Option C
The explicit formula for the arithmetic sequence is [tex]a_n = 9 - 6n[/tex]
Solution:
Given that the arithmetic sequence is:
3, -3, -9, -15, -21, ...
To find: Explicit formula for the arithmetic sequence
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
Where [tex]a_n[/tex] is nth term of sequence
n is the term's location
[tex]a_1[/tex] is the first term of sequence
d is the common difference between terms
In an arithmetic sequence, the difference between successive terms is constant. This means that we can move from any term to the next one by adding a constant value.
In the given sequence:
3, -3, -9, -15, -21, ...
[tex]a_1 = \text{ first term } = 3[/tex]
d = difference between any two terms in sequence
[tex]d = a_2 - a_1[/tex]
d = -3 - (3) = -6
Substituting the values in above formula,
[tex]a_n = 3 + (n - 1)(-6)\\\\a_n = 3 -6n + 6\\\\a_n = 9 - 6n[/tex]
Thus the explicit formula to find any term in sequence is found
18. Ten students from a school appear in one or more subjects for an inter school
Answer:
Step-by-step explanation:
(G n m) = [Max, Anael]
(G u S) = [Acel, Action, Anael, Max, Carl, Dario, Carlin, Kia, Barak]
The students appearing for General Knowledge (G) are Acel, Acton, Anael, Max, Carl, and Dario and the students appearing for Math (M) are Barek, Bay, Max, Kai, Anael, and Carlin and the students appearing for Science (S) are Carlin, Acton, Anael, Kai, Dario, and Barek.
To determine the students in each subject set, we need to carefully analyze the table. Let's start with the General Knowledge (G) set. The students listed under General Knowledge are Acel, Acton, Anael, Max, Carl, and Dario.
Next, we move on to the Math (M) set. The students listed for Math are Barek, Bay, Max, Kai, Anael, and Carlin.
Lastly, we look at the Science (S) set. The students listed for Science are Carlin, Acton, Anael, Kai, Dario, and Barek.
To find the intersection students in each subject set, we simply extract the names listed under each subject. When a student appears in more than one subject, we include them in the respective sets accordingly.
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let this be an easy 5 points for your brainly account all is ask for in return is a "thank you"
Answer:
deze nuts thanks u
Step-by-step explanation:
Answer: thank
Step-by-step explanation:
you
Solve Ixl<13{(-13, 13}
{xl-13
[XIX<-13 or x 13)
Answer:
-13 < X < 13
Step-by-step explanation:
It is given |X| < 13.
Note that we have: |x| < a, for any real number 'a', then it equals:
-a < X < a.
So, in this case, |X| < 13 should be equal to -13 < X < 13.
Hence, the answer.
Write an equation with a slope of 1/2 and a Y intercept of -2
Step-by-step explanation:
y=1/2×-2 @$@@$@$@$@%@%@%#_##%#%
HELP ME 20 POINTS!!!!!
Consider the characteristics of the graph. Which statement DOES NOT describe the data set?
A) The interquartile range (IQR) is 13.
B) The data is skewed right.
C) The data is skewed left.
D) The median is 50.
Answer:
B) The data is skewed right.
Step-by-step explanation:
The data is not skewed right. You can tell because the left side of the box is longer than the right, meaning that it is skewed left.
Answer:
B) The data is skewed right.
Step-by-step explanation:
The data is skewed right does not describe the data.
In this set of data, the left side tail is longer.
The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of
the cone's base is 5 centimeters, and its height is 10 centimeters.
The number of times one needs to use the completely filled cone to completely fill the cylinder with water is
Reset
Next
Answer: 24times
Step-by-step explanation:
Formula for the volume of a cylinder = πr²h
Volume of the cone = 1/3πr²h
Therefore the volume of the cylinder = 22/7 x 10² x 20
= 22/7 x 10 x 10 x 20
= 6285.71cm³
Therefore , the volume of the cone = 1/3 x 22/7 x 5² x 10
= 1/3 x 22/7 x 5 x 5 10
= 5500/21
= 261.9cm³
Therefore the number of times needed to use the completely filled cone to completely filled the cylinder with water = 6285.71/261.9
= 24times.
PLS HELP
What is the perimeter of the rhombus below?
