Jean-pierre consumes only apples and bananas. he prefers more apples to less, but he gets tired of bananas. if he consumes fewer than 28 bananas per week, he thinks that one banana is a perfect substitute for one apple. but you would have to pay him one apple for each banana beyond 28 that he consumes. the indifference curve that passes through the consumption bundle with 31 apples and 40 bananas also pass through the bundle with x apples and 23 bananas, where x equals:

Jane will walk 733.34 yards around the edge of the rectangular park after converting the width from feet to yards and calculating the perimeter.

Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. To determine how far Jane will walk, we need to calculate the perimeter of the rectangle. First, let's convert all measurements to the same unit. Since the length is given in yards and the width in feet, we can convert the width to yards (1 yard = 3 feet).

Width in yards: 200 feet \/ 3 feet per yard = 66.67 yards.

Now that both measurements are in yards, we can calculate the perimeter:

Perimeter = 2 ×(length + width) = 2 × (300 yards + 66.67 yards) = 2 ×366.67 yards = 733.34 yards.

Therefore, Jane will walk 733.34 yards around the edge of the park.

Here is your answer:

Solving the equation:

Hope this helps!

Step 1

Find the equation of the line that passes through points [tex](1, 2)[/tex] and [tex](2, 5)[/tex]

Find the slope of the line

The formula to calculate the slope is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{5-2}{2-1}[/tex]

[tex]m=\frac{3}{1}[/tex]

[tex]m=3[/tex]

Find the equation of the line

The equation of the line into slope-point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=3[/tex]

[tex](1, 2)[/tex]

substitutes

[tex]y-2=3(x-1)[/tex]

[tex]y=3x-3+2[/tex]

[tex]y=3x-1[/tex]

Step 2

Find the equation of the inequality

we know that

The solution is the shaded area below the solid line

therefore

the inequality is

[tex]y\leq 3x-1[/tex]

the answer is

[tex]y\leq 3x-1[/tex]

see the attached figure to better understand the problem

The expression for the total area made up by the square and the circle as a function of x is f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) square inches.

To solve this problem, you need to know the formulas for the areas of a square (Area = side^2) and a circle (Area = pi * radius^2). If a piece of the wire with length x inches is to be bent into the shape of a square, then each side of the square will be x/4 inches long (since a square has 4 equal sides). Therefore, the area of the square = (x/4)^2 = x^2/16 sq.inches.

The remaining piece of the wire is 5-x inches long and is to be bent into the shape of a circle. The circumference of the circle is 5-x inches (since it uses the remaining wire), therefore the radius of the circle is (5-x)/(2*Pi) inches. Therefore, the area of the circle = Pi*((5-x)/(2*Pi))^2 = (25 - 10x + x^2)/(4*Pi) sq.inches.

The total area made up by the square and the circle is the sum of their areas, therefore the function representing the total area f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) sq.inches.

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p=2w+2(6w-4) can be simplified to:

p=2w+12w-8

p=14w-8

if w=4

p=14(4)-8

p=56-8 = 48 yards

check:

 w = 4

length = 6w-4= 6(4)-4 = 24-4=20

perimeter = 4*2 + 20*2 = 8+40 = 48

 it checks out, perimeter = 48 yards

An acre, a unit of area commonly used in the Imperial and U.S. customary systems, is approximately 4047 square meters. This is calculable by using the known conversions between acres, square miles, and square meters.

To determine the number of square meters in an acre, it's helpful to understand the relationship between these units. A square mile is equivalent to 640 acres. Therefore, the area of one acre is 1/640 of a square mile. However, these are both Imperial measurements, and we want to convert to a metric measurement - square meters.

To make this conversion, we need to identify the conversion factor between square miles and square meters. There are 2,589,988.11 square meters in a square mile.

Our starting point is that 1 acre = 1/640 square mile. Next, we substitute the number of square meters in a square mile:

1 acre = 1/640 x 2,589,988.11 square meters = 4046.86 square meters.

Therefore, there are approximately 4047 square meters in an acre.

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The area of the square with radius 17√2 is 1156 square inches.

The area is the amount of space within the perimeter of a 2D shape

The formula for the area of square is

[tex]A = \frac{1}{2} d^{2}[/tex]

Where, d is the length of the diagonal of the square.

According to the given question.

The radius of the square is [tex]17\sqrt{2}[/tex] in.

⇒ Diameter or the length of the square  = 2 × 17 √2 = 34√2

Therefore,

The area of the square

= [tex]\frac{1}{2}( 34(\sqrt{2)} )^{2}[/tex]

= [tex]\frac{2312}{2}[/tex]

=[tex]1156\ in^{2}[/tex]

Hence, the area of the square with radius 17√2 is 1156 square inches.

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The standard form of 8 hundred + 2 hundred will be 1000.

A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.

Given that the number is 8 hundred + 2 hundred the standard form of the number will be:-

Standard form = 8 hundreds + 2 hundreds

Standard form = 800 + 200

Standard form = 1000

Therefore, the standard form of 8 hundred + 2 hundred will be 1000.

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The parabola and the circle have the same axis of symmetry, and can intersect at one point only.

The statement that must be true is; The maximum number of solution is one

Reason:

The given parameters are;

Location of the center of the circle = The origin (0, 0)

Location of the vertex of the parabola opening upwards = (0, 9)

Point where the circle intersects the parabola = The vertex

Required:

The statement that must be true

Solution;

The equation of the circle is x² + y² = r²

The vertex (0, 9) is a point on the circle, therefore;

0² + 9² = r²

The radius, r = 9

The highest point on the circle is the point with the maximum vertical

distance from the center, which is the point (0, 9), which is also the lowest

point on the parabola.

Therefore, the parabola and the circle can intersect at only the point (0, 9),

which gives;

The maximum number of solution is one.

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13 square units

Consider attachment for details.

We make a KLMN rectangle that touches all the vertices of the ABCD parallelogram. Consequently, the ABCD parallelogram is right inside the KLMN rectangle.

Let us take the following strategic steps:

The Process:

As a result, we get the area of the parallelogram ABCD is 13 square units.

Keywords: what is the area of parallelogram ABCD, in square units, graph, cartesian coordinates, triangle, rectangular, congruent, touches all the vertices

From the computation, a half of two dozen shirts will be greater.

A dozen = 12

It should be noted that a half dozen pair of shirts will be:

= 1/2 × 12

= 6 shirts

A half of two dozen shirts will be:

= 1/2 × (2 × 12)

= 12 shirts

Therefore, a half of two dozen shirts will be greater.

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5x=17

x=17/5 = 3.4

15x-11 =

15(3.4)-11 = 51-11 = 40

Final Answer:

The standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15) is  (x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1

Explanation:

To write the standard form of the equation of a hyperbola with the given vertices and a focus, we'll follow these steps:

1. Determine the center of the hyperbola.
2. Calculate the distance between the vertices and the center to find the length of the transverse axis (2a).
3. Calculate the distance between a focus and the center to find the focal distance (c).
4. Use the relationship c^2 = a^2 + b^2 to determine the length of the conjugate axis (2b).
5. Write the standard form equation based on the orientation of the hyperbola.

Step 1: Determine the center of the hyperbola.
The center of the hyperbola is the midpoint of the line segment joining the two vertices. Since the vertices are at (-10, -15) and (70, -15), the center (h, k) can be found as follows:

h = (-10 + 70) / 2 = 60 / 2 = 30
k = (-15 + (-15)) / 2 = -30 / 2 = -15

So, the center of the hyperbola is at (30, -15).

Step 2: Calculate the length of the transverse axis (2a).
The distance between the vertices is the length of the transverse axis. The vertices are 80 units apart because they are at (-10, -15) and (70, -15). This means:

2a = 80
a = 40

Therefore, the length of the semi-transverse axis a is 40 units.

Step 3: Calculate the focal distance (c).
The focal distance is the distance between the center and one of the foci. We were given one focus at (-11, -15). Since the center is at (30, -15), the focal distance c is:

c = |30 - (-11)| = |30 + 11| = 41

Step 4: Use the relationship c^2 = a^2 + b^2 to determine b.
We know that a = 40 and c = 41. Plugging these values into the relationship gives us:

41^2 = 40^2 + b^2
1681 = 1600 + b^2
b^2 = 1681 - 1600
b^2 = 81
b = 9

Therefore, the length of the semi-conjugate axis b is 9 units.

