The value of the sequence aₙ₊₁ is -5.5
How to determine the value of the sequenceThe definition of the sequence is given as
8.0, 6.5, 5.0, 3.5, . . .
The above definitions imply that we simply subtract 1.5 from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ₊₁ = aₙ - 1.5
From the question, we have
aₙ = -4.0
Substitute the known values in the above equation, so, we have the following representation
aₙ₊₁ = -4.0 - 1.5
Evaluate
aₙ₊₁ = -5.5
Hence, the value of aₙ₊₁ is -5.5
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A dairy farm ships crates of milk to food stores. There are 48 quarts of milk
for every 3 crates shipped. Plot points on the graph to show how many
quarts of milk there are for shipments of 3, 4, 6, and 9 milk crates. Label each
point with its ordered pair.
WANNOW SNG.2006mol
sway
Ay
sdruouo 30 0/losy Sma
Quarts of Milk
128.
96
64
32
0
0
44
2 4 6 8
Milk Crates
X
There are 48, 64, 96 and 144 quarts of milk for 3,4,6 and 9 crates shipped.
What is coordinate pair?
Coordinate pair means the two numerical pair bounded by a parenthesis but separated by comma. The first numerical term denotes the X coordinate and the 2nd numerical term indicate Y coordinate. The coordinate pair is used to locate a point on the cartesian plane.
What is the coordinate pair for the given statement?A dairy farm ships crates of milk to food store. There are 48 quarts of milk for every 3 crates shipped.
for every 3 crates shipped there are 48 quarts of milk.
for 4 crates shipped there will be milk quarts = (48 × 4) / 3
= 64 quarts
for 6 crates shipped milk quarts = (6 × 48) / 3 = 96 quarts milk
for 9 crates shipped number of milk quarts = (9×48)/ 3 = 144
if ship crates are denoted by X axis and milk quarts is denoted by Y axis
then the coordinate pairs will be (3, 48), (4, 64), (6, 96) and (9, 144)
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Karen has 20 one-dollar bills. She wants to give each of her 6 children the same number of bill
give each child How many bills will Karen have remaining?
Answer:
2
Step-by-step explanation:
because 6 can't Divide 20 so,
18/6
rem:2
now,
Total money-Giving money
20-18
2$
what is the half-life of the radionuclide that shows the following decay curve?
Decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay. The rate of change is determined by the equation dN/dt = N, where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.
When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.
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The decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.
The rate of change is determined by the equation dN/dt = N,
where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.
When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.
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Multiply. V6. V22 . v55
Using exponents law, the required product is [tex]v^{83}[/tex]
What are Exponents?
A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable. Exponent times power is how you raise a number with an exponent to a power.
[tex]v^6 \times v^{22} \times v^{55}[/tex]
Use the exponents law:
[tex]a^m \times a^n = a^{m+n}[/tex]
So, we get [tex]v^{6+22+55} = v^{83}[/tex]
Thus, the required product is [tex]v^{83}[/tex]
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The difference of 5 and the product of 5 and a number
Answer: 5-5x
Step-by-step explanation:
Find the exact length of the curve. x = 1/3√y(y - 3), 4 ≤ y ≤ 16.
The exact length of the given curve is 62/3
We can calculate the above answer by following the steps given below,
We have been given the following values,
x = 1/3 √y (y - 3), 4 ≤ y ≤ 16
The curve is of the length, x = f(y) from y =a to y = b is given by:
x = 1/3 √y (y - 3)
x = 1/3 (- 3)
dx/dy = 1/3 [(3/2)- (3/2)]
= 1/3 [(3/2) - (3/2)]
= 1/2 [ - 1/]
= (y-1)/2√y = f'(y)
Now we will calculate the length of the curve
= [tex]\int\limits^a_b {\sqrt{1+f'(y)^{2} } } \, dy[/tex]
= [tex]\int\limits^a_b{\sqrt{1+ (\frac{y-1}{2\sqrt{y} } )^2} } \, dy[/tex] (here a= 4, b=16)
= [tex]\int\limits^{16} _4 {\sqrt{1+ (\frac{y^2+2y-1}{4y} } )^} } \, dy[/tex]
= [tex]\int\limits^{16} _4 {\sqrt{\frac{4y+ y^2+ 2y-1}{4y} } } \, dy[/tex]
= [tex]\int\limits^{16}_4 {\frac{y+1}{2\sqrt{y} } } \, dy[/tex]
= [tex]\int\limits^{16}_4 {\frac{1}{2}\sqrt{y} } \, dy+ \int\limits^{16}_4 {\frac{1}{2\sqrt{y} } } \, dy[/tex]
= [1/3 (64-8)] +[4-2]
= (56/3)+2
= 62/3
Therefore the exact length of the curve that we get after solving the equation for curve is x = 1/3, 4 ≤ y ≤ 16, is 62/3.
