The arithmetic sequence is A = 14 , 11 , 8 , 5 , ...
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic sequence be represented as A
Now , the equation will be
The first term of the AP is a₁ = 14
The common difference of the AP is d = -3
So , the second term of the AP is a₂ = a + d
a₂ = 14 - 3 = 11
The third term of the AP is a₃ = a + 2d
a₃ = 14 - ( 6 ) = 8
The fourth term of the AP is a₄ = a + 3d
a₄ = 14 - ( 9 ) = 5
Therefore , the value of A is A = 14 , 11 , 8 , 5 ...
Hence , the AP is solved
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Answer:
14, 11, 8, 5, . .
Step by-step explanation:
got it right on test
based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). which of the following statements is true?
90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch. Hence, the correct statement is option (d).
A confidence interval is a range of values that are expected to contain the true population parameter with a certain degree of confidence, usually expressed as a percentage. Here, a 90% confidence interval means that if we were to repeatedly take random samples of 50 students and compute a 90% confidence interval for each sample, we would expect that 90% of these intervals would contain the true mean amount of money that all students spend on lunch at this high school.
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The complete question is -
Based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). Which of the following statements is true?
(a) 90% of the time, the mean amount of money that all students spend on lunch at this high school will be between $3.45 and $4.15.
(b) 90% of all students spend between $3.45 and $4.15 on lunch at this high school.
(c) 90% of all random samples of 50 students obtained at this high school would result in a sample mean amount of money students spend on lunch between $3.45 and $4.15.
(d) 90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.
An artist invests in a mutual fund account paying 5% and $5000 more than four times as much in a mutual fund account paying 4%. Her total annual interest income from the investments is $1145. How much does she invest at each rate?
The artist invests $4500 in the 5% account and $23000 in the 4% account.
Let's call the amount invested in the 5% account x. Then, the amount invested in the 4% account is 4x + 5000.
The total annual interest income from the investments is 1145, so we can write an equation:
0.05x + 0.04(4x + 5000) = 1145
Expanding the second term:
0.05x + 0.04(4x) + 0.04(5000) = 1145
0.05x + 0.16x + 200 = 1145
0.21x + 200 = 1145
0.21x = 945
x = 4500
So the artist invests $4500 in the 5% account and $18000 + 5000 = $23000 in the 4% account.
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data from what length of time are represented on a climograph? view available hint(s)for part b data from what length of time are represented on a climograph? 30 years 300 years it varies from one climograph to another; there is no standard length of time. 30 days 30 months submit
Option b is the correct answer. It varies from one climograph to another; there is no standard length of time.
A climograph is a graphical representation of climate data that shows the average temperature and precipitation patterns over a certain period of time. The length of time represented on a climograph can vary and there is no set standard. It could be a few months, a year, several years, or even decades. It depends on the specific data and purpose of the climograph. Some climographs may show data from the last 30 years, while others might show data from the last 300 years. The important thing to remember is that the length of time represented on a climograph will vary and there is no set rule for how long it should be.
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The complete question is:
data from what length of time are represented on a climograph? view available hint(s)for part b data from what length of time are represented on a climograph?
a. 30 years 300 years
b. it varies from one climograph to another
c. there is no standard length of time.
d. 30 days 30 months submit
For the function defined here, find f(0), ƒ(2), and f(4) by using the graph below.
x² - 1
f(x) = {¹
-x+1
if
if
x < 2
x > 2
The values of the functions are f(0) = 2, f(2) = 0 and f(4) = -2
How to evaluate the piece-wise functionThe graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the first curve is a quadratic function,
Also, it has an open circle at x = 1
So, we have:
x² + 2 if x < 1
Next, we have a linear equation with a closed circle at x = 1
So we have:
y = -x + 2 for x ≥ 1
This means that
f(0) = 0^2 + 2 = 0f(2) = -2 + 2 = 0f(4) = -4 + 2 = -2Read more about piecewise functions at:
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let j, s, and k denote the propositions that jasmine, samir, and kanti attend, respectively. express the given conditions using logical connectives.
