y = 20500 + 24090(x - 1) can be used to find the tuition y for x years after 2000. The tuition at this college in 2020 was $5,02,300.
We assume that the rate of increase in the cost of tuition fee per year is linear and hence the tuition fees of subsequent years will be in an Arithmetic Progression. The formula for determining the nth term of an arithmetic sequence which is expressed as-
Tn = a + (n - 1)d
Where
a = first term of the sequence.
d = common difference.
n = number of terms in the sequence.
According to the question,
a = $20500 (amount in 2000)
From 2000 to 2018, the number of terms is 19, hence,
n = 19
Thus, T19 = 454120
Therefore,
4,54,120 = 20500 + (19 - 1)d
454120 - 20500 = 18d
18d = 433620
d = 433620/18
d = 24,090
Therefore, the equation that can be used to find the tuition y for x years after 2000, is as follows-
y = 20500 + 24090(x - 1)
Now, the number of terms between 2000 and 2020 is 21, hence
x = 21
y = 20500 + 24090(21 - 1)
y = 20500 + 481800
y = $502300
Therefore, the tuition at this college in 2020 was $5,02,300.
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Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 3? Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
Based on the fact that Lines a and m are parallel, the degree measure of angle 3 is 127
What is the degree measure?Based on the fact that a and m are parallel lines, then this means that the angle 127 degrees is corresponding to angle 1.
This means that the measure of angle 1 is 127 degrees as well because corresponding angles are congruent.
Angle 1 and Angle 3 are vertical angles. Vertical angles are also congruent. This means that if Angle 1 is 127 degrees then angle 3 will be 127 degrees as well.
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How do you solve
9
x
−
4
=
81
?
[tex]9x = 81+4[/tex]
[tex]9x = 85[/tex]
[tex]x = 85/9[/tex](divide using calculator)
if you take 3/10 of a number and add 2 , you get 17
Step-by-step explanation:
Are you asking for the number?
Rectangular paintings hang on the wall of an art gallery. One painting has a area of 24 square feet and another has an area of 32 square feet the paintings have whole number side lengths and have one pair of side lengths in common. What could the common side lengths be?
The common side length of the paintings is 8 feet
What are areas?The area of a shape is the amount of space on the shape
How to determine what common side lengths could be?The given parameters are
Area of painting 1 = 24 square feet
Area of painting 2 = 32 square feet
Express the areas as the product of their factors
So, we have
24 = 2 * 2 * 2 * 3
32 = 2 * 2 * 2 * 4
Multiply the common factors
Common factors =2 * 2 * 2
Evaluate the product
Common factors = 8
This represents the common side length
Hence, the common side length of the paintings is 8 feet
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Which expression best estimates-18-
-181-232
O 18+3
O-18+3
O-18+(-3)
O 18+(-3)
Answer:O 18+3
O-18+3
O-18+(-3)
Step-by-step explanation:O 18+3
O-18+3
O-18+(-3)
[tex] \displaystyle \rm \sum_{n = 0}^ \infty \frac{(n! {)}^{2} }{(2n + 1)!} [/tex]
Observe that
[tex]\dfrac{(n!)^2}{(2n+1)!} = \dfrac{n!(2n-n)!}{(2n+1)(2n)!} = \dfrac1{(2n+1)\binom{2n}n}[/tex]
Starting with a well-known series
[tex]\displaystyle 2\arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]
we take some (anti)derivatives to find a sum that more closely resembles ours.
Let [tex]f(x)=2\arcsin^2(x)[/tex]. Then
[tex]\displaystyle f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{n \binom{2n}n}[/tex]
[tex]\displaystyle x f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{n \binom{2n}n}[/tex]
[tex]\displaystyle x f''(x) + f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{\binom{2n}n}[/tex]
[tex]\displaystyle x^2 f''(x) + x f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{\binom{2n}n}[/tex]
Noting that both sides go to zero as [tex]x\to0[/tex], by the fundamental theorem of calculus we have
[tex]\displaystyle \sum_{n=1}^\infty \frac{2^{2n} x^{2n+1}}{(2n+1)\binom{2n}n} = \frac14 \int_0^x (t^2 f''(t) + t{}f'(t)) \, dt[/tex]
so that when [tex]x=\frac12[/tex], and rearranging some factors and introducing a constant, we recover a useful sum.
[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac12 \int_0^{1/2} (x^2 f''(x) + x f'(x)) \, dt[/tex]
Integrate by parts.
[tex]\displaystyle \int_0^{1/2} x^2 f''(x) \, dx = \frac14 f'\left(\frac12\right) - 2 \int_0^{1/2} x f'(x) \, dx[/tex]
[tex]\displaystyle \int_0^{1/2} x f'(x) \, dx = \frac12 f\left(\frac12\right) - \int_0^{1/2} f(x) \, dx[/tex]
Then our sum is equivalent to
[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac18 f'\left(\frac12\right) - \frac14 f\left(\frac12\right) + \int_0^{1/2} \arcsin^2(x) \, dx[/tex]
The remaining integral is fairly simple. Substitute and integrate by parts.
