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svetoff [14.1K]
2 years ago
14

Vanna is saving for a trip. The hotel room will be $298.17 for 3 nights, and there will be additional fees. What is her daily co

st? a. Write an inequality for the situation. b. Solve the inequality. Then provide a statement that represents the solution of the problem.
Mathematics
1 answer:
docker41 [41]2 years ago
7 0

Answer:

Step-by-step explanation:

Total cost for the three nights

Total_3 = $298.17 + 3*u

Where <em>u </em>represents the unknown fees for a single day

To find the daily cost, we divide the previous equation by three

Daily cost = ($298.17 + 3*u)/3

Daily cost = ($99.39 + u)

So, if we create an inequality for the daily cost

Let x = Daily cost

x > $99.39

She will pay more than $99.39 per night

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A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the
Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

V_s=\frac{4}{3} \pi r^3

The radius is half the diameter. The diameter of the sphere is 10, thus:

r = d/2 = 10/2 = 5

5^3 = 5*5*5 = 25*5 = 125

V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125

The volume of a cylinder, which will be the shape of the increase in water, is the following:

V_c=\pi r^2 h

We know the radius r, as we know the diameter.

r=d/2=40/2=20

V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

V_s = V_c

\frac{4}{3} * 125 * \pi = 400 * h * \pi

We can get rid of pi by dividing both sides by pi:

\frac{4}{3} * 125 = 400 * h

And now divide both sides by 400:

\frac{4}{3} * \frac{125}{400}= h

Just reversing it and putting h to the left:

h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}

I see that I can divide both the numerator and the denominator by 4:

h =\frac{125}{3 * 100}= \frac{125}{300}

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

\frac{5}{12} ≈ 0.416666667 ≈ 0.42

7 0
1 year ago
A friend asks to borrow $900 for three months and agrees to pay 5% simple interest per year. How much interest will you earn in
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Answer:

$11.25 intrest

Step-by-step explanation:

the amount times the months divided by 12 times the percent gives you the intrest

7 0
1 year ago
The volume of a sphere whose diameter is 18 centimeters is 246 324 648 972 π cubic centimeters. If its diameter were reduced by
Dmitry [639]
1/4, since the radius is also halved if the diameter is halved, meaning (radius/2)^2 is radius^2 * 1/4.
5 0
1 year ago
Read 2 more answers
Gina wants to save money for a holiday to bali at the end of the year. she estimates that if would cost her $2200 but she only h
inessss [21]
That's a funky problem... :/  I mean it would depend on how much she earns weekly. If she were working 40 hours each week and earning 10$ an hour then yes, she would have enough. Even is she were per say a student on a part time working 30 hours and earning 8$ per hour, she would still have enough.
6 0
1 year ago
Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m\overarc RS + m\overarc ST + m\overarc TQ + m\overarc
LekaFEV [45]

Answer:

360°

Step-by-step explanation:

From the figure attached,

R, S, T and Q are the points on a circle O.

Since, "measure of an arc of a circle is equal to the measure of the angle subtended by the arc at the center."

By this statement,

m(\widehat{RS})=m(\angle ROS)

m(\widehat{ST})=m(\angle SOT)

m(\widehat{TQ})=m(\angle TOQ)

m(major arc RQ) = m(∠QOR)

Now m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major arc RQ) = m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)

Since sum of all angles at a point = 360°

m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major arc RQ) = 360°

4 0
1 year ago
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