A restaurant can only have 285 customers at one time.
At 12:00 p.m., this restaurant had 216 customers.
Part A:
3
Over the course of a lunch period, of the customers
leave and 147 new customers come to the restaurant.
Does the new amount of customers exceed 285?
Show your work.
Part B:
At dinner, there are 47 tables of 4 and 16 tables of 5.
How many customers are in the restaurant? Show your
work.

By using properties for quotients we will see that:

a^v = 1

Only if v = 0.

We need to remember two properties.

First, the quotient of two equal numbers is always equal to 1. So for any real number a different than zero, we can write:

a/a = 1

The second property is for the quotient of powers with the same base, we can write:

a^n/a^m = a^{n - m}

Now, notice that if we take the quotient of two numbers with the same exponent, we will get:

(a^n)/(a^n) = a^{n - n} = a^0

And that is the quotient between two equal numbers, then that is equal to 1, so:

a^0 = 1

For any real number a different than zero.

Then the value of v such that:

a^v = 1

must be v = 0.

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A SSS (side-side-side) theorem is kind of Congruence rule where two triangles with three congruent sides. So, we can solve it by showing the congruency between two triangles.

Statement: Side-Side-Side (SSS) ,the congruence theorem states that two triangles are congruent if three of their sides are equal to the corresponding sides of the other triangle.

Proof: Given, AB = DE, BC = EF, AC = DF.

To prove: ΔABC ≅ ΔDEF.

We know that the three sides of both triangles are equal in size and length. With both triangles superimposed, DE is placed on AB, EF is placed on BC, and DF is placed on AC. That is, AB = DE, BC = EF, AC = DF. Therefore, we can say that ΔABC ≅ ΔDEF.

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On solving the provided question, we can say that -- the value of the  function will be f(x) = [tex]x^{-2}[/tex]

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

here,

we have the function

x^2 + 37xy + y^5

the answer is =  [tex]x^{-2}[/tex]

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You must discover the point at which the total cost of each process is equal in order to identify the crossover point between processes a and b. The sum of the fixed cost and the variable cost per unit, multiplied by the number of units, is the cost of process A as a whole. The sum of the fixed cost and the variable cost per unit, multiplied by the quantity of units, is the cost of process b as a whole.

 You can make the overall cost of each process equal to one another and solve for the number of units to determine the crossover point.

  When x is the number of units, the total cost of process an is equal to $1000 + (5 * x).

Process B has a total cost of $500 plus (7.50 * x), where x is the number of units.

When we equalize  these two expressions, we obtain:

$1000 + (5 * x) = $500 + (7.50 * x)

     2.5 *x=500

        x=200$

    So, 200$ is the crossover point between a and b.

   Therefore,200$ crossover point between process a and process  b.

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Answer:

98

Step-by-step explanation:

B456789X+235575336

Answer:

To find the inverse of a function, you need to switch the roles of the x and y variables. So the inverse of ƒ(x) = 4x² for x ≤ 0 is written as ƒ^(-1)(y) = ?.

To find the inverse function, we can solve for x in terms of y:

4x² = y

x² = y/4

x = √(y/4)

So the inverse of ƒ(x) = 4x² for x ≤ 0 is ƒ^(-1)(y) = √(y/4). Note that this inverse function is only defined for y ≤ 0, since the original function is only defined for x ≤ 0.

After the rotation of 270° counter-clockwise about the origin, the coordinates become A'(6, - 9).

Given is the coordinate of point as (6, 9). It is rotated by 270° counter clockwise about the origin.

After the rotation of 270° counterclockwise about the origin, the coordinates will become -

A(x, y) → A'(y, - x)

So, the coordinates will become -

A(6, 9) → A'(6, - 9)

Therefore, after the rotation of 270° counter-clockwise about the origin, the coordinates become A'(6, - 9).

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The period of the function f(x) = cos 2x is π

A function is defined as a relation between a set of inputs having one output each.

Given is a function, f(x) = cos 2x

If we express the cosine function in the following way :

y = a cos(bx+c)+d

Then:

∣a∣ = the amplitude

2π/|b| = the period

-c/b = the phase shift

d = the vertical shift

For given function we have :

∣b∣=2

So period is :

2π/2 = π

Hence, The period is π

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Answer:

2001

Step-by-step explanation:

First, let us find the circumference of the wheel ( circle ) using the below formula.

C = 2πr

Here,

r ⇒ radius ⇒ 28 cm

Let us solve it now.

C = 2 × π × 28

C = 175.93 cm

And now let us covert the travelling distance to centimeters.

( For that, multiply km by 100000 )

3.52km = 352000 cm

Now, to find the number of revolution, divide the total distance travelled by its circumference.

352000/175.93 = 2000.79

Approximately, 2001 revolutions

The number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.

Given,

Radius, r = 28cm

Circumference = 2πr = 56π cm

Circumference = Distance traveled in one revolution

The distance traveled by wheel = 3.52km = 3520m = 352000cm

Let N = number of revolution

Now we know that,

Total distance = Number of revolutions × 1 revolution distance(circumference)

or 352000 = N × 56π

or N = 352000/56π

or N = 2000.8

Therefore, the number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.

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The curvature of the curve is k = [tex]\sqrt{\frac{5}{(1 \:+\: 5t^2)^3}}[/tex].

The complete question is in the attachment. The parameterized curve

r(t) = t i + t² j + t²/2 k

The curvature of the curve

k = |v(t) × a(t)| ÷ |v(t)|³

k = |v(t) × a(t)| ÷ |v(t)|³

[tex]k \:=\: \frac{\sqrt{5}}{(\sqrt{1 \:+\: 5t^2})^3}[/tex]

[tex]k \:=\: \sqrt{\frac{5}{(1 \:+\: 5t^2)^3}}[/tex]

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Answer:

It is 63 cm

Step-by-step explanation:

Take 28/4 = 7. That is what1 equals in the proportion. So, we take 2 x 7, 3 x 7, and 4 x 7. Then you just add the sides together and it equals 63 cm.

Answer: 63

Step-by-step explanation:

In the ratio, the longest side is 4. 4x7 is 28, so to make the ratios proportional again, you multiply all the sides by 7, getting 14:21:28.

These are the side lengths of the triangle, and to find the perieter you add all of them up, getting 63.

Hope this helps :)

Part 1: A = 0, B = 2, C = 3, D = 0, E = -2

Part 2: The derivative f'(3) is 6.

Part 3: The equation of the tangent line to the curve y = f(x) at x = 3 is y = 6x – 15.

This equation of the tangent line can be found by substituting x = 3 into the simplified difference quotient expression C + Dh + Eh2 , and then taking the limit as h approaches 0.

This expression can then be rearranged to give the equation of the line, which is y = 6x – 15. The equation of the tangent line gives the slope of the line at the given point, in this case x = 3. The slope of the line is 6, which is the same as the derivative of the function at the given point.

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If you divided the number of letters in “Merry Christmas” by the number of thieves in the first “Home Alone” movie, then the answer will be 7.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 split into 3 groups of equal size results in 4 in each group. Creating equal groupings or determining how many people are in each group after a fair distribution is the basic objective of division.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A division problem has three primary components: the dividend, the divisor, and the quotient. The amount that will be shared is the dividend. The quantity of "people" among whom the number is split is referred to as the divisor. The answer is the quotient.

Number of letters in Merry Christmas is 14

Number of thieves in Home Alone is 2

The quotient is given as 14/2 = 7

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The equation of the parabola shown with its focus on this graph is D. y = [tex]-\frac{1}{12} \text x^2[/tex] + 1.

A parabola is a mirror-symmetrical, roughly U-shaped plane curve that is used in mathematics. It corresponds to a number of mathematical explanations that appear to differ on the surface but which all define the same curves.

A line and a point (the focus) are two ways to describe a parabola (the directrix). Not the directrix is the main focus. The location of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

Conic sections, which are formed when a right circular conical surface and a plane perpendicular to another plane that is tangential to the conical surface intersect, are another way to describe parabolas.

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Answer: it's not its  [tex]\frac{1}{27}[/tex]

Step-by-step explanation:

Because the negative in the exponent moves it to the denominator then just cube 3 in the denominator

[tex]\frac{1}{3^{3} }[/tex]

[tex]\frac{1}{27}[/tex]

But [tex]2^{-3} =\frac{1}{8}[/tex]

because [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

We have found the missing angle x = 60° using the angle sum property.

The triangle's angle sum property states that the sum of its angles can equal 180 degrees. Since a triangle has three sides, each of its vertices has an angle. Regardless of whether a triangle is acute, obtuse, or right-angled, its interior angles always sum to 180 degrees.

The triangle's angle sum property is one of the geometry's most frequently used properties. The main application of this property is in the calculation of the unknown angles. The angle sum property is used to calculate the measure of an unknown interior angle when the values of the other two angles are known.

Here,

Given that

Let the angles be y, z and x

y = 80°

z = 40°

x = ?

Using the angle sum property

Sum of the interior angle of a triangle = 180°

x + y + z = 180°

x + 80 + 40 = 180

x + 120 = 180

x = 180 - 120

x = 60°

Thus, we have found the missing angle x = 60° using the angle sum property

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The first special case of the chain rule for the composition f o c states that the derivative of f(c(t)) is equal to f'(c(t))c'(t).

For case (a):

(f o c) (t) = f(c(t)) = f(e cos(t)) = e cos(t) sin(t)

Therefore, (f o c)' (t) = f'(c(t))c'(t) = [e cos(t) sin(t)]' (e cos(t))' = e sin(t) cos(t) (e cos(t))' = e cos(t) (-sin(t)) = -e cos2(t)

For case (d):

(f o c) (t) = f(c(t)) = f(t, -t) = t exp(-t)

Therefore,

(f o c)' (t) = f'(c(t))c'(t) = [t exp(-t)]' (t, -t)' = exp(-t) (t, -t)' = exp(-t) (1, -1) = t exp(-t) (-1) = -t exp(-t)

The first special case of the chain rule for the composition f o c states that the derivative of f(c(t)) is equal to the product of f'(c(t)) and c'(t). This means that the derivative of the composition of two functions, f and c, is equal to the product of the derivative of the outermost function and the derivative of the innermost function. To verify this for each case, we need to calculate the derivatives of both f and c, then substitute them into the equation for the derivative of the composition. For example, in case (a), we have (f o c) (t) = f(c(t)) = e cos(t) sin(t). Therefore, (f o c)' (t) = f'(c(t))c'(t) = e sin(t) cos(t) (e cos(t))' = -e cos2(t). Similarly, for case (d), we have (f o c) (t) = f(c(t)) = t exp(-t). Therefore, (f o c)' (t) = f'(c(t))c'(t) = exp(-t) (t, -t)' = -t exp(-t).

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The complete question is

Verify the first special case of the chain rule for the composition f o c in each of the cases. (a) f(x, y) .xy, c(t) (e cos(t)) (f o c) (t) '(cos (t) sin t (f o c) (t) (e e Y 2t 2t (f o (c) (t) n e (d) f(x, y) x exp(x y c (t) (t, -t) (f o c) (t) 4t 1 exp(-t ) (f o c) (t) t exp(-t )

Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Adding the equations yields [tex]4y=4[/tex]. Therefore, [tex]y=1[/tex].

The production level that will maximize profit is 300 units

Given,

C(x) = 12000 + 400x − 3.8x^2 + 0.004x^3

P(x) = 4000-8x

First we need to find revenue function

R(x) = x.P(x) = x(4000-8x) = 4000x-8x^2

Now, we need to find marginal revenue

R'(x) = d/dx (4000x-8x^2) = 4000-16x

And now we'll find marginal cost

C'(x) = d/dx (12000+4000x-3.8x^2=0.004x^3) = 400-7.6x+0.012x^2

for maximum profit,

C'(x) = R'(x)

or, 4000-16x = 400-7.6x+0.012x^2

or, 0.012x^2+8.4x-3600 = 0

or, x^2+700x-300000=0

or, (x+1000) (x-300) = 0

so, x=-1000 or, x=300

Production level can not be negative.

So, the production level is 300 units

The production level that will maximize profit is 300 units

The production level that will maximize profit is 300 units

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=========================================================

Explanation:

Method 1

The exterior angles of any polygon always add to 360 degrees.

3x+8x+9x = 360

20x = 360

x = 360/20

x = 18

Then,

which represent the exterior angles of this triangle.

As a check: 54+144+162 = 360 which confirms we have the correct values.

The smallest exterior angle is therefore 54 degrees

---------------------

Method 2

The exterior angles 3x, 8x, and 9x have the corresponding interior angles of 180-3x, 180-8x, and 180-9x in that order.

For any triangle, the interior angles always add to 180 degrees.

angle1+angle2+angle3 = 180

(180-3x)+(180-8x)+(180-9x) = 180

540-20x = 180

-20x = 180-540

-20x = -360

x = -360/(-20)

x = 18

This then leads to 3x = 3*18 = 54 degrees as the final answer.

Therefore the numerical order of the dimensions of rectangular prism is 8, 12

The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one since a point on it may be specified by a single coordinate, such as the point at 5 on a number line.

We have a minimum set when a group of words can all be distinguished from one another by altering one phoneme (always in the same location in the word). feat, fit, fat, fate, and foot were used. Big, Pig, Rig, Fig, Dig, and Wig might be included in another minimum list based on consonant phonemes.

The equation for the volume of a rectangular prism:

V = l × w × h

Given dimensions are x, x-2, and x+8

V = (x)(x-2)(x+8) = 96

x^3 - 2x^2 + 8x = 96

x^3 - 2x^2 + 8x - 96 = 0

(x-12)(x+4)(x-8) = 0

Therefore, x = 12, -4, 8

As the dimension of prism can't be negative, we can discard -4 as one of the dimension.

Thus, the numerical order of the dimensions of rectangular prism is 8, 12

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The probability of getting a 3 on the first roll and a 4 on the second roll when a the probability of getting a 3 on the first roll and a 4 on the second roll is 1/36.

Therefore the answer is 1/36.

The probability of rolling a 3 on the first roll and a 4 on the second roll is the product of the probabilities of rolling each number separately.

Since the number cube is fair, the probability of rolling any number on a single roll is 1/6. Therefore, the probability of rolling a 3 on the first roll and a 4 on the second roll is

(1/6) × (1/6) = 1/36.

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The probability of rolling a 3 on the first roll and a 4 on the second roll is 1/36, or approximately 0.028.

This is because the probability of rolling any particular number on a 6-sided number cube is 1/6. Therefore, the probability of rolling a 3 on the first roll is 1/6, and the probability of rolling a 4 on the second roll is also 1/6. Since these events are independent (rolling a 3 on the first roll does not affect the probability of rolling a 4 on the second roll), you can multiply the probabilities of each event to find the probability of both events occurring.

Therefore, the probability of rolling a 3 on the first roll and a 4 on the second roll is (1/6) * (1/6) = 1/36. This can also be written as a decimal as 0.028.

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The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x - 18.

Therefore, the answer is b) y = −2x − 18.

The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To find the equation of a line that is perpendicular to another line, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. This means that if the slope of one line is m, the slope of a line perpendicular to it is -1/m.

The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:

2x – 4y = 17

-4y = -2x + 17

y = (1/2)x - (17/4)

The slope of the line 2x – 4y = 17 is (1/2). Therefore, the slope of a line perpendicular to it is -2.

To find the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2), we can use the slope-intercept form of a line's equation and plug in the slope (-2) and the coordinates of the point p(-8, -2):

y = -2x + b

-2 = -2×(-8) + b

b = -18

--The question is incomplete, the complete question is given below--

"Give the slope-intercept form of the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(–8, –2).

a. y = −2x + 8

b. y = −2x − 18

c. y = −2x − 12

d. y = −2x + 2"

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The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x – 18

y = mx + b is the slope intercept form of a line’s equation. Here, m = slope of the line and b = y-intercept.

The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:

2x – 4y = 17

-4y = -2x + 17

y = (1/2)x - (17/4)

The slope of the line is 1/2. Hence m = ½

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Since Larry needs 3 bags of mulch and each bag costs $3.25, the total cost of the mulch will be 3 × $3.25 = 9.75$

Larry is only ready to put mulch on 3/4 of his rose garden, so he will need 3/4 × $9.75 = 7.31$

answer: 7.31$

The value of (x + 4)² will be x² + 8x + 16

The value of (7x + 5y)² will be 49x² + 70xy + 25y²

The value of (4x + 5y)² will be 16x² + 40xy + 25y²

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

The value of (x + 4)² will be:

(x + 4)²

= (x + 4)(x + 4)

= x² + 4x + 4x + 16

= x² + 8x + 16

(7x + 5y)² will be:

= (7x + 5y)(7x + 5y)

= 49x² + 35xy + 35xy + 25y²

= 49x² + 70xy + 25y²

(4x + 5y)² will be:

= (4x + 5y)(4x + 5y)

= 16x² + 20xy + 20xy + 25y²

= 16x² + 40xy + 25y²

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Answer:
-5, -4, 0, 6.009, 6.3

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From the given data about population, we found out answers:

a) The percentage of the panels that will be scrapped is 4.55%.

b) The percentage of the panels that will need rework is 45.45%.

c) In order to reduce the scrap percentage to 1%, the manufacturer must re-center the process with a new mean value of 10.50 mm.

d) The rework percentage with the new mean value is 0.33%.

This is because the new mean value (10.60 mm) is within the specified range (10.50 +0.50 mm). Thus, there will be no rework or scraped panels due to the mean being outside of the specified limits.

To better understand this, it is important to consider the normal distribution of the data and the specified limits for the hole size. The normal distribution of the data means that the majority of the holes will be of the mean size, with very few being either significantly larger or smaller.

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The values of angles for the intervals given are obtained as 135°,  405° and -135° respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

The given trigonometric equation is sin(θ) = √2/2.

It can be written as,

sin(θ) = √2/2

⇒ sin(θ) = 1/√2

⇒ θ = 45°

(a) The value of the angle in interval 90° < θ < 270° is given as,

⇒ 180°- θ = 180° - 45° = 135°

(b)  The value of the angle in interval 270° < θ < 450° is given as,

⇒ 360°+ θ = 360°+ 45° = 405°

(c) The value of the angle in interval -270° < θ < -90° is given as,

⇒ -180° + θ = -180° + 45° = -135°

Hence, the required values of angles for the given interval are 135°,  405° and -135° respectively.

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