Many credit card companie chard a compound interet rate of 1. 8% per month Nelon owe 950 on a credit card
Answers
Following is the geometric progression of Nelson's debt after each month: (E) 950,967.1, 984.51, 1002.23, 1020.27
What is a geometric sequence?A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
So, in this issue, the interest rate is as follows: 1.8%.
The debt will therefore be equal to the debt from the previous month multiplied by 100 + 1.8 = 101.8% = 1.018 each month, and the common ratio is as follows: 1.018.
In light of this, the terms of the series are as follows:
2nd term: 950 x 1.018 = $967.1
3rd term: 967.1 x 1.018 = $984.51
4th term: 984.51 x 1.018 = $1002.23
5th term: 1002.23 x 1.018 = $1020.27
Therefore, the following is the geometric progression of Nelson's debt after each month: (E) 950,967.1, 984.51, 1002.23, 1020.27
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Complete question:
Many credit card companies chard a compound interest rate of 1.8% per month Nelson owes 950 on a credit card. If he makes no purchases or payments he will go deeper and deeper into debt.
Related Questions
innequality of |2x+7|+9 >18.
Answers
For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.
What is meant by inequality?The state of not being equal, particularly in terms of status, rights, and opportunities, is a fundamental concept in social justice theories. It can be perplexing in public conversation since it typically has distinct meanings to different individuals. However, some variations are common. An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is unfair. Various notations are used to denote different kinds of inequality, including:
A less than sign, such as a, denotes that an is greater than b.
Given inequality is:
|2x+7|+9 >18.
First we have to rearrange all the variables to the left side of the given equation:
Then,
|2x+7|>18-9
|2x+7|>9
2x+7>9 or 2x+7< -9
S0, x>1 or x< -8
Therefore, x< -8 or x>1
Hence, For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.
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need help with this i was not here for it
Answers
Answer:
83
Step-by-step explanation:
(78+72+87+90+x)/5=82
327+x=82*5
327+x=410
x=410-327
x=83
The odd numbers in this group add up to an even number: 15, 32, 5, 13, 82, 7, 1.
Answers
Suppose UV=17, BV=18, SAU=92, and TBV=24
Answers
The required angles ∠TBS and ∠TCV are 48° and 22° respectively.
What is right angled triangle ?A right-angled triangle is a kind of triangle that has one of its points equivalent to 90 degrees. The other two points summarize to 90 degrees. The sides that incorporate the right point are opposite and the foundation of the triangle. The third side is known as the hypotenuse, which is the longest side of each of the three sides
According to question:∠TBV = 24°
∠VBS = 24°
So, ∠TBS = (24° ) = 48°
And,
∠SAU = 92°,
So,
∠VAU = 46°
In ΔTAC
∠TAC + ∠TCA = 90°
∠TCA = 90° - 46° = 44°
This angle is bisect by CV
Then,
∠TCV = 44/2 = 22°
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∠TBS = 48°
SV = 17
∠TCV = 20°
What is a angle bisector?
In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.
As given in question:
AV , BV and CV are the angle bisector of ΔABC
UV = 17, BV = 18
∠SAU =92° and ∠TBV = 24°
Now,
∠TBV = ∠SBV = 24° ( BV is angle bisector)
So, ∠TBS = ∠TBV + ∠SBV
∠TBS = 24° + 24° = 48°
SV = UV = 17 (V is the incenter of ΔABC.)
∠SAU + ∠TBS + ∠TCU = 180° (Sum of angles of a triangle)
92° + 48° + ∠TCU = 180°
∠TCU = 180° - 140°
∠TCU = 40°
So, [tex]\angle TCV = \frac{40\degree}{2}[/tex]
∠TCV = 20°
∴ ∠TBS = 48°
SV = 17
∠TCV = 20°
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A total of 420 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adult tickets sold how many adult tickets were sold
Answers
Answer: I believe 140
Step-by-step explanation: This is how I found my answer:
420 / 3
= 140
420-140
= 280
420= number of all tickets sold.
140= number of adult tickets sold
280= number of student tickets sold
You might wonder how I know why it's 140. I know it's 140, because using my context clues, it stated:
"the number of student tickets sold was three times the number of adult tickets."
So, the one that was the bigger amount must be the student's tickets sold, while the lower amount has to be the adult's tickets sold. I hope this helped!