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938.120 in word form
Answer:
Nine hundred thirty-eight one hundred twenty thousandths.
-Hope this helps!
Sophia is going to invest in an account paying an interest rate of 3.4% compounded monthly. How much would Sophia need to invest, to the nearest dollar, for the value of the account to reach $1,450 in 14 years?
Answer:
To calculate the amount Sophia needs to invest to reach a certain value in a specific time, given an interest rate compounded monthly, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial principal or investment amount
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the investment is held
Since the interest is compounded monthly, we need to divide the annual rate by 12 to find the monthly rate. So:
r/12 = 0.034/12 = 0.002833
Now we can plug in the values into the formula:
A = P(1 + 0.002833)^(12*14)
A = P(1.002833)^(168)
We know that A = $1,450 and we want to find P (the initial principal or investment amount).
So we can rearrange the equation to find P:
P = A/(1.002833)^(168)
Solving for P, we get:
P ≈ $973.99
So Sophia would need to invest around $973.99 to reach $1,450 in 14 years with an annual interest rate of 3.4% compounded monthly.
Step-by-step explanation:
Help needed! ( question attached )
Answer:
The circumference of the wheel is 2 * pi * r = 2 * 3.14 * 225 mm = 1413.8 mm.
The number of arcs between each spoke is 25 - 1 = 24.
So, the arc length between each spoke is the circumference of the wheel divided by the number of arcs, which is 1413.8 mm / 24 = 58.91 mm.
4.) You noticed that the store brand of your favorite drink is on sale at your local grocery
store for a 12 pack of cans for $2. You try it and like it. So, you go back and buy another 3
12-packs. How much money will you save over the course of a month if you drink one can a
day at work instead of spending $1.25 at the vending machine assuming there is 20 working
days in a month? How much would you save in a year?
So on solving the provided question, we can say that by unitary method saving = 25 - 7.3333333336 = $17.6666666664
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
by unitary method,
12 pack of can, costs = $2
cost of 3 12 pack can - $2 *3 = $6
12 pack can = 12 days
1 can = $2/12 = $0.1666666667
8 can = $0.1666666667*8 = $1.3333333336
original cost of 1 can = $1.25
ordinal cost of 20 cans = $1.25*20 = 25
sale cost of 20 cans = $1.3333333336 + $6 = 7.3333333336
saving = 25 - 7.3333333336 = $17.6666666664
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A coin is flipped 200 times. The table shows the frequency of each event.
Outcome | Frequency
Heads | 96
Tails | 104
Determine the experimental probability of landing on heads.
A. 48%
B. 50%
C. 96%
D. 104%
Answer:
Below
Step-by-step explanation:
96 heads out of 200 flips
96/200 = 48 %
Answer: 48%
Step-by-step explanation: 96 is 48% of 200, therefore the probability of landing on heads is 48%.
****************EXTRA CREDIT!!**********************
Anya makes 14 baskets throughout a basketball game. Some of the baskets were worth 2 points. while the others were worth 3 points. in total, anya scored 30 point. how many 2-point baskets did she make?
Part A: Define your variables
Part B: Write two equations for this scenario.
Part C: Determine how many 2-point baskets Anya made.
let x = the number of 2-point baskets Anya made
y = the number of 3-point baskets Anya made
Equations:
x + y = 14
2x + 3y =
Multiply the 1st equation by 3 to get:
3x + 3y = 42
Subtract above equation by 2nd equation to get:
(3x-2x) + (3y - 3y) = 42 -30
x = 12
Anya made 12 2-point baskets.
PLEASEEEEEEE HELPPPPPPPP!!!!!!!!!
Answer: 2
Step-by-step explanation: The value x in f(x) is a value on the x-axis that we input into the function. F(x) is a value on the y-axis. F(2) means we are inputting the value of 2 on the x-axis and looking for the corresponding point on the y-axis. If we look at the graph at x=2, we can see that the graph is above when y=2. This means that (2,2) is a point that satisfies f(x).
given the angle ABC equals 114. What is the angle BAD
Answer:
A. 63°
Step-by-step explanation:
You want to know the base angle in the isosceles triangle in the given figure.
Angle sumAngle ABC is the sum of its parts:
∠ABC = ∠ABD +∠DBC
The figure shows ∆DBC is equilateral, so ∠DBC = 60°. This lets us solve for the measure of angle ABD:
114° = ∠ABD +60°
54° = ∠ABD
Base angle∆ABD is isosceles, so the two base angles are congruent. The sum of angles in the triangle is 180°, so we have ...
∠ABD +∠BAD +∠BDA = 180°
54° +2(∠BAD) = 180° . . . . . . . ∠BAD =∠BDA
∠BAD = 90° -27° . . . . . . divide by 2, subtract 27°
∠BAD = 63°
Is 24/36 equal to 4/5?
