Write the sequences equation for the table . Your equation should be in the form a(n)=man+b
Answers
Answer:
a(n) = 3.25n + 1.25Step-by-step explanation:
7.75-4,5 = 3.25
11-7.75 = 3.25
14.25-11 =3.25
17.5-14,25 = 3.25
It’s clear that this is an arithmetic sequence with common difference of 3.25
The equation form of such sequence is a(n) = a×n + b ,where ‘a’ is the common difference.
Then
a = 3.25
The first term a₁ = 4.5
On the other hand, a₁ = 3.25 ×(1) + b
Then
4.5 = 3.25 ×(1) + b
Then
b = 4.5 - 3.25 = 1.25
Conclusion:
a(n) = 3.25n + 1.25
Related Questions
What is the measure of YVZ in degrees
Answers
Answer:
the answer is 56
Step-by-step explanation:
2x+3x+5=90
5x=90-5
5x=85
x=85/5
x=17
YVZ= 3(17)+5
YVZ=51+5
YVZ=56
Enter the value of x that makes the equation −11(x + 4) + 10x = 27 true
Answers
Answer:
x = - 71
Step-by-step explanation:
-11x -44 + 10 x =27
-x = 71
x = - 71
Answer:
-71
Step-by-step explanation:
You can first distribute the numbers in the parenthesis.
-11x-44 (-11*x-11*4)
-11x-44+10x=27
You can now combine like terms.
-11x+10x=-1x
-1x-44=27
This is now a two-step equation problem.
-1x-44=27
+44=+44
-1x=71
[tex]\frac{-1x}{-1}[/tex] =[tex]\frac{71}{-1}[/tex]
x=-71
Follow the steps to simplify this expression.
2x(2 + 1) – 3(x + 3)
1. Distribute 2x and –3 through the parentheses:
2. Find each product:
3. Combine like terms.
2x(2) + 2x(1) −3(x) − 3(3)
4x + 2x − 3x − 9
What is the simplified expression?
Answers
Answer:
3x - 9
Step-by-step explanation:
We already have the expression 4x + 2x − 3x − 9. Now, we just have to add like-terms. This will give us 3x - 9.
Step-by-step explanation:
2x(2)+2x(1)-3(x)-3(3)
4x+2x- 3x-9
since they are of same like terms we add them
=3x - 9
In a class test of 15 questions, (+4) marks are given for every correct answer, (– 2) marks are
given for every incorrect answer and 0 marks are given for questions that are not attempted. Punit
scored (– 2) marks. If he answered 3 questions correctly, how many did he get wrong? How many
questions did he not attempt?
Answers
If he answered 3 questions correctly, then the number of questions is got wrong is 7 and the number of questions that he did not attempt is 5.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
In a class test of 15 questions, (+4) marks are given for every correct answer, (– 2) marks are given for every incorrect answer, and 0 marks are given for questions that are not attempted. Punit scored (– 2) marks.
If he answered 3 questions correctly, then the number of the question are got wrong and the number of the question that he did not attempt.
Let x be the correct question and y be the incorrect question, z be the number of questions that he did not attempt, and A be the number of the total score. Then we have
4x – 2z = A
x + y + z = 15
If A = -2 and x = 3, then we have
4 × 3 – 2z = -2
12 + 2 = 2z
z = 7
Then the value of y will be
3 + y + 7 = 15
y = 5
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A survey asks teachers and students whether they would like the new school mascot to be a Viking or a Patriot. This table shows the results. Vikings Patriots Total Students 80 20 100 23 Teachers 5 20 25 Total 85 40 125 A person is randomly selected from those surveyed. Are being a student and preferring "Viking" independent events? Why or why not? = A. No, they are not independent because P(student) = 0.80 and P(student|Viking) =0.94. B. Yes, they are independent because P(student) = 0.80 and P(student|Viking) = 0.94 C. No, they are not independent because P(student) = 0.80 and A(student|Viking) = 0.68. KOTID D. Yes, they are independent because P(student) = 0.80 and P(student|Viking) = 0.68.
Answers
Using conditional probability, it is found that the correct option regarding whether the events are independent is given by:
A. No, they are not independent because P(student) = 0.80 and P(student|Viking) =0.94.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.An event B is classified as independent if:
P(B|A) = P(B).
In this problem, 100 out of the 125 people sampled are students, hence the probability is given by:
P(student) = 100/125 = 0.8.
Out of the people that prefer to be a Viking, 80 out of 85 people are students, hence:
P(student|Viking) = 80/85= 0.94.
The probabilities are different, hence the events are not independent, and option A is correct.
