Since we know the sequence is quadratic, we expect the [tex]n[/tex]-th term to have the general form
[tex]x_n = an^2 + bn + c[/tex]
Plug in the first 3 known values of the sequence to form a system of equations.
[tex]x_1 = 3 = a + b + c[/tex]
[tex]x_2 = 12 = 4a + 2b + c[/tex]
[tex]x_3 = 25 = 9a + 3b + c[/tex]
Eliminating [tex]c[/tex] gives
[tex](4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9[/tex]
[tex](9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11[/tex]
Eliminating [tex]b[/tex] gives
[tex](4a + b) - (3a + b) = 11 - 9 \implies a = 2[/tex]
Solving for [tex]b,c[/tex], we get
[tex]4a + b = 11 \implies b = 11-4\cdot2 = 3[/tex]
[tex]a+b+c=3 \implies c=3-2-3 = -2[/tex]
So, the [tex]n[/tex]-th term of the sequence is
[tex]x_n = \boxed{2n^2 + 3n - 2}[/tex]
Kevin is filing his return under the single status. His taxable income is $125,500 per year. What tax bracket would he be in?
Since Kevin is filing his tax return under the single status, he would be in the tax bracket of $86,376 to $164,925 with a marginal tax rate of 24%.
What is a tax bracket?Under the progressive tax system, a tax bracket is a range of taxable incomes that is subject to a marginal tax rate.
Tax brackets provide a systematic way of progressively taxing taxpayers' income.
Data and Calculations:Taxable income = $125,500
Since he falls under the tax bracket of $86,376 to $164,925, Kevin's tax rate is 24%.
Thus, as a single taxpayer, Kevin falls under the tax bracket of $86,376 to $164,925 with a marginal tax rate of 24% of taxable income.
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Question Completion:Personal Income Tax Brackets for Single Filers:
Tax rate Taxable income bracket Tax owed
10% $0 to $9,950 10% of taxable income
12% $9,951 to $40,525 $995 plus 12% of the amount over $9,950
22% $40,526 to $86,375 $4,664 plus 22% of the amount over $40,525
24% $86,376 to $164,925 $14,751 plus 24% of the amount over $86,375
Please help. Which spinner will give maria the best probability of winning a prize
Explain why.
find the value of a x 7 when a=6
Answer:
=> 42 ..
Step-by-step explanation:
Given : a = 6
=> a × 7
=> 6 × 7
=> 42
Show Work Please Thank You
The angles in degrees to radian is as follows:
-54 degrees = -3π / 10 radian
How to convert from degree to radian?The measurement is in degrees. Let's convert it to radian with respect to π.
Therefore,
180 degrees = π radian
-54 degrees = ?
cross multiply
Hence,
angle in radian = -54 × π / 180
angle in radian = - 54π / 180
angle in radian = - 6π / 20
angle in radian = -3π / 10 radian
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What is the first step to solve the equation A. Square both sides of the equation. B. Add 5 to both sides of the equation. Square. 5, and -3. C. D. None, because there is no solution. 2x-5--3?
Hi :)
I'd start by adding 5 to both sides of the equation. That would make the equation easier.
[tex]\boldsymbol{\sqrt{2x}-5=3}}[/tex]
[tex]\boldsymbol{\sqrt{2x}=2}[/tex]
The next step is to get rid of the radical sign.
Which operation will undo the square root? Squaring.
So that's why we square both sides:
[tex]\boldsymbol{2x=4}[/tex]
And Now we just divide both sides by 2
[tex]\boldsymbol{x=2}[/tex]
~[tex]\textit{\textbf{Learn More; Work Harder}}[/tex]~
:)
A closed box with a square base is to have a volume of 16000 cubic centimeters. The material
for the top and bottom of the box costs $3 per square centimeter while the material for the sides
costs $1.50 per square centimeter. Find the dimensions of the box that will minimize the total
cost of materials. What is the minimum total cost?
The most suitable measurements for a box with a square base are 5cm (width) x 5cm (length) x 640cm (height). This box would be worth $4875
How to calculate the minimum value of the box?To find the minimum value of a box that must have a square base and 16000 cm³, we must try different measurements to find the variable that represents the least value.
In this case, the variable that represents less value is a base of 5cm x 5cm and a height of 640cm. This means that the box would be worth $4875 as shown below.
