An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The nth term of the arithmetic series can be defined as hₙ = 4n - 2.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
The nth term of an arithmetic sequence is given by the formula,
aₙ = a₁ + (n-1)d
Since the first term of the arithmetic sequence is 2, while the difference is 4. Therefore, the definition for the nth term of arithmetic sequence,h can be written as,
hₙ = 2 + (n-1)4
hₙ = 2 + 4n -4
hₙ = 4n - 2
Hence, the nth term of the arithmetic series can be defined as hₙ = 4n - 2.
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What is the first incorrect step?
A Angelina did not make a mistake. Her work is correct
B Angelina first made a mistake in Step 3. The formula she should have used is an = 0n-1 + d.
Angelina first made a mistake in Step 4. When she distributed the - 7 to the -1, she should have gotten +7
D Angelina first made a mistake in Step 6. In order to find the 41st term, she should have plugged 40 into her equation.
Mac has 40 ounces of juice. He pours 6 ounces in each glass. How many glasses can he fill?
Answer:
6
Step-by-step explanation:
Which function can be used to model the graphed geometric sequence? f(x 1) = five-sixthsf(x) f(x 1) = six-fifthsf(x) f(x 1) = five-sixths superscript f (x) f(x 1) = six-fifths superscript f (x)
The function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x
Exponential functionsThe standard exponential function is expressed as y = ab^x
Using the coordinates (3, 900) and (4, 750)
Create the equations
900 = ab^3 ............. 1
750 = ab^4 ................. 2
Divide
900/750 = 1/b
b = 75/90
b = 5/6
Determine the value of "a"
900 = a(5/6)^3
900 = (125/216)a
a = 1555.2
Determine the required equation
y = 1555.2(5/6)^x
Hence the function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x
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Answer:
a
Step-by-step explanation:
What is the solution to the system of equations below? y = negative four-fifths x 6 and y = –30 (45, –30) (–30, 30) (–30, 45) (30, –30)
The solution to the system of equations is (45, –30)
How to determine the solution to the system of equations?The equations are given as:
y =-4/5x + 6
y = –30
Substitute y = –30 in y =-4/5x + 6
-30 =-4/5x + 6
Subtract 6 from both sides
-36 = -4/5x
Divide both sides by -4
9 = 1/5x
Multiply both sides by 5
x = 45
So, we have:
(x,y) = (45, –30)
Hence, the solution to the system of equations is (45, –30)
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Answer:
(45, –30)
Step-by-step explanation:
A linear regression is done on data the line of best fit is y= 1.25x-6.25. What is the residual for the point (1,1)?
Answer:
6
Step-by-step explanation:
Find the predicted y value when x=1:
[tex]\hat{y}=1.25x-6.25\\\hat{y}=1.25(1)-6.25\\\hat{y}=1.25-6.25\\\hat{y}=-5[/tex]
Find the residual:
[tex]\text{Residual}=\text{Actual Value}-\text{Predicted Value}\\\text{Residual}=y-\hat{y}\\\text{Residual}=1-(-5)\\\text{Residual}=1+5\\\text{Residual}=6[/tex]
Because our residual is positive, this is an indicator that our predicted y value is too low.
Find the value of y when x=-2
y=5x+6
y=
Answer:
Soln;
From the given question, We know that:
x= -2
So,
y= 5x+6
= 5*(-2)+6
= -4 Ans
Therefore, The value of y is -4.Select the correct answer from the drop-down menu. a machine needs two of its gears replaced. you find two gears, one manufactured 5 years ago and the other manufactured 10 years ago. the specification sheet says that the chance of gear failure is 5% after 5 years and increases to 8% after 10 years. if the gears on the machine are not linked to each other, the probability that both replacement gears will fail is %.
Based on the probability that each gear will fail and the fact that the gears are not linked, the probability that both will fail is 0.4%.
What is the probability that both gears will fail?Because the gears are not linked together, the probability that both will fail can be found as:
= Probability that gear fails after 5 years x Probability that gear fails after 10 years
Solving gives:
= 5% x 8%
= 0.4%
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In ⊙P, QR≅ST. Which statement must be true? Select all that apply.
