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2 years ago

The drama club spent $35 on decorations and $8.50 per person on food for a cast party. The total cost of the food

Mathematics

1 answer:

jenyasd209 [6]2 years ago

5 0

Answer:

Option C) 27 people

Step-by-step explanation:

Let

x ----> the number of people

we know that

The cost of decorations ($35) plus the number of people (x) multiplied by the cost per person on food ($8.50) must be equal to $264.50

The linear equation that represent this situation is

$35+8.50x=264.50$

solve for x

Subtract 35 both sides

$8.50x=264.50-35$

$8.50x=229.50$

Divide by 8.50 both sides

$x=229.50/8.50$

$x=27\ people$

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A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

3 0

3 years ago

Aaron used the Pythagorean theorem to find the height of a tree. He calculated that the tree was √625 feet tall. Which of the fo

frutty [35]

Answer:

25 feet

Step-by-step explanation:

8⅓ yards

300 inches

1.52 rods

4⅙ fathoms

7.62 meters

3 0

3 years ago

if a coin is tossed 4 times, the odds of it coming up either heads every time or tails every time are 1:7.What is the probabilit

ivanzaharov [21]

Answer:

$1$

Explanation:

From the question, we have it that the probability of heads coming up every time or tail coming up every time is 1:7 if the coin is tossed in 4 tosses

What this means is that we have a probability of 1/8 of head showing up and a probability of 7/8 that a tail will show up in each toss of the coin

For four throws, it means all four are heads or all four are tails

If all four are heads, we have the probability of this happening as:

$\text{ (}\frac{1}{8})^{}$

if all four are tails, we have the probability as:

$\frac{7}{8}$

Now, the probability of either heads or all tails after 4 tosses will be:

$\text{ }\frac{1}{8}\text{ + }\frac{7}{8}\text{ = 1}$

8 0

1 year ago

Please help me i need to complete this by tomorrow

lisov135 [29]

Answer:

Step-by-step explanation: Need to work out your scale factor which is 1.5.

8 * 1.5 = 12

CE = 12

12 * 9 = 108/2 = 59 that is the area of triangle ACE

8 * 6 = 48/2 = 24 that is the area of triangle BCD

ACE - BCD = ABDE

59 - 24 = 35cm^2

8 0

1 year ago

An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 5 hours and 30 minutes. The retur

yawa3891 [41]

Answer: a) 490.91 mph

b) 540 mph

c) speed of the wind = 49.1 mph

Step-by-step explanation:

Given that flight between Joppetown and Jawsburgh took 5 hours and 30 minutes.

Time t = 5.5hours

Distance = 2700 miles

Speed = distance/ time

Speed = 2700/5.5

Speed = 490.91 mph

The return flight took 5 hours of the same distance from = 2700 miles

Speed = 2700/5 = 540 mph

speed of the wind = the difference in the two speed

speed of the wind = 450 - 490.91

speed of the wind = 49.1 mph

Speed = 540m/s

6 0

2 years ago