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Xelga [282]
3 years ago
6

Josie took a road trip. She drove for 45 minutes at 70 miles per hour. Then she drove 15 minutes at 20 miles per hour. How far d

id Josie drive? Round to the nearest mile.
Mathematics
1 answer:
Hunter-Best [27]3 years ago
3 0

Answer:

Therefore Josie drove  57.5 miles.

Step-by-step explanation:

Speed: The ratio of distance to time.

To find the distance we use the following formula

Distance= time \times speed

Given that Josie drove 45 minutes at 70 miles per hour.

45 \ minutes= \frac{45}{60}\ h=\frac34\ h

In 45 minutes, she traveled  = (70\times \frac34) \ miles

                                                =52.5 miles.

The she drove 15 minutes at 20 mile per hour.

15 \ minutes= \frac{15}{60}\ h=\frac14\ h

In 15 minutes, she traveled =(20\times \frac 14) \ miles

                                            =5 miles

Therefore Josie drove (52.5+5) miles= 57.5 miles.

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Find the exact volume of the cylinder.
Verizon [17]

Answer:

\boxed {\boxed {\sf C. \ 200 \pi \ ft^3}}

Step-by-step explanation:

We are asked to find the volume of the cylinder. The formula for calculating a cylinder's volume is:

v= \pi r^2 h

We know the height of the cylinder is 8 feet. We are given the diameter, the distance from edge to edge through the center. We want to find the radius, the distance from the edge to the center.

The radius is half the diameter.

  • r = d/2
  • r= 10 ft/2
  • r=5 ft

We know both variables (h= 8ft and r=5 ft) and can substitute them into the formula.

v= \pi (5 \ ft)^2 * (8 \ ft)

Solve the exponent.

  • 5 ft * 5ft = 25 ft²

v= \pi (25 \ ft^2)(8 \ft)

Multiply the numbers in parentheses.

v= \pi (200 \ ft^3)

v= 200 \pi \ ft^3

The volume of the cylinder is <u>200π cubic feet and choice C is correct.</u>

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2 years ago
One yard is approximately 0.91 meter. Write a direct variation equation that relates x yards to y meters.
IgorC [24]
Y = kx is the direct variation equation with k being the "constant of variation"
The constant here being the conversion decimal .91
y = 0.91x
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2 years ago
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Carmen and Matt are conducting different chemistry experiments in school. In both experiments, each student starts with an initi
dangina [55]

This question is incomplete and it lacks an attached graph. Find attached to this answer, the appropriate graph.

Complete Question

Carmen and Matt are conducting different chemistry experiments in school. In both experiments, each student starts with an initial amount of water in a flask. They combine two chemicals which react to produce more water. Carmen's experiment starts with 30 milliliters of water in a flask, and the water increases in volume by 8.5 milliliters per second. Matt's experiment starts with 10 milliliters of water and increases in volume by 28% each second. The graph represents the volume of water in the two flasks in relation to time. Which two conclusions can be made if f represents the volume of water in Carmen's flask and g represents the volume of water in Matt's flask? a) The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [0, 2].

b) The volume of water in Carmen's flask is increasing at a faster rate than the volume of water in Matt's flask over the interval [6, 8].

c) The volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.

d) The volume of water in Matt's flask will eventually be greater than the volume of water in Carmen's flask.

e) The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [4, 6].

Answer:

c) The volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.

e) The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [4, 6].

Step-by-step explanation:

Looking at the graph, the average rate of change is given as [0,2], [4,6], and [6,8].

From the graph and question, we can tell that Matt's experiment starts with 10 milliliters of water and increases in volume by 28% each second

Which would gives us:

28% of 10 milliliter of water = 2.8 millimeters per second.

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Because, Carmen starts with 30 milliliters of water in his flask, the volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.

Secondly, comparing the quantity as which the volume of the flask increases per second, at the interval of [4, 6], the volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval

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Answer: C

Step-by-step explanation:

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