, so we now have only two equations):
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
We can take the second equation and simplify it:
S + M = 160oz/5 = 32oz
S = 32oz - M
Now we can replace it in the first equation and solve it for M
2*S + (22/3)*M = 2*(32oz - M) + (22/3)*M = 160oz
62oz - 2*M + (22/3)*M = 160oz
-(6/3)*M + (22/3)*M = 98oz
(18/3)*M = 98oz
M = (3/18)*98oz = 16.33 oz
Then:
L = (4/3)*M =(4/3)*16.33oz = 21.78 oz
and:
S = 32oz - M = 32oz - 16.33oz = 15.67oz
In the diagram below, if AD= 100 and AC = 34, find CD.
A 59
B 76
C 45
D 66
Answer:
D. 66
Step-by-step explanation:
Well if AD is 100 and AC is 34 that leaves CD so we can just subtraction 34 from 100 and get 66.
Answer:
D. 66
Step-by-step explanation:
AD = 100
AC = 34
The whole line is 100. A part of the line is 34. The other part will be 66.
100 - 34 = 66
Explain how to write an equivalent expression for the expression 3(4x + 2y) + 5x. Be sure to explain which properties you used. What method can you use to prove the 2 expressions are equivalent?
Answer:
Using multiplicative and additional property .
= 17x +6y
Step-by-step explanation:
3(4x + 2y) + 5x.
Multiplicative property.
Using 3 to multiply what's inside the bracket.
= 3*4x + 3*2y +5x
= 12x + 6y +5x
Addition property.
Collection of all like terms together.
All values with same alphabets are going to be added together
= 12x +5x +6y
= 17x +6y
To prove if 3(4x + 2y) + 5x.= 17x +6y
Let's assume both x and y to be 1
We have
3(4(1) + 2(1)) + 5(1) = 17(1) + 6(1)
3(6)+5=17 +6
23= 23.
Proved.
What is the value of a?
Answer:
[tex]\huge\boxed{a=\dfrac{16}{3}=5\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\triangle ZYW\sim\triangle WYX\ (AAA)\\\\\text{Therefore corresponding sides are in proportion}\\\\\dfrac{YX}{YW}=\dfrac{YW}{ZY}\\\\\text{substitute}\\\\YX=a;\ YW=4;\ ZY=3\\\\\dfrac{a}{4}=\dfrac{4}{3}\qquad\text{multiply both sides by 4}\\\\4\cdot\dfrac{a}{4}=4\cdot\dfrac{4}{3}\qquad\text{cancel 4}\\\\a=\dfrac{16}{3}[/tex]
What is the %_ee of a sample of carvone that exhibits an observed rotation of -20, given that the specific rotation of (R)-carvone is -61
Answer: 44
Step-by-step explanation:
44
Wilbur landed his plane, causing it to descend at a rate of 0.2 kilometers per minute. He reached the ground after 15 minutes.
Answer:
The first dot should be on 3, and the second should be at 15 so its a linear line.
Step-by-step explanation:
Brainliest for correct awnser! Which variable is most important in this problem? One year, a farmer harvested 50,000 bushels of wheat on her family farm. Three years later, she harvested 12,000 more bushels of wheat from the same fields. How much wheat did she harvest that year?A.The area of the farmB.The amount of wheat harvested in the later yearC.The change in the amount of wheat harvested
Answer:
C. the change in the amount of wheat harvested.
Step-by-step explanation:
Already, the question states "...how much wheat...", which implies that you must find a amount of wheat.
Also, another implication is "...12,000 more..." (emphasis added), which usually amounts to you adding (hence more) to the original amount.
~
C - the change in the amount harvested.
Step-by-step explanation:There are three options.
1) The area of the farm
2) The amount of wheat harvested in the later year
3) The change in the amount of wheat harvested.
Let's look at the possible answers.
1) The area of the farm - it doesn't tell us anything important at all. The area of the farm isn't important in this case. We can cross it off.
2) The amount of wheat harvested in the later year - How much of wheat was harvested in the later year doesn't really tell us anything. If he harvested 60000 bushels the second year, he could have harvested million bushels the third year or 0 bushels the third year. We don't really know and this option won't tell us anything about that.
3) The change in the amount of wheat harvested. - If we know, that he harvested 50,000 bushels the first year and they give us information, that the amount changed by 12,000 between the first and third year, we can do easy math. 50,000+12,000=62,000. Here we are. This option provided us with enough information to solve the problem. That's why it is the most important information.
At noon, ship A is 120 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answer:
1.39 km/h
Step-by-step explanation:
Let the initial position of ship B represent the origin of our coordinate system. Then the position of ship A as a function of time t is ...
A = -120 +20t . . . (east of the origin)
and the position of B is ...
B = 15t . . . (north of the origin)
Then the distance between them is ...
d = √(A² +B²) = √((-120 +20t)² +(15t)²) = √(625t² -4800t +1440)
And the rate of change is ...
d' = (625t -2400)/√(625t² -4800t +14400)
At t = 4, the rate of change is ...
d' = (625·4 -2400)/√(625·16 -4800·4 +14400) = 100/√5200 = 1.39 . . . km/h
The distance between the ships is increasing at about 1.39 km/h.
