A newspaper writers compensation package includes the total cost of a $150 per month health insurance plan the total cost of a $55 per month life insurance plan and a salary of 45,000 per year what would the yearly value of the compensation package be

The bakery takes up 1/10 of the total shopping center space. Since the shopping center is 4,500 square feet, the bakery is 450 square feet.

To determine the size of the bakery in square feet, we need to calculate 1/10th of the total shopping center's area. The shopping center is 4,500 square feet in total. So, the calculation would be:

Here's the step-by-step calculation:

Therefore, the bakery takes up 450 square feet of space within the shopping center.

The minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].

[tex]f(x,y)=2x^2+3y^2-4x-2, g(x,y)=x^2+y^2-16.[/tex]

[tex]f_x (x,y)=4x+0-4-0=4(x-1)[/tex]

[tex]f_y (x,y)=0+6y-0-0=6y[/tex]

[tex]4(x-1)=0, x=1[/tex]

[tex]6y=0, y=0.[/tex]

So, critical points of [tex]f(x,y)[/tex] is [tex](1,0)[/tex].

Put this in [tex]g(x,y)=x^2+y^2-16[/tex].

[tex]g(1,0)=1^2+0^2-16=-15<0[/tex].

So, critical point is in the interior point of the given region.

[tex]g_x (x,y)=2x+0-0=2x[/tex]

[tex]g_y (x,y)=0+2y-0=2y[/tex]

Let there is a parameter [tex]\lambda[/tex] such that [tex]f_x = \lambda g_x[/tex] and [tex]f_y = \lambda g_y[/tex].

[tex]4(x-1)=\lambda (2x)[/tex] and [tex]6y=\lambda (2y)[/tex]

So, [tex]2(x-1)=x\lambda[/tex] and [tex]\lambda=3[/tex]

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

So, [tex]-2=x[/tex]

Put [tex]x=-2[/tex] in [tex]x^2+y^2=16[/tex], to determine the value of [tex]y[/tex].

[tex](-2)^2+y^2=16[/tex]

[tex]y^2=12[/tex]

[tex]y=\pm 2\sqrt{3}[/tex]

So, the obtained possible extrema are [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].

Now, find [tex]f(x,y)[/tex] at [tex](1,0), (-2, -2\sqrt{3}),[/tex] and [tex](-2, 2\sqrt{3})[/tex].

[tex]f(1,0)=2(1)^2+3(0)^2-4(1)-2[/tex]

[tex]=2-4-2[/tex]

[tex]=-4[/tex]

[tex]f(-2,-2\sqrt{3})=2(-2)^2+3(-2\sqrt{3})^2-4(-2)-2[/tex]

[tex]=8+36+8-2[/tex]

[tex]=50[/tex]

[tex]f(-2,2\sqrt{3})=2(-2)^2+3(2\sqrt{3})^2-4(-2)-2[/tex]

[tex]=8+36+8-2[/tex]

[tex]=50[/tex]

So, the minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].

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The length of DF is equal to 25 units. Then the correct option is D.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The two triangles ABC and DEF are congruent to each other and all the sides of one triangle will be the same as all the sides of the other triangle. The value of DF is equal to AC. AC is 25 so DF is equal to 25.

Hence, option D is correct.

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China's population is 2.4 x 10^4 times larger than Marshall Islands's population.

The number is written in the form  [tex]a \times 10^b[/tex] where we have   [tex]1 \leq a < 10[/tex]. The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. Scientific notations have some of the profits as; Better readability due to compact representation. Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

We have given that

China's population = 1.446 × [tex]10^9[/tex]. Marshall Islands's population is 6.025× [tex]10^4[/tex]).

Then ;

(1.446 × [tex]10^9[/tex]) ÷ (6.025 × [tex]10^4[/tex])

= 0.24 x 10 power of 5

= 2.4 x [tex]10^4[/tex]

Therefore, China's population is 2.4 x 10^4 times larger than Marshall Islands's population.

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The value of x and y are 0.5 and 4 respectively.

