Since this limit is infinite, and the series 1/n diverges, we can conclude that WE +7 also diverges.
To determine whether these series converge, we can use the ratio test. For the series +7 VE (D), we have:
lim n->inf |(+7 VE (D)_(n+1)) / (+7 VE (D)_n)| = lim n->inf |(7/2)^(n+1) / (7/2)^n|
= lim n->inf |7/2|
Since this limit is greater than 1, the series +7 VE (D) diverges.
For the series WE +7, we have:
lim n->inf |(WE +7)_(n+1) / (WE +7)_n| = lim n->inf |(n+2) / (n+1)|
= 1
Since this limit is equal to 1, the ratio test is inconclusive for WE +7. However, we can use the limit comparison test with the series 1/n. We have:
lim n->inf |(WE +7)_n / (1/n)| = lim n->inf |n(n+7) / 7|
= inf
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Hi, i would really appreciate if someone helped me out!
A corner store sells two kinds of baked goods: cakes and pies. A cake costs $11 and a pie costs $10. In one day, the store sold 11 baked goods for a total of $117. How many cakes did they sell?
Answer:
7cakes and 4 pies
Step-by-step explanation:
A water sprinklers sprays water on a lawn over a distance of 6 meters and rotates through an angle of 135 degrees. Find the exact valve of the area of the lawn watered by the sprinkler.
A = (1/2)θ (r²)
The exact value of the area of the lawn watered by the sprinkler can be calculated using the formula A = (1/2)θ(r²), where A is the area, θ is the angle in radians, and r is the radius.
To find the area of the lawn watered by the sprinkler, we can use the formula for the area of a sector of a circle. The formula is A = (1/2)θ(r²), where A represents the area, θ is the central angle in radians, and r is the radius.
In this case, the sprinkler sprays water over a distance of 6 meters, which corresponds to the radius of the circular area. The sprinkler also rotates through an angle of 135 degrees. To use this value in the formula, we need to convert it to radians. Since there are 180 degrees in π radians, we can convert 135 degrees to radians by multiplying it by (π/180). Thus, the central angle θ becomes (135π/180) = (3π/4) radians.
Substituting the values into the formula, we have A = (1/2)(3π/4)(6²) = (9π/8)(36) = (81π/2) square meters. This is the exact value of the area of the lawn watered by the sprinkler.
In summary, the exact value of the area of the lawn watered by the sprinkler is (81π/2) square meters, obtained by using the formula A = (1/2)θ(r²), where θ is the angle of 135 degrees converted to radians and r is the radius of 6 meters.
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Meredith is 160 cm tall. Jane’s height is 90% of Meredith’s height. How tall is jane?
Work out
5.2
% of
628.55
km
Give your answer rounded to 2 DP.
What is the decrease percentage of 62 to 31
Answer:
50%
Step-by-step explanation:
Answer: 50%
Step-by-step explanation:
31 is half of 62, so it was a 50% decrease.
Given: ABCD is a parallelogram; BE | CD; BF | AD
Prove: BA EC = FA BC
Using the properties of parallelograms and the given information, we proved that BAEC is equal to FABC. We utilized angle-angle similarity and the proportional relationships of corresponding sides in similar triangles to establish the equality.
To prove that BAEC = FABC, we will use the properties of parallelograms and the given information.
Given:
ABCD is a parallelogram.
BE is parallel to CD.
BF is parallel to AD.
To prove:
BAEC = FABC
Proof:
Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Let's denote the length of AB as a, BC as b, AD as c, and CD as d.
Since BE is parallel to CD and AD is parallel to BF, we have angle ABE = angle CDF and angle ADB = angle BFD.
By alternate interior angles, angle CDF = angle FAB.
Now, we have two pairs of congruent angles: angle ABE = angle CDF and angle ADB = angle BFD.
Using angle-angle similarity, we can conclude that triangle ABE is similar to triangle CDF and triangle ADB is similar to triangle BFD.
