How is the greatest common factor of 8x^5, 12x^3, and 20x^2 4x^2 when 2 does not go evenly into 5?
Answers
We can factor each of the given terms so that 4x^2 shows up
8x^5 = 4x^2*2x^3
12x^3 = 4x^2*3x
20x^2 = 4x^2*5
This shows how 4x^2 is the GCF of 8x^5, 12x^3, and 20x^2
-----------------
Here's how to find the GCF of terms involving variables.
First, find the GCF of the coefficients 8, 12 and 20.
List the prime factorizations
8 = 2*2*212 = 2*2*320 = 2*2*5Then circle "2*2" since it is found in all three factorizations. Do not circle 3 because it's not found in 8 or 20. Do not circle 5 since it's not found in 8 or 12.
Therefore, the GCF of {8,12,20} is 2*2 = 4.
As for the variable terms, we look for the smallest exponent.
The exponents for x^5, x^3, x^2 are 5,3,2 in that order. The smallest exponent is 2, so x^2 is part of the GCF.
----------------
Summary:
We found the GCF of the coefficients was 4.
The GCF of the variable terms was x^2
That's how we arrive at the GCF of 4x^2
Related Questions
In a jar of lollies there are 6 more orange lollies than green ones and there is only one red lolly. If there are 47 lollies in the jar, how many orange ones are there?
Answers
Answer:
Let's use "g" to represent the number of green lollies in the jar.
According to the problem, there are 6 more orange lollies than green ones, so the number of orange lollies is "g + 6".
We also know that there is only one red lolly.
The total number of lollies in the jar is 47, so:
g + (g + 6) + 1 = 47
Simplifying the equation:
2g + 7 = 47
Subtracting 7 from both sides:
2g = 40
Dividing by 2:
g = 20
So there are 20 green lollies in the jar.
And since there are 6 more orange lollies than green ones, there must be:
g + 6 = 20 + 6 = 26 orange lollies in the jar.
Step-by-step explanation:
Find the multiplying integers -2x24=
Answers
The multiplying integers -2x24= -48
Multiplication of Integers:Here is some rules of multiplication of integers:
1. Positive integer × negative integer = negative.
2. Positive integers × Positive integers = positive.
3. Negative integers × Negative integers = positive.
Here, To find the the multiplying integers
-2x24 = -48
When you multiply integers :
Negative x Positive = Negative
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Need help solving this problem please help
Answers
The height of tree is given as follows:
40 ft.
How to obtain the height of the tree?The height of the tree is obtained applying the proportions in the context of this problem.
The proportions are applied as a rule of three can be formed between the heights and the shadows for both the tree and the person, as follows:
h/30 = 6/4.5
Applying cross multiplication, the value of h is obtained as follows:
4.5h = 30 x 6
4.5h = 180
h = 180/4.5
h = 40 ft.
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Simplify the expression: 8y + 4 - 3y + 12
Answers
Can someone help me please
Answers
The expansion and simplification of the expression (x - 2)² is x² - 4x + 4.
What is an expression?An algebraic expression is a combination of variables with constants, numbers, and values using the mathematical operands addition, subtraction, multiplication, or division.
Algebraic Expression:(x - 2)²
Expanding the square:
(x - 2)² = (x - 2)(x -2)
Distributing the square:
x(x - 2) - 2(x - 2)
x² - 2x - 2(x -2)
x² - 2x - 2x + 4
Solution:x² - 4x + 4
Thus, after expanding and simplifying the algebraic expression (x - 2)², the solution is x² - 4x + 4.
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33% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities. Due Saturday night
Answers
The cumulative probability is
P(at most 2 ) = 0.187560896 [answer]
How to solvea)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 12
p = the probability of a success = 0.33
x = the number of successes = 3
Thus, the probability is
P ( 3 ) = 0.21509867 [answer]
***********
b)
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 12
p = the probability of a success = 0.33
x = our critical value of successes = 4
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 3 ) = 0.402659566
Thus, the probability of at least 4 successes is
P(at least 4 ) = 0.597340434 [answer]
***************
c)
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 12
p = the probability of a success = 0.33
x = the maximum number of successes = 2
Then the cumulative probability is
P(at most 2 ) = 0.187560896 [answer]
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Prove by mathematical induction that:
[tex]2 + 4 + 8 + ... + {2}^{n} = {2}^{n + 1} - 2 [/tex]
Answers
By the principle of mathematical induction, the statement holds for all positive integers n.
How did we arrive at this assertion?Using mathematical induction:
Base case:
For n=1, results into:
2 = 2^2 + 1 - 2
which is true.
Inductive step:
For some positive integer k, we have:
2+4+8+...+2^k = 2^(k+1) + 1 - 2
This implies the statement for n=k+1, i.e.,
2+4+8+...+2^k+2^(k+1) = 2^(k+2) + 1 - 2
From the left-hand side of the equation, we can rewrite it as:
2+4+8+...+2^k+2^(k+1) = (2+4+8+...+2^k) + 2^(k+1)
Applying the induction hypothesis, substitute the expression for 2+4+8+...+2^k:
2+4+8+...+2^k+2^(k+1) = (2^(k+1) + 1 - 2) + 2^(k+1)
Simplify:
2+4+8+...+2^k+2^(k+1) = 2^(k+2) - 1
Using the formula for the sum of a geometric series to simplify the right-hand side of the original statement:
2^(k+2) + 1 - 2 = 2^(k+2) - 1
Thus, the statement holds for n=k+1, supposing it holds for n=k. By the principle of mathematical induction, the statement holds for all positive integers n.
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What is the area of this polygon?
Answers
Answer:
78
Step-by-step explanation:
(5+8)×12/2=78
(5+8)×12/2=78
Find the area of the triangle:
(Please show work so I can learn how to do it)
Answers
Step-by-step explanation:
Area of a traingle = 1/2 * base * height
area = 1/2 * 6 * 4 = 12 cm^2
I'm needing help with setting up these equations
Answers
The sides show that we have an equilateral triangle
What is the measure of each of the sides?An equilateral triangle is a triangle in which all three sides are of equal length. Since all three sides are equal, all three angles are also equal and measure 60 degrees each.
We know that;
12x - 22 = 10x - 6
Collect like terms;
12x - 10x = -6 + 22
2x = 16
x = 8
Thus the sides of the triangle are;
12(8) - 22 = 74
10(8) - 6 = 74
7(8) + 18 = 74
In the second triangle;
4x - 25 = x + 14
4x - x= 14 + 25
3x = 39
x = 13
Thus the sides are;
4(13) - 25 = 27
13 + 14 = 27
6(13) - 51 = 27
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I am unsure about how to do this problem, pictured below.
Answers
Answer:
Step-by-step explanation:
150/2 = 75
500/75 = 6.6666666667 hours
it will take 6.2/3 hours to reach 500 bacteria cells
NOT SURE ABOUT EXPERSION BUT YOU COULD TRY THIS
p = 75t
Given that a culture of bacteria grows at a rate proportional to its size. Where the culture starts with 50 cells, then grows 150 after time, "t" equals 2 hours.
We are asked to:
> (a) Find an expression, P(t), to model the number of cells present after "t" hours.
> (b) Determine the time at which the population is at 500 cells.
For part (a):
Since the culture of bacteria grows at a rate proportional to its size, we can model it as the following differential equation.
[tex]\Rightarrow \frac{dP}{dt}=kP; \ Where \ P =P_0 \ at \ t=0 \ and \ P=3P_0 \ at \ t=2[/tex]
Solve the first-order separable differential equation with the given initial condition.
[tex]\Longrightarrow \frac{dP}{dt}=kP \Longrightarrow \frac{1}{P}dP=kdt \Longrightarrow \int\limits {\frac{1}{P} } \, dP=\int\ {k} \, dt \Longrightarrow ln(P)=kt+c[/tex]
[tex]\Longrightarrow e^{ln(P)}=e^{kt}+e^{c} \Longrightarrow P=ce^{kt}[/tex]
Plug in the initial condition.
[tex]\Longrightarrow P_0=ce^{k(0)} \Longrightarrow P_0=c(1) \Longrightarrow \boxed{c=P_0}[/tex]
[tex]\Longrightarrow P=ce^{kt} \Longrightarrow \boxed{P=P_0e^{kt}}[/tex]
Use the second initial condition to find "k."
[tex]\Longrightarrow 3P_0=P_0e^{k(2)} \Longrightarrow 3=e^{k(2)} \Longrightarrow 3=e^{2k} \Longrightarrow ln(3)=ln(e^{2k})[/tex]
[tex]\Longrightarrow k=\frac{ln(3)}{2} \Longrightarrow \boxed{k \approx 0.5493}[/tex]
Thus, the equation to model the situation is,
[tex]\boxed{\boxed{P(t)=50e^{0.5493t}}} \therefore Sol.[/tex]
For part (b):
[tex]P=10P_0[/tex]
[tex]\Rightarrow 10P_0=P_0e^{0.5493t} \Longrightarrow 10=e^{0.5493t} \Longrightarrow ln(10)=ln(e^{0.5493t})[/tex]
[tex]\Longrightarrow ln(10)=0.5493t \Longrightarrow t=\frac{ln(10)}{0.5493} \Longrightarrow \boxed{t=4.192 \ hrs}[/tex]
Thus, the time it takes the population to reach 500 is approx. 4.192 hours.
