Three janitors work the night shift at the local hospital. Working alone, it takes Marla five more hours than it takes Tom, and it takes Bob four times as long as it takes Marla. So in one hour, Tom can clean 1 1 of the building. Marla can clean of the building and Bob can clean of the building. If x + 5 4x + 20 all three janitors work together, how much of the building can they clean in one hour?
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Answer: f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Step-by-step explanation: Using the given recursive formula:

f(1) = 0

f(n) = f(n-1) + 2

We can find the values of f(n) for different values of n:

f(1) = 0

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

f(5) = f(4) + 2 = 6 + 2 = 8

And so on.

We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:

f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Answer:

-13

Step-by-step explanation:

-6 + 28 ÷ (-4)​

= -6 - 7

= -13

So, the answer is -13

The interpretation of the slope and y-intercept of this equation is that: C. The slope predicts a temperature increases of about 1/6 for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x = 0), the temperature is 60 degrees.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Since Ronnie determined that the association between the number of chirps per minute (x) that crickets make at different temperatures (y) in degrees Fahrenheit is linear and that the line of best fit is given by;

y = 1/6(x) + 60

By comparison, we have the following:

Slope, m = 1/6.

y-intercept = 60.

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The two triangles are congruent since they have equal angles and equal sides.

Congruent triangles are two triangles that have exactly the same size and shape.

In other words we can say that they have the same angles and the same side lengths.

So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.

For the given triangles

The missing value of angle C = 180 - (18 + 110) = 52⁰

The missing value of angle F = 180 - (18 + 52) = 110⁰

So it is obvious that the two triangles are congruent since they have equal angles and equal sides.

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To find when the two equations 65x + 20 = y and 730 + 35x = y will meet on the graph, we need to solve for the value of x that satisfies both equations.

We can begin by setting the right-hand sides of the two equations equal to each other:

65x + 20 = 730 + 35x

Subtracting 35x from both sides, we get:

30x + 20 = 730

Subtracting 20 from both sides, we get:

30x = 710

Dividing both sides by 30, we get:

x = 23.67

Now that we have found the value of x that satisfies both equations, we can substitute it into either equation to find the corresponding value of y. Let's use the first equation:

y = 65x + 20

y = 65(23.67) + 20

y = 1539.55

Therefore, the two equations will meet on the graph at the point (23.67, 1539.55).

The diameter of Earth is about 2.7 times greater than the diameter of Mercury.

We have,

to determine the scale factor

Given the following values

Diameter of Mercury = 4.9×10^3km

Diameter of Earth = 1.3×10^4km

Taking the ratio of the diameters:

Ratio =  1.3×10^3/4.9×10^4

Ratio = 2.7

This shows that the diameter of Earth is about 2.7 times greater than the diameter of Mercury.

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complete question:

The diameter of Mercury is approximately 4.9×103 kilometers. The diameter of Earth is approximately 1.3×104 kilometers. About how many times greater is the diameter of Earth than the diameter of Mercury? 2.7 27 270 2700

The solution is,  2.5 miles per hour was her walking rate in miles per hour.

We know that,

Speed is measured as distance moved over time.

The formula for speed is speed = distance ÷ time.

To work out what the units are for speed, you need to know the units for distance and time.

In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

Here, given that,

Bao walked 15 miles in 6 hours.

so, we get,

in 6 hours = 15 miles

so, in 1 hour = 15 / 6 miles

                    =2.5 miles

Hence, The solution is,  2.5 miles per hour was her walking rate in miles per hour.

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Answer:

x = 8

Step-by-step explanation:

[tex]5|x-8|+2=2 \\ −5∣x−8∣=0 \\ ∣x−8∣=0 \\ x = 8[/tex]

First, you need to cancel out the 2 by subtracting 2 from both sides. Then, we divide both sides by -5. And finally, we remove the absolute value.

Answer:

( x - 3 ) 3 .

Step-by-step explanation:

Since f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) ) = x , then f−1(x)=3√x+3 f - 1 ( x ) = x 3 + 3 is the inverse of f(x)=(x−3)3 f ( x ) = ( x - 3 ) 3 .