[tex]\displaystyle \int_0^{1/2} \arcsin^2(x) \, dx = \int_0^{\pi/6} u^2 \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} - 2 \int_0^{\pi/6} u \sin(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 2 \int_0^{\pi/6} \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1[/tex]
Together with
[tex]f\left(\dfrac12\right) = 2 \arcsin^2\left(\dfrac12\right) = \dfrac{\pi^2}{18}[/tex]
[tex]f'\left(\dfrac12\right) = \dfrac{4\arcsin\left(\frac12\right)}{\sqrt{1-\frac1{2^2}}} = \dfrac{4\pi}{3\sqrt3}[/tex]
we conclude that
[tex]\displaystyle \sum_{n=0}^\infty \frac{(n!)^2}{(2n+1)!} = \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} \\\\ ~~~~~~~~~~~~~~~~~~ = 1 + \left(\frac18\cdot\frac{4\pi}{3\sqrt3}\right) - \left(\frac14\cdot\frac{\pi^2}{18}\right) + \left(\frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \boxed{\frac{2\pi}{3\sqrt3}}[/tex]
How many tens are in the number 345
Answer:
Step-by-step explanation:
34 with a remainder of 5. so basically you can say 34 1/2
Answer:
350
Step-by-step explanation:
Rounding 345=350
345 to the nearest thousands is 0
345 to the nearest hundreds is 300
345 to the nearest tens is 350
345 to the nearest whole number is 345
345 to the nearest tenths is 345.0
Round 3,532 to the nearest thousand
Answer:
4,000
Step-by-step explanation:
I can't remember if I already posted this one....
so here we are *again (possibly*)
also ignore that I picked A it was an accident :')
Answer:
B
Step-by-step explanation:
3/20 15%,20%, 25%, 1/3 33%
All my work and answer is provided in the attached screenshot to my answer! :)
Have a great day!
The area of circle Z is 64 ft².
What is the value of r?
A- r= 4 ft
B- r= 8 ft
C- r = 16 ft
D - r = 32 ft
Answer:
Step-by-step explanation:
[tex]A=64\pi ft^2[/tex]
[tex]r=\sqrt{\frac{A}{\pi } }[/tex]
[tex]r=\sqrt{\frac{64\pi }{\pi } }[/tex]
[tex]r=\sqrt{64}[/tex]
[tex]r=8[/tex]
So the radius is 8 ft.
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Question 11 of 18
What is the length of the diagonal of the square shown below?
5
45
90°
5
5
S
OA. 5,2
B. 5
OC. √5
OD. 5√5
OE. √10
OF. 25
SUBMIT
The square's diagonal length is (E) d = 5√2.
What is a diagonal?A diagonal is a line segment that connects two vertices (or corners) of a polygon. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. It connects the vertices of a polygon, excluding the figure's edges. A diagonal is defined as something with slanted lines or a line connecting one corner to the corner farthest away.A diagonal is a line that connects the bottom left corner of a square to the top right corner.So, we must determine the length of the square's diagonal.
The formula for the diagonal of a square is d = a2; where 'd' is the diagonal and 'a' is the side of the square.Now, d = 5√2. (Refer to the diagram of the square given below)Therefore, the square's diagonal length is (E) d = 5√2.
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The correct question is given below:
What is the length of the diagonal of the square shown below? 5 45° 5 5 90° 5 O A. 5
B. 10
C. 5
D. 5/5
E. 5√2
F. 25
Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total number of tickets she sold.
Based on the table, write an equation for the relation between the number hours Gwen worked and the number of tickets she sold.
t = h/23
h = 23t
ht = 23
t = 23h
The equation that shows the relation between the number of hours worked and tickets sold is t = 23h (fourth option)
What is the equation?Examining the table, it can be seen that the number of tickets sold increases by 23 for every hour that Gwen works.
Tickets sold when Gwen works for 2 hours = 23 x 2 = 46
Tickets sold when Gwen works for 2 hours = 23 x 3 = 69
Because the tickets sold increase by a constant number, the equation would be modelled as a linear function.
Linear equations have the form : a + bx
Ticket sold = (number of hours x ticket sold in the first hour)
t = 23h
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Write an equation that can be used to solve the problem. Find the solution to the problem. Angles A and B are complementary angles. Determine the measures of angles A and B if angle A is 8 times the size of angle B.
