Answer: 23 x 32 x 71
Step-by-step explanation: The orange divisor(s) above are the prime factors of the number 504. If we put all of it together we have the factors 2 x 2 x 2 x 3 x 3 x 7 = 504. It can also be written in exponential form as 23 x 32 x 71.
A chain letter starts when a person sends a letter to five others. Each person who receives the letter either sends it to five other people who have never received it or does not send it to anyone. Suppose that 10,000 people send out the letter before the chain ends and that no one receives more than one letter. How many people receive the letter, and how many do not send it out?
Answer:
50,001 people sent out the letter.
40,001 did not send it out
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Step-by-step explanation:
780 people receive the letter before the chain ends.
9,220 people do not send out the letter.
We have,
In the given scenario, the chain letter starts with one person sending it to five others.
Each recipient of the letter has the option to either send it to five new recipients or not send it to anyone.
Let's analyze the chain letter progression:
The first person sends the letter to 5 recipients.
Each of those 5 recipients has the choice to send the letter to 5 new recipients or not send it.
If each of the 5 recipients sends the letter to 5 new recipients, we have a total of 5 x 5 = 25 new recipients.\
If any of the 5 recipients choose not to send the letter, they are out of the chain.
Now, we have 25 recipients who received the letter and have the same choice: send it to 5 new recipients or not send it.
If each of the 25 recipients sends the letter to 5 new recipients, we have a total of 25 * 5 = 125 new recipients.
If any of the 25 recipients choose not to send the letter, they are out of the chain.
This process continues until the chain ends.
To determine how many people receive the letter and how many do not send it out, we can observe the pattern:
After the first step, there are 5 recipients.
After the second step, there are 5 + (5 * 5) = 30 recipients.
After the third step, there are 5 + (5 * 5) + (5 * 5 * 5) = 155 recipients.
After the fourth step, there are 5 + (5 * 5) + (5 * 5 * 5) + (5 * 5 * 5 * 5) = 780 recipients.
We can see that the number of recipients follows a geometric progression with a common ratio of 5.
The formula for the sum of a geometric progression is:
[tex]Sum = a (r^n - 1) / (r - 1)[/tex]
Where:
a = initial term = 5
r = common ratio = 5
n = number of steps
We are given that the chain ends after 10,000 people send out the letter. Let's calculate the number of recipients:
[tex]Sum = 5 (5^4 - 1) / (5 - 1)[/tex]
= 5 (625 - 1) / 4
= 5 624 / 4
= 780
Therefore, 780 people receive the letter before the chain ends.
To find the number of people who do not send it out, we subtract the number of recipients from the total number of people who sent out the letter:
Number of people who do not send it out = Total number of people - Number of recipients
= 10,000 - 780
= 9,220
Therefore, 9,220 people do not send out the letter.
Thus,
780 people receive the letter before the chain ends.
9,220 people do not send out the letter.
Learn more about geometric sequence here:
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Plz help !!!!!! I don’t understand
how to solve this? im not sure if i get the correct answer
Answer:
k = 3.5
Step-by-step explanation:
Area of a rectangle = length × width
Area of the bigger triangle - Area of the smaller triangle = 35 cm²
Thus:
(2k + 6)(k) - (3)(k) = 35 cm²
2k² + 6k - 3k = 35
2k² + 3k - 35 = 0
Factorise
2k² + 10k - 7k - 35 = 0
2k(k + 5) -7(k + 5) = 0
(2k - 7)(k + 5) = 0
2k - 7 = 0
2k = 7
k = 3.5
Or
k + 5 = 0
k = -5
The value of k would be the positive number which is 3.5.
If the radius is 21 cm and the angle at
center of circle is 140° then the length of
the arc is ?
Step-by-step explanation:
Given: Radius , r =21 cm
The angle at the center of the circle, n° =140°
Length of an arc =?
W.K.T Formula, Length of an arc = 2πr( n°÷360°) units
= 2*(22/7)*21*(140°/360°)
= 154/3
= 51.33cm
Answer:
2*(22/7)*21*(140°/360°)
= 154/3
= 51.33cm
Step-by-step explanation:
Question #5
Consider the equation.
72 +48 = 8
1+6)
Enter the unknown number that makes the equation true.
Your answer
Σ
Find the unit rate.
You earn $15 in 3/4 of a month. At this rate, how much do you make in 1 month?
