The ratio of the area of the smaller circle to the area of the larger circle is 1/2.
How to calculate the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
From the information, the square is inscribed in a circle and then a smaller circle is inscribed in the square.
Let the radius of smaller circle be 2r, then length of side of larger square is ✓2r and the length of side of smaller square is
The ratio of area of smaller square to larger square is:
= 4r² / 4(✓2r)²
= 1/2
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let x be a normal random variable with a mean of 2.69 and a standard deviation of 4.76. a)calculate the corresponding standardized value (z) for the point x
The standardized value for x = 2.69 is 0.
The standardized value (z) is given by:
z = (x - mean) / standard deviation
where x is the value to be standardized, mean is the normal distribution's mean, and standard deviation is the normal distribution's standard deviation.
So, for x = 2.69, with a mean of 2.69 and a standard deviation of 4.76, the standardized value (z) is:
z = (2.69 - 2.69) / 4.76 = 0
As a result, the standardized value for x = 2.69 is 0.
Standard deviation is a measure of the spread or dispersion of a set of data values around their mean (average). It provides a quantitative indication of how far apart each data value is from the mean and from each other. A low standard deviation means that the data values are close to the mean, while a high standard deviation indicates that the data values are more spread out.
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(2 points) a ball is thrown into the air by a baby alien on a planet in the system of alpha centauri with a velocity of 24 ft/s. its height in feet after t seconds is given by y
A) The average velocity for the time period [1, 1.01] is equals to the -22.23 ft/s.
ii) The average velocity for the time period [1, 1.005] is equals to -22.115 ft/s.
iii) The average velocity for the time period [1, 1.001] is equals to -22.023 ft/s.
B) The estimate value of the instanteneous velocity when t = 1s is equals to -22 ft/s.
The average velocity over an interval [a,b] for a defined position function f(t) can be displayed by the difference quotient {f(b)-f(a)}/{b-a}. When these two points come very close to each other and at any point both of them appear almost the same point then the average velocity becomes instantaneous velocity at that time, which is also the derivative of the function at that point. We have, baby alien throw a ball into the air with a velocity of 24 ft/s on planet. The height in feet or
the displacement relation is defined as ,
y (t) = 24t - 23t².
where, y--> displacement/height
t --> time
Initial time , to = 1 sec
Therefore, the velocity will be
dy/dt = v(t) = 24 - 46t
A) The average velocity on an interval [a,b] is
Vₐᵥ = { y( b) - y(a) }/(b - a)
Now, see the intervals ,
beginning when t = 1s and lasting t = 0.01s, [1, 1.01]Vₐᵥ = {y( 1.01) - y(1)}/(1.01 - 1)
= {24(1.01) - 23(1.01)² - 24×1 + 23× 1 }/0.01
= {24.24 - 24 - 23.4623 + 23}/0.01
= - 22.23 ft/s
beginning when t = 1s and lasting t = 0.005s, [1, 1.005]Vₐᵥ = {y( 1.005) - y(1)}/(1.005 - 1)
= {24(1.005) - 23(1.005)² - 24×1 + 23× 1 }/0.005
= -22.115 ft/s
beginning when t = 1s and lasting t = 0.001s, [1, 1.001]Vₐᵥ = {y( 1.001) - y(1)}/(1.001 - 1)
= {24(1.001) - 23(1.001)² - 24×1 + 23× 1 }/0.001 = { 24.024 - 24 + 23 - 23(1.001)²}/0.001 = - 22.023 ft/s
B) The instanteneous velocity is defined as V (t) = dy/dt = 24 - 46t
At t = 1 s then V(t) = 24 - 46(1) = 24 - 46
=> V = - 22 ft/s
Hence, instanteneous velocity is - 22 ft/s.
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Complete question:
A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 24 ft/s. Its height in feet after t seconds is given by y = 24t - 23t².
A. Find the average velocity for the time period beginning when t=1 and lasting
.01 s:
.005 s:
.001 s:
NOTE: For the above answers, you may have to enter 2 or 3 significant digits if you are using a calculator.
B. Estimate the instanteneous velocity when t=1.
the ta will get you started on the following exercises. complete independently and submit as le 1.1 on this assignment page. 1. given the following data, develop a python program that uses a linear regression to model the relationship: angle
Here's a sample code in Python that uses the scikit-learn library to perform linear regression on the given data:
import numpy as np
from sklearn.linear_model import LinearRegression
# Angle data
angle = np.array([0, 30, 45, 60, 90]).reshape(-1, 1)
# Modeling the relationship using Linear Regression
reg = LinearRegression().fit(angle, angle)
# Predicting the values
angle_pred = reg.predict(angle)
print("Predicted values: ", angle_pred)
The task is to develop a Python program that uses a linear regression model to predict the relationship between a dependent variable (angle) and an independent variable (in this case, the angle itself).
