Based on experimental probability, Abdul should expect 10 tails in the next 40 flips.
The experimental probability of getting tails is calculated as the ratio of the number of tails obtained in the experiment to the total number of coin flips.
In this case, the experimental probability of getting tails is 16/64, which simplifies to 1/4 or 0.25.
This means that in the long run, we would expect approximately 25% of coin flips to result in tails.
To determine how many of the next 40 flips Abdul should expect to come up tails based on experimental probability,
we can multiply the experimental probability by the total number of flips.
Abdul should expect 0.25 × 40 = 10 tails in the next 40 flips.
Experimental probability of getting tails = Number of tails obtained / Total number of coin flips
Experimental probability of getting tails = 16/64
Experimental probability of getting tails = 0.25 or 25%
Expected number of tails in the next 40 flips = Experimental probability of getting tails × Total number of flips
Expected number of tails in the next 40 flips = 0.25×40 = 10 tails
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2. an insurance salesman sells policies to 10 men, all of identical age and all of whom are in good health. according to his company's records, the probability that a man of this particular age will be alive in 20 years is 0.69. find the probability that in 20 years the number of the men that are still alive will be: a) exactly five b )more than 8 c)at least two
a) The probability that exactly five men will still be alive in 20 years is approximately 0.024.
b) The probability that more than eight men will still be alive in 20 years is approximately 0.057.
c) The probability that at least two men will still be alive in 20 years is approximately 0.999.
To calculate the probabilities, we can use the binomial distribution formula, where n is the number of trials, p is the probability of success, and x is the number of successes. Therefore,
a) P(X = 5) = (10 choose 5) * (0.69)⁵ * (0.31)⁵ ≈ 0.024
b) P(X > 8) = P(X = 9) + P(X = 10) = [(10 choose 9) * (0.69)⁹ * (0.31)¹] + [(10 choose 10) * (0.69)¹⁰ * (0.31)⁰] ≈ 0.057
c) P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) = 1 - [(10 choose 0) * (0.69)⁰ * (0.31)¹⁰] - [(10 choose 1) * (0.69)¹ * (0.31)⁹] ≈ 0.999
In summary, we have used the binomial distribution formula to calculate the probability that exactly five men, more than eight men, and at least two men will still be alive in 20 years, given that the probability that a man of this particular age will be alive in 20 years is 0.69.
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What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/4
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 8
New = 2
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 2/8
Evaluate
Scale factor = 1/4
Hence, the scale factor for the similar figures is 1/4
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1. )Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).
2. )Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
3. ) Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
1) x+y=4. This is the equation of the line in standard form.
2) x+y=4. This is the equation of the line in standard form.
3) The equation of the other diagonal is x=0.
1) The median of a trapezoid connects the midpoints of the non-parallel sides. The midpoint of RT is ((-1+7)/2,(5-2)/2)=(3,1.5) and the midpoint of SU is ((1+2)/2,(8+0)/2)=(1.5,4). The line containing the median passes through these two points, so we can use them to find the equation of the line. The slope of the line is (4-1.5)/(1.5-3)=1.5/(-1.5)=-1. The midpoint formula for a line gives us (y-1.5)=-1(x-3), which simplifies to x+y=4. This is the equation of the line in standard form.
2) To find the altitude to the hypotenuse of a right triangle, we need to find the midpoint of the hypotenuse and the slope of the hypotenuse. The midpoint of PQ is ((-1+3)/2,(1+5)/2)=(1,3), and the midpoint of PR is ((-1+5)/2,(1-5)/2)=(2,-2). The slope of PQ is (5-1)/(3-(-1))=4/4=1, so the slope of the altitude is -1. We can use the point-slope form of a line to get y-3=-1(x-1), which simplifies to x+y=4. This is the equation of the line in standard form.
