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padilas [110]
1 year ago
15

Sandra wants to rent a car to take a trip and has a budget of $90. There is a fixed rental fee of $30 and a daily fee of $10. Wr

ite an inequality that would be used to solve for the maximum number of days for which Sandra can rent the car on her budget. 30x + 10 ≤ 90 30 + 10x ≤ 90 30x + 10 ≥ 90 30 + 10x ≥ 90
Mathematics
1 answer:
nikdorinn [45]1 year ago
4 0

Option B is the correct answer

Step-by-step explanation:

Step 1 :

Given,

Maximum budget Sandra has for the trip is $90

Fixed rental fee = $30

Daily fee = $10

Step 2 :

Let x be the number of the days for which Sandra can go for the trip

If the daily fee is $10, the cost for x number of days would be 10*x

the fixed fee is $30

So the equation is represent the cost of the trip is 30 + 10 x

given that the maximum budget is $90, the above cost should always be less $90

So the required inequality is 30 + 10x ≤ 90

Option B is the correct answer

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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 company makes a product and has no way to determine which ones are faulty until an unhappy customer returns it. Three percent
Vitek1552 [10]
<span>(x) - (0.03)(200) = 2.00 
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7 0
2 years ago
Read 2 more answers
The manager of a symphony in a large city wants to investigate music preferences for adults and students in the city. Let pA rep
monitta

Answer:

Answer E

Step-by-step explanation

The statement gives a probability of approximately 0.022 for the difference in sample proportions, pˆA−pˆS, being greater than 0.

6 0
1 year ago
Craig has $1850 dollars in a bank account that he uses to make automatic payments of $400.73 on his car loan. If Craig stops mak
Ivenika [448]

Given:

Amount in the bank account = $1850

Monthly payment of can loan = $400.73

To find:

When would automatic payments make the value of the account zero?

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On dividing the amount by monthly payment, we get

\dfrac{1850}{400.73}=4.61657

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6 0
2 years ago
The local skating rink pays marry a fixed rate per pupil plus a base amount to work as a skating instructor. she earns $90 for i
Ganezh [65]
You have to make a system of equations: lets make a equal the amount marry makes per student and b be her base amount.
90=15a+b (you have to subtract the top equation by the bottom equation)
62=8a+b   (90-62=28, 15a-8a=7a, and b-b=0)
Since b canceled out, you are left with 7a=28 which means a=4.  you can than plug a into the equation 62=8a+b to find that b=30.

since Lisa makes half of the base amount marry, her base amount is 15.  However, she also make twice the amount per kid so she makes 8 per kid.
using the found values found you can make the equations (m=the amount Marry makes, l=the amount Lisa makes, and c is the number of children)
m=4c+30
l=8c+15
set c=20 and you should get m=110 and l=175.  Based off of that information, we can say that Lisa makes more money instructing a class of 20 students.
I hope this helps.
8 0
1 year ago
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