Four times a number is at least 10
Answer:
4x>= 10
Step-by-step explanation:
i believe thats the answer
Select the graph that would represent the best presentation of the solution set. \(4x-2 < 10\)
Answer:
A bar graph with x-axis labeled from 0 to 10, and y-axis labeled from 0 to 4, with 4x-2 marked with a solid line.
Use the distributive property to write an equivalent expression. Then
evaluate the expression.
(10-7)5
Equivalent Expression
=
Answer:
Equivalent expression:
= 15
Step-by-step explanation:
Distributive proprty:
(10-7)5 = 10*5 + 10*-7
= 50 - 35
= 15
Evaluate:
(10-7)5 = 3*5
= 15
The triangle shown below has an area of 5 units 2 squared.
Find the missing length: x
The missing length x is equal to the square root of 10 units.
What is triangle?A triangle is a three sided polygon with 3 angles and three sides it is one of the most basic and fundamental safe in geometry and is used in many different areas of methane science triangle are also after use in architecture art in other areas of the design triangle come in many different form such as equatorial isosceles and scalene and can be classified by their angles side or both.
The formula for finding the area of a triangle is A = 1/2(base × height). In this case, the base and height are both x, so A = 1/2(x2). Plugging in the given area of 5, we have 1/2(x2) = 5 and solve for x to get x = √(10). So the missing length x is equal to the square root of 10 units.
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Tiana tried to evaluate an expression. Here is her work
Note that Tiana's work is wrong. Tiana made a mistake going from Step 2 to Step 3. Tiana should have subtracted 2 from 21 before adding. The order of operations says to add and subtract from left to right. The rule in operation here is known as PEMDAS. Note that when corrected and evaluated, the expression results in 27. (Option B)
What is PEMDAS?
The order of operations is a rule that specifies the right sequence of actions to be taken while evaluating a mathematical equation. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Using the order of operations (PEMDAS), the expression 21 - 2 + 60 ÷ 15*2 would be evaluated as follows:
Parentheses - None
Exponents - None
Multiplication and Division (from left to right) - 60 + 15 = 4
Addition and Subtraction (from left to right) - 21 - 2 + 4*2 = 19 + 8 = 27
So the correct result is 27.
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Full Question:
See attached Image.
August is selling tickets for his school play.
-Adults pay $7 a ticket while students pay $5 a ticket.
-August sells 35 tickets and collects $160.
How many of each type of tickets did he sell?
A. 40 students and 32 adults
B. 20 students and 15 adults
C. 4 students and 5 adults
D. 15 students and 20 adults
The number of each type of tickets which August sold is equal to: B. 20 students and 15 adults.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of student tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable a represent the number of adult tickets sold.Let the variable s represent the number of students tickets sold.Since Adults pay $7 a ticket while students pay $5 a ticket for a total cost of $205, an algebraic equation to model is given by;
7a + 5s = 205
For the sales of 35 tickets, we have:
a + s = 35
Solving for a, we have the following:
7a + 5(35 - a) = 205
7a + 175 - 5a = 205
2a = 205 - 175
2a = 30
a = 30/2
a = 15 adult tickets.
For the number of student tickets, we have:
s = 35 - a
s = 35 - 15
s = 20 student tickets.
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Complete Question:
August is selling tickets for his school play.
-Adults pay $7 a ticket while students pay $5 a ticket.
-August sells 35 tickets and collects $205.
How many of each type of tickets did he sell?
A. 40 students and 32 adults
B. 20 students and 15 adults
C. 4 students and 5 adults
D. 15 students and 20 adults
What should I do please help
3⁵ means, multiply 5 factors of 3.
shelby is attending a school orchestra concert. She sees her math teacher seated 45 feet ahead of her and her sciene teacher seated 28 feet to her right. How far apart are the two teachers?
If shelby is attending a school orchestra concert. The two teacher are far apart by 35ft.
How to find the length?Using Pythagoreans theorem formula to find the length
c² = √ a² -b²
Where:
c = Length of the hypotenuse
a = 45
b= 28
Let plug in the formula
c² = √45² - 28²
c² = √2025 -784
c² = √1241
c = 35ft
Therefore we can conclude that the two teacher are far apart by 35ft.
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The stadium capacity allows for players, radio and newspaper reporters, and stadium workers in addition to spectators. How many of these people could be at a game?
No. of players and reporters in stadium = 275
No. of spectators and stadium workers in stadium = 42225
What is seating arrangement?Seating Arrangement is a process of making a group of people sit as per a prefixed manner.