3) The diagonals of a square are perpendicular bisectors of each other, so we can find the equations of both diagonals using the midpoint and slope formulas. The midpoint of AC is ((3-3)/2,(3-3)/2)=(0,0), and the midpoint of BD is ((-3+3)/2,(3-3)/2)=(0,0). The slope of AC is (3-(-3))/(3-(-3))=6/6=1, so the slope of BD is -1. Using the point-slope form of a line, we can get y-0=-1(x-0), which simplifies to y=-x. This is the equation of one diagonal. To find the equation of the other diagonal, we use the midpoint of AB ((-3+3)/2,(3+3)/2)=(0,3) and the midpoint of CD ((3-3)/2,(-3-3)/2)=(0,-3). The slope of AB is (3-3)/(3-(-3))=0, so the slope of the other diagonal is undefined (since it's perpendicular to AB). The equation of the other diagonal is x=0.
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Calculate the interest and total value on a $6,300 deposit for 8 years at a compound interest rate of 4. 5%
The interest is $2,659.23 and the total value is $8,959.23.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Here the given principal P = $6300
Number of years = 8
Rate of interest = 4.5% = 4.5/100 = 0.045
Now using compound interest formula then,
=> Amount = [tex]P(1+r)^{t}[/tex]
=> Amount = 6300[tex](1+0.045)^8[/tex]
=> Amount = [tex]6300(1.045)^8[/tex]
=> Amount = $8,959.23
Then Interest = Amount - Principal
=> Interest = $8,959.23 - $6300 = $2,659.23.
Hence the interest is $2,659.23 and the total value is $8,959.23.
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Please help me with this question!
I need an explanation on how to get the answer!
Answer:
C - 136
Step-by-step explanation:
Something important to remember here is that whenever you replace a variable with something else, that something else needs to go in parentheses.
3(7)² - 2(7) + 3
Following PEMDAS, you need to take care of that exponent before anything else. While parentheses are included as coming first, that is referring to operations within parentheses, which we don't have here.
3(49) - 2(7) + 3
Multiplication is the next step...
147 - 14 + 3
And finally, addition and subtraction.
147 - 11
136
Answer:
136
Step-by-step explanation:
Since the question stated that x= 7 you simply substitute all x in the expression with 7 and it would look something like this
3 (7)^2 - 2 (7) +3
PLEASE BRAINLIEST
Which of the fraction, decimai, percent equivalencies are correct? Select THREE correct answers
The fractions, decimals, and percent equivalencies that are correct are:
b. 3/8 = 0.375 = 37.5%
c. 24% = 0.24 = 6/25
e. 24/30 = 80% = 0.8
What are fractions, decimals, and percentages?A fraction is a part of a whole.
The number is represented mathematically as a quotient, where the numerator and denominator are split.
In a simple fraction both the numerator and denominator are integers.
In a complex fraction, a fraction appears in the numerator or denominator.
In a proper fraction, the numerator is less than the denominator.
A decimal is a fraction that contains a decimal point.
A percentage is a value out of 100 parts.
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Simplify (write each expression without using the absolute value symbol.)
|x÷3|, if x<0
When dealing with absolute value expressions, we must consider both the positive and negative values of the argument.
In this case, we are asked to simplify[tex]|x÷3| if x<0[/tex], which means that x is a negative number.
To simplify this expression, we must first evaluate x÷3, which gives us a negative number divided by a positive number, resulting in a negative quotient.
However, since we are only interested in the absolute value of this quotient, we must ignore the negative sign and write the expression as:
[tex]|x÷3| = -(x÷3)[/tex]
Note that the negative sign in front of the expression serves to cancel out the negative sign of the quotient, thus giving us a positive result.
Therefore, the simplified expression for[tex]|x÷3| if x<0 is -(x÷3)[/tex]. This expression can be used to evaluate the value of |x÷3| for any negative value of x, by simply plugging in the corresponding value for x.
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The prism shown has a surface area of 1,500 mm squared. What is the height, h, of the prism?
The height of the triangular base prism is 10 mm.
How to find the surface area of a prism?The prism above is a triangular base prism. The surface area of the prism can be calculated as follows:
surface area of the triangular prism = (a + b + c)l + bh
where
a, b, and c are the side of the triangular basel = height of the prismb = base of the triangleh = height of the triangleTherefore,
surface area of the triangular prism = (20 + 30 + 40) + 20 × 30
1500 = 90l + 600
1500 - 600 = 90l
90l = 900
divide both sides by 90
l = 900 / 90
l = 10 mm
Therefore,
height of the prism = 10 mm
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Use the quadratic formula to determine the exact solutions to the equation.
