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3 years ago

5

tomorrow joelle wants to travel a total of 4 miles by walking and running. she plans to run for 20 minutes at a rate of 6 miles

per hour. how many minutes should she's walk at a rate of 3 miles per hour to finish traveling the 4 miles?

1 answer:

serg [7]3 years ago

7 0

Answer:

40 minutes

Step-by-step explanation:

Joelle wants to run for 20 minutes at rate 6 miles per hour so the distance traveled in this duration will be calculated by multiplying speed and time(in hours).

So, distance traveled in 20 minutes = $6 \times \frac{20}{60}$ = 2 miles.

As Joelle have to travel total 4 miles, the distance remaining after 20 minutes of traveling = 4 - 2 = 2 miles.

Now she has to walk for the remaining distance i.e. 2 miles with a speed of 3 miles/hour.

The time required to travel 2 miles will be calculated by dividing distance with speed.

So, time required = $\frac{2}{3}$ hours.

Thus time in minutes = $\frac{2}{3}\times 60$ = 40 minutes.

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Dahasolnce [82]

Answer:

a) $x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i$ , $\forall i \in \mathbb{N}_{O}$ , $x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i$ , $\forall i \in \mathbb{N}_{O}$ , b) $x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i$ , $\forall i \in \mathbb{N}_{O}$ , $x_{2} = \frac{5\pi}{3}\pm 2\pi\cdot i$ , $\forall i \in \mathbb{N}_{O}$

Step-by-step explanation:

a) The equation must be rearranged into a form with one fundamental trigonometric function first:

$\sqrt{3}\cdot \csc x - 2 = 0$

$\sqrt{3} \cdot \left(\frac{1}{\sin x} \right) - 2 = 0$

$\sqrt{3} - 2\cdot \sin x = 0$

$\sin x = \frac{\sqrt{3}}{2}$

$x = \sin^{-1} \frac{\sqrt{3}}{2}$

Value of x is contained in the following sets of solutions:

$x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i$ , $\forall i \in \mathbb{N}_{O}$

$x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i$ , $\forall i \in \mathbb{N}_{O}$

b) The equation must be simplified first:

$\cos x + 1 = - \cos x$

$2\cdot \cos x = -1$

$\cos x = -\frac{1}{2}$

$x = \cos^{-1} \left(-\frac{1}{2} \right)$

Value of x is contained in the following sets of solutions:

$x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i$ , $\forall i \in \mathbb{N}_{O}$

$x_{2} = \frac{5\pi}{3}\pm 2\pi\cdot i$ , $\forall i \in \mathbb{N}_{O}$

7 0

3 years ago

8 less than the product of 5 and -4

Karolina [17]

The answer would be:
5(-4) - 8
-20 - 8
-28

4 0

3 years ago

( -5 , 12) and ( 2 , 26)

Deffense [45]

<h2>Answer:</h2><h2>The slope is 2</h2><h2 /><h2>Hope this helps!!</h2>

8 0

3 years ago

Read 2 more answers

Answers should be exact decimals (please do not leave as fractions or unfinished calculations).

aksik [14]

Answer:

P(rolling the die results in a 3 or a 6)=0.3333

P(rolling the die results in not getting a 6)=0.8333

P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333

P(rolling the die results in an even number or a 5)=0.6667

P( rolling the die twice results in a 6 followed by a 4)=0.0278

P(rolling the die three times results in all 6's)=0.0046

Step-by-step explanation:

a)

As the all outcomes are equally likely, so each number has equal probability of occurring.

For six sided die the sample space is {1,2,3,4,5,6} and each outcome has equal probability of 1/6.

1)

P(rolling the die results in a 3 or a 6)

P(rolling the die results in a 3 or a 6)=P(3)+P(6)=1/6+1/6=2/6=1/3

P(rolling the die results in a 3 or a 6)=0.3333

P(rolling the die results in not getting a 6)

P(rolling the die results in not getting a 6)=1-P(6)=1-1/6=5/6

P(rolling the die results in not getting a 6)=0.8333

P(rolling the die results in the number being either greater than 2 or less than 5)

number either greater than 2 or less than 5={3,4}

P(rolling the die results in the number being either greater than 2 or less than 5)=2/6=1/3

P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333

P(rolling the die results in an even number or a 5)

number is an even number or a 5={2,4,5,6}

P(rolling the die results in an even number or a 5)=4/6=2/3

P(rolling the die results in an even number or a 5)=0.6667

P( rolling the die twice results in a 6 followed by a 4)

For six sided die rolled twice the sample space is

S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}.

n(S)=6²=36.

rolling the die twice results in a 6 followed by a 4={(6,4)}

P( rolling the die twice results in a 6 followed by a 4)=1/36.

P( rolling the die twice results in a 6 followed by a 4)=0.0278

P(rolling the die three times results in all 6's)

When three die are rolled the number of outcomes=n(S)=6³=216.

rolling the die three times results in all 6's={(6,6,6)}

P(rolling the die three times results in all 6's)=1/216

P(rolling the die three times results in all 6's)=0.0046

Note: All answers are rounded to four decimal places.

8 0

3 years ago

A fire department in a rural county reports that its response time to fires is approximatelyNormally distributed with a mean of

____ [38]

Answer:

Option C) 0.25

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 22 minutes

Standard Deviation, σ = 11.9 minutes

We are given that the distribution of response time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(response times is over 30 minutes)

P(x > 30)

$P( x > 30) = P( z > \displaystyle\frac{30 - 22}{11.9}) = P(z > 0.6722)$

$= 1 - P(z \leq 0.6722)$

Calculation the value from standard normal z table, we have,

$P(x > 30) = 1 - 0.749= 0.251 = 25.1\%$

Thus, the correct answer is

Option C) 0.25

3 0

2 years ago

Read 2 more answers