Use the graph of g(x) to answer the following question. The graph of g(x) is a translation of f(x)=x^2 Write the equation for g(x) in vertex form.
Answers
The equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
Writing the equation for g(x) in vertex form.From the question, we have the following parameters that can be used in our computation:
The graph of g(x)
Also, we have
The graph of g(x) is a translation of f(x)=x^2
From the graph, we can see that
Using the above as a guide, we have the following:
g(x) = f(x - 2) + 3
Substitute the known values in the above equation, so, we have the following representation
g(x) = (x - 2)^ + 3
Hence, the equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
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sketch the graph of each function.
22. g(x)= -2x³-8x2 +18x+72
Answers
The graph of the cubic equation is in the equation of the end.
How to sketch the graph of the function?To do it, we need to find some points that are solutions of the equation. Then we can graph these points on a coordinate axis and then connect these points with a curve proper of a cubic relation.
when x = 0
g(0) = -2*0³-8*0² +18*0+72 = 72
So we have the point (0, 72)
when x = 1
g(1) = -2*1³-8*1² +18*1+72
= -2 - 8 + 18 + 72 = 80
So we have the point (1, 80)
when x = -1
g(-1) = -2*-1³-8*-1² +18*-1+72
= 2 - 8 - 18 + 72 = 48
(-1, 48)
And so on, when you have enough points, you can connect them. The graph that should you get is one like the graph in the image at the end.
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What is the amount of your employer's contributions if the company matches 50% of the first 4% of your salary, and you make $72,000 a year?
O $1,440.00
O $1,000.00
O $2,880.00
O $36,000.00
Answers
4% of $72,000 is:
$72,000 x 0.04 = $2,880
50% of $2,880 is:
$2,880 x 0.5 = $1,440
Therefore, the employer's contribution would be $1,440.00. Option A is the correct answer.
4% of $72,000 is:
$72,000 x 0.04 = $2,880
50% of $2,880 is:
$2,880 x 0.5 = $1,440
Therefore, the employer's contribution would be $1,440.00. Option A is the correct answer.
QUICK, I’LL MARK U BRAINLIEST!! Help me solve this problem!
Answers
Based on the information, bIda would owe $3700 at the end of 12 months.
Ida would owe $3808 at the end of 12 months.
How to calculate the interestThe formula will be:
I = P * r * t
I = 2500 * 0.04 * 12 = $1200
So, Ida would owe $2500 + $1200 = $3700 at the end of 12 months.
b. For option b, , the monthly interest rate is:
r = 0.01 * 4.33 = 0.0433
Using the same simple interest expression:
I = 2500 * 0.0433 * 12 = $1308
Ida would owe $2500 + $1308 = $3808 at the end of 12 months.
Therefore, option a is the better choice due to the fact she would owe less in total with a simple interest rate of 4% annually.
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A wallet contains 34 notes, all of which are either $5 or $10 notes. If it amounts to $235, how many $10 notes are there?
Answers
According to the problem, we know that:
- x + y = 34 (since the wallet contains a total of 34 notes)
- 5x + 10y = 235 (since the total amount of money in the wallet is $235)
We can use the first equation to solve for x in terms of y:
x = 34 - y
Substituting this expression for x into the second equation, we get:
5(34 - y) + 10y = 235
Simplifying and solving for y, we get:
y = 15
Therefore, there are 15 $10 notes in the wallet.
Answer:
For this question, you can use the simultaneous equation to solve this problem.
Equation 1 reads: x + y = 34. (There are 34 notes in total.)
Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)
To find x in terms of y, we can apply equation 1:
x = 34 - y
When we use this expression to replace x in equation 2, we obtain:
5(34 - y) + 10y = 235
By condensing and figuring out y, we get at:
y = 15
There are 15 $10 bills in the wallet as a result.
Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $700, r=7%, t=8 years; compounded quarterly
Answers
I=PRT
I=$700*7%*8 years
I=$392
Now we have found the interest let us find the amount of the number
A=interest+principle
A=$392+$700
A=$1092
Answer:
$1092
Step-by-step explanation:
The distance between cities A and B on a map is 12.5 in. The distance from city B to city C, is 8.5 in, and the distance from C to A is 16.25 in. If the bearing
from A to B is N75°E, find the bearing from C to 4. Round to the nearest tenth of a degree.
