Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the sample mean for x and for y. Round your answer to the nearest tenth. x: 11 0 36 22 34 24 25 -11 -11 -22 y: 9 -3 28 14 23 16 14 -3 -4 -9
Answer:
(a). Σx= 108, Σx^2 = 4984, Σy^2 = 2,157.
(b). 10.8, 0.1.
(C) and (d) => check explanation.
Step-by-step explanation:
To Calculate for Σx we will have to add all the values for x that is the summation of x-values.
Σx = 11 + 0 + 36 + 22 + 34 + 24 + 25 + -11 + -11 + -22 = 108.
Σx^2 = 11 × 11 + 0 × 0 + 36 × 36 + 22 × 22 + 34 × 34 + 24 ×24 + 25 × 25 + -11 × -11 + -11 × -11 + -22 × -22 = 4984.
Σy^2 = 9× 9 + -3 × -3 + 28 ×28 + 14 × 14 + 23 × 23 + 16 × 16 + 14× 14 + -3 ×-3 + -4 × -4 + -9 × -9= 2,157.
(b). Sample mean for x = 108/10 = 10.8.
Variance for x:
11 - 10.8 = 0.3
0 - 10.8 = -10.8
36 - 10.8 =25.2.
22 - 10.8=11.2.
34 - 10.8 = 23.2
24 -10.8 = 13.2.
25 - 10.8= 14.2
-11 - 10.8 = -21.8.
-11 - 10.8 = - 21.8
-22 -10.8 = -32.8.
Total=0.1
Standard deviation for x = √ s^2 = 0.3162
This can be done for y too
(c). 75% Chebyshev interval around the mean for x values = 10.8 + 2 (0.3162); 10.8 - 2(0.3162).
=> (11.4324, 10.1676).
(d). The coefficient of variation= (0.3162)/10.8 × 100 = 2.92%.
The sample means for annual returns of the Vanguard Total Stock Index (x) and Vanguard Balanced Index (y) have been computed as 10.8 and 8.5 respectively. The inclusion of bonds in a portfolio can lower overall return slightly while also reducing the risk.
Explanation:The student's task revolves around the subject of statistical analysis, here applied to investment portfolio management. Their goal is to compute the sample mean (average) for two variables - x and y - which each represent annual returns for certain types of portfolios.
Portfolio x represents a 100% stock holding in the Vanguard Total Stock Index, while y represents a 60% stock and 40% bond holding in the Vanguard Balanced Index. Such portfolios carry varying degrees of risk, with all-stock portfolios generally accepted to be more volatile, yet offering higher potential returns than mixed portfolios.
In order to calculate the sample means for x and y, you simply add together all the annual returns for each, then divide by the number of years.
For x: (11 + 0 + 36 + 22 + 34 + 24 + 25 - 11 - 11 - 22)/10 = 10.8 (rounded to the nearest tenth)
For y: (9 - 3 + 28 + 14 + 23 + 16 + 14 - 3 - 4 - 9)/10 = 8.5 (rounded to the nearest tenth)
As seen, stocks did yield a higher average return over the period in consideration, though the range of returns was also much wider. By adding bonds to the portfolio (shown by y), the overall return reduced slightly, but so did the risk (variability) of returns.
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what is the area of a triangle with 9mi and 20 mi
Answer:
Area=90mi
Step-by-step explanation:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles.
Dorris has 3 books weighing 2 kilograms each and one container weighing 4 kilograms in a box. How much does the box weigh in kilograms?
Answer:
The weight of a box is 10 kg.
Step-by-step explanation:
Weight of each book is 2 kg
So, the weight of 3 books is 6 kg.
Weight of a container is 4 kg
3 books and one container is in a box. We need to find the weight of the box.
It is equal to the sum of weights of 3 books and one container. So,
Total weight = 6 kg + 4 kg
W = 10 kg
So, the weight of a box is 10 kg.
Imagine that the rectangle is rotated counterclockwise
Make a conjecture as to which properties of a figure
stay the same after the rotation
vertices
sides
angles
lengths
shape
size
Answer:
All of them
Step-by-step explanation:
Answer:
A,B,C,D,E,F
Step-by-step explanation:
to sum it up all of them !
