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2 years ago

Write a fraction that is less than 5/6 and has a denominator of 8

1 answer:

4 0

One of those fractions could be 1/8.
If we want to compare it to 5/6:
5/6 * 8/8 = 40/48
1/8 * 6/6 = 6/48
And: 40/48 > 6/48
So: 5/6 > 1/8.
Answer: Fraction 1/8.

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Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled

Pavel [41]

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

$t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)}$

$t = \frac{32 \pm 30.98}{2}$

$t_1 = \frac{32 + 30.98}{2}$

$t_1 = 31.49$

$t_2 = \frac{32 - 30.98}{2}$

$t_2 = 0.51$

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

4 0

2 years ago

Read 2 more answers

Let X represent the amount of time until the next student will arrive in the library parking lot at the university. If we know t

Ber [7]

Answer:

The probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

Step-by-step explanation:

The random variable X is defined as the amount of time until the next student will arrive in the library parking lot at the university.

The random variable X follows an Exponential distribution with mean, μ = 4 minutes.

The probability density function of X is:

$f_{X}(x)=\lambda e^{\lambda x};\ x\geq 0, \lambda >0$

The parameter of the exponential distribution is:

$\lambda=\frac{1}{\mu}=\frac{1}{4}=0.25$

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10}{0.25e^{-0.25x}}\, dx$

$=0.25\times \int\limits^{\infty}_{10}{e^{-0.25x}}\, dx\\=0.25\times |\frac{e^{0.25x}}{-0.25}|^{\infty}_{10}\\=(e^{-0.25\times \infty})-(e^{-0.25\times 10})\\=0.0821$

Thus, the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

3 0

2 years ago

You and your friend are making 30 liters of sodium water. You have liters of 10% sodium and your friend has liters of 22% sodium

iren [92.7K]

X liters of 10% + (30 - x) liters of 22% = 30 liters of 15%

Plugging in the numbers 
x(10) + (30 - x)22 = 30(15) 

Distribute 
10x + 660 - 22x = 450 

Combine like terms 
-12x = -210 

Divide both sides by -12 
x = 17.5 
30 - x = 12.5 

17.5 liters of 10% + 12.5 liters of 22% = 30 liters of 15%

THE TRICK IS TO JUST USE ONLY ONE VARIABLE

4 0

2 years ago

A train travelled a distance of 6,000km from Lahore to Karachi in 22 hours. And during travel from Karachi to Lahore the train g

VashaNatasha [74]

The average speed of train:
12,000 km / ( 28 + 22 hr) =12,000 km / 50 hr = 240 km/hr
Answer: D)

5 0

2 years ago

The average price of a gallon of orange juice from October 2013 to September 2014 can be modeled by the function f shown, where

Hatshy [7]

Answer:

The average price of a gallon of orange increased by $0.03 each month.

Step-by-step explanation:

It is 11 months between October 2013 and September 2014 so the price after 11 months =

f(11) = 6.12 + 0.03(11)

= 6.12 + 0.33

= $6.45.

This is an increase of 0.33 / 11 = 0.03 / month.

5 0

2 years ago