Given,
Stadium capacity = 42500
General capacity seating = 31750
Reserved Seating = 10475
Total spectator seating = 31750 + 10475
= 42225
No. of players, radio and newspaper reporters = 42500 - 42225
= 275
There could be 275 players, news and radio reporters and 42225 spectators in addition to stadium workers, at the game.
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Given:
What’s the statement and reasons
The statement and reasons are
1. AB ≅ BC, AE ≅ FC 1. Given2. AC ≅ AC 2. Reflexive property of congruence3. <BAC ≅ <BCA 3. Base angles of isosceles ∆BAC4. ∆AEC ≅ ∆AFC. 4. SAS5. <AEC ≅ <AFC. 5. CPCTCHow to determine the proof of the trianglesThe complete question is added as an attachment
With the given information and the image attached below, we can state that the two triangles are congruent by SAS,
Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.
Part of the proof is as follows:
Statement Reason
1. AB ≅ BC, AE ≅ FC 1. Given
2. AC ≅ AC 2. Reflexive property of congruence
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the supplement of an angle is 113 degrees what is the measure of the angle ?
A protractor is used to measure angles in degrees (°). With the aid of a protractor, one may measure and calculate angles in terms of degrees.
What is the measure of angle?Through the use of a protractor, angles are measured in degrees (°). In order to calculate or draw angles in terms of degrees, a protractor is a measuring tool that is utilised. Using a protractor, for instance, we can observe that the black arrow in the image below crosses the 90° line at 100°. Thus, the angle has a 100° measurement.
Generally speaking, supplementary angles are those where the total of two angles is greater than 180 degrees. A supplement to another angle is stated to exist for each of the angles. By deducting an angle's complement from 180 degrees, we can calculate its value.
A 113 degree angle's complement is a 67 degree angle.
Therefore, the answer is 67 degree.
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Which of these is the result of form having the illusion of the third dimension?
Depth is the result of form having the illusion of the third dimension.
Even while the human brain perceives many flat pictures, such as those in movies and photographs, as being two dimensional, nothing actually exists without all three dimensions (2D). This is due to the fact that everything physically existing is made of atoms, which are imperceptible to the human sight yet include all three spatial dimensions. Human eyes have the capacity to perceive "depth" or three dimensions. The three spatial dimensions of the world may be perceived by someone who possesses depth perception. Each human eye's visual brain first interprets the three spatial dimensions as 2D pictures. Contrarily, stereoscopic vision, which is unique to humans, alters the image seen by the two eyes.
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Which equation has the same solution as: 7-8(x-3) = x -14
Answer: x = 5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
7 − 8(x − 3) = x − 14
7 + (−8)(x) + (−8)(−3) = x + − 14 (Distribute)
7+ (−8x) + 24 = x + (−14)
(−8x) + (7+24) = x − 14 (Combine Like Terms)
−8x + 31 = x − 14
−8x + 31 = x − 14
Step 2: Subtract x from both sides.
−8x + 31 − x = x − 14 − x
−9x + 31 = −14
Step 3: Subtract 31 from both sides.
−9x + 31 − 31 = −14 − 31
−9x = −45
Step 4: Divide both sides by -9.
−9x/−9 = −45/−9
x = 5
The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.
The bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20. The solution has been obtained using the unitary method.
What is a unitary method?
The value of a single unit is calculated in the unitary approach before the value of the necessary number of units is determined. In order to obtain value of a single unit from a given multiple, the unitary technique is used, to put it simply.
We know that Cost per brick = number of bricks / price of bricks
Therefore, using this, we get
1500/$1110 = $1.35
1300 / $845 = $1.54
230 / $170.20 = $1.35
100 / $75 = $1.33
35 / $25.90 = $1.35
Hence, the bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20.
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Question: The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.
1500 bricks for $1,110.00
1300 bricks for $845.00
230 bricks for $170.20
100 bricks for $75.00
35 bricks for $25.90
What’s the answer please
Answer:
m is equal to [tex]34\sqrt{2}[/tex]
Step-by-step explanation:
We can use the cosine function to evaluate m.
Note that [tex]m[/tex] is the hypotenuse in this triangle.
[tex]cos(x)=\frac{A}{H}[/tex]
[tex]A[/tex] is the adjacent side
[tex]H[/tex] is the hypotenuse
Lets look at the 60 degree angle.
The side adjacent to it is [tex]17\sqrt{2}[/tex].
Therefore we can say that
[tex]cos(60)=\frac{17\sqrt{2} }{H}[/tex]
Lets solve for [tex]H[/tex].
[tex]cos(60)[/tex] is equal to [tex]\frac{1}{2}[/tex].
[tex]\frac{1}{2} =\frac{17\sqrt{2} }{H}[/tex]
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
[tex]1*H=17\sqrt{2}*2\\H=17\sqrt{2}*2\\H=34\sqrt{2}[/tex]