Answer:
A = 80
B = 10
Step-by-step explanation:
a + b = 90
a = 8b
above are the two equations that we will used to find A and B.
substitute in 8b for a in the first equation.
a + b = 90
8b + b = 90 Combine like terms
9b = 90 Divide both sides by 9
b = 10
If b is 10, than a must be 80.
suppose that the length of a certain rectangle is 7 meters less than four times its width. The perimeter of the rectangle is 46 meters. find the length and width of the rectangle.
The answer to the given question is length is 17m and width is 6m
Given that a rectangle's length is 7 meters less than its width.
And also given the perimeter of the rectangle is 46 meters.
We know that the rectangle's perimeter is twice the sum of its length and width.
l - length of the rectangle
w - width of the rectangle
P - perimeter of the rectangle
Then we have P = 2 × (l + w)
Given that a rectangle's length is 7 meters less than its width.
⇒ l = 4 × w - 7
Given the perimeter of the rectangle is 46 centimeters.
⇒ 2 × ( l + w) = 46
⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)
⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)
⇒ 5w - 7 = 23
⇒ 5w = 23 + 7
⇒ 5w = 30
⇒ w = 6 (dividing both sides by 5)
Using the width value in the length equation, we get
l = 4 × 6 - 7
⇒ l = 24 - 7
⇒ l = 17
Therefore, The rectangle is 17 meters in length and 6 meters in width.
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Question
what is the domain of the
function y = 3 sqtx
What are the slope and the y-intercept of the linear function that is represented by the equation y=9x-2
Answer:
Gradient: 9
Y-intercept: -2
Step-by-step explanation:
The equation of a line is expressed in this format:
y = mx + c
Where m is the gradient (slope) of the line, and c is the y intercept.
The equation in the question is already in this format, meaning the values can be read directly from it without needing any rearranging.
m = 9, c = -2.
the nth term of 1,3,5,7, … is
Answer: an=2(n-1)+1
Step-by-step explanation:
1,3,5,7, …
As the terms progress in the sequence, each term get increased by 2 to get to the next term. Hence, the change is linear and can be modeled with the function y=2(x-1)+1 where y=term value, x=term number and 1 is the first term in the sequence.
y=2(x-1)+1
an=2(n-1)+1 ==> n=term number while an=term value. an=nth term
dave has built a storage box and needs to decorate it. It is cuboid 32cm long, 20cm wide and 30 cm tall. what is the volume of daves storage box and what is the surface area?
The volume of Daves storage box is 19200 and the surface area is 4400
What is the volume of daves storage box and what is the surface area?The given parameters are
Length = 32 cm
Width = 20 cm
Height = 30 cm
The volume is
Volume = Length * width * height
So, we have
Volume = 32 * 20 * 30
Evaluate
Volume = 19200
The surface area is
A =2 *(LW + LH + WHW)
So, we have
A = 2 * (32 * 20 + 20 * 30 + 32 * 30)
Evaluate
A = 4400
Hence, the volume of Daves storage box is 19200 and the surface area is 4400
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What does x=
How to figure this out?
The length of the side x of the triangle ADE is 16.5 units.
What are similar triangles?If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be similar (corresponding sides). When compared individually, similar triangles may have different side lengths, but they must all have the same ratio of their side lengths and equal angles.
From figure, it is given that:
AB = 3 units
BC = 2 units
AD = x units
DE = 11 units
We know that the triangle ABC ~ ADE.
Therefore, the ratio of corresponding sides of the triangles will be same.
Now,
AB/ AD = BC/ DE
3/x = 2/11
Cross multiply to get:
2x = 3(11)
2x = 33
x = 33/2
x = 16.5 units
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PLEASE HELIP ITS DUE TODAY
Answer:
x = 6
Step-by-step explanation:
As stated, the scale factor from two figures is 1/4
To find the value of x we can simply use the following equation
[tex] \frac{(1.5)}{x} = \frac{1}{4} [/tex]
cross multiply expressions
x = 6
A sum of money is to be divided among A B and C in the ratio 2:3:5 the smallest share amounts
to $600 what is the total sum of money to be shared
The correct answer is $3000.
It is quite effective to compare two or more values using the division approach. Therefore, it would be accurate to state that a ratio is a comparison or simplification of two quantities of the same type. This relationship illustrates how many times one quantity is equivalent to the other. The ratio may be defined as the number we use to represent one quantity as a percentage of the others.
As given ratio A:B:C = 2:3:5
let, A=2x, B=3x, C=5x
2x=600
x=600/2
x=$300
Total money = 2x+3x+5x
=x(2+3+5)
=x(10)
=300×10
=$3000
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help asap i will give crowns to the best
Answer: the answer is 42.5
Based on the histogram below, how are data distributed, and where is the mean located in relation to the median?
Answer:
C) Positively skewed, and the mean is to the right of the median.
Step-by-step explanation:
A histogram is a graphical representation of the distribution of numerical data.
