Answer:
[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]
Step-by-step explanation:
⭐What is the formula of a geometric sequence/progression?
[tex]a_n = a_1+1(d)^{n-1}[/tex][tex]a_1[/tex] is the first term of the geometric sequence[tex]d[/tex] is the common ratio (the number each consecutive term gets multiplied by) of the geometric sequence[tex]n[/tex] is the number term you want to findWe are given the geometric sequence.
Thus, we need to find the first term and the common ratio, and substitute those values into the geometric sequence formula.
The first term is [tex]\frac{1}{6}[/tex]
⭐How do we find the common ratio?
divide one term by another termmake sure both terms are consecutive of each otherI am choosing term 1 and term 2, but you can choose any other 2 terms that are consecutive.
term 1 = [tex]\frac{1}{6}[/tex]
term 2 = [tex]1[/tex]
[tex]\frac{term2}{term1} = \frac{1}{\frac{1}{6}}[/tex]
[tex]\frac{term2}{term1} = 6[/tex]
∴ The common ratio of this sequence is 6.
Now, substitute these values (common ratio & first term) into the geometric sequence equation.
[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]
Alexa is trying to pick out an outfit for the first day of school. She can choose from 8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes. How many different outfits does Alexa have to choose from?
The number of different outfits is 576
How to determine the number of different outfits?From the question, we have the following parameters that can be used in our computation:
8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes
The number of different outfits is the products of the count of each apparel
This is represented as
Different outfits = Pants * T-shirts * Sweaters or hoodies * Pairs of shoes
Substitute the known values in the above equation
Different outfits = 8 * 6 * 6 * 2
Evaluate
Different outfits = 576
Hence, there are 576 different outfits
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A box is dragged without acceleration in a straight-line path across a level surface by a force of 100 n. What is the frictional force between the box and the surface?.
The frictional force between the box and the surface is 100 newtons .
Since the body being dragged across the surface is not accelerating, the acceleration of the body is 0m/s².
From Newtons second law of motion, F = ma where;
F is the sum of the forces acting on the body
m is the mass of the body
a is the acceleration
If the box is dragged along a straight line by a force of 100 N, its moving force (Fm) is 100 N and the frictional force (Ff) will act opposite to this force.
Resultant force acting on the box along the horizontal will be Fm+(-Ff)
Therefore;
Fm+(-Ff) = ma
Fm-Ff = ma
Since a = 0m/s²
Fm-Ff = m(0)
Fm-Ff = 0
Fm = Ff
This shows that for a static body, the moving force acting on the body will be the same as the frictional force. Since Fm = 100 N
Frictional force (Ff) = 100 N
Therefore, the frictional force between the box and the surface is 100 N
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a number m is either less than 2 or greater than 9
What is the answer for 2x 3y 12?
Linear equations are one-degree equations. So, the two solutions of the equation is (0,-4)(6,0).
How do one express the standard form of a linear equation?It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0. A linear equation has the following standard form: ax + by + c = 0.
Here, variables are x and y and constants a, b, and c are used. Also, a ≠ 0, and b ≠ 0.
We can find the solution of the linear equation by putting x = 0 and y = 0 so that two points form which are the solution of the linear equation,
Put x = 0 in the linear equation 2x - 3y = 12,
2 × (0) - 3y = 12
or, - 3y = 12
or, y = -4
The points is (0,-4)
Put y = 0 in the linear equation 2x - 3y = 12,
2x - 3 × (0) = 12
or, 2x = 12
or, x = 6
The points is (6,0)
Therefore, the two solutions of the equation is (0,-4)(6,0)
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The complete question is as follows:
What is the answer for 2x - 3y = 12?
What is the coefficient of y2 in the expression 3y2 4x?
The coeficient of y² in the expression is the number 3
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
3y² + 4x
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.
3 is the coefficient of y²
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Please help !!!!!???
The height of Dubai fountain is 500 feet tall.
Define basic arithmetic.The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics. The Greek term "arithmos," which means "numbers," is where the word "arithmetic" originates. Arithmetic is one of the oldest and most basic concepts in mathematics. It deals with numbers and the basic operations (addition, subtraction, multiplication, and division) that can be carried out on them.
Given
The Burj Khalifa in Dubai is the tallest building in the world, at 2,717 feet.
Burj Khalifa is 217 feet taller
Height of Dubai fountain
Subtracting
2717 - 217
2500
5 times the height
Divide by 5,
2500/5
500
The height of Dubai fountain is 500 feet tall.
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A covered Bridge is 8 yards long. In a photograph for sale at a gallery The Bridge is 5/12 foot-long which statements are true?
