3. The grade-point averages of 20 college seniors selected at random from a graduating class are as follows:
3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9 Calculate the standard deviation.
Answers
The standard deviation of the grade points average of the college seniors is 0.57.
The given parameters:
3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9
The sum of the given data is calculated as follows;
∑x = 3.2 + 1.9 + 2.7 + 2.4 + 2.8 + 2.9 + 3.8 + 3.0 + 2.5 + 3.3 + 1.8 + 2.5 + 3.7 + 2.8 + 2.0 + 3.2 + 2.3 + 2.1 + 2.5 + 1.9
∑x = 53.3
The mean of the distribution is calculated as follows;
[tex]\bar x = \frac{\Sigma x}{N} \\\\\bar x = \frac{53.3}{20} \\\\\bar x = 2.665[/tex]
The square of the difference between the grade point and the mean;
[tex]\Sigma (x - \bar x)^2 = (3.2- 2.665)^2 + (1.9-2.665)^2 + (2.7- 2.665)^2 + (2.4-2.665)^2 \\\\+(2.8-2.665)^2 +(2.9 - 2.665)^2 + (3.8 - 2.665)^2 + (3-2.665)^2+ \\\\(2.5 -2.665)^2 + (3.3 - 2.665)^2 + (1.8-2.665)^2 + (2.5 - 2.665)^2 + \\\\(3.7-2.665)^2 + (2.8 - 2.665)^2 + (2-2.665)^2 + (3.2-2.665)^2 + \\\\(2.3 - 2.665)^2 + (2.1-2.665)^2 + (2.5-2.665)^2 + (1.9 - 2.665)^2\\\\\Sigma (x - \bar x)^2 = 6.5055[/tex]
The standard deviation of the grade points is calculated as follows;
[tex]\sigma = \sqrt{\frac{\Sigma (x-\bar x)^2}{N} } \\\\\sigma = \sqrt{\frac{6.5055}{20} } \\\\\sigma = 0.57[/tex]
Thus, the standard deviation of the grade points average of the college seniors is 0.57.
Learn more about standard deviation here: https://brainly.com/question/12402189
Related Questions
The function g(x)=8(4*) is reflected across the x-axis to
create f(x).
What is the equation of f(x)?
O f(x)=8(4)
O f(x)=-8(4)*
14
9(x)
12
10
o f(x)=8(4)
o f(x)=-8()
do
OR
4
2
A
-3
-2
2
3
х
-10
-12
f(x)
14
Answers
9514 1404 393
Answer:
(b) f(x) = -8(4^x)
Step-by-step explanation:
Reflection across the x-axis multiplies the function by -1.
f(x) = -g(x) = -8(4^x)
Calculate the break even sales dollars if the fixed expenses are $7,000 and the contribution ratio is 40%.
Answers
Answer:
Break even sales = $17,500 (Approx.)
Step-by-step explanation:
Given:
Fixed expenses = $7,000
Contribution ratio = 40%
Find:
Break even sales dollars
Computation:
Break even sales = Fixed expenses / Contribution ratio
Break even sales = 7,000 / 40%
Break even sales = 7,000 / 0.40
Break even sales = 17,500
Break even sales = $17,500 (Approx.)
Factor the trinomial. Write the answer in binomial fctor form.
2x^2– 13x + 11
Answers
9514 1404 393
Answer:
(2x -11)(x -1)
Step-by-step explanation:
The middle term can be rewritten as a sum using the coefficients of the first and last terms. Then the expression can be factored by pairs of terms.
2x^2 -13x +11 = 2x^2 -2x -11x +11 = 2x(x -1) -11(x -1)
= (2x -11)(x -1)
Damaged items are marked down 25% to 40%. A newspaper coupon holder; to an additional 10% markdown of the new price due to the damage. What is the lowest price of a damaged item that was originally marked GHC100?
