if I drop a book from the same height as a feather which will land first?

Final answer:

The average yearly decrease in the value of Juan's baseball card collection, which decreased by $300 over 5 years, is $60. This integer represents the yearly reduction in value.

Explanation:

Juan's baseball card collection was worth $800. Over the last 5 years, the collection decreased by $300 in value. To find the average decrease in value each year, we can use the formula: Average decrease per year = Total decrease / Number of years.

Given that the total decrease is $300 and the time period is 5 years, the calculation would be:
Average decrease per year = $300 / 5 = $60.

Therefore, the integer that represents the average decrease in value each year for Juan's baseball card collection is $60.

The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.

We have,

Let x be the number of pounds of hamburgers that Andrew purchases, and let y be the number of pounds of hot dogs that he purchases.

The cost of x pounds of hamburgers is 3x dollars, and the cost of y pounds of hot dogs is 2y dollars.

According to the problem, Andrew has budgeted a maximum of $60 for hamburgers and hot dogs.

Therefore, we can write the following inequality:

3x + 2y ≤ 60

This inequality describes the possible combinations of x and y that Andrew can purchase, such that the total cost of hamburgers and hot dogs does not exceed his budget of $60.

Thus,

The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.

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Answer:

B

Step-by-step explanation:

The slope intercept equation is [tex]y=\frac{4}{3}x+1[/tex] is true statement. Option C is correct.

From the given information the slope of the line is 4/3 and it is passing through point (3, 5).

Now, determine the equation of line in slope intercept form.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

To find the equation, first find the y intercept by considering the point values (3, 5).

[tex]5 = \frac{4}{3}+b[/tex]

[tex]5=4+b[/tex]

[tex]b=1[/tex]

Now plug in the values of slope and y intercept in slope intercept form:

[tex]y=\frac{4}{3}x+1[/tex]

Hence, Option C is correct, he equation of the line is [tex]y=\frac{4}{3}x+1.[/tex]

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The complete question is given in the attachment.

The vertex form of a quadratic equation is expressed as y = a(x - h)^2 + k. The vertex of the parabola is (-1, 2)

The vertex form of a quadratic equation is expressed as:

y = a(x - h)^2 + k

where (h, k) is the vertex of the equation

Given the equation of the parabola as  y = (x - 1)^2 + 2, On comparing;

h = -1

k =2

Hence the vertex of the parabola is (-1, 2)

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The fourth term in the arithmetic sequence 13, 10, 7 is 4.

The arithmetic sequence 13, 10, 7 has a common difference of -3. To find the fourth term, we can start with the first term and keep subtracting the common difference. So, 13 - 3 = 10, 10 - 3 = 7, and 7 - 3 = 4. Therefore, the fourth term in the arithmetic sequence 13, 10, 7 is 4.

Answer:

D. All positive real numbers

Step-by-step explanation:

The range of a function f(x) are all the possibles values that f(x) can take. So in  the function of the question it doesn't matter what value takes x, f(x) is always going to be a positive number. For example:

f(0)=[tex]4^{0}[/tex]=1

f(-1)=[tex]4^{-1}[/tex]=1/4

f(2)=[tex]4^{2}[/tex]=16

Then, the range of f(x) is all positive real numbers.

Answer: Cost per mile m = $4.78.

Step-by-step explanation:

Since we have given that

Pick up rate = $2

Charges for a 7 mile trip = $19.50

Charges for a mile trip would be

[tex]\dfrac{19.50}{7}\\\\=2.78[/tex]

So, amount of taxi's drivers is given by

[tex]\$2.78+\$2\\\\=\$4.78[/tex]

Hence, cost per mile m = $4.78.

Answer:

5.69999

Step-by-step explanation:

To find the mass of a stack of 20 pennies, multiply the mass of a single penny by 20.

Mass of a single penny: A single penny weighs around 3 grams on average.

Answer:

The volume flow rate of the air being pumped into the football is approximately [tex]\( 5.261 \times 10^{-7} \)[/tex] cubic feet per second.

Explanation:

To find the volume flow rate of the air being pumped into the football, we first need to calculate the cross-sectional area of the needle of the pump.

Given:

- The radius of the needle, [tex]\( r = 4.5 \)[/tex] millimeters.

The cross-sectional area, [tex]\( A \)[/tex], of the needle can be calculated using the formula for the area of a circle:

[tex]\[ A = \pi r^2 \][/tex]

Converting the radius from millimeters to feet:

[tex]\[ r = \frac{4.5}{1000} \text{ feet} \][/tex]

Now, let's calculate the cross-sectional area:

[tex]\[ A = \pi \left( \frac{4.5}{1000} \right)^2 \][/tex]

[tex]\[ A \approx \pi \left( \frac{0.0045}{1000} \right)^2 \][/tex]

[tex]\[ A \approx \pi \times 2.025 \times 10^{-8} \text{ square feet} \][/tex]

Now, we can find the volume flow rate, [tex]\( Q \)[/tex], of the air being pumped into the football. The volume flow rate is the product of the cross-sectional area of the needle and the speed of the air:

[tex]\[ Q = A \times \text{Speed} \][/tex]

Given:

- Speed of the air, [tex]\( \text{Speed} = 8.2 \)[/tex] ft/s

Now, let's calculate the volume flow rate:

[tex]\[ Q = \pi \times 2.025 \times 10^{-8} \text{ square feet} \times 8.2 \text{ ft/s} \][/tex]

[tex]\[ Q \approx 5.261 \times 10^{-7} \text{ cubic feet/s} \][/tex]

Answer: 2900 Square Feet

Step-by-step explanation: i took the test

The correct option is:  A.  2 years

Explanation

The given growth equation is:   [tex]20000e^0^.^1^5^t = 28000[/tex], where  [tex]t[/tex] is the number of years the population has been growing.

For finding the number of years, we will solve the above equation for  [tex]t[/tex].

First, dividing both sides by 20000, we will get........

[tex]\frac{20000e^0^.^1^5^t}{20000}=\frac{28000}{20000}\\ \\ e^0^.^1^5^t = 1.4[/tex]

Now taking 'natural log' on both sides, we will get........

[tex]ln(e^0^.^1^5^t)=ln(1.4)\\ \\ 0.15t*ln(e)= ln(1.4)\\ \\ 0.15t*1=ln(1.4)\\ \\ t=\frac{ln(1.4)}{0.15}=2.243..... \approx 2[/tex]

So, the population of the town has been growing about 2 years.

The town has been growing for 17 years

Given the exponential function

Given the expressions 20,000e^0.15t=28,000

We are to find the value of "t" which is the time.

e^0.15t = 28000/20000

e^0.15t = 7/5

e^0.15t = 1.4

Take the ln of both sides

lne^0.15t = ln 1.4

0.15t = 2.639

t = 2.639/0.15

t = 17years

Hence the town has been growing for 17 years

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