Solve your formula from problem 12 for m. Then find the taxi driver’s hourly rate of his pickup rate is $2 and he charges $19.50 for a 7 - mile trip

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: 2900 Square Feet

Step-by-step explanation: i took the test

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.

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]

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.

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 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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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:

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] .