Answer:
Let's use "x" to represent the total number of students in the class.
According to the problem, the number of boys is 7/10 of the total number of students, and the number of girls is 3/10 of the total number of students. We can set up the following equation based on this information:
Number of Boys = 7/10 x
Number of Girls = 3/10 x
The problem also tells us that there are 16 more boys than girls in the class. We can set up another equation based on this information:
Number of Boys = Number of Girls + 16
Now we can use these two equations to solve for the total number of students:
7/10 x = 3/10 x + 16
Subtracting 3/10 x from both sides, we get:
4/10 x = 16
Multiplying both sides by 10/4, we get:
x = 40
Therefore, there are 40 students in the class. To find the number of boys and girls, we can use the equations we set up earlier:
Number of Boys = 7/10 x = 7/10 * 40 = 28
Number of Girls = 3/10 x = 3/10 * 40 = 12
So there are 28 boys and 12 girls in the class.
a store owner wants to develop a new snack mix by mixing chocolate and trail mix. how many pounds of chocolate costing $21.10 per pound should be mixed with 14 pounds of trail mix costing $3.10 per pound to create a mixture worth $12.41 per pound.
To solve this problem, we can use the method of mixtures. Let x be the number of pounds of chocolate to be mixed with the trail mix. We can set up the following equation based on the given information:
(21.10x + 3.10(14)) / (x + 14) = 12.41
Simplifying and solving for x, we get:
21.10x + 43.40 = 12.41x + 173.54
8.69x = 130.14
x = 15
Therefore, the store owner should mix 15 pounds of chocolate costing $21.10 per pound with 14 pounds of trail mix costing $3.10 per pound to create a mixture worth $12.41 per pound.
To check this answer, we can verify that the total cost of the mixture equals the total cost of the chocolate and trail mix:
15(21.10) + 14(3.10) = 315 + 43.40 = 358.40
And the total weight of the mixture is:
15 + 14 = 29
So the cost per pound of the mixture is:
358.40 / 29 = 12.41
which matches the desired cost per pound.
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Rotate the figure 180 degrees
The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Calculating the coordinates of the imageGiven that
T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)
Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.
This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.
Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:
(x', y') = (-x, -y)
Using the above, the image is
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
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Complete question
Rotate the figure 180 degrees about the origin
T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)
T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th
T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)
T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)
a family has five children 3 boys and 2 girls. determine the experimental(empirical) probability that the next child is a boy.
The experimental (empirical) probability that the next child is a boy given that a family has five children: 3 boys and 2 girls is 0.6.
Given that the family has five children, 3 of whom are boys and 2 are girls. If we want to know the experimental probability that the next child is a boy, we need to find the ratio of the number of boys to the total number of children. Since the family has three boys and two girls, the total number of children is:
Total number of children = 3 + 2 = 5
Therefore, the probability of the next child being a boy is given by the ratio of the number of boys to the total number of children.
P(B) = Number of boys/Total number of children
P(B) = 3/5P(B) = 0.6
Therefore, the experimental (empirical) probability that the next child is a boy is 0.6.
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Match the following terms with the descriptions. a. total purchase price b. unit pricing c. comparison shopping d. coupons e. rebates f. markdown g. markdown rate h. sale price 14. A technique that allows shoppers to compare prices 15. The total selling price plus the sales tax - 16. Discount 17. Regular selling price minus the markdown 18. Locating the best value for your money
a. Total purchase price: 15.The total selling price plus the sales tax.
b. Unit pricing: 18. Locating the best value for your money
c. Comparison shopping: 14. A technique that allows shoppers to compare prices
d. Coupons: 16. Discount
e. Rebates: 16. discount
f. Markdown: 17. regular selling price minus the markdown.
g. Markdown rate: 16. Discount
h. Sale price: 18. Locating the best value for your money
What is selling price?Selling price is the amount of money a customer pays for a product or service. It is the amount that a customer pays for the product or service after any discounts, taxes, or fees have been applied.
a. Total purchase price: The total selling price plus the sales tax. This amount is the total cost the customer pays for the good or service, including any taxes and fees.
b. Unit pricing: The cost per unit of a good or service. This allows shoppers to compare the cost of similar items and make an informed decision about which item offers the best value.
c. Comparison shopping: A technique that allows shoppers to compare prices, quality, and other factors when making a purchase.
d. Coupons: A form of discount that can be used when making a purchase. Coupons are often found in newspapers, magazines, or online and can be used to reduce the total purchase price.
e. Rebates: A form of discount where customers receive money back after making a purchase. Rebates are often found in the form of a check or a prepaid debit card.
f. Markdown: The regular selling price minus the markdown. The markdown is the amount that is discounted from the regular selling price.
g. Markdown rate: The percentage of the regular selling price that is discounted. This rate is used to calculate the amount of the markdown.
h. Sale price: The discounted price of a good or service. This is the amount the customer pays after any discounts or coupons have been applied.
