a boat used 1/24 of a gallon of gas to drive 1/3 of a mile.At this rate how many miles can the boat go using 1 gallon of gas.

The correct option is A. x = 1(1/3) and y = 2(1/3) in the mixed fractions.

A system of equations is a collection of equations that all have the same variables.

Now, the given equation in the question are-

7x - y = 7      ........(equation 1)

and x + 2y = 6     ........(equation 2)

Multiplying both side of equation 1 with 2, we get

14x - 2y = 14         ........(equation 3)

Add equation 2 and 3.

x + 2y + 14x - 2y = 6 + 14

15x = 20

x = 4/3

x = 1(1/3)

Substitute the value of x in equation 1.

4/3 + 2y = 6

2y = 6 - 4/3

2y = 14/3

y = 7/3

or y = 2(1/3)

Therefore, the values for variables x and y are calculated as:

x = 1(1/3) and y = 2(1/3).

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a) Both the length and the width of the rectangle are square roots of integers.

b) The length and the width of the rectangle are 6√5 units and 3√5 units, respectively.

Irrational numbers are numbers that not rational, that is, numbers that not of the form m / n, where m and n are integers and n is different of zero. Rational numbers may be integers or not.

Now, the statement indicates that the length and the width of rectangle have measures of 2 · x and x, respectively, and that the area of the rectangle is equal to 90 square units. The area formula is presented below:

90 = (2 · x) · x

90 = 2 · x²

x² = 45

x = √45

x = √(9 × 5)

x = √9 × √5

x = 3√5

a) Both the length and the width of the rectangle are square roots of integers.

b) The length and the width of the rectangle are 6√5 units (approx. 13.416 units) and 3√5 units (approx. 6.708 units), respectively.

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The picnic area is 20 inches wide in the drawing in her scale of 1 inch : 4 yards.

Unitary method is a technique for first solving the value of a single digit unit and from there we can find the value of any given unit.

According to the given question lillian drew a scale drawing of a county park. the scale she used was 1 inch : 4 yards.

The picnic area is 80 yards wide in real life.

∴ The width of the picnic area in here drawing in inches will be

= 80/4 inches.

= 20 inches.

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Answer:

Step-by-step explanation:

135.8 minus 47.5

Functions are expressed by writing a variable in terms of other variables known as the independent. The derivative of the given function is -3/(x-2)².

Given the function below;

f(x) = 3/x-2

Since it is a quotient, we can use the quotient rule to express the equation as shown:

let u = 3 and v = x -2

du/dx = 0 and dv/dx = 1

According to the rule;

dy/dx = (x-2)(0) - 3(1)/(x-2)²

dy/dx = 0-3/(x-2)²

dy/dx = -3/(x-2)²

Hence the derivative of the given function is -3/(x-2)²

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The swimming pool will take 135850 seconds to fill with water.

Given the dimensions of the pool are:

7.15 m

21 m

1.9

The swimming pool is being filled with water at a constant rate of 2.1 liters per second.

hence the volume of the swimming pool is :

volume = 7.15 × 21 × 1.9

volume = 285.285 m³

convert from meters to liters.

volume = 285.285 × 1000

= 285285 liters.

to find out the time required to fill the pool, we need to divide the volume by the flow rate.

⇒ 285285 ÷ 2.1

= 135850

hence the swimming pool will take 135850 seconds to fill with water.

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Answer:

neither

Step-by-step explanation:

i am goung to assume that the quarter really is just a quarter unit on the y-axis

Answer:

The line with a slope of [tex](-4)[/tex] is perpendicular to the line with a slope of [tex](1/4)[/tex] since the product of the two slopes is [tex](-1)[/tex].

Slope of [tex]8[/tex] and slope of [tex](-8)[/tex]: neither parallel nor perpendicular.

Slope of [tex]7[/tex] and slope of [tex]17[/tex]: neither parallel nor perpendicular.

The line with a slope of [tex]2[/tex] is parallel to the other line of slope [tex]2\![/tex] since the two lines have the same slope.

Step-by-step explanation:

Two lines in a cartesian plane are parallel to one another if and only if their slopes are equal. Two lines in a cartesian plane are perpendicular to one another if and only if the product of their slopes is [tex](-1)[/tex].

For example, a line with a slope of [tex]m[/tex] is parallel to another line of the same slope, [tex]m\![/tex].

Since [tex](-m)\, (1/m) = -1[/tex], a line with a slope of [tex](-m)[/tex] would be perpendicular to a line of slope [tex](1/m)[/tex].

Answer:

14,987

Step-by-step explanation:

There are 22 even numbers in the top 10 rows.

Pascal's triangle is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle.

The tip of the triangle starts with 1 and the 1 starts continuing to both the ends of the triangle in each row and in between there is the sum.