Base
5cm × 5cm = 25cm²25cm² x 3 = $75Sides
5cm × 640cm = 3200cm²3200cm² × $1.50 = $4800$4,800 + $75 = $4,875Additionally, we can check that the volume of the box is the required 16000cm³, as shown below:
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Classify the figure. Identify its vertices, edges and bases.
Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.
1. x = 0.3y
2. y = 0.3x
3. y = 3x
4. y = 0.25x
The direct variation function is y = 0.3x
How to determine the direct variation function?The direct variation from y to x is represented as:
y = kx
When y = 1.5 and x = 5, we have
1.5 = 5k
Divide by 5
k = 0.3
Substitute k = 0.3 in y = kx
y = 0.3x
Hence, the direct variation function is y = 0.3x
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Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1057 adults, 89% said that they have a cell phone. Find the value of the test statistic. The value of the test statistic is nothing. (Round to two decimal places as needed.)
Answer:
suma todos los decimales
Step-by-step explanation:
empieza sumando 1059-94%eso te da 993,58 luego le sumas 89% lo que te da 884,2862 espero haberte ayudado
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so
the equation to solve is 2a + b = 15.7.
ayer/
If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side,
which lengths make sense for possible values of b? Select two options.
The value of the base b in the isosceles triangle is 3.1 inches.
According to the statement
we have given that the
equation is 2a + b = 15.7 and if one longer sides is 6.3 centimeter.
And we have to find the length of the base. Then
2a + b = 15.7
Here a is 6.3 cm then
Substitute the values in it then
2a + b = 15.7
2(6.3) + b = 15.7
After solving the equation
12.6 + b = 15.7
b = 15.7 - 12.6
Now we get the value of base b which is 3.1.
So, b = 3.1
So, The value of the base b in the isosceles triangle is 3.1 inches.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
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The question is attached
Answer:
We call the denominator rational.
Step-by-step explanation:
For example:
[tex]\frac{1}{\sqrt{2}} = \frac{\sqrt2}{\sqrt2 \cdot \sqrt2} = \frac{\sqrt2}{2}[/tex]
It's clear that the denominator is now a rational number, not an irrational one anymore.
(GIVING BRAINLYST) 1(Multiple Choice Worth 2 points) (15.01 LC) Which number sequence follows the rule subtract 15 starting from 105? O 15, 30, 45, 60, 75 O 15, 10, 25, 20, 35 O 105, 100, 95, 90, 85 O 105, 90, 75, 60, 45
D
Step-by-step explanation:
The correct answer is option D, which is 105, 90, 75, 60, 45.
Static and Reasoning:
Isabella is studying the fairness of a six-sided numbered cube with numbers 1, 2, 3, 4, 5, and 6. The numbered cube is rolled 36 times, and the numbers on the top side are recorded in the table below.
Based on the data, what conclusion would you make about the fairness of the numbered cube? Justify your answer.
Based on the data recorded by Isabella, it can be concluded the cube is rather fair.
How many times did Isabella get each number?Based on the data, here are the results:
Getting a 1: 6 timesGetting a 2: 5 timesGetting a 3: 7 timesGetting a 4: 5 timesGetting a 5: 6 timesGetting a 6: 7 timesThis implies, in total Isabella got the same number between five and seven times. For example, the number 2 was obtained 5 times, but the number 3 was obtained 7 times.
What can be concluded based on the results?Even though Isabella did not get the same number of times each number, the dice is rather fair because by rolling the dice thirty six times you will obtain the same number at least five times.
Moreover, there is not a big difference in the number of times you obtain each number.
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PLEASE HELP ME SOLVE THIS
2. Us i ng the filled table above,
a) calculate just one PED.
b) Is the demand elastic or inelastic?
c) Based on your answer to c) what price change would you recommend to increase TR?
The price elasticity of demand of the pen will be -0.2.
How to compute the elasticity?The demand and supply schedule will be:
Price Qd. Qs
$10. 250. 100
$20. 200. 90
$30. 180. 80
The price elasticity of demand from $1 to $2 will be:
= Percentage change in quantity demanded/percentage change in price
Percentage change in quantity demanded will be:
= (200 - 250)/250 × 100
= -20%
Percentage change in price will be:
= (20 - 10)/10 × 100
= 100%
Therefore, the elasticity of demand will be:
= -20/100
= - 0.2
The value gotten illustrates an inelastic demand.