2x2−9x+1=0
I feel like it's either b or d. I keep getting the same answer when I solve it but the thing is, it's not on the answer choices. My answer was (9 ± √ - 89 )/ 4
but it's not thereeeee :((
The exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
To solve the quadratic equation 2x² - 9x + 1 = 0 using the quadratic formula, we first need to identify the values of a, b, and c. From the given equation, we can see that a = 2, b = -9, and c = 1.
The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a, b, and c, we get:
x = (-(-9) ± √((-9)² - 4(2)(1))) / 2(2)
x = (9 ± √(81 - 8)) / 4
x = (9 ± √73) / 4
So, the exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.
As for the answer choices, it's possible that the answer key has simplified the solution further. However, your answer is correct and provides the exact solutions to the equation.
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In two or more complete sentences, describe the transformation(s) that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2
The transformations that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2 are horizontal compression and vertical shift.
What transformations took place in the function?The transformations are a horizontal compression and a vertical shift.
Horizontal compression: The factor of 3 in the argument of the logarithm function causes a horizontal compression by a factor of 1/3. This means that the graph of g(x) is narrower than the graph of f(x) and it is shifted to the left.Vertical shift: The constant term of -2 is subtracted from the logarithm function, causing a vertical shift downwards by 2 units.Therefore, the transformations can be expressed mathematically as follows:
g(x) = log(-3x - 6) - 2
= log(-3(x + 2)) - 2
= log(1/3)log(-3(x + 2)) - 2
Therefore, the transformations are a horizontal compression by a factor of 1/3 and a vertical shift downwards by 2 units.
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Suppose that an insurance company has 190 policy holders, and pays out $38000 in claims in a given year. The company also spends $1750 for marketing, $6000 for labor, and wants to earn a 20% profit. Given we do not have risk groups, what would a fair price be for annual premiums for the policy holders to pay?
The fair price for annual premiums for the policy holders to pay is $288.42
To determine the fair price for annual premiums, we need to take into account the company's expenses and desired profit. The company's total expenses can be calculated as the sum of the claims paid, marketing expenses, and labor expenses:
Total expenses = Claims paid + Marketing expenses + Labor expenses
Total expenses = $38000 + $1750 + $6000
Total expenses = $45750
To calculate the fair price for annual premiums, we need to add the desired profit to the total expenses and divide by the number of policy holders:
Fair price = (Total expenses + Desired profit) / Number of policy holders
Fair price = ($45750 + 20% of $45750) / 190
Fair price = ($45750 + $9150) / 190
Fair price = $54900 / 190
Fair price = $288.42
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Explain how you decided to divide your wholes into fractional parts and how you decided where your number scale should begin and end
The decision of how to divide a whole into fractional parts and where to begin and end a number scale depends on the context and purpose.
How do you decide on fractional division?when dividing a whole into fraction parts, the decision of how to divide it depends on the context and the specific problem being solved. For example, if a pizza needs to be divided among 4 people, it would make sense to divide it into 4 equal parts or fourths. If a recipe calls for 1/3 cup of flour, then the whole cup would be divided into 3 equal parts or thirds.
Regarding number scales, they can begin and end at different points depending on the context and purpose. For example, a temperature scale could start at 0 degrees and end at 100 degrees for Celsius, or start at 32 degrees and end at 212 degrees for Fahrenheit.
A financial scale could start at negative numbers for debts and end at positive numbers for assets. In general, number scales are designed to provide a clear and consistent way of measuring and comparing quantities in a particular context.
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in the absence of predators the natural growth rate of rabbits is 4% per year. a population begins with 100 rabbits. the function f(x) = 100(1.04) ^x gives the population of rabbits in x years. how long will it take the population of rabbits to double? how long will it take the population of rabbits to reach 1000?
a) It will take approximately 16.85 years for the rabbit population to double.
b) It will take approximately 37.28 years for the rabbit population to reach 1000.
