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3 years ago

Each table at a restaurant has six chairs placed around it.

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

3 0

Answer:

4/24

Choice B is correct

Step-by-step explanation:

From the information given, there is 1 table for every 6 chairs at the restaurant. In ratio form this can be expressed as;

1:6

The ratio that is equivalent to this given ratio is 4/24. This can easily be checked through simplification of this ratio;

4/24; If we divide both the numerator and the denominator by 4 we obtain

1/6 which is equivalent to 1:6

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F(x)=-1/2(x-2)^2-4 <br> Graph the function

telo118 [61]

Answer:

see below

Step-by-step explanation:

The function is written in vertex form. It has a negative vertical scale factor, so you know ...

the vertex is (2, -4)
the vertical scale factor is 1/2
the parabola opens downward

Vertex form is ...

f(x) = a(x -h)^2 +k . . . . . . . . . . vertical scale factor "a", vertex (h, k)

Since you know the vertex and scale factor, you can plot some points on the graph. I find it convenient to think in terms of units either side of the vertex. These are values of x that would make (x-2)^2 be 1^2, 2^2, 3^2, 4^2 and so on. The vertical scale factor of -1/2 tells you that the y-differences for these points will be -1/2, -4/2, -9/2, -16/2 from the vertex. Then we have ...

vertex: (2, -4)

1 unit either side of the vertex: (1, -4.5), (3, -4.5)

2 units either side of the vertex: (0, -6), (4, -6)

3 units either side of the vertex: (-1, -8.5), (5, -8.5)

4 units either side of the vertex: (-2, -12), (6, -12)

You can plot these points and draw a smooth curve through them. Or, you can let a graphing calculator do it. The result will be similar to that shown below.

6 0

3 years ago

Fill in the box with the appropriate measure.<br> quick please I have only a few min left

Art [367]

Step-by-step explanation:

first box on the left

r=4

d=8

circumference= 2π*4= 8π

area = π*4*4= 16π

Second box on the left

d=6

r= 3

circumference= 2π*3= 6π

area =π*3*3= 9π

third box on the left

A=36π

A=36πarea= π*r*r

A=36πarea= π*r*rr= 6

A=36πarea= π*r*rr= 6d=12

A=36πarea= π*r*rr= 6d=12circumference= 2π*6= 12 π

the last box

C=18π

C=18πC= 2π*r

C=18πC= 2π*rr= 9

C=18πC= 2π*rr= 9d=18

C=18πC= 2π*rr= 9d=18area= π*9*9= 81π

8 0

2 years ago

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker sys

il63 [147K]

Answer:

a) $P(x)=-0.042x^2+530x-18000$

b) $P'(x)=-0.084x+530$

$P'(4000)=194$

$P'(9500)=-268$

Step-by-step explanation:

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

$P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000$

This is the profit function.

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

$\frac{d}{dx}(x^n)=nx^{n-1}$

Now, we differentiate the profit function to get the marginal profit function (P'):

$P(x)=-0.042x^2+530x-18000\\P'(x)=2(-0.042)x^1+530x^0-0\\P'(x)=-0.084x+530$

This is the marginal profit function , P'.

We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:

$P'(x)=-0.084x+530\\P'(4000)=-0.084(4000)+530\\P'(4000)=194$

and

$P'(x)=-0.084x+530\\P'(9500)=-0.084(9500)+530\\P'(9500)=-268$

6 0

3 years ago

The inequality of the most people that can be seated in the auditorium

WINSTONCH [101]

Let x be the number of people that can be seated.

The value of x is some number 0 or greater, such that this number is a whole number (we can't have half a person). This means that $x \ge 0$ which is the same as saying $0 \le x$

The instructions state that we can seat up to 1200 people. This is the max capacity. We can't go over this amount. So we will also have $x \le 1200$ indicating that x can be less than 1200 or equal to 1200.

So putting the two inequalities together, we get $0 \le x \le 1200$

Note: if you haven't learned about compound inequalities yet, then the teacher may only want $x \le 1200$ as the answer.

3 0

3 years ago

In a bolt factory, machines 1,2, and 3 respectively produce 20%, 30% and 50% of the total output. of their respective outputs 5%

lorasvet [3.4K]

Answer:

a. 1/10 or 10%

b. 1/2 or 50%

Step-by-step explanation:

Since the combination of machines 1, 2 and 3 produce 100% of the total output when added together, then the probability of choosing a bolt at random that is defective is: 5 + 2 + 3 = 10% out of 100% or 10/100, which is 1/10 or 10%.

If the bolt that is choosen at random is defective, than the probability that it came from machine 1 is 5/10 or 1/2 which is also 50%.

3 0

4 years ago