In order to increase the total revenue, the price can be reduced as it will lead to more sales.
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Complete question:
Choose any product or service. Create the demand and supply schedule.
Calculate just one PED.
Is the demand elastic or inelastic?
What price change would you recommend to increase TR?
Identify an acute angle and give its measure.
Angle HEJ measures 15 degrees.
just need these 3 please and thanks in advance
The conclusion that can be made based on the hypothesis is:
1. It's a valid conclusion.
2. It is a valid conclusion.
3. It is a valid conclusion.
How to illustrate the information?According to the law of detachment, when the conditional and the hypothesis are true, the conclusion will be true.
Therefore, if 6x < 42, the value of x will also be less than 6. This is valid.
When an angle is more than 90°, it's an obtuse angle and since A is 103°, it's valid.
Also, the statement about the violin being a string instrument is logically valid.
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the perimeter of a rectangle if 24 inches. the rectangle is enlarged so that each side is twice as long as the original. what effect does this enlargement have on the perimeter?
The perimeter becomes double when each side is twice as long as the original.
According to the statement
we have given that the perimeter of a rectangle is 24 inches. and we have to find that the what effect does this enlargement have on the perimeter.
So, For this purpose, we know that the
A rectangle is a parallelogram all of whose angles are right angles especially : one with adjacent sides of unequal length.
The formula to find the perimeter of rectangle is 2(L + B)
And we the length is goes to increased by double then the perimeter will also goes to double.
Because perimeter is directly proportional to the length and breadth of rectangle.
So, The perimeter becomes double when each side is twice as long as the original.
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Please help! Need em doneee
The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 63% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 59%. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level
Using the z-distribution, it is found that since the p-value is less than 0.02, we reject the null hypothesis.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is of at most 59%, that is:
[tex]H_0: p \leq 0.59[/tex]
At the alternative hypothesis, it is tested if the proportion is greater than 59%, hence:
[tex]H_1: p > 0.59[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.59, n = 900, \overline{p} = 0.63[/tex]
Hence the value of the test statistic is found as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.63 - 0.59}{\sqrt{\frac{0.59(0.41)}{900}}}[/tex]
z = 2.44.
What is the p-value and the conclusion?Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is higher than a value, with z = 2.44, the p-value is of 0.0073.
Since the p-value is less than 0.02, we reject the null hypothesis.
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Find mEHFˆ. PLEASE HELP ASAP
Answer:
30°
Step-by-step explanation:
[tex]\frac{195-(8x+17)}{2}=5x-10 \\ \\ 178-8x=10x-20 \\ \\ 198=18x \\ \\ x=11[/tex]
So, this means arc FH measures 105 degrees.
Since the circumference of a circle measures 360 degrees, arc EF measures 60 degrees.
By the inscribed angle theorem, angle EHF measures 30°.
Solve the following equation for W.
P=2L+2W
**Disclaimer** Hi there! I assumed the question is to represent W in terms of all other variables (P, L). The following answer corresponds to this understanding. If it is incorrect, please let me know and I will modify my answer.
Answer: W = (P/2) - L
Step-by-step explanation:
Given equation
P = 2L + 2W
Factorize 2 out
P = 2 (L + W)
Divide 2 on both sides
P / 2 = 2 (L + W) / 2
P / 2 = L + W
Subtract L on both sides
(P / 2) - L = L + W - L
[tex]\Large\boxed{W=\frac{P}{2} -L}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\displaystyle{W = \dfrac{P}{2} - L}[/tex]
Step-by-step explanation:
To solve for W, we have to isolate the W-variable. First, we can factor the expression 2L + 2W to 2(L+W):
[tex]\displaystyle{P = 2(L+W)}[/tex]
Next, we'll be dividing both sides by 2:
[tex]\displaystyle{\dfrac{P}{2} = \dfrac{2(L+W)}{2}}\\\\\displaystyle{\dfrac{P}{2} = L+W}[/tex]
Then subtract both sides by L:
[tex]\displaystyle{\dfrac{P}{2} - L= L+W-L}\\\\\displaystyle{\dfrac{P}{2} - L= W}[/tex]
Therefore, we'll obtain W = P/2 - L.
Note that the given formula is perimeter formula of a rectangle where Perimeter = 2 * Length + 2 * Width.
