Answers
Answer:
a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:
A(t) = A0 * (1/2)^(t/8)
where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.
Substituting the given values, we get:
A(t) = 7 * (1/2)^(t/8)
b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:
A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)
Simplifying, we get:
A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)
c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:
A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)
Related Questions
HELP ASAP WILL GIVE 100 PTS FOR THE CORRECT ANSWER AND WILL GIVE BRAINLYEST
Answers
Answer: Answer is below <3
The quotient of three times a number and 7: 3n/7
The difference between 5 and a number is x: 5 - n = x
The product of 3 times a number and 7: (3n)(7)
Two times the sum of a number and 9: 2 (n + 9)
The sum of twice a number and 9: 2n + 9
5 less than a number is x: x = n - 5
1. How many telephones per 100 inhabitants did Bermuda have?
2. In 2005, the population of Luxembourg was 470,000. How many telephones were in use in Luxembourg?
Please help with two questions!!!
Answers
In Bermuda, there are a total of 90 telephones for each 100 people. Also there are a total of 3,76,000 telephones in use in Luxembourg according to simple calculations.
Here, they given that a telephone symbol is equal to 5 telephones.
Then according to the given diagram,
1. There are:
= (5 + 5 + 5 + 3) 5 telephones
= ( 18 ) 5 telephones
= 90 telephones.
Therefore, there are a total of 90 telephones for each 100 people.
2. In 2005, the population of Luxembourg was 470,000.
According to the given diagram, there are 80 telephones available for every 100 people.
For 4,70,000:
100 -------------- 80
4,70,000 ------ (x)
After cross multiplication,
x * 100 = 80 * 470000
x = 8 * 47000
x = 3,76,000
Therefore, there are total of 3,76,000 telephones in use in Luxembourg.
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Jolen has a bag with 25 popsicles sticks, each numbered 1-25. How many sticks are labeled with a prime number?
A. 8
B. 9
C. 10
D. 11
Show your work.
Answers
Answer:
B: 9
Step-by-step explanation:
The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.
5.7. Suppose n = 2911 and e = 11. Encrypt the following messages as in
Example (5.3).
a) "OK"
b) "HELP" (Break this up into two blocks.)
Answers
Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).
To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.
a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:
"O" = 79
"K" = 75
Next, we use the RSA encryption formula:
C ≡ [tex]M^{e}[/tex] (mod n)
For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)
For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)
Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).
b) To encrypt "HELP", we break it up into two blocks:
Block 1: "HE"
Block 2: "LP"
For block 1, we have:
"H" = 72
"E" = 69
Using the RSA encryption formula, we get:
C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)
C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)
Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).
For block 2, we have:
"L" = 76
"P" = 80
Using the RSA encryption formula, we get:
C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)
C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)
Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).
The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).
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Can these lengths form a triangle 13, 15, 9
Answers
Answer:
[tex]9 + 15 = 24 > 13[/tex]
[tex]9 + 13 = 22 > 15[/tex]
[tex]15 + 13 = 28 > 9[/tex]
So the lengths 13, 15, and 9 can form a triangle.
can i please get some help with this it is math
Answers
Answer:
C) Pi
Step-by-step explanation:
Pi is an irrational number, it cannot be written down as non-infinite decimal, basically meaning that in order for it to be a rational number you need an approximate value for Pi.
Kyle wrote a matrix to represent a system of equations. The matrix is shown below.
[1 -3 1 4 | 4]
[3 2 1 | 3]
[-6 -4 -2 | 1]
Which of the following describes the solution to the system of equations?
- consistent
- dependent
- inconsistent
- independent
Answers
The system is inconsistent and has no solution. Therefore, the answer is "inconsistent".Since the last row is of the form [0 0 0 | b], where b is nonzero (b=7
To determine whether the system of equations represented by the given matrix has a solution, we can use row operations to put the matrix into reduced row echelon form. If the resulting matrix has a row of the form [0 0 ... 0 | b], where b is nonzero, then the system is inconsistent and has no solution. If there are any free variables in the reduced row echelon form, then the system has infinitely many solutions and is dependent. If there are no free variables and no rows of the form [0 0 ... 0 | b], then the system has a unique solution and is independent.
Using row operations, we can put the given matrix into reduced row echelon form as follows:
[tex][1 -3 1 4 | 4] (R1)[3 2 1 | 3] (R2)[-6 -4 -2 | 1] (R3)[/tex]
([tex]R2 - 3*R1) - > R2:[/tex]
[tex][1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[-6 -4 -2 | 1] (R3)(R3 + 6*R1) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 -22 4 | 25] (R3)(R3 + 2*R2) - > R3:[1 -3 1 4 | 4] (R1)[0 11 -2 |-9] (R2)[0 0 0 | 7] (R3)[/tex]
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Given that ABCD is a rhombus, find the value of x. 4 (X +40) A. 75 B. 52 C. 25 D. 46 F. 26
Answers
the value of variable x in the rhombus is Option (c) 25.