A pinball machine which normally sells for $1999 is on sale for $1750. Find the discount and the rate of discount.
HELP ME THIS IS DUE TODAY!!
Answers
Answer: 12.5%
Step-by-step explanation:
Take 1750 divided by 1999, then time 100% = 87.5%
100% - 87.5% = 12.5%
The rate of discount is 12.5%
A population of chipmunks moves into a new region at time t=0 months. At time t (in months), the population size is given by
P(t) = 100[1+0. 3t+(0. 04)t^2].
How long does it take for this population to double its initial size P(0)? Include the units in your answer.
What is the average rate of population change between time t=0 and time t=20? Include the units in your answer.
What is the instantaneous rate of growth of the population when the population size is P=200? Include the units in your answer
Answers
Part a: Time taken to double the population of chipmunks is 5/2 months.
Part b: Population at population size; P = 200 is 50.
Explain the term average rate of population change?the country, region, or geographic area's average yearly rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and indeed the overall population for that year.Part a: Time taken to double the population of chipmunks;
P(t) = 100[1 + (0.3)t + (0.04)t²].
P(0) = 100[1 + 0 + 0] = 100
P(t) = 200 = 100 + 30t + 4t²
4t² + 30t − 100 = 0
2t² + 15t − 50 = 0
(2t − 5)(t + 10) = 0
t = 5/2
It will take 5/2 months population to double its initial size P(0).
Part b: Population at population size; P=200
P'(t) = 0 + 30 + 8t
P = 200 when t = 5/2
P'(200) = 30 + 8(5/2)
P'(200) = 30 + 20
P'(200) = 50
Thus, the instantaneous rate of growth of the population when the population size is P=200 is 50.
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Abha is climbing a mountain. While cvering 20 yards of horizontal distance. Abha's elevation increases by 40 yards. consider Abha's climb as a linear function. 1. what is the slope her climb,? 2. does the line 54y=13x pass through the origin? daliyah is given one point on a like as (3,-1) and the slope of the line as -5. 3. what is the y-intercept of the line?and 4. how to write the equation of the line?
Answers
1. The slope of Abha's climb is 2 (rise/run).
2. No, the line 54y=13x does not pass through the origin.
3. The y-intercept of the line is 5.
4. The equation of the line is y = -5x + 3.
What does linear function mean?A linear function is one that has one or two variables and no exponents, according to the definition given in mathematics. It is a graphing function that produces a straight line.
How is a linear function determined?To finish the graph, use a straightedge to draw a line through the two points as two points decide a line. The formula for a linear function is f(x)=mx+b, where m and b are real values representing the slope. Set f(x)=0 and work out the value of x to determine the x-intercept, if one exists. We can use y and f(x) interchangeably because y=f(x).
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If A+K=4 and AK=3 then find the vale of A³+K³
Answers
Answer:
Below
Step-by-step explanation:
k = 4-a
a (4-a) = 3
-a^2 +4a -3 = 0 ====> Quadratic Formula ===> a = 1 and k = 3
1^3 + 3^3 = 28
5. What are the real and complex solutions of the polynomial equation? (1 point)
x-8=0
01+i3, and 1-i√√3
O2,-1+13, and-1-i√√3
O2, 1+2i √√3, and 1-2i √√3
02, 2+2i √√3, and 2-2i
Answers
The real and complex solutions of the polynomial equation [tex]x^{3} - 8[/tex] = 0 is 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i. option 2 is correct.
Polynomial equation: what is it?Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree. By factoring polynomials according to their degree and the variables in the equation, we may find their solutions.
Our equation is [tex]x^{3} - 8[/tex]
and we know that: [tex]x^{3} = 8[/tex]
then we can write our equation as: [tex]x^{3} - 2^{3}[/tex]
And using the identity: [tex]a^{3} - b^{3} = (a-b) *(a^{2} +ab+b^{2} )[/tex]
where a = x and b = 2, then our equation is:
them, if x = 2 the first part is zero, so x = 2 is a solution, and now we need to see the second part in order to find the complex solutions.
