The location of all the relative and absolute extrema is (0, 0) (local minimum); (1, 1) (local maximum); (3, 3) (absolute maximum)
To find the relative and absolute extrema of the function f(x) = 2x - x^2 on the domain (0,3), we first take the derivative:
f'(x) = 2 - 2x
Setting this equal to zero, we find the critical point:
2 - 2x = 0
x = 1
To determine the nature of the critical point, we need to examine the second derivative:
f''(x) = -2
Since the second derivative is negative at x = 1, this critical point is a local maximum. To find the absolute extrema, we also need to examine the endpoints of the domain, x = 0 and x = 3:
f(0) = 0
f(3) = 3
So the function has an absolute maximum at x = 3 and an absolute minimum at x = 0. Therefore, the location of all the relative and absolute extrema, from smallest to largest x, is:
(0, 0) (local minimum)
(1, 1) (local maximum)
(3, 3) (absolute maximum)
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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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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 length of side x.
Give answer to 1dp.
Answer:
Set your calculator to degree mode.
Use the Law of Cosines.
x^2 = 18^2 + 15^2 - 2(18)(15)(cos 105°)
x^2 = 688.7623
x = 26.2 cm
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:
π × 4 to the second power × 3 ( with steps !! )
Review the equation used in writing a partial fraction decomposition.
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
Which system of equations can be used to determine the values of A and B?
The answer is B. 5A=-15 -2A+B=10
have a lovely day my darlings <3
To determine the values of A and B, we can use the following system of equations: 1. 5A = -15 2. -2A + B = 10 This system of equations can be used to find the values of A and B.
To review the equation used in writing a partial fraction decomposition, we start with a fraction that has a denominator that can be factored into linear or quadratic factors. The partial fraction decomposition separates the fraction into a sum of simpler fractions, each with a single linear or quadratic factor in the denominator.
The equation you provided for partial fraction decomposition is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
This equation shows that the original fraction can be decomposed into two simpler fractions, one with a linear factor of (5x - 2) in the denominator (A/(5x - 2)), and one with a quadratic factor of (5x - 2)² in the denominator (B/(5x - 2)²).
To determine the values of A and B, we need to solve for them using a system of equations. In this case, we can use the coefficients of x in the numerator of each fraction to create the following system of equations:
5A = -15
-2A + B = 10
We get the first equation by setting the numerator of the first fraction (A/(5x - 2)) equal to -15x + 10, and the second equation by setting the numerator of the second fraction (B/(5x - 2)²) equal to -15x + 10 and subtracting the first equation from it.
Solving this system of equations gives us:
A = -3
B = 5
Therefore, the partial fraction decomposition of the original fraction is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction -3 Over 5 x minus 2 EndFraction + StartFraction 5 Over (5 x minus 2) squared EndFraction
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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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I would like to see the process steps of solving this as well please! Thank you!
You must begin to brake 234643.2 feet from the intersection.
What is stopping distance?In Mathematics and Science, stopping distance can be defined as a measure of the distance between the time when a brake is applied by a driver to stop a vehicle that is in motion and the time when the vehicle comes to a complete stop (halt).
Based on the information provided above, the speed of this car is represented by the following equation;
s = √(30fd)
Where:
f is the coefficient of friction.d is the stopping distance (in feet).By substituting the given parameters, we have:
20 = √(30(0.3)d)
400 = 9d
d = 400/9
d = 44.44
Conversion:
1 mile = 5,280 feet.
44.44 miles = 234643.2 feet.
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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.
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?
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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Lines lll, mmm, and nnn are parallel to each other and ppp is a transversal.
Also, 2\angle{x}=3\angle{y}2∠x=3∠y2, angle, x, equals, 3, angle, y
The measure of angle x is: x = (3/5)(180 - z) = (3/5)(180 - 90) = 36 degrees
And the measure of angle y is:y = (2/5)(180 - z) = (2/5)(180 - 90) = 24 degrees
Since lines lll, mmm, and nnn are parallel to each other and ppp is a transversal, we can use the angle properties of parallel lines to find the relationship between angle x and angle y.
From the given information, we have: 2x = 3y
Simplifying this equation, we get: x = (3/2)y
Now, we can use this relationship to find the measures of angles x and y in terms of a common variable. Let's use z as the common variable.
x + y + z = 180 (angles on a straight line)
Substituting x = (3/2)y, we get: (3/2)y + y + z = 180
Simplifying this equation, we get: (5/2)y + z = 180
Now, we can express y in terms of z:
(5/2)y = 180 - z
y = (2/5)(180 - z)
Similarly, we can express x in terms of z:
x = (3/2)y = (3/2)(2/5)(180 - z) = (3/5)(180 - z)
Now, we can use the relationship between angle x and angle y to find the measure of angle x in terms of z: 2x = 3y
2[(3/5)(180 - z)] = 3[(2/5)(180 - z)]
Simplifying this equation, we get: (6/5)z = 108
z = (5/6)(108) = 90
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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]
Use the figure below to determine the value of the variable and the
lengths of the requested segments. Your answers may be exact or
rounded to the nearest hundredth. The figure may not be to scale.
Using tangents theorem, we can find the value of the missing length,
n = 18.7units.
Define a tangent?"To touch" is how the word "tangent" is defined. The same idea is conveyed by the Latin word "tangere". A tangent, in general, is a line that, while never entering the circle, precisely touches it at one point on its circumference. A circle has a number of tangents. They make a straight angle with the radius.
Here in the diagram,
We can see that as per the central angle and tangent theorem,
AB/BC = ED/DC
⇒ 17/10 = n/11
Cross multiplying:
⇒ 17 × 11 = n × 10
⇒ 10n = 187
⇒ n = 187/10
⇒ n = 18.7
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A group of students collected old newspapers for a recycling project. The data shows the mass, in kilograms, of old newspapers collected by each student.
23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55
98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.
What percent of students collected between 49 kilograms and 98 kilograms of newspapers? Explain how you got to your solution
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
Total number of students is 22.
To find the percentage of students who collected between 49 and 98 kilograms of newspapers, we first need to count the number of students who collected within this range. From the given data, we can see that the following students collected between 49 and 98 kilograms of newspapers
87, 64, 90, 76, 60, 55, 57, 75, 56, 88
Percentage of students = (number of students in range / total number of students) x 100
= (10 / 22) x 100
= 45.45%
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
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7x-1 is less than or equal to 62 answer
The value of the variable is 9
How to determine the valueIt is important to note that inequalities are described as non- equal comparison of numbers or expressions.
The signs of inequalities represents;
< represents less than> represents greater thanFrom the information given, we have that;
7x - 1 is less than or equal to 62
This is represented as;
7x - 1≤ 62
collect the like terms, we have;
7x ≤ 62 + 1
Add the values
7x ≤ 63
Divide both sides by the coefficient, we get;
x ≤ 63/7
x ≤ 9
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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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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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(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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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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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
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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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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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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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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A person places $81200 in an investment account earning an annual rate of 3. 6%,
compounded continuously. Using the formula V = Pent, where Vis the value of the
account in tyears, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 13 years.
If a person places $81200 in an investment account earning an annual rate of 3. 6%, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
To solve this problem using the formula V = Pent, we need to plug in the given values.
P = $81200 (the principal initially invested)
r = 0.036 (the annual interest rate, expressed as a decimal)
t = 13 years
Using the formula V = Pent, we get:
V = $81200e^(0.036*13)
Using a calculator, we can evaluate e^(0.036*13) to be approximately 1.5498.
So V = $81200*1.5498 = $125689.60
Therefore, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
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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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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
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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