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Answer for x=
Please
Answer:
53°
Step-by-step explanation:
it’s vertical, verticals are always identical, I think
andy has 15 coins made up of quarters and half dollars, and their total value is $5.00 how many quarters does he have
Andy has 15 coins made up of quarters and half dollars, and their total value is $5.00.
He has 10 quarters and 5 half dollars.
To find this answer, we can set up the following equation: 0.25Q + 0.50H = 5.00, where Q represents the number of quarters and H represents the number of half dollars. Solving for Q, we get Q = 10. Therefore, Andy has 10 quarters and 5 half dollars.
To solve this equation, we can use algebra to isolate the variable Q. We can start by subtracting 0.50H from both sides, giving us 0.25Q = 5.00 - 0.50H.
Next, we can divide both sides by 0.25, giving us Q = (5.00 - 0.50H) / 0.25. Therefore, we can substitute the values for 5.00 and 0.50H and solve for Q, giving us Q = 10.
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C. Steve is working on his electrical system. He knows the output of the system is equal to the
equation y = -x2 + 12x - 20. At what input will he reach his maximum output?
To achieve the maximum output from his electrical system, Steve should set the input to 6, the x-coordinate of the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex].
To find the input that will result in the maximum output of the electrical system, we need to find the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola is the point where the curve reaches its highest or lowest point, depending on whether the parabola opens upward or downward. In this case, the coefficient of [tex]x^2[/tex] is negative, which means the parabola opens downward, and the vertex represents the maximum point.
We need to find the vertex of the parabola given by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola with equation [tex]y = ax^2 + bx + c[/tex] is given by the formula x = -b/2a.
In this case, a = -1, b = 12, and c = -20, so the x-coordinate of the vertex is:
x = -b/2a = -12/(2*(-1)) = 6
Therefore, the input at which Steve will reach his maximum output is x = 6.
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a stadium can seat 63,026 people. for each game, the amount of money that the organization brings in through ticket sales is a function of the number of people, `n`, in attendance. if each ticket costs $30.00, find the domain and range of this function:
Answer: 63056$
Step-by-step explanation: i learned that in school 2 hours ago
which function produces a range of (-11,-5,1,7,13) given a domain of (-2,0, 2, 4, 6)?
01(x)==+2
Of(x) = -52 +3
01(z)-38 +4
01 (2)-32-5
1 of 10
M
P
(318
0
The function f(x) = 3x - 5 has the defined set of range and domain of the function.
Which function have the given set of range and domain?The range {−11,−5,1,7,13} and the domain {−2,0,2,4,6} of the function
Taking the first function;
f(x) = 3x - 5
When x = -2, f(x) = 3(-2) - 5 = -11
When x = 0, f(x) = 3(0) - 5 = -5
When x = 2, f(x) = 3(2) - 5 = 1
When x = 4, f(x) = 3(4) - 5 = 7
When x = 6, f(x) = 3(6) - 5 = 13
Therefore, the function f(x) = 3x - 5 produces the given range when the domain is {−2,0,2,4,6}.
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complete question :
Which function produces a range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6}
f(x) = 3x − 5
f(x) = −3x + 4
f(x) = x + 2
f(x) = −5x + 3
1) Is 2nd drawing a reduction or enlargement?
2) What is the scale factor?
Answer:
1. reduction
2. scale factor of 1/2
Step-by-step explanation:
1. the second image is smaller than the original
2. 18*1/2= 9 and 6*1/2=3
Consider the system of equations
below. What is the solution of the
system?
y=4x-8
4x + 2y = 20
Answer:
x = 3, y = 4
Step-by-step explanation:
Substitute 4x - 8 in for y and then solve for x:
4x + 2(4x - 8) = 20
Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.
Once you have x, you can solve for y.
y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4
So, x = 3, y = 4
HELP PLEASE AND SHOW HOW YOU DID IT
The volume of the cylinder with radius 19 yd and height 21 yd is 23,804.34 cubic yard
What is the volume of the cylinder?Volume refers to the unit of three-dimensional measure of space that comprises a length, a width and a height. It is measured in units of cubic centimeters in metric, cubic inches or cubic feet.