C. The function that describes the area A, in square feet, in terms of x is A(x) = 2x^2 + 9x + 4

To find the area A of a rectangle, you multiply its length by its width. In this case, the side lengths of the rectangle are (x+4) feet and (2x+1) feet. So, we can write the area function A(x) as follows:

A(x) = (x+4)(2x+1)

Now, we'll expand the expression:

A(x) = x(2x+1) + 4(2x+1)

A(x) = 2x2 + x + 8x + 4

Now, combine like terms:

A(x) = 2x^2 + 9x + 4

So, the correct answer is:

C.) A(x) = 2x^2 + 9x + 4

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The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.

Let's expect that the round and hollow drum includes a stature of h and a span of r.

The volume of a barrel is given by: V = πr^2h.

We know that the drum includes a capacity of 806 cubic yards, so able to compose:

πr^2h = 806

We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.

The zone of the beat and foot of the drum is given by: A = πr^2.

The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:

C_topbottom = 2A = 2πr^2

The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:

A_side = 2πrh

The whole fetched of building the drum is in this manner:

C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh

Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:

h = 806/(πr^2)

Substituting this expression for h into the taken a toll condition, we get:

C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r

To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:

dC/dr = 4πr - 27404/r^2 =

Fathoming for r, we get:

r = (27404/(4π))^(1/3) ≈ 10.19 yards

Substituting this esteem of r back into the expression for h, we get:

h = 806/(π(10.19)^2) ≈ 2.46 yards

Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:

Span: 10.19 yards

Stature: 2.46 yards

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The correct statements about the circle equation are:

Remember that the general circle equation is:

(x - a)² + (y - b)² = R²

Where (a, b) is the center and R is the radius.

Here the given equation is.

x² + y² - 2x - 8 = 0

We can complete squares in x to get:

(x - 1)² - 1 + y² - 8 = 0

(x - 1)² + y² = 9

(x - 1)² + y² = 3

So, the center is (1, 0) and the radius is 3.

The correct statements are:

The radius of the circle is 3 units.

The standard form of the equation is (x – 1)² + y² = 3.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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The solution to the system of linear equation is:

x = 10 2/3, y = 5

The correct option is the last option   10 2/3, 5

From the question, we are to solve the given system of linear equation.

The given system of linear equations is

1/2x + 1/3y = 7

1/4x + 2/3y = 6

Multiply the first equation by 2

1/2x + 1/3y = 7      × 2

x + 2/3y = 14

Subtract the second equation from the resulting equation

     x + 2/3y = 14

- 1/4x + 2/3y = 6

--------------------------

3/4x = 8

Multiply both sides of the equation by 4/3

4/3 × 3/4x = 8 × 4/3

x = 32/3

x = 10 2/3

Substitute the value of x into

x + 2/3y = 14

To determine y

(10 2/3) + 2/3y = 14

32/3 + 2/3y = 14

Multiply through by 3

32 + 2y = 42

Subtract 32 from both sides

32 - 32 + 2y = 42 - 32

2y = 10

Divide both sides by 2

2y / 2 = 10 / 2

y = 5

Hence, the solution is:

x = 10 2/3, y = 5

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For 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.

To find how much sauce and oregano will be needed to make 6 servings, we can use the ratio of sauce to oregano in the recipe.

For 4 servings, the recipe calls for 8 cups of sauce and 1/2 teaspoon of oregano. To find how much sauce and oregano are needed for 6 servings, we can set up a proportion:

sauce : oregano = 8 cups : 1/2 teaspoon = 16 cups : 1 teaspoon

So, for 6 servings, we need:

sauce : oregano = 16 cups : 1 teaspoon

To convert this to cups and tablespoons, we can multiply both sides of the proportion by 3/4:

sauce : oregano = (16 x 3/4) cups : (1 x 3/4) teaspoons

sauce : oregano = 12 cups : 3/4 teaspoon

sauce : oregano = 48 cups : 3 teaspoons

Therefore, for 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.

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The requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.

There are three ways to write a ratio:

Thus, the requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.

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Result:

The number of children having an age of 6 1/2 years more than 7 1/4 years = 3/4.

To do this, we would subtract the number of children who are 7 1/4 years old from the number of children who are 6 1/2 years old: x - y

Let x = number of children 6 1/2 years old

Let y = number of children 7 1/4 years old

x = 6 1/2 years or 13/2 years

y= 7 1/4 years or 29/4 years

= 13/2 - 29/4

= (26/4) - (29/4)

= -3/4

Coverting to the absolute value, we get:

|-3/4| = 3/4

Thus, 3/4 more children are 6 1/2 years old than 7 1/4 years old.