As the corresponding sides of similar triangles are proportional, we have the following ratios:
AB/CD = AE/CF (from triangle ABE and triangle CDF similarity)
AD/BC = BD/CF (from triangle ADB and triangle BFD similarity)
Cross-multiplying the ratios, we get:
AB * CF = CD * AE (equation 1)
AD * CF = BC * BD (equation 2)
Adding equation 1 and equation 2, we have:
AB * CF + AD * CF = CD * AE + BC * BD
Factoring out CF, we get:
CF * (AB + AD) = CD * AE + BC * BD
Since AB + AD = CD (opposite sides of a parallelogram are equal), we have:
CF * CD = CD * AE + BC * BD
Simplifying, we get:
CF = AE + BC
Therefore, we have shown that BAEC = FABC.
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What is the sum of the given polynomials in standard form? (x2 – 3x) + (–2x2 + 5x – 3)
Answer:
-x² + 2x - 3
Step-by-step explanation:
Simply combine like terms together.
x² terms are added together
x terms are added together
Constants are added together
Answer: -x^2 + 2x - 3
Step-by-step explanation:
(x^2 - 3x) + (-2x^2 + 5x - 3)
Combine like terms
x^2 - 2x^2 - 3x + 5x - 3
x^2 - 2x^2 = -x^2
-3 + 5x = 2x
How many ways are there to
adjust two quantities so that they are in a
given proportional relationship?
Answer:
2 or 3
Step-by-step explanation:
I really need help, struggling. Question is in image.
Answer:
164
Step-by-step explanation:
Checkpoint 2= -187
Checkpoint 1= -23
The negatives mean how much lower they are from the surface.
To find "how much lower," we need to subtract -23 from -187.
-187-(-23) is the same as -187+23 (2 negatives=1 positive)
-187+23= -164.
However, it's not negative in the answer because by asking how much lower, we don't need to have a negative. "How much lower" is a distance, and a distance is always positive.
draw the mail carrier's position-versus-time graph. assume that x=0m at t=0s.
The position of mailbox after 10s is equal to sum displacements is 14m.
The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).
Given velocity time graph understand in three parts.
1. first 6s mailbox have constant velocity 3m/s
the displacement covered by it = area under v-t graph(square shape)
s1=3 x 6 =18m
2. the mailbox at rest at 6-8 s.
the displacement covered by it s2=0
3. the mail returned with constant velocity 2m/s
Displacement is defined to be the change in position of an object. It can be defined mathematically with the following equation:
Displacement=Δx=\(x_{f} - x_{0}\)
\(x_{f}\)=refers to the value of the final position.
\(x_{0}\)= refers to the value of the initial position.
Δx is the symbol used to represent displacement
the displacement covered by it s3 =(10-8) (-2) =-4m
the position of mailbox after 10s is equal to sum displacements=s1+s2+s3 =18+0-4=14m the displacement - time graph.
Therefore, the position of mailbox after 10s is equal to sum displacements is 14m.
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Draw the mail carrier's position-versus-time graph. Assume that x=0m at t=0s
What is the position of the mailbox?
a. Work out the value of v when u = 1.1. a = 1.5 and = 1.2
b. Work out the value of value when u =2.5. a = -1.2 and t = -1.5
v=u+at
Step-by-step explanation:
.......I am not sure...
a parabolic archway is 12 meters high at the vertex. at a height of 10 meters, the width of the archway is 8 meters. how wide (in m) is the archway at ground level? (round your answer to one decimal place.)
The archway is about 20.8 meters wide at ground level.
We can start by using the formula for a parabolic archway:
y = a\((x-h)^{2}\) + k
where y is the height, x is the width at a certain height, h is the horizontal distance from the vertex to the center of the archway, k represents the height of the vertex, and a determines the shape of the parabola.
We know that the archway is 12 meters high at the vertex, so we can plug in the values we have:
12 = a\((0-h)^{2}\) + k
12 = a\(h^{2}\) + 12
Simplifying this equation, we get:
a = -1/(4h)
We also know that at a height of 10 meters, the width of the archway is 8 meters. Plugging in these values:
10 = a\((4-h)^{2}\) + 12
10 = -1/(4h)\((16-8h)^{2}\) + 12
Simplifying this equation, we get a quadratic equation in terms of h:
0 = 2\(h^{2}\) - 3h - 14
h = 2 or h = -7/2
Since h represents a distance, it cannot be negative, so we take h = 2.