The code above models a trivial relationship between the angle and itself. This is just a simple example to show how linear regression can be performed in Python. Please make sure to use appropriate data and fit the model based on the problem statement.
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What value of k makes the statement true?
x^ky^4(2x^3 + 7x^2y^4) = 2x^4y^4 + 7x^3y^8
The value of k that makes the statement true is k = 4.
What is value?Value is relative worth,merit of importance of something.if can refer to an intangible concept such as a person principal of a tangible object such as a rare coin.value vary widely across cultures, society and individual and can even vary within the same individual over time.
To show this, we can expand both sides of the equation and compare the terms. The left side of the equation becomes:
x⁴y⁸ + 7x³y¹²
The right side of the equation becomes:
2x⁴y⁸ + 7x³y¹²
Since both sides of the equation are identical, we can conclude that the value of k that makes the statement true is k = 4.
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Multiply 6 * 5/8. Simplify the answer and express it as a mixed number.
Answer:
[tex]3 \frac{3}{4} [/tex]
Answer:
3.75 or 15/4
Step-by-step explanation:
3⋅5 = 15
8 divided by 2 = 4
15/4
the displacement (in meters) of a particle moving in a straight line is given by 2sin(pi)t 3cos(pi)t
The displacement of the particle at t = 1 second is -3 .meters
The displacement of a particle in a straight line can be calculated using the following formula: Displacement (d) = 2sin(πt) + 3cos(πt). This formula takes into consideration the sine and cosine of the angle, pi (π), multiplied by the time (t). The sine of the angle represents the vertical displacement, while the cosine represents the horizontal displacement.
For example, let's say we want to calculate the displacement of a particle at t = 1 second. First, we'll plug in the values into the formula:
d = 2sin(πt) + 3cos(πt)
d = 2sin(π*1) + 3cos(π*1)
d = 2sin(π) + 3cos(π)
d = 0 + (-3)
d = -3
Therefore, the displacement of the particle at t = 1 second is -3 meters.
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Factorise 2x^2-6x-10
by using taylor series one can be sure that for all values of x that satisfy |x|<1/2, |cos x-(1-x^2/2)| is less than or equal to what numerical value
All values of x that satisfy |x|<1/2, |cos x-(1-x^2/2)| is less than or equal to 1/4.
The Taylor series for the cosine function is given by:
cos x = 1 − x2/2! + x4/4! − x6/6! + x8/8! − x10/10! + . . .
For|x| < 1/2, we can ignore the higher order terms, and thus the series reduces to:
cos x = 1 − x2/2
Therefore,[tex]|cos x − (1 − x2/2)| = |x2/2| = |x|2/2[/tex]. Since |x| < 1/2, we have |x|2/2 < 1/4. Hence,
[tex]|cos x − (1 − x2/2)| < 1/4.[/tex]
Therefore, for all values of x that satisfy [tex]|x| < 1/2, |cos x-(1-x^2/2)|[/tex] is less than or equal to 1/4.
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what is the 4th term of 3n+5
Answer:
17
Step-by-step explanation:
if the sequence is 3n+5
we do 3x4(since we are working out the 4th term) +5
3x4=12 12+5=17
Each parking spot is eight and one-half feet wide. A parking lot has 24 parking spots side by side. How long is the row of parking spaces in yards?
Calculating parking ratios involves dividing a building's entire rentable square footage by its overall parking spaces. This offers the square footage available for rent per parking space, which is commonly stated as 1 parking space. 200 SF
How big is a single parking spot?The dimensions of a typical perpendicular parking place are nine feet (9') wide by eighteen feet (18') long.
To start, multiply 8 by 24 to determine how far apart each parking space is from the others (in other words the width of the parking lot).
8×24= 192 feet
Given that the question asks for an answer in yards, you know that 1 foot equals 1/3 of a yard and that 192 feet equals 64 yards.
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if a gallon of gasoline contains 120 mj how many gallons of gasoline does iit take to make the trip by car
To calculate the number of gallons of gasoline required, you need to know the energy consumption of the car in MJ and the distance of the trip.
The first step is to determine the energy consumption of the car in MJ per unit distance (e.g. per mile or per kilometer). This information can be obtained from the car's fuel consumption specifications or from real-world tests.
Once the energy consumption is known, the number of gallons of gasoline required for a given trip can be calculated by dividing the total energy consumption of the trip by the energy content of a gallon of gasoline (120 MJ). This will give you the number of gallons of gasoline required to make the trip.
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100%
What is the value of (5+2)2 +0.62? Enter the answer in the box.
Shannon manages a small zoo and she has been analyzing the attendance data. Shannon finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 3x. Shannon also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by g(x) = −x + 4. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.
Graph increasing exponentially from the left, crosses the y axis at one and goes to infinity and intersects a linear graph that decreases and crosses the y axis at four and the x axis at four
The solution to the two functions f(x) = 3ˣ and g(x) = -x + 4 is, 1
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The number of visitors increases exponentially as the temperature increases, and this situation can be expressed by the function
f(x) = 3ˣ
The number of people who leave the park early depending on the change in temperature, and it can be expressed by the function,
g(x) = −x + 4
the solution of both the graphs = ?
the intersection of the two curves of graphs of the functions is the solution,
Basically, it represent that,
both function have same value for particular value of x,
So,
when both functions have same value that will be our solution,
f(x) = 3ˣ
g(x) = −x + 4
it is shown in the graph, both functions are intersecting each other at x = 1
f(1) = 3
g(1) = −1 + 4 = 3
Hence, the solution for the equations is 1
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if one card is drawn from a standard 52 card playing deck, determine the probability of getting a jack or a queen or a heart.
The probability of drawing a jack or a queen or a heart from a standard 52-card deck is 1/4.
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
There are a total of 52 cards in a standard playing deck, and there are 4 jacks, 4 queens, and 13 hearts.
The probability of drawing a jack or a queen or a heart is equal to the sum of the probabilities of drawing each individual card type.
So, the desired probability is:
P(jack or queen or heart) = P(jack) + P(queen) + P(heart)
= 4/52 + 4/52 + 13/52
= 21/52
= 1/4
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Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis y=x3/2 y=27 x=0 5. -11 points LarCalc11 7.3.022. Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the x-axis. y=x y=0
The volume of the solid generated by revolving the plane region about the x-axis is 125/6 units3.
The volume of the solid generated by revolving the plane region about the x-axis can be found by using the Shell Method. This method involves integrating the area of the cross-section of the solid with respect to the x-axis. The area of the cross-section can be found by calculating the area of the region bounded by the curve y=x and the origin, which is a triangle. The area of the triangle is 1/2 * base * height, or 1/2 * x * x. The definite integral that represents the volume of the solid is then given by:
[tex]V = ∫0 x (1/2 x2) dx[/tex]
Evaluating this integral yields[tex]V = (1/6 * x3)|0x[/tex]. Plugging in x=0 and x=5 yields [tex]V = (1/6 * 53)|0x = 125/6[/tex] units3. Therefore, the volume of the solid generated by revolving the plane region about the x-axis is 125/6 units3.
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A. Make it Clear!
Starting with the graph of f(x) = 4s, find a formula for the function that results
from:
Shifting 4 units upwards
Shifting 3 units downwards
Shifting 2 unitsleft
Shifting 5 unitsright
Reflecting about the x-axis
Reflecting about the y-axis
The graphs of the transformations in each case are as follows;
a) f(x) =4+4 = 8
b) f(x) = 4-3 = 1
c) f(x) = 4
d) f(x) = 4
e) f(x) = 4
f) f(x) = 4
What are transformations?The shifts, reflections, rotations and dilation operations are facilitated by transformation operations. On this note, it therefore follows that the graph of the given function as given is a straight horizontal line which is parallel to the x-axis and consequently, the transformations are as given above.
here, we get,
a) f(x) =4+4 = 8
b) f(x) = 4-3 = 1
c) f(x) = 4
d) f(x) = 4
e) f(x) = 4
f) f(x) = 4
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Brayden is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $1.75 per mile driven. How much would a taxi ride cost if Brayden is riding for 9 miles? How much would a taxi ride cost that is mm miles long?
The total cost of the taxi ride is given by the equation A = $ 19.25
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of taxi ride be represented as A
Now , the equation will be
The initial cost for the pickup = $ 3.50
The cost of the ride per mile = $ 1.75
The cost for riding 9 miles = 9 x cost of the ride per mile
Substituting the values in the equation , we get
The cost for riding 9 miles = 9 x 1.75 = $ 15.75
So , the total cost of taxi ride A = initial cost for the pickup + cost for riding 9 miles
The total cost of taxi ride A = 3.50 + 15.75
The total cost of taxi ride A = $ 19.25
So , if the ride is m miles long , the cost is A = 3.50 + ( 1.75 )m
Hence , the equation is A = $ 19.25
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An experienced ice skater spins on the ice, creating a perfect circle with a diameter of 2 yards. What is the circle's circumference? Use 3.14 for .