A circle with center point P and four points Q,R,S,T on the circumference. Line segments join the points to make three chords QR,RS and ST. All the four points are connected to center point P making three triangles QPR,RPS and SPT.
A. △QRP ≅ △STP
B. QR¯¯¯¯¯¯¯¯ ≅ RS¯¯¯¯¯¯¯
C. ∠QPS ≅ ∠RPT
D. △RPS ≅ △SPT
E. QR¯¯¯¯¯¯¯¯ ≅ ST¯¯¯¯¯¯¯Which is the length of PQ expressed in terms of π?
A circle with center point N and radius 1. It has a minor arc PQ whose angle measures 99 degree
A. 1140π
B. 2940π
C. 1120π
D. 2920π
The true statement about the circle with center P is that triangles QRP and STP are congruent, and the length of the minor arc is 11/20π
The circle with center PGiven that the circle has a center P
It means that lengths PQ, PR, PS and PT
From the question, we understand that QR = ST.
This implies that triangles QRP and STP are congruent.
i.e. △QRP ≅ △STP is true
The length of the minor arcThe given parameters are:
Angle, Ф = 99
Radius, r = 1
The length of the arc is:
L = Ф/360 * 2πr
So, we have:
L = 99/360 * 2π * 1
Evaluate
L = 198/360π
Divide
L = 11/20π
Hence, the length of the minor arc is 11/20π
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What is the valuAt which integer value of x are the functions y = 1 2 x + 12 and y = ( 1 4 ) x closest to being equal? A. –2 B. 12 C. 11 D. –1e of x in this triangle? 18493 A. 30 B. 45 C. 90 D. 60
The closest integer value of x where both functions are equal is 1
How to determine the integer value of x?The equations are given as:
y = 12x + 12
y = (14)^x
Next, we plot the graph of both equations.
From the attached graph, both functions intersect at:
x = 1.249
Approximate this value
x = 1
Hence, the closest integer value of x where both functions are equal is 1
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Can you create a data set which contains median=6 and mode=4?
1, 4, 6, 9, 15, 4, 3, 12, 11
Answer:
hey!
Step-by-step explanation:
Select the correct answer. Determine which equation has the same solutions as the given equation. x2 − 10x − 11 = 0 A. (x − 10)2 = 21 B. (x − 10)2 = 36 C. (x − 5)2 = 21 D. (x − 5)2 = 36
Answer:
D. [tex](x - 5)^{2} = 36[/tex]
Step-by-step explanation:
given equation: [tex]x^{2} - 10x - 11 = 0[/tex]
Practice solving problems involving the area Assignment Which are true about the area of a circle? Check all that apply. The diameter is used in the formula. The units are always squared. The area can be found when given the diameter by first finding the radius. The area is the distance around the circle. Circumference can be used to find area.
Type the correct answer in each box. use numerals instead of words. consider the quadratic equation x2 10x 27 = 0. completing the square leads to the equivalent equation (x )2 = .
The equivalent equation using the completing the square method is (x+5)² = -2
Completing the square method.Quadratic equations are equation that has a degree of 2. Given the equations expressed as:
x^2+10x+27 = 0
Subtract 27 from both sides
x^2+10x = -27
Complete the squares
x^2+10x = -27
x^2+10x + 5^2= -27 + 25
(x+5)² = -2
Hence the equivalent equation using the completing the square method is (x+5)² = -2
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I really need help with this. This is for AP Calculus. I just need to find the derivative for this function.
Answer: 40x^4 + 56x^3 − 16x − 14
Step-by-step explanation:
1. For any two functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.
2. The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0.
3. Simplify
4. Multiply 4x^2 + 7x^1 times 6x^2
5. Multiply 2x^3 - 2 times 8x^1 + 7x^0
6. To multiply powers of the same base, add their exponents.
7. Simplify
8. Combine like terms
9. For any term t, t^1 = t
10. For any term t except 0, t^0 = 1
There are two squares. the perimeter of square x is half the perimeter of square y.
how do the areas of the two squares compare?
o a. the area of square x is one-sixteenth the area of square y.
o b. the area of square x is one-eighth the area of square y.
oc. the area of square x is one-fourth the area of square y.
d. the area of square x is one-half the area of square y.