A. [tex]8\sqrt{5}[/tex]
B. [tex]5\sqrt{8}[/tex]
C. [tex]4\sqrt{5}[/tex]
D. [tex]5\sqrt{4}[/tex]
Answer:
8√5 units.
Step-by-step explanation:
See the diagram in the coordinate plane attached.
A rhombus has four equal sides and to find the perimeter of the rhombus we have to measure any of the sides of the figure of the rhombus.
The coordinates of the topmost point are (-1,-1) and that of the rightmost point are (3,-3).
Therefore, side length of the rhombus will be
[tex]\sqrt{(- 1 - 3)^{2} + (- 1 - (- 3))^{2}} = \sqrt{20} = 2\sqrt{5}[/tex] units.
So, the perimeter of the rhombus will be (4 × 2√5) units = 8√5 units. (Answer)
The distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] on a coordinate plane is given by
[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]
IF THIS WRONG I FAIL!!!!
Matt has started a car washing business to save money for college. Each week, he
washes 3 more cars than he did the week before.
Part A: Matt started by washing 6 cars his first week in business. Write an explicit formula that can be used to find the number of cars he washed on any given week.
Part B: Part B: How many cars will Matt wash on his 11th week in business?
Answer:
Part A:
An= 6 + 3(n-1)
Part B:
36 cars
Max travel 324 miles in six hours write the unit rate
Answer:
54mph
Step-by-step explanation:
Answer:
= 54 miles per hour
Showing WorkThis is a fraction equal to
324 miles ÷ 6 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 6
324 miles
÷ 6
6 hours
÷ 6
=
54 miles
1 hour
=
54 miles
hour
= 54 miles per hour
Answer:
Step-by-step explanation:
Speed v = distance d/ time t
v = 324/6
v = 54miles/hr
Each cube in this rectangular prism is 1 cm3.What is the volume of the rectangular prism?
A.40 cm3
B.20 cm3
C.48 cm3
D.9 cm3
The volume of the rectangular prism is b. 20 cubic cm
What is the volume of the rectangular prism?
From the question, we have the following parameters that can be used in our computation:
the rectangular prism
Where, we have
Length = 2
Height = 2
Width = 5
The volume of the rectangular prism is the product of the dimensions
So, we have
Volume = 2 * 2 * 5
Volume = 20 cubic cm
Hence, the volume of the rectangular prism is b. 20 cubic cm
Isaac purchased a house for $179,300,00. Every year, Isaac makes improvements so that the value of the house goes up by 4%.
Which of the following equations can be used to determine the number of years after purchase, that the value of Isaac's house will
be equal to 5197.230.002
Answer:
The number of years in which house value goes up is 145 years .
Step-by-step explanation:
Given as :
The initial purchased value of the house = p = $179,300,00
The value of house goes up every years at the rate = r = 4%
Let The number of years in which house value goes up = t years
The value of the house after t years = $A = $5197,230,002
Now, According to question
The value of the house after t years = The initial purchased value of the house × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
I.e A = $p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or,$5197,230,002 = $17930000 × [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{5197,230,002}{179,300,00}[/tex] = [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]
Or, 289.86 = [tex](1.04)^{t}[/tex]
Now, taking Log both side
So, [tex]Log_{10}[/tex]289.86 = [tex]Log_{10}[/tex] [tex](1.04)^{t}[/tex]
or, 2.462 = t × [tex]Log_{10}1.04
or, 2.462 = t × 0.01703
∴ t = [tex]\dfrac{2.462}{0.01703}[/tex]
I.e t = 144.56 ≈ 145
So, Number of years = t = 145 years
Hence The number of years in which house value goes up is 145 years . Answer
To determine the number of years it will take for the value of Isaac's house to reach $5,197,230.002 with an annual appreciation rate of 4%, use the compound interest formula. Solving for the number of years, the approximate result is 84 years.
