Answer:
[tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].
Step-by-step explanation:
We are given a geometric sequence { -16, 4, -1, .... }
i.e. [tex]a_{1} =-16[/tex], [tex]a_{2} =4[/tex], [tex]a_{3} =-1[/tex], ...
We will first find the common ratio 'r'.
Now, [tex]r=\frac{a_{n}}{a_{n-1}}[/tex]
i.e. [tex]r=\frac{a_{2}}{a_{1}}[/tex]
i.e. [tex]r=\frac{4}{-16}[/tex]
i.e. [tex]r=\frac{1}{-4}[/tex]
Similarly, i.e. [tex]r=\frac{a_{3}}{a_{2}}[/tex]
i.e. [tex]r=\frac{-1}{4}[/tex]
So, we get that the common ratio is [tex]r=\frac{-1}{4}[/tex].
Now, the recursive formula for the geometric sequence is given by,
[tex]a_{n} =r \times a_{n-1}[/tex]
i.e. [tex]a_{n} =\frac{-1}{4} \times a_{n-1}[/tex]
i.e. [tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].
Hence, the recursive formula for this sequence is [tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].
Find the product. (7 q - 5)(7 q + 5)
49q^2 - 10q - 25
49q^2 + 10q - 25
49q^2 - 25
[tex]Use\ (a-b)(a+b)=a^2-b^2.\\\\(7q-5)(7q+5)=(7q)^2-5^2=\boxed{49q^2-25}[/tex]
Final answer:
The product of the binomials (7q - 5) and (7q + 5) is found using the difference of squares formula, resulting in 49q² - 25.
Explanation:
To find the product of the given expressions (7q - 5)(7q + 5), we can use the difference of squares formula, which states that (a - b)(a + b) = a² - b².
Here, a is 7q and b is 5.
Applying the formula, we get:
(7q)² - (5)²49q² - 25This is because the mixed term +7q(-5) and the term -7q(+5) cancel each other out, leaving us with just the square terms.
What is the 30th term of the arithmetic series 4, 7, 10, …? 88 89?
How far does a bus travel in 2.5 hours at 65mph?
How many solutions does the equation have?
7x+3−x=3(1+2x)7x+3−x=3(1+2x)
0
1
infinitely many
Answer:
0
if you were confused to the one on top
The Wilsons drove 324 miles in 6 hours if they drilled the same number of miles each hour how many miles did they drive in 1 hour
The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true?
a.The function is positive for all real values of x where x > –4.
b.The function is negative for all real values of x where –6 < x < –2.
c.The function is positive for all real values of x where x < –6 or x > –3.
d.The function is negative for all real values of x where x < –2.
Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. if you choose the upside-down cone to have the largest possible volume, what fraction of the volume of the larger cone does it occupy?
When a smaller, upside-down cone is placed inside a larger cone, both cones being similar and the vertex of the smaller one being at the center of the base of the larger one, the smaller cone would occupy 1/8 or 12.5% of the volume of the larger cone.
Explanation:The relationship between the volume of the larger cone and the smaller, upside-down cone placed inside it is represented through the formula for the volume of a cone, which is 1/3 * π * r² * h, where 'r' is the radius of the base and 'h' is the height. If you manage to place the smaller cone such that it has the largest possible volume (which will happen when the smaller cone is similar to the larger cone), the smaller cone will have a height and radius proportionately smaller than the larger one.
Thus, the volumes are proportional to the cube of their corresponding proportions, so the smaller cone will occupy 1/n³ of the volume of the larger cone, where 'n' is the proportion between their linear dimensions. In this particular set-up, the 'n' will equal 2 because when the vertex of the smaller cone is at the center of the base of the larger cone, the smaller cone's height is half that of the larger cone. Hence, the smaller cone will occupy 1/2³ = 1/8 or 12.5% of the volume of the larger cone.
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if 2 inches equals 25 miles. how many miles would 0.25in (1/4 inch) equal?
Evaluate without the use of a calculator 10^-2
Given the functions m(x) = 4x − 11 and n(x) = x − 10, solve m[n(x)] and select the correct answer below. (2 points)
Select one:
a. m[n(x)] = 4x − 51
b. m[n(x)] = 4x − 29
c. m[n(x)] = 4x^2 − 51
d. m[n(x)] = 4x^2 − 29
Answer:
got it right and was option A thx
Step-by-step explanation:
What is 1/10 of an income of $97.50?