The circumference of the circle is 6.28 .
What is a circle?Circle is a closed figure or curve that we get by drawing a line which passes through the points which are at an equal distance from a common point.
What is a perimeter?Perimeter of a closed figure is the total length of the line used for making that closed figure.
For example if we have three sticks of Length 2 cm, 3 cm, 5 cm. We make a triangle using the above sticks so the perimeter of the triangle will be
= 2+3+5= 10 cm
This indicates that total length of stick used to form the triangle is 10 cm.
For a circular figure its perimeter is known as circumference.
Now for the given question:
Diameter of the circle ( D ) = 2 yards.
π= 3.14 ( given in question)
Circumference of a circle = π×D
= 3.14×2
= 6.28
Hence circumference of the circle is 6.28 yards.
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Benjamin, audrey and luis are siblings and want to buy a new gaming console. benjamin has $164.67, luis has $373.24, and audrey has $235.13. the console costs $400 and luis only wants to pay up to one third of his total money. how much will his siblings have to contribute to evenly pay for the remaining cost?
Answer:
$137.80
Step-by-step explanation:
We can solve for [tex]\frac{1}{3}[/tex] of Luis's money using this equation:
373.24 ÷ 3 = 124.41 (Rounded to the nearest hundredth)Subtracting that from the total cost:
400 - 124.41 = 275.59275.59 is the leftover cost of the new gaming console that the siblings have to evenly split. To find out how much the sibling have to pay each, you can use this equation:
275.59 ÷ 2 = 137.80 (rounded to the nearest hundredth)Therefore, to pay for the new gaming console, Benjamin and Audrey will need to each contribute $137.80 to evenly pay for the remaining cost.
Solve for x in the drawing below.
Answer:
x=14
Step-by-step explanation:
Half circle total degree is 180°
180°=(2x-4)+101°+47°
so, 2x-4=180-101-47
2x-4=32
2x=32-4
2x=28
x=14
Sebastian decided to research the relationship between the length in inches
Based on the best-fitting line, the approximate weight of a catfish 33 inches long is 30pounds.
What is researchResearch is a term that is often used when talking about science. This is because scientists use step-by-step research to prove what is right and what is wrong. In research, researchers try and learn something by doing experiments.
Research is a process that is carried out by turning problems into questions. Research is a step carried out with the intention of research to answer that question. Research is a project that starts with a problem that comes from an observation.
The full question is:
Sebastian decided to research the relationship between the length in inches and the weight of certain species of catfish. He measured the length and weight of a number of specimens he caught, then threw them back into the water. After plotting all of his data, he drew the line that fit best. Based on the best-fitting line, what is the approximate weight of a catfish 33 inches long?
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Determine whether the system of equations has no solution, one solution, or an infinite number of solutions.
y=2/3x−7
2x−3y=−21
Answer the quetion in the picture below
The two equations have thesame slope therefore , the system has no solution
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
y = 2/3x - 7
multiply all by 3
3y = 2x -21
3y -2x = -21
2x - 3y = 21 equation 1
2x -3y = 21 equation 2
The two equations has thesame slope,
Since equation 1 is equal to equation 2 , the system has no solution
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Pls help with the attached images
9) The two column proof below has been used to prove that EG bisects HF.
10) The two column proof below has been used to prove that EG ≅ HF
11) The two column proof below has been used to prove that EI ⊥ KT
How to use two column proof?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
9) We want to prove that EG bisects HF.
In a rectangle opposite sides are equal and parallel.
In ΔMHE and ΔMFG, ∠MEH = ∠MGF
[Alternate interior angles; HE ∥ GF and EG as transversal]
HE = GF [Opposite sides of a rectangle are equal]
∠MHE = ∠MFG
[Alternate interior angles; HE ∥ GF and HF as transversal]
Thus;
ΔMHE ≅ ΔMFG
[By ASA congruence rule]
Equating the corresponding parts of congruent triangles, we get:
HM = FM
GM = EM
Diagonals of a rectangle bisect each other.
10) The proof that EG ≅ HF is as shown above in the previous proof.
11) TIKE is a Kite //Given
(2) KI = KE //(1) definition of a kite
(3) KP = KP //Common side, reflexive property of equality
(4) ∠IKT ≅ ∠EKT // (1), in a kite the axis of symmetry bisects the angles at those corners
(5) △KPI ≅ △KPE //Side-Angle-Side postulate.
(6) ∠KPI ≅ ∠KPE //Corresponding angles in congruent triangles (CPCTC)
(7) EI ⊥ KT //Linear Pair Perpendicular Theorem
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Which function family does the graphed function belong to?