Isaac purchased a house for $179,300. Every year, the value of the house increases by 4%. To determine the number of years after purchase that the value of Isaac's house will reach $5,197,230.002, we can use the formula for compound interest:
FV = PV × (1 + r)ⁿ
FV is the future value of the house, $5,197,230.002.PV is the present value or the initial value of the house, $179,300.r is the annual increase rate, 4% or 0.04.n is the number of years.We need to solve for n in the equation:
$5,197,230.002 = $179,300 × (1 + 0.04)ⁿFirst, isolate the exponential expression:
(1 + 0.04)ⁿ = $5,197,230.002 / $179,300(1.04)ⁿ ≈ 29Next, apply the natural logarithm to both sides to solve for n:
ln[(1.04)n] = ln(29)n × ln(1.04) = ln(29)n = ln(29) / ln(1.04)n ≈ 83.95 yearsSo, the value of Isaac's house will reach $5,197,230.002 approximately 84 years after purchase.
Select the correct answer.
During the summer, Jody earns $10 per hour babysitting and $15 per hour doing yardwork. This week she worked 34 hours and earned $410.
If x represents the number hours she babysat and y represents the number of hours she did yardwork, which system of equations models
this situation?
A.
X+ y = 34
10x+ 15y = 410
OB. X + y = 410
10x + 15y = 34
C.
X+ y = 34
15x+10y= 410
OD. x + y = 410
15x+10y = 34
Answer:
A
Step-by-step explanation:
x+y=34 (add the seperate hours together to get the total amount of hours)
10x+15y=410 (multiply the money made each hour by the hours worked and add them together to get the amount of money joy made)
The system which creates a mathematical representation of the given condition will be X+ y = 34 and 10x+ 15y = 410 so option (A) will be correct.
How to form an equation?When trying to set up or construct a linear equation to fit a real-world application, identify the known quantities and use the unknown quantity as a variable.
In other words, an equation is a set of variables that are constrained through a situation or case.
x = number of hours babysitting.
y = number of hours yard work.
Given that
She worked a total of 34 hours
So x + y = 34 will be the correct formation.
Jody earns $10 per hour babysitting
So a total of 10x money Jody will earn through babysitting.
$15 per hour doing yardwork
So a total of 15x money Jody will earn through yard work.
Given that
A total of $410 Jody earned so
10x + 15y = 410 will be the correct formation.
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Maya has $2740 of play money
Emily has $3560 of play money. Maya gives some money to Emily. If Emily ends up with 4 times Maya amount. How much money does each girl has in the end
Answer:
Maya = $1260
Emily = $5040
Step-by-step explanation:
2740+3560 =6300
M + (4M) = 6300
5M=6300
M=6300/5
M=1260
E=5040
Maya has $1260, and Emily has $5040 in the end. Maya gives $1480 to Emily.
How the amount of money was calculatedMaya has $2740, and Emily has $3560.
We're looking for the amount Maya gives to Emily so that Emily ends up with 4 times as much as Maya.
Let M be the amount Maya gives to Emily.
Emily ends up with 4 times Maya's amount:
Emily's amount = 4 * Maya's amount
$3560 + M = 4 * ($2740 - 4M
Simplify:
$3560 + M = $10960 - 4M
$3560 + M + 4M = $10960
5M = $10960 - $3560
5M = $7400
Divide by 5 to solve for M:
M = $7400 / 5
M = $1480
So, Maya gives $1480 to Emily.
To find how much each girl has in the end:
Maya: $2740 - $1480 = $1260
Emily: $3560 + $1480 = $5040
Maya has $1260, and Emily has $5040 in the end.
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Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
7x+3y= 30
-2x+3y= 3
ОА. (3, 5)
ОВ. (3, 3)
Ос. (6, 5)
D. (6, 3)
Help me this is worth a lot of points
Answer:
Area of ABCD = 100m²
Step-by-step explanation:
Area of a square is the square of the side.
A = s²
A = (10m)² = 10²m² = 100m²
Answer:
Area of ABCD = 100m²
Step-by-step explanation:
A circle has a radius of 30cm what is the area
r = 30 cm
formula: A = πr²
A = πr²
A = π30²
A = 900π
if π = 3.14, then the answer is 2,826 cm
if π is not defined, the answer is 2,827.43 cm
Write a fraction greater than 1 for the parts that are shaded. + a mixed #. Please I need an answer for all of them
Answer:
2. 7/4 and 1 3/4
3. 5/3 and 1 2/3
4. 14/5 and 2 4/5
5. 21/6 and 3 3/6 (Lowest terms=3 1/2)
6. 20/8 and 2 4/8 (lowest terms= 2 1/2)
Hope it helped!!