$9.75
$0.98
$975.00
$9,750.00
The purple shape is a dilation of the black shape. What is the scale factor of the dilation?
Answer:
Scale factor = [tex] \frac{1}{2} [/tex]
Explanation:
The purple shape is a dilation of the black shape.
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
Now findd the scale factor.
If given two shapes and need to find the scale factor, We must know which one was the original and which one is the image or the new shape. Then we need to know the length of corresponding sides and set them up in a ratio like so:
Scale Factor = [tex] \frac{purple}{black} [/tex]
Scale factor = [tex] \frac{10}{20} = \frac{1}{2} [/tex]
What is the value of z in the equation z − 3 = 22? 7.33 19 25 66
Answer:
The answer is 25
Step-by-step explanation:
A carpenter's square is a tool that is used to draw right angles. suppose you are buildong a toy car and you have four small circles of wood that will serve as the wheels . you need to drill a hole in the center of each wheel for axle. explain how you can use the carpenter 's square to find the center of each wheel. answer
Final answer:
To find the center of a wooden wheel for a toy car, use a carpenter's square to draw two perpendicular diameters across the wheel; their intersection is the center where the axle hole should be drilled.
Explanation:
To find the center of a wooden wheel using a carpenter's square, which is used to draw right angles, follow these steps:
Place the wheel on a flat surface.Use the carpenter's square to draw two diameters across the wheel by aligning the square with the edge of the wheel and drawing a line from one side of the wheel to the opposite side.Turn the wheel or the square 90 degrees and draw another diameter that intersects the first one. The two lines should cross at the wheel's center, providing the exact location to drill a hole for the axle.This method effectively divides the wooden wheel into four equal quadrants, and the intersection point of the diameters marks the center, where the axle hole should be drilled.
A(n) _ shows you the schedule of payments on a loan and the total interest and payments at the end of the loan.
A. payoff table
B. amortization table
C. payment table
D. interest table
Secured debts must have _.
A. collateral
B. real property
C. low interest rates
D. certified lenders
You are purchasing a car for $12,985.00 with the help of your parents. How much interest is saved in the first month by you using their good credit rating compared to your fair credit rating?
A. $14.61
B. $54.15
C. $15.15
D. $69.25
(Secured APR for good credit is 5.00%, and for the unsecured APR it is 5.90%. Secured APR for fair credit is 6.40%, and for unsecured APR it is 7.25%.)
Answer: 3.A
Step-by-step explanation: At the exallent rating
A circle has a diameter with endpoints (7, -7) and (5, -3). What is the equation of the circle?
Final answer:
To find the circle's equation from its diameter's endpoints, calculate the circle's center using the midpoint formula, then determine the radius with the distance formula. Finally, use these values in the circle's standard equation.
Explanation:
To find the equation of the circle, we first need to determine its center and radius. The midpoint of the diameter will give us the center of the circle, and the distance from one of the endpoints to the midpoint will give us the radius.
Step 1: Find the Center of the Circle
The midpoint formula ((x1 + x2)/2, (y1 + y2)/2) gives us the center of the circle. Applying this to our points (7, -7) and (5, -3):
Center = ((7 + 5) / 2, (-7 - 3) / 2) = (6, -5)
Step 2: Calculate the Radius
We use the distance formula, √((x2 - x1)² + (y2 - y1)²), between one of the endpoints and the center:
Radius = √((7 - 6)² + (-7 + 5)²) = √(1 + 4) = √5
Step 3: Write the Equation
Using the standard equation, (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius:
Equation: (x - 6)² + (y + 5)² = 5
This equation gives the precise location and size of the circle based on its diameter's endpoints.
Please help, picture included!
State the domain of the relation.
A) {-4, -3, -2, -1, 0, 2, 5, 8}
B) {-4, -3, -2, -1, 0}
C) {-4, -3, -2, -1}
D) {-4, -1, 2, 5, 8}
QRS~TUV. What is the measure of V?
What’s the answer?