A histogram is:
Positively skewed (right-skewed) if the long tail is on the positive side of the peak.Negatively skewed (left-skewed) if the long tail is on the negative side of the peak.Since the long tail of the given histogram is on the positive side of the peak, the histogram is positively skewed (right-skewed).
The mode is the value that occurs most often in a set of data.
In a histogram, the mode is the highest point.
The median and mean fall to the right of the mode in a right-skewed (positively skewed) histogram, and the mean is always to the right of the median: mode < median < mean.
The median and mean fall to the left of the mode in a left-skewed (negatively-skewed) histogram, and the mean is always to the left of the median: mean < median < mode.
So the correct definition of the given histogram is:
C) Positively skewed, and the mean is to the right of the median.Given the following values, find the perimeter of the figure shown below:
AB = 7 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm.
Do not include "cm" with your response.
By using the definition of perimeter and addition and subtraction of sides, the perimeter of the composite figure is 22 centimeters.
How to calculate the perimeter of a composite figure
According to the image attached aside, we find a composite figure created by adding three quadrilaterals. The perimeter is the sum of the lengths of all sides of the composite figure, that is, we need to add the lengths of the eight sides of the figure.
p = AB + BC + CD + DE + EF + FG + GH + AH
GH = AB - EF - CD
GH = 7 cm - 3 cm - 1 cm
GH = 3 cm
AH = BC - DE + FG
AH = 3 cm - 2 cm + 1 cm
AH = 2 cm
p = 7 cm + 3 cm + 1 cm + 2 cm + 3 cm + 1 cm + 3 cm + 2 cm
p = 22 cm
The perimeter of the composite figure is 22 centimeters.
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A bottle of ant killer holds 1,5 L of concentrate.
To make up a solution, 5 capfuls are added to 1
L of water. Each capful is 20 mL. How many
litres of solutions can be made if you use the
entire bottle of concentrate? [2]
82,5 L
16,5 L
15 L
Using multiplication, Correct option is B. The amount of solution that can be made from 15 L of concentrate is 16.5L.
What is meant by multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
Given,
Total ant killers added in the water is 5 × 20mL = 100mL = 0.1L (using 1L = 1000mL)
Total quantity of solution is 0.1L + 1L = 1.1L
It takes 0.1 mL of ant killer to make 1.1L of solution.
⇒ Total solution that can be made from 15L of concentrate is -
⇒ 15L × 0.1L = 16.5L
∴ The solution that can be made from 15L of concentrate is 16.5L
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T is the midpoint of SU if ST is 3x and TU is x+8 what is TU
The value of the line segment TU is 12 units.
What basically is a line segment?A line segment is a fixed-length section of the a line to two ends.
It is distinct from a line in that it has no origins or ending points and can be expanded in both directions.a line segment AB, the span of which is proportional to the distance between its endpoints A and BAccording to the question;
TU = x + 8 and ST = 3x are the lengths.
SU is the total length of the line segment.
Now, it is clear that SU is divided into parts such that;
SU = ST + TU
As, T is the mid point of the line SU;
The,
ST = TU
Equating the values;
3x = x + 8
Solving the equation;
3x -x = 8
x = 4
Put the value of x in TU;
TU = x + 8
TU = 4 + 8
TU = 12
Therefore, the value of the line segment TU is found as 12 units.
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Jay sells his smartphone to Louise and makes a 20% profit. Louise then sells the
smartphone after a year to Angel, and makes a 10% loss. Louise sold the smartphone
to Angel for £652. How much did Louise pay for the smartphone, and how much did
Jay pay for the smartphone originally?
Answer:
Jay paid £573.76 for the smart phone originally.
What is the sum of 15 and a number plus 12
Answer:
15 + (n + 12)
Step-by-step explanation:
glider begins its flight 3/4
mile above the ground. After 45 minutes, it is 3/10
mile above the ground. Find the change in height of the glider. If it continues to descend at this rate, how long does the entire descent last?
Answer:
1hour 15
Step-by-step explanation:
The glider begins its flight a mile above the ground.
Distance above the ground after 45 minutes =
Change in height of the glider
Next, we determine how long the entire descent last.
Expressing the distance moved as a ratio of time taken
Therefore: Total Time taken =45+30=75 Minutes
=1 hour 15 Minutes
A light bulb consumes 12600 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
A light bulb will consume 3,600 watts - hours in 1 day if it consumes 12,600 watts in 3 days 12 hours.
We are given that:
Consumption in 3 days 12 hours = 12,600 watts
12 hours = 12 / 24 days = 0.5 days
Days = 3 + 0.5 days = 3.5 days
Now, by using the unitary method, we get that the consumption by a light bulb in 1 day will be equal to:
3.5 days = 12,600 watts
1 day = 12,600 / 3.5 watts
1 day = 3,600 watts
Therefore, a light bulb will consume 3,600 watt - hours in 1 day if it consumes 12,600 watts in 3 days 12 hours.
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