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3 years ago

7

A buffet-style restaurant has 18 tables that seat 23 people each. A church group of 401 has rented the restroom for a banquet. I

f the pastor of another church, his wife, and their nine children come as invited guests, what is the least number of people that can sit at any one table?

1 answer:

ElenaW [278]3 years ago

4 0

12 people can sit at each seat.

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The interior angle measures of a convex pentagon are consecutive multiples of 4. find the measure of each interior angle.

lawyer [7]

Answer:

100°, 104°, 108°, 112°,116°

Step-by-step explanation:

Let the smallest angle be $4x$ . Since, the interior angles are consecutive, the other angles are $4(x+1)$ , $4(x+2)$ , $4(x+3)$ and $4(x+4)$ .

Sum of interior angles = 540°

$4x+4(x+1)+4(x+2)+4(x+3)+4(x+4)=540$ °

$20x+40=540$ °

$20x=(540-40)$ °

$20x=500$ °

$x=(500/20)$ °

$x=25$

Using the value of x to calculate the angles:

$4x=4*25=100$ °

$4(x+1)=4*26=104$ °

$4(x+2)=4*27=108$ °

$4(x+3)=4*28=112$ °

$4(x+4)=4*29=116$ °

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3 years ago

"If Jason reads7 1/2 pages in 1/4 hour, what is his average reading rate in pages per hour?

Paul [167]

The answer would be 30 pages

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4 years ago

Read 2 more answers

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3 years ago

Which value of a would make the following expression completely factored?

ehidna [41]

Answer:

12

Step-by-step explanation:

x^2 - a

If a is a perfect square we could factor

x^2 - b^2 = (x-b)(x+b)

So a cannot be 36,49,81 since they are perfect squares

a must be 12

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3 years ago

The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu

rjkz [21]

The balloon has a volume $V$ dependent on its radius $r$ :

$V(r)=\dfrac43\pi r^3$

Differentiating with respect to time $t$ gives

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}$

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

$10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}$

The surface area of the balloon is

$S(r)=4\pi r^2$

and differentiating gives

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}$

so that at the moment the radius is 3 m, its area is increasing at a rate of

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}$

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3 years ago