Answer:
you make 20 dollars in a month
Step-by-step explanation:
15 is 3/4 a month, unit rate would be 5 dollars a week so therefore a whole month would be 20
I need this fast please
Answer: It is B/Spinner 2
the temperature at 4 p.m. was -2 °c an hour later the temperature had decreased 3°c what was the temperature at 5:00 pm ?
Answer:
Step-by-step explanation:
3 degrees Celsius
It says at 4 p.m. was -2 degrees C. Then an hour later which would be 5 pm the temperature was 3 degrees C.
A baker had additional flour at the end of the day. He uses 1/8 of a bucket of flour to bake two cakes. How much flour did he use to make one cake?
Answer:
0.0625
Step-by-step explanation:
You can convert this into a fraction by entering this into a calc
Manuel ate lunch in 5 minutes. How many seconds is this?
Answer:
300 seconds
Step-by-step explanation:
1 minute= 60 seconds
5 x 60 = 300
Answer:
1 minute is 60 seconds, so 60 x 5 is 300. So your answer is 300 seconds
Juan pago $50.00 pesos por 3 cajas de paquetes y 5 cajas de clavos, mientras que Pedro compró 5 cajas de taquetes y 7 cajas de clavos y tuvo que pagar $ 74.00 pesos . ¿ Cual es el precio de cada caja de taquetes y clavos ?
a) ¿ Cuantas incógnitas hay en el problema ?
b) ¿ Cuántas ecuaciones puedes construir según el texto?
c) ¿ Cuales son esas ecuaciones?
Carly earned some money doing odd jobs last summer and put it in a savings account that earns 5% interest compounded quarterly. After 2 years, there is $400.00 in the account. How much did Carly earn doing odd jobs? * A. 155.90 B. 441.79 C. 390.18 D. 362.16
Choose the diagram that correctly represents the ordered pairs below.
(1,4), (4, -1), (2,3), (-3, 1), (0,-5)
Answer:
Step-by-step explanation:
Is there a picture
Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10 workers from each of the six departments. Abel's sample is a
Answer:
disproportionate stratified sample
Step-by-step explanation:
Based on the given information we can say that Abel's sample is a disproportionate stratified sample. This is the case mainly because the department worker population ranges from 40 to 120 workers. This changing population makes the 10 workers that were chosen for the sample not proportionate to the entire population. Therefore, under different population sizes workers have different chances of getting selected for the study which ultimately creates different results.
The surface area of a three-dimensional object is the sum of the area of the faces. If represents the length of the side of a cube, write a formula for the surface area S of the cube.
Answer:
S = 6e²
I don't know what variable you're using here.
Step-by-step explanation:
There are 6 faces on a cube and they are all the same. Because of this, 6 is the coefficient in this equation.
A square's area can be found by squaring the side length (Which I'll represent with e). So e² is the variable.
Thus, the equation is S = 6e²
Whats the answer to part b and above?
Answer:
4/5 would be at the 8th line, and 3/10 would be on the 3rd
Step-by-step explanation:
5.00 minus2.40minus1.33= plz show me how you got that answer step by step
Answer:
5.00 -2.40= 2.60
2.60-1.33= 1.27
The answer is 1.27
Step-by-step explanation:
PLEASE I NEED HELP WITH MATH
Answer:
117
Step-by-step explanation:
Hi, If you were to add 75 to 42, you would get 117. Since a triangle's angles all have to add up to 180, the last angle would be 63. However, you are looking for the outside angle, which would then just be 117. Hope this is right!
Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below: A(-1,2) B(-1,5) C(-3,5) D(-3,2) A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2)
What transformation did Kim perform to create rectangle A'B'C'D? (5 points)
A)Reflection across the y-axis
B)Rotation of 270 degrees counterclockwise about the origin
C)Reflection across the x-axis
D)Rotation of 90 degrees counterclockwise about the origin
Answer:
C) Reflection across the x-axis.
Step-by-step explanation:
From Linear Algebra we define the reflection across the x-axis is for [tex]P(x,y) =(x,y)[/tex]:
[tex]P'(x,y) = (x, -y)[/tex] (1)
If we know that [tex]A(x,y) = (-1, 2)[/tex], [tex]B(x,y) =(-1,5)[/tex], [tex]C(x,y) = (-3, 5)[/tex] and [tex]D(x,y) =(-3, 2)[/tex], then the reflected points are, respectively:
[tex]A'(x,y) = (-1, -2)[/tex]
[tex]B'(x,y) = (-1,-5)[/tex]
[tex]C'(x,y) = (-3,-5)[/tex]
[tex]D'(x,y) = (-3,-2)[/tex]
In consequence, Kim performed a reflection across the x-axis to create triangle A'B'C'D'. The correct answer is C.