A GHC 35.60
B GH 5000
C. GHC 18.00
D. GHC 40.80
E GHC 23.40
Answers
Markdown is the difference (at sale) between the price an item is placed at for retail sale, and the actual price the item is sold
The correct option is; B. GHC 50.00
The reason for choosing option B is as follows;
The known parameters
The percentage by which damaged items are marked down = 25% to 40%
The percentage markdown offered by the newspaper coupon = 10%
The original marked price of the item = GHC 100
Strategy:
Apply the damaged items and coupon markdown percentages to the original marked price of GHC100 sum the results to find the total markdown
Solution:
Markdown due to damage:
Given that the item is damaged, to have the lowest price, we apply the largest markdown of 40%;
40% is removed from the price to which the item marked down due to damage, as follows;
The markdown due to damage = 40/100 × GHC 100 = GHC 40
Markdown due to Coupon Holder:
The markdown the coupon holder is to get = 10% off the retail price
Given that the damage is not mentioned in the newspaper, we have;
∴ The markdown the coupon holder is to get = 10/100 × GHC 100 = GHC 10
Total markdown:
The total markdown is therefore equal to GHC 40 + GHC 10 = GHC 50
The Lowest Price of A Damaged Items marked GHC100:
The lowest price of the item = Original price - Maximum markdown
The lowest price of the item = GHC 100 - GHC 50 = GHC 50
Learn more about markdown and markup concepts here;
https://brainly.com/question/20705786
A 6-pound container of detergent costs $4.38. what is the price per pound?
Answers
Answer:
.73 per pound
Step-by-step explanation:
Take the total cost and divide by the number of pounds
4.38/ 6
.73 per pound
a coin is tossed succesively three times times . determine tje probabiliy of getting all three heads
Answers
Answer:
Answer : 1/8.
Step-by-step explanation:
Hey there!
Please see the attached picture for your answer.
Hope it helps!
(x + y, 2) = (13, 2x - y)
Answers
Answer: (x, y) = (5,8)
Step-by-step explanation:
x + y = 13 2x - y = 2
y = -x + 13
2x - (-x + 13) = 2 3x =15
x=5
x=5 y = -x + 13
y = -(5) + 13 = 8
I need help answering this ASAP
Answers
Answer:
A
Step-by-step explanation:
The graph is a square root function
Which of the following questions are equivalent to the answer below x 3/5
Answers
Answer:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]
Step-by-step explanation:
Given
[tex]x^\frac{3}{5}[/tex]
Required
The equivalent expressions
We have:
[tex]x^\frac{3}{5}[/tex]
Expand the exponent
[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]
So, we have:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent
Express 1/5 as roots (law of indices)
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent
The above can be rewritten as:
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent
Please help asap! Easy question :)
Two fair dice are rolled. Determine the following probability:
P(one number is a multiple of 4 and the other is a multiple of 6)
Answers
Answer:
P(one number is a multiple of 4 and the other is a multiple of 6) = 1/18
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Desired outcomes:
One multiple of 4 and one multiple of 6.
2 possible outcomes: (4,6) or (6,4)
Probability:
2 outcomes out of 36, so:
[tex]p = \frac{2}{36} = \frac{1}{18}[/tex]
Then
P(one number is a multiple of 4 and the other is a multiple of 6) = 1/18
.
.
.
.
.
.
.
.
.
.
.
“””” HELP PLEASE “”””
.
.
.
.
.
.
.
.
.
.
.
Answers
9514 1404 393
Answer:
x = 14 cm
Step-by-step explanation:
We can only solve for x if the triangles are similar. The arrows on the left and right legs say those are parallel. Since alternate interior angles at each of the transversals are congruent, the triangles are AA similar.
ΔABC ~ ΔDEC, so we have ...
EC/ED = BC/BA
x/(18 cm) = (35 cm)/(45 cm)
x = (18 cm)(7/9) = 14 cm
Help me please and thank you
Answers
Answer:
D) 0.89
Step-by-step explanation:
round 0.885 to 0.89
Please help I need the answer ASAP!!
Answers
The hypotenuse will always be the longest side of the triangle. Option C is correct: AB > DC.
AB is the hypotenuse of triangle ABC. Therefore, it is greater than leg AC. AC is the hypotenuse of triangle ACD. If AC is less than AB, then DC must also be less than AB because DC is less than AC.
Hope this helps!
find the missing side length below brainly
Answers
Let it be x
[tex]\\ \sf\longmapsto \dfrac{3}{5}=\dfrac{x}{x+4}[/tex]
[tex]\\ \sf\longmapsto 3(x+4)=5x[/tex]
[tex]\\ \sf\longmapsto 3x+12=5x[/tex]
[tex]\\ \sf\longmapsto 5x-3x=12[/tex]
[tex]\\ \sf\longmapsto 2x=12[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{12}{2}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
You take out a 60-day loan for $5000. At the end of the loan, you owe $73.97 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
Answers
The PERCENTAGE ANNUAL RATE is 9.0% to the nearest tenth using the SIMPLE INTEREST FORMULA
The question is related to a SIMPLE INTEREST problem:
Loan period = 60 days
using 365 days a year ;
converting to years , 60 days = (60 / 365) years
interest on loan = 73.97
principal = 5000
Using the formula:
interest = (principal * rate * time)
73.79 = (5000 * rate * (60/365)
Rate = 73.79/(5000 * (60/365)) =8.977%
rate = 9%
Therefore, PERCENTAGE ANNUAL RATE is 9.0%
Learn more : https://brainly.com/question/3880193
Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The determinant of a triangular matrix is the sum of the entries on the main diagonal Choose the correct answer below.
A. The statement is true. Cofactor expansion along the row (or column) with the most zeros of a triangular matrix produces a determinant equal to the son of the tries to the radar
B. The statement is true. The determinant of A is the following finite series. n det A= (-1)* laj, det A1 J = 1 In a triangular matrix, this series simplifies to the sum of the entries along the main diagonal.
C. The statement is false. The determinant of a matrix is the arithmetic mean of the entries along the main diagonal OD The statement is false. The determinant of a triangular matrix is the product of the entries along the main diagonal
Answers
A student decides she wants to save money to buy a used car, which costs $2600.She comes upwith what she thinks is a very modest savings plan. She decides to save 2 cents the first day anddouble the amount she saves each day thereafter. On the second day she plans to save 4 cents, onthe third day, 8 cents, and so on.
(a)Write an expression that represents the amount savedon dayn;(b)Write an expression that represents the total amount savedby dayn (including day n);(c)Determine how long it will take her to save enough money to buy the car (The answermay surprise you!)
Answers
Answer: total cost to be saved is $2600. Her saving pattern is 2, 4, 8,…
a) The pattern of her saving is in geometric sequence. i.e. a=2, r=4/2=2 0r 8/4=2 ( a = First term, r = common ratio) so, expression for amount saved on day (n) = t(n) = ar^(n-1), where: a = first day of saving r = common ration n = number of day
b) Expression that represents the total amount saved by day (n) (including day n) = S = a(r^n-1)/r-1 where: S = sum of amount saved a = first day of saving r = common ration n = number of day
c) To buy the car, she needs at least $2600 which is equal 260000 cents. S = a(r^n-1)/r-1 = 260000 = 2(2^n-1)/r-1 = 260000/2 = 2^n-1/2-1 = 130000 = 2n^-1 = 130000+1 = 2^n = 130001 = 2^n = n = ln(130001)/ln(2) = n = 16.988
So… for n to satisfy the least value of 130001 cents, n should be at least 17 Therefore it will take at least 17 days for her to save enough money to buy a car
Step-by-step explanation:
It will take her about 17 days to buy the car worth 260000 cents
If a student decides she wants to save money to buy a used car that cost $2600 (260,000 cents)
If she saves 2 cents the first day and doubles the amount thereafter, the sequence of savings will be:
2, 4, 8...
This sequence is geometric in nature
In order to determine how long it will take her to save 260,000, we will use the sum of a GP formula expressed as:
[tex]S_n = \frac{a(r^n-1)}{r-1}[/tex]
Given the folowing
a = 2
r = 4/2 = 8/4 = 2
Sn = 260,000
Substitute into the formula the given parameters
[tex]260000= \frac{2(2^n-1)}{2-1}\\260000/2=2^n-1\\130000 = 2^n - 1\\2^n = 130000 + 1\\2^n = 130001\\nlog 2=log130001\\n = \frac{log130001}{log2} \\n \approx 17[/tex]
This shows that it will take her about 17 days to buy the car worth 260000 cents
Learn more here: https://brainly.com/question/20548958
find the two intersection points
(x+1)^2 +(y+2)^2 = 16
3x+ 4y = 1
Show your steps please
Answers
Answer:
Our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Step-by-step explanation:
We want to find where the two graphs given by the equations:
[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]
Intersect.