Which system is equivalent to
{y=-2x2
y=x-2}
Answer:
OPTION C: y = -2y² - 8y - 8
x = y + 2
Step-by-step explanation:
The given equations are:
[tex]$ y = -2x^2 \hspace{20mm} \hdots (1) $[/tex]
[tex]$ y = x - 2 \hspace{20mm} \hdots (2) $[/tex]
From Equation (2), we get:
x = y + 2
Substituting this value of x in Equation (1), we get:
y = -2(y + 2)²
Expanding it in [tex]$ (a + b)^2 = a^2 + 2ab + b^2 $[/tex], we get:
y = -2{y² + 4y + 4}
⇒ y = - 2y² - 8y - 8
Therefore, OPTION C is the answer.
Answer: C on edge 2022
Step-by-step explanation:
if wrong i’m gay and Bidens a good president *they almost all suck anyways*
Given the diagram below, what is sin (30°) ?
Answer:
A. 1/2.
Step-by-step explanation:
The ratio of the sides of a 30-60-90 triangle is 2:1:√3 where 2 is the hypotenuse. 1 is the shortest leg and √3 is the longest leg.
In the diagram we see that the longest leg is opposite the 60 degree angle.
So the longest leg is 3.5√x and the shortest leg ( from applying the ratios) = 3.5√x / √3.
and the hypotenuse is 2 * 3.5√x / √3 (using the ratios again).
So sin 30 = shortest leg / hypotenuse = 3.5√x / √3 / 2 * 3.5√x / √3
= 1/2.
Otto's investment portfolio consisted of shares of internet stock and copper stock. During the year, the value of his internet shares increased $10\%$, but the value of his copper shares decreased from $\$10{,}000$ to $\$9{,}000$. During the same year, the total value of his portfolio increased by $6\%$. What was the dollar value of his internet shares at the end of the year?
Answer:
44000
Step-by-step explanation:
Let w be the initial value of Otto's internet stock, in dollars. At the beginning of the year, the total value of his portfolio is w+10,000 dollars. At the end of the year, the total value of his portfolio is 1.1w+9,000 dollars. Since increasing by 6% is equivalent to multiplying by 1.06, we have
1.06(w+10,000)=1.1w +9,000
Distributing and collecting terms, we find w=40,000. At the end of the year, his internet stock is worth 40,000* 1.1=44,000 dollars.
*credits: AoPS
Every student in the senior class is taking history or science. There are $200$ seniors in the class. If there are $126$ seniors taking history and $129$ seniors taking science, how many students are taking both history and science?
Answer: 55
Step-by-step explanation:
126+129= 255
255-200=55
55 students are taking both history and science.
To solve this, we set up the problem as follows: Let H represent the set of students taking history, S represent the set of students taking science, and N represent the total number of seniors. We're given that N = 200, |H| = 126 (the number of students taking history), and |S| = 129 (the number of students taking science). The number of students taking both can be found by adding the number of students in sets H and S and subtracting the total N. This calculation is often represented by the formula |H ∩ S| = |H| + |S| - N, where |H ∩ S| is the number of students taking both history and science.
Using the formula, we calculate: |H ∩ S| = 126 + 129 - 200 = 55. Therefore, 55 seniors are taking both history and science.
Find the area of the trapezoid by decomposing it into other shapes. A) 56 cm2 B) 60 cm2 C) 64 cm2 D) 72 cm2 Eli
Answer:
Option C. [tex]64\ cm^2[/tex]
Step-by-step explanation:
see the attached figure N 1 to better understand the problem
we know that
The trapezoid can be decomposed into two right triangles and a rectangle
see the attached figure N 2
so
The area of the trapezoid is equal to the area of two right triangles and one rectangle
The area of trapezoid is equal to
[tex]A=\frac{1}{2}(5)(4)+(12)(4)+\frac{1}{2}(3)(4)[/tex]
[tex]A=10+48+6[/tex]
[tex]A=64\ cm^2[/tex]
What is the greatest common factor of 9 and 5
Answer:45
Step-by-step explanation:5 10 15 20 25 30 35 40 45
9 18 27 36 45
The greatest common factor of the number 9 and 5 is 1.