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To install the gas riser in 10 days, a total number of 11 plumbers would be needed.

We can use the formula:

(number of workers) × (time) = (constant amount of work)

Let's let x be the number of plumbers needed to install the gas riser in 10 days. We can set up the equation:

(7 workers) × (15 days) = (x workers) × (10 days)

Simplifying the left side, we get:

105 worker-days = (x workers) × (10 days)

Dividing both sides by 10 days, we get:

10.5 workers = x

Since we can't have a fraction of a worker, we need to round up to the nearest whole number.

Therefore, we would need 11 plumbers to install the gas riser in 10 days.

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To determine the range you need to evaluate and find a maximum/minimum if you can.

For a function f(x) = y, we define the range as the set of the possible outputs of the function.

So, to find the range of any function, we need to evaluate it and try to find the minimum and maximum values of the function. To do so it is useful to understand the behavior of different types of functions.

For example linear ones have a range of all the real numbers.

Quadratic ones have a range that depends on its vertex, and so on.

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The radius of the sphere with a volume of 10000 m³ is approximately 13.4 meters.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the volume of the sphere is 10000 m³, we can set up the equation:

Volume =  (4/3)πr³

r³ = Volume / (4/3)π

r = ∛( Volume / (4/3)π )

r = ∛( 10000/ ( (4/3) × 3.14) )

r = 13.4 m

Therefore, the radius is 13.4 m.

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Answer:

a=52+b

Step-by-step explanation:

he earns $52 without selling books.

since he only earns 1$ per book, there is no need to put it as the coefficient of b since it won't change

therefore,

$52+b=a or a=$52+b

The formula for T in terms of m and p is: [tex]T = 15m + 40p[/tex]

We are given that number of marbles in each small bag is 15, and Rosanna sells m small bags, so the total number of marbles in the small bags is: [tex]15m[/tex]

Also given that number of marbles in each large bag is 40, and Rosanna sells p large bags, so the total number of marbles in the large bags is:[tex]40p[/tex]

So, total number of marbles that Rosanna sells is the sum of the marbles in the small bags and in the large bags will be addition of both values which will give us: [tex]T = 15m + 40p[/tex].

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The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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Answer:

[tex]\huge\boxed{\sf Mean = 11.1 \ hours}[/tex]

Step-by-step explanation:

18, 7, 6, 13, 8, 17, 9

[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data} \\\\Mean = \frac{18+7+6+13+8+17+9}{7} \\\\Mean = \frac{78}{7} \\\\Mean = 11.1 \ hours\\\\\rule[225]{225}{2}[/tex]

Answer:

11.1

Step-by-step explanation:

The mean is simply the average of a given set of numbers

To find the mean we find the sum of the given numbers and divide that by the number of given values.

Given set of values:

Mean:

The mean of the number of hours the students watched of tv is 11.1 hours

Answer:

  $264

Step-by-step explanation:

You want to know Jenny's annual finance charges if her credit card balance averages $1100 and her interest rate is 24%.

The annual interest charge will be the product of the annual interest rate and the average balance over the course of the year.

  24% × $1100 = $264

Jenny spends about $264 per year on credit card interest.

Answer:

May is 52 inches tall

Step-by-step explanation:

stephan=46in

sister=6+stephan(in inches)=6+46=52

Answer: 2 2/3+ 8

Step-by-step explanation: it goes 2 under the ten

Answer:

See provided explanation

Step-by-step explanation:

Slope=change in y/change in x

General equation for a line: y=mx+b

You know that the slope(m) is 8/3, and the y-intercept is 8. So your graph will intersect the y axis at the point (0,8). from there, use slope=rise/run to graph the remaining points. Starting at (0,8), move 8 up and 3 right, this is your next point. Do the same in the other direction, starting at (0,8) move down 8 and left 3 points. Doing this will get you the points (-3,0) and (3,16). repeat this process until you have enough points to form a line. I attatched a picture of what the graph should look like.

The lines are neither parallel nor perpendicular to line p

From the question, we have the following parameters that can be used in our computation:

y = -3x + 10

As a general rule

Using the above as a guide, we have the following:

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Answer:

A. The blue line has the slope with the greatest value. The blue line is the steepest of the lines.

Answer:$ 24,679.20 or 514.15 a month

Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20