When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.
Since the linear equation is easier to solve, solve it for y:
[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]
Substitute this into the first equation:
[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]
Simplify:
[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]
Square. We can use the perfect square trinomial pattern:
[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]
Multiply both sides by 16:
[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]
Combine like terms:
[tex]25x^2+-22x+97=256[/tex]
Isolate the equation:
[tex]\displaystyle 25x^2 - 22x -159=0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 25, b = -22, and c = -159. Substitute:
[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]
Hence, our two solutions are:
[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]
We have our two x-coordinates.
To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:
[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]
And:
[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]
Thus, our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 159 miles in a day. Round your answer to four decimal places.
Answers
Answer:
the probability that a truck drives less than 159 miles in a day = 0.9374
Step-by-step explanation:
Given;
mean of the truck's speed, (m) = 120 miles per day
standard deviation, d = 23 miles per day
If the mileage per day is normally distributed, we use the following conceptual method to determine the probability of less than 159 miles per day;
1 standard deviation above the mean = m + d, = 120 + 23 = 143
2 standard deviation above the mean = m + 2d, = 120 + 46 = 166
159 is below 2 standard deviation above the mean but greater than 1 standard deviation above the mean.
For normal districution, 1 standard deviation above the mean = 84 percentile
Also, 2 standard deviation above the mean = 98 percentile
143 --------> 84%
159 ---------> x
166 --------- 98%
[tex]\frac{159-143}{166-143} = \frac{x-84}{98-84} \\\\\frac{16}{23} = \frac{x-84}{14} \\\\23(x-84) = 224\\\\x-84 = 9.7391\\\\x = 93.7391\ \%[/tex]
Therefore, the probability that a truck drives less than 159 miles in a day = 0.9374
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to find x.)
Answers
Set the proportion as shown:
2660/4.75 = x/1
Cross multiply:
4.75x = 2660
Divide both sides by 4.75
x = 560
Answer: 560 miles per hour
–20 ÷ 5 =
I need help
Answers
-20 divided by 5 ^
What is the order of rotational symmetry for the figure?
A. 3
B. 2
C. 4 or more
D. 1
Answers
9514 1404 393
Answer:
C. 4 or more
Step-by-step explanation:
Rotating the figure in increments of 90° will give the same figure. There are 4 such rotations in a full turn. The order of rotational symmetry is 4.
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 2 + 4x What does the y-intercept of this function represent? (1 point) The original height of the plant was 4 mm. The original height of the plant was 2 mm. The height of the plant increases by 2 mm for every hour of sunlight it receives. The height of the plant increases by 4 mm for every hour of sunlight it receives.
Answers
Answer:
The original height of the plant was 2 mm
Step-by-step explanation:
Given
[tex]y = 2 + 4x[/tex]
Required
Interpret the y-intercept
The y-intercept is when [tex]x = 0[/tex]
So, we have:
[tex]y = 2 + 4 *0[/tex]
[tex]y = 2 + 0[/tex]
[tex]y = 2[/tex]
This implies that the original or initial height was 2 mm
HELP !
Find the measure it the given angle.
Answers
Answer:
it's 90
Step-by-step explanation:
inscribed angle intercepts a semicircle is always 90
Because you have to find the radius and x by pi
Two chords in a circle intersect. One chord is made of 6 and 5, and the other is made of x +1 and x. What is x?
Answers
Answer:
x = 5 and -6
Step-by-step explanation:
Using the intersecting chord theorem which states that the products of the lengths of the line segments on each chord are equal.
Hence:
let
a = 6, b = 5, c = x+1 and d = x
Therefore, ab = cd
6*5 = x(x+1)
30 = x²+x
x²+x - 30 = 0
x²+ 6x - 5x - 30 = 0
x(x+6) - 5(x+6) =0
(x-5)(x+6) = 0
x-5 =0 and x+6 = 0
x = 5 and -6
g A gift shop sells 40 wind chimes per month at $110 each. The owners estimate that for each $11 increase in price, they will sell 2 fewer wind chimes per month. Find the price per wind chime that will maximize revenue.