If Hank shoots from inside the three-point line, what can be said about his distance from the center of the basket?
Answer:
If Hank shoots from inside the three-point line we can say that he has to shoot 246 inches to make the ball into the hoop.
Hank's distance from the center of the basket, if he is shooting from inside the three-point line, would be less than the distance of the three-point line from the basket. This distance varies between 6.75 metres (NBA, FIBA) or 6.1 metres (college games).
Explanation:When a player stands inside the three-point line in basketball, it can be said that they are less than 6.75 metres (for NBA and FIBA) or 6.1 metres (for college games) from the centre of the basket. This distance varies because different basketball associations have different guidelines for the distance of the three-point line from the center of the basket. For instance, the NBA has its line located 7.24 metres from the basket, FIBA has it at 6.75 metres, and in college games, it's 6.1 metres away. As such, if Hank is shooting inside the three-point line, he is definitely standing closer than these distances to the basket's center.
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Martha, A statistician wishes to analyze teachers’ salaries in the state of California. She determines that teacher’s salaries in California are normally distributed with a mean salary of $37,764 and a standard deviation of $5,100. Answer the following questions. a) What is the probability that a randomly selected teacher’s salary in California is greater than $45,000?
Answer:
0.078 or 7.8%
Step-by-step explanation:
Mean salary (μ) = $37,764
Standard deviation (σ) = $5,100
The z-score for any given teacher's salary in California, X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = $45,000:
[tex]z=\frac{45,000-37,764}{5,100}\\ z=1.419[/tex]
A z-score of 1.419 corresponds to the 92.20th percentile of a normal distribution. Therefore, the probability that a salary is greater than $45,000 is:
[tex]P(X>\$45,000) = 1-0.9220\\P(X>\$45,000) = 0.078=7.8\%[/tex]
The probability is 0.078 or 7.8%.
To find the probability of a teacher's salary being more than $45,000 in California, calculate the Z-score using the formula given and find the corresponding probability. This calculation reveals there's a 7.78% chance of a randomly selected teacher's salary exceeding $45,000.
Explanation:To find the probability that a randomly selected teacher’s salary in California is greater than $45,000 when the salaries are normally distributed with a mean of $37,764 and a standard deviation of $5,100, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. In this case, X = $45,000, μ = $37,764, and σ = $5,100.
Calculating the Z-score gives us: Z = ($45,000 - $37,764) / $5,100 ≈ 1.42. Using the Z-table or a calculator with normal distribution functions, we find that the area to the right of Z = 1.42 corresponds to the probability we are looking for.
This area represents the probability that a teacher’s salary is greater than $45,000. Since we know the total area under the normal curve equals 1 (or 100%), the area to the right of Z = 1.42 is approximately 0.0778, which means there is a 7.78% chance that a randomly selected teacher’s salary in California is greater than $45,000.
Melissa ran 6 2/5 miles north 2 3/4 west and 2 1/3 south how far did she run
Answer:11.5
Step-by-step explanation:
distance=6 2/5 + 2 3/4 + 2 1/3
d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3
d=32/5 + 11/4 + 7/3
d=(12x32+15x11+20x7) ➗ 60
d=(384+165+140) ➗ 60
d=689 ➗ 60
d=11.5
The total distance did she run is 11.5 miles.
It is required to find the total distance.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
Melissa ran 6 2/5 miles north ,2 3/4 west and 2 1/3 south.
According to given question we have,
Total distance=6 2/5 + 2 3/4 + 2 1/3
d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3
d=32/5 + 11/4 + 7/3
d=(12x32+15x11+20x7) /60
d=(384+165+140) / 60
d=689 / 60
d=11.5 miles.
Therefore, the total distance did she run is 11.5 miles.
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Please help me find the Area
Answer:
8 x 17 x 15 = 2040 that's your area
Step-by-step explanation:
good day and be safe
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⊕ΘΞΠΤ⊕
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Answer:
60 units squared
Step-by-step explanation:
The formula for the area of the triangle is: [tex]\frac{base*height}{2}[/tex]
To work this out you would first have to multiply 8 by 15, which gives 120. Then you would divide 120 by 2, Which gives you 60. This is because the formula is the same for the area of a square however the triangle is half of a square that has the same dimensions.
1) Multiply 8 by 15.
[tex]8*15=120[/tex]
2) Divide 120 by 2.
[tex]120/2=60^{2}[/tex]
What is another word of magnitude
Answer:
largeness
Step-by-step explanation:
look up in dictionary
Jordan has $5.37, which he is using to buy ingredients to make salsa. He is buying one red pepper for $1.29 and
three pounds of tomatoes. If Jordan has exactly the right amount of money he needs, what is the price per pound of
the tomatoes?
Choose the correct equation to represent this real-world problem.
Solve the equation and verify the reasonableness of your answer.
A pound of tomatoes costs
Answer:
The price of tomato per pound is $1.36
Step-by-step explanation:
Jordan has $5.37.
He is buying one red pepper for $1.29
He is also buying three pounds of tomatoes.
If he has exactly the right amount of money he needs, then
5.37 = 1.29 + 3x
Where x is the price of tomato per pound
And( 5.37 = 1.29 + 3x) is the equation to solve for x
5.37 = 1.29 + 3x
5.37-1.29 = 3x
4.08 = 3x
4.08/3 = x
1.36 = x
The price of tomato per pound is $1.36
To verify it again..
3*1.36 + 1.29
= 4.08 +1.29
= 5.37 ( which is the initial total amount)
Answer:
Jordan has $5.37, which he is using to buy ingredients to make salsa. He is buying one red pepper for $1.29 and three pounds of tomatoes. If Jordan has exactly the right amount of money he needs, what is the price per pound of the tomatoes?
Choose the correct equation to represent this real-world problem.
✔ 5.37 = 3x + 1.29
Solve the equation and verify the reasonableness of your answer.
A pound of tomatoes costs
✔ $1.36
.
Step-by-step explanation:
A restaurant offers three courses, appetizers, main dishes and desserts. It has 6 choices of appetizers, 10 choices of main dishes and 8 choices of desserts. How many different meals are there if a customer can order only one dish from each course and can have a meal consisting of one course only, two different courses or a meal with all three courses.
Answer:
692 different meals are possible.
Step-by-step explanation:
- There are 3 courses, appetizers, main dishes and desserts.
- There are 6 choices of appetizers, 10 choices of main dishes and 8 choices of desserts.
- A customer can order only one dish from each course and can have a meal consisting of one course only, two different courses or a meal with all three courses.
To find the number of different meals possible, we take the choice of number of courses one by one.
- If a customer decides to take a meal with only one course.
The customer can take only 1 choice out of 6 choices of appetizers or 1 choice out of 10 choices of main dishes or 1 choice out of 8 choices of desserts.
6C1 + 10C1 + 8C1 = 6 + 10 + 8
= 24 different meals
- If a customer decides on a two course meal
The customer can combine a choice of appetizer with a choice of main dish or a choice of appetizer with desert or a choice of main dish with dessert with order unimportant.
(6C1 × 10C1) + (6C1 × 8C1) + (10C1 × 8C1)
= (6 × 10) + (6 × 8) + (10 × 8)
= 60 + 48 + 80
= 188 different meals
- If a customer decides to take a combination of all the 3 courses.
This means a combination of a choice from each of the courses for the 3 courses.
6C1 × 8C1 × 10C1
= 6 × 8 × 10
= 480 different meals.
Total number of different meals possible
= 24 + 188 + 480
= 692 different meals.
Hope this Helps!!!
Answer:
692
Step-by-step explanation:
The mean number of sick days per employee taken last year by all employees of a large city was 10.6 days. A city administrator is investigating whether the mean number of sick days this year is different from the mean number of sick days last year. The administrator takes a random sample of 40 employees and finds the mean of the sample to be 12.9. A hypothesis test will be conducted as part of the investigation. Which of the following is the correct set of hypotheses?
H0:μ=10.6Ha:μ>10.6 A
H0:μ=10.6Ha:μ≠10.6 B
H0:μ=10.6Ha:μ<10.6 C
H0:μ=12.9Ha:μ≠12.9 D
H0:μ=12.9Ha:μ<12.9 E
Answer:
For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.