Step 5: Write the standard form equation.
Since the hyperbola is horizontal (the vertices have the same y-coordinate), the standard form of its equation is:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

Plugging in the values for h, k, a, and b, we get:

(x - 30)^2 / 40^2 - (y + 15)^2 / 9^2 = 1

Simplify further by squaring the values of a and b:

(x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1

This is the standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).

The question is about calculating the new price of an item after a discount. The original price of the item was $51.00, and it was reduced by 15%, making the new price $43.35.

The subject of this question is Mathematics and it is looking for a solution to a percentage price reduction problem. The item had an original price of $51.00 and its price has been reduced by 15%. To find the new price after the discount, we have to calculate the amount of the reduction and subtract it from the original price.

First, let's calculate the amount of the discount: 15/100 * 51 = $7.65.}

Now, we subtract this amount from the original price: 51 - 7.65 = $43.35.

Therefore, the new price of the item after a 15% discount is $43.35.

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The series is convergent, but the number of terms needed to find the sum to a specific accuracy cannot be determined.

To determine the convergence of the series sum_(n=1)^(infinity) (-1)^(n+1)/( n^7), we can use the Alternating Series Test. The Alternating Series Test states that if the terms of a series alternate in sign and decrease in absolute value, then the series is convergent. In this case, the terms of the series alternate in sign and decrease as n increases, so the series is convergent.

To find the number of terms needed to achieve a sum with an error less than 0.00005, we need to use the Remainder Estimation Theorem. However, this theorem requires that the terms of the series decrease in absolute value, which is not the case in this series. Therefore, we cannot determine the number of terms needed to reach the desired accuracy.

Overall, the series is convergent, but we cannot determine the number of terms needed to reach a specific accuracy.

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The valid method is the owner asked every third customer to rate all the pizza toppings in order of preference. The correct option is A.

information that is utilized as a foundation for improvement, such as data on how people react to a product or how well someone performs a task.

I suggest method 1 because it is unbiased and systematic.  The second method requires a lot of the initiative of customers and is likely to have extreme cases only (liked very much or disliked very much).  

The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas. Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.

Therefore, the valid method is for the owner to ask every third customer to rate all the pizza toppings in order of preference. The correct option is A.

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Final answer:

By forming a system of equations and applying the elimination method, we conclude that the ice cream shop sold 51 deluxe cones and 44 regular cones on Saturday.

Explanation:

How to Solve for the Number of Deluxe and Regular Cones Sold

To solve for the number of deluxe cones and regular cones sold at the ice cream shop, we need to set up a system of equations. We are given that a total of 95 cones were sold and the total money collected was $628. Deluxe cones are sold for $8 and regular cones for $5. Let's define our variables:

Now, we can establish our equations:

To solve the system, we can use the substitution or elimination method. Let's use elimination for this example.

Multiply the first equation by 5:

Now subtract this from the second equation:

With 51 deluxe cones sold, we can substitute that into the first equation to find y:

So, 51 deluxe cones and 44 regular cones were sold on Saturday.

Answer:

Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.

Step-by-step explanation:

Number of green marbles = 2 and Number of Yellow marbles = 1

Then, total number of marbles = 2+1 = 3

A person selects two marbles one after another after replacing them.

So, the probabilities of selecting different combinations of colors are,

[tex]1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}[/tex]

[tex]2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}[/tex]

[tex]3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}[/tex]

[tex]4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}[/tex]

Now, we have that,

If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.

If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.

Then, the expected value of points for Derek is,

[tex]E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}[/tex]

And the expected value of points for Mia is,

[tex]E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}[/tex].

Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.

Answer: P(GG)= 4/9

P(GY)= 2/9

P(YG)= 2/9

P(YY)= 1/9

Derek, E(X) = -1/9

Mia, E(X) = 1/9

Step-by-step explanation: just did it on edge