Now we can find the width of the archway at ground level (where y = 0):
0 = a\((x-2)^{2}\) + 12
-a\((x-2)^{2}\) = 12
-a = 12/\((x-2)^{2}\)
Putting our value for a, we get:
1/(4h) = 12/\((x-2)^{2}\)
Solving for x, we get:
x = 20.8 meters
Therefore, the archway is about 20.8 meters wide at ground level.
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Hi can somebody help me with this?
Answer:
Step-by-step explanation:
The product of two rational numbers is 34/3. If one of the numbers is 17/6,
find the other.
Answer:
/173
Step-by-step explanation:
Functions Question (image attached)
Answer:
\(x {}^{2} \times + 4x\)
Step-by-step explanation:
\(f(x + 4) = (x + 4) {}^{2} - 3(x + 4) - 4 \\ = x {}^{2} + 8x + 16 - 3x - 12 - 4 \\ = x {}^{2} + 4x\)
Solve this system of equations using the substitution method.
y = 2x+17
y = 6x - 3
Answer:
this is awnser
Step-by-step explanation:
Answer:
X=5 y=27
Step-by-step explanation:
2x+17=6x-3
Take away 2x both sides
17=4x-3
Add 3 to get x on one side
20=4x
20/4 =5
x=5
Subsitute 5 in, 6 x 5 = 30 30-3=27
If −105 = −7 5 + 2 , then −2 =?
Answer:
-8
Step-by-step explanation:
brandon rolls a six sided die twenty times, and records the result in the table below. how many times did brandon roll above the average?
The expected value for each roll is \((1+2+3+4+5+6)/6 = 3.5.\)
The average of Brandon's rolls, we simply add up all the results and divide by the number of rolls:
\((1+2+2+3+4+6+2+1+5+6+1+6+2+6+4+6+2+6+4+6)/20 = 3.6\)
So the average of Brandon's rolls is 3.6.
Now we need to count how many times he rolled above the average. To do this, we simply count how many rolls were greater than 3.6:
4, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 6
There were 18 rolls that were greater than 3.6, so Brandon rolled above the average 18 times.
In summary, Brandon rolled a six-sided die 20 times and recorded the results in a table. To find out how many times he rolled above the average, we first calculated the average roll to be 3.6. We then counted how many times he rolled above this value and found that he did so 18 times.
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A local men's clothing store is being sold. From a previous inventory analysis, the current owners determined that 37% of the merchandise was outdated. The buyers would like a more current estimate of the proportion of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. What size sample do the buyers need in order to be 99% confident that the margin of error of their estimate is about 0.06
ANSWER:
the answer is
using only the conversions 1l=1000cm3 and 1in=2.54cm, express this volume in cubic inches.
To express the volume in cubic inches, we first need to convert from liters to cubic centimeters (\(cm^{3}\)) using the conversion 1l = 1000\(cm^{3}\).
Volume in \(cm^{3}\) = 5.2l x 1000\(cm^{3}\)/l = 5200\(cm^{3}\)
Next, we can use the conversion 1in = 2.54cm to convert from \(cm^{3}\) to cubic inches.
Volume in cubic inches = 5200\(cm^{3}\) x \((1 in/2.54cm)^3\)= 317.01 \(in^3\) (rounded to two decimal places)
Therefore, the volume is 317.01 cubic inches.
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Please help me I've been stumped on this problem
The measure of ∠CFE is 40°
How do we find ∠CEF?To solve for triangle ∠CEF, we know that
Parallel to DE is BC
Arc length BD = 58°
Arc length DE = 142°
We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.
The arcs BD and DE are split in half by the line ZT.
Which is:
Arc SC = 1/(1/2(arc BC) = 1/(58)
Arc SC = 29°
142 = 1/2(arc DE) + arc TE
Arc TE = 71°
Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE
29° + Arc CE + 71° = 180°
Arc CE + 100° = 180°
Arc CE = 180-100
Arc CE = 80°
Angle inscribed equals half of angle intercepted
CFE = 1/2 of Arc CE
<CFE = 1/2(80)
< CFE = 40°
The above answer is based on the full question below;
In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer
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jeff paid $4773 for 6 identical printers and 3 identical cameras. ron bought 4 such printers and 6 such cameras and paid $5002 in all. what is the cost of each printer?
The cost of each printer is $568.