The area of square x will be one-fourth of the area of square y. Then the correct option is C.
What is a square?It is a polygon with four sides. The total interior angle is 360 degrees. A square's opposite sides are parallel and all sides are equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
There are two squares.
The perimeter of square x is half the perimeter of square y.
Let the side of the square x be a and the side length of the square y be b. Then we have
Perimeter x = Perimeter y / 2
4a = 2b
2a = b
Then the area of the square x will be
Area of square x = (2a)²
Area of square x = 4a²
Then the area of the square y will be
Area of square x = (b)²
Area of square x = b²
Then the area of square x will be one-fourth of the area of square y.
Thus, the correct option is C.
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The relationship between the number of pounds (lb) of almonds and the price in dollars is shown in the graph. What is the unit price of almonds?
Answer:
B
Step-by-step explanation:
Slope is change of y over change of x
Y is going up by 8 and x is going over by 1
Therefore, $8/1 lb
The vertices of a feasible region are (14, 2), (0, 9), (6, 8), and (10, 3). what is the maximum value of the objective function p if p = 180x 250y? 2,940 3,020 3,080 3,250
The maximum value of the objective function p if p = 180x + 250y is 3020
How to determine the maximum value?The coordinates of the feasible region are given as;
(14, 2), (0, 9), (6, 8), and (10, 3)
The objective function is given as:
P = 180x + 250y
Substitute the coordinates of the feasible region in the above function
P = 180 * 14 + 250 * 2 =3020
P = 180 * 0 + 250 * 9 = 2250
P = 180 * 6 + 250 * 8 = 3080
P = 180 * 10 + 250 * 3 = 2550
The maximum value in the above computation is:
P = 180 * 14 + 250 * 2 =3020
Hence, the maximum value of the objective function p if p = 180x + 250y is 3020
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Linear Programming Quiz - Edge
Question 1: D
Question 2: D
Question 3: D
Question 4: B
Question 5: C
Question 6: C
Question 7: D
Question 8: A
Question 9: C
Question 10: C
It says I can't add anymore attachments but the rest are correct trust me
need help asap, much appreciated!!!!!!!!!!!
Step-by-step explanation:
there are 13 out of 52 diamond cards.
and there are 26 out of 52 black cards.
so, for the first card to be diamond the probability is
13/52 = 1/4 = 0.25
but now, he does not put the card back.
he pulls the second card out of 51 possible cards.
the desired cases are still 26.
so, the probability to pull a black card as the second card under the restriction that the first card was a diamond is
26/51 = 0.509803922...
the probability for that combined event is then
1/4 × 26/51 = 26/204 = 13/102 = 0.12745098...
so, c. is the right answer.
Solve the following quadratic equation for all values of x in simplest form.
4(6 — 5x)² + 11 = 20
Answer:
4-20(6x-5x)^2+11
(6-5x)^2=11+(-16)
6^2-10x+25=-5
6^2-10x+20
HELP ASAP PLS
a survey asked two age groups about the car color that they most preferred. the results are down in the table below. which car color eat most preferred by people ages 16-24 and what is the relative frequency within this age group?
A.) Blue, 71.4%
B.)Red, 60.6%
C.)Blue, 26.8%
D.)33.9%
Answer:
blue i think good luck
How many solutions are in 18+6x=20+6x
Answer:
the equation has no solutionStep-by-step explanation:
How many solutions are in 18+6x=20+6x
18+6x=20+6x
take away 6x from both side
18 = 20
the equation has no solution, 18 is not 20.
