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Stells [14]
2 years ago
13

During the first seconds after takeoff, a rocket traveled 208 kilometers in 50 minutes at a constant rate suppose a penny is dro

pped from a skyscraper and could travel 153 kilometers in 1/2 hours at a constant rate. Which of these objects has a faster unit rate per hour? How much faster?
Mathematics
1 answer:
andrezito [222]2 years ago
6 0

the penny travels at a faster rate by 56.4 kilometers

penny = 153 for 30 min

penny = 306 for 1 hour

rocket = 208 in 50 min

208/5 = 41.6 *6 = 249.6 in 1 hour

penny is faster by 56.4 kilometers

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URGENT<br>Which of the following is the graph of y=0.5sec (x+pi/3)-2?
arlik [135]

Answer:

See attachment.

Step-by-step explanation:

The given function is

y=0.5\sec(x+\frac{\pi}{3})-2

This is the graph of y=\sec(x) that is shifted down 2 units and shifted to the left \frac{\pi}{3} units.

When x=0, y=0.5\sec(0+\frac{\pi}{3})-2

y=0.5\sec(\frac{\pi}{3})-2

y=1-2=-1

The y-intercept is -1.

The correct choice is shown in the attachment

7 0
1 year ago
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2 years ago
A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his
Karolina [17]

Answer:

a) The ratio of passenger cars to pickup trucks is \frac{5}{7}

The ratio of pickup trucks to passenger cars is \frac{7}{5}

The ratio of passenger cars to total vehicles is \frac{5}{12}

The ratio of pickup trucks to total vehicles is \frac{7}{12}

b) The tape diagram is shown in the attached picture.

c) The tape diagram has 12 equal-sized parts.

d) The total quantity that the tape diagram represent is 192.

e) The value of each individual part of the tape is 16.

f) There were registered 80 passenger cars and 112 pickup trucks.

Step-by-step explanation:

a) According to the information in the problem, that for every 5 passenger cars registered, there were 7 pickup trucks registered.

So the ratios are:

Passenger cars to pickup trucks: \frac{5}{7}

Pickup trucks to passenger cars: \frac{7}{5}

If we calculate the total vehicles: 5+7=12

So, we can get two ratios more:

Passenger cars to total vehicles is \frac{5}{12}

Pickup trucks to total vehicles is \frac{7}{12}

b) We make a tape diagram where each box represents a vehicle so we draw 5 boxes for cars and 7 boxes for pickup trucks.

c) If we count the total quantity of boxes, there are 12.

d) This diagram represents the total quantity of registrations in August which is 192.

e) To get the representation of each part of the tape diagram we have to divide 192 by 12. 192÷12=16

f) Finally, we multiply 16 by the number of boxes of each type of vehicle:

Cars: 16×5=80

Pickup trucks: 16×7=112

6 0
2 years ago
The triangle DEF is shown in the diagram.<br>Find the exact value of x.<br>​
vladimir1956 [14]

Answer:

x = 4

Step-by-step explanation:

Using cosine triangle formula, we know that;

c² = a² + b² - 2ac(cos C)

From our diagram;

a = 2x

b = x + 1

c = 7

C = 60°

Thus;

7² = (2x)² + (x + 1)² - 2(2x)(x + 1)cos 60

49 = 4x² + (x² + 2x + 1) - (4x² + 4x)(0.5)

49 = 5x² + 2x + 1 - 2x² - 2x

3x² + 1 - 49 = 0

3x² - 48 = 0

3x² = 48

x² = 48/3

x² = 16

x = √16

x = 4

8 0
1 year ago
What is 15 tens - 1 gross ​
vampirchik [111]

Answer:

see the explanation

Step-by-step explanation:

we know that

A gross is equal to 120 ones or ten dozen

what is 15 tens - 1 gross

we know that

15 tens means ----> That you are adding 10, 15 times or multiplying 10 by 15, which gives you

10(15)=150

1 gross means ---> That you are adding 10, 12 times or multiplying 10 by 12

which gives you

10(12)=120

so

The algebraic expression of 15 tens - 1 gross is equal to

150-120=30

Convert to word expression

3  tens

8 0
1 year ago
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