On solving the provided question we can sat that, the geometric series' total is 12.34, and they care convergent.
What is geometric series?An infinite series in mathematics known as a geometric series has the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. One straightforward illustration is the geometric series with a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, totaling 2 (or 1 if the first term is locked out).
The answer to the query is
The geometric series is made up of the numbers 100/81, 10/9, 1, 9/10, 81/100, 729/1000, and so on.
The provided series appears to be moving forward geometrically with a fixed ratio r.
r = second term, first term, or a2, a1.
[tex]= (10/9) / (100/81)[/tex]
[tex]= > 9/10[/tex]
We are aware that convergence occurs when 'r' is smaller than 1.
In this case, 9/10 1 is convergent.
This sums up an endless geometric sequence, without a doubt.
Infinite series' sum in GP equals a. (1 - r)
The usual ratio is 9/10, where an is the first word.
The geometric series' sum is equal to (100/81) / (1 - 9/10).
[tex]= > (100 / 81) / ( 1 / 10)\\ = > 100 / 8.1\\ = > 12.34[/tex]
The given series is therefore convergent, and its total is 12.34.
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The range of sound intensities that the human ear can detect is so large that a special decibel scale (named after Alexander Graham Bell) is used to measure and compare sound intensities. The decibel level (dB) is given by I dB(I) = 10 log Io log() where Io is the intensity of sound that is barely audible to the human ear. Use the decibel level formula to find the decibel level for the following sounds. Round to the nearest tenth of a decibel. I = 1.58 x 108 · 10 (a) Automobile traffic, dB I = 10,800 · Io (b) Quiet conversation, dB (c) Fender guitar, dB I = 3.16 * 1011.10 (d) Jet engine, dB I = 1.58 x 1015. Io
For automobile traffic, dB=81.987657 dB.
For quiet conversation is 40.33423 dB.
For fender guitar, 115.56302 dB.
For jet engine, 151.98657 dB.
(A)
The intensity of automobile traffic is, I=1.58x10^8 I.
Given: dB=10 log (I/I0)
Substituting the value of I,
dB= 10 log (1.58x10^8 I/I)
=10 log (1.58x10^8)
Using the logarithm property,
=10 (log (1.58)+log (10^8))
=10 (log (1.58)+8 log (10)
=10( log (1.58)+8(1)
=80+1.98657
=81.98657
Thus, for automobile traffic, dB=81.987657 dB.
B)
Quiet conversation, I=10800 I0
dB= 10 log (10800 I0/I0)
=10 log (10800)
=10 log (1.08x10^4)
=10 log (1.08)+log (10^4)
=10 (log (108)+4log (10))
=10 (log (1.08+4*(1))
=40+10 log (1.08)
=40+0.33423
=40.33423 dB.
Thus, for quiet conversation is 40.33423 dB.
C)
Fender guitar, I=3.16x10^11 I0
dB= 10 log (3.16x10^11 I0/I0)
=10 (log (3.16)+11)
=110+10 log (3.16)
=110+5.56302
=115.56302
Thus, for fender guitar, 115.56302 dB.
D)
Jet engine, I=1.58x10^5 I0
dB= 10 log (1.58x10^15 I0/I0)
=10 (log (1.58)+15)
=150+10 log (1.58)
=150+1.98657
=151.98657
Thus, for jet engine, 151.98657 dB.
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What are the degree and leading coefficient of the polynomial?
-9-8w+3w+12w³
The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of w is 3, so the degree of the polynomial is 3.
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this case, the leading coefficient is 12.
In summary, the polynomial -9-8w+3w+12w³ has degree 3 and leading coefficient 12.
What is √x⁵y⁶ expressed in simplified form?
x²y³√x
xy√xy
x²y²√xy
x²y√x
The simplified form of the expression [tex]\sqrt{x^5y^6}[/tex] is [tex]x^2y^3\sqrt{x}[/tex]
The given expression is [tex]\sqrt{x^5y^6}[/tex]
The expression the mathematical statement that consist of different types of variables, numbers and the mathematical operators. The mathematical operators are addition, subtraction, division and multiplication. The equal sign and the inequality sign will not be the part of the expression
Here the given expression is
[tex]\sqrt{x^5y^6}[/tex]
We know that
[tex]\sqrt{x^2}[/tex] = x
Therefore, for each square values we can take that term outside of the square root
Here you can take x^4 take outside as x^2 and one x will remain in the square root, similarly you can take y^6 outside of the square root as y ^3
The final result = [tex]x^2y^3\sqrt{x}[/tex]
Therefore, the simplified form is [tex]x^2y^3\sqrt{x}[/tex]
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A rectangular field is 60 meters wide and 100 meters long.
Give the length and width of another rectangular field that has the same perimeter but a larger area.
Answer:
80 Meters by 80 Meters
Step-by-step explanation:
Perimeter is the distance around the rectangle. 60+60+100+100 = 320
The perimeter is 320 meters.
Area = Length times width
The area would be
100x 60 = 6,000 [tex]m^{2}[/tex]
If we change the length and width to 80 meters we would have the same perimeter
80+80+80+80 = 320 Meters, but the area would be larger
Area = 80 x 80 = 6,400 [tex]m^{2}[/tex]
Luisa and Jacob each solve the radical equation √5+4x = x. Luisa determines that the solution is
H= 5. Jacob thinks that the solution is a = -1. Use the space below to identify which student is
correct. Use words and mathematics to justify your answer and show any work completed to make your
selection.
Answer: Luisa is correct.
Step-by-step explanation: Luisa is correct. To find the solution to the equation, we need to isolate the radical expression on one side of the equation. If we subtract x from both sides, we get √5 + 4x - x = x - x, or √5 = 0. Since the square root of any number is always positive, this equation has no solution. Therefore, the solution is H = 5.
On the other hand, if we square both sides of the equation, we get 5 + 8x + 4x^2 = x^2. If we simplify this equation, we get x^2 + 8x - 5 = 0. This equation can be solved using the quadratic formula, which gives us x = (-8 +/- sqrt(64 + 20))/2. This simplifies to x = (-8 +/- sqrt(84))/2. The solutions to this equation are x = -1 and x = 5. However, since we squared both sides of the original equation, we have to check whether these solutions actually work in the original equation. Substituting x = -1 into the original equation gives us √5 + 4(-1) = -1, or √5 = -1. This is not a valid solution, since the square root of any number is always positive. However, substituting x = 5 into the original equation gives us √5 + 4(5) = 5, or √5 = 0. This is a valid solution, since the square root of any number is always positive. Therefore, the only solution to the original equation is x = 5, which is the solution that Luisa found.
A line passing through the points (-8, 13) and (-6, 19)
Answer:
y = 3x + 37
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 8, 13 ) and (x₂, y₂ ) = (- 6, 19 )
m = [tex]\frac{19-13}{-6-(-8)}[/tex] = [tex]\frac{6}{-6+8}[/tex] = [tex]\frac{6}{2}[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 8, 13 ) , then
13 = 3(- 8) + c = -24 + c ( add 24 to both sides )
37 = c
y = 3x + 37 ← equation of line
g if the determinant of a matrix is , and the matrix is obtained from by adding times the second row to the first, then
Therefore the solution to the given matrix problem is
a)det(B) = det(A) = 3 ,det(B) = 3*det(A) = 9 and c)det(B) = -det(A) = -3
What is matrix ?A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity.
Here,
The following will be demonstrated using determinant properties:
A)Det(B) = 3
B) Det(B) = 9
C) det(B) = -3
Assuming A is a 4x4 matrix, we can see that:
det(A) = 3.
a) In this case, we are adding one row to another row by performing a transformation to the data in A. These operations don't alter the matrix's determinant, therefore in this instance:
det(B) = 3 = det(A)
b) If K is used to multiply a row of A to produce B, then:
B = det(K*det) (A).
