Plzz I need help
math word problem

a) Yes, The average speed of the train could have been greater than 145 km/h,

b) the new maximum average speed, correct to 2 decimal places, is approximately 2.46 km/minute.

a) To determine if the average speed of the train could have been greater than 145 km/h, we need to calculate the maximum possible average speed given the track length rounded to the nearest 10 km.

The track length is 290 km, rounded to the nearest 10 km. This means the actual track length could be anywhere between 285 km (290 km - 5 km) and 295 km (290 km + 5 km).

To find the maximum average speed, we'll assume the train took the minimum possible time (120 minutes) to cover the maximum possible track length (295 km):

Maximum Average Speed = (Maximum Possible Track Length) / (Minimum Possible Time)

Maximum Average Speed = 295 km / 120 minutes ≈ 2.4583 km/minute (rounded to 4 decimal places)

Since 2.4583 km/minute is greater than 145 km/h (which is approximately 2.4167 km/minute), the answer is:

Yes, the average speed of the train could have been greater than 145 km/h.

b) Now that we know the track was measured to the nearest 5 km, we'll calculate the new maximum average speed in km per minute based on the maximum possible track length (295 km) and the minimum possible time (120 minutes):

Maximum Average Speed = (Maximum Possible Track Length) / (Minimum Possible Time)

Maximum Average Speed = 295 km / 120 minutes ≈ 2.4583 km/minute (rounded to 4 decimal places)

So, the new maximum average speed, correct to 2 decimal places, is approximately 2.46 km/minute.

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The population density of Colorado is 48.09 people per mile²

Population density

Population density is the concentration of individuals within a specific area. It is given by:

Population density = number of people / land area

Land area = length  * width = 280 * 380 = 106400 mile²

Population density = 5,116,800 / 106400 = 48.09 people per mile²

The population density of Colorado is 48.09 people per mile²

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Answer:

Step-by-step explanation:

160miles • 330miles= 52,800square miles

Now it wants the population density in people per square miles, so you need to divide the population by the number of square miles.  

4779736/52800=90.5 which is about 91people per square mile.  

Final answer:

The given expression -8 ÷ 343 can situationaly be written in power notation as -8 ÷ 7^3. This transformation changes '343' to '7^3' since 343 is 7 cubed.

Explanation:

The expression -8 ÷ 343 cannot be directly written in 'power notation', as the concept of'power notation' commonly refers to writing an expression in the form of a base value raised to an exponent.

Power notation is typically represented as a^n, where 'a' is the base and 'n' is the exponent. However, '343' can be written in power notation since it is 7 cubed (7^3).

So, while we should clarify the details, one way to write the expression could be -8 ÷ 7^3.

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Answer:?

Step-by-step explanation:?

The label on the soup can has area of 62.4π square inches. The Option D is correct.

What is the area of the label on the soup can?

The label is represented by the rectangle in the figure.

The height of rectangle is given as 7.8 inches. The length is equal to the circumference of the circular base of the cylinder.

The circumference of a circle is: 2πr

In this case, the radius of each circle is 4 inches. So, the circumference of each circle is:

= 2π(4)

= 8π

As length of rectangle represents circumference, its length is equal to 8π inches. The height of rectangle is given as 7.8 inches.

We will calculate the area of the rectangle:

Area = Length × Height

Area = (8π) × 7.8

Area = 62.4π.

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The division of (4x³ + 3x² - 30x - 10) by (x - 3) is equal to 4x² + 3x - 21 with a remainder of -73.

How to divide the polynomial

To divide the polynomial (4x³ + 3x² - 30x - 10) by (x - 3), we can use long division Divide the first term of the dividend by the first term of the divisor:

4x³ / x = 4x²

4x² * (x - 3) = 4x³ - 12x²

(4x³ + 3x² - 30x - 10) - (4x³ - 12x²) = 3x²- 30x - 10

Bring down the next term from the dividend:

3x² - 30x - 10

3x² / x = 3x

Multiply the divisor (x - 3) by the result from step 5:

3x * (x - 3) = 3x² - 9x

(3x² - 30x - 10) - (3x²- 9x) = -21x - 10

Bring down the next term from the dividend:

-21x - 10

-21x / x = -21

Multiply the dvisor (x - 3) by the result from step 6:

-21 * (x - 3) = -21x + 63

(-21x - 10) - (-21x + 63) = -73

The result of the division is the sum of the quotients obtained in each step:

4x² + 3x + (-21)

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