Jeff has a balance of $2,513.77 on his credit card. He would like to pay off his card over the course of a year and a half by making identical monthly payments. The APR on his card is 10.66%, compounded monthly. Assuming that Jeff makes no additional purchases with his card, how much will he have to pay every month to reach his goal? (Round all dollar values to the nearest cent.) a. $151.73 b. $162.57 c. $139.65 d. $147.64 Please select the best answer from the choices provided A B C D
Using the monthly payment formula, it is found that the amount he will have to pay is given as follows:
a. $151.73.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, the parameters are given as follows:
P = 2513.77, r = 0.1066, n = 1.5 x 12 = 18.
Hence:
r/12 = 0.1066/12 = 0.008883.
[tex]A = 2513.77\frac{0.008883(1 + 0.008883)^{18}}{(1 + 0.008883)^{18} - 1} = 151.73[/tex]
Hence option A is correct.
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Which equation is graphed here?
y−1=−13(x−1)
y−1=−13(x+1)
y+4=3(x−1)
y−4=−3(x+1)
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through (negative one, four) and (one, negative two).
Answer: Choice D
y-4 = -3(x+1)
========================================================
Explanation:
Let's first find the slope of the line through (-1,4) and (1,-2)
[tex](x_1,y_1) = (-1,4) \text{ and } (x_2,y_2) = (1,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 4}{1 - (-1)}\\\\m = \frac{-2 - 4}{1 + 1}\\\\m = \frac{-6}{2}\\\\m = -3\\\\[/tex]
The slope is -3, which tells us that the answer must be choice D.
Choices A,B, & C can be eliminated because choices A and B have a slope of -13, while choice C has a slope of 3.
Refer to the point-slope format [tex]y-y_1 = m(x - x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point the line goes through.
12250 depreciates by 6% per year how much is the tractor worth after six years
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &12250\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=12250(1 - 0.06)^{6}\implies A=12250(0.94)^6\implies A\approx 8450.90[/tex]
three times a number increased by 2 is greater than zero or less than or equal to negative three
Step-by-step explanation:
Let the number be X
3×X=3X
Increased by 2
3X+2>0≤-3
carolyn and emily are searching online for tickets to a concert. two weeks ago, the cost was $20. now the cost is $29. carolyn said the percent increase is 45% and emily said the percent of increase is about 31%. who is correct?
Answer:
Carolyn
Step-by-step explanation:
Carolyn:
45% = 0.45
We multiply the orignal price with 0.45 to see how much it increased.
[tex]20(0.45) = 9[/tex]
We then add it to the original price
[tex]20+9 =29[/tex]
Emily:
31% = 0.31
We multiply the orignal price with 0.31 to see how much it increased.
[tex]20(0.31) = 6.2[/tex]
We then add it to the original price
[tex]20+6.2=26.2[/tex]
That means that Carolyn is correct.
(3x-5y)+(x+2y)? Someone help me. Will give brainliest
Answer: 4x - 3y (choice B)
===========================================================
Explanation:
The letter x is a variable, and a placeholder for a number. Which number? We don't know. It's basically a box where a number goes inside.
x represents having 1 box
2x is two boxes, and so on
If we add 3x and 1x, then we'll have four boxes and 3x+1x = 4x
We can only add the x terms together, which we consider to be called "like terms".
The y terms -5y and 2y are the other pair of like terms, which combine to -3y
If you want, you can draw a vertical number line. Start at -5 which is five units below zero. Then move up two spaces to arrive at -3. This is a visual way to demonstrate that -5+2 = -3, and by extension, -5y+2y = -3y
Find a number “a so that the numbers 42, 46, a, a, a have a mean and mode both equal.
Answer:
44
Step-by-step explanation:
The mode will be a as it is the most in frequency.
Calculating 'a' by taking the mean
42 + 46 + a + a + a / 5 = a88 + 3a = 5a2a = 88a = 44please give answer asap i’ll give brainlist to correct answer
Answer:
I believe the answer is; The median is 4.5 inches.
let me know if this is right for you! :)
Step-by-step explanation:
Graph the line 2x – 3y = 12.
Answer:
-6, -4
Step-by-step explanation:
I got it right