[tex]x^{2} + 2x +2^{2}[/tex] = 0
Here we need to use.
a[tex]x^{2}[/tex] + bx + c = 0 if for a, b and c constants, then:
x = [tex]-b +-\sqrt{b^{2} - 4ac } /2a[/tex]
in our problem we have:
x = -2 +-[tex]\sqrt{4 - 16}[/tex] /2
x = -1 +-[tex]\sqrt{-3}[/tex]
x = -1 +-[tex]\sqrt{3}[/tex] i
So here we have two complex solutions: -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
So the value of x are 2, -1 + [tex]\sqrt{3}[/tex]i and -1 - [tex]\sqrt{3}[/tex]i
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I think you mean
What are the real and complex solutions of the polynomial equation? (1 point)
[tex]x^{3} - 8[/tex] = 0
( the equation is [tex]x^{3} - 8[/tex] = 0 and not x-8 =0)
convenience sampling allows for generalizations to a larger population, and probability sampling does not. group of answer choices true false
Answers
Probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.
Explain the term convenience sampling?Convenience sampling is any non sampling technique where units are chosen for the sample based on their accessibility to the researcher.
This may be as a result of close proximity geographically, availability at a specific moment, or willingness to take part in the study. Convenience sampling, sometimes known as inadvertent sampling, is a non-random sampling technique.Research projects in qualitative and medical fields frequently employ convenience sampling.In medical science, convenience sampling frequently entails choosing clinical cases or volunteers who are accessible nearby (such as at a hospital) or from a database of medical information.Convenience sampling is frequently employed in qualitative research in the social sciences and in education where it is practical to use which was before groups, including such students.Thus, probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.
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What is the value of the expression -9x2.2
Answers
Answer:
-1.8x^2
Step-by-step explanation:
The rate of change is
Answers
Answer:
-4
Step-by-step explanation:
Take two points and plug into the distance formula [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
We will use (-2, 17) for ([tex]x_{1} , y_{1}[/tex]) and (-1, 13) for ([tex]x_{2} , y_{2}[/tex])
[tex]\frac{13- 17}{-1- -2}[/tex] = [tex]\frac{-4}{1} = -4[/tex]
how often and for how long should meditation be practiced in order for a person to realize its benefits? multiple choice twice a week for 20 minutes at a time daily for several hours at a stretch once a month for two hours twice a day for 20 minutes
Answers
Twice a day for 20 minutes is the required time to realize that meditation practiced is beneficial for persons physical and mental health.
Meditation practiced helps person in different ways:
It helps to work on our physical and mental health.Sitting silently and reciting mantra meditation is called the transcendental Meditation technique.It helps to improve our mental health.Breathing mediation techniques helps us to improve our physical health.Twice a week is very less time and does not make consistency.
Incorrect option.
Several hours at a stretch is not possible for all individual and it is not practical .
Incorrect option.
Twice a day for 20 minutes is the best time and helps individual to practice meditation.
Therefore, Option C. twice a day for 20 minutes is the best time for mediation.
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Determine the domain of (g ∘ f)(x) if f (x) = x2 + 2x − 4 and g of x is equal to 1 over the quantity x plus 1 end quantity period
{x ∈ ℝ}
{x ∈ ℝ| x ≠ −1}
{x ∈ ℝ| x ≠ −3, 1}
{x ∈ ℝ| x ≠ −3, −1, 1}
Answers
The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.
Given that, f(x)=x²+2x-4 and g(x) =[tex]\frac{1}{(x+1)}[/tex].
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, (g·f)(x) can be determined as follows
(g·f)(x)=g(x)×f(x)
= [tex]\frac{1}{(x+1)} \times x^2+2x-4[/tex]
Find the domain by finding where the expression is defined.
Interval Notation:
(-∞,-1)∪(-1,∞)
Set-Builder Notation:
{x∈ℝ|x ≠ -1}
The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.
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You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets. Your friend finds $1 near your table and asks if it belongs with the ticket money. Do you think it does?
Answers
The 1 dollars found near the table by your friend is likely the money for the tickets.
How to find if the money belong to the ticket money?You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets.
let
x = number of individual ticket
y = number of couple tickets = 2x
Therefore, using equation,
2x(10) + 6x = 1075
2x + x = 195
Hence,
20x + 6x = 1075
3x = 195
x = 195 / 3
x = 65
Hence,
26x = 1075
26(65) = 1690
Therefore, the money on the table is the ticket money because the money is short of the amount of the tickets in dollars.
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Eliza bought a hat for $21. The regular price is %30. What percent of the regular price did she pay?
