A business serves 18 customers with 67 staff to maintain a strong ratio of staff to guests. How many staff members would be needed if 298 customers are expected?

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1. a. No, g(x) is not a function because f(x) is not invertible. This is because it's not a monotonic function, which we gather from the table. On the interval [-2, 3], f(x) decreases from 7 to -2, but on the following interval [3, 4], f(x) increases to 3 and becomes positive once more. At best, f(x) is locally invertible.

1. b. This is impossible to determine... We can't know g(4) without knowing for which x we have f(x) = 4, but that's not included in the table.

1. c. The slope of the tangent line to f(x) at x = -2 is f'(-2) = -4.5. Then the equation of the tangent to f(x) at x = -2 - which means it passes through the point (-2, f(-2)) = (-2, 7) - is

y - 7 = -4.5 (x - (-2))   ⇒   y = -4.5x + 16

2. Given f(x) = arctan(3x) - ln(1 + 9x²), compute the derivative:

f'(x) = 3/(1 + (3x)²) - 18x/(1 + 9x²)

f'(x) = (3 - 18x)/(1 + 9x²)

Find the critical points of f(x), where f'(x) = 0 or doesn't exist. Only the first case can happen since the denominator is never zero. So

3 - 18x = 0   ⇒   x = 1/6

is the only critical point.

Also compute the second derivative, then check its sign at the critical point:

f''(x) = (-18 - 54x + 162x²) / (1 + 9x²)²

f''(1/6) = -72/5 < 0

The negative sign indicates that x = 1/6 is the site of a local maximum of

f(1/6) = arctan(1/2) - ln(5/4) ≈ 0.241

Also check the values of f(x) at the endpoints of the interval [0, 1]:

f(0) = 0

f(1) = arctan(3) - ln(10) ≈ -1.054

So, the maximum value of f(x) on [0, 1] is f(1/6) ≈ 0.241.

Ajay wraps a gift box in the shape of a triangular pyramid. The amount

of wrapping paper he uses is 173.2 square inches.

The formula for calculating the total surface area is expressed as:

Area = 4(area of triangle)

The area of the triangle

A = 0.5(8.66)(10)

A = 43.3 square inches

The total surface area will be

TSA = 4(43.3)

TSA = 173.2 square inches

Hence the amount of wrapping paper Ajay uses is 173.2 square inches

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Answer:

hr

Step-by-step explanation:

The area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The length of the rectangle = [tex]64\dfrac{5}{7}[/tex]  m = 453/7 m

The breadth of the rectangle = [tex]23\dfrac{3}{8}[/tex] m = 187/8 m

The area of the rectangle hall:

= (453/7)(187/8)  = 1512.69 ≈ 1512.7square m

Thus, the area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

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Answer:

See below

Step-by-step explanation:

sin ( 60 + 45) = sin60 cos 45  + cos45 sin60

                      = sqrt3 / 2 * sqrt2/2   + sqrt2/2 * 1/ 2

                        sqrt6/4    + sqrt 2/ 4

                          (sqrt6 + sqrt 2) / 4

Answer:

60

Step-by-step explanation:

10 x sqrt64 - 5 x 4

10 x 8 - 5 x 4

80 - 20

60

Answer:

180

Step-by-step explanation:

bcoz it's a straight angle

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b² + c² - a²)/2bc

cos B= (a² + c²- b²)/2ac

cos C = (a²+ b²- c²)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s² + s² - s²)/(2s×s)

cos A = (s² )/(2s²)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s² + s² - s²)/(2s×s)

cos B = (s²)/(2s²)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s² + s² - s²)/(2s×s)

cos C = (s² )/(2s²)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

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Answer:

The angles are vertical, and the value of x is 128 degrees

Step-by-step explanation:

You can tell vertical angles apart from adjacent by looking at their position. Adjacent angles are side by side, right next to each other. Vertical angles are directly across from each other, with their points touching.

Since the angle measures of vertical angles are equal, the value of x is 128

i hope this helps

Using the given information, Aina's net income is for the month is 35,834 PHP

From the question, we are to determine the net Aina's net income

Aina's net income is the value of her total income minus all other expenses

From the given information,

Aina's monthly salary is 35,000 PHP per month and also receives 3,500 PHP for a monthly allowance

∴ Aina's total income = 35,000 PHP + 3,500 PHP

Aina's total income = 38,500 PHP

Sum of her other expenses = 1,466 PHP + 300 PHP + 800 PHP + 100 PHP

Sum of her other expenses = 2,666 PHP

∴ Aina's net income = 38,500 PHP - 2,666 PHP

Aina's net income = 35,834 PHP

Hence, Aina's net income is for the month is 35,834 PHP.

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Answer:

The y-intercept is 4

Step-by-step explanation:

You find the y-intercept by finding where x is zero. In the table, when x=0 the y=4. The y-intercept is 4. The graph of the function crosses the x-axis at the point (0,4).

Answer:

4

Step-by-step explanation:

the y-intercept is the y-coordinate where the line intersects the facis.So if we want to figure out the intercept,we're going to set x=0 and sdue for Y.

Answer:

The equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x+y=-5 is 2x+y=4

C+

if you get a C+ in term three and four then I don't think you will pass if you get a C+ in term three but get your grade up to B+ A- or A+ i term four you will and if you get in the B range for term 3 at least and keep it up in term four you will pass you just have to study and pay attention in class i believe in you. you can do it

Answer:

[tex]f(x) = cos(x - \frac{\pi }{4} ) -1[/tex]

Step-by-step explanation:

In this graph, we have the coordinate point ([tex]\frac{\pi }{4} , 0[/tex]). Without translations, cos(0) = 0, which means that the graph is shifted to the right by [tex]\frac{\pi }{4}[/tex]. We also know that the graph is shifted down by 1 because we have the point

([tex]\frac{5\pi }{4} , -2[/tex]), but accounting for the right shift, this point should really by ([tex]\pi , -2[/tex]). cos([tex]\pi[/tex]) = -1, but on the graph it is -2, meaning that it is shifted down by 1.

Therefore, accounting for the right shift by [tex]\frac{\pi }{4}[/tex] and the shift down by 1, our equation is [tex]f(x) = cos(x - \frac{pi}{4} ) - 1[/tex].

Answer:

D: humor.

Step-by-step explanation:

it's just common sense. I am not a gen z so I should know.

Step-by-step explanation:

[tex] = \frac{2}{9} \times \frac{3}{5} \\ [/tex]

[tex] = \frac{6}{45} \\ [/tex]

Change into lowest term...

[tex] = \frac{2}{15} \\ [/tex]

The  Indication of the position of port Q on the drawing is shown by using the example of the image attached.

To Indicate the position of port Q on the drawing (use the x tool).

12 * 5  = 60km

Note that S=  VT

Because 1cm represent 3km

1/3 =x/60

3x = 60

x= 60/3

x= 20

So therefore, 60km needs 20cm.

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Triangle ABC is congruent to triangle DEF based on the SAS congruence theorem.

The SAS theorem is a triangle congruence theorem that states that two triangles are congruent if they have two pairs of congruent sides that are corresponding to each other, and a pair of congruent included angles.

Triangles ABC and DEF have:

Therefore, they are congruent by SAS.

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Answer:

y = (x + 1)(x - 2)(x -3)

Step-by-step explanation:

Looking at the graph we see our zeros which is on the x-axis is -1 , 2, 3.

Thus create an equation.

y = (x + 1)(x - 2)(x -3)

Answer:

it's either 20 or 80..

Answer:

80 shoes

Step-by-step explanation:

40×2

Answer:

Step-by-step explanation:

Because a square must be positive no matter what the sign of x is.

(-2)^2 = 4

2^2 = 4

Answer:

The third box model

Step-by-step explanation:

Since she earns 162 from babysitting and got a total of $810, it would eman that (x represents the amount of money she got from mowing lawns) 810-162=x

x=648 so the third box model is correct

Answer:

n = 9 / 2 or 4.5

Step-by-step explanation:

2/3 = 3/N

cross multiply

2 x n = 2n

3 x 3 = 9

2n = 9

divided both sides by 2

2n / 2 = 9 / 2

n = 9 / 2

Using the table of values, the probability of selecting a girl that likes Michigan is 0.11

The table is given as:

           Ohio State   Michigan    NC State   Total

Boys        56                14                20           90

Girls         50               22               38            110

Total       106              36                58          200

In the above table, 22 girls out of the total sample size of 200 like Michigan.

This means that the required probability is:

P = 22/200

Evaluate the quotient

P = 0.11

Hence, the probability of selecting a girl that likes Michigan is 0.11

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Answer:

Steps

-x/3 >5

Multiply both sides by 3

3(-x/3)>5.3

Simplify

-X> 15

Multiply both sides by - 1 (reverse the inequality)

(-x)(-1)<15(-1)

Simplify

X< -15

so C is the answer

Answer:

One solution

Step-by-step explanation:

The only solution is x = 2/3

Answer:

10

Step-by-step explanation:

it is 10 I jus did it 120 =12 x x =12 10