Answers
Answer:
90
Step-by-step explanation:
Answer:
It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:
Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?
To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:
x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)
To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:
x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)
Substitute the expression for x into the second equation and solve for y:
x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20
Substitute y = 20 into the expression for x to get:
x = 180 - 3y/2 x = 120
Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.
Step-by-step explanation:
full method please
-8+27÷(-3)-(-2)
Answers
The solution of the expression -8+27÷(-3)-(-2) is determined by applying the rule of BODMAS as -35.
What is the solution of the expression?
The solution of the expression is calculated by applying the following formula as shown below;
BODMAS;
B - stands for bracketO - stands for ofD - stands for divisionM - stands for multiplicationA - stands for AdditionS - stands for subtractionBased on the rule of BODMAS, we solve the bracket first, then division, before addition and subtraction.
-8+27÷(-3)-(-2) = -8+27÷ -1
-8+27÷ -1 = -8 - 27
-8 - 27 = - 35
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When an object is dropped vertically from a platform, its height after
seconds can be estimated with the formula shown.
ℎ=ℎ0−162
ℎ
is the height of the object in feet.
ℎ0
is the initial height of the object in feet.
is the time in seconds after the drop.
Which equation and solution tells how long it takes the object to reach a height of 96
feet if its initial height is 208
feet?
Answers
An equation and solution that tells how long it takes the object to reach a height of 96 feet if its initial height is 208 feet is:
D. 96 = 208 - 16t²
t = √7
How to determine the time when the object would reach a height of 96 feet?Based on the information provided, we can logically deduce that the height (h) in feet, of this object above the ground is related to time by the following quadratic function:
h(t) = h₀ - 16t²
When the initial height is 208 feet and final height is 96 feet, the height function becomes;
h(t) = h₀ - 16t²
96 = 208 - 16t²
16t² = 208 - 96
16t² = 112
t² = 112/16
Time, t = √7 seconds.
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At their practices, the volleyball team ran a total of 10 miles in 14 days. The tennis team ran a total of 8 miles in 7 days. Which team ran more miles per day?
Answers
Answer:
tennis team
Step-by-step explanation:
because they ran 8 miles is 7 days to get equal amount of days you multiply by 2 on both 8 miles and 7 days so they ran 16 miles in 14 days thats y tennisbteam ran more miles
Which of the following has the polar coordinates negative five comma two pi over 3
Options:
Q
R
U
W
Answers
3x+10<3 or 2x-5 ≥ 5 solve the inequality
Answers
Answer: x is greater than or equal to 5 (I can't put the symbol in)
Step-by-step explanation:
Add 5 to both sides then simplify, which will get you 2x is greater than or equal to 10, then divide by 2.
Answer:
Step-by-step explanation:
3x+10<3
3x<3-10
3x<-7
x<-7/3
2x-5≥5
2x≥5+5
2x≥10
x≥10/2
x≥5
so x<-7/3 or x≥5
Square with top and left sides labeled 1. The square is divided into 6 equal sections vertically and the first section is divided into 2 equal sections horizontally. The first of these sections is shaded.
Number line from 0 to 1. There are 5 large tick marks equally spaced between 0 and 1. There are 3 equally spaced smaller tick marks between every pair of large tick marks. The first of these smaller tick marks has a dot on it.
Question
Raj combined white sand with black sand to make 14 pound mixture of sand. Raj then put an equal amount of this sand mixture into each of 5 vases. All of Raj's sand mixture went into the vases.
How much sand was in each vase?
Responses
140 lb
1 over 40, , lb
120 lb
, 1 over 20, , lb
14 lb
1 fourth, , lb
45 lb
4 over 5, , lb
Answers
The amount of sand in each vase is 2.8 pounds by dividing the total amount by the number of vases.
Given that,
Raj combined white sand with black sand to make 14 pound mixture of sand.
Total amount of sand = 14 pounds
Number of vases to which sand is put = 5 vases
Amount of sand in each vase can be found by dividing the total amount by the number of vases.
Amount of sand in each vase = 14 / 5 = 2 4/5 pounds = 2.8 pounds
Hence the total amount of sand is 2.8 pounds.
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HELPPP DUE TOMORROW
Answers
Answer: 1/2 cup oats 2/3 cup flower
the french club is holding a car wash fundraiser. They are going to charge $20 per car, and expect between 30 and 100 cars. Identify the independent and dependent quality in the situation, and find reasonable domain and range values
Answers
Correct option is,
A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.
