find the extremes of 4x−4y subject to condition x2 + 2y2 = 1

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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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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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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The limit of (sin(9x))/x as x approaches 0 is equal to 9.

To evaluate this limit analytically, we can use L'Hopital's Rule.

Taking the derivative of the numerator and denominator with respect to x, we get:lim (sin(9x))/x = lim (9cos(9x))/1as x approaches 0.

Substituting x = 0, we get:lim (sin(9x))/x = 9cos(0)/1 = 9Therefore, the limit of (sin(9x))/x as x approaches 0 is equal to 9.

We know already how to apply or make the procedures mathematically talking so this short program will eventually help you how to find logic.

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The height of the triangular base prism is 10 mm.

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

Therefore,

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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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.

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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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 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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The equation for the cost of a taxi ride as c = 0.75(d - 0.5) + 3.

Distance traveled refers to the total distance covered by an object or person over a certain period of time or within a given context. It can be measured in units such as meters, kilometers, miles, or any other unit of length.

Equation:

Let d be the distance travelled in kilometres, and let c be the cost in dollars. Then we can write the equation for the cost of a taxi ride as:

c = 0.75(d - 0.5) + 3

This equation takes into account the initial $3.00 fee, as well as the additional $0.75 for every 0.5km

Table:

Distance (km) Cost ($)

0.5 3.38

1 3.75

1.5 4.13

2 4.50

2.5 4.88

3 5.25

3.5 5.63

4 6.00

4.5 6.38

5 6.75

5.5 7.13

6 7.50

6.5 7.88

7 8.25

7.5 8.63

8 9.00

8.5 9.38

9 9.75

9.5 10.13

10 10.50

Graph:

The x-axis represents the distance in kilometers, and the y-axis represents the cost in dollars. We start the graph at (0, 3), and then plot a point at (0.5, 3.75), (1, 4.5), (1.5, 5.25), and so on, until we get to (10, 18). We then draw a line connecting all of these points to create a line graph.

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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]

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:

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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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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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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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.

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.

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?

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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Answer:

       To change a mixed number to an improper fraction quickly we can multiply the whole number by the denominator, add the numerator and then write that over the original denominator.

Answer: x-0.5y=1.5

Step-by-step explanation:

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 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.

The transformations are a horizontal compression and a vertical shift.

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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Answer:

the answer to your problem is 3

To find the probability of a contestant liking cats and dogs but not rabbits, we can use the formula for calculating the probability of independent events. That is, P(A and B and not C) = P(A) * P(B) * P(not C).

So in this case, P(cats and dogs and not rabbits) = 0.1 * 0.9 * 0.4 = 0.036. Therefore, the probability of a contestant liking cats and dogs but not rabbits is 0.036 or 3.6%.

As for the most likely outcome of this contestant's preferences, we can see that 90% of the contestants like cats, so it's very likely that this contestant likes cats. However, only 10% of the contestants like dogs, so it's less likely that this contestant likes dogs.

And 60% of the contestants like rabbits, so it's even more likely that this contestant does not like rabbits. Therefore, the most likely outcome is that this contestant likes cats but does not like dogs or rabbits.

In conclusion, given the probabilities provided, we can calculate the probability of a contestant liking cats and dogs but not rabbits, and we can also determine the most likely outcome of this contestant's preferences. The independence of the events allows us to use simple probability calculations to make these determinations.

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The dimensions of the poster with an area of 392 square inches is equal to 14 inches and 28 inches.

Area of rectangular poster to print = 392 square inches

Let us assume that dimensions of the posters are,

Width of the poster is x inches and the length of the poster is y inches.

Area of the rectangular poster is,

xy = 392

Add 2 inches to the top and bottom margins for a total of 4 inches

And 1 inch to the left and right margins for a total of 2 inches.

Total area of the poster including the margins using the following equation,

Total area = (x + 2) × (y + 4)

Minimize the total area of the poster while still satisfying the area constraint.

Use the first equation to solve for one variable

And substitute it into the second equation,

y = 392/x

Total area = (x + 2) × (392/x + 4)

⇒ Total area = 4x + 392 +784/x + 8

⇒Total area = 4x + 400 +784/x

Minimize the total area, take the derivative of this expression with respect to x and set it equal to 0,

d/dx (4x + 400 +784/x ) = 0

⇒  4 + 0 - 784/x² = 0

⇒ x² = 784 /4

⇒ x = 14

Substituting this value of x back into the equation for y, we get,

y = 392/14

  = 28

Therefore, the dimensions of the poster should be 14 inches by 28 inches.

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Answer:

I believe the answer is D.

Step-by-step explanation:

Her car tires need to be ATLEAST 28. So, the number will be 28 or above.

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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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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The value of the scale factor for the similar figures is 1/4

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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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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