Answers
Answer:
The price that maximizes the revenue is $165
Step-by-step explanation:
We can model the price as a function of sold units as a linear relationship.
Remember that a linear relationship is something like:
y = a*x + b
where a is the slope and b is the y-intercept.
We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
For this line, we have the point (40, $110)
which means that to sell 40 units, the price must be $110
And we know that if the price increases by $11, then he will sell 2 units less.
Then we also have the point (38, $121)
So we know that our line passes through the points (40, $110) and (38, $121)
Then the slope of the line is:
a = ($121 - $110)/(38 - 40) = $11/-2 = -$5.5
Then the equation of the line is:
p(x) = -$5.5*x + b
to find the value of b, we can use the point (40, $110)
This means that when x = 40, the price is $110
then:
p(40) = $110 = -$5.5*40 + b
$110 = -$220 + b
$110 + $220 = b
$330 = b
Then the price equation is:
p(x) = -$5.5*x + $330
Now we want to find the maximum revenue.
The revenue for selling x items, each at the price p(x), is:
revenue = x*p(x)
replacing the p(x) by the equation we get:
revenue = x*(-$5.5*x + $330)
revenue = -$5.5*x^2 + $330*x
Now we want to find the x-value for the maximum revenue.
You can see that the revenue equation is a quadratic equation with a negative leading coefficient. This means that the maximum is at the vertex.
And remember that for a quadratic equation like:
y = a*x^2 + b*x + c
the x-value of the vertex is:
x = -b/2a
Then for our equation:
revenue = -$5.5*x^2 + $330*x
the x-vale of the vertex will be:
x = -$330/(2*-$5.5) = 30
x = 30
This means that the revenue is maximized when we sell 30 units.
And the price is p(x) evaluated in x = 30
p(30) = -$5.5*30 + $330 = $165
The price that maximizes the revenue is $165
find the equation of straight line passes through point (3,1) such that the intercept on y-axis exceeds that on the x- axis by 4.
Answers
Answer:
Step-by-step explanation:
please please help its timed -H.M
Answers
Answer:
1
General Formulas and Concepts:
Algebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
f(-2)
Step 2: Evaluate
f(-2) is x = -2 for function f(x).
According to the table, when x = -2, f(x) = 1.
∴ f(-2) = 1
Use the integral test to determine whether the series is convergent or divergent. [infinity] n = 2 n2 n3 + 1 Evaluate the following integral. [infinity] 2 x2 x3 + 1 dx
Answers
I think the given series is
[tex]\displaystyle\sum_{n=2}^\infty \frac{n^2}{n^3+1}[/tex]
You can use the integral test because the summand is clearly positive and decreasing. Then
[tex]\displaystyle\sum_{n=2}^\infty\frac{n^2}{n^3+1} > \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx[/tex]
Substitute u = x ³ + 1 and du = 3x ² dx, so the integral becomes
[tex]\displaystyle \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx = \frac13\int_9^\infty\frac{\mathrm du}u = \frac13\ln(u)\bigg|_{u=9}^{u\to\infty}[/tex]
As u approaches infinity, we have ln(u) also approaching infinity (whereas 1/3 ln(9) is finite), so the integral and hence the sum diverges.
1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.
2. You are given the 3rd and 5th term of an geometric sequence. Describe how to determine the 10th term without finding the general term.
Answers
Step-by-step explanation:
1. In an arithmetic sequence, the general term can be written as
xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.
Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =
x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get
x₅-x₃ = 2d
divide by 2 to isolate d
(x₅-x₃)/2 = d
This lets us solve for d. Given d, we can say that
x₃ = y+d(2)
subtract 2*d from both sides to isolate the y
x₃ -2*d = y
Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of
xₙ = y + d(a-1)
2.
Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is
x₃* r * r
= x₃*r² = x₅
divide both sides by x₃ to isolate the r²
x₅/x₃ = r²
square root both sides
√(x₅/x₃) = ±r
One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.
Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence
