The general rule for the given Sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.
The given sequence –1, –3, –5, –7, –9,... follows a specific pattern or rule. To determine the general rule for n = 1, 2, 3,..., we can observe the sequence and identify the relationship between the terms.
Looking at the sequence, we notice that each term is decreasing by 2. Starting with –1, we subtract 2 to get the next term –3. Then, we subtract 2 again to get –5, and so on. Therefore, the rule for generating the terms in this sequence is to start with –1 and subtract 2 from each subsequent term.
We can express this rule algebraically as follows:
a_n = a_1 + (n – 1) * d
Where:
a_n represents the nth term of the sequence,
a_1 represents the first term of the sequence,
n represents the position of the term in the sequence,
d represents the common difference between the terms.
In this case, a_1 = –1 and d = –2 (since each term is decreasing by 2). Plugging these values into the equation, we get:
a_n = –1 + (n – 1) * (–2)
Simplifying further, we have:
a_n = –1 – 2n + 2
a_n = 1 – 2n
Therefore, the general rule for the given sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.
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Note the full question may be :
From the following sequence: – 1, – 3, – 5, – 7, – 9,…, What is the general rule for n=1, 2, 3,…?
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Answer:
radius of semi circle is 16mm.
diameter of semi circle is 32mm.
perimeter of triangle=sum of all sides.
perimeter of triangle = 20mm+20mm+32mm
perimeter of triangle =72mm
perimeter of semi circle=pi×r
perimeter of semicircle = 3.14×16mm
perimeter of semicircle =50.24mm
perimeter of the figure= 72mm+50.24mm=122.24mm
Factor the expression.
20b + 35 =
(Factor completely.)
Answer:
I think it would be 5(4b+7)
Step-by-step explanation:
I divided both terms by 5.
Find the Mode:
88, 82, 81, 89, 77, 95
89, 90, 81, 75
Answer:
81 is the mode
Step-by-step explanation:
THe mode is the number ina. Set of data that appears the most. In this case, 81 appears twice while all the other numbers only appeared once. So 81 in this case is the mode.
4. The measures of segment BS and segment PS are both 4.5 feet and m_PBS = 56°.
a. Find the measure of BSP. Item 2 says that “Angle QPS is supplementary to PSR."
b. Is BPS a unique triangle, or can more than one triangle be formed using the given segment
lengths and angle measures? Explain.
An ice company has y lbs of ice in stock. The company sells 500 lbs of ice and then receives a new shipment of 5x lbs of ice. Which expression represents the
weight of ice the ice company has now?
Answer:
yes
Step-by-step explanation:
no sabo
The manager of a restaurant recorded how many people are in different groups of customers and how much does group spent on food and beverages. The scatterplot below shows the date if she recorded. Based on this scatterplot, about how much money would a group of 10 people be expected to spend on food and beverages at this restaurant?
Answer:
$135
Step-by-step explanation:
Select all numbers that have an absolute value of 4.
Answer: 4 and -4
Step-by-step explanation: There isn't an actual explanation I can give for this answer, it is based on technical meaning.
Answer: 4 & -4
Absolute (denoted by the vertical bars) means that everything between them is converted to non-negative. So |−4|=4 and so is |4|=4 .
Step-by-step explanation:
I need help with solving this equation.
Answer:
66 m².
Step-by-step explanation:
From the question given above, the following data were obtained:
Diagonal 1 (d₁) = 11 m
Diagonal 2 (d₂) = 12 m
Area (A) =?
The area of a rhombus when the diagonals are given can be obtained as follow:
A = ½(d₁d₂)
A = ½ × (11 × 12)
A = ½ × 132
A = 66 m²
Thus, the area of the rhombus is 66 m²
Andrew randomly selects a number from 1-15. What is the probability that the number he selects is an even number?
Answer:
7/15
Step-by-step explanation:
Probability= Number of even numbers / Total numbers
There are 7 even numbers between 1 and 15
P = 7/15
Identify the graph of the equation (x+3)2+(y+1)2=9
The resulting graph is a circle with center at (-3,-1) and radius 3.
The graph of the equation (x+3)²+(y+1)²=9
is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.
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Find the area of the following figure: 11in 10in
Answer:
(no simplification) = 55 + (25[tex]\pi[/tex]/2) in^2
(with simplification) = (110 + 25[tex]\pi[/tex])/2 in^2
(with pi rounded to 3.14) = 94.25 in^2
Step-by-step explanation:
Let's start with the easier shape, the triangle. The formula for area of a triangle is 1/2(base)(height). Since at the far right we have 10 in, we can apply that to the triangle to get the base = 10 inches. The height is given as 11 inches so we can then calculate the area which is 55 in^2.
Then, the circle. We know that area of a whole circle = [tex]\pi r^{2}[/tex]. Since we know that a semicircle is 1/2 of a full circle, we can find the area of the entire circle then divide it by 2.
It gives the diameter as 10, divide that by 2 to get the radius. r=5. Plug 5 into the equation of [tex]\pi r^{2}[/tex] and you get 25[tex]\pi[/tex]. Divide that by 2 to get 25[tex]\pi[/tex]/2.
Add the triangle and the semicircle areas.
(no simplification) = 55 + (25[tex]\pi[/tex]/2) in^2
(with simplification) = (110 + 25[tex]\pi[/tex])/2 in^2
(with pi rounded to 3.14) = 94.25 in^2
The incomes in a certain large population of college teachers have a normal distribution with a mean $75,000 and standard deviation $10,000. 16 teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is more than $77,500?
Answer:
The probability that their average salary;
standard error
= 10,000/sqrt(16)
=10,000/4
= 2500
(77,500 - 75000)/2500
2,500/2500
= 1
p (z > 1) = .1587
So, the probability that their average salary is more than $77,500 is 0.1587
Step-by-step explanation:
 Consider the line segment LP with endpoint at L (-3, -5) and P (9, 7) and midpoint M.
What is the x—coordinate of N, the point that partitions segment MP in a 1 : 1 ratio?
A. 4
B. -4
C. -6
D. 6
Answer:
D. 6Step-by-step explanation:
M is midpoint of LP and N is midpoint of MP
Use midpoint formula:
x = (x₁ + x₂)/2Find x-coordinate of M:
x = (-3 + 9)/2 = 3Find x-coordinate of N:
x = (3 + 9)/2 = 6Correct choice is D
Finding missing angles
180°
35°
X
Answer:
90 degree and 55 degree
plz mark me as brainliest
Mathematics challenge
Get the equation of the line containing PQ using the point-slope formula:
y - (-2) = 3/2 (x - (-6))
Solve for y to get it in slope-intercept form:
y = 3/2 x + 7
so the y-intercept is (0, 7).
The line containing QR is then
y - 7 = -3/4 (x - 0)
or
y = -3/4 x + 7
The point R is on the x-axis, so its y-coordinate is 0. Plug in y = 0 and solve for x to get the other coordinate:
0 = -3/4 x + 7
3/4 x = 7
x = 4/3×7 = 28/3
So the point R has coordinates (28/3, 0).
Answer:
Point R is on the x-axis, so its y-coordinate is 0. Plug in y = 0 and solve for x to get the other coordinate:
0 = -3/4 x + 7
Take off the zero...
3/4 x = 7
Answer
x = 4/3×7 = 28/3
And there it is
Point R has the coordinates (28/3, 0).
Step-by-step explanation:
Which TWO expressions can be used to represent the tiles shown here?
Answer:
4(2a + b)
and
8a + 4b
Step-by-step explanation:
Hope this helped :)
Step-by-step explanation:
8a+4b
4(2a+b)
hope this helps
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
7 x - 9 + 11 x - 9 = 180
Step-by-step explanation:
For the equation: 7 x - 9 + 11 x - 9 = 180
Value of X is 11
7x - 9 + 11x - 9 = 180
combine values
18x - 18 = 180
18x = 198
18x/18 = 198/18
x = 11
Angle Measures is
7 (11) - 9 = 77-9 = 68 degrees
11 (11) - 9 = 112 degrees
what is the measurements of the circle?
Answer:
what is the circle
○ YW 42
combine like terms !-3r - 5 + 2r - 3r - 2s
HELP ASAP
Rewrite 7^-2 using a positive exponent an evaluate the result.
Name:
L153
Mean Absolute Deviation
Find the mean absolute deviation of each set of data. Round your answer to two decimal
places.
1) 61, 87, 46, 79,53, 46
2) 9, 2, 1, 3
Absolute
Absolute
Data Mean Difference
Data Mean
Value
Difference
Value
Answer:
amen
Step-by-step explanation:
amen you shall pass
A building 240 feet tall casts a 40 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.)
9514 1404 393
Answer:
80.38°
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
The person is standing 40 ft from the building. The point they're looking at is 236 ft above their eyes. So the angle α is found from ...
tan(α) = 236/40
α = arctan(236/40) ≈ 80.38°
Grant started a marathon at 8:00 am. He took 4 hours 49 minutes to complete the marathon. When did he cross the finish line
Please help
here the question
Rosalina just started a new job. She has $500 in her bank account. Every week, she deposits $40 into her bank account.
A)
Write an expression to represent how much Rosalina has in her account at any given time using x to represent the number of weeks.
I ALREADY SOLVED A BUT I NEED HELP WITH C
B) Rosalina wants to save $700 for the new smart tv write and equation to determine how many weeks (x) it will take for rosalina to have enough money to purchase her new tv
C) using your equation from b will rosalina have enough money for her new tv in four weeks?
also) how would the equation change if rosalina stopped working wasn't able to deposit $40 and had to instead withdraw $40 a week? Which part of your equation would change?
please help!
THANK YOU!!
Answer:
Let M represent the amout at any time.
She saves $40 per week so total amount becomes 40x in any specified week.
where x is the number of weeks.
In the start she has $500 in her bank account so we 'll add this amount into the savings per week. So expression becomes
M = 40x+500
Simply put number of week in place of x and find the total amount.
Step-by-step explanation:
Answer:
for c it is no
Step-by-step explanation:
it is no because she deposits 40 a week, in 4 weeks she deposits 40x4=160, which is nowhere close to the 700 she needs. Even if you count the 500 in her account it is still no since it would total up to 660, not 700
What's the slop of the line with the two points 3,2 and 7,9
A cylinder has a height of 10 centimeters. It's volume is 5306.6 cubic centimeters. What is the radius of the cylinder
Answer: 13
Step-by-step explanation: r=V
πh=5306.6
π·10≈12.9967
AABC is isosceles.
MZA = 48° and mZB = 4x + 4.
A
B
x= [?]
Look at the pattern below. Which fraction would complete the pattern?
1/4, 2/8, ___, 4/12.
answer
A. 3/12
B. 3/14
C. 3/9
D. 3/15
The answer is: A. 3/12
15 POINTS
Consider the line in the coordinate plane that passes through the point (-7, -3) and the origin. Find the slope of a line perpendicular to the line described.
A) - 1, 3
B) - 3, 7
C) - 7, 3
D) 3, 7
Answer:
C. -7/3Step-by-step explanation:
The slope of the line that passes through points (0, 0) and (-7, -3) is:
m = (y₂ - y₁)/(x₂ - x₁) m = (-3 - 0)/(-7 - 0) = 3/7Perpendicular lines have opposite-reciprocal slopes:
-1 / (3/7) = - 7/3Correct choice is C
13. Reasoning In 2016, the world's oldest
tree was 5,066 years old. Write the
number that is one hundred more using
number names?
Answer:
five thousand, one hundred and sixty six years old.
Step-by-step explanation: