Name a fraction between 1 /5 and 1/6 .

Answer:  p=-2 and q=-1 [(p^2)(q^-3)]^-2. 1. See answer

Step-by-step explanation:

Answer:

y = 1/3x + 3

Step-by-step explanation:

Points on the graph: (0, 3) and (3, 4)

Slope:

m=(y2-y1)/(x2-x1)

m=(4-3)/(3-0)

m= 1/3

Point-slope intercept:

y - y1 = m(x - x1)

y - 3 = 1/3(x - 0)

y - 3 = 1/3x

y = 1/3x + 3

Answer:

Area of red square = 64

Area of circle = π((4√2)^2) = 32π

P = 64/(32π) = 2/π = about .64

= about 63.66%

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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The missing angle represented by 6 is 107 degrees

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that, when combined, create a straight line, then they are supplementary angles.

Angles on a straight line are supplementary and hence the potion that has 6 is equal to say x

x + 73 = 180

x = 180 - 73

x = 107 degrees

Supplementary angles can be found in many geometric shapes, such as triangles, quadrilaterals, and polygons.

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The expression is factorized as A = ab ( 3a + 4b )

a) 1, 3, a, a², b, ab, 3a, 3a², 3b, 3ab, 3a²b

b) 1, 2, 4, a, b, b², ab, 2b, 4b, 2ab, 4ab, 4ab²

Given data ,

Let the given expression be represented as A

Now , the value of A is

A = 3a²b + 4ab²

On factorizing the above expression , we get

A = ab ( 3a + 4b )

So , the equation is A = ab ( 3a + 4b )

For the expression 3a²b, the possible factors are:

1, 3, a, a², b, ab, 3a, 3a², 3b, 3ab, 3a²b

For the expression 4ab², the possible factors are:

1, 2, 4, a, b, b², ab, 2b, 4b, 2ab, 4ab, 4ab²

Hence , the factorized equation is A = ab ( 3a + 4b )

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Answer:

61.68cm

Step-by-step explanation:

Perimeter of the semicircle = 2πr

r is the radius = 12/2 = 6cm

Perimeter of the semi circle = 2(3.14)(6)

Perimeter of the semi circle = 37.68cm

Adding the remaining sides of the polygon

Perimeter of the figure = 37.68+ 10 + 6 + 8

Perimeter of the figure = 61.68cm

Hence the perimeter of the figure is 61.68cm

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

Answer: The sum is 127

Step-by-step explanation:

A 2-digit number N = ab can be written as (where a and b are single-digit numbers)

a*10 + b.

Now, we want that:

(a + 2)*(b + 2) = a*10 + b.

So we must find all the solutions to that equation such that a can not be zero (if a = 0, then the number is not a 2-digit number)

We have:

(a + 2)*(b + 2) = a*b + 2*a + 2*b + 4 = a*10 + b

a*b + 2*b - b + 4 = a*10 - a*2

a*b + 4 + b = a*8

a*b + 4 + b - a*8 = 0.

Now we can give one of the variables different values, and see if the equation has solutions:

>a = 1:

1*b + 4 + b - 8 = 0

2*b - 4 = 0

b = 4/2 = 2

Then the number 12 has the property.

> if a = 2:

2*b + 4 + b -16 = 0

3b -12 = 0

b = 12/3 = 4

The number 24 has the property.

>a = 3 is already known, here the solution is 35.

>a = 4.

4*b + 4 + b - 8*4 = 0

5*b + 4 - 32 = 0

5*b = 28

b = 28/5

this is not an integer, so here we do not have a solution.

>if a = 5.

5*b + 4 + b - 8*5 = 0

6b + 4 - 40 = 0

6b - 36 = 0

b = 36/6 = 6

So the number 56 also has the property.

>if a = 6

6*b + 4 + b - 8*6 = 0

7b + 4 - 48 = 0

7b - 44 = 0

b = 44/7 this is not an integer, so here we do not have any solution.

>if a = 7

7*b + 4 + b -8*7 = 0

8b -52 = 0

b = 52/8 = 6.5 this is not an integer, so we here do not have a solution.

>if a = 8

8*b + 4 + b -8*8 = 0

9*b + 4 - 64 = 0

9*b = 60

b = 60/9 this is not an integer, so we here do not have any solution:

>if a = 9

9*b + 4 + b - 8*9 = 0

10b + 4 - 72 = 0

10b -68 = 0

b = 68/10 again, this is not an integer.

So the numbers with the property are:

12, 24, 35 and 56

And the sum is:

12 + 24 + 35 + 56 =  127

Planets around other stars can be detected by carefully measuring the "brightness" or "light intensity" of stars.

When a planet orbits a star, it causes a slight change in the brightness or light intensity of the star. This is known as the transit method of planet detection. As the planet passes in front of the star from our line of sight, it blocks a small portion of the star's light, causing a temporary decrease in its brightness. By carefully measuring these changes in brightness over time, scientists can infer the presence and characteristics of planets orbiting the star. This method has been instrumental in the discovery of numerous exoplanets in recent years.

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Answer:

$497.90

Step-by-step explanation:

8.25% sales tax becomes 0.0825 as a decimal fraction.

Then the total cost would be $459.95 plus 0.0825($459.95), or, in more compact form,

Total Cost = (1.0825)($459.95) = $497.90

The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

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a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

\(V'(x) = 48x - 36x^2 - 4x^3\)

Setting this equal to zero and solving for x, we get:

\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

\(V''(x) = 48 - 72x - 12x^2\)

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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Answer:it is d

Step-by-step explanation:

The statement "a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its endpoints." is True because a line segment is defined as a part of a line that is bounded by two distinct end points and contains all the points on the line between those endpoints.

A line segment is a part of a line that has two endpoints and connects them. It is the shortest distance between two points and has a definite length, but no width or height. A line segment can be part of a straight line or a curved line.

A line segment is a section of a line that is defined by two distinct end points and includes every point on the line between them. It is the basic building block of geometry and can be used to measure distances, angles, and shapes.

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Answer:

the answer is 3

Step-by-step explanation:

3=4

Answer:

80696,tons

Step-by-step explanation:

let's assume 115280 tons is 100%

100% ‐ 30% = 70%

100% —> 115280tons

70% —> 115280tons ÷ 100 × 70

= 80695.999999997

= 80696 (round to nearest whole number)

Answer:

1.80

2.Overestimate.

Step-by-step explanation:

Answer:

Sorry I'm late

Step-by-step explanation:

Answer:

x+y ≤20

3.50 x +8 y ≤150

Step-by-step explanation:

Hi, the rest of the question is:

How do you write a system of linear inequalities to model the situation?

So, for the first inequality:

The sum of the number of soil bags (x) and plants(y) bought must be less or equal to 20.

x+y ≤20

For the second inequality:

The product of the number of soil bags (x) and the price of each bag (3.50) ; plus the number of plants bought(y) and the price of each plant (8) must be less or equal to 150.

3.50 x +8 y ≤150

In conclusion, the system is:

x+y ≤20

3.50 x +8 y ≤150

Answer:

(m-15)(m+2)

Step-by-step explanation:

when you expand it you get m²-13m-30

There are approximately 27,735 shoppers in the store at the end of the sale (t = 12).

What is a function?

A function is a mathematical concept that relates a set of inputs (called the domain) to a set of outputs (called the range). It is a rule or relationship that assigns a unique output value to each input value. In other words, for every input, there is exactly one corresponding output.

A function is typically denoted by a symbol, such as "f," followed by parentheses containing the input value. The output value is obtained by applying the rule or formula defined by the function to the input value.

To determine the number of shoppers in the store at the end of the sale (t = 12), we need to calculate the net change in the number of shoppers from the beginning of the sale to the end.

The net change in the number of shoppers is obtained by subtracting the number of shoppers leaving the store from the number of shoppers entering the store during the 12-hour sale.

Using the provided functions, we have:

\(S(t) = 0.5t^4 - 16t^3 + 144t^2\) (number of shoppers entering the store)

\(L(t) = -80 + \frac{4400}{t^2 - 14t + 55}\) (number of shoppers leaving the store)

To find the number of shoppers at the end of the sale (t = 12), we can calculate:

\(Number of shoppers =\int\limits^{12}_0(S(12) -L(t) )dt\)

Substituting the values into the equation:

\(Number of shoppers =\int\limits^{12}_0 (S(12) - (-80 + \frac{4400}{t^2 - 14t + 55}))dt\)

Evaluating the integral and substituting t = 12:

\(Number of shoppers =[(0.1t^5-4t^4+t^3 )- (-80t + {ln|t-11|-ln|t-5|})]\) evaluate from 0 to 12.

Calculating further:

\(Number of shoppers = 24883.2 - [-80(12) +\frac{2200}{3}[ {ln|12-11|-ln|12-5|}]] + [-80(0) +\frac{2200}{3} [ {ln|0-11|-ln|0-5|}]]\)

Number of shoppers = 24883.2 - [-2273.95 ] + 578.2

Finally, we need to substitute t = 12 into the S(t) function to obtain the number of shoppers:

Number of shoppers = 24883.2+2852.15

Calculating:

Number of shoppers ≈ 27,735

Therefore, according to the model, there are approximately  27,735 shoppers in the store at the end of the sale (t = 12).

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Answer:

the answer is 380

Step-by-step explanation:

The number of pennies they lose altogether is 288 pennies.

How to find the number of pennies they lost together?

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they lose can be calculated as follows;

Katya losses = 1 / 2 × 192 = 96

Mimi losses = 2 / 3 × 288  = 192

Therefore, they lost 96 + 192 = 288 pennies altogether.

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Answer

C.9

Step-by-step explanation:

This is because 13 divided by 3 = 4.3 and 39 divided by 4.3 equals 9

The correct answer is 9 for the k12 exam called

4.14 Application of Linear Functions - Part 1

Answer:

.7

Step-by-step explanation:

Answer:

y=6x

Step-by-step explanation:

1. find the slope m. Pick two points on the line, such as (0,0) and (1,6). Plug those points into the slope formula.

m=change in y/change in x

m=6-0/1-0   Plug in (0,0)(1,6)

m=6/1    simplify

m=6  

The slope is 6

2. Find the y-intercept. Since the line crosses the y-axis at 0, the y-intercept is 0.

3. Use the slope m=6 and the y-intercept b=0 to write the equation in slope-intercept form.

y=mx+b

y=6x+0   Plug in m=6 and b=0

y=6x

Answer :

4x-ay=15

Step-by-step explanation:

Answer:

1. 3 themes : space, safari, comics

2. 2 locations : skating rink, park

3. 3 days of the week : Friday, Saturday, Sunday

4. A safari theme at the skating rink on Saturday.

A comics theme at the park on Friday.

5. 6 different possible outcome are in the sample space.

I'm not sure if it's right but I hope it helps.

Answer:

the first car has 15 passengers and the second has 10

Step-by-step explanation:

Therefore, the domain of f(g(x)) will be the set of all real numbers, as long as the values of g(x) = x + 3 do not cause any issues with the domain of f(x).

To find the domain of the composite function f(g(x)), we need to consider two things:

The domain of g(x)

The values of g(x) within that domain that are also within the domain of f(x)

Let's start with the first step. The function g(x) = x + 3 is a linear function defined for all real numbers. Therefore, the domain of g(x) is the set of all real numbers.

Next, we need to determine the values of g(x) within its domain that are also within the domain of f(x). Since we don't have information about the specific domain of f(x), we'll assume it is the set of all real numbers unless stated otherwise.

For any real number x, g(x) = x + 3. To find the values of x that make g(x) within the domain of f(x), we need to ensure that g(x) does not produce any values that are outside the domain of f(x).

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The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

The equation of the circle is given as x² + y² - 32x+24y +396 = 0.

Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.

The center of circle is C = (-g, -f)

The radius of circle is r = √g² + f² - c

Therefore, from the given equation,

2g = -32

g = -16

2f = 24

f = 12

C( -16, 12)

And the radius is

r = √(-16)² + (12)² - 396

= √256 + 144 -396

=√4

= 2

Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

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