Then the system of hypothesis are:
Null hypothesis: [tex]\mu =10.6[/tex]
Alternative hypothesis: [tex]\mu \neq 10.6[/tex]
And the best option would be:
H0:μ=10.6Ha:μ≠10.6 B
Step-by-step explanation:
For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.
Then the system of hypothesis are:
Null hypothesis: [tex]\mu =10.6[/tex]
Alternative hypothesis: [tex]\mu \neq 10.6[/tex]
And the best option would be:
H0:μ=10.6Ha:μ≠10.6 B
And the data from the sample is:
[tex]\bar X = 12.9[/tex] represent the sample mean
[tex]n =40[/tex] the sample size
A coin is tossed 18 times. It lands on heads 12 times. What is the experimental probability
of the coin landing on tails? reduce the fraction!
1/2
2/3
1/3
Answer:
The experimental probability of the coin landing on tails is 1/3
Step-by-step explanation:
Total no. of times coin tossed = 18
No. of times lands on head = 12
No. of times lands on tail = 18-12
No. of times lands on tail = 6
We are supposed to find the experimental probability of the coin landing on tails
So, the experimental probability of the coin landing on tails =[tex]\frac{\text{favorable outcome}}{\text{Total outcome}}[/tex]
So, the experimental probability of the coin landing on tails =[tex]\frac{6}{18}[/tex]
So, the experimental probability of the coin landing on tails =[tex]\frac{1}{3}[/tex]
Hence the experimental probability of the coin landing on tails is 1/3
What is 15 divided 1/3
Answer: 45
Explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.
Also, think of the 15 in this problem as 15/1.
So we can rewrite 15/1 ÷ 1/3 as 15/1 · 3/1.
Multiplying across the numerators and the denominators,
we find that our answer is 45/1 or just 45.
15 divided by 1/3 is equal to 45.
To divide 15 by 1/3, we can interpret it as finding how many groups of 1/3 can be made from 15.
To begin, we can convert the division of 15 by 1/3 into a multiplication problem by taking the reciprocal of 1/3, which is 3/1 or simply 3.
So, we have:
15 ÷ (1/3) = 15 x 3
Multiplying 15 by 3, we get:
15 x 3 = 45
Therefore, 15 divided by 1/3 is equal to 45.
In other words, 15 can be divided into 45 equal parts of size 1/3. Each of these parts represents the quotient when dividing 15 by 1/3.
When we multiply 1/3 by 45, we get 15. This confirms that 15 divided by 1/3 is indeed equal to 45.
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In circle G with m angle of FGH = 90 and FG = 9 units find area of sector FGH. Round
to the nearest hundredth.
Answer:63.6 units
Step-by-step explanation:
Theta=90°
Radius =9
area of sector=(theta)/360 x π x r x r
area of sector=90/360 x 3.14 x 9 x 9
area of sector=(90x3.14x9x9)➗360
area of sector=22890.6 ➗ 360
area of sector=63.535
area of sector=63.6 approximately
Answer:
It's 63.62
Step-by-step explanation:
Calculate the surface area of the composite figure shown.
2 rectangular prisms. One prism has a length of 8, width of 8, and height of 2. The second prism has a length of 8, width of 2, and height of 4.
Back Prism:
1 base: 8 by 8
4 lateral faces: 8 by 2
One shared base: 64 – 32 = 32 square units
Front Prism:
1 base: 8 by 4
2 lateral faces: 8 by 2
2 lateral faces: 2 by 4
One shared base: area covered by other prism
To calculate the surface area, the formula is the sum of the areas of all faces in a shape.
Back Prism:
1 base: 8 by 8.
4 lateral faces: 8 by 2.
One shared base: 64 – 32 = 32 square units.
Front Prism:
1 base: 8 by 4.
2 lateral faces: 8 by 2.
2 lateral faces: 2 by 4.
Therefore, one shared base: an area covered by another prism.
Total surface area: 240 square units.
What is a surface area?
A surface area is the outer part of the uppermost layer of something. This is known in maths as the amount of space covering the outside of a three-dimensional shape.
Hence, we can see that to calculate, the formula is the sum of the areas of all faces in a shape which sums up to 240 square units.