In this situation, we have:
det(A) = 3*det(B) = 9
c) If we switch two rows around once (this is an odd permutation), the determinant's sign changes:
det(B) = -det(A) = -3
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The complete question is "If the determinant of a 4 by 4 matrix A is det(A) = 6, and the matrix D is obtained from A by adding 9 times the third row to the first, then det(D) is equal to?"
An electric car battery, when fully charged, can travel 260 miles. The car uses 232 miles of charge on a drive.
Enter the percentage of miles the car has left in battery charge?
The percentage of miles the car has left in battery charge is 10.77%
Total distance traveled when fully charged = 260 miles
The total charged used by the car = 232 miles of charges
The remaining charges left in the car battery = Total distance traveled when fully charged - The total charged used by the car
Here we have to use the subtraction
Substitute the values in the equation
= 260 - 232
= 28 miles of charges
The percentage of miles the car has left in battery charge = (28/260) × 100
= 10.77%
Therefore, 10.77% miles of charge left in the battery
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Which of the following is the correct representation of permutation?
A.rPn
B .P (n,r)
C. C(n, r)
D .nCr
(Will mark brainlist)
Answer:
P (n,r)
Step-by-step explanation:
The correct representation for a permutation is P (n,r).
Read the following prompt and type your response in the space provided.
Look at the problem and work shown. In which line was an error made and what should have been done differently?
Six less than 4 times a number is 50. What is the number?
6 – 4n = 50 (line 1)
6 – 6 – 4n = 50 – 6 (line 2)
–4n = 44 (line 3)
–4n÷ –4 = 44÷ –4 (line 4)
n = –11 (line 5)
.
Answer: Line 1
Step-by-step explanation:
Without looking at the context given, everything seems to be normal, everything is correct. Inputting n = -11 into line 1 makes it true. But when we take a look at the context given, we can see that the equation that it said "6 less than 4 times a number" meaning we were supposed to take 6 and subtract it from 4 times the number, meaning the actual equation is
4n - 6 = 50
Therefore, line 1 made an error
In the diagram below, AB || CD, AD || BC, m/ABC = 110°,
m/CDE = 37° and m/ECB = 43°. Find m/DEC.
A
B
110°
E
D
37°
43°
C
Use photo to understand better PLEASE HELP
use the central limit theorem to approximate the probability that the total number of magazines that charlie reads in one full year (12 months of 30 days each) is between and . (note that you are asked about the number of magazines, not the number of minutes of total reading time.) (give an answer accurate to at least 3 decimal places.) (please answer the question as is, even if you have doubts.)
Applying central limit theorem number of books reads in one full year is equal to 720.
As given in the question,
Let X be the number of magazine read by Charlie.
Number of days in 12 months consider 30 days in each month 'n'
= 12 × 30
= 360 days
Number of magazine lies between 3500 and 3600
Consider μ = 2 and σ = √2
Central limit theorem , we have
z =( [tex]\bar{X}[/tex] - μ )/ σ/√n
[tex]\bar{X}[/tex] = X / n
Probability of total number of magazine reads between ( 3500 to 3600)
= P ( 3500 ≤ X ≤ 3600 )
= P( 3500/360 ≤ X/ n ≤3600/360)
= P( 9.72< X/n≤ 10 )
= P [ (9.72 - 2)/ √2/√360 ≤ ( X/n - μ)/σ/√n ≤(10 - 2)/ √2/√360]
= P(130.2 ≤ Z ≤107.4)
= P( 0≤Z≤107.4) - P (0≤Z≤130.2)
= φ( 130.2) + φ(107.4)
= 1 + 1 { φ(a) = 1 , a>1}
= 2
Number of books Charlie reads in one year =
∑2ₙ where n = 1 to 360
= 2+ 2+ 2+ ....+ 2 ( 360 times)
= 720 books
Therefore, using central limit theorem number of books reads in one full year is equal to 720.
The above question is incomplete , the complete question is :
Use the central limit theorem to approximate the probability that the total number of magazines that Charlie reads in one full year (12 months of 30 days each) is between 3500 and 3600. (Note that you are asked about the number of magazines, NOT the number of minutes of total reading time.) (Please answer the problem as written.) (Give an answer accurate to at least 3 decimal places.)
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You are doing a Diffie-Hellman-Merkle key exchange with Aisha using generator 7 and prime 437. Your secret number is 227. Aisha sends you the value 308. Determine the shared secret key.
Answer:
382^2 mod
Step-by-step explanation:
To determine the shared secret key, we need to use the formula (g^a mod p)^b mod p = (g^b mod p)^a mod p, where g is the generator, p is the prime, a is our secret number, and b is the value sent by Aisha. Plugging in the values, we get (7^227 mod 437)^308 mod 437 = (7^308 mod 437)^227 mod 437.
To solve for the shared secret key, we first need to calculate (7^308 mod 437). This can be done by raising 7 to the 308th power and then taking the remainder when divided by 437. We can do this by repeatedly squaring 7 and taking the remainder each time. This results in the following sequence:
7^2 mod 437 = 49
7^4 mod 437 = 161
7^8 mod 437 = 267
7^16 mod 437 = 9
7^32 mod 437 = 49
7^64 mod 437 = 161
7^128 mod 437 = 267
7^256 mod 437 = 9
7^512 mod 437 = 49
Since 512 is greater than 308, we can stop here and use the value 49 as the result of 7^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: (49^227 mod 437)^308 mod 437 = (49^308 mod 437)^227 mod 437.
To solve for the shared secret key, we need to find the value of 49^308 mod 437. This can be done using the same method as before, by repeatedly squaring 49 and taking the remainder each time. This results in the following sequence:
49^2 mod 437 = 67
49^4 mod 437 = 382
49^8 mod 437 = 221
49^16 mod 437 = 67
49^32 mod 437 = 382
49^64 mod 437 = 221
49^128 mod 437 = 67
49^256 mod 437 = 382
Since 256 is greater than 308, we can stop here and use the value 382 as the result of 49^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: 382^227 mod 437 = 382^227 mod 437.
To find the shared secret key, we need to calculate 382^227 mod 437. This can be done using the same method as before, by repeatedly squaring 382 and taking the remainder each time. This results in the following sequence:
9
Tom and Adil are the two runners in a 200-metre race.
Tom completes the race in 24 seconds.
Adil completes the race at an average speed of 28.8 kilometres per hour.
Who wins the race?
You must show your working.
[3
Answer:
Since Adil takes 25 seconds to complete the race, and Tom takes 24 seconds, Tom wins the race.
Step-by-step explanation:
To determine who wins the race, we need to first convert the given information into comparable units. The speed of Adil is given in kilometers per hour, while the time taken by Tom to complete the race is given in seconds. We can convert Adil's speed to meters per second by dividing by 3.6:
28.8 km/hr = 28.8 km/hr * (1 hour / 3600 seconds) * (1000 meters / 1 km)
= 8 meters/second
We can then use this value to find the time it takes Adil to complete the race:
time = distance / speed
= 200 meters / 8 meters/second
= 25 seconds
Since Adil takes 25 seconds to complete the race, and Tom takes 24 seconds, Tom wins the race.
2/3 • 6 = ?
Can someone please explain step by step on how I solve this equation?
Answer:
4
Step-by-step explanation:
2/3 • 6
*Multiply 2 and 6 by 3.
= (2 × 6) / 3
= 12/3
*12 divided by 3 is equal to 4.
= 4
___________
hope it helps!
Again, please just please help
The perimeter of ΔMNP is calculated as; 130
How to find the perimeter of the triangles?
From the given image, it is clear that some sides are congruent to others as indicated.
Thus, we see the following;
QM is parallel and congruent to RS.
Similarly, we see that QR is parallel and congruent to MS.
PR is parallel and congruent to QS.
NR = PR because of line segment division.
Thus, we can plug in the relevant values to get;
PR = QS = 22 = NR
Similarly, MS = SP = QR = 25
RS = x + 4 and so;
x + 4 + x + 4 = 5x - 34
42 = 3x
x = 14
MN = 5(14) - 34
MN = 36
Thus, the perimeter of ΔMNP = 36 + 25 + 25 + 22 + 22
= 130
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Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
The value of the other points in the number line for each case are;
a) M = -2¹/₂
N = -1
R = 4
b) M = -1
P = 1
R = 1.6
c) M = -125
P = 125
N = -50
d) N = -6
P = 15
R = 24
How to interpret Number Lines?a) We are given that P = 2¹/₂
From the point 0 of the number line to point P is 5 units and as such;
Each unit = 2¹/₂/5 = ¹/₂
Thus;
M = -2¹/₂
N = -1
R = 4
b) We are given that N = -0.4
From the point 0 of the number line to point N is 2 units and as such;
Each unit = 0.4/2 = 0.2
Thus;
M = -1
P = 1
R = 1.6
C) We are given that R = 200
From the point 0 of the number line to point R is 8 units and as such;
Each unit = 200/8 = 25
Thus;
M = -125
P = 125
N = -50
D) We are given that M = -15
From the point 0 of the number line to point N is 5 units and as such;
Each unit = 15/5 = 3
Thus;
N = -6
P = 15
R = 24
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What is 7/4 of 2b. Hope you see this
Answer:
Step-by-step explanation:3.5 bytes
4. Here is the graph of a linear equation.
Select all true statements about the line and its equation.
A. One solution of the equation is (3,2).
B. One solution of the equation is (-1,1).
C. One solution of the equation is (1, 3/2).
D. There are 2 solutions.
E. There are infinitely many solutions.
F. The equation of the line is y=1/4x+5/4.
G. The equation of the line is y=5/4x+1/4
The true statements are
One solution of the equation is (3,2) One solution of the equation is (-1,1) One solution of the equation is (1, 3/2) There are infinitely many solutions The equation of the line is y=1/4x+5/4Consider the two points in the line
(-1, 1) and (3, 2)
The slope of the line = (2-1) / (3 -(-1))
= 1/4
The slope intercept form is
y = mx + b
2 = (1/4)3 + b
2 = 3/4 + b
b = 2 - (3/4)
b = 5/4
The equation of the line y = (1/4)x + 5/4
(3, 2) and (-1, 1) are points on the line
Consider the point (1, 3/2)
3/2 = (1/4)1 + 5/4
3/2 = 1/4 + 5/4
3/2 = 3/2
Therefore, (1, 3/2) is the solution of the line
It has infinitely many solutions
Therefore, the correct statements are statements A, B, C, E, F
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The temperature of a 3.0-kg material increases by 5.0°C when 6,750 J of thermal energy are added to it. What is the specific heat of the material? J/(kg-°C)
Answer:
450J/(kg-°C)
Step-by-step explanation:
the basic stuff of temperature is 3.0kg×5.0°C ，then assumed to be x
the thermal energy was y
then it was a functions y=kx,the k was the specific heat of the material
[tex]k=\frac{6750}{15}[/tex]=450 J/kg·°C
Colorectal cancer (CRC) is the third most commonly diagnosed cancer among Americans (with nearly 147.000 new eases), ami the third leading cause of cancer death (with over 50.000 deaths annually). Research was done to determine whether there is a link between obesity and CRC mortality rates among African Americans in the United States by county. Below is the least-squares regression analysis from R-Studio. Parameter estimates: What does the slope mean in the context of the problem? The correlation between obesity rates and mortality rales is (circle one): Strong Very weak Moderately strong Write the equation for the least squares regression line (make sure to use the correct variable names):
The correlation between the obesity rate and the mortality rate is moderately strong.
In math correlation is defined as the a statistical measure that expresses the extent to which two variables are linearly related
Here we have given that Colorectal cancer (CRC) is the third most commonly diagnosed cancer among Americans (with nearly 147.000 new eases), ami the third leading cause of cancer death (with over 50.000 deaths annually).
Here the Research was done to determine whether there is a link between obesity and CRC mortality rates among African Americans in the United States by county.
And we need to find the correlation between obesity rates and mortality rates.
While we looking into the given question we have identified that the regression analysis was carried out to find the relationship between the obesity and CRC mortality rates so the response variable is mortality rate and input variable is obesity.
Therefore, the correlation is moderately stronger than the analyzed data.
Therefore, option (c) is correct.
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A 6 percent, semiannual coupon bond has a yield to maturity of 7.4 percent and a Macaulay duration of 5.7. The bond has a modified duration of _____ and will have a _____ percentage increase in price in response to a 25 basis point decrease in the yield to maturity5.4966; 1.37
25 bps decrease in interest rate, bond price increases by 1.425% when A bond with a 6 percent semiannual coupon has a 5.7.
Given that,
A bond with a 6 percent semiannual coupon has a 5.7 Macaulay duration and a 7.4 percent yield to maturity. A 25 basis point drop in yield to maturity will result in a ____ percentage price rise for the bond, which has an adjusted duration of .
We have to fill the blank.
We know that,
% increase in bond price = Duration of bond × % change in interest rate
= 5.70×0.25%
= 1.4250%
Therefore, 25 bps decrease in interest rate, bond price increases by 1.425% when A bond with a 6 percent semiannual coupon has a 5.7.
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the graphical solution method of linear programming employs the corner point method to find the optimal solution.
True, the graphical solution method of linear programming employs the corner point method to find the optimal solution.
Linear Programming
The most straightforward method of problem optimization is linear programming. We can turn a real-world issue into a mathematical model using this approach. Linear programming can be used to handle a wide range of issues in many different fields, although it is typically applied to issues where the goal is to maximize profit, cut costs, or use resources as sparingly as possible.
Explanation:
The corner point method of graphical linear programming involves plotting the linear equations representing the constraints of the problem onto a graph and then finding the points of intersection of the equations. These points of intersection are called the corner points, and the optimal solution will be located at the corner point that produces the greatest value.
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Question 3 (10 points)
How many 8' 2x4's and 12' 2x4's do you need to build a wall that is 12' long and 8' high
The wall has a single bottom plate, double top plate and 10 studs.
a
(10) 8' and (3) 12'
b
(12) 8' and (3) 12'
c
(10) 12'
d
(13) 8¹
Answer:
The answer is (10) 8' and (3) 12 A
Step-by-step explanation:
To build a wall that is 12' long and 8' high, you will need (10) 8' 2x4's and (3) 12' 2x4's. This will give you the necessary length for the bottom and top plates and 10 studs. Each stud should be spaced about 16" on center, so 10 studs will be enough to support the wall.
If P = (-1,-1), find the image
of P under the following rotation.
90° counterclockwise about the origin
([?], [])
Enter the number that belongs in
the green box.
The image of P after the rotation of 90° counterclockwise is (-1, 1)
How to find the image after the rotation?
Here we have the point P = (-1, -1), notice that both values are negative, thus, the point is on the third quadrant.
For any point (x, y) on the third quadrant, if we apply a rotation of 90° counterclockwise the new coordinates of the point (coordinates of the image) after the reflection are (y, -x)
In this case the original coordinates are (-1, -1), so the coordinates after the reflection are (-1, -(-1)) = (-1, 1)
The image after the rotation is (-1, 1).
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20. Beatrice bought a new car for $28,000. She put down $5,000 and paid $550 for 60 months. What's the total finance charge to Beatrice?
A. $12,000
B. $10,000
C. $16,000
D. $23,000
Answer: B. $10,000
Step-by-step explanation:
$550x60+5,000=38,000
Subtract $38,000 by purchase price.: $28,000.
total is $10,000.
Gerolamo Cardano in his book, The Gambling Scholar, written in the early
1500s, considers the following carnival game. There are six dice. Each of the
dice has ve blank sides. The sixth side has a number between 1 and 6|a
dierent number on each die. The six dice are rolled and the player wins a
prize depending on the total of the numbers which turn up.
(a) Find, as Cardano did, the expected total without nding its distribution.
(b) Large prizes were given for large totals with a modest fee to play the
game. Explain why this could be done.
As calculated from the data (1/6)² is the probability of getting 5 of same number on all the dice.
b.)If we will limit the number of winners then we will be able to provide them with large prizes and that also by taking moderate rate from everyone.