Volume of a cylinder = π × r ²× h
Where,
π = 3.14
Radius, r = 19 yd
Height, h = 21 yd
So,
Volume of a cylinder = π × r² × h
= 3.14 × 19² × 21
= 3.14 × 361 × 21
= 23,804.34 cubic yard
Ultimately, 23,804.34 cubic yard is the volume of the given cylinder.
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Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Thank you in advance!
The approximate circumference of this Spaceship is equal to 157 meters.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this mathematical expression:
Volume = 4/3 × πr³
Where:
r represents the radius.
By substituting the given points into the volume of a sphere formula, we have the following;
65,417 = 4/3 × 3.14 × r³
r³ = 65,417/4.1867
Radius, r = ∛15,624.96
Radius, r = 25 meters.
How to determine the circumference of this Spaceship?Mathematically, the circumference of a sphere can be calculated by using this mathematical expression:
Circumference of a sphere, C = 2πr
Circumference of a sphere, C = 2 × 3.14 × 25
Circumference of a sphere, C = 157 meters.
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10 points worth
Please answer correctly
please help!! the answers are not 9, 18, 54, or 6
Answer:
If x = 3 and y = 2.3^3, then we can evaluate y using exponents:
y = 2.3^3 = 2.3 × 2.3 × 2.3 = 12.167
So, y = 12.167 when x = 3.
Next, if we want to solve the equation y = 2[?] using order of operations, we need to evaluate what is inside the brackets first. We know that y = 12.167, so we can substitute that value into the equation:
y = 2[?]
12.167 = 2[?]
To solve for the missing value inside the brackets, we need to divide both sides by 2:
12.167 ÷ 2 = ?
6.0835 = ?
Therefore, the solution is y = 2(6.0835), or y = 12.167, which we already found earlier.
A salesperson earns a commission of $448 for selling $2800 in merchandise. Find the commission rate. Write your answer as a percentage.
Answer:
16%
Step-by-step explanation:
translation
x% times 2800 = 448
x% = 448 divided by 2800
x% = 0.16 = move decimal 2 spaces to the right = 16%
To find the commission rate we just have to divide the total commission by the total amount of merchandise sold. The commission was $448 and the amount of merchandise sold was $2800.
[tex]\dfrac{448}{2800}=0.16[/tex]
Then, to rewrite a decimal as a percentage, we just need to multiply the number by 100.
[tex]0.16=\dfrac{0.16\times100}{100} =\dfrac{16}{100} =16\%[/tex]
The commission rate is 16%.
can yall help me with this math question
The area of the trapezoid is 70 square centimeters.
Which trapezoid formula is appropriate?locating a right trapezoid's area. A = (a + b) x h/2 is the formula to calculate the area of a right trapezoid.
We must apply the following calculation to determine the area of the trapezoid:
A = (b1 + b2) * h/2
where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides (or the distance between the parallel sides).
We can observe that in this instance, b1 = 12 cm, b2 = 8 cm, and h = 7 cm. When we plug these numbers into the formula, we get:
A is equal to (12 + 8) x 7 cm / 2.
A = 20 cm * 7 cm / 2
A = 70 cm²
Hence, the trapezoid has a surface area of 70 square centimetres.
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Boris paid for dinner and added $8 tip (which is 20% of the total). What was the total before the tip.
HELPP PLSSSSS NOW!!!!!!
Inc pairs of numbers with a sum of 207, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms. Answer
The value of both numbers in fractions will be 207/2 and 207/2.
Given that:
Equation: x + y = 207
The two numbers' product is:
P = xy
P = x(207 - x)
P = 207x - x²
Differentiating P with regard to x. Then we have
dP/dx = 0
207 - 2x = 0
x = 207/2
Then the other number is calculated as,
x + y = 207
207/2 + y = 207
y = 207/2
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random sample of size is selected from a population with . a. what is the expected value of (to decimals)? .40 b. what is the standard error of (to decimals)? .048 c. show the sampling distribution of . (to decimals) (to decimals) d. what does the sampling distribution of show? - select your answer -
Random sample of size is selected from a population:
expected value of the sample proportion is 0.40standard error of the sample proportion is 0.0024.sampling distribution follows a normal distribution = 0.40sampling distribution p ∼ N ([tex]p, \frac{p(-p)}{n}[/tex]) as n → ∞.The sample statistic that is calculated for the sample values serves as the foundation for the sampling distribution. To estimate the population percentage, the sample proportion, a sample statistic, is computed from the sample values.
In statistics, a simple random sample is a subset of individuals selected at random from a larger population with an equal probability of selection.
Given that we have,
n = 100
p = 0.40
a) The expected value of the sample proportion is defined as:
E(p) = p = 0.40
b) The standard error of the sample proportion is defined as:
[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]
= [tex]\sqrt{\frac{0.40(1-0.40)}{100} }[/tex]
S.E = 0.0024.
c) The sample proportion's sampling distribution follows a normal distribution, with an expected value of 0.40.
E(p) = 0.40
d) According to the central limit theorem, as the sample size approaches infinity, the sample statistic (sample percentage) tends to the population parameter (population proportion).
so,
p ∼ N ([tex]p, \frac{p(-p)}{n}[/tex]) as n → ∞.
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Complete question:
A random sample of size 100 is selected from a population with p = 0.40 .
a. what is the expected value of p (to decimals)? .
b. what is the standard error of p (to decimals)?
c. show the sampling distribution of p
d. what does the sampling distribution of show?
Alyssa has 4.5 liters of lemonade to pour into pitchers. Each pitcher holds 0.9 liter of lemonade. Alyssa pours an equal amount of lemonade into each pitcher. Alyssa draws the model below to show how many pitchers she fills. Is Alyssa’s model correct? Explain
80x something will
=480
Answer:
400
Step-by-step explanation:
480-80=400
Answer
x=6
Step-by-step explanation:
80*x=480
80*6=480
X =-1 y=8 Are the two linear equations parallel, perpendicular, or neither?
Answer:
Step-by-step explanation:
they're perpendicular
the apothem of a regular polygon is 7. and the polygon's perime- ter is 56. find the polygon's area.
Answer:
A = 196 units²
Step-by-step explanation:
the area (A) of a regular polygon is
A = [tex]\frac{1}{2}[/tex] perimeter × apothem
here perimeter = 56 and apothem = 7 , then
A = [tex]\frac{1}{2}[/tex] × 56 × 7 = 28 × 7 = 196 units²
Solve for x 5x
-2(x+1)=10
Step-by-step explanation:
5x-2(x+1)=10
5x-2x+2=10
3x+2=10
3x=10-2
3x=8
8/3
2.7 if you do round it
2.666666667 before you do
x=2.7
(I think it's right Because I've already been taught this if not just tell me.)
the elephant population in northwestern namibia and etosha national park can be predicted by the expression 2 , 649 ( 1.045 ) b , where b is the number of years since 1995. what does the value 2,649 represent?
The value 2,649 represents the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 and the estimated population was 618.4.
The formula for population growth can be represented as:
P = P0ert
Here, P is the population of elephants, P0 is the initial population, e is the base of the natural logarithm, r is the rate of growth or decay, and t is the time in years.
Now, as per the given data, P = 2,649P0 = initial population r = 1.045 (as per the given expression)b = t - 1995 (as per the given formula)Now, putting these values in the population growth formula,
P = P0ert2,649 = P0e1.045(b-1995)Dividing by P0 on both sides, we get:e1.045(b-1995) = 2649/P0
Taking the natural logarithm on both sides,
ln e1.045(b-1995) = ln (2649/P0)
Applying the property of logarithm,1.045(b-1995) ln e = ln (2649/P0)1.045(b-1995) = ln (2649/P0)
vAs we need to find the value of P0, substitute the value of b = 0,1.045(0-1995) = ln (2649/P0)-1.045*1995 = ln (2649/P0)ln (2649/P0) = -2069.95
Taking anti-logarithm or exponentiation on both sides,2649/P0 = eln (2649/P0) = e^(-2069.95)2649/P0 = 4.29P0 = 2649/4.29P0 = 618.4
Therefore, the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 was 618.4.
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the chance of getting a rare disease is .03 per person. out of 1,000 people, how many of them are expected to get the disease?
Answer:
I believe the answer would be 30 people.
Step-by-step explanation:
To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.
A gallon of latex paint can cover 400 square feet. How many
gallon containers of paint should be bought to paint two
coats on each wall of a rectangular room whose dimensions
are 14 feet by 18 feet? (Assume 8-foot ceilings.)
To find:-
The amount of paint required to paint two coats on the wall of a rectangular room of dimensions 14ft × 18ft × 8ft .Answer:-
We are here given that 1 gallon of paint can be used to paint 400 sq ft. of an area .
There are 4 walls in a room and the area of opposite walls are equal.
So let's find out the area of wall ABCD , its area would be equal to the area of the wall EFGH . So ,
Area of wall ABCD and EFGH :-
Area = lb
Area = 18ft * 8ft
Area = 144ft.²
Therefore area of wall EFGH will also be 144ft.² .
===============================================
Again,
Area of wall DAHE and CBGF :-
Here both the areas of the wall would again be equal, as they have same dimensions of 14ft × 8ft .
Area = lb
Area = 14ft * 8ft
Area = 112ft.²
Therefore area of walls DAHE and CBGF is 112ft.²
==============================================
Calculating total area of the four walls :-
Total area = 2( 112ft.² + 144ft.² )= 512ft.²
Hence total area of four walls is 512ft.²
Now since there will be two coats of paints , total area to be painted would become double that is 1024ft.²
Now we may use Unitary Method :-
To paint 400ft.² 1 gallon of paint is needed.
To paint 1ft.² 1/400 gallon of paint is needed.
To paint 1024ft.² , 1/400*1024 = 2.56 gallons of paint would be needed.
Hence the total paint required is 2.56 gallons.
and we are done!
Answer:
3 one-gallon containers of paint.
Step-by-step explanation:
First, find the total surface area that needs to be painted.
To find the surface area of the walls of a rectangular room, calculate the area of each of the four walls and then add them together.
The area of a rectangle is the product of its width and length.
For the walls of the given room, the "length" is the height of 8 ft, since we want to paint from the floor to the ceiling.
The room has four walls:
Two walls with dimensions 14 ft × 8 ftTwo walls with dimensions 18 ft × 8 ftTherefore, the total surface area is:
[tex]\begin{aligned}\textsf{Total surface area}&=2(14 \times 8)+2(18 \times 8)\\&=2(112)+2(144)\\&=224+288\\&=512\;\sf ft^2\end{aligned}[/tex]
Since we want to apply two coats of paint, we need to double the surface area:
[tex]\implies 2 \times 512=1024 \; \sf ft^2[/tex]
Now, we can find how many gallons of paint are needed by dividing the total surface area by the coverage per gallon:
[tex]\implies \dfrac{1024}{400}=2.56\; \sf gallons[/tex]
Therefore, we need 2.56 gallons of paint to paint two coats of each wall of the rectangular room.
Since we cannot buy a fraction of a gallon, we need to round up to the nearest gallon. Therefore, we need to buy 3 one-gallon containers of paint.
If the ratio of the number of cats to dogs at an
animal shelter is 9 to 5, which of the following is
the possible number of cats to dogs at the animal
shelter?
Answer:
If the ratio of the number of cats to dogs at the animal shelter is 9 to 5, this means that for every 9 cats at the shelter, there are 5 dogs.
We can express this ratio as:
number of cats : number of dogs = 9 : 5
To find the possible number of cats to dogs, we need to look for pairs of numbers that have a ratio of 9:5. Here are some possible pairs:
9 cats : 5 dogs
18 cats : 10 dogs
27 cats : 15 dogs
36 cats : 20 dogs
45 cats : 25 dogs
54 cats : 30 dogs
...
We can see that there are infinitely many possible pairs of numbers that have a ratio of 9:5. To narrow down the possibilities, we need more information such as the total number of animals at the shelter or the number of cats or dogs at the shelter.
a radioactive material decays according to the formula , where a is the final amount, is the initial amount and t is the time in years. find k, if 700 grams of this material decays to 550 grams in 8 years.
the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.
The formula for radioactive decay is given by:
a = [tex]e^(-kt)\\[/tex] * A
where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.
We can use the given information to solve for k as follows:
When t = 0, a = A. So, we have:
A = [tex]e^(0 * k)[/tex] * A
Simplifying this gives:
1 = e^0
Therefore, we can see that k = 0 at the start of the decay process.
Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:
550 = [tex]e^(-8k)[/tex] * 700
Dividing both sides by 700 and taking the natural logarithm of both sides, we get:
ln(550/700) = -8k
Simplifying this gives:
k = ln(700/550)/8
Using a calculator, we can evaluate this expression to get:
k ≈ 0.0445
Therefore, the decay constant for this material is approximately 0.0445.
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