Find cost per unitTo find the cost of each printer, we need to use a system of equations.
Let's call the cost of each printer "p" and the cost of each camera "c".
The first equation we can create is: 6p + 3c = 4773
The second equation we can create is: 4p + 6c = 5002
Now we can use the elimination method to solve for one of the variables.
Let's eliminate the "c" variable by multiplying the first equation by -2: -12p - 6c = -9546
And then add the two equations together: -8p = -4544
Now we can solve for "p" by dividing both sides by -8: p = 568
So the cost of each printer is $568.
To find the cost of each camera, we can plug the value of "p" back into one of the original equations and solve for "c":
6(568) + 3c = 4773
3408 + 3c = 4773
3c = 1365
c = 455
So the cost of each camera is $455.
Therefore, the cost of each printer is $568 and the cost of each camera is $455.
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Is a function or non function explain
Answer:
It is a non function.
Step-by-step explanation:
Numbers cannot repeat in functions
The Ninoy Aquino International Airport (NAIA) and Singapore Changi Airport (SIN) are about 2,400 kilometers apart. A Singapore Airlines passenger plane leaves NAIA, traveling towards SIN at an average speed of 800 kilometers per hour. A Philippine Airline passenger plane leaves SIN at the same time, traveling toward NAIA, averaging 640 kilometers per hour. How long will it take them to meet?
The relative velocity of one plane with respect to the other plane is given
by the sum of the velocity of the two planes.
The time it would take the two planes to meet is \(\underline{1. \overline 6 \ km/hr}\)Reasons:
The distance between the two airports = 2,400 km
Speed of the plane from NAIA = 800 kilometer per hour
Speed of the plane coming from SIN = 640 kilometers per hour
Let t represent the time after which the two planes meet, we have;
800 × t + 640 × t = 2,400
\(\displaystyle t = \frac{2,400 \ km}{800 \ km/hr + 640 \ km/hr} = \frac{5}{3} \ km/hr = 1.\overline 6 \ km/hr\)
The time after which the two planes meet, t = \(\underline{1. \overline 6 \ km/hr}\)
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complete the table and find the values of m and b for the straight
line that provides the best least-squares fit to the data.
Complete the table and find the values of m and b for the straight line that provides the best least-squares fit to the data. Complete the table. X y xy 1 8 8 2 10 3 12 4 3 12 16 Σχ= 10 | Σy = 20 �
the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.To find the values of m and b for the straight line that provides the best least-squares fit to the data, we need to complete the table and use the formulas for calculating the slope (m) and y-intercept (b).
First, let's complete the table by calculating the xy column:
X y xy
1 8 8
2 10 20
3 12 36
4 3 12
Σχ=10 Σy=20 Σxy=76
Now, we can use the formulas:
m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)
b = (Σy - m(Σx))/n
Plugging in the values from the table:
m = (76 - (10)(20)/4) / (30 - (10)²/4)
= (76 - 200/4) / (30 - 100/4)
= (76 - 50) / (30 - 25)
= 26 / 5
= 5.2
b = (20 - 5.2(10))/4
= (20 - 52)/4
= -32/4
= -8
Therefore, the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.
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Which expression below represents,”A number increased by five?”
A.10 divided by 5
B.n-5
C.5+n
D.n x 5
PLEASE HELP ME!! I WILL GIVE BRAINLIEST. QUESTIONS 21 AND 22!
Answer:
22 is C and I don't know 21
If m∠A = m∠B and m∠A + m∠C = ∠D, then
m∠B + m∠C = ∠D.
Which property is shown?
reflexive property
substitution property
symmetric property
transitive property
Answer:
Substitution Property
Step-by-step explanation:
The change from the first equation to the final equation is m∠A has been replaced by m∠B. In other words, m∠B was substituted for m∠A.
Answer:
Substitution property
Step-by-step explanation:
Have a nice day!
She has 18 pairs of shoes, and 2 of them are boots. What is the probability, at random, that she will get the boots?
Answer:
1/9
Step-by-step explanation:
2. We know that FGH 2 KGJ
because they are____angles
Adjacent. 
supplementary.
Vertical
Answer:
Vertical angles and I hope this'll help
Answer:
Vertical
Step-by-step explanation:
lets go almost a year late
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