For example:

                  1

                1   1

             1    2   1

         1   3    3     1

In the above manner, it continues.

now, for 10 rows the pascal triangle will be:

                       1

                     1   1

                  1    2   1

              1   3    3     1

          1   4    6      4      1

      1     5   10    10    5     1  

    1    6    15   20   15    6    1

  1    7    21    35   35  21    7    1

1   8     28   56   70   56   28   8  1

1   9   36    84   126  126   84  36 9  1

for five rows in the top, the even numbers are 2, 4, 6, 4 which are 4 in total.

for 10 rows in the top, the numbers are 2, 4, 6, 4, 10, 10, 6, 20, 6, 8, 28, 56, 70, 56, 28, 8, 36, 84, 126, 126, 84, 36

Hence there are 22 even numbers in the top 10 rows.

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Distance, D = 5,760,000/2,160 = 2666.67 (approx)

The Excel DATE/TIME capabilities include the TIME Function. We can construct a time using distinct hour, minute, and second components with the aid of TIME.

We might want to date a report while performing financial analysis. In these circumstances, TIME can be used to transform a text string into a format that indicates the time in decimal form. Additionally, the function can be used to combine different values into a single time value.

formula= TIME (hour, minute, second)

distance = rate X time

D = RT

T = D/R

20 feet per second = 1200 feet per minute

16 feet per second = 960 feet per minute

[of minutes to flowerbed] + 14 minutes + [of minutes back to hive] = 19 minutes

(D/R) + 14 + (D/R) = 19

(D/R) + 14 + (D/R) = 19

(D/1200) + 14 + (D/960) = 19, This is the equation we can use to find the distance from the flowerbed to the​ hive.

(D/1200) + (D/960) = 5

(D(1200)(960))/1200 + (D(1200)(960))/960 = 5(1200)960

960D + 1200D = 5(1200)960

2,160D = 5,760,000

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Answer:

Step-by-step explanation:

Expression given:

Find its value when g = 10:

The area of triangle HIJ is 7 square units.

Given that, the vertices of triangle HIJ are H(-9,-8), I(-5,-5), and J(-7,-3) respectively. By using the vertices of triangle HIJ we have to evaluate its area in square units. So, let's procced to solve the question.

Area of ΔHIJ = 1/2|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|

So, x₁ = -9, x₂ = -5, x₃ = -7 and y₁ = -8, y₂ = -5, y₃ = -3

Put all the listed values in the formula of area of triangle HIJ.

By using the above formula, we get

=1/2|-9(-5+3)+(-5)(-3+8)+(-7)(-8-(-5))|

=1/2|-9(-2)-5(5)+(-7)(-3)|

=1/2|18-25+21|

=1/2|14|

= 1/2 x 14

= 7

Therefore, the area of triangle HIJ is 7 square units.

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Answer:translation

Step-by-step explanation:

The names of 0 employees are written on 0 cards. the cards are placed in a​ bag, and three names are picked from the bag - here simple random sampling technique was used.

Basic irregular testing can provide you with an extremely precise image of how your motto performs with the typical individual, yet it won't give you nitty gritty data about unambiguous gatherings. Utilizing straightforward irregular testing permits scientists to make speculations about a particular populace and leave out any inclination. This can assist with deciding how to settle on future choices. It has been expressed that "the rationale behind straightforward arbitrary examining is that it eliminates predisposition from the choice method and ought to bring about delegate tests".

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Answer:

y = -4/3x + 12

Step-by-step explanation:

y - y1 = m (x - x1)

the y1 and x1 are where your coordinates go. The m is the slope.

So now we just plug it in.

y - (-4) = -4/3 (x - 12)

we can clean it up some more to make it into the y = mx + b format.

y + 4 = -4/3x - (-4/3)12

y + 4 = -4/3x + 16

y = -4/3x + 12

Answer:

evaluating a function means finding the value of f(x) or f(y).......

Answer:

replace all the x variables with whatever x has been assigned

Step-by-step explanation:

evaluating a function means finding the value of f (x) = or y equals that corresponds to a given value of x to do this simply replace all the x variables with whatever x has been assigned for example if we are asked to evaluate f (4) then x has been assigned the value of 4

The simplified expression for the area of the given rectangle is 12x + 40

As per the given figure:

The length of the rectangle given in the question: 3/5x + 2

The breadth of the rectangle given in the question: 20

The formula for the area of a rectangle is given by:

Area of rectangle  = Length of the rectangle * Breadth of the rectangle

Area of rectangle  = (3/5x +2)*20

=(3x + 10)/5 * 20

= (3x + 10) * 4

= 12x + 40

Area of rectangle  = 12x + 40

So, the simplified expression for the area of the rectangle with the given length and breadth is 12x + 40

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We want to find the value of t such that the area to the left of −|t| plus the area to the right of |t| equals 0.1.

That is level of significance (α) = two-tail area = 0.1

what is a level of significance in research?

The significance stage (also called kind I mistakes rate or the extent of statistical importance) refers back to the chance of rejecting a null hypothesis that is in truth true. This amount stages from 0 (0.0) to at least one (1.zero) and is generally denoted through the Greek letter alpha (a).

What are the three levels of significance?

commonplace importance stages are 0.10 (1 risk in 10), 0.05 (1 risk in 20), and zero.01 (1 hazard in one hundred). The result of a speculation check, as has been seen, is that the null hypothesis is both rejected or now not.

