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3 months ago

Part A: During what interval(s) of the domain is the water balloon's height increasing?

Mathematics

1 answer:

tester [12.3K]3 months ago

6 0

Answer:

Below is the answer

Step-by-step explanation:

The linear model illustrates the height, f(x), of a water balloon thrown from a building over time, x, in seconds: It shows ordered pairs at 0, 60 and 2, 75 and 4, 75 and 6, 40 and 8, 20 and 10, 0 and 12, 0 and 14, 0. The x-axis indicates Time in seconds, while the y-axis represents Height in feet. Part A: At what interval(s) is the water balloon's height increasing? (2 points) Part B: At what interval(s) does the water balloon's height remain constant? (2 points) Part C: At what interval(s) is the decrease in the water balloon's height most rapid? Use complete sentences to explain. (3 points) Part D: Utilizing real-world conditions, predict the water balloon's height at 16 seconds.

Answer:

Part A: The water balloon's height increases between 0 and 2 seconds, from 60 feet to 75 feet.

Part B: The balloon’s height remains at 75 feet from 2 to 4 seconds. At 10 seconds, it is at 0 feet.

Part C: The most rapid decrease in height occurs from 4 to 6 seconds, where it falls from 75 feet to 40 feet (about -17.5 ft/s).

From 6 to 8 seconds, it decreases from 40 feet to 20 feet (around -10 ft/s).

Between 8 and 10 seconds, it drops from 20 feet to 0 feet (also about -10 ft/s).

Therefore, the steepest decline is between 4 and 6 seconds.

Part D: Based on real-world constraints, at 16 seconds, the balloon will still be on the ground, so its height is 0 feet.

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What is the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008 . What might have been the

AnnZ [12381]

Answer:

The exact population of Vermont in 2008 could have been around 618,000

Step-by-step explanation:

* Here's how rounding to the nearest ten thousand works:

- Numbers ending with the last four digits between 0001 and 4999 are rounded down to the nearest lower multiple of ten thousand

- Example: 83,525 rounds down to 80,000.

- If the last four digits are 5000 or above, round up to the next higher ten thousand

- Example: 58,988 rounds up to 60,000

* Applying this rule to the problem given:

Since the rounded population is 620,000 to the nearest ten thousand, the actual population could be any value with the last four digits from 0001 to 4999 (like 618,000) or from 5000 upwards (like 624,000).

Therefore, 618,000 might represent the actual population of Vermont in 2008

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3 months ago

Moesha and Keyon are mailing invitations for their wedding. They have $50 to spend and each invitation costs $1.25 to mail. The

zzz [12365]

Answer:

The solution to the equation is 40

This indicates the max number of wedding invitations they can afford to send within their budget.

Step-by-step explanation:

To find the zero of the function, we set the dependent variable (here, m) to zero.

So we have;

0 = 50-1.25w

1.25w = 50

w = 50/1.25

w = 40

What implication does this have in this context?

Essentially, it means that the couple can send out invitations to a total of 40 people based on their budget.

7 0

2 months ago

1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms? Round your answer t

AnnZ [12381]

The weight of an orangutan is 64.5 kilograms

Solution:

It is stated that the orangutan's weight is 142 pounds

Additionally,

1 kilogram is approximately 2.2 pounds

We will now convert 142 pounds into kilograms

1 kilogram = 2.2 pounds

$\text{1 pound } = \frac{1}{2.2} \text{ kilograms }$

As a result, 142 pounds translates to

$142 \text{ pound } = \frac{1}{2.2} \times 142 \text{ kilogrmas }$

$\rightarrow \frac{1}{2.2} \times 142 = 64.545 \text{ kilograms }$

When rounding to the nearest tenth, we obtain 64.5 kilograms

Therefore the mass of the orangutan is 64.5 kilograms

3 0

2 months ago

The monthly cost of running a small business consists of retail space rental at $2400, wages at $1800 and utilities at $480. If

lawyer [12517]

Response:

5.8%

Detailed reasoning:

For the business,

retail space rental = $2400

wages = $1800

utilities = $480

Total operating cost = $4680

However,

retail space rent decreased by 5%, which results in;

5% of $2400 = 0.05 x $2400 = $125

The new rental amount for retail space = $2400 - $125

= $2275

wages were lowered by 6%, calculated as;

6% of $1800 = 0.06 x $1800 = $108

The revised wages = $1800 - $108

= $1620

Utilities experienced a 7% increase, calculated as;

7% of $480 = 0.07 x $480 = $33.6

The adjusted utilities cost = $480 + $33.6

= $513.6

New total operating costs = $2275 + $1620 + $513.6

= $4408.6

The percentage change in monthly expenses = $\frac{(4680 - 4408.6)}{4680}$ x 100%

x 100% $\frac{271.4}{4680}$ = 5.8%

8 0

1 month ago