The table shows the number of badges earned, based on the number of boxes of cards sold. What does b(20) = 3 mean in terms of the problem
Answer:
b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.
Step-by-step explanation:
The number of badges earned based on the number of boxes of cards sold means that badges earned are a function of the number of boxes of cards sold.
b(20) means the number of badges earned for selling 20 boxes of cards.
b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.
Answer:
Someone who sells 20 boxes of cards earn 3 badges.
Step-by-step explanation:
Find an equation of the tangent line to the curve at the given point.
y = √ (x) , (16, 4)
Answer: y=1/8*x+2
Step-by-step explanation:
The equation of any tangent line is y=a*x+b (1)
To the equation of the tangent line we have to find the coefficients a and b and the to substitute them to equation (1).
As we know a=y'(x0) ( where x0=16)
So y'(x)= (√ (x) )' = 1/(2*√x)
a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8
So lets substitute a in equation (1):
y=1/8 *x+b
Now we have to find b
We know that the point (16, 4) belongs to the tangent line.
That means
4=1/8*16+b => 4=2+b => b=2
SO the equation of the tangent line is y=1/8*x+2
Alexis and Jessica are shopping. Alexis buys 4 pairs of pants and 3 necklaces and pays $216. Jessica buys 7 pairs of pants and 2 necklaces and pays $300. Solve for the price of each item. Each pair of pants costs _____ dollars Each necklace costs________ dollars
Step-by-step explanation:
let us keep the price of pants as x
and price of necklace as y
Simultaneous equations comes as follows:
4x + 3y = 216 for Alexis
7x + 2y = 300 for Jess
we'll make either x or y equal
here let's make y equal
2 ( 4x + 3y = 216)
3 ( 7x + 2y = 300)
8x + 6y = 432
21x + 6y = 900
21x - 8x = 900 - 432
13x = 468
x = $36
so a pant costs $36
And
3y = 72
y = $ 24
so a necklace costs $36
Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?
Answer:
27.03 years
Step-by-step explanation:
The nper excel function can be used to determine the period in which the winnings would last as below:
=nper(rate,pmt,-pv,fv,type)
rate is the annual interest rate on the account
pmt is the amount of annual withdrawal which is $65000
pv is the current amount in the account which is $1,000,000
fv is the future balance in the account after all withdrawals are made i.e$0
type is 1 which means withdrawals are made at the beginning of the year
=nper(5%,65000,-1000000,0,1)= 27.03
HELP HELP PLEASE!!!
A laptop computer is purchased for $2250. After each year, the resale value decreases by 30%. What will the resale value be after 5 years?
Answer:
2260(0.70)^5=3.80
Step-by-step explanation:
could you please answer quickly?????!! thank you!
Answer:
31,5
Step-by-step explanation:
=7*3+(7*3)/2
Answer:
length x width = area
7 x 3 = 21 so the area of the rectangle is 21
divide 7 by 2 so we can find the length of each triangle. 7 / 2 = 3.5
length (or base) x height / 2 = area of triangle
3.5 x 3 = 10.5
You do not have to divide by two because there are two triangles
10.5 + 21 = 31.5 so the area is 31.5
Hope this helps
Step-by-step explanation:
Select the correct answer from each drop down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
Answer:
the slope of A'B' = 3
A'B' passes through point O
Step-by-step explanation:
A dilation with scale factor 3 gives the effect of stretching the line AB three times longer. As dilation does not change the direction of the line, the slope will stay the same. If point O lies on AB and is the center of dilation, then the point O must also lie on A'B'
The required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Given that,
To Select the correct answer from each drop-down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
The scale factor is defined as the ratio of modified change in length to the original length.
Here, is o is the center of the line AB and slope of line AB is 3 than the line dilated with scale factor 3 A1B1 has also a scale factor of 3 because Position of dilation is center 0 thus dilation did not get any orientation.
And the center of dilation is O so line A1B1 passes through O.
Thus, the required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Learn more about line Scale factors here:
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Please answer this correctly
Answer:
Question 1
Step-by-step explanation:
1) Let the outside temperature = x ° F
Now, the inside temperature = (x + 3)° F
Outside temperature has increased by 3,
So, outside temperature at lunch time = (x + 3)°F
So, at lunch time the outside & inside temperature are same.
So, the difference in temperature at lunch time is 0
Brainliest? Get this correct What is the difference of the rational expressions below?