The formula for calculating the population of rabbits in x years, starting with 100 rabbits and a natural growth rate of 4% per year, is given by:
f(x) = 100(1.04)ˣ
(a) To find out how long it will take for the rabbit population to double, we need to solve the following equation:
100(1.04)ˣ = 200
Dividing both sides by 100, we get:
(1.04)ˣ = 2
Taking the logarithm of both sides with base 1.04, we get:
x = log₁.₀₄ 2
Using a calculator, we get:
x ≈ 16.85
(b) To find out how long it will take for the rabbit population to reach 1000, we need to solve the following equation:
100(1.04)ˣ = 1000
Dividing both sides by 100, we get:
(1.04)ˣ = 10
Taking the logarithm of both sides with base 1.04, we get:
x = log₁.₀₄ 10
Using a calculator, we get:
x ≈ 37.28
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Which table shows a proportional relationship between x and y?
A charitable group will be shipping packages to an area of the country that has been devastated by tornadoes. they plan to ship two kinds of packages: food and clothing. they have donations of good and clothing and money. the money will be used to pay the shipping costs.
they collected $126. each package of food costs $18 to ship and each package of clothing costs $14 to ship.
write an inequality to represent this situation.
The charitable group has collected $126 to packages of food and clothing to the tornado-affected area
To represent the situation where a charitable group is shipping food and clothing packages to an area devastated by tornadoes, we can use the following inequality:
Let F be the number of food packages and C be the number of clothing packages. The shipping cost for food packages is $18 per package and for clothing packages is $14 per package.
They have collected $126 for shipping costs. The inequality representing this situation is:
18F + 14C ≤ 126
This inequality indicates that the total cost of shipping food packages (18F) plus the total cost of shipping clothing packages (14C) should be less than or equal to the available budget ($126).
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The answer and what is the value of a
Answer:a=40
Step-by-step explanation:
angles on a straight line add to 180. This means that the missing angle that isn't a is 40. Angles in a triangle add to 180 so a=40
A home improvement store advertises 60 square feet of flooring for $253.00, plus $80.00 installation fee. What is the cost per square foot for the flooring?
A. $4.95
B. $5.25
C. $5.55
D. $6.06
If the store advertises 60 square foot flooring for $253, then the cost for "per-square foot" is (c) $5.55.
To find the cost per square foot for the flooring, we need to divide the total cost of the flooring including the "installation-fee' by the total square footage of the flooring.
⇒ Total cost of flooring + installation fee = $253 + $80 = $333,
⇒ Total square footage of the flooring = 60 sq. ft.
So, Cost per square foot = (Total cost of flooring and installation fee)/(Total square footage of the flooring),
⇒ Cost per square-foot = 333/60,
⇒ Cost per square foot = $5.55/sq. ft.
Therefore, the correct option is (c).
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Solve for the missing side. Formula: a^2+b^2=c^2
Answer:
[tex] \frac{7 \sqrt{39} }{5} [/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]( {11.2})^{2} - { {7} }^{2} = 76.44 > 0[/tex]
The missing side is equal to:
[tex] \sqrt{76.44} = \frac{7 \sqrt{39} }{5} [/tex]
at state college last term, 50 of the students in a physics course earned a's, 75 earned b's, 114 got c's, 98 were issued d's, and 50 failed the course. if this grade distribution was graphed on pie chart, how many degrees would be used to indicate the b region? round your answer to the nearest whole degree, but do not include a degree symbol with your response.
The angle in degrees used to indicate the b region is 70.
The total number of students= Sum of the number of students with different grades and the failed ones.
= 50+75+114+98+50
= 387
Now,
The number of students in b region, that is, those who got b's
=75 (given)
We know that,
The sum of all angles due to different grades in the pie chart = 360 degrees.
So the distribution of degrees to b region in the pie chart will be in proportion to the number of students in b region out of total students
Let x degrees be used to indicate the "b" region.
∴ x/360=75/387 (because of the same proportion)
⇒x=75/387×360
⇒x=69.76≅70
Hence, the angle in degrees used to indicate the b region is 70.
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Find the surface area of the square pyramid (above) using its net (below).
The surface area of the square pyramid is approximately 41.83 cm².
To start with, let's define a square pyramid.
The slant height of the pyramid can be found using the formula:
l = √(h² + (s/2)²)
where h is the height of the pyramid and s is the length of one side of the base.
Plugging in the given values, we get:
l = √(7² + (4/2)²) = √(57)
Now that we know the slant height, we can find the area of each triangular face using the formula:
A = (1/2)bh
where b is the base of the triangle, and h is the height of the triangle.