This question is based on the reflection of x- axis. Hence the correct answer is C, reflection across the x-axis.
Given:
Transform rectangle ABCD to rectangle A'B'C'D',
The vertices of rectangle ABCD is A(-1,2) B(-1,5) C(-3,5) D(-3,2).
The vertices of rectangle A'B'C'D is A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2).
We need to determined the transformation that Kim perform to create rectangle A'B'C'D.
From Linear Algebra we define the reflection across the x-axis is for,
P(x,y) = (x,y)
P(x,y) = (x,-y) .....(1)
It is given that A(-1,2), B(-1,5), C(-3,5) and D(-3,2).
Therefore from equation (1) above point becomes,
A'(x,y) = (-1,-2)
B'(x,y) =(-1,-5)
C'(x,y) =(-3,-5)
D'(x,y) =(-3,-2)
Therefore, It is observe that Kim performed a reflection across the x-axis to create triangle A'B'C'D'. Hence the correct answer is C, reflection across the x-axis.
For further details, please refer this link:
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Answer this please i need help
Answer:
Slope m = -3
y-intercept (0, 0)
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = -3x
Step 2: Break Function
Identify Parts.
Slope m = -3
y-intercept b = 0
Definition of dilation in geometry
Answer:
Geometry
Step-by-step explanation:
Evaluate the following expression using the values given:
Find 5x − 3y − z if x = −2, y = 2, and z = −3
Answer: -13
Step-by-step explanation:
just substitute the letters for the numbers.
5(-2) - 3(2) -(-3)
then, remove the parenthesis.
-10 - 6 + 3
finally, just calculate it.
-13
a bowling alley charges $4.00 per game and will rent a pair of shoes for $2.00 for any number of games. The bowling alley has an earnings goal of $400 for the day. write the linear equation.
Answer:
We need 130 games to reach the goal
Step-by-step explanation:
pamela ran 7/10 miles on tuesday and 3/8 mile on thursday. How much farther did she sun on tuesday ?
Answer:
she ran 0.325 more on tuesday then tursday
Step-by-step explanation:
because i know
Twelve of the 28 students in the 6th grade class have a dog. What is the ratio of students who have a dog to the students who do not have a dog? Write this ration in 3 different ways. Then, explain which ratio is greater. Please help
Answer:
1:4
Step-by-step explanation:
As, number of students have 12
Which don't, are 28 - 12 = 16
So ratio = 12:16
1:4
A cell phone manufacturer samples cell phones from the assembly to test. She noticed that the number of faulty cell phones in a production run is usually small and that the quality of one day’s run seems to have no bearing on the next day.
a) What model might you use to model the number of faulty cell phones produced in one day?
(write a name of this probability model)
An analysts estimates the mean number of defective cell phones to be 2 per day.
b) What is the probability of having a day with no faulty cell phone in a production run?
(write to 3 decimal places)
c) What is the probability of having a day with more then 3 faulty cell phones in a production run?
probability:
Answer:
b
Step-by-step explanation:
probability can't be defined
At a sports event, Luke scored 8.65 points. Mel scored 9.2 points. How many more points did Mel score than Luke? * PLZ HELP
Answer:
0.55
Step-by-step explanation:
9.2-8.64=0.55
i hope it helps
PLZ HELP if u know the answer for sure
WILL MARK BRAINLIEST
what type of transformation is described by (x,y) —> (x+2, y+16)?
This transformation takes a vector (x,y) and maps it to the vector (x+2, y+16). In other words, it moves the X coordinate of the vector 2 units to the right, and the Y coordinate of the vector is moved 16 units upwards.
If you would take a set of points and apply this transformation, you would see the entire set moving upwards and to the right, with no stretching ou rotating. This type of transformation is called a translation transformation.
3) Luan is borrowing $5000 to buy Sacramento Kings season tickets
for her family. She is planning to pay it back over three years.
She can borrow the money from a finance company at a 6.5% add-on
interest rate for three years or she can borrow it instead from
her credit union, making 36 monthly payments of $164.50. Find the
total amount Luan will have to pay back with each option and the
APR (to the nearest half percent) of each loan.
Answer:
16000
Step-by-step explanation:
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