Actually, the likelihood of winning is closer to one-third (25/72).
Carnival game organizers want you to believe, like I did, that a game is fair so that you will participate.
The likelihood that you would win a game was just about 1/3, so you probably wouldn't squander your money.
Therefore,
The likelihood of getting five of the same number on all six dice is (1/6)².
Probabilities are mathematical representations of the likelihood that an event will occur or that a statement is true.
Probability can also be expressed using a tree diagram.
The tree diagram makes it easier to organize and see all of the potential outcomes. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end.
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There are 15 dogs in an obedience class. Five of the dogs are Dalmatians. Aside from that, the rest are all different breeds. Assume that the instructor can only distinguish between the dogs by their breeds. (In other words, he can’t tell the Dalmatians apart!) At the beginning of class all of the dogs are lined up in a row.
a. As far as the instructor can tell, how many ways can the dogs be lined up in a row? (Remember,the Dalmations are indistinguishable.)
b. Assume that the dogs are given sweaters that completely disguise what breed they are. 3 wear yellow sweaters, 4 wear red sweaters, 3 wear blue sweaters, and 5 wear green sweaters. At this point, the instructor can only distinguish between the dogs by their sweater colors. (In other words, all the dogs with the same color sweater look alike to him!) As far as the instructor can tell, how many ways can the dogs be lined up in a row? (You may assume that the dogs will wear the sweaters without objection.)
c. Assume the sweater scenario in part (b). What is the probability that the instructor sees all of the dogs with the same sweater color sitting next to each other (for example: RRRRYYYGGGGGBBB)?
a) The number of ways in which the dogs can be lined up in a row is = 15! / 5!
b) The number of ways in which the dogs can be distinguished by their sweater colours is 15! / (3! × 4! × 3! ×5!)
c) The probability that the instructor sees all of the dogs with the same sweater colour sitting next to each other is
(a) The total number of dogs is 15, of which 5 dogs are Dalmatians and others are different.
So, by using permutation the number of dogs can be arranged in 15! / 5! ways.
(b) There are 3 dogs wearing yellow sweater, 4 dogs wearing red sweater, 3 dogs wearing blue sweater, and 5 dogs wearing green sweater.
Thus, the number of dogs can be arranged in 15! / (3! × 4! × 3! ×5!) ways.
(c) The 15 dogs can be arranged in 15! ways.
There are sweaters of 4 different colours, so the 4 colours can be arranged in 4! ways.
There are 3 dogs wearing yellow sweater, so they can be arranged in 3! ways.
There are 4 dogs wearing red sweater, so they can be arranged in 4! ways.
There are 3 dogs wearing blue sweater, so they can be arranged in 3! ways.
There are 5 dogs wearing red sweater, so they can be arranged in 5! ways.
Therefore, the probability that the instructor sees all of the dogs with the same sweater colour sitting next to each other is
4! (3! × 4! × 3! ×5!) / 15!
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during a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. show that there must be a period of some number of consecutive days during which the team must play exactly 14 games
The period of some number of consecutive days during which the team must play exactly 14 games should be that 2 games plays at these days 1,5,10,15,20,25,30 individually....
As there are 30 days in a month.
So we have to arrange these 14 games during this time period of 30 days,
Which will be arranged as:
suppose its 1 st month of 2023,
So,
2 games at day = 1/1/2023
2 games at day = 5/1/2023
2 games at day = 10/1/2023
2 games at day = 15/1/2023
2 games at day = 20/1/2023
2 games at day = 25/1/2023
2 games at day = 30/1/2023
So from here we conduct:
2+2+2+2+2+2+2= 14 games
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Help quick!! Very confused, create equivalent expression.
Answer:
Either A or B
Step-by-step explanation:
Brainliest, Please!Answer:
B
Step-by-step explanation:
(1.3^4 / 1.2^3)^7
1.2^ (3 · 7) = 1.2^(21)
1.3 ^ (4 · 7) = 1.3^(28)
1.3^(28)/1.2^(21)