∠V is calculated to be 70°.
When two triangles are similar (QRS ~ TUV), their corresponding angles are equal. This means:
∠Q corresponds to ∠T∠R corresponds to ∠U∠S corresponds to ∠VGiven ∠R = 47° and ∠Q = 63°, we know that ∠T = 63° and ∠U = 47°.
Since the sum of the angles in any triangle is 180°:
∠Q + ∠R + ∠S = 180°
Substituting the known values:
63° + 47° + ∠S = 180°
Solving for ∠S:
∠S = 180° - 63° - 47° = 70°
Therefore, ∠V = 70° because ∠S corresponds to ∠V in the similar triangles.
Complete question: Triangle QRS is similar to triangle TUV. ∠R=47°, ∠Q=63°. What is the measure of angle V?
A) –72
B) 72
C) –36
D) 36
In this fulcrum, the weights are perfectly balanced. How far must the fulcrum be located from the 40 lb. weight if the bar is 11 feet long? x (to the nearest tenth) =
Answer:
[tex]x=6.11 feet[/tex]
Step-by-step explanation:
Given that in a fulcrum weights are perfectly balanced.
One side 40 lb weight is there and another side 50 lb weight is given
Let x be the length of 40 lb weight from fulcrum. Then 50 lbs is at a distance of 11-x.
Then we have since weights are perfectly balanced
[tex]40x = 50(11-x)\\90x=550\\x=6.111[/tex]
Thus we get [tex]x=6.11[/tex]feet
Which rule describes the translation?
PLEASE ANSWER
(x, y) → (x – 8, y – 3)
(x, y) → (x – 3, y + 8)
(x, y) → (x + 8, y – 3)
(x, y) → (x + 3, y + 8)
Answer:
its C
Step-by-step explanation:
(x, y) → (x + 8, y – 3)
Use Distributive Property to write 4m + 4p
Factor out the common numbers/variables from the terms given
4 is a common number
4m + 4p
4(m + p) is your answer
hope this helps
Kaylie had $1250 in her savings account. She withdrew $82 each month for 8 months in order to pay for a summer vacation. How much did Kaylie have in her account at the end of the 8 months?
which completely describes the polygon
Answer:
NONE OF THE ABOVE!!
Step-by-step explanation:
A regular polygon is equilateral and equiangular, and also, can be inscribed into a circle. The polygon shown doesn't meet any of these conditions.
ryan invests a sum of money in a saving account with a fixed annual interest rate of 4.31% compounded monthly. After 10 years, the balance reaches $12,835.94. What was the amount of the initial investment?
We calculate P to be approximately $7,759.58, which is the amount Ryan invested initially.
To determine the initial investment that Ryan made, which grew to $12,835.94 after 10 years with an annual interest rate of 4.31% compounded monthly, we will use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We know that:
A = $12,835.94
r = 4.31/100 = 0.0431
n = 12
t = 10
We need to solve for P:
P = A /[tex](1 + r/n)^{nt}[/tex]
Substituting the known values, we get:
P =[tex]$12,835.94 / (1 + 0.0431/12)^{12*10}[/tex]
P = $12,835.94 / [tex](1 + 0.0035925)^{120}[/tex]
P = $12,835.94 / ([tex]1.0035925)^{120}[/tex]
Calculating the value inside the parenthesis first:
[tex](1.0035925)^{120}[/tex] = 1.654297553
Now, we divide the final amount by this compound factor:
P = $12,835.94 / 1.654297553
P ≈ $7,759.58
Therefore, Ryan's initial investment was approximately $7,759.58.
In how many ways can you choose 3 kinds of ice cream and 2 kinds of toppings from a dessert buffet with 10 differnt kinds of ice cream and 6 kinds of toppings
To choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet with 10 different kinds of ice cream and 6 kinds of toppings, you can use the concept of combinations. The total number of ways to choose is 1800.
Explanation:To determine the number of ways to choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet, we can use the concept of combinations. We have 10 different kinds of ice cream to choose from, and we want to choose 3 of them. The number of combinations can be calculated using the formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of objects (10 ice cream flavors) and r is the number of objects to be chosen (3 ice cream flavors), and ! denotes factorial.
