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Doss [256]
3 years ago
10

To gather data for a statistics project, a student asked 10 friends how many hours of sleep they got on the previous night. The

data are shown in the following list.
Mathematics
1 answer:
inn [45]3 years ago
4 0

Answer:

3

Step-by-step explanation:

INTERQUARTILE RANGE (IQR) = Q3 - Q1

Rearranging the data: 3, 4, 5, 5, 6, 7, 7, 8, 9, 9

Q3 = 0.75(n+1)th term

Q3 = 0.75(10 + 1) th term

Q3 = 0.75(11)th term = 8.25th term

Taking the 8th term = 8

Q1 = 0.25(11)th term = 2.75th

Taking the average of the 8th and 9th term:

(5 + 5) / 2 = 10/2 = 5

Q3 - Q1 = (8 - 5) = 3

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A tank contains 120 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu
gtnhenbr [62]

If A(t) is the amount of salt in the tank at time t, then A(0) = 50 g and

A'(t) = (1 g/L)*(3 L/min) - (A(t)/120 g/L)*(3 L/min)

\implies A'+\dfrac A{40}=3

Multiply both sides by e^{t/40}, so that the left side can be condensed as the derivative of a product:

e^{t/40}A'+\dfrac{e^{t/40}}{40}A=3e^{t/40}

\left(e^{t/40}A\right)'=3e^{t/40}

Integrate both sides and solve for A(t).

e^{t/40}A=120e^{t/40}+C

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Given that A(0) = 50 g, we have

50=120+C\implies C=-70

so that the amount of salt in the tank at time t is

\boxed{A(t)=120-70e^{-t/40}}

7 0
4 years ago
Solve the system of equations. 4y + 11x – 67 = 0 2y + 5x - 19 = 0 x= y=​
katen-ka-za [31]

Answer:

x = 29, y = -63

Step-by-step explanation:

Solve the following system:

{4 y + 11 x - 67 = 0 | (equation 1)

{2 y + 5 x - 19 = 0 | (equation 2)

Express the system in standard form:

{11 x + 4 y = 67 | (equation 1)

v5 x + 2 y = 19 | (equation 2)

Subtract 5/11 × (equation 1) from equation 2:

{11 x + 4 y = 67 | (equation 1)

{0 x+(2 y)/11 = -126/11 | (equation 2)

Multiply equation 2 by 11/2:

{11 x + 4 y = 67 | (equation 1)

{0 x+y = -63 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{11 x+0 y = 319 | (equation 1)

{0 x+y = -63 | (equation 2)

Divide equation 1 by 11:

{x+0 y = 29 | (equation 1)

{0 x+y = -63 | (equation 2)

Collect results:

Answer: {x = 29, y = -63

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3 years ago
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What is the sum of all of the integers from -4 to +5?
sukhopar [10]
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A buyer purchases 75 yards of material for $120. Then an additional 90 yards are ordered. What is the additional cost?
dezoksy [38]

Answer:

$128

Step-by-step explanation:

1. We need to find how much 1 yard of material cost.

If needed, use a calculator*

120/75=1.6

2. Now we need to know how much 15 yards of material cost.

1.6 times 15=24

3. The buyer ordered an additional 90 yards. If we know how much 75 yards cost, and 15 yards, all you have to do is...

120+24=144

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4. The additional cost is $144

(Note: the total cost would be $264 (120+144=264))

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