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Rashid [163]
3 years ago
11

Megan started biking to the internet cafe traveling 9 mph, after some time the bike got a flat so Megan walked the rest of the w

ay, traveling 7 mph. If the total trip to the internet cafe took 9 hours and it was 75 miles away, how long did Megan travel at each speed
Mathematics
2 answers:
Mariulka [41]3 years ago
8 0

Answer: d=54 miles

Step-by-step explanation:

We let the distance megan covered =d

And the distance she walked to the cafe will be :

75 - d

Therefore

d/9 + (75 - d) / 7 =9

L.c.m is 63

7d+9(75-d)=63×9

7d+675-9d=567

-2d=567-675

d=108/2

d=54

d=54 miles

Bess [88]3 years ago
5 0

Answer:

Megan travelled at 9mph for 6 hours and 7mph for 3 hours

Step-by-step explanation:

Speed = distance / time

Speed*time = distance

Assuming that Megan travelled x hours at 9mph

(9*x) + (7*(9-x)) = 75

x = 6 hours

So Megan travelled at 9mph for 6 hours and 7mph for 3 hours

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Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card
Viktor [21]

Answer:

a) i) No

ii) Probability of drawing a diamond and then spade without replacement is 0.0637.

b) i) Yes

ii) Probability of drawing a diamond and then spade with replacement is 0.0625

Step-by-step explanation:

Part a) Without replacement:

i) Are these events independent?

No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.

ii) Determine the probability of drawing a diamond and then a spade without replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after taking diamond = 52 -1 =51

Spades = 13

Probability of drawing a spade  = 13/51

Probability of drawing a diamond and then spade = 13/52 * 13/51

= 169/2652

=0.0637

So, Probability of drawing a diamond and then spade without replacement  is 0.0637

Part b) With replacements

i) Are these events independent?

Input Yes or No:

Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.

ii) Determine the probability of drawing a diamond and then a spade with replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after replacing diamond = 52

Spades = 13

Probability of drawing a spade  = 13/52

Probability of drawing a diamond and then spade = 13/52 * 13/52

= 169/2704

=0.0625

So, Probability of drawing a diamond and then spade with replacement is 0.0625

7 0
3 years ago
I need to find the limit
Digiron [165]
For x=\dfrac{1}{2} the function is undefined.

\displaystyle
\lim_{x\to\tfrac{1}{2}^-} x\sec (\pi x)=\infty\\
\lim_{x\to\tfrac{1}{2}^+} x\sec (\pi x)=-\infty\\\\
\lim_{x\to\tfrac{1}{2}^-}x\sec (\pi x)\not = \lim_{x\to\tfrac{1}{2}^+}x\sec (\pi x)

So, the limit doesn't exist.
8 0
2 years ago
The difference of the squares of two consecutive odd integers is 24. Find the integers.
katen-ka-za [31]
It’s a few home boy
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.78 3/11 as a percent
Anestetic [448]
.78 will be 78% and 3/11 will be 27% hope I helped!
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Danielle needs to walk 2.5 miles. If she wants to reach her destination in 30 minutes (1/2hour), how fast does she need to walk?
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She would need to walk .83 miles per minute
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