To find the greatest common factor (GCF) of 9 and 5, determine the largest number that evenly divides both 9 and 5.
The factors of 9 are 1, 3, and 9.
The factors of 5 are 1 and 5.
From these lists, the only common factor of 9 and 5 is 1.
Therefore, the greatest common factor of 9 and 5 is 1.
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I don’t understand question 49 someone pls explain.
Answer:
Below in bold.
Step-by-step explanation:
a, That would be
m = 7 + 8(d - 1) where m = the no. of minutes and d = the day number.
b. On day 9 the number of minutes m = 7 + 8(9 - 1)
= 7 + 64
= 71.
You moved within a short walking distance to work and you no longer need to spend the $20 per week budgeted for bus
fare. Considering this, what is your new weekly budget surplus if your previous surplus was $175?
a) $30
b) $66
Oc) $120
O d) $195
Find the solutions to x2 = 18.
Answer:
6^3
Step-by-step explanation:
Ape-x
The solutions are [tex]\(x = 3\sqrt{2}\)[/tex] and [tex]\(x = -3\sqrt{2}\)[/tex]. Each represents a square root of 18.
To find the solutions to [tex]\( x^2 = 18 \)[/tex], you need to take the square root of both sides of the equation.
[tex]\[ x = \pm \sqrt{18} \][/tex]
[tex]\[ x = \pm 3\sqrt{2} \][/tex]
So, the solutions to [tex]\( x^2 = 18 \)[/tex] are [tex]\( x = 3\sqrt{2} \)[/tex] and [tex]\( x = -3\sqrt{2} \).[/tex]
Teresa stated that the heights of the students in her class were not a function of their ages. Which reasoning could justify Teresa’s statement?
Answer: Two students are the same age but have different heights.
Which decimals are rational numbers? Select all that apply
A. 72/100
B. π
C. 1 1/3
D. 8/526
E. 0.212212221...
F. 5/9
Answer:
Your answers are A, C, D, FStep-by-step explanation:
Fractions are always rational.
A --> this is rational because it can be represented by a fraction.
B --> this is irrational because it cannot be represented by a fraction
C --> 1 1/3 is rational because it can be represented as a fraction
D --> 8/526 is rational because it can be represented as a fraction
E --> this is irrational because it cannot be represented by a fraction
F --> this is rational because it can be represented as a fraction
I hope this helps!
Rational numbers can be expressed as the ratio of two integers. From the list provided, the rational numbers are 72/100 (A), 1 1/3 (C), 8/526 (D), and 5/9 (F). The number π (B) is irrational, and it is unclear if 0.212212221... (E) is a repeating decimal, so it cannot be confirmed as rational without additional information.
Explanation:Rational numbers are numbers that can be written as a fraction, where both the numerator and the denominator are integers and the denominator is not zero.
This includes both terminating and repeating decimals.
A. 72/100 is a rational number because it can be simplified to the fraction 18/25, which is a ratio of two integers.B. π (pi) is not a rational number because it is an irrational number; it cannot be expressed as a fraction of two integers.C. 1 1/3 is a rational number as it is equivalent to the fraction 4/3, a ratio of two integers.D. 8/526 is a rational number as it is already in fraction form with two integers.E. 0.212212221..., if this is a non-terminating, non-repeating decimal, it would be irrational; however, if the pattern repeats at some point, it would be rational. Since the pattern is not explicitly stated as repeating, we cannot assume it is rational.F. 5/9 is a rational number because it is a fraction that represents a ratio of two integers.Thus, the rational numbers from the list provided are A, C, D, and F.
evaluat5-44*(-0.75)-18/ 2/380.8+(-4/5)
Answer:37.17 or 37.1763655462
Explanation:i just did the equation and evaulated it it's hard to explain sorry
Answer:
i dont know know because i have the same question but a little different its 5-44*(-0.75)-18 / 2/3 *.8 - 4/5
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
see explanation
Step-by-step explanation:
The diagrams show triangular figures
The first figure has 1 dot
The second has 1 + 2 = 3 dots
The third has 3 + 3 = 6 dots
The fourth has 6 + 4 = 10 dots
Note the pattern is + 2 , + 3, + 4
Thus the fifth pattern is 10 + 5 = 15 dots