Genghis Khan's army organizational structure can be used to calculate the total number of men under him: For an army of 10,000 soldiers, the total is 11,110 men; for an army of 5,763 soldiers, it is 6,404 men.
To solve both parts of the student's question, we use the military organizational structure implemented by Genghis Khan that is based on the 'decimal' system. We start with the lowest level groups of 10 soldiers and move up in orders of magnitude (10, 100, 1,000, and 10,000).
Part (a): Army of 10,000 soldiers
Groups of 10: There are 1,000 groups of 10 in an army of 10,000 soldiers.
Leaders of 10: Each group of 10 has 1 leader, resulting in 1,000 leaders of 10.
Groups of 100: 1,000 leaders of 10 make up 100 groups of 100 (because 1,000/10 = 100).
Leaders of 100: There are 100 leaders of 100.
Groups of 1,000: 100 leaders of 100 make up 10 groups of 1,000 (because 100/10 = 10).
Leaders of 1,000: There are 10 leaders of 1,000.
Adding it all together: 10,000 soldiers + 1,000 leaders of 10 + 100 leaders of 100 + 10 leaders of 1,000 = 11,110 total men under the command of Khan for an army of 10,000.
Part (b): Army of 5,763 soldiers
Groups of 10: There are 576 full groups of 10 and 1 incomplete group (with 3 soldiers), resulting in 577 groups.
Leaders of 10: There are 577 leaders of 10.
Groups of 100: 577 leaders of 10 make up 57 full groups of 100 and 1 incomplete group (with 7 leaders of 10), resulting in 58 groups.
Leaders of 100: There are 58 leaders of 100.
Groups of 1,000: 58 leaders of 100 make up 5 full groups of 1,000 and 1 incomplete group (with 8 leaders of 100), resulting in 6 groups.
Leaders of 1,000: There are 6 leaders of 1,000.
Adding it all together: 5,763 soldiers + 577 leaders of 10 + 58 leaders of 100 + 6 leaders of 1,000 = 6,404 total men under the command of Khan for an army of 5,763 soldiers.
The area of a rectangular wall of a barn is 42 square feet. Its length is 8 feet longer than twice its width. Find the length and width of the wall of the barn.
Answer:
The answer to your question is: length = 14 ft; width = 3 ft
Step-by-step explanation:
Data
Area = 42 ft²
length = 8 + 2w
w = width = ?
length = ?
Formula
Area = length x width = l x w
Substitution
42 = (2w + 8)w
42 = 2w² + 8w
2w² + 8w - 42 = 0
Dividing by 2
w² + 4w - 21 = 0 Factorize
(w + 7) (w - 3) = 0
w1 = -7 w2 = 3
It's not possible to have negative widths
So the answer is w = 3 ft
length = 2(3) + 8
length = 6 + 8
length = 14 ft
The length and width of the rectangle barn are 14 feet and 3 feet, respectively.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangle be represented by x. Therefore, the dimension of the barn is,
Width = x
Length = 2x + 8
The area of a rectangular wall of a barn is 42 square feet.
Area = Width × Length
Area = x × (2x+8)
42 square feet = x(2x + 8)
42 = 2x² + 8x
2x² + 8x - 42 = 0
x² + 4x - 21 = 0
x² + 7x - 3x - 21 = 0
x(x + 7) - 3(x + 7) = 0
(x + 7)(x - 3) = 0
x = -7, 3
Since width can not be negative, therefore, the length and the width of the wall of the barn are,
Width = x = 3
Length = 2x+8 = 2(3)+8 = 14
Hence, the length and width of the rectangle barn are 14 feet and 3 feet, respectively.
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Roberto invested a total of $10000,part at 6% and part at 9%. How much did he invest in the Higher interest account if the total interest earned in one year was $810?
Answer:
$7000 at 9%Step-by-step explanation:
Let x represent the amount invested at 9%. Then Roberto's interest was ...
x(9%) +(10000-x)(6%) = 810
0.03x + 600 = 810 . . . . . . . . . simplify
0.03x = 210 . . . . . . . . . . . . . . . subtract 600
x = 210/0.03 = 7000 . . . . . . . divide by the coefficient of x
Roberto invested $7000 at the higher interest rate.
To solve the problem, set up a system of equations using x and y for the amount invested at 6% and 9% respectively. Solve the system of equations to find the values of x and y, which represent the amounts invested at each interest rate. Roberto invested $3000 at 6% and $7000 at 9%
Explanation:To solve this problem, we can set up a system of equations. Let x represent the amount invested at 6% and y represent the amount invested at 9%. The equation for the total amount invested is x + y = $10000. The equation for the total interest earned is 0.06x + 0.09y = $810. We can solve this system of equations to find the values of x and y.
From the first equation, we can express x in terms of y: x = $10000 - y.Substitute the value of x in the second equation: 0.06($10000 - y) + 0.09y = $810.Simplify and solve for y: 600 - 0.06y + 0.09y = $810.Combine like terms: 0.03y = $210.Divide by 0.03: y = $7000.Substitute the value of y back into the first equation to find x: x = $10000 - $7000 = $3000.Therefore, Roberto invested $3000 at 6% and $7000 at 9%.
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Is the selection a permutation, a combination, or neither? A student checks out 5 novels from the library. Choose the correct answer below.
A. The selection is a combination.
B. The selection is a permutation.
C. The selection is neither a permutation or a combination.
Answer:
A. The selection is a combination.
Step-by-step explanation:
A combination is a selection of all or part of a set of objects, without regard to the order in which they were selected.
Then, a permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.
For example, the student scans the novels to be checked out in no particular order hence it is a combinations problem. Scanning novels with titles A, B, C, D and E in the order B, C, D, E and then A produces the same result. When it comes to library books, the order in which we scan the novels for check out is of no importance since in the end the same novels are carried out the door by the library patron.
Rewrite the following conditional statement as a converse, inverse, and contrapositive: If two angles are supplementary, then one of the two angles is acute.
Answer:
Part 1) The converse is "If one of the two angles is acute then two angles are supplementary"
Part 2) The inverse is " If two angles are not supplementary, then one of the two angles is not acute"
Part 3) The contrapositive is "If one of the two angles is not acute then two angles are not supplementary"
Step-by-step explanation:
we have
The following conditional statement " If two angles are supplementary, then one of the two angles is acute"
The hypothesis is "If two angles are supplementary"
The conclusion is " one of the two angles is acute"
Part 1) Rewrite the conditional statement as a converse
we know that
To form the converse of the conditional statement, interchange the hypothesis and the conclusion
therefore
The converse of " If two angles are supplementary, then one of the two angles is acute" is "If one of the two angles is acute then two angles are supplementary"
Part 2) Rewrite the conditional statement as a inverse
we know that
To form the inverse of the conditional statement, negating both the hypothesis and conclusion of a conditional statement.
therefore
The inverse of " If two angles are supplementary, then one of the two angles is acute" is " If two angles are not supplementary, then one of the two angles is not acute"
Part 3) Rewrite the conditional statement as contrapositive
we know that
To form the contrapositive, switching the hypothesis and conclusion of a conditional statement and negating both
therefore
The contrapositive of "If two angles are supplementary, then one of the two angles is acute" is "If one of the two angles is not acute then two angles are not supplementary"
Country A has a growth rate of 3.4% per year. The population is currently 4,118,000, and the land area of Country A is 29,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answer:
time period is 260.57 years
Step-by-step explanation:
given data
growth rate = 3.4 % = 0.034
population = 4118000
area P = 29000000000 square yard
to find out
time period that one person for every square yard of land need
solution
we will apply here population growth formula that is
total population P = initial population × [tex]e^{rt}[/tex] ..............1
here r is rate of growth and t is time period and
we consider here initial population is current population
so put value in equation 1 to get t
29000000000 = 4118000 × [tex]e^{0.034t}[/tex]
take ln both side
ln 7042.25 = ln [tex]e^{0.034t}[/tex]
8.8596 = 0.034 t
t = 260.57
so time period is 260.57 years
It is estimated that a brachiosaurus weighed around 124, 000 pounds. A tyrannosaurus Rex weighed about 8.16*10^3 kilograms. Of a Tyrannosaur eats an entire Brachiosaurus, about how much will the Tyrannosaur weigh? Use scientific notation and give your answer in grams.
Answer:
6.44×10⁷ g
Step-by-step explanation:
The scenario seems unlikely, as a brachiosaurus weighs about 6.9 times as much as a tyrannosaur. The sum of the two weights is ...
8.16×10³ kg + 1.24×10⁵ lb
= 8.16×10³ kg + (1.24×10⁵ lb)/(2.2046 lb/kg)
= 8.16×10³ kg + 5.62×10⁴ kg
= 6.44×10⁴ kg . . . . . rounded to 3 significant figures
= 6.44×10⁷ g . . . . . . weight of not-so-hungry tyrannosaur
_____
1 kg = 10³ g
Find the total amount. $3600 at 6.5% compounded annually for 2 years.
Answer:
$4083.21
Step-by-step explanation:
Compound interest is an interest rate that stacks on top of each other
So basically I did 3600 × 1.065 for the first year
=3834
then i did 3834 × 1.065 again to calculate the second year
=4083.21
Hope this helps! If you have any questions ask! :)
Answer:
D. $4083.21
Step-by-step explanation:
Concetta had a 2kg bag of flour. She used 180g of flour to make biscotti. How many kilograms of flour are left in the bag?
Provide your answer below:
___ kg
Concetta initially had 2kg of flour. After using 180g to make biscotti, she was left with 1820g of flour. This equates to 1.82kg when converted back from grams to kilograms.
Explanation:At the beginning, Concetta had a bag of flour weighing 2kg. We need to convert kilograms to grams first to make the units the same, and we know that 1kg is equal to 1000g. Therefore, she initially had 2000g of flour.
After making biscotti, she used 180g of flour. So, to find out how much she has left, we subtract the amount used (180g) from the total amount (2000g), which results in 1820g of flour remaining.
Finally, we need to convert this back to kilograms. Because there are 1000g in 1kg, we divide 1820 by 1000, which gives us that Concetta has 1.82kg of leftover flour.
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Malachi is a pretty good football player. During the first seven games of the season he scored between three and eighteen touchdowns. Fans are now confident that he will score at least ten touchdowns in the next game. What is a problem with this conclusion?
Answer: so in the first 7 games, eh scored between 3 and 18 touchdowns.
if you assume there is a even distribution, you will get a media of (18 -3) /2 + 3 = 10.5
so yes, in theory he will score 10.5 more or less.
the first error is assuming that he will score at least 10.5 on watching this result, 10.5 is the most probable number, not the minimum.
the second problem here, is that you are doing statistics with just 7 samples, that is not enough samples to do proper statistics.
Suppose that the universal set is U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Express each of these sets with bit strings, where the ith bit in the string is 1 if i is in the set and 0 otherwise:
a){ 3, 4, 5 }
b){ 1, 3, 6, 10 }
c){ 2, 3, 4, 7, 8, 9 }
Answer:
a.0011100000
b.1010010001
c.0111001110
Step-by-step explanation:
We are given that a universal set
U={1,2,3,4,5,...10}
We have to express each given set with bit strings , where the ith bit in the string is 1 if i is in the set and 0 otherwise
a.{3,4,5}
For 1=0 because 1 is not in the given set
For 3=1, For 4=2 , For 5=1 because 3,4 and 5 are in the set
For 2=0
For 6=0
For 7=0
For 8=0
For 9=0
For 10=0
Therefore, bit string=0011100000
b.{1,3,6,10}
For 1,3,6 and 10 write 1 because these elements are present in the set and for 2,4,5,7,8,9 write 0 because these elements are not present in the set
Bit string =1010010001
c.{2,3,4,7,8,9}
Similarly
Those elements which are present in the set then for those elements write 1 otherwise 0.
Bit string =0111001110
Which function results after applying the sequence of transformation to f(x)=x^5 reflection over the x axis vertically stretch by a factor 2 shift down 1 unit
Answer:
Step-by-step explanation:
y = -2x^5 - 1
Desired reflection would be f'(x) = -2x⁵ -1
How to find a reflection in the graph?The reflection over the x-axis equation's basic guidelines The reflection equation of the new reflected graph will be y=f(x) y = f (x) given an equation, y=f(x) y = f (x). Simply multiplying the function by 1 will result in a curve that is mirrored across the x-axis.
Given the equation f(x) = x⁵, From reflection rile, the reflection of this graph would be f'(x) = - x⁵.
asked to stretch the graph by 2 and shift down 1 unit.
Therefore, the function results after applying the sequence of transformation are f'(x) = -2x⁵ -1. for better understanding a graph is attached below.
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How many different ways are there to choose a chairman, assistant chairman, and a treasurer department of 20 people? How many ways are there to choose a committee of 4 people from this same committee? If the committee is required to be comprised of 2 women and 2 men, and there are 5 women in the department, how many different committees are possible?
Answer:
1) 6840
2) 4845
3) 1050
Step-by-step explanation:
1) How many different ways are there to choose a chairman, assistant chairman, and a treasurer department of 20 people?
As it ordered:
C AC TD
20 19 18 = 20.19.18 = 6840
2) How many ways are there to choose a committee of 4 people from this same committee?
Not ordered:
C₂₀,₄ = 20! = 20.19.18.17.16! = 20.19.18.17 = 4845
16! 4! 16! 4.3.2.1 4.3.2.1
3) If the committee is required to be comprised of 2 women and 2 men, and there are 5 women in the department, how many different committees are possible?
5 women and 15 men
committee: 2 w and 2 m
C₁₅,₂*C₅,₂ = 105*10=1050
C₁₅,₂ = 15! = 15.14.13! = 15.14 = 105
13! 2! 13! 2.1 2
C₅,₂ = 5! = 5.4.3! = 5.4 = 10
3! 2! 3! 2.1 2
My brother and I walk the same route to school every day. My brother takes 40 minutes to get to school and I take 30 minutes. Today, my brother left 4 minutes before I did. How long will it take me to catch up with him?
Answer:
24 minutes.
Step-by-step explanation:
Let D represent the distance from school to home and T represent time.
We have been given that your brother takes 40 minutes to get to school.
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
[tex]\text{Your brother's speed}=\frac{D}{40}[/tex]
You take 30 minutes to get to school.
[tex]\text{Your speed}=\frac{D}{30}[/tex]
Your brother left 4 minutes before you did, so distance traveled by him would be:
[tex]\frac{D}{40}\times (T+8)[/tex]
You speed: [tex]\frac{D}{30}\times T[/tex]
You will catch your brother, when both distances would be same:
[tex]\frac{D}{40}\times (T+8)=\frac{D}{30}\times T[/tex]
Cross multiply:
[tex]30D(T+8)=40DT[/tex]
Use distributive property:
[tex]30DT+240D=40DT[/tex]
[tex]30DT-30DT+240D=40DT-30DT[/tex]
[tex]240D=10DT[/tex]
Switch sides:
[tex]10DT=240D[/tex]
[tex]\frac{10DT}{10D}=\frac{240D}{10D}[/tex]
[tex]T=24[/tex]
Therefore, it will take you 24 minutes to catch up your brother.
To catch up to your brother who has a 4-minute head start, it will take you 12 minutes.
Explanation:To determine how long it will take for you to catch up with your brother on the way to school, we need to consider the different walking speeds and the time advantage your brother has.
First, let's determine your walking speeds. If your brother takes 40 minutes to reach school and you take 30 minutes for the same route, then assuming you both walk at a constant speed, we can say that your walking speed is 4/3 times faster than your brother's speed because 40 minutes divided by 30 minutes equals 4/3.
Now, given that your brother has a 4-minute head start, let's calculate the time it takes for you to catch up to him:
Since your speed is 4/3 times that of your brother's, in every 4 minutes, you gain a 1-minute advantage over him because 4 minutes divided by (4/3) equals 3 minutes, which means you walk the same distance 1 minute faster. Your brother's head start is 4 minutes, so you will catch up to him in 4 minutes * 3/1 = 12 minutes.
Therefore, it will take you 12 minutes to catch up with your brother.
Alondra challenges you to play a math game. She says, "I am thinking of a whole number. If you double my number and subtract 6, the result is less than 2 units away from 0. What number am I thinking of?"
Answer:
3
Step-by-step explanation:
Let "a" represent Alondra's number. Then the math she performs on it is ...
2a-6 . . . .double my number and subtract 6
| 2a-6 | < 2 . . . . . the result is less than 2 units from zero
This absolute value expression can be "unfolded" to two of them ...
-2 < 2a -6 < 2
Dividing by 2 gives ...
-1 < a -3 < 1
Adding 3, we get ...
2 < a < 4
The only whole number in this range is ...
a = 3
Alondra is thinking of the number 3.
And engineer in blueprint calls for a 10.5 foot clearance from some pipes to the wall the pipes are currently 8.25 feet from the wall how many feet will the pipes need to be moved
Answer:222
Step-by-step explanation:
add it
The pipes need to be moved 2.25 feet.