1. One yard of the covered Bridge is represented by 1.6 inches in the photograph
2. One inch on the photograph represents 1.6 yards of the real bridge.
3. A tree that is 3 inches tall in the photograph is 4.8 yards tall.
4. The people walking over the bridge are about 2.5 inches tall in the photograph.
5. A river that is 12 yards wide is 7.5 inches wide in the photograph.
(PLEASE EXPLAIN)
Answer:
2. One inch on the photograph represents 1.6 yards of the real bridge.
Step-by-step explanation:
1 yd = 36 in.
8 yd = 36 in./yd × 8 yd = 288 in
1 ft = 12 in.
5/12 ft × 12 in./ft = 5 in.
5 in. in the picture equals 288 inches real.
1 in. in the picture equals 57.6 inches real.
57.6 in. × (1 yd)/(36 in.) = 1.6 yd
1 in. in the picture equals 1.6 yd real
Answer:
2. One inch on the photograph represents 1.6 yards of the real bridge.
How do you find the duplicate number on a given integer array in Python?
The duplicate number on a given integer array in Python can be found through two loops.
How do you find the duplicate number on a given integer array in Python?We need to print the duplicate elements present in the array. This can be done through two loops. The first loop will select an element and the second loop will iteration through the array by comparing the selected element with other elements. If a match is found, print the duplicate element.
ALGORITHM:
STEP 1: Declare and initialize an array.
STEP 2: Duplicate elements can be found using two loops. The outer loop will iterate through the array from 0 to length of the array. The outer loop will select an element. The inner loop will be used to compare the selected element with the rest of the elements of the array.
STEP 3: If a match is found which means the duplicate element is found then, display the element.
PYTHON PROGRAM:
#Initialize array
arr = [ ];
print("Duplicate elements in given array: ");
#Searches for duplicate element
for i in range(0, len(arr)):
for j in range(i+1, len(arr)):
if(arr[i] == arr[j]):
print(arr[j]);
The duplicate number on a given integer array in Python can be found through two loops.
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5 ≤ y + 2 ≤ 11 find the compound inequality
Answer:jkd
Step-by-step explanation:
d
What is the relationship between a scalene triangle and
the location of its centroid? Explain.
O A. The centroid will always be inside the scalene
triangle, since the centroid is always inside
any type of triangle.
O
O
O
B. The centroid will always be outside the
scalene triangle, since the centroid is always
outside any type of triangle.
C.
The centroid will always be on the scalene
triangle, since the centroid is always on a
triangle with no congruent side lengths.
D.
The centroid will be inside, on, or outside the
scalene triangle, depending on whether it is
acute, right, or obtuse, respectively. The
number of congruent sides does not affect
the location of the centroid.
The relationship between a scalene triangle and the location of its centroid is; A: The centroid will always be inside the scalene
triangle, since the centroid is always inside any type of triangle.
What is the location of the centroid of the triangle?A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures.
Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent.
Now, a centroid of a triangle is defined as the point formed by the intersection of the medians of the triangle. Now, the medians of a triangle always lie within a triangle. This means that their intersection point which is the centroid of a triangle always lies inside a triangle.
Thus, the centroid of the scalene triangle can be concluded to always lie inside the triangle.
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Is physics science hard?
Yes, it is hard but with a lot of practice and putting effort one can also find it easy.
Why physics is hard?Physics requires the ability to solve problems, which can only be acquired via practice. In addition to these difficult ideas, there are theoretical concepts, mathematical calculations, and laboratory experiments.
How to deal with physics?It is better to comprehend the derivations than to memorise the formulas. Making a mess of several formulas will just increase your anxiety over the topic. Instead, if you strive to comprehend where they originate, you will begin to appreciate physics and its applications.
Physics is a difficult topic since it combines science and arithmetic, which may be challenging for the best of us. Nevertheless, despite how difficult it is, you can achieve if you follow a few simple guidelines and put yourself through some practice.
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megan wants to test her assumption on the amount of sleep students are getting. she decides to focus her efforts on examining if students are getting less than eight hours of sleep. what should megan state for the null hypothesis and alternative hypothesis?
Your research question can also be answered by the alternative hypothesis (Ha). The populace, according to the assertion, is affected.
What is an alternative hypothesis?Your alternate theory and research hypothesis are frequently same. It is the assertion that you anticipate or hope will be accurate, to put it another way.The complementary idea to the null hypothesis is the alternative theory. The extensive nature of the null and alternative hypotheses ensures that they account for every scenario. As only one of them may be true at once, they are also mutually exclusive.When writing a research paper or thesis, use caution when describing the findings of a statistical test. When the null hypothesis is rejected, the alternative hypothesis is said to be supported. Conversely, if you are unable to disprove the null hypothesis, you can conclude that the alternative hypothesis is unsupported. Never assert that a theory has been supported or refuted.Alternative hypotheses frequently make use of words like "an effect," "a difference," or "a relationship." A mathematical inequality (often, but occasionally or >) is always included in alternative hypotheses. The formulation of an alternative hypothesis can be expressed in a variety of ways, just like null hypotheses.To Learn more About alternative hypothesis refer to:
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How do you tell if a function is positive or negative on a graph?