Answers
Answer:
27.3
Step-by-step explanation:
21 times 1.3 = 27.3 = original price
She paid 70% of the regular price of $30.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Eliza bought a hat for $21. The regular price is $30. The percentage will be calculated as,
Percentage = 21 / 30
Percentage = 0.7 x 100
Percentage = 70%
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HELP i need help asap
Answers
The inequality that is used to find the domain of the function would be B x - 3 ≥ 0
What is the domain of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The given function is f(x) = √x - 3
Here we have to find the inequality that is used to find the domain of the function.
Therefore, the function (x - 3) must be greater than or equal to 0
That is;
x - 3 ≥ 0
We will use the above inequality to find the domain of the function.
When we solve the above inequality, we get the domain of the function then;
x - 3≥0
Now add 3 on both sides, we get;
x - 3 + 3 ≥ 0 + 3
x ≥ 3
Therefore, the answer is x - 3 ≥ 0
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Mr. Miller weigh 180pound. If hi weight decreae by 10% how much i hi new weight?
Answers
In linear equation, 162 is his new weight .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Mr. Miller weigh = 180pound
10% decrease = 180 * 10/100
= 18
new weight = 180 - 18
= 162
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A quare i drawn on a grid. Two of it vertice are at (3,3) and (7,7) What i the perimeter of the quare?
Answers
Therefore the solution of this question is the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units
What is perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
Here,
The perimeter of the square drawn on the grid
The vertices given in the question are (3,3) & (7,7)
The length of the vertices given=[tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2}- y_{1})^{2} }[/tex]
Thus at vertices (3,3) & (7,7)
=>[tex]\sqrt{(7 -3)^{2} +(7-3)^{2} }[/tex]
=>4[tex]\sqrt{2}[/tex]
Therefore the perimeter of the square = 4a
thus,
=>4*4[tex]\sqrt{2}[/tex]
=>16[tex]\sqrt{2}[/tex] units
Therefore the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units
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In the triangle below, with right angle ZA, suppose that m B = (2x)° and mC = (5x-8)°.
Find the degree measure of each angle in the triangle.
B
(2x)
A
A
-
(x – 8)=
mZA
=
mZB =
mZC =
X
Answers
Answer:
m angle B = 27.54 degree
m angle C = 60.85 degree
Step-by-step explanation:
angle A is 90º so the other two angles must sum to 90º
2x+5x-8=90
7x-6=90
7x=96
x=13.77
therefore,
m angle B = 27.54 degree
m angle C = 60.85 degree
in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables.
true
false
Answers
The given statement " in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables. " is false.
In math chi square test means the process of determine if there is a significant relationship between two nominal (categorical) variables.
Here we have the statement, in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables.
And we need to find the statement is true or not.
According to the definition of chi square test, we know that it checks whether two variables are likely to be related or not.
Here we have counts for two categorical or nominal variables.
So, there is no large value comparision take palce.
Therefore, the statement is false.
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Find the measure of angle f given the information below. Please help!! (New Question )
Answers
The value of measure of ''angle f'' in the figure will be 46°.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
In the figure,
The value of angle a and e are;
⇒ a = 115°
⇒ e = 69°
Now,
Since, There are two parallel lines shown in figure.
Hence, We know by the definition of alternate angles of parallel lines,
⇒ ∠a = ∠f + ∠e
Here, We have to given that;
The angles are,
⇒ a = 115°
⇒ e = 69°
So, We get by substitute the value of angle a and e;
⇒ ∠a = ∠f + ∠e
⇒ 115° = ∠f + 69°
Subtract 69° both side, we get;
⇒ ∠f = 115° - 69°
⇒ ∠f = 46°
Thus, The value of measure of angle f;
⇒ ∠f = 46°
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A motel has 200 rooms. Those with a window view rents for $50 a night. Those without a window view rent for $40 a night. When the motel is 100 percent occupied the motel earns $8,500 for the night. How many rooms does the motel have that have a window view? How many rooms does the motel have that don't have a window view? Rooms with window view: Rooms without window view:
Answers
Answer:
Window view rooms is 50, no window view rooms is 150.
Step-by-step explanation:
I just multiplied the prices times random number of rooms until they added together to 8,500$. It was purely by chance that I discovered the answer ngl to you lol
can you please help me with my sisters homework ?
Answers
Answer:
Bro you require a protector to measure angle
Answer:
A. 45 degrees
B.90 degrees
Step-by-step explanation:
If you deposit $25,000 now at 6.5% compounded quarterly, how much will you have in 30 years?
Answers
A=25000•1.01625^120
A=25000•6.919378
A= $172984.45
In 30 years you will have $172984.45
Answer:
$172,984.44 (nearest cent)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $25,000r = 6.5% = 0.065n = 4 (quarterly)t = 30 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies A=25000\left(1+\dfrac{0.065}{4}\right)^{4 \cdot 30}[/tex]
[tex]\implies A=25000\left(1.01625\right)^{120}[/tex]
[tex]\implies A=25000\left(6.9193776...\right)[/tex]
[tex]\implies A=172984.4404[/tex]
Therefore, if you deposit $25,000 now at 6.5% compounded quarterly, you will have $172,984.44 (nearest cent) in 30 years.
Find The Cartesian Coordinates Of The Given Polar Coordinates. Then Plot The Point. (A) (2,Pi) (X,Y) = (---------) (B) (6, ?
Answers
The cartesian coordinates of the given polar coordinates are
(A) (2, π); (X, Y) = (-2, 0)
(B) (6, -2π/3); (X, Y) = (-3, -3√3)
How to convert polar coordinates into cartesian coordinates?The cartesian coordinates for the polar coordinates are calculated by the formulae,
x = rcosθ, and y = rsinθ
Where the polar coordinates are (r, θ).
Calculation:The cartesian coordinates for the given polar coordinates are as follows:
(A) (r, θ) = (2, π)
Then,
x = r cosθ = 2 cos(π) = 2(-1) = -2
y =r sinθ = 2 sin(π) = 2(0) = 0
Therefore, the cartesian coordiantes are (X, Y) = (-2, 0).
(B) (r, θ) = (6, -2π/3)
Then,
x = r cosθ = 6 cos(-2π/3) = 6(-1/2) = -3
y =r sinθ = 6 sin(-2π/3) = 6(-√3/2) = -3√3
Therefore, the cartesian coordinates are (X, Y) = (-3, -3√3)
The plot for the given polar coordinates on a polar grid is shown below:
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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 440 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.
Answers
In linear equation, 20x + 45y = 440 , y = 2x Where x is the number of small boxes sent and y is the number of large boxes sent.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let be x the number of small boxes sent and y the number of large boxes sent.
Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this
20x + 45y = 440
According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation
y = 2x
Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is
20x + 45y = 440
y = 2x
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There are 4,328 people at a football
game. There are 6 times as many
people at a baseball game. How many
people are at the baseball game?
4) 24,828
6) 24,968
7) 25,828
8) 25,968
Answers
The 3rd term in a geometric sequence is -18 and the 6th term is 9216.
Find the a) common ratio, b) the first term a1, and c) the 4th term a4 in this geometric sequence.
Answers
Answer: The common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.
Step-by-step explanation: The common ratio r of a geometric sequence is found by dividing the second term by the first term, and the nth term of the geometric sequence is given by a1 * r^(n-1), where a1 is the first term.
To find the common ratio r of this geometric sequence, we can use the fact that the 3rd term is -18 and the 6th term is 9216:
-18 = a1 * r^2
9216 = a1 * r^5
Dividing these two equations, we get:
-18/9216 = (a1 * r^2) / (a1 * r^5)
-18/9216 = r^-3
r = (-18/9216)^(-1/3)
Since r is the common ratio, it must be positive. Since (-18/9216)^(-1/3) is negative, we must take the positive root:
r = ((-18/9216)^(-1/3))^(1/3)
r = ((-18/9216)^(1/9))
r = (9216/-18)^(1/9)
r = (-512)^(1/9)
r = (-8)^(1/9)
r = (-2)^(2/9)
r = (-2)^(2/3)
r = (1/4)^(2/3)
r = 1/2
To find the first term a1, we can use the fact that the 3rd term is -18 and the common ratio is 1/2:
-18 = a1 * (1/2)^2
-18 = a1/4
a1 = -72
To find the 4th term a4, we can use the fact that the first term is -72 and the common ratio is 1/2:
a4 = (-72) * (1/2)^3
a4 = -9
Therefore, the common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.