A robot can complete 7 tasks in 4/5 hour. Each task takes the same amount of time.

First calculate the total amount of liters consumed:

Volume gas consumed = (6 L / 100 km) * 2000 km = 120 L

Then calculate the total cost:

Cost = ($1.20 / L) * 120 L = $144

Since there are three of them, so each must pay:

Payment of each = $144 / 3 = $48 per person

Answer:

$48 per person

The equation of the line passing through the point (-3,6) with a slope of a third is y = 1/3x + 7. The graph of this line can be drawn by plotting the y-intercept at (0,7) and using the slope to plot other points.

The provided point through which the line passes is (-3,6) and the slope is a third. The general slope-intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept. That is, it represents the point where the line intersects the y-axis.

Let's use this information to find the equation of the line. We know that y = mx + b. We can substitute the slope (m=1/3) and the point (-3, 6) into this equation: 6 =(1/3)(-3) + b.

Solving this for b gives us b = 6 + 1 = 7. Therefore, the equation of the line in slope-intercept form is y = 1/3x + 7.

To graph the line, you can start by plotting the y-intercept at (0,7) on the y-axis, then rise 1 unit and run 3 units (since the slope = rise/run = 1/3) from the y-intercept point to plot the second point. Connect these points to draw the line.

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To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2. The two points are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2.

First, we find the derivative of the function:

dy/dx = 3x^2 - 12x - 34

Next, we set the derivative equal to 2 and solve for x:

3x^2 - 12x - 34 = 2

3x^2 - 12x - 36 = 0

Using the quadratic formula, we find the solutions for x:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values a = 3, b = -12, and c = -36 into the quadratic formula, we get:

x = (-(-12) ± √((-12)^2 - 4(3)(-36)))/(2(3))

x = (12 ± √(144 + 432))/6

x = (12 ± √(576))/6

x = (12 ± 24)/6

x = 12/6 ± 24/6

x = 2 ± 4

So the two points where the slope of the tangent line is 2 on the curve are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

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Final answer:

To make the lengths the same, she would have to cut 0.3 feet from the longer piece.

Explanation:

To find the amount she would have to cut to make the two lengths the same, we need to subtract the smaller length from the larger length.

The first length is 3 4/5 feet, which can also be written as 3 + 4/5 = 3 + 0.8 = 3.8 feet.

The second length is 3 1/2 feet, which can also be written as 3 + 1/2 = 3 + 0.5 = 3.5 feet.

Subtracting the smaller length (3.5 feet) from the larger length (3.8 feet), we get:

3.8 feet - 3.5 feet = 0.3 feet.

So she would have to cut 0.3 feet from the longer piece to make the lengths the same.

A) unknown information is how much she spent on the taxi ride

B) 31 = x +16+6

C ) 31= x +22

     x =31-22 = 9

   She spent $9 on the taxi

(A) How much money Hera spent on the taxi ride.

(B) 31 = x + 16 +6

(C) 16 + 6 = 22 31 - 22 = 9

(D) She spent $9 on the taxi.

(also sorry im uh 4 years late aldksjfladfoajsdflkj)

use order of operations

8^2 = 64

4(64+4*4*8)

4(64+128)

4(192)

768

Answer:

CHEATING

Step-by-step explanation:

becaus eI got it right on egde

The information given that the skier covered 2.6509 miles is wrong because the decimal was wrongly put.

Since the cross-country skier skied at a rate of 10.82 miles per hour, it should be noted that in 2.45 hours, we've to multiply 10.82 miles by 2.45 hours and this will be:

= 10.82 × 2.45

= 26.509 miles

From the information given, we are told that in 2.45 hours, the skier covered 2.6509 miles, this is incorrect as the miles covered is 26.509 miles.

Therefore, information given that the skier covered 2.6509 miles is wrong because the decimal was wrongly put.

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To calculate the property taxes on a townhouse valued at $73,000, divide the value by $100 to find the number of $100 increments, and then multiply this by the tax rate of $1.15.

To find the property taxes on a townhouse valued at $73,000, we need to calculate the tax amount based on the given tax rate. The tax rate is $1.15 for every $100 of home value.

First, we need to find how many $100 increments are there in the home value.

Divide $73,000 by $100:

$73,000 ÷ $100 = $730

Now, multiply the number of $100 increments by the tax rate:

$730 × $1.15 = $839.50

Therefore, the property taxes on a townhouse valued at $73,000 would be $839.50.