Jasmine (j) and Samir (s) will attend the event, while Kanti (k) will not. This can be expressed using the logical connective (∧) and its negation (¬).
j ∧ s ∧ ¬k
j - Jasmine attends
s - Samir attends
¬k - Kanti does not attend
∧ - Logical And operator
j ∧ s ∧ ¬k -
Jasmine (j) and Samir (s) will attend the event, while Kanti (k) will not. This can be expressed using the logical connective (∧) and its negation (¬). The resulting statement is j ∧ s ∧ ¬k. This statement means that Jasmine and Samir will attend the event, but Kanti will not. This statement can be read as "Jasmine and Samir attend and Kanti does not attend".The resulting statement is j ∧ s ∧ ¬k. This statement means that Jasmine and Samir will attend the event, but Kanti will not. This statement can be read as "Jasmine and Samir attend and Kanti does not attend".
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PLEASE HELP 10 Points
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{4(2y + 1)}\\\mathsf{= 4(2y) + 4(1)}\\\mathsf{= 8y + 4}\\\mathsf{\rightarrow 4y + 4y + 4}\\\mathsf{\rightarrow 2(4y + 2)}\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{Option\ A. \ 4y + 4y + 4}}\huge\checkmark\\\\\huge\boxed{\mathsf{Option\ B. \ 4y + 4y + 4}}\huge\checkmark\\\\\huge\boxed{\mathsf{Option\ E.\ 8y + 4}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Question in Screenshot
The functions for this problem are given as follows:
a) (f + g)(x) = x² - 16x + 43.
b) (f - g)(x) = x² - 8x + 29.
c) (fg)(x) = -4x³ + 71x² - 284x + 301.
d) (f/g)(x) = (x - 6)²/(7 - 4x), x different of 7/4.
How to obtain the functions?The functions in this problem are defined as follows:
f(x) = (x - 6)² = x² - 12x + 36.g(x) = 7 - 4x.Then the addition function, combining the like terms, is given as follows:
(f + g)(x) = x² - 12x + 36 + 7 - 4x = x² - 16x + 43.
The subtraction function, combining the like terms, is given as follows:
(f - g)(x) = x² - 12x + 36 - (7 - 4x) = x² - 12x + 36 - 7 + 4x = x² - 8x + 29.
The product is given as follows:
fg(x) = (x² - 16x + 43)(7 - 4x) = -4x³ + 71x² - 284x + 301.
(multiplying all the terms applying the associative property and then combining the like terms).
The quotient is given as follows:
(f/g)(x) = f(x)/g(x) = (x - 6)²/(7 - 4x), x different of 7/4.
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Change this radical to an algebraic expression with fractional exponents.
The required algebraic form of the given radical form ∛a is [tex]a^{1/3}[/tex].
What is an algebraic expression?The algebraic expression consists of constant and variable. eg x, y, z, etc.
Here,
Given expression,
= ∛a
since we know that, [tex]a^{1/n} = \sqrt[n]{a}[/tex]
So ∛a = [tex]a^{1/3}[/tex].
Thus, the required algebraic form of the given radical form ∛a is [tex]a^{1/3}[/tex].
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Graph the points A (1, 6) and B (9, 6). Find the
midpoint of AB. Find the distance of AB
Answer:
Step-by-step explanation:
Midpoint= x1-2/y1-y2
8/0
Midpoint = 0,0
s) determine which of the following subsets of p2 are subspaces of p2. you should use the subspace test from the lectures to show that a given subset is a subspace, or, if it is not a subspace, exhibit one of the axioms of a vector space that fails to be satisfi
To determine which of the following subsets of P2 are subspaces of P2, you should use the subspace test from the lectures.
For each subset, you need to check if it is closed under vector addition, closed under scalar multiplication, and contains the zero vector. If the subset satisfies all three conditions, then it is a subspace.
For example, the subset S = {2x2+3x+1, x2+3x+2} is a subspace of P2 because it is closed under vector addition (2x2+3x+1 + x2+3x+2 = 3x2+6x+3) and closed under scalar multiplication (2*(2x2+3x+1) = 4x2+6x+2).
Additionally, it contains the zero vector (0x2+0x+0). Therefore, it is a subspace of P2.
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Simplify: (4w³ - 4) + (2w³ + 6w + 9)
Bring the like terms together by rearranging the question4w³+2w³+6w+9-4Answer 6w³+6w+5
applied partial differential equations with fourier series and boundary value problems 5th edition solution
The 5th edition of Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by John D. Fenton covers a wide range of topics related to the use of Fourier series and boundary value problems to solve various partial differential equations.
The solution to the given differential equation is
[tex]$y(x) = \frac{-1}{2 \pi} \sin(4x)$.[/tex]
One example of a solution, to the ODE differential equation
[tex]$\frac{d^2y}{dx^2} + 4y = 0$[/tex]
with the boundary conditions
[tex]$y(0) = 0$[/tex] and [tex]$y(\pi) = 0$[/tex]
is given by the Fourier series
[tex]$y(x) = A \sin(2x) + B \cos(2x) + C \sin(4x) + D \cos(4x)$[/tex]
Where the constants A, B, C, and D are determined by the boundary conditions.
Using the boundary conditions, we find
[tex]$A = 0$[/tex] and [tex]$B = 0$[/tex]
[tex]$C = \frac{-1}{2 \pi}$[/tex] and [tex]$D = 0$[/tex]
Therefore, the solution to the given differential equation is
[tex]$y(x) = \frac{-1}{2 \pi} \sin(4x)$.[/tex]
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fill in the blank. a simple linear regression equation relates r and w as follows: the explanatory variable is___, and the dependent variable is___. the slope parameter is___, and the intercept parameter is___. when w is zero, r equals___. for each one unit increase in w, the change in r is___units.
w, r, the coefficient of w, the constant term in the equation, the intercept parameter, equal to the slope parameter in units are ans of fill in the blank respectively.
A simple linear regression equation is used to model the relationship between two variables, where one variable is the independent or explanatory variable and the other is the dependent or response variable. The equation has the form:
y = β0 + β1x,
where y is the dependent variable, x is the explanatory variable, β0 is the intercept parameter, and β1 is the slope parameter. The intercept parameter represents the value of y when x is zero, and the slope parameter represents the change in y for each one-unit change in x. In this problem, the explanatory variable is w, and the dependent variable is r. The slope and intercept parameters need to be estimated from the data to obtain the regression equation. The equation can be used to make predictions about the response variable given a certain value of the explanatory variable.
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first, use trigonometric identities to write 8cos4(4x) as an expresion involving only sines and cosines to the first power.
8cos(4x) can be written as an expression involving only sines and cosines to the first power as 8 - 16sin^2(2x)
The expression 8cos(4x) can be written in terms of sines and cosines to the first power using the double angle identity:
cos(2θ) = 1 - 2sin^2(θ)
First, we can rewrite 4x as 2(2x), and then apply the double angle identity:
cos(4x) = cos(2(2x)) = 1 - 2sin^2(2x)
Next, we can use the identity:
cos(θ) = cos(-θ)
to rewrite cos(2x) as cos(-2x):
cos(4x) = 1 - 2sin^2(2x) = 1 - 2sin^2(-2x)
Finally, we can multiply both sides by 8:
8cos(4x) = 8(1 - 2sin^2(-2x)) = 8 - 16sin^2(-2x)
And since sin(-θ) = -sin(θ), we can write this as:
8cos(4x) = 8 - 16sin^2(2x)
So, 8cos(4x) can be written as an expression involving only sines and cosines to the first power as:
8 - 16sin^2(2x)
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Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible
quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest
he earns during t = 0 to t = 1. Find the exact value of R.
Let X be the amount Mr Saver invests at t = 0.
The interest he earns during t = 0 to t = 1 can be expressed as:
Interest = X * R * (1/4)
The interest he earns during t = 0.5 to t = 1.5 can be expressed as:
Interest = X * R * (3/4)
Since the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1, we can set up the following equation:
X * R * (3/4) = 1.0816 * (X * R * (1/4))
Solving for R, we get:
R = 4.3264 Therefore, the exact value of R
Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2.
This system of equations models the scenario:
4x + 2y ≤ 16
x + y ≥ 4
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
The graph is attached, the point (2, 3) included in the solution area for the system and (4, 0) is the solution of area for the system.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings.
Each cupcake costs $4, and each piece of fudge costs $2.
4x + 2y ≤ 16
x + y ≥ 4
The graph for system of inequalities is attached.
The point (2, 3) included in the solution area for the system
4(2)+2(3)≤ 16
14≤ 16 is true.
2+3≥ 4 is true.
Point (2, 3) included in the solution area for the system.
From the graph (4, 0) is the solution of area for the system.
Hence, the graph is attached, the point (2, 3) included in the solution area for the system and (4, 0) is the solution of area for the system.
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_ / 6 < 9/6 what is the missing number?
The complete expression is 8/6 < 9/6
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
_ / 6 < 9/6
Express properly
So, we have the following representation
_ / 6 < 9/6
Represent the blank with x
x / 6 < 9/6
Multiply both sides of the expression by 6
So, we have the following representation
x < 9
This means that x is any value less than 9
An instance is 8
Hence, the solution to the expression is 8/6 < 9/6
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Try This question out and I’ll give you brainliest
The horizontal distance rounded to the nearest hundredth will ve 139.5 feet. Then the correct option is A.
What are the roots of the equation?Let the equation be ax² + bx + c = 0. Then the roots of the equation will be given as,
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
Paulo hit a baseball. The path of the ball was h = - 0.01d² + 1.37d + 3.5.
Then the horizontal distance is given as,
h = 0
- 0.01d² + 1.37d + 3.5 = 0
0.01d² - 1.37d - 3.5 = 0
Solve the equation by formula, then we have
d = [-(-1.37) ± √{(-1.37)² - 4 × 0.01 × (-3.5)}] / (2 × 0.01)
d = (1.37 ± 1.42) / 0.02
For the plus sign, then we have
d = 2.79 / 0.02
d = 139.5 feet
The horizontal distance rounded to the nearest hundredth will ve 139.5 feet. Then the correct option is A.
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Jim has gotten scores of 78 and 73 on his first two tests. What score must he get on his third test to
keep an average of 94 or greater? Write your answer as an interval.
The range of score Jim must get to have an average score of 94 or more is x≥ 131
What is inequality?inequality, In mathematics is a statement of an order relationship with greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Average is the sum of items divided by the number of items.
Represent the theirs score by x
(78+73+x)/3 ≥ 94
151+x ≥ 94×3
151 + x ≥ 282
x ≥ 282-151
x≥ 131
therefore for Jim to get an average greater than 94, his third score must be greater than 131
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Circles C 1 ,C 2 ,C 3 have their centres at (0,0),(12,0),(24,0) and have radii 1,2 and 4 respectively. Line t 1 is a common internal tangent to C 1 and C 2 and has a positive slope and line t 2 is a common internal tangent to C 2 and C 3 and has a negative slope. Given that lines t 1 and t 2 intersect at (x,y) and that x=p−q√r, where p,q and r are positive integers and r is not divisible by the square of any prime, find p+q+r.a.P+Q+R=26b.P+Q+R=24c.P+Q+R=28d.P+Q+R=27
The sum of p, q, and r is 27.
The point of intersection of the lines t1 and t2, (x,y), can be found by using the equation of the lines. The equation of t1 is y=mx+c, where m is the slope, and c is the y-intercept. The equation of t2 is y=mx+c, where m is the slope, and c is the y-intercept.
The equations of t1 and t2 can be written as y= 1/2 x + 1 and y= -1/4 x + 7/2 respectively.
By setting the two equations equal to each other, we can find the x-coordinate of the point of intersection (x,y).
x=2 - 7/4 =4/4 - 7/4 = -3/4
Since x=p−q√r, we can write -3/4 = p−q√r.
Rearranging this equation, we get p+q+r= 4/3 + 7/3 + 4/3 = 27/3 = 9.
Therefore, P+Q+R=27.
Therefore, the sum of p, q, and r is 27.
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write a multiplication equation that represents this model
The multiplication equation represented by the diagram is:
3*2 = 6
Which is the multiplication represented by the model?On the model we can see a diagram, in that diagram there are:
2 red rectangles.
3 purple rectangles
6 blue rectangles.
We can assume that we are taking the product between the red ones and the purple ones, then we can write:
3*2 = 6
That is a true equation, so that is the multiplication equation represented by the model.
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Solve for the 2 problems below, show your work and submit the answers.
