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lawyer [7]
3 years ago
8

Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the sam

e path at 5 mi/h. How long (in hours) will it be before Amanda catches up to Ben?
Mathematics
1 answer:
Travka [436]3 years ago
7 0

Answer:

2 hours 15 minutes

Step-by-step explanation:

Given that :

Ben's speed = 3 mi/hr

One and half hours after Ben leaves = 1.5 hours

Ben's distance = 3 mi/hr * 1.5 = 4.5 miles

Amanda's speed = 5 mi/hr

Time taken before Amanda catches up:

Let time taken = x

Distance = speed * time

Ben's distance = Amanda's distance

4.5 mi + (3 * x) = 5 * x

4.5 + 3x = 5x

4.5 = 5x - 3x

4.5 = 2x

x = 4.5 / 2

x = 2.25 hours

Time taken = 2.25 * 60 = 135 minutes = 2 hours 15 minutes

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Find the new amount of the original amount is 45 grams and the percent of decrease is 36%.
Semenov [28]

Answer:

28.8

Step-by-step explanation:

the original is 45=100%

it reduced by 36% meaning;100%-36%=64%

if45=100%

? =64%

45*64=2880/100=28.8

6 0
3 years ago
Need help with 8-9.
ANTONII [103]
So it is 5cm to 1m or 5cm to 1000cm
So the scale is the ratio which is 5:1000. this can be reduced to 1:200

10. if the room is 15cm on one side I can say that the ratio to actual size is 15/x. and scale is 1/200 so:
15/x = 1/200
3000 = x is one side

other side:
20/x = 1/200
4000 = x
7 0
3 years ago
Not sure how difficult this would be to solve
mr_godi [17]
F (x) = x^2 - 2x + 1
f (x) = (-2)^2 - 2(-2) + 1
= 4 + 4 + 1
= 9
f (x) = ( 0 )^2 - 2 (0) + 1
= 0 - 0 + 1
= 1
0 = x^2 - 2x + 1
x^2 = 2x - 1 = 1
f (2) = 2^2 - 2(2) + 1
= 4 - 4 + 1
= 1
f (3) = 3^2 - 2(3) + 1
= 9 - 6 + 1
= 3 + 1
= 4

3 0
2 years ago
Julio and David were in Target and decided to check out the clearance section. They found pencils and erasers that were on sale
Sati [7]

Answer:

Cost of one pencil: \$0.07

Cost of one eraser: \$0.03

Step-by-step explanation:

Let be "p" the cost in dollars of one pencil and "e" the cost in dollars of one eraser.

Based on the information given in the exercise, you can set up the following system of equations:

\left \{ {{4p+3e=0.37} \atop {3p+4e=0.33 }} \right.

You can use the Elimination Method to solve the system of equations.

Multiply the first equation by -3 ad the second one by 4. Then add the equations and solve for "e":

{\left \{ {{-12p-9e=-1.11} \atop {12p+16e=1.32}} \right.\\..........................\\7e=0.21\\\\e=0.03

Substitute the value of "e" into any original equation  and solve for "p":

4p+3(0.03)=0.37\\\\p=\frac{0.28}{4}\\\\p=0.07

5 0
3 years ago
The diameter of the base of the cone measures 8 units.
kati45 [8]

Answer:   32\pi cubic units.

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

V_{cone}=\frac{1}{3}\pi r^2h

Where "r" is the radius and "h" is the height.

You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:

r=\frac{8units}{2}\\\\r=4units

Since you already know that height and  the radius, you can substitute them into the formula. Then, the volume of this cone is:

V_{cone}=\frac{1}{3}\pi (4units)^2(6units)

V_{cone}=32\pi \ units^3

8 0
3 years ago
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