Plugging in the given values, we get:
A = (1/2)(4)(√(57)) = 2√(57)
Since there are four triangular faces, the total area of all the triangular faces is:
4A = 8√(57)
Finally, we can find the total surface area of the pyramid by adding the area of the square base to the area of all the triangular faces:
surface area = 16 + 8√(57) = approximately 41.83 cm²
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Complete Question:
Find the surface area of the square pyramid where the base is 4cm and the height is 7cm.
One similar figure has an area that is nine times the area of another. The larger figure must have dimensions that are
times the dimensions of the smaller figure.
three
eighteen
eighty-one
nine
Since the area of a similar figure is proportional to the square of its linear dimensions, if one similar figure has an area that is nine times the area of another, the larger figure must have dimensions that are three times the dimensions of the smaller figure.
This is because the area is the square of the linear dimensions. So, if we increase the linear dimensions by a factor of 3, the area increases by a factor of 3^2 = 9.
Therefore, the answer is 3.
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DON'T GIVE FAKE ANSWERS OR I'LL REPORT!
What is the area of a sector with a central angle of 45° and a diameter of 5. 6 in. ? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. What is the area of a sector with a central angle of 120° and a radius of 18. 4 m? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box
The area of a sector with a central angle of 45° and a diameter of 5.6 in. is 1.23 square inches.
To see why, you can use the formula for the area of a sector, which is:
A = (θ/360) x π x r^2
where θ is the central angle in degrees, r is the radius, and π is approximately 3.14.
First, you need to find the radius of the sector, which is half of the diameter:
r = d/2 = 5.6/2 = 2.8 in.
Next, you can plug in the values for θ and r into the formula:
A = (45/360) x 3.14 x 2.8^2 = 1.23 square inches
Therefore, the area of the sector is 1.23 square inches.
The area of a sector with a central angle of 120° and a radius of 18.4 m is 1908.57 square meters.
To see why, you can use the same formula for the area of a sector:
A = (θ/360) x π x r^2
First, you need to convert the radius from meters to centimeters, since π is in terms of centimeters:
r = 18.4 m x 100 cm/m = 1840 cm
Next, you can plug in the values for θ and r into the formula:
A = (120/360) x 3.14 x 1840^2 = 1908.57 square meters
Therefore, the area of the sector is 1908.57 square meters.
A cylinder has a base area of 64π m2. Its height is equal to twice the radius. Identify the volume of the cylinder to the nearest tenth
The volume of the cylinder is approximately 1024π cubic meters.
We are given the base area of the cylinder as 64π square meters, which means that the radius of the cylinder is 8 meters (since the area of a circle is given by πr^2). We are also given that the height of the cylinder is twice the radius, which means that the height is 16 meters.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Substituting the given values, we get V = π(8^2)(16) = 1024π cubic meters. Therefore, the volume of the cylinder is approximately 1024π cubic meters.
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Answer:
[tex]3217.0 m ^{3}[/tex]
Step-by-step explanation:
Monica deposits $ 300 into a savings account that pays a simple interest rate of 3.4%. Paul deposits $400 into a savings account that pays a simple interest rate of 3.3 %. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Monica's claim is incorrect. Even though her interest rate is higher, she will earn less interest, $10.20, after one year than Paul because her initial deposit is lower.
Paul will earn more interest of $13.20 because he deposited more money, even though his interest rate is slightly lower.
To determine who will earn more interest in one year, we shall calculate the interest earned by each person using the simple interest formula.
What is the simple interest formula?The formula for simple interest is:
I = P * r * t
where:
I = the interest earned
P = the principal (the amount deposited)
r = the interest rate (as a decimal)
t =s the time (in years)
For Monica, we are given:
P = $300
r = 0.034 (the interest rate is 3.4%)
t = 1 (the interest earned in one year)
Plugging these values, we have:
I = 300 * 0.034 * 1 = $10.20
So, Monica will earn $10.20 in interest after one year.
For Paul, we are given:
P = $400
r = 0.033 (interest rate = 3.3%)
t = 1 (interest earned in one year)
Plugging the values, we get:
I = 400 * 0.033 * 1 = $13.20
So, Paul will earn $13.20 in interest after one year.