So if we solve for W (Width) then we'll get Width = Perimeter / 2 - Length which can be useful to find width with given perimeter and length.
PLEASE HELP ME .IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer: [tex]\frac{10\pi}{3}[/tex] m
Step-by-step explanation:
[tex](2)(\pi)(4) \left(\frac{150}{360} \right)=\frac{10\pi}{3}[/tex]
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Sin A= Answer
Check the picture below.
Let x, y, z be three natural numbers such that x < y < z. If GCF(x, y, z) = 3, GCF (y, z) = 15, LCM (x, y, z) = 3150, and x is even number greater than 10, then find the values of x, y and z.
Answer:
one of several possible solutions :
18, 75, 105
Step-by-step explanation:
prime factors of 3150 :
3150 ÷ 2 = 1575
1575 ÷ 2 no
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 3 no
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 5 no
7 ÷ 7 = 1
3150 = 2¹ × 3² × 5² × 7¹
these are the product of the longest streaks of prime factors in x, y and z.
the GCF(y, z) = 15.
the prime factors of 15 are simply 3¹×5¹.
so, y and z share only the factors 3 and 5.
the GCF(x, y, z) = 3.
since x is an even number, the elimination of 5 in the GCF is not surprising.
let's try the following :
x = 2¹ × 3² = 2×9 = 18
y = 3¹ × 5² = 3×25 = 75
z = 3¹ × 5¹ × 7¹ = 3×5×7 = 105
that uses all the factors of 3150, and their LCM is as the product of the longest streaks of their prime factors is
2¹ × 3² × 5² × 7¹.
fits.
the GCF(75, 105) is the product of the prime factors they have in common : 3¹ × 5¹ = 15.
fits.
the GCF(18, 75, 105) is the product of the prime factors ask 3 numbers have in common, which is only 3¹ = 3.
fits.
18 < 75 < 105
fits.
18 is an even number greater than 10.
fits.
there are more than 1 solutions.
e.g.
z = 2¹ × 3¹ × 5¹ × 7¹ = 210
is also possible.
If f(x) = 5x, what is ƒ˜¹ (x)?
[tex]y = 5x \\ switch \: y \: and \: x \\ x = 5y \\ solve \: for \:y \\ y = \frac{x}{5} [/tex]
Which table of values represents a function?
x y
-3 10
4 4
-5 -3
4 4
x y
2 8
6 9
6 3
5 7
x y
1 2
1 4
1 6
1 8
x y
5 2
-3 2
2 2
1 7
The table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
How to determine the table of values represents a function?The table of values is given as:
Table 1
x y
-3 10
4 4
-5 -3
4 4
Table 2
x y
2 8
6 9
6 3
5 7
Table 3
x y
1 2
1 4
1 6
1 8
Table 4
x y
5 2
-3 2
2 2
1 7
For a table to represent a function, each of the x value on the table must correspond to exactly one y value
i.e.
x1 = y1
x2 = y2
And so on
Using the above highlights, the table that represents a function is table 1
Hence, the table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
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Scenario 2 You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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Which value of w makes 14 = 11 + w/8 x 6 a true statemen?
choose 1 answer:
w = 1
w = 4
w = 16
w = 24
answer
is true statement w= 4
Find the measures of angles a and b when 0=44
Determine which quadrilaterals have the properties given in the table.
kite
square trapezoid rectangle
Opposite sides are congruent.
Diagonals are perpendicular.
Exactly one pair of opposite angles are
congruent.
rhombus
parallelogram
Diagonals are congruent.
Diagonals bisect opposite interior angles.
Consecutive interior angles are
supplementary.
The two quadrilateral with the listed properties are kite and rhombus respectively.
Properties of a kiteIt has two diagonals intersecting at right anglesA kite is symmetrical about its main diagonalAngles opposite to the main diagonal are equalThe kite can be viewed as a pair of congruent triangles with a common baseIts diagonals are perpendicularProperties of a rhombusAll sides of the rhombus are equalThe opposite sides are parallelOpposite angles are equalDiagonals bisect each other at right anglesDiagonals bisect the anglesThe sum of two adjacent angles is equal to 180 degrees, that is, are supplementaryThus, the two quadrilateral with the listed properties are kite and rhombus respectively.
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Answer:
your welcome
Step-by-step explanation: