Your car averages 380 miles on a 14-gallon tank of gas. You run out of gas on a deserted highway, but have One-half gallon of lawn mower gas with you. At the current rate of travel, how far will you be able to go and will you reach the nearest gas station 15 miles away?

Henry's savings in Week 10 would be $\(15.50\).

Based on the given information, Henry's savings appear to be increasing by $\(1.00\) every week. The pattern suggests that there is a constant increment of $\(1.00\) in the savings amount from week to week.

To find Henry's savings in Week 10, we can use the following formula for an arithmetic sequence:

\(\[ a_n = a_1 + (n-1)d \]\)

where \(a_n\) represents the nth term, \(\(a_1\)\) is the initial term, \(\(n\)\) is the position of the term, and \(d\) is the common difference.

In this case, the initial term \(a_1\) is $\(6.50\) and the common difference \(\(d\)\) is $1.00. Substituting these values into the formula, we can find Henry's savings in Week 10 \((\(a_{10}\))\):

\(\[ a_{10} = $6.50 + (10-1) \times $1.00 \]\[$6.50 + 9 \times $1.00 \] $6.50 + $9.00 \]\\ $15.50 \]\)

Therefore, if the pattern continues, Henry's savings in Week 10 would be $\(15.50\).

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Answer:

The standard form of the equation of a circle with center at (h, k) and radius r is:

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

We are given that the center of the circle is (4, -1), so h = 4 and k = -1. We also know that the circle passes through the point (-4, 1), which means that the distance from the center of the circle to (-4, 1) is the radius of the circle.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So the radius of the circle is:

r = sqrt((-4 - 4)^2 + (1 - (-1))^2) = sqrt(100) = 10

Now we can substitute the values of h, k, and r into the standard form equation of a circle:

(x - 4)^2 + (y + 1)^2 = 10^2

Expanding the equation gives:

x^2 - 8x + 16 + y^2 + 2y + 1 = 100

Simplifying and putting the equation in standard form, we get:

x^2 + y^2 - 8x + 2y - 83 = 0

Therefore, the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1) is:

x^2 + y^2 - 8x + 2y - 83 = 0

Answer:

Step-by-step explanation:The car will appear to be 0.8 m behind the mirror.

Answer:

The size of the image is 4/9 times larger than the actual size of the truck.

the image is magnified and virtual

Step-by-step explanation:

We can use the mirror formula to find the position and nature of the image formed by the rear-view mirror in the car:

1/f = 1/u + 1/v

where:

f = radius of curvature of the mirror = 4m (given)

u = distance of the object (the truck) from the mirror = -5m (negative sign indicates that the object is behind the mirror)

v = distance of the image from the mirror (positive sign indicates that the image is in front of the mirror)

Substituting the given values, we get:

1/4 = 1/-5 + 1/v

Simplifying this equation, we get:

v = m

v=20/9 m

This means that the image of the truck is formed at a distance of 20/9meters from the rear-view mirror, behind the driver's seat.

To find the size of the image relative to the size of the truck, we can use the magnification formula:

m = v/u

Substituting the values we get:

m =(-20/9) / (-5) = 4/9

This means that the image of the truck formed by the rear-view mirror in the car is 4/9 times larger than the actual size of the truck.

So, the image is magnified and virtual (since the image is formed behind the mirror), and its distance from the mirror is 20/9 meters. The size of the image is 4/9 times larger than the actual size of the truck.

The exponential function that represents this situation is 25000(1.03)ˣ

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

Inital visitors, a = 25000

Rate of increase, r = 3%

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

The function of the situation is

f(x) = a * (1 + r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 25000 * (1 + 3%)ˣ

So, we have

f(x) = 25000(1.03)ˣ

Hence, the function is 25000(1.03)ˣ

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The magnitude of the resultant force is approximately 9.07 lb.

We have,

To use the parallelogram rule to find the magnitude of the resultant force for the two forces, we first draw a diagram:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb)  |

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

where A and B are the magnitudes of the given forces, and θ is the angle between them.

Using the parallelogram rule, we draw a parallelogram with sides AB and BC:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb) D

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

The diagonal BD represents the magnitude and direction of the resultant force.

To find its magnitude, we use the Law of Cosines:

BD^2 = AB^2 + BC^2 - 2(AB)(BC)cos(θ)

BD^2 = (7 lb)^2 + (11 lb)^2 - 2(7 lb)(11 lb)cos(133 degrees)

BD^2 = 49 + 121 - 2(77)cos(133 degrees)

BD^2 = 170 - 154cos(133 degrees)

BD ≈ 9.07 lb (rounded to two decimal places)

Therefore,

The magnitude of the resultant force is approximately 9.07 lb.