Definition of a rhombusA parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.
Let O be the intersection point of the line AC and the line BD in the rhombus.
This two lines intersect at a 90° angle in the center. ( Property of Rhombus)
∠AOD=90°
According to the question:∠AOD+∠OAD+∠ODA=180° (triangle sum property)
90°+x+x+40°=180°
2x=180°-130°
x=25
Hence the value of x=25.
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im sorry for asking this i forgot to add this
A turtle and a snail are 300 feet apart when they start moving toward
each other. The turtle walks 5 feet per minute, and the snail crawls 1
foot per minute.
(How fast are the turtle and snail approaching each other?)
Answers
8.5 Refer to Exercises 8.1 and consider the unbiased estimator θˆ that you proposed in Exercise 8.3. a Express MSE(θˆ ) as a function of V(θ)ˆ . b Give an example of a value of a for which MSE(θˆ ) < MSE(θ)ˆ . c Give an example of values for a and b for which MSE(θˆ ) > MSE(θ)ˆ .
Answers
After answering the prοvided questiοn, we can cοnclude that Sο, we can equatiοn chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), like a = 0.9 and b = 0.5.
What is equatiοn?An equatiοn in mathematics is a prοcedure that affects the equaIity οf equatiοns. Twο sides οf an equatiοn are cοnnected by the algebraic οperatοr (=). Fοr instance, the claim "2x + 3 = 9" asserts that the cοmment "2x + 3" means the value "9" in tοtal. The gοal οf sοlving equatiοns is tο identify the factοr(s) that will cause the equatiοn tο be true.
Equatiοns may be straightfοrward οr cοmplex, cοnstant οr nοn-linear, and cοntain οne οr mοre variables. Examples include raising the variable x tο the pοwer οf 2 in the equatiοn "x² + 2x - 3 = 0," fοr example. In mathematics, particularly in algebra, equatiοns, and geοmetry, lines are frequently used.
MSE(θˆ) = E[(θˆ − θ)²]
= E[((X1 + · · · + Xn)/n − μ²)²]
= E[((X1 − μ) + · · · + (Xn − μ))/n]²
= V[(X1 − μ)/n + · · · + (Xn − μ)/n]
= V[(X1 − μ)/n] + · · · + V[(Xn − μ)/n] (since the Xi's are independent)
Thus, MSE(θˆ) = σ²/n
b. Fοr MSE(θˆ) < MSE(θ), we want:
We can see that this is satisfied fοr any value οf a such that 0 < a < 1.
c. Fοr MSE(θˆ) > MSE(θ), we want:
σ/n > V[(1 − a)X¯ + aμ] = (1 − a)²Var(X¯) + aVar(μ) + 2a(1 − a)Cοv(X¯, μ)
σ²/n > (1 − a)(σ²/n) + 2a(1 − a)Cοv(X¯, μ)
Cοv(X¯, μ) < (1 − a)/2 σ²/n
Sο, we can chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), such as a = 0.9 and b = 0.5.
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Suppose that 14% of the population of the U.S. is left-handed. If a random sample of 190 people from the U.S. is chosen,
approximate the probability that fewer than 25 are left-handed. Use the normal approximation to the binomial with a correction
for continuity.
Round your answer to at least three decimal places. Do not round any intermediate steps.
(If necessary, consult a list of formulas.)
Answers
The formula for the normal approximation to the binomial with a correction for continuity is
P(X ≤ x) ≈ Φ(z), where z = (x + ½ - μ)/σ
In this case, μ is the expected number of left-handed people in the sample, which is 0.14*190 = 26.6
σ is the standard deviation of the sample, which is (0.14*(1-0.14))^0.5*190 = 5.58
x is the desired number of left-handed people in the sample, which is 24.5 (since fewer than 25)
Therefore, z = (24.5 + ½ - 26.6)/5.58 = -1.03
The probability that fewer than 25 people in the sample are left-handed is then Φ(-1.03) = 0.1545, to at least 3 decimal places.
James wants to sort the numbers on his teddy bears from greatest to least. After he sorts the numbers. What number would come next?
Answers
If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted. For example, if the numbers he has sorted are 9, 5, and 3, then the next number would be 1.
What is sort?Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is a computer algorithm that sorts a list, typically of numbers, words, or other items, into increasing or decreasing order. It is often used to arrange data so that it can be more easily analyzed or used in other applications. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order. Sorting algorithms are used in many areas of computing, including data structures, artificial intelligence, databases, and programming languages.
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The numbers on teddy bears are sorted as 656, 666, 676, 686. The pattern rule is adding 10 so, the next number will be 696.
Give a brief account on data sorting.Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is often used to arrange data so that it can be more easily analyzed or used in other calculation. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order.
If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted.
The numbers on teddy bears are sorted as 656, 666, 676, 686.
Now, observe the pattern.
656 + 10 = 666
666 + 10 = 676
676 + 10 = 686
This indicates that the pattern rule is "adding 10", which means the next number in series is:
686 + 10 = 696
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The complete question is as follows:
Anyone Want to Give me 6th Grade Inequalities?
Reward- Brainliest and 10 Tokens
Answers
Answer:
3x + 4 < 13
2y - 5 > 7
6n - 1 ≤ 23
8m + 2 ≥ 18
4a - 7 < 5a + 2
9b + 3 > 6b + 10
Step-by-step explanation:
I dunno if this is what you're asking for
Answer:
ok.....
x + 2 < 5
|x - 4| > 4
x + 7 [tex]\geq[/tex] 8
-x < -5
x - 5 < 9
5x + 18 > 2
|3x - 1| < 8
Evaluate the following limit. Enter the exact answer in fraction form, if necessary.
Answers
Answer:
To evaluate this limit, we can factor out the highest power of x from the numerator and denominator, which is x^14. Then, we can divide both the numerator and denominator by x^14. This gives:
lim x→∞ (6x^14 + 8x^11 + 37x^14) / x^14
= lim x→∞ (6x^14 / x^14 + 8x^11 / x^14 + 37x^14 / x^14)
= lim x→∞ (6 + 8 / x^3 + 37)
= 6 + 0 + 37 (since as x approaches infinity, 8/x^3 approaches zero)
= 43
Therefore, the value of the limit is 43.
14509772 rounded to the nearest ten thousand
Answers
The nearest ten thousand of the digits 14509 is 14, 000.
How to round to the nearest ten thousand?The rule for rounding to the nearest ten thousand is to look at the last four digits.
If the last four digits of the number is greater than 5000, we have to round the value up but if the number is below 5000 we have to round below.
For example let's round up 27567 to the nearest ten thousands.
Therefore, 7567 is above 5000, Hence, we have to round up. The nearest ten thousand of 27567 is 30000.
Let's round 14509 to the nearest ten thousand.
The nearest ten thousand of 14509 is 14, 000
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3x-4+2x+6+x=
write and solve an equation to find x
Answers
Answer:
x=-1/3
Step-by-step explanation:
3x-4+2x+6+x=0
6x+2=0
6x=-2
x=-2/6
x=-1/3
What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches.
Answers
The first thing we must do for this case is to find the surface area of the rectangular prism.
We have then:
[tex]A = 2 \times (l \times h) + 2 \times (h \times w) + 2 \times (w \times l)[/tex]
Where,
w: width
l: long
h: height
Substituting values we have:
[tex]A = 2 \times (10 \times 8) + 2 \times (8 \times 8) + 2 \times (8 \times 10)[/tex]
[tex]A = 448 \ in ^ 2[/tex]
Answer:
the least amount of wrapping paper needed to wrap the gift box answer is:
A = 448 in²
Ricardo took out a single payment loan for $2500 at 7.8% ordinary interest to pay his federal income tax bill. Find the maturity value of the loan if he had to pay it back after 180 days.
Answers
Answer:
Therefore, the maturity value of the loan is $2568.75.
Step-by-step explanation:
To calculate the maturity value of the loan, we need to add the interest to the principal.
First, we need to find out how much interest Ricardo will owe for the 180-day period.
The formula for calculating ordinary interest is:
Interest = Principal x Rate x Time
where:
Principal = $2500
Rate = 7.8% = 0.078 (expressed as a decimal)
Time = 180/360 (since the interest is for a 180-day period and the rate is an annual rate)
Time is expressed as a fraction of a year because the rate is an annual rate. In this case, the time is 180/360 because the loan is for 180 days, which is half of a year.
Using the formula above, we can calculate the interest as follows:
Interest = $2500 x 0.078 x 180/360 = $68.75
Therefore, Ricardo will owe $68.75 in interest for the 180-day period.
To find the maturity value of the loan, we add the interest to the principal:
Maturity Value = Principal + Interest = $2500 + $68.75 = $2568.75
Therefore, the maturity value of the loan is $2568.75.
The answer please cause I don’t know if somebody could help m
Answers
Answer:
bottom two
Step-by-step explanation:
if "=", equation
if no "=", expression
Answer:
The ones without an equal sign.
Hope this helps!
Step-by-step explanation:
4x - 7 = 5
4x - 7 is the expression
4x, 7, and 5 are terms
4x - 7 = 5 is the equation
3x and 2x are supplementary what is the value of x
Answers
Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .
what is angles ?Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.
given
The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:
3x + 2x = 180
Putting similar phrases together on the left side, we get:
5x = 180
When we multiply both sides by 5, we get:
x = 36
Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .
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Pleaseeeeeee helps meeeeeeee I'd really appreciate it
Answers
Answer:
5683200
Step-by-step explanation:
Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.
What is the lowest common multiple of 8 and 12?
Answers
Answer:
2 hope that helps
Step-by-step explanation:
Solution:
24
ms walker has 15 kilograms of clay she wants to give 3 students an equal amount of clay what is the mass of the clay that each student will get
Answers
Answer: 5kg
Step-by-step explanation:
If Ms. Walker has 15 kilograms of clay that she wants to distribute evenly among 3 students, all you need to do is divide 15 by 3. Doing so, we get:
15 kg / 3 = 5 kg
Therefore, each student will receive 5 kilograms of clay.
The mass of clay that each student will get is 5kg.
Here, the given questions ask for a solution that deals with the concept of the basic principle of division. hence implementing the principle we can see that,
The given total amount of clay by Ms. walker is 15 kilograms(kg).
Furthermore, this total amount of clay needs to be divided equally between the 3 students.
Then, let the mass of clay given to each student equally be denoted by M in the equation to find out the solution can be written as
M = Total amount of clay ÷ Total number of students
Then,
M = 15 ÷ 3
M = 5 kg
Therefore, The mass of clay that each student will get is 5kg.
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HELPPPPPP PLEASE PLEASEEEEEE
Determine a function type that
could represent the values in the
table.
x f(x)
0 −18
1 −15
2 −12
3 −9
4 −6
◻ linear
◻ quadratic
◻ exponential
Answers
Answer: Linear
Step-by-step explanation:
Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3
f(2) - f(1) = -12 - (-15) = 3
f(3) - f(2) = -9 - (-12) = 3
f(4) - f(3) = -6 - (-9) = 3
Since the differences are constant and equal to 3, this confirms that the function is linear.
To find the equation of the linear function, we can use the slope-intercept form of a linear equation:
y = mx + bwhere m is the slope and b is the y-intercept.
We can use the first two points (0, -18) and (1, -15) to find the slope:
m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3
Now we can use the slope and one of the points to find the y-intercept:
y = mx + b
-18 = 3(0) + b
b = -18
Therefore, the equation of the linear function is:
f(x) = 3x - 18
So the function type that could represent the values in the table is linear.
1. You purchase a car using a $12,500 loan with a 5.6% simple interest rate.
(a) Suppose you pay the loan off after 6 years. How much interest do you pay on your loan? Show your work.
(a) Suppose you pay the loan off after 3 years. How much interest do you save by paying the loan off sooner? Show your work.
Answers
The interest that is paid on the loan in 6 years will be $4,200.
The amount of interest that is saved is $2,100.
What is the interest on the loan?The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.
Simple interest = loan x time x interest rate
Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200
Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100
Interest saved = $4200 - $2100 = 2100
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Gina started making sugar cookies for her friends at 12:15 P.M. It took her 1 hour and 15 minutes to make
Answers
Gina finished making sugar cookies at 1:30 P.M.
What is the basic arithmetic operations?The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find out what time Gina finished making sugar cookies, we need to add the time it took her to make them to the starting time.
Starting time: 12:15 P.M.
Time it took to make cookies: 1 hour and 15 minutes
To add the time, we first convert 1 hour and 15 minutes to hours by dividing the minutes by 60:
1 hour and 15 minutes = 1 + 15/60 hours = 1.25 hours
Now we can add 1.25 hours to 12:15 P.M.:
12:15 P.M. + 1.25 hours = 1:30 P.M.
Hence, Gina finished making sugar cookies at 1:30 P.M.
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Complete question:
Gina started making sugar cookies for her friends at 12:15 P.M. It took her 1 hour and 15 minutes to make. By what time Gina finished making sugar cookies?
3. days B) 5 days C) 4 days A can do a certain work in 15 days and B can do same work in 18 days. They work together but A had left the work after some days, and B finished the remaining work in 7 days. After how many days A had left the work?
Answers
A left the work after 3 days was solved by using work formula.