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X²-11x=-24 solve the quadratic equation by factoring
Answer:
x=8,3
Step-by-step explanation:
Move
24 to the left side of the equation by adding it to both sides.
x 2−11x+24=0
Factor x2−1 1x+ 24
using the AC method.
(x−8)(x−3)=0
If any individual factor on the left side of the equation is equal to
0 , the entire expression will be equal to 0
x−8=0 x−3=0
Set the first factor equal to
0 and solve.
x =8
Set the next factor equal to 0 and solve.
x = 3
The final solution is all the values that make
( x− 8)(x−3)=0 true.
x =8,3
Solving:
Move constants to the left
[tex]x^2-11x=24\\[/tex]
write as a difference
[tex]x^2-11x+24=0[/tex]
factor
[tex]x^2-3x-8x-+24=0[/tex]
factor again
[tex]x(x-3)-8(x-3)=0[/tex]
separate
[tex](x-3)(x-8)=0[/tex]
solve all possible equations.
[tex]x-3=0\\x-8=0[/tex]
therefore, our answers are:
[tex]x=3,x=8[/tex]
If f(x) is the slope of a trail at a distance of x miles from the start of the trail, what does 7 f(x)dx 5 represent? The change in the elevation between x = 5 miles and x = 7 miles from the start of the trail. The elevation at x = 5 miles from the start of the trail. The elevation at x = 7 miles from the end of the trail. The elevation at x = 7 miles from the start of the trail. The change in the elevation between x = 5 miles and x = 7 miles from the end of the trail.
Answer:
The answer is option A
Step-by-step explanation:
[tex]\int\limits^7_5 {f(x)} \, dx[/tex]
From the question given, the limit is between 5 and 7, the differentiation starts from the beginning of the trail
In this exercise we have to solve the integral and classify the correct alternative:
The answer is option A.
In this case we will have to solve the integral:
[tex]\int\limits^7_5 {f(x)} \, dx[/tex]
From the question given, the limit is between 5 and 7 the differentiation starts from the beginning of the trail.
The answer is option A.
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Given the following list of the number of paintings randomly selected art students created during a watercolor class, find the median.
21,28,30,31,17,16,12
Answer: 21
Step-by-step explanation: If you lost the numbers in order from creates to least, and cross the least and the greatest the number in the middle or median is 21
What is the solution of the equation s=-4s+30
Answer:
6
Step-by-step explanation:
The answer is 168 but what is it cm2 cm3 or just cm?
Answer:
if its length then its cm
if its area then its cm²
if its volume then its cm³
Step-by-step explanation:
Find the closest point to y in the subspace W spanned by Bold v 1 and Bold v 2. yequals[Start 4 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 1 3rd Row 1st Column 1 4st Row 1st Column 13 EndMatrix ], Bold v 1equals[Start 4 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 2 3rd Row 1st Column negative 1 4st Row 1st Column 2 EndMatrix ], Bold v 2equals[Start 4 By 1 Matrix 1st Row 1st Column negative 4 2nd Row 1st Column 1 3rd Row 1st Column 0 4st Row 1st Column 3 EndMatrix ]The closest point to y in W is the vector [Start 4 By 1 Matrix 1st Row 1st Column nothing 2nd Row 1st Column nothing 3rd Row 1st Column nothing 4st Row 1st Column nothing EndMatrix ].
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for the detailed step by step solution of the given problem.
To find the closest point to y in subspace W, see the projection of y onto W. Solve the appropriate equations to find the scalars for v1 and v2. The sum of these scaled vectors will yield the closest point.
Explanation:The closest point to y in the subspace W spanned by v1 and v2 can be determined using the projection formulas. First, find a and b such that a*v1 + b*v2 equals the projection of y onto W. To do this, set up the equations a*(v1 . v1) + b*(v1 . v2) = y . v1 and a*(v1 . v2) + b*(v2 . v2) = y . v2. Solve these equations for a and b. The solution will give you the scalars for v1 and v2, respectively. The vector a*v1 + b*v2 will be the closest point in W to y.
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Of the five quadratics listed below, four of them have two distinct roots. The fifth quadratic has a repeated root. Find the value of the repeated root.
-x^2 + 18x + 81
3x^2 - 3x - 168
x^2 - 4x - 4
25x^2 - 30x + 9
x^2 - 14x + 24
Answer: 3/5
Step-by-step explanation: The fourth quadratic in the list is the square of a binomial:
25x^2 - 30x + 9 = (5x - 3)^2
Therefore, the repeated root of this quadratic is the solution to 5x - 3=0, which is 3/5
Define interest rate
Answer:
In my own words interest rate is the proportion of a loan that is charged as interest to the borower, typically expressed as an annual percentage of the loan outstanding. :D Hope this help and do you like brownies
Step-by-step explanation:
Final answer:
The interest rate is the cost of borrowing money or the return on investment deposited in financial institutions. It's influenced by financial regulations like usury laws, which cap the maximum interest rate to prevent excessive charges.
Explanation:
The interest rate is often referred to as the "price" of borrowing money in the financial market, and it's also the rate of return on an investment. When you deposit money into a savings account at a bank, the bank will pay you interest, which is a percentage of your deposits. This is the interest rate. Conversely, when you take out a loan, you will pay interest to the lender, which is the cost of borrowing the funds you need to purchase something, like a car or a computer.
There are also regulations like usury laws that set maximum limits on the interest rates that can be charged, ensuring that lenders do not exceed legal thresholds. The concept is similar to the idea of minimum wage, which sets a 'price floor' for hourly wages, below which it is illegal for employers to pay employees.
5. Solve the equation.
6i - 10 = - 82
Equation:
Answer:
i=-12
Step-by-step explanation:
1.) Add 10 to -82 to get the equation 6i=-72
2.) Divide -72 by 6 to get the answer i=-12
Need help on these, thank you, and i'll need this answer soon
∠AGB and ∠EGD are □ angles.
∠DGC and ∠CGB are □ angles.
Find m∠EGD.
Find m∠AGF.
Find m∠EGF.
Answer:
∠AGB and ∠EGD are vertical angles.
∠DGC and ∠CGB are supplementary angles.
m∠EGD = 30
m∠AGF = 50
m∠EGF = 100
Step-by-step explanation:
Answer:
veryical
Step-by-step explanation:
The scatter plot shows the number of tickets sold and the price of the tickets.
Using the trend in the scatter plot, about how much will people pay for a ticket if 50 tickets are sold?
Answer: People will pay about $5 for a ticket if 50 are sold.
Step-by-step explanation:
What we can deduce from this graph is the more expensive the tickets are, the less tickets are sold.
So far, the greatest number of tickets sold are 40 with a price of around $10.
Now, if people were to sell 50 tickets, following with the graph, it
would mean that the price would have to be less than 10.
Only one of the options is less than 10, and that is 5, so therefore, the answer is 5.
Prehistoric cave paintings were discovered in a cave in France. The paint contained 3% of the original carbon-14. Use the exponential decay model for carbon-14, A=A0e^-0.000121t, to estimate the age of the paintings.
The painting area approximately __ years old.
Answer:
The painting area is approximately 28980 years old.
Step-by-step explanation:
The model for the amount of carbon-14 after t years is given by:
[tex]A(t) = A(0)e^{-0.000121t}[/tex]
In which A(0) is the original amount.
The paint contained 3% of the original carbon-14.
This means that [tex]A(t) = 0.03A(0)[/tex]. This means that we have to find t.
[tex]A(t) = A(0)e^{-0.000121t}[/tex]
[tex]0.03A(0) = A(0)e^{-0.000121t}[/tex]
[tex]e^{-0.000121t} = 0.03[/tex]
[tex]\ln{e^{-0.000121t}} = \ln{0.03}[/tex]
[tex]-0.000121t = \ln{0.03}[/tex]
[tex]t = -\frac{\ln{0.03}}{0.000121}[/tex]
[tex]t = 28980[/tex]
The painting area is approximately 28980 years old.
(-8) . (-8) . (-8) . (-8) . (-8) . (-8) . (-8)
Answer:
-2097152
Step-by-step explanation:
(-8)(-8)(-8)(-8)(-8)(-8)(-8) =
-2097152
Answer: -2097152
Step-by-step explanation:
(-8)(-8)(-8)(-8)(-8)(-8)(-8)=
(-8)^7
=-2097152
Please help me with this.
Answer:
3.5, three-and-a-half, 7/2