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Rom4ik [11]
4 years ago
15

Problem solving with inequalities

Mathematics
1 answer:
anzhelika [568]4 years ago
8 0

Option D:

15c ≤ 200

Solution:

Let c be the number of cases of tea bags.

Cost of each tea bag = 15 gold coins

Total gold coins Mad have = 200

<u>Set up an inequality:</u>

Cost of c tea bags = 15 × c = 15c

Mad can buy tea bags at most 200 gold coins.

(At most 200 means 200 is the greater value)

15 × c ≤ 200

15c ≤ 200

Hence option D is the correct answer.

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Sherry claims that the expression 1/x will always be equivalent to a repeating decimal whenever x is an odd number greater than
fomenos

Answer:

The correct options are :

b. 5

e. 25

Step-by-step explanation:

The question is incomplete. The missing part is :

'' Which of these values will prove Sherry's claim is false :

a. 3

b. 5

c. 7

d. 11

e. 25 ''

One way to prove that Sherry's claim is false is finding one odd number greater than 1 that when we replace it in the denominator of the expression \frac{1}{x} the result isn't equivalent to a repeating decimal.

Let's analyze each option :

  • a. 3

3 is an odd number greater than 1 ⇒ If we replace in the expression \frac{1}{x} ⇒

\frac{1}{3}  ≅ 0.3333 (repeating decimal)

The option a. 3 won't prove that Sherry's claim is false.

  • b. 5

5 is an odd number greater than 1 ⇒ If we replace in the expression \frac{1}{x} ⇒

\frac{1}{5}=0.2

The result isn't a repeating decimal.

The option b. 5 will prove that Sherry's claim is false.

  • c. 7

7 is an odd number greater than 1 ⇒ If we replace in the expression \frac{1}{x} ⇒

\frac{1}{7} ≅ 0.1428 (repeating decimal)

The option c. 7 won't prove that Sherry's claim is false.

  • d. 11

11 is an odd number greater than 1 ⇒ If we replace in the expression \frac{1}{x} ⇒

\frac{1}{11} ≅ 0.0909 (repeating decimal)

The option d. 11 won't prove that Sherry's claim is false.

  • e. 25

25 is an odd number greater than 1 ⇒ If we replace in the expression \frac{1}{x} ⇒

\frac{1}{25} ≅ 0.04

The result isn't a repeating decimal

The option e. 25 will prove that Sherry's claim is false.

3 0
3 years ago
Ben and Susan are truck drivers who start at the same location. Ben drives 300 miles due west and Susan drives 160 miles due sou
Paul [167]

Answer:

Ben and Susan will be 340 miles apart

Step by Step Solution

Step 1: We plot the problem on a graph to visualize the problem

Step 2: We notice that the problem creates a right triangle with the distance Ben and Susan travel as the legs of the right triangle

Step 3: We can use the Pythagorean Theorem: a²+b²=c² to solve the distance between Ben and Susan

Step 4: We enter the numbers into the formula

a² + b² = c²

300² + 160² = c²

90000 + 25600 = c²

115600 = c² *square root both sides

c = 340

Therefore Ben and Susan are 340 miles apart

8 0
3 years ago
a jogger runs 4 miles per hour faster downhill than uphill. if the jogger can run 5 miles downhill in the same time that it take
Serga [27]

Answer: the rate uphill is 6 mph.

The rate downhill is 10 mph

Step-by-step explanation:

Let x represent the rate at which the jogger ran uphill.

The jogger runs 4 miles per hour faster downhill than uphill. This means that speed at which the jogger ran downhill is (x + 4) mph

Time = distance/speed

if the jogger can runs 5 miles downhill, then the time taken to run downhill is

5/(x + 4)

At the same time, the jogger runs 3 miles uphill. It means that the time taken to run uphill is

3/x

Since the time is the same, it means that

5/(x + 4) = 3/x

Cross multiplying, it becomes

5 × x = 3(x + 4)

5x = 3x + 12

5x - 3x = 12

2x = 12

x = 12/2

x = 6

The rate downhill is 6 + 4 = 10 mph

8 0
4 years ago
Read 2 more answers
¿Cuál es el capital que colocado al 6% quincenal<br> genera en 2 meses un monto de S/. 7200?
Zinaida [17]

Answer:

$27428.57

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

P = Po * (1 + r)^(t)

Where P is the final value, Po is the inicial value, r is the rate of interest, t is the time.

With r = 0.06, t = 4 (The rate is for every 15 days, and the time is 2 months, so we have that 2 months = 4 periods of 15 days) and P = Po + 7200, we have:

Po + 7200 = Po * (1 + 0.06)^4

Po + 7200 = Po * 1.2625

Po * 0.2625 = 7200

Po = 7200 / 0.2625 = $27428.57

3 0
3 years ago
How is this number read? 18.73
Nana76 [90]

Answer:

18 and 73 hundredths

the number is 18 plus .73 .73 is 73 hundredths

7 0
4 years ago
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