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Carrier A is 2104 feet long and carrier B is 2094 feet.

This problem can be solved using simple algebra. Let's denote the length of carrier A as 'a' and the length of carrier B as 'b'. We know two things about these lengths from the question:

Now, you can add these two equations together to eliminate 'b'. This will give: 2a=4208. Hence, by dividing by 2, you will find that a=2104. Now, substitute a=2104 back into the first equation: a+b=4198. This will give: 2104+b=4198, which simplifies to b=2094. So, the length of carrier A is 2104 feet and the length of carrier B is 2094 feet.

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Writing 3.441 in expanded form shows that each digit represents a different value depending on its place in the decimal number. This is determined by the power (exponent) of 10 corresponding to the decimal shift from the right side of the digit. This understanding is essential for scientific notation and handling large and small numbers.

Writing the number 3.441 in expanded form helps to clarify why the same digit can possess different values based on its position in the decimal number. To write 3.441 in expanded form we break it down into the addition of its respective place values, like this:

3.441 = 3 x 1 + 0.4 x 1/10 + 0.04 x 1/100 + 0.001 x 1/1000.

As we can see, each digit represents a different value based on its placement. This is determined by the power (exponent) of 10 which is equal to the number of places the decimal is shifted from the right side of the digit. This method is also applicable to scientific notation, transforming both very large and very small numbers into more manageable expressions for calculations.

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The probability of drawing an ace and rolling a "2" is 0.012859.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the probability of drawing an ace from a deck of cards is 0.077 and the probability of rolling a "2" using a fair die is 0.167.

The probability of drawing an ace and rolling a "2" is calculated as,

Probability = 0.077 × 0.167

Probability = 0.012959

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Final answer:

Larry's new solution has an approximate salt concentration of 11.33%. This was calculated by adding the initial mass of salt in the solution (10.5 g) to the extra salt added (15 g), resulting in a new total mass of salt (25.5 g), then dividing by the total mass of the new solution (225 g), and finally multiplying by 100%.

Explanation:

To find the percent of salt in Larry's new solution, we first need to calculate the total mass of the solution and how much of that mass is salt. Initially, we have 210 grams of a 5% salt solution. To find out how much salt that is, we use the percentage:

210 g × 0.05 = 10.5 g of salt

Now, Larry adds 15 grams of salt to this solution, so we add that amount to the initial salt mass:

10.5 g + 15 g = 25.5 g of salt

The total mass of the new solution is the sum of the mass of the original solution and the added salt:

210 g + 15 g = 225 g

Finally, to find the mass/mass percent concentration of the new solution, we divide the total mass of salt by the total mass of the solution and multiply by 100%:

((25.5 g / 225 g) × 100% = 11.33%

So, the percent of salt in Larry's new solution is approximately 11.33%.

Answer:  The required simplified fraction is [tex]\dfrac{2}{1}.[/tex]

Step-by-step explanation:  We are given that in a grocery store there are 4 self-checkout lines and 8 lines with cashiers.

We are to find the ratio of the number of lines with cashiers to the number of self-checkout lines.

Let n represents the number of lines with cashier and m represents the number of self-checkout lines.

Then, we have

n = 8 and  m = 4.

Therefore, the required ratio of the number of lines with cashiers to the number of self-checkout lines is given by

[tex]\dfrac{n}{m}=\dfrac{8}{4}=\dfrac{2}{1}.[/tex]

Thus, the required simplified fraction is [tex]\dfrac{2}{1}.[/tex]

The differential equation for the amount of salt a(t) in the tank at time t > 0 is dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t).

To find the differential equation for the amount of salt a(t) in the tank at time t > 0, we need to consider the rate of change of the salt concentration in the tank.

Let A(t) represent the amount of salt in the tank at time t. The salt entering the tank each minute is given by the concentration (4 lb/gal) multiplied by the rate of inflow (3 gal/min), which is 12 lb/min.

The salt leaving the tank each minute is given by the concentration in the tank (A(t)/V(t)) multiplied by the rate of outflow (2 gal/min), which is 2A(t)/(35 + (3 - 2)t).

Therefore, the rate of change of the salt in the tank is given by the difference between the rate of inflow and the rate of outflow: dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t). This is our differential equation for the amount of salt in the tank.

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