2x+3y=13 ..... i

4x-y=-2 ...... ii

Multiply equation i by 4

Multiply equation ii by 2

8x + 12y = 52 ..... iii

8x - 2y = -4 ...... iv

Subtract iv from iii

14y = 56

Divide both side by 14

14y/14 = 56/14

y = 4

Since 4x-y=-2

4x - 4 = -2

4x = -2 + 4.

4x = 2

x = 2/4 = 0.5

Therefore, x = 0.5 and y = 4

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Answer:

The water will be 4 times more as compared to the original.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The average value of f(x) = 9 sin²(x) cos³(x) over the interval [-π, π] is 0.

Integrate and Divide: To find the average value of a function f(x) over an interval [a, b], we calculate the definite integral of f(x) over the interval and divide by the interval's width:

Average value = (1/(b-a)) * ∫a^b f(x) dx

In this case, a = -π and b = π, so b - a = 2π.

Integrate f(x): Unfortunately, integrating f(x) = 9 sin²(x) cos³(x) directly is quite complex. However, we can use the trigonometric identity sin²x = (1 - cos²x) to rewrite the function:

f(x) = 9 sin²(x) cos³(x) = 9 (1 - cos²x) cos³(x)

Integrating this form of f(x) is more manageable, although it still involves integration by parts due to the product of three terms.

Zero Integral: After integrating and simplifying, the definite integral of f(x) over [-π, π] evaluates to 0.

Average Value: Dividing the integral by the interval's width (2π) confirms the average value of f(x) on [-π, π] is 0:

Average value = (1/2π) * 0 = 0

Therefore, the average value of f(x) = 9 sin²(x) cos³(x) on the interval [-π, π] is 0, despite the function's non-zero values within the interval.

Answer: The expression for number of faces of a pyramid =1+n

Step-by-step explanation:

A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .

Its base describe the number of other faces of it.

For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....

So the total number of faces in a pyramid = base + lateral faces

If a pyramid has n sides therefore it give rise to n lateral faces such that

The total number of faces in a pyramid= 1+n .

The total number of faces of the pyramid is [tex]n+1[/tex].

A pyramid is a three-dimensional structure whose lateral sides converge to a single step at the summit, roughly forming a pyramid in the geometric sense. A pyramid's base can be trilateral, quadrilateral, or any other polygon shape.

For a pyramid having triangular base then, the total number of faces will be [tex]3+1=4[/tex].

In a similar way, if a pyramid has four sides at the base then, the total number of faces will be [tex]4+1=5[/tex].

Hence, in the given question the pyramid has [tex]n[/tex] sides at the base so, the total number of faces of the pyramid is [tex](n+1)[/tex].

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Answer:

f(n)= -6.5n +14.5

f(1)= 8, f(n+1) = f(n) - 6.5

Step-by-step explanation:

the arithmetic sequence 8, 1.5, –5, –11.5 . . .

First term is 8

Now we find difference between the terms

1.5 - 8= -6.5

-5-1.5= -6.5

difference is -6.5

The formula is f(n)= a1 + (n-1)d

where a1 is the first term and d is the difference

f(n)= 8 + (n-1)(-6.5)

f(n)= 8 -6.5n+6.5

f(n)= -6.5n +14.5

To get recursive formula we use

f(n+1) = f(n)+ difference

f(1)= 8, f(n+1) = f(n) - 6.5

The functions that represent the arithmetic sequence is given by:

f(n) = –6.5n + 14.5

f(n+1) f(n) – 6.5, f(1) = 8

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In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d, and the nth term is given by:

[tex]f(n) = a_1 + (n-1)d[/tex]

The sequence can also be represented by a recursive sequence, given by:

[tex]f(1) = a_1[/tex]

[tex]f(n+1) = f(n) - d[/tex]

In this sequence:

Thus, the possible representations are:

[tex]f(n) = a_1 + (n-1)d[/tex]

[tex]f(n) = 8 - 6.5(n-1)[/tex]

[tex]f(n) = 8 - 6.5n + 6.5[/tex]

[tex]f(n) = -6.5n + 14.5[/tex]

And

[tex]f(1) = a_1[/tex]

[tex]f(n+1) = f(n) - d[/tex]

[tex]f(1) = 8[/tex]

[tex]f(n+1) = f(n) - 6.5[/tex]

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