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7,614 is closer to ___ than it is to ____
Answers
Answer:
closer to 8000 than it is to 7000
Answer:
Hope this helps :)
7,614 is closer to 8,000 than it is to 7,000
This is because if the number has the hundreds place with 500 or more than it would be round up. If it's less than 500 than round down.
Also 7,614 rounded to the nearest thousand is 8,000 because the 6 in the hundreds place is more than 5 so we round up in the thousands place. The final answer would be 8,000.
Trapezoid area calculations
Answers
#1
1/2(Sum of parallel sides)Height=AreaArea
1/2(6+14)(5.5)1/2(20)(5.5)10(5.5)55in²#2
Apply Pythagorean theorem
B²=14²-12²=196-144=52B\approx 7Area
1/2(52+8)(12)6(60)360yd²#3
Area
1/2(Diagonals)1/2(6+6)(9+3)1/2(12)12)6(12)72ft²Answer:
Formulas Used
[tex]\textsf{Area of a Trapezoid}=\dfrac{1}{2}(a+b)h[/tex]
where:
a and b are the bases (parallel sides)h is the height (perpendicular to the parallel sides)[tex]\textsf{Pythagoras' Theorem}: \quad a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side, opposite the right angle)[tex]\textsf{Area of a Kite}=\dfrac{1}{2}pq[/tex]
where:
p and q are the diagonals-----------------------------------------------------------------------------------------
Question g (Trapezoid)
[tex]\textsf{Formula}: \quad A=\dfrac{1}{2}(a+b)h[/tex]
[tex]\textsf{Substitution}: \quad A=\dfrac{1}{2}(6+14)5.5[/tex]
[tex]\textsf{Answer}: \quad A=55\:\: \sf in^2[/tex]
Question h (Trapezoid)
[tex]\textsf{Formula}: \quad A=\dfrac{1}{2}(a+b)h[/tex]
Find the missing side length of the right triangle using Pythagoras' Theorem:
[tex]\implies a=\sqrt{14^2-12^2}=\sqrt{52}[/tex]
Therefore, top edge of trapezoid = √52 + 8
[tex]\textsf{Substitution}: \quad A=\dfrac{1}{2}(\sqrt{52}+8+8)12[/tex]
[tex]\textsf{Answer}: \quad A=96+12\sqrt{13}=139.3\:\: \sf yd^2\:(nearest\:tenth)[/tex]
Question i (Kite)
[tex]\textsf{Formula}: \quad A=\dfrac{1}{2}pq[/tex]
[tex]\textsf{Substitution}: \quad A=\dfrac{1}{2}(6+6)(3+9)[/tex]
[tex]\textsf{Answer}: \quad A=72\:\: \sf ft^2[/tex]
It took Vaughn 3 hours to drive to his sisters house. He took the same route on the way back home, but this time the trip took 2.5 hours. If Vaughn drove 10 mph faster on his return trip, how fast did he drive on his way to his sisters house?
Answers
The speed to his sister house is 50mph.
What is Speed?The speed of an object is the magnitude of the rate of change of its position with time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity.
Here, let the speed of his sisters house be x mph.
then, 3x = 2.5(x+10)
3x = 2.5x + 25
3x - 2.5x = 25
0.5x = 25
x = 25 / 0.5
x = 50
Thus, The speed to his sister house is 50mph.
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At a sale this week, a desk is being sold for 128.80. This is a 72% discount from the original price. What is the original price?
Answers
Answer:
$460
Step-by-step explanation:
If the 128.80 is the price of the desk after a 72% discount, it means that 128.80 is 100-72=28% of the original price.
From here, we can divide 128.80 by 28 to find what 1% of the price is then multiply the value by 100 to find 100%, or the original price.
128.80/28 = 4.6
4.6 x 100 = 460
Original price = $460
Hope this helped!
there are 672 eggs in 6 identical boxes. How many eggs are in each box.
Answers
Answer:
112
Step-by-step explanation:
672/6 = 112
Answer:
112
Step-by-step explanation:
672 divided by 6 is 112. There are 112 eggs in each box.
Please help me yall
A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the accompanying
table. Write the linear regression equation that represents this set of data, rounding
all coefficients to the nearest tenth. Using this equation, find the projected test grade,
to the nearest integer, for a student with a homework grade of 45.
Homework Grade (x) Test Grade (y)
78
66
89
76
54
42
86
90
74
68
73
73
86
84
63
54
64
54
Answers
Answers in bold:
Regression equation: y = 1.2x - 21.3Final Answer: 33=======================================================
Explanation:
I'm not sure how your calculator works, but I'm assuming you can copy/paste the given numbers into the calculator somehow to have it determine the regression equation.
The tool I used is GeoGebra and the regression equation it produced was
y = 1.2x - 21.3
Each decimal value is approximate and rounded to the nearest tenth.
---------------------------
Once we determine the regression line, plug the homework grade x = 45 to find the associated test grade (y). This is a predicted test grade.
y = 1.2x - 21.3
y = 1.2*45 - 21.3
y = 32.7
y = 33
If a student got a 45 on a homework, then we predict their test grade should be around 33.
A number cube is rolled. Identify the probability of getting 1 or 6 as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent.
1/3, 0.33, 30%
1/3, 0.33, 33%
2/3, 0.33, 30%
2/3, 0.67, 67%
Answers
Answer: The second option, 1/3, 0.33, 33%
Step-by-step explanation:
We will put the number of wanted outcomes over the number of total outcomes. 1 and 6 is two wanted outcomes.
2 / 6 = 1/3
Now, 1/3 is equal to 0.33. A decimal multiplied by 100 is a percent, so it is also equal to 33%. Your answer is:
1/3, 0.33, 33%
How many places do you need to move the decimal to the left to write the number below in scientific notation 120,000,000
Answers
Answer:
9
Step-by-step explanation:
1.2 * 10 (9) You need to move it 9 places to the left
Yolanda went to get her car fixed. It cost $50 for the art and $200 for each hour the mechanic worked on it. If the mechanic worked on the car for 5 hours, what would be the total cost.
Answers
Answer:
1050
Step-by-step explanation:
just add 200 x 5 then add 50 its simple
4x - 8y = 16 solve for y
Answers
Answer:
y=1/2x-2
Step-by-step explanation:
4x - 8y = 16
-8y = 16-4x
y=-2+ 1/2x
y=1/2x-2
mark brainliest pls
i need help on question 8 ....
Answers
Answer:
8a - 6b
You have to substitute in you other numbers:
a = 4 and b = 3
Your new equation would be:
8(4) - 6(3)
Now solve:
8 x 4 = 32
6 x 3 = 18
New problem:
32 - 18
= 14
So your answer is 14.
Step-by-step explanation:
Hope this helps!
From your neighborhood softie :)
In numbering pages of a book, a printer used 3289 digits. How many pages were in the book, assuming the first page of the book was number 1? Justify your answer. (b) Find the number of digits the printer will need for a book with n pages, for any positive integer n. Write this function of n as simple a form you can.
Answers
The number of the pages in the book if the first page will be numbered as 1 will be 1099 pages. And if the number of the pages is n then the function is shown below.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
In numbering pages of a book, a printer used 3289 digits.
Then the number of the pages in the book if the first page will be numbered as 1.
One digit number = 1 - 9 = 9 digits
Two digit number = 10 - 99 = 2 x 90 = 180 digits
Three digit number = 100 - 999 = 3 x 900 = 2700 digits
Then the total number of the digit is used will be
→ 9 + 180 + 2700
→ 2889
The number of the remaining digits will be
→ 3289 - 2889
→ 400
Then the four-digit number will be
→ 400/4
→ 100
Then the total number of the pages will be
Total pages = 9 + 90 + 900 + 100
Total pages = 1099
If n pages are there, then the number of the digits are required will be
[tex]\left\{\begin{matrix}n, & 1\leq n\leq 9 \\9+(n-9)2, & 10\leq n\leq 99 \\189+(n-9)3, & 100\leq n\leq 999 \\. & . \\. & . \\\end{matrix}\right.[/tex]
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Convert the rectangular equation to polar form. X2 y2 = 64
Answers
The polar form of the equation represents all the points with a distance of 8 from the origin, which is a circumference with a radius of 8, centered on the origin.
What is the polar form of the equation?The polar form is represented with the aid of polar coordinates of real and imaginary numbers in the coordinate system.
The horizontal and the vertical axis of the polar form denote the real axis and the imaginary axis, respectively.
The given equation to polar form is;
[tex]\rm x^2+y^2=64[/tex]
Using the formulae that link Cartesian to Polar coordinates.
x = rcosθ and y = rsinθ
Substitute these values into the equation.
[tex]\rm x^2+y^2=64\\\\(rcos\theta)^2+(rsin\theta)^2=64\\\\r^2cos^2\theta +r^2sin^2\theta =64\\\\r^2(cos\theta^2+sin\theta^2)=64\\\\Where ; \ sin^2\theta + cos^2\theta=1\\\\r^2(1)=64\\\\ r^2=8^2\\\\r=8[/tex]
Hence, the polar form of the equation represents all the points with a distance of 8 from the origin, which is a circumference with a radius of 8, centered on the origin.