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If the median of 6 consecutive integers is 9, the largest number is equal to 8.5.

Given the following data:

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

For the largest number, we have:

Since consecutive integers must follow each other sequentially with a difference of 1, so the largest number is given by:

Largest number = Median + (n - 1)/2

Substituting the given parameters into the formula, we have;

Largest number = 6 + (6 - 1)/2

Largest number = 6 + (5)/2

Largest number = 6 + 2.5

Largest number = 8.5.

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Rounding off the given decimal to the nearest hundredth, tenth and ones place are 1.50, 1.5 and 2 respectively.

The given decimal number is 1.496.

We need to round off the given decimal number.

There are some basic rules that need to be followed for rounding numbers.

Now, rounding off 1.496 to the hundredth place is 1.50

Rounding off 1.496 to the tenth place is 1.5

Rounding off 1.496 to the ones place is 2

Therefore, rounding off the given decimal to the nearest hundredth, tenth and ones place are 1.50, 1.5 and 2 respectively.

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Answer: 32, but I'm not sure

Step-by-step explanation:

the correct solution for the equation is 4.5

The charges for a week in which Charlene's facility did 35 oil changes and tuned 5 four-cylinder engines, and 7 six-cylinder will be $2313.25.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that charges per oil change are $33.95, charges for a four-cylinder engine $72.50, charges for a six-cylinder engine $82.50, and, charges for an eight-cylinder engine $92.50.

The total charges will be calculated as below:-

No oil changes done by Charlene = 35

price of 5 - four-cylinder engines = 5 × 72.50

= 362.50                                .....(1)

Price of 7 - six cylinder engines = 7 × 82.50

= 577.50                                ........(2)

Price of 2 - eight-cylinder engines = 2 × 92.50

= 185                                       ...........(3)

Now, adding (1), (2),(3)

= 362.50 + 577.50 + 185

= 1125                                        ...........(4)

Total charges for oil = 33.95 × 35

= 1188.25                                  ..........(5)

Add equations (4) and (5) to get the total charges.

= 1125 + 1188.25

= 2313.25

Therefore, the total charges will be $2313.25.

The complete question is given below:-

Charlene operates an oil change and tune-up service. she charges $33.95 per oil change. a tune-up is $72.50 for a four-cylinder engine, $82.50 for a six-cylinder engine, and $92.50 for an eight-cylinder engine. what are the charges for a week in which Charlene's facility did 35 oil changes and tuned 5 four-cylinder engines, and 7 six-cylinder?

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The value of m ∠ F L H is 57°

From the information given, we have that

m ∠ F L G and m ∠ H L G are congruent angles

Note that congruent angles are angles are equal or equivalent to each other

Given that;

Equate the expression for both angles

14x + 5 = 17 x − 1

collect like terms

14x - 17x = -1 - 5

Subtract like terms

-3x = -6

Make 'x' the subject of formula

-3x/-3 = -6/-3

x = 2

But we know that;

m ∠ F L G = ( 14 x + 5 ) = 14(2) + 5 = 28 + 5= 33°

m ∠ F L H = 90 - 33 = 57°

Thus, the value of m ∠ F L H is 57°

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The 12.5  tablespoons of the spray will he need to use for 5 gallons of water.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

For mixing a spray to kill weeds, Howard is to use 2 1/2 tablespoons for each gallon of water.

We have to find How many tablespoons of the spray will he need to use for 5 gallons of water..

According to given question we have

2 1/2 =5/2 tablespoons for each gallon of water.

5/2 tablespoons =1 gallon of water.

1 gallon of water=5/2 tablespoons

5 gallons of water=5/2*5 tablespoons

5 gallons of water=25/2 tablespoons=12.5  tablespoons

Therefore, the 12.5  tablespoons of the spray will he need to use for 5 gallons of water.

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685.8 feet

Sea level is a reference to elevation of the ocean or land interface called the shoreline.

Land that is above this elevation is higher than sea level and lower is below sea level.

The bottom of the canon is at 51 3/10 below the sea level which is also written as -51 3/10 ……(1)

The nest is at 737 1/10 feet above the sea level so it is expressed as

737 1/10  ….(2)

To find the distance between the bottom of the canyon and the bird’s nest we subtract (2) from (1)

737.1 – 51.3

= 685.8 feet

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Answer:

See the table below
For n, the answer is 2n+1

Step-by-step explanation:

The number of trees in each figure represents an arithmetic sequence where the difference between subsequent figures is 2  (caled the common difference)

So the sequence is

Figure(n)    Number of Trees

1                  3
2                 5  
3                 7
4                 9  (7+2)
5                11   (9+2)

n                 2n + 1

In general, for any arithmetic sequence we can write an equation for the nth term as [tex]a_n = a_0 + d(n-1)[/tex] where [tex]a_0[/tex] is the first term and d is the common difference

So for this example, we have [tex]a_0 = 3[/tex] and d=2 giving
[tex]a_n = 3 + 2(n-1) = 3 + 2n -2 = 2n + 1[/tex]

This is