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Bumek [7]
3 years ago
7

Liam is riding his bike at a rate of 7 miles per hour he wants to beat his own one day riding record to do so he has to run more

than 32 miles he'sridden 4 Miles which statement describes how many more hours Liam must ride to beat his record.
He must ride fewer than 4 more hours
He must ride more than 4 more hours
He must ride no less than 5 more hours
He mus ride no more than 5 more hours
Mathematics
2 answers:
brilliants [131]3 years ago
7 0

Answer:

Liam must ride more than 4 hours! Yes this is right! I took the test

Svetradugi [14.3K]3 years ago
4 0
Let h represent the number of hours Liam must ride to beat his record.

distance-ridden + distance-to-ride ≥ record-distance
distance-ridden + (speed × time-to-ride) ≥ record-distance
  4 +7h ≥ 32 . . . . . . . . an inequality representing the distance Liam wants
  7h ≥ 28 . . . . . . . . . . subtract 4
  h ≥ 4 . . . . . . . . . . . . . divide by 7

He must ride for more than 4 hours.
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Ron is 25 years old and is retiring at the age of 65. When he retires, he will need a monthly income of $4,123 for 20 years. If
valentinak56 [21]

Answer:

Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

Step-by-step explanation:

Given monthly income of Ron is $3,142.23

Ron contributes 10% of his monthly income that is $ 314.223

Given : Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.

Total amount he contribute in 40 years paying 5.5% compounded monthly is given by

interest rate(r) =\frac{0.055}{12}

time period = 40 years = 480 months

Principal amount = $ 314.223

Future value = P(\frac{(1+r)^n-1}{r} )

Substitute , we get,

=3142.23\cdot\frac{.10\left(\left(1+\frac{.055}{12}\right)^{12\cdot40}-1\right)}{\frac{0.055}{12}}

Thus, future value is $547074.681009.

After retirement his monthly income when he has $547074.681009 amount.

P=\dfrac{A\cdot\frac{i}{12} }{1-(1+\frac{i}{12})^{-n}}

Putting values , we get,

P=\frac{\left(547074.68\cdot\frac{.055}{12}\right)}{1-\left(1+\frac{0.055}{12}\right)^{-240}}

P = $3763.25

He will receive a monthly income of $3763.25.

But  given he will need a monthly income of $4,123 for 20 years which is not met by Ron.

So,the amount he need to supplement his monthly income when he retires by (4123-3763.25)= $359.74

Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

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3 years ago
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