Answer:
You can tell if a function is positive or negative by checking the Y values. If all the Y values are above the x-axis it should be positive, and if the all y values are below the x-axis the function should be negative.
Good luck!
Please someone help me with this!
A projectile is fired from the ground at an angle of 30 degrees above the horizon with an initial velocity of 960 ft/sec. If the height as a function of time t is given by h(t)=480t-16t^2, find,
The time when the projectile hits the ground
The maximum height
I think
h(t)=480t–16t^2
Max height is the vertex of the parabola at t = -b/2a
t = -480/-32 = 15 seconds
--> h(15)
The population of a city has decreased by 35% since it was last measured. If the current population is 20,800, what was the previous population?
help pls
The previous population of the city was 32,000.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The current population of the city = 20,800.
Let the previous population was 100%.
Since, The population of the city decreased by 35%,
So, the current population of the city = 100 - 35 = 65%
According to given condition,
65 % = 20800
1 % = 20800 / 65
1 % = 320
100% = 320 x 100
= 32,000
Hence, the initial population was 32,000.
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Fill in the blanks to complete the proofs
Answer:
Look at the image I attached to my response.
Step-by-step explanation:
For proof #3, I did it according to the way I was taught how to do proofs in my state/school, so what you wrote could be correct.
jksjsisks 78i2o
[tex]32. \frac{33}{31?} [/tex]
Answer:
34.064516129
Step-by-step explanation:
[tex]32 \times \frac{33}{31} = \frac{1056}{31} [/tex]
[tex] = 34.064516129[/tex]
i hope this helps
Choose if each statement is True or False. {(2, 2), (3, 2), (4, 2), (6, 2)} is a function: {(-1, 5), (0, 8), (3, 12), (6, 21)} is a function: 5 -10 0 -5 15 -10- 5 0 -5 -10+ 5 5 10 is a function: 10 15 is a function:
Answer:
True False True False
Step-by-step explanation:
pls help me I’m confused i’ll give brainliest
Answer:
I would say the length is near 8
Answer:
In the given right angled triangle,
base(b)=2 mm and perpendicular(p)=7mm
hypotenuse (h)=?
By using Pythagoras theorem,
h²=p²+b²
or,h²=(7)²+(2)²
or,h²=49+4
or,h²=53
or,h=√53
or,h=7.28
The length of unknown side is 7.28 mm and it is not determined exactly.
The length 7.28 mm is between integers 7 and 8 and it is more closer to 7.
Need help (100 easy points)
Answer:
Step-by-step explanation:
Is Root 3x² 2x a polynomial?
Yes, √3x² - 2x is a polynomial.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
√3x² - 2x
This is in the form of ax² - bx
This is a polynomial with degree 2.
Thus,
√3x² - 2x is a polynomial.
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Which quadratic function has one real solution
0=2(x+7)(x-5)
0=2/3(x-3)(x-3)
0=2.4(x-2)(x+2)
0=1/2(x-2)(x-1)
Answer: [tex]0=\frac{2}{3}(x-3)(x-3)[/tex]
Step-by-step explanation:
The roots are [tex]-7[/tex] and [tex]5[/tex].There is one only distinct root, which is [tex]3[/tex].The roots are [tex]\pm 2[/tex].The roots are [tex]1[/tex] and [tex]2[/tex].How do you find the Y intercept x intercepts vertical asymptotes and horizontal asymptotes in a rational function?
To find the x-intercept of a rational function we put y=0 in the given and find the corresponding value of x.To find the y-intercept of a rational function we put x=0 in the function and the value of y.
what are intercepts?The x-intercept is the point where a line crosses the x-axis.At this point y=0 and the y-intercepts is the point where a line crosses the y-axis.At this point x=0
It is point where the graph of the rational function intersects the x-axis or y-axis.
How do we find vertical and horizontal asymptotes of rational function?For Horzontal asymptotes
The horizontal asmptotes of a rational function can be determined by looking at the degree of the numerator and denominator.if Nis the degree of numerator and Dis the degree of denominator.Then N<D
So horizontal asymtote is y=0
To finding horizontal asymptotes we can just focus on degree of numerator and denominator.
For vertical asymptotes
vertical asymptotes occur where the denominator of a rational function approaches zero.A rational function cannot cross a vertical asymptotes because it would be dividing by zero. we set denomintor to zero and solve value of x.The values of x are vertical asymptotes.
Hence we can find easily horizontal and vertical asymptotes of rational function.
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What doe the expreion 3x4y repreent?