In this case, the number of combinations of ice cream flavors is:
C(10, 3) = 10! / (3!(10-3)!) = 120
Similarly, we have 6 different kinds of toppings to choose from, and we want to choose 2 of them. The number of combinations of toppings is:
C(6, 2) = 6! / (2!(6-2)!) = 15
Therefore, the total number of ways to choose 3 kinds of ice cream and 2 kinds of toppings is the product of the number of combinations of ice cream flavors and toppings:
Total number of ways = 120 * 15 = 1800
does y vary directly as x in this function? y= -3x+4
"how many distinct ways can the letters in tallahassee be arranged"
The number of distinct ways the letters in TALLAHASSEE can be arranged is calculated using permutations with repetitions. It involves taking the factorial of the total number of letters and dividing by the factorial of the number of times each letter repeats.
To determine the number of distinct ways the letters in TALLAHASSEE can be arranged, we must consider it as a permutation problem with repeating elements. We need to calculate the factorial of the total number of letters and then divide by the factorial of the number of times each individual letter repeats.
The word TALLAHASSEE contains 11 letters in total:
'T' occurs once.'A' occurs twice.'L' occurs twice.'H' occurs once.'S' occurs twice.'E' occurs twice.The permutation formula considering repetitions is:
Number of arrangements = Total letters factorial / (Product of each letter's factorial)
Therefore:
Number of arrangements = 11! / (2! * 2! * 2! * 2!)
This would give us the total number of distinct arrangements of the letters in TALLAHASSEE.
Kia has 10 coins in a bag. T here are three $1 coins and seven 50 pence coins. Kia takes at random 3 coins from the bag. workout the probability she takes out exactly $2.50
Answer:
7/40
Step-by-step explanation:
once again not bothered
The probability she takes out exactly $2.50 is 7/40.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of coins in Kia bag = 10 coins
Number of $1 coins = 3
Number of 50 pence coins = 7
Kia takes at random 3 coins from the bag and the number of ways are
[tex]10C_{3} =\frac{(10)(9)(8)}{(1)(2)(3)}[/tex]
⇒ [tex]10C_{3} =\frac{720}{6}[/tex]
⇒ 120
Kia takes out exactly $2.50
So the combination could be two $1 coins and one 50 pence coins,
⇒ [tex](3C_{2}) (7C_{1} )[/tex]
⇒ [tex](\frac{(3)(2)}{(1)(2)} )(7)[/tex]
⇒ 21
Thus the probability she takes out exactly $2.50 is P(E) = [tex]\frac{21}{120}[/tex]
⇒ 7/40
Hence we can conclude that the probability she takes out exactly $2.50 is 7/40.
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At summer camp, 150 kids had the opportunity to choose their activities. of those kids selected archery for their morning activity. Of that group, also chose to study drama in the afternoons. How many kids chose both archery in the morning and drama in the afternoons?
The correct answer is [tex]D = 23[/tex]
To solve this problem , let's define the given information:
Let [tex]T[/tex] be the total number of kids at the summer camp:
[tex]T = 150[/tex]
Let [tex]A[/tex] be the number of kids who chose archery for their morning activity:
[tex]\frac{A}{T} = \frac{3}{5}[/tex]
Let [tex]D[/tex] be the number of kids from the archery group who also chose drama in the afternoons:
[tex]\frac{D}{A} = \frac{1}{4}[/tex]
We want to find the value of [tex]D[/tex], which represents the number of kids who chose both archery in the morning and drama in the afternoons.
We can set up the following equations:
[tex]\frac{A}{T} &= \frac{3}{5}[/tex]
[tex]A &= \frac{3}{5}T[/tex]
[tex]A &= \frac{3}{5}(150)[/tex]
[tex]A &= 90[/tex]
[tex]\frac{D}{A} &= \frac{1}{4}[/tex]
[tex]D &= \frac{1}{4}A[/tex]
[tex]D &= \frac{1}{4}(90)[/tex]
[tex]D &= 22.5[/tex]
Therefore, the number of kids who chose both archery in the morning and drama in the afternoons is [tex]22.5 or 23[/tex] (since we cannot have a fractional number of kids).
[tex]D = 23[/tex]