Since, An independent variable is a variable that represents a quantity that is being controlled in an experiment.
A dependent variable represents a quantity whose value depends on how the independent variable is controlled.
Now, In the given question;
The number of cars represents the independent variable while money raised represents independent variable .
Domain is the set of values the independent variable can take .
The number of cars 30 to 100 represents the Domain.
The range is corresponding y values .
The charge per car is $20.
Hence, Range = 30 x 20
=600
to Range = 100 x 20
= 2000.
Thus, Correct option is,
A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.
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Complete question is,
The French club is holding a car wash fundraiser. They are going to charge $20 per car, and expect between 30 and 100 cars. Identify the independent and dependent quantity in the situation, and find reasonable domain and range values.
A: number of cars; money raised; 30 to 100 cars; $600 to $2000
B: money raised; number of cars; 30 to 100 cars; $600 to $2000
C: number of cars; money raised; $600 to $2000; 30 to 100 cars
D: money raised; number of cars; $600 to $2000; 30 to 100 cars
NO LINKS!!! URGENT HELP PLEASE!!!!
Please assist me with these problems.
Answers
Answers in bold
7. Not congruent
8. Congruent by the HL theorem
HL = hypotenuse leg
==========================================
Explanation for problem 7
The tickmarks on segments MA and AT tell us that these segments are congruent. Another pair of congruent segments would be AE = AE by the reflexive property.
Then angle EMA = angle ETA because of the similar arc markings for those angles.
We have these congruence facts:
MA = AT (side)AE = AE (side)angle EMA = angle ETA (angle)But recall that the "side side angle" rule isn't a valid congruence theorem. Search out "SSA ambiguous case" for more information.
We cannot use SAS because the angle is not between the sides mentioned.
Therefore, we don't have enough information to determine if the triangles are congruent or not. We can't say they are congruent, so the only thing we can do is say "not congruent" until more info comes along.
------------
Explanation for problem 8
We use the HL (hypotenuse leg) theorem. It works for right triangles only.
The congruent legs are segment ON = segment ON because of the reflexive property.
The congruent hypotenuses are MN = RO because of the tickmarks.
In short, the triangles are congruent by the HL theorem.
Joey's current monthly expenses include a rent payment of $1,100, a $178 car payment, and a combined minimum payment of $220 for his credit card debt. His current gross monthly income is $3,600. If Joey moves to a new apartment, what is the maximum monthly rent payment he can make and still maintain a DTI ratio of 36%?
a.
$702
b.
$898
c.
$922
d.
$960
Answers
Based on Joey's debt-to-income ratio, the maximum monthly rent payment he can make and still maintain the DTI ratio would be; b. $898.
WE are given that Joey has a DTI ratio of 36% which means that his maximum debt payment should be 36% of his income.
This amount would be:
= DTI x monthly income
= 36% x 3,600
= $1,296
Maximum monthly rent can be found as:
= Maximum monthly debt payment - Car payment - Credit card payment
= 1,296 - 178 - 220
= $898
In conclusion, option B is correct.
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SOMEONE PLEASE HELP
The number of chips of different colors in Gail's bag is shown below
-2 blue chips
-4 pink chips
-8 white chips
Gail takes out a chip from the bag randomly without looking, She replaces the chip and then takes out another chip from the bag. What is the probability that Gail takes out a white chip in both draws?
Answers
Answer:
8 over 15 multiplied by 7 over 14 is equal to 56 over 210
8 over 15 plus 7 over 14 is equal to 217 over 210
8 over 15 plus 8 over 15 is equal to 16 over 15
8 over 15 multiplied by 8 over 15 is equal to 64 over 225
She's taking it out and then she replaces it
and so that means the denominator would stay 15 both times
and since it's a white chip in both draws, it would be 8/15 * 8/15
An airplane company flies 39 airplanes daily. The CEO collects the following passenger counts for a random sample of airplanes from the fleet, as shown below. 123, 132, 158, 77, 158, 123, 132, 123, 158, 77 Assuming that the sample is representative of the entire fleet of airplanes, what would be the mean daily passenger count per plane?
Answers
Answer:
To find the mean daily passenger count per plane, we need to calculate the average of the passenger counts for the sample.
We can do this by adding up all the passenger counts and dividing by the number of planes in the sample:
(123 + 132 + 158 + 77 + 158 + 123 + 132 + 123 + 158 + 77) / 10
= 1259 / 10
= 125.9
Therefore, the mean daily passenger count per plane is approximately 125.9 passengers.
Step-by-step explanation: