if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?

Answer:

5.69999

Step-by-step explanation:

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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Answer:

0.1151

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 500, \sigma = 75[/tex].

What is the probability that a family spends less than $410 per month?

This probability is the pvalue of Z when X = 410. So:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{410 - 500}{75}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151. This is the answer.

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:

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]

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: 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.

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:

The circumference of a circle is  [tex]72\pi [/tex] .

Step-by-step explanation:

Forrmula

[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]

Where r is the radius of the circle .

As given in the question

The radius of the circle is 36 inches .

Put all the values in the formula

[tex]Circumference\ of\ a\ circle = 2\times 36\pi [/tex]

[tex]Circumference\ of\ a\ circle = 72\pi [/tex]

Therefore the circumference of a circle is  [tex]72\pi [/tex] .

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.

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.

Answer: 2900 Square Feet

Step-by-step explanation: i took the test