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The given graph representing function is a relation.

For the given question,

For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.

Thus, the graph shows the relation of the function.

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Answer:

no.

Step-by-step explanation:

Answer: -2x-18

Step-by-step explanation:

Answer:

B( 11

Step-by-step explanation:

90-35 = 55

55÷5 = 11

X equals 11

Answer:

like terms are 12x and -3x, 9 and -4.

Step-by-step explanation:

12x and -3 have a variable of x. 9 and -4 are constants. Since they are like terms you can group them to be 9x+5. 12x-3x is 9x and 9-4 is 5.

Hi!

Answer:

12,879

Step-by-step explanation:

If 477 toys are sold and they each cost $27 then you times 477 by 27(because you could add 27 to 27 477 times but that would take forever and this is the equivalent of that)

Hope this helped :)

Answer:

Step-by-step explanation:

1 )

\(\frac{2}{5}( \frac{5x}{4} - \frac{10}{3})-\frac{4x}{3} \\\frac{x}{2} - \frac{4}{3} - \frac{4x}{3}\\ \frac{-5x}{6}-\frac{4}{3}\)

2 )

\(\frac{17x}{8}+\frac{3x}{4}+\frac{1}{6}-\frac{7x}{12}+\frac{17}{3}\\ \frac{51x}{24}+\frac{18x}{24}-\frac{14x}{24}+\frac{35}{6}\\\frac{55x}{24}+\frac{35}{6}\)

The solution is, the percent of error, rounded to the nearest percent is 25%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

now, we have to find the percent of error, rounded to the nearest percent.

so, we get,

Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

so, error = 750 - 600

              = 150

so, we get,

the percent of error = 150 * 100 / 600

                                 = 25%

Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.

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Answer:

4x+7=3x+7

Step-by-step explanation:

-3(2x-5)=15-6x is infinite solution

top left is x=-3

top right is x=5 5x

A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

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Given:

\(4\dfrac{1}{2}\) subtracted from 5.33.

To find:

The value for the given statement.

Solution:

\(4\dfrac{1}{2}\) subtracted from 5.33 can be written as:

\(5.33-4\dfrac{1}{2}\)

On simplification, we get

\(=5.33-\dfrac{8+1}{2}\)

\(=5.33-\dfrac{9}{2}\)

\(=5.33-4.5\)

\(=0.83\)

Therefore, the correct option is C.

Answer:

m<10 = 92°

m<5 = 106° (I think because of correspondence)

m<8 =92°

m<14 = 74°

m<3 = 106°

<1 and <4 are corresponding angles

<2 and <3 are same side interior angles

<3 and <4 are vertical angles

<4 a d <6 are Alt. Interior Angles

Answer:

Step-by-step explanation:

It is important to have these skills because you want to show everyone that you have the skills and the determination to be an accountant

Answer: 19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

9+10=21

Wait...

We move all terms to the left:

7x-19-(x+5)=0

We get rid of parentheses

7x-x-5-19=0

We add all the numbers together, and all the variables

6x-24=0

We move all terms containing x to the left, all other terms to the right

6x=24

x=24/6

x=4

Answer:

93.84

Step-by-step explanation:

I think I'm not sure

Answer:

8

Step-by-step explanation:

A=a+b/2h

120=13+17/2h

120=30/2h

120/15=h

h=8 m

Answer:64

Step-by-step explanation:16 × 4

An airplane has an airspeed of 528 mi/hr bearing 25⁰ west of north. The path can be described as a vector v =  (528 cos 115⁰) i + (528 sin 115⁰) j

Suppose we have a vector  with magnitude v and angle α with the positive x-axis, then the vector can be expressed as its component as:

vx = v cos α

vy = v sin α

or

v = vx i + vy j

v =  (v cos α) i +  (v sin α) j

In the given problem, the magnitude is 528, while the angle is:

α = 25⁰ west of north = 25⁰ + 90⁰ = 115⁰

Hence,

vx = 528 cos 115⁰

vy = 528 sin 115⁰

v =  (528 cos 115⁰) i + (528 sin 115⁰) j

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Answer: 112 business cards

Step-by-step explanation:

    We will divide the number of business cards by the number of days cards were handed out to see how many cards were handed out per day.

5,376 cards / 48 days = 112 business cards

Answer:

$16.67

Step-by-step explanation:

$19.38*14%=$2.71

$19.38-2.71=$16.67

Answer with Explanation:

The YMZ and QMP are Identical, which means that they both have the same shape and size or one can be obtained by Gemomatrically transforming the other:

The remaining measurements are as follows:

Answer:

45 + .25x

Step-by-step explanation:

x represents the thing that changes, assuming this is for any given month and not multiple, 45 + .25x would be the answer