A. The total number of baket of tomatoe and bag of onion the cutomer purchaed
B. The cot per baket for the tomatoe plu the cot per bag for the onion
C. The total cot, in dollar, for the cutomer’ purchae
D. The number of baket of tomatoe and the number of bag of onion that can be purchaed for $7
The expression 3x+4y represents 3 bags of $3 tomatoes and 4 bags of $4 onions.
What is an expression?
The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of logical grammar, such as the operation order.
Given that a basket of tomatoes costs $3, whereas an onion package costs $4. A customer buys y sacks of onions and x baskets of tomatoes.
Three bags of $3 tomatoes and four bags of $4 onions are denoted by the equation 3x+4y.
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Which system of equations can be used to find the roots of the equation 4x 5 12x?
The system of equations that can be used to find the roots of the equation 4x 5 12x is:x = -5/8
1. Set up the equation: 4x - 12x = 5
2. Simplify the equation on the left side: -8x = 5
3. Solve for x: x = -5/8
To find the roots of the equation 4x - 12x = 5, we must first set up the equation. On the left side of the equation, we can simplify it to -8x = 5. Then, we can solve for x by dividing both sides by -8, giving us x = -5/8. This is the solution to the system of equations, and the root of the original equation.
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What are the roots of 3x² 5x 2 0?
The equation 3x² + 5x + 2 = 0 has two solutions, x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.
To solve 3x² + 5x + 2 = 0, we must first find the roots of the equation. To do this, we can use the quadratic formula to solve for the two roots. The quadratic formula is x = [-b ± √(b² - 4ac)]/2a, where a, b, and c are the coefficients of the equation. To apply this to our equation, we have a = 3, b = 5, and c = 2, so the formula becomes x = [-5 ± √(5² - 4(3)(2))]/2(3). Simplifying this equation gives us x = [-5 ± √29]/6. The two solutions of this equation are x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.
x = [-5 ± √29]/6
x = [-5 + √29]/6 = -2
x = [-5 - √29]/6 = -1/3
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lins family had completed 60% of a trip. they have traveled 30 miles. how many miles is the trip
Lin's family make a trip of length 50 miles.
What is a trip?
People move between far-off geographic regions when they travel. Travel can be done with or without luggage, on foot, by bicycle, car, rail, boat, airline, ship, or by another mode of transportation. It can also be one way or round trip.
Given that Lin's family had completed 60% of a trip.
Thus they have to travel (100 - 60)% = 40% of the trip.
Also given that, they have traveled 30 miles..
Therefore,
60% of the trip is equal to 30 miles.
1% of the trip is equal to 30/60% miles.
100% the trip is equal to (30× 100%)/60% miles.
= 50 miles.
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Find the product:
[2 1 0] x [1 -1 2] = [a b c]
[-1 -2 1]
[0 1 1]
Step-by-step explanation:
the multiplication result is found by row×column multiplications.
1st row × 1st column = a
2×1 + 1×-1 + 0×0 = 2 - 1 = 1 = a
1st row × 2nd column = b
2×-1 + 1×-2 + 0×1 = -2 + -2 = -4 = b
1st row × 3rd column = c
2×2 + 1×1 + 0×1 = 4 + 1 = 5 = c
Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate.) / e4x dx 19 e8x e4x C 8 19 e4x 19 4x 19 + C 19 19 19 C 19 + C 19 19 + C 8 19 4x 19 0/1 points | Previous Answers SCalcET8 7.6.023. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 33 sec5(x) dx X Use the Table of Integrals to evaluate the integral. 6х4е-x dx
The integration is as follow
[tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex] = 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C[tex]\int\limits {33 sec^5 (x)} \, dx[/tex] = 33/4 tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + CWhat is Integration?Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.
Given:
first, [tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex]
= [tex]\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx[/tex]
let [tex]e^{4x}[/tex] = z
4[tex]e^{4x}[/tex] dx = dz
= 1/4 [tex]\int\limits {dz / \sqrt{19} ^2 -z^2} \,[/tex]
= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C
= 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C
Second,
[tex]\int\limits {33 sec^5 (x)} \, dx[/tex]
= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]
= 33/4 tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]
= 33/4 tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C
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Given the system: 2x + 3y = 12 2x - y = 4 What is the value of x + y?
The value of x + y is 5.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given linear equations are
2x + 3y = 12 ....(i)
2x - y = 4 ......(ii)
To solve the give linear equation, using elimination method.
Subtract equation (ii) from equation (i)
2x + 3y = 12
2x - y = 4
(-) (+) (-)
________
4y = 8
Divide both sides by 4:
y = 2
Putting y = 2 in equation (ii)
2x - 2 = 4
Add 2 with both sides:
2x = 6
Divide both sides by 2
x = 3
Putting x = 3 and y =2 in x + y:
x + y = 3 + 2 =5
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