Answer:
A. [tex]\frac{x^2-3x+6}{x^2 - 2x}[/tex]
Step-by-step explanation:
1. Move all of numerators above the corresponding common denominator
2. Multiply inside the parentheses then remove any remaining parenthesis to get your final answer to get your fraction.
Answer:
[tex] \dfrac{x^2 - 3x + 6}{x^2 - 2x} [/tex]
Step-by-step explanation:
[tex] \dfrac{x}{x - 2} - \dfrac{3}{x} = [/tex]
[tex] = \dfrac{(x)x}{(x)(x - 2)} - \dfrac{(x - 2)(3)}{(x - 2)(x)} [/tex]
[tex] = \dfrac{x^2}(x - 2)} - \dfrac{3x - 6}{(x - 2)(x)} [/tex]
[tex] = \dfrac{x^2 - (3x - 6)}{x^2 - 2x} [/tex]
[tex] = \dfrac{x^2 - 3x + 6}{x^2 - 2x} [/tex]
volume of a cube size 7cm
Answer:
343 cm3
Step-by-step explanation:
Answer:
side(s) =7cm
volume (v)=l^3
or, v = 7^3
therefore the volume is 343cm^3.
hope its what you are searching for..
what's the difference of the two polynomials? (9x²+8x)-(2x²+3x)
A)7x²+5x
7x²+5x
Step-by-step explanation:(9x²+8x)-(2x²+3x)
We will subtract the like terms. That means that we will subtract [tex]2x^{2}[/tex] from [tex]9x^{2}[/tex] and 3x from 8x.
Triangle ABC has vertices A(-5, -2), B(7, -5), and C(3, 1). Find the coordinates of the intersection of the three altitudes
Answer:
The coordinates of the intersection of the three altitudes = (-3.5, -1)
Step-by-step explanation:
The altitude of a triangle is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.
There are therefore three altitudes possible in a triangle, one from each vertex. All three altitudes always intersect at the same point called the orthocenter of the triangle.
Let the triangle ABC have altitudes AD, BE and CF as shown in the attached image to this solution. Let the orthocentre be O.
The point O is the point where all the coordinates AD, BE and CF meet.
Hence, to obtain the coordinates of O, we just need to equate the equations of two of the lines that serve as the altitude.
Before that, we need to c9mpute the equations of the two altitudes that we will use.
Noting that the altitudes are perpendicular to the sides of the triangle, we can compute the slopes of the altitudes from caldilating the slopes of the sides.
Slope of AB
= (y₂-y₁)/(x₂−x₁)
= (-5 - (-2))/(7 - (-5))
= (-3/12)
= (-1/4)
Slope of its altitude, CF
= -1 ÷ (Slope of AB)
= -1 × (-1/4)
= 4
The equation of CF is given using point C as,
y – y₁ = m(x – x₁)
y - 1 = 4 (x – 3)
y - 1 = 4x - 12
y = 4x + 13
Slope of BC
= (y₂-y₁)/(x₂−x₁)
= (1 - (-5))/(3 - 7)
= (6/-4)
= (-3/2)
Slope of AD
= −1 ÷ (Slope of BC)
= -1 ÷ (-3/2)
= (2/3)
The equation of AD using point A given as,
y – y₁ = m(x – x₁)
y – (-2)) = (2/3) (x – (-5))
y + 2 = (2x/3) + (10/3)
y = (2x/3) + (4/3)
Now equation the equations of the altitudes CF and AD
y = 4x + 13
y = (2x/3) + (4/3)
4x + 13 = (2x/3) + (4/3)
4x - (2x/3) = (4/3) - 13
(10x/3) = (-35/3)
10x = -35
x = -3.5
y = 4x + 13
y = (4×-3.5) + 13 = -14 + 13 = -1
coordinates of the orthocentre of the triangle = (-3.5, -1)
Hope this Helps!!!
BEST GETS BRAINLIEST Proof for Pythagoras Theorem (I’ll take multiple different approaches) Please make it logical/satisfying.
Answer:
Proofs for Pythagoras Theorem usually use visual/geometry approaches. I don't post pictures in my answers, so I will present a linear algebra approach. You can see it in the blog posted by Professor Terence Tao.
Note that there are several elegant proofs using animations and drawings, but this is just personal.
I've seen this some time ago, it is really interesting proof.
It states that [tex]a^2+b^2=c^2[/tex] is equivalent to the statement that the matrices
[tex]%\begin{pmatrix}a & b \\ -b & a%\end{pmatrix}%[/tex] [tex]\begin{pmatrix}a& b \\-b & a\\\end{pmatrix}[/tex] and [tex]\begin{pmatrix}c & 0\\0 & c \\\end{pmatrix}[/tex] have the same determinant.
The determinant of the first matrix is [tex]a^2+b^2[/tex]
The determinant of the second matrix is [tex]c^2[/tex]
Once the linear transformations associated with these matrices differ by rotation, we claim that
[tex]a^2+b^2=c^2[/tex]
Express it in slope-intercept form.
Please Assist With This Equation
*Please Show Work*
Answer:
240 hours
Step-by-step explanation:
One person hour is a unit indicating the rate at which one person is working on the project .
The company estimates that it will take 2880 person- hours to complete the job
So let's determine how many hours it will take 12 workers to complete same job
The rate = 2880 person/hour
12 persons or workers =( 2880 person/hour)/12 persons
12 persons or workers = 2880/12
12 persons or workers=240 hours
It will take 12 workers 240 person hour to finish the project.
Thank you
Simplify (20x^-3/10x^-1)^2
Answer: 4 / x^4
Step-by-step explanation:
(20x^-3 / 10x^-1)^2
Simplify,
(2 / x^2)^2
= 4 / x^4