Therefore, Monica's claim is incorrect. Monica will earn $10.20 in interest after one year while Paul will earn $13.20 in interest after one year.
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π × 4 to the second power × 3 ( with steps !! )
(c) Give a specific example of a rule for the function f such that the series Σα) f(n)/n^2does not converge. You must justify your answer.
One specific example of a rule for the function f such that the series Σα) f(n)/n^2 does not converge is the function f(n) = (-1)^n.
To justify this, we can use the alternating series test, which states that if a series has alternating signs and the absolute values of its terms decrease monotonically to 0, then the series converges. However, if the absolute values of its terms do not decrease monotonically to 0, then the series diverges.
In this case, we have Σα) f(n)/n^2 = Σα) (-1)^n/n^2. The absolute value of each term is 1/n^2, which does decrease monotonically to 0. However, the signs of the terms alternate, meaning that the series does not converge. Therefore, this is a valid example of a rule for the function f such that the series Σα) f(n)/n^2 does not converge.
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39 A sample of a substance with an initial mass of 963 grams is decaying
at a rate of 27% per hour.
Create a function that can be used to find y, the mass of the
substance in grams remaining after x hours.
Record your answer in the space provided.
A function that can be used to find y, the mass of the substance in grams remaining after x hours is [tex]P(x) = 963(0.63)^x[/tex]
How to create a function that can be used to find the mass of the substance?In Mathematics and Statistics, a population or substance that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or substance that decreases by r percent per unit of time is an exponential equation of this form:
[tex]P(x) = I(1 - r)^x[/tex]
Where:
P(x) represents the total mass or population.x represents the time or number of years.I represents the initial value of the substance.r represents the decay rate.By substituting given parameters into the , we have the following:
[tex]P(x) = I(1 - r)^x\\\\P(x) = 963(1 - 0.27)^x\\\\P(x) = 963(0.63)^x[/tex]
In conclusion, we can reasonably infer and logically deduce that the decay rate is equal to 63%.
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If the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
The value of n is 6
Given expression is [tex]\frac{48a^{12}b^8c^{15}}{(2a^2bc^4)^3}=6a^nb^mc^r[/tex]
To find the value of n, we need to simplify the expression:
(48 × a¹² × b⁸ × c¹⁵) / (2 × a² × b × c⁴)³
First, we can simplify the denominator:
(2 × a² × b × c⁴)³ = 2³ × (a²)³ × b³ × (c⁴)³
= 8 × a⁶ × b³ × c¹²
(48 × a¹² × b⁸ × c¹⁵) / (8 × a⁶ × b³ × c¹²) = (8 × 6a⁶ × a⁶ × b⁵ × b³ × c₁₂ × c³) / (8 × a⁶ × b³ × c¹²)
Simplifying further, we get:
= 6 × a⁶ × b⁵ × c³
on comparing with R H S
a⁶ = aⁿ
So, n=6
Therefore, the value of n is 12, since that is the exponent of the variable "a".
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Given question is incomplete, the complete question is given below
For the expression below
[tex]\frac{48a^{12}b^8c^{15}}{(2a^2bc^4)^3}=6a^nb^mc^r[/tex]
If the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
Sally is 21 years old and has a resting heart rate of 72 beats per minute. what is her estimated maximum heart rate (mhr)
Sally's estimated maximum heart rate (MHR) is 199 beats per minute.
To estimate Sally's maximum heart rate (MHR), we will use the following formula:
MHR = 220 - age
1. First, note Sally's age, which is 21 years old.
2. Then, apply the formula: MHR = 220 - 21.
3. Calculate the result: MHR = 199 beats per minute.
Sally's estimated maximum heart rate (MHR) is 199 beats per minute.
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Scientists measured 24 geodes in kilograms and got the following data: 0.9, 1.1, 1.1, 1.2, 1.5, 1.6, 1.7, 1.7, 1.7, 1.9, 2.0, 0.8, 2.3, 5.3, 6.8, 7.5, 9.6, 10.5, 11.2, 12.0, 17.6, 23.9, and 26.8
How many items belong to the interval 10.1-15
Answer:
the answer to your problem is 3