What is algebraic equation?An algebraic equation is a mathematical statement that asserts that two expressions are equal. These expressions can contain variables, which are represented by letters, and the equation states that the values of the expressions are equal for some particular values of the variables.
What is work formula?The work formula is a mathematical concept used to determine how long it will take two or more workers to complete a job together. The formula is based on the idea that the amount of work done is directly proportional to the time spent working.
In the given question,
Let's assume that A worked for x days, and therefore he left the work unfinished for (15 - x) days. During this time, B finished the remaining work in 7 days.
According to the work formula, the amount of work done by A and B together in one day is:
1/15 + 1/18 = 11/90
This means that in one day, they can complete 11/90th of the work together.
During the x days when A worked, the amount of work he did is:
x * (11/90)
And during the remaining (15 - x) days, the amount of work left undone is:
(15 - x) * (11/90)
When A left, B completed the remaining work in 7 days, so we can set up an equation:
(11/90) * 7 = (15 - x) * (11/90)
Simplifying and solving for x, we get:
x = 3
Therefore, A left the work after 3 days.
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these 3 How 5. Cindy loves candy. She bought 3 candy bars and paid 9% in taxes. The cost of the candy bars are shown in the chart. How much money did she pay the cashier in total? Round your answer to the hundredths place. Giant Kit Kat $3.59 Mini Snickers $0.75 Twix TENDO $1.99
Answers
Cindy paid the cashier a total of $6.90 for the three candy bars, including taxes.
What is expression ?
Expressions can be used to represent various mathematical concepts and relationships, and they are used extensively in algebra, calculus, and other branches of mathematics.
To calculate the total cost of the candy bars with taxes, we need to first find the cost of each candy bar and then add up all three costs.
The cost of the Giant Kit Kat is $3.59, but we need to add 9% tax to get the total cost:
$3.59 + 0.09($3.59) = $3.91 (rounded to the nearest cent)
The cost of the Mini Snickers is $0.75, but we need to add 9% tax to get the total cost:
$0.75 + 0.09($0.75) = $0.82 (rounded to the nearest cent)
The cost of the Twix TENDO is $1.99, but we need to add 9% tax to get the total cost:
$1.99 + 0.09($1.99) = $2.17 (rounded to the nearest cent)
Now we can add up the total cost:
$3.91 + $0.82 + $2.17 = $6.90
Therefore, Cindy paid the cashier a total of $6.90 for the three candy bars, including taxes.
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Leo says that the product n x 4/5 is greater than 4/5 because multiplication always increases a number. Which of the following values for n shown that Leo is incorrect?
a. 2
b. 7/6
c. 5/8
d. 5/4
e. 6/6
Answers
Answer: Let's plug in each value for n and compare the results:
a. n = 2
2 x 4/5 = 8/5 which is greater than 4/5.
b. n = 7/6
7/6 x 4/5 = 28/30 which simplifies to 14/15 which is greater than 4/5.
c. n = 5/8
5/8 x 4/5 = 20/40 which simplifies to 1/2 which is less than 4/5.
d. n = 5/4
5/4 x 4/5 = 20/20 which simplifies to 1 which is greater than 4/5.
e. n = 6/6
6/6 x 4/5 = 24/30 which simplifies to 4/5.
Therefore, the answer is (c) 5/8, which shows that Leo is incorrect. In this case, the product is less than 4/5.
15 points! please help pleasee!
Answers
Step-by-step explanation:
the perimeter is the sum of the lengths of all outside sides.
at the top is a triangle.
at the bottom is a rectangle.
the triangle looks like an isoceles triangle (both legs are equal), but the given measurement tells us otherwise.
if it were isoceles, the height would split the baseline into 2 equal halves (20/2 = 10ft).
per Pythagoras the 12 ft Hypotenuse would be
Hypotenuse² = 10² + 10² = 100 + 100 = 200
Hypotenuse = sqrt(200) = 14.14213562... and NOT 12 ft.
so, we need to calculate the actual part of the 20ft baseline (again Pythagoras) :
12² = 10² + part²
144 = 100 + part²
44 = part²
part = sqrt(44) = 6.633249581... ft
that means the 2nd part of the baseline is
20 - 6.633249581... = 13.36675042... ft
and we get the second leg of the large triangle again via Pythagoras :
leg² = 10² + 13.36675042...² = 100 + 178.6700168...
leg² = 278.6700168...
leg = sqrt(278.6700168...) = 16.69341238... ft
we need to sum up both legs of the triangle, 2 widths and one length of the rectangle, as the triangle base line and the second length of the rectangle cover each other up, and are not visible to the outside of the combined object.
P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈
≈ 64.69 ft