Answer:
Logarithmic
Step-by-step explanation:
In a School sports day, the number of points the 8th grade team scores is given by 3x + 2y + z,
is the red team; y is yellow team, and z is the blue team. What is the total number of points scored by 10* graders when red scores 3 three points, yellow 5 points, and blue 2 points?
The total number of points scored is given by the equation A = 23 points
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total points scored be represented as A
Now , the equation will be
Substituting the values in the equation , we get
A = 3x + 2y + z be equation (1)
where x = red team = 3 points
y = yellow team = 5 points
z = blue team = 2 points
So , A = 3 ( 3 ) + 2 ( 5 ) + 2
A = 9 + 10 + 2
A = 21 points
Hence , the equation is A = 21 points
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I need help in percentage
Answer:
1a) 75
1b) 135
2a) 60
Step-by-step explanation:
Let's do the first 3 so you can see the pattern I use.
1a.) 150% of 50
First step I do is take the 150 and put a dot at the end.
150.
Next, I move that dot to the left two times, making it...
1.50
Now I take that and multiply by the number it's asking, which is 50
[tex]1.50 \times 50 = 75[/tex]
1b.) 150% of 90
150.
1.50
[tex]1.50 \times 90 = 135[/tex]
2a.) 100% of 60
100.
1.00
[tex]1.00 \times 60 = 60[/tex]
A college student would like to investigate the prices of large sandwiches offered near college campuses. Two random samples of 50 shops that sell sandwiches near the campuses of two colleges were taken and the price they charge for a large sandwich was recorded. One sample was taken for shops near City College, and one sample was taken for shops near Main Line University. The results are displayed in the cumulative relative frequency histograms below.
2 histograms. A histogram titled City College has price (dollars) on the x-axis and cumulative relative frequency on the y-axis. 8 to 9, 8 percent; 9 to 10, 41 percent; 10 to 11, 62 percent; 11 to 12, 80 percent; 12 to 13, 90 percent; 13 to 14, 100 percent. A histogram titled Main Line University has price (dollars) on the x-axis and cumulative relative frequency on the y-axis. 8 to 9, 21 percent; 9 to 10, 35 percent; 10 to 11, 58 percent; 11 to 12, 97 percent; 12 to 13, 98 percent; 13 to 14, 100 percent.
Which is a correct comparison of sandwich prices based on the histograms?
The interval from $11 to $12 contains the most shops for both college locations.
More shops charge between $12 and $13 near Main Line University than City College.
The median price lies between $10 to $11 for both City College and Main Line University.
Fewer shops sell sandwiches for under $10 near City College than near Main Line University.
Based on the information in the graphs, it can be inferred that the correct conclusion is Fewer shops sell sandwiches for under $10 near City College than near Main Line University.
How to identify the correct conclusion?To identify the correct conclusion we must read each of the options and compare with the graphics to verify the veracity of each of the statements. In accordance with the above, we can discard the first three statements and select the last option as the correct one because it is the one that matches the information in the graph.
In this case the percentage of stores that sell large sandwiches in City College is less than Main Line University.
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Area of figure pleaseeeee
Answer:
[tex]103 \: square \: inches[/tex]
Nine out of 60 cans of dog food have been eaten. What percent of the dog food has been eaten?
Answer: 15%
Step-by-step explanation:
60 cans ---------- 100%
1 can --------------- 100/60 %
9 cans -------------- (100 * 9) / 60
900/60 %
90/6 %
15%
Answer:
Step-by-step explanation:0.15
Sparkle clean car decreased the price of a car wash from $12 to $9 and noticed that the weekly quantity demanded for car polish increased from 200 to 350. Calculate the cross elasticity of demand for car polish with respect to the price of a car wash.
The gross elasticity of demand for car polish with respect to the price of a car wash is 3.
What is elasticity of demand?The elasticity of demand refers to the change in demand when there is a change in another economic factor, such as price or income.
Given that, Sparkle clean car decreased the price of a car wash from $12 to $9 and noticed that the weekly quantity demanded for car polish increased from 200 to 350.
We are asked to find elasticity of demand,
First, we will find the increase in the customers:
Customer increasing = 350 - 200 / 200 × 100
= 75
Now, the fluctuation in the price =
Price fluctuation = 12 - 9 / 12 × 100
= 25
Elasticity = increased rate / fluctuated price
= 75 / 25
= 3
The elasticity of demand is 3 which is greater than 1, so, that mean, the demand is elastic.
Hence, the gross elasticity of demand for car polish with respect to the price of a car wash is 3.
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