In the isosceles triangle, the value of x for the first figure is 15
for the second figure,
x = 5the missing angle is 110How to find the value of xThe value of x is solved using the knowledge of isosceles triangle
An isosceles triangle has the base angles equal hence
2x - 5 = 35
2x = 35 - 5
2x = 30
x = 15
Second figure
7x = 35
x = 5
let the angle at the peak be p
35 + 35 + p = 180 (sum of angles in a triangle)
70 + p = 180
p = 180 - 70
p = 110
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ank the following functions in increasing order of (asymptotic) magnitude dragged and dropped options will be automatically saved. for keyboard navigation...show more press space or enter to grab [math] log {3} n [/math] press space or enter to grab [math] n log (3 n) [/math] press space or enter to grab [math] 3 n [/math] press space or enter to grab [math] n^{3} [/math] press space or enter to grab [math] (3!)^{3} [/math] press space or enter to grab [math] 3^{n} [/math]
The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n.
The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n. This means that the function with the smallest asymptotic magnitude is (3!)3, while the function with the largest asymptotic magnitude is 3n.
To confirm this, let's calculate the growth rate of each function. The growth rate of (3!)3 is 3!3 ≈ 216, which is less than the growth rate of 3n (3n) = 3n, which is greater than the growth rate of n log(3n) (n log3n) = n log3n, which is greater than the growth rate of n3 (n3) = n3, which is greater than the growth rate of 3n (3n) = 3n, which is greater than the growth rate of 3n (3n) = 3n.
Therefore, we can conclude that the order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n.
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Answer:The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n
Step-by-step explanation:
please someone help me quick
Answer:
Top one is (SAS) Middle one is (AAS) Bottom one is (AAA)
Step-by-step explanation:
I hope these were helpful.
Solve.
4 There are 42 tubes of oil paint on trays. Each tray
holds 6 tubes. How many trays of tubes are there?
Show your work.
7
Answer: 7
Step-by-step explanation:
Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.
Please help me, it would be helpfull
Answer:
A:[tex]y = 4x + 3[/tex]
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A water park keeps track of the number of times each visitor goes down water slides during their visit . The data shows the number of times 12 visitors went down a water slide.
4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11, 1
Create a histogram of this data.
To create a histogram, hover over each age range on the x-axis. Then click and drag up to plot the data.
Histogram of given data is attached below.
What is histogram?A histogram is a graphical representation of data points organized into user-specified ranges.
Given,
Data shows the number of times, 12 visitors went down a water slide.
4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11, 1
Histogram can be drawn as below,
Hence, following is the histogram of given data.
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a restaurant offers delivery for pizzas. The total cost includes $11 per pizza and the delivery fee. A delivery of 5 pizzas costs $58.
Write an equation to represent the total cost, y for x number of pizzas. Use your wquation to find the cost of delivery of 80 pizzas.
Answer:
y=883
Step-by-step explanation:
The total cost includes $11 per pizza and the delivery fee. A delivery of 5 pizzas costs $58.
11 (dollars per pizza) x 5 (pizzas were delivered) = 55 dollars
58 (total cost) - 55 (total cost for pizza) = 3 (fee)
11x+3=y (Equation)
input the 80 pizzas to the equation
11(80)+3=y
y= 883
Hope this helps! I took a similar question 3 years ago! =)
7. Higher Order Thinking A bagel is cut
into same-size pieces. Some
friends share the bagel.
Each friend gets one piece.
How many friends share
the bagel?
friends
The number of friends sharing the bagel will be n.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A bagel is cut into same-size pieces. Some friends share the bagel. Each friend gets one piece.
Let the same size pieces of the bagel be 1/n. Then the number of friends who share the bagel is given as,
⇒ 1 / (1/n)
⇒ 1 x n / 1
⇒ n
The number of friends sharing the bagel will be n.
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8) Mrs. Smith drove 20 miles at a speed of 55 mph. She then drove 40 miles at a spe)ed of 60 mph. How
far did Mrs. Smith drive?
The total distance travelled by Mrs. Smith was 60 miles
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Speed is the ratio of the total distance travelled to total time taken. It is given by:
Speed = distance / time
Mrs. Smith drove 20 miles at a speed of 55 mph. She then drove 40 miles at a speed of 60 mph. Hence:
Total distance = 20 miles + 40 miles = 60 miles
The total distance travelled was 60 miles
Find out more on equation at: https://brainly.com/question/2972832
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