To determine how many feet the pipes need to be moved:
Start with the required clearance: 10.5 feet.Subtract the current distance of the pipes from the wall: 8.25 feet.Calculate the difference to find the distance the pipes need to be moved: 10.5 - 8.25 = 2.25 feet.Therefore, the pipes need to be moved 2.25 feet away from the wall to achieve the required clearance.
Please help me! I don’t understand these problems
(Geometry) PB is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
PLEAS EXPLAIN HOW TO DO THIS STEP BY STEP!
Answer:
the answer is 5
Step-by-step explanation:
if you have any questions or a more detailed explanation feel free to ask in the comments.
State the practical meaning of the slope and y-intercept for the situation described. The cost, in dollars, of retaining the services of a computer repairman in Anchorville is given by C = 48x + 18, where x is the number of hours worked.
Explanation:
The cost for retaining the services when no time is spent is $18. That $18 is the minimum cost of the service call.
The added cost each hour is $48, so the per-hour charge is $48.
What is the slope of the equation y – 3 = –4(x – 5)?
Answer:
[tex] -4 = m[/tex]
Step-by-step explanation:
According to the Point-Slope Formula, y - y₁ = m(x - x₁), m represents the rate of change [slope], so in this case, -4 is our slope.
I am joyous to assist you anytime.
There are three boxes of eggs. In each box there is either a set of big eggs, small eggs or big and small eggs mixed. The boxes are labelled (shock) LARGE, SMALL and MIXED but each box is labelled incorrectly. What is the least number of boxes you can open to know which eggs are in which box and why?
Answer: Hi!
Let's start, you have 3 boxes and 3 types off eggs inside of each. The fact that they each box is labelled incorrectly means that inside the box labelled Large, only can be the set of small or mixed eggs.
So, let's suppose we open this Box labelled LARGE and inside of it we find the small eggs.
now we have two remaining boxes, the labeled SMALL and the labelled MIXED.
the MIXED can only contain the set of large eggs or the set of small, because you know that is wrong labelled, and also you know that the small eggs are in the first box that you oppened, so here are the large eggs, and now in the last box is the last set of eggs, the mixed one.
So you only will need to open one box to know which eggs are in what box.
A hiker walks 4 km north and then 5 km northeast. Draw displacement vectors representing the hiker's trip and draw a vector that represents the hiker's net displacement from the starting point.
Answer:
[tex]u+v =8.323717394km[/tex]
Ф=[tex]64.86489406[/tex]°
Step-by-step explanation:
[tex]u=4km[/tex]
[tex]v=5km[/tex]
For easy calculations let's decompose the vector in its rectangular components:
[tex]u_x=u*cos(\alpha )=4000*cos(90)=4000*0=0[/tex]
[tex]u_y=u*sin(\alpha )=5000*sin(90)=4000*1=4000[/tex]
[tex]v_x=v*cos(\beta )=5000*cos(45)=3535.533906[/tex]
[tex]v_y=v*sin(\beta )=5000*sin(45)=3535.533906[/tex]
Now lets calculate the resultant vector:
[tex]u+v=R[/tex]
[tex]R=R_x+R_y[/tex]
[tex]R_x=u_x+v_x=0+3535.533906=3535.533906[/tex]
[tex]R_x=u_y+v_y=4000+3535.533906=7535.533906[/tex]
Finally let´s calculate the magnitude and direction of R:
║[tex]R[/tex]║=[tex]\sqrt{(R_x)^{2}+(R_y)^{2} }=\sqrt{(3535.533906)^{2}+(7535.533906)^{2} } =8.323717394km[/tex]
Ф=[tex]arctan(\frac{R_y}{R_x})=arctan(\frac{7535.533906}{3535.533906})=64.86489406[/tex]°
Sarah is going to The store 2.5 miles away. She has only 15 minutes to get there before they close. At what average speed must she ride to get to the store before they close?
Answer:
Sarah must has to ride with average speed 10 miles per hour.
Step-by-step explanation:
Average Speed tells the rate at which object is travelling his whole journey.
[tex]Average\ Speed\=\ \frac{Total\ distance\ traveled}{Total\ time\ taken}[/tex]
∴ [tex]Average\ Speed=\dfrac{2.5}{\frac{15}{60}}[/tex]
⇒ [tex]Average\ Speed=\dfrac{2.5}{15}\times 60[/tex]
⇒ Average Speed = 10 miles per hour
Hence, Sarah has to travel with average speed more than 10 miles per hour.