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simplify the following radical expression
Answers
Answer:
[tex]2\sqrt{6} -13\sqrt{3} +4\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{24} -5\sqrt{12} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=\sqrt{4\times 6} -5\sqrt{4\times 3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=\sqrt{4} \times \sqrt{6} -5\times\sqrt{4} \times \sqrt{3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=2\sqrt{6} -5\times2\sqrt{3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=2\sqrt{6} -10\sqrt{3} +4\sqrt{2} -3\sqrt{3}[/tex]
[tex]=2\sqrt{6} -13\sqrt{3} +4\sqrt{2}[/tex]
Answer:
[tex] \boxed{ \tt 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2} }[/tex]
or
[tex] \boxed{ \tt \approx - 12.1}[/tex]
Step-by-step explanation:
Simplify:
[tex] = \tt \sqrt{ {2}^{2} \times 6} −5 \sqrt{12} +4√2−3√3[/tex]
[tex] = \tt \: 2 \sqrt{6} - 5 \sqrt{12} + 4 \sqrt{2 } - 3 \sqrt{3} [/tex]
[tex] = \tt2 \sqrt{6} - \sqrt{ {2}^{2} \times 3} + 4 \sqrt{2} - 3 \sqrt{3} [/tex]
[tex] = \tt \: 2√6−5(2√3)+4√2−3√3[/tex]
[tex] \tt = 2√6−10√3+4√2−3√3[/tex]
[tex] \tt = 2 \sqrt{6} - 13 \sqrt{3 } + 4 \sqrt{2} [/tex]
[tex] \tt \approx \: - 12.1[/tex]
[tex] \rule{225pt}{2pt}[/tex]
Help me solve pls don’t know the equation
Answers
I WILL MARK BRAINLIEST
Answers
Answer:D.6
Step-by-step explanation:
just divide
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
your answer is 9
Step-by-step explanation:
3+3/4+5+1/4
3+5=8
3/4+1/4=4/4
4/4=1/1
1/1=1
8+1=9
9 miles
NEED HELP ASAP, What is the angle of rotation from ARST TO AR'ST? Assume that the center of rotation is the origin.
A. 180° clockwise
B. 90° clockwise
C. 90° counterclockwise
D. 270° counterclockwise
Answers
Answer:
c if not d
Step-by-step explanation:
Someone help me solve just these two questions
Answers
Answer:
(0.173)¹¹(0.87)²Step-by-step explanation:
Q1
(0.173)⁹ × (0.173)² When two terms with equal bases with different powers are multiplied, it is equal to the base with the sum of the powers(0.173)⁹⁺² (0.173)¹¹Q2
0.87⁵/0.87³When two terms with equal bases with different powers are divided, it is equal to the base with the difference of the powers(0.87)⁵⁻³(0.87)²Find the inverse function answer to the question in the image attached.
Answers
The inverse function is:
[tex]g(x) = 27*x^3 - 4[/tex]
And g(2) = 212.
How to get the inverse function?
We need to find g(x) such that:
g(h(x)) = x.
We know that:
[tex]h(x) = \frac{\sqrt[3]{x + 4} }{3}[/tex]
Then our function must be a cubic, multiplied by 3^3 = 27, and then subtracts 4, it is:
[tex]g(x) = 27*x^3 - 4[/tex]
As you can see, if you evaluate in h(x), the outcome is x.
Now we can evaluate this in x = 2, we get:
[tex]g(2) = 27*2^3 - 4 = 212[/tex]
The correct option is C.
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Explain the difference between a unit rate and a percentage
Answers
Answer:
Ratio is the proportion between two numbers.
Percent is the ratio times 100.
Rate is the change of a number per unit time.
Step-by-step explanation:
1.A rate refers to the frequency by which a certain event happens while a ratio refers to the relationship between the size, number, or degree of two or more things.
2.A rate is a comparison between two measurements of the same units while a ratio is the proportion of one thing to another.
3.A rate refers to the fixed quantity of two things while a ratio refers to the relationship between various things.
4.A ratio indicates the difference between things while a rate indicates the changes in their measurements or units.
5.A ratio is indicated by the quotient of one quantity divided by the other while a rate is indicated by the comparison between two things.
Hope it helped ! Have a nice day
im doing an i ready test and i am very lost and confuse .
Answers
Answer: Ok
Step-by-step explanation:
Step-by-step explanation:
what are y'all doing so sad I can relate
true or false each triangular face has the same base and height
Answers
A walker has travelled 9 km along a trail. If he has completed 80% of the trail, how much further does he still have to go
Answers
Answer:
2.25km
Step-by-step explanation:
Calculate the total distance:
9km/ 0.80 x 100% = 11.25km
The walker has travelled 9km, so
11.25km - 9km = 2.25km left
pls help me sovle i cant heck this app and answer the test so i heck brainly to give me answer im seruos pls if i fail i die i have 13mins pls hurry
Answers
Answer:
3/16
Step-by-step explanation:
you do length x width x height, and get 3/16