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Which of the following is equivalent to 5 square root 13^3?
When trying to find a root of a number ( the little number included with the square root symbol) this is the same as raising the number to that fraction.
Example : ∛5 would be the same as 5^1/3
So in the given problem the 5th root can be written as x^1/5
Now the number is 13^3, so to simplify the 5th root, the value could be written as 13^3/5
Answer:
When trying to find a root of a number ( the little number included with the square root symbol) this is the same as raising the number to that fraction.
Example : ∛5 would be the same as 5^1/3
So in the given problem the 5th root can be written as x^1/5
Now the number is 13^3, so to simplify the 5th root, the value could be written as 13^3/5
Step-by-step explanation:
Given any triangle in the plane, associate to each side an outward pointing normal vector of the same length as the side. Show that the sum of these three vectors is always 0.
Let , a, b and c be the length of three sides of triangle, represented in terms of vectors as [tex]\vec{a},\vec{b},\vec{c}[/tex].
Now, vector of same Magnitude acts as normal vector to each side.
So, equation of any vector p having normal q is given by
[tex]\vec{p} \times\vec{q}[/tex]
Now sum of three vector and it's normal is given as
[tex]=\vec{a} \times\vec{a}+\vec{b} \times\vec{b}+\vec{c} \times\vec{c}\\\\=0+0+0\\\\=0[/tex]
Cross product of two identical vectors is Zero.
[tex]\rightarrow \vec{i} \times\vec{i}=0[/tex]
The sum of the outward normal vectors of a triangle's sides is always 0 due to vector closure around the triangle.
Let us denote the vertices of the triangle as A, B, and C. The sides of the triangle are AB, BC, and CA. We need to show that the sum of the outward normal vectors of these sides is zero.
Assign Vectors:Let u be the outward normal vector of side AB.
Let v be the outward normal vector of side BC.
Let w be the outward normal vector of side CA.
These normal vectors are each associated with a side of the triangle and have the same length as the corresponding side.
Triangle Property:For any triangle, the vector from one vertex to another can be expressed as the difference of position vectors:
AB = B - A
BC = C - B
CA = A - C
Sum of Normal Vectors:The normal vector u to side AB can be aligned such that u is perpendicular to AB and has magnitude equal to the length of AB.
Similarly, v is perpendicular to BC and has magnitude equal to the length of BC.
Similarly, w is perpendicular to CA and has magnitude equal to the length of CA.
To show that the sum of these vectors is zero, consider that the sum of vectors around a closed polygon (in this case, the triangle) is zero. The outward normal vectors form a closed system since each side’s normal vector effectively cancels out with the adjacent ones due to their perpendicularity and length.
Thus:
u + v + w = 0.
Emina took out a 5/1 variable-rate mortgage for $120,000. The interest rate for the first period was fixed at 5.25%, and the loan was amortized over 30 years. At the end of the initial loan period, the interest rate was 6.75%, plus a 1.5% margin. What was Emina's monthly mortgage payment during the initial fixed-rate period? Show your work.
Answer:
662.64
Step-by-step explanation:
i got it wrong on apex and it told me the right answer. you're welcome.
Answer:
$662.63
Step-by-step explanation:
Cost of mortgage = $120,000
Interest rate of first period = 5.25%
The loan was amortized over 30 years.
The interest rate at the end of the initial loan period = 6.75%
Margin = 1.5%
The loan was amortized for over (30*12) months
= 360 months
The interest rate of the first period per month = 5.25% / 12
= 0.0525/12
= 0.004375
Payment for monthly mortgage =
(120000(0.004375)) / 1 - (1 + 0.004375)^-360
= 525 / 1 - (1.004375)^-360
= 525 / (1 - 0.2077)
= 525 /0.7923
= 662.63
= $662.63
Take a stick of unit length and break it into three pieces, choosing the break point at random. (The break points are assumed to be chosen simultaneously). What is the probability that the three pieces can be used to form a triangle?
Answer:
We can form a triangle if none of the resulting pieces is at least 1/2, i.e. if no ... It is not hard to show that if you choose a point randomly in this triangle, the distances to the three ... of lengths that you obtain by breaking a stick at two random points. ..... we get line segments joining the midpoints of the edges of the triangle.
Step-by-step explanation:
The probability that three pieces from breaking a unit length stick can form a triangle, based on the triangle inequality theorem and geometric probability principles, is 1/4.
Explanation:The question belongs to the area of Mathematics called geometric probability. Here, we are asked to find the probability that three stick pieces formed from a unit length stick can form a triangle.
The rule which applies to this situation is the triangle inequality theorem. This theorem states that for any triangle, the length of any side (say c) must be less than the sum of the lengths of the other two sides (say a and b). In mathematical terms, a + b > c.
Considering the above theorem, since we break the stick into three pieces simultaneously, the break points must be such that each piece is less than 0.5 units to be able to form a triangle. In this case, the length of the longest piece (c) will be less than the sum of the lengths of the other two pieces.
So, to form a triangle, each piece must be less than 0.5 in length. The region where this condition is satisfied forms a triangle in a unit square, thus giving a geometric probability of 1/4. Hence, the probability that the three pieces can form a triangle is 1/4.
Learn more about Geometric Probability here:https://brainly.com/question/33899096
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A rectangular swimming pool measures 50 meters in length and 25 meters in width. Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters.A scale drawing of a school bus has a scale of 1/2 inch to 5 feet. If the length of the school bus is 4 1/2 inches on the scale drawing, what is the actual length of the bus? Explain or show your reasoning
Answer:
Part A) In the scale drawing the length of the swimming pool is 10 cm and the width is 5 cm
Part B) The actual length of the bus is 45 ft
Step-by-step explanation:
Part A) Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters
we know that
The scale is [tex]\frac{1}{5} \frac{cm}{m}[/tex]
To find out the dimensions of the pool in the scale drawing, multiply the actual dimensions by the scale factor
Find the length in the scale drawing
[tex]\frac{1}{5} \frac{cm}{m}(50\ m)=10\ cm[/tex]
Find the width in the scale drawing
[tex]\frac{1}{5} \frac{cm}{m}(25\ m)=5\ cm[/tex]
Part B) What is the actual length of the bus?
we know that
The scale is [tex]\frac{0.5}{5} \frac{in}{ft}=0.1\frac{in}{ft}[/tex]
The length of the school bus is 4 1/2 inches on the scale drawing
To find out the actual length of the bus, divide the length in the scale drawing by the scale
Convert mixed number to an improper fraction
[tex]4\frac{1}{2}\ in=\frac{4*2+1}{2}=\frac{9}{2}\ in[/tex]
Find the actual length of the bus
[tex]\frac{\frac{9}{2}\ in}{0.1\frac{in}{ft}}=45\ ft[/tex]
Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: eight percentage points; confidence level 90%; from a prior study, ModifyingAbove p with caret is estimated by the decimal equivalent of 34%.
Answer:
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Step-by-step explanation:
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a chocolate company makes chocolate malt balls that are 0.75 inches in diameter. the carton they are to be packed in is approximately a rectangular prism with the dimensions 3 inches by 3 inches by 7.5 inches. how many malt balls will fit in the carton?
(reminder: you can assume that for random packing space 190% of the volume of the sphere is needed to pack the spheres and volume if sphere is 4/3π x r^3)
A. 160 balls
B. 210 balls
C. 305 balls
D. 82 balls
Answer:
A. 160 balls
Step-by-step explanation:
First we find the volume of each sphere.
diameter = d = 0.75 in.
radius = r = d/2 = 0.75/2 in. = 0.375 in.
V = (4/3)π(r^3) = (4/3)(3.14159)(0.375 in.)^3 = 0.221 in.^3
Because of the assumption about the space occupied by a sphere in random packing, we now calculate 190% of the volume of the sphere.
190%V = 1.9 * 0.221 in.^3 = 0.420 in.^3
Now we calculate the volume of the box.
V = LWH = 3 in. * 3 in. * 7.5 in. = 67.5 in.^3
To find out the number of balls that fit in the box, we divide the volume of the box by the randomly packed ball volume.
number of balls = (67.5 in.^3)/(0.420 in.^3) = 160.8
Answer: 160 balls
Gift bags are being distributed at a birthday party. If there was a total of 140 jolly ranchers and 60 candy bars placed into gift bags, what is the greatest number of gift bas made if each candy is equally distributed between them? How many of each candy will be in the seperate bags?
Answer:8,400. I think that is the answer. Hope you get it right.