Round off to the nearest
3,142

The car can go 44.25 miles on one gallon of gas

Xavier's car used 1 1/3 gallons to travel for 59 miles

The number of miles travelled on one gallon of gas can be calculated as follows

1 1/3 gallons= 59 miles

1 gallon= x

Cross multiply both sides

4/3x= 59

4x= 177

x= 177/4

x= 44.25

Hence Xavier's car can travel 44.25 miles on one gallon of gas

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The missing coordinates of given vectors a, b, c, d, and e are 0,0,0, -0.8, and 0. Then, the vectors are [tex]\vec{u}=\left[\begin{array}{ccc}-0.6\\0.8\\0\end{array}\right][/tex], [tex]\vec{v}=\left[\begin{array}{ccc}0\\0\\1\end{array}\right][/tex], and [tex]\vec{w}=\left[\begin{array}{ccc}-0.8\\-0.6\\0\end{array}\right][/tex]

We refer to two vectors as being orthogonal if they are perpendicular to one another. So these vectors' dot product will be zero. Let the given three vectors be [tex]\vec{u}[/tex], [tex]\vec{v}[/tex], and [tex]\vec{w}[/tex]. And the unknowns be a, b, c, d, and e.

Then, the vectors are written as

[tex]\vec{u}=\left[\begin{array}{ccc}-0.6\\0.8\\a\end{array}\right][/tex], [tex]\vec{v}=\left[\begin{array}{ccc}b\\c\\1\end{array}\right][/tex], and [tex]\vec{w}=\left[\begin{array}{ccc}d\\-0.6\\e\end{array}\right][/tex]

First, take [tex]\vec{u}[/tex] and consider unit length, we get,

[tex]1=\sqrt{(-0.6)^2+(0.8)^2+a^2}\\1=1+a^2\\a=0[/tex]

For [tex]\vec{v}[/tex], we get,

[tex]1=\sqrt{(b)^2+(c)^2+1^2}\\1=1+b^2+c^2\\b=0\;\text{and}\;c=0[/tex]

We know that [tex]\vec{w}[/tex] is orthogonal to both vectors, then,[tex]\vect{w}\cdot{\vec{v}=0[/tex]. Substituting, the values of [tex]\vec{v}[/tex] and [tex]\vec{w}[/tex], we get,

[tex]\begin{aligned}\langle d, -0.6, e\rangle \;\cdot\;\langle 0, 0, 1\rangle&=0\\e&=0\end{aligned}[/tex]

Also, [tex]\vect{u}\cdot{\vec{w}=0[/tex],  Substituting, the values of [tex]\vec{u}[/tex] and [tex]\vec{w}[/tex], we get,

[tex]\begin{aligned}\langle -0.6, 0.8, 0\rangle \;\cdot\;\langle d, -0.6, e\rangle&=0\\-0.6d-0.48+0&=0\\-0.6d&=0.48\\d&=-0.8\end{aligned}[/tex]

Therefore, the required answers for a, b, c, d, and e are 0,0,0, -0.8, and 0.

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Answer:

providing goods

Step-by-step explanation:

i need 20 words so here, you can you go without the hard rock you can you go without it is not the first half way to you by the

The  probability of selecting a boy then a girl is 24/91

Probability is defined as the chance of occurrence of an event

E.  It is the ratio of the number of required outcome over the total of all possible outcomes in an even.

the given parameters that will help us to determine the probabilities are

The probability of the event is

P(E) = Pr(B) Then Pr(G)

Pr(E) = 8/14 *6/13

Simplify the fractions to have  48/182

= 24/91

Conclusively the selection is 24/91

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The one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

A one sided limit will not exist when it is outside the domain of the function.

The domain of a function is composed by the set of all the input values of the function, hence on the graph it is given by the values of x.

For this problem, the domain is then given as follows:

-6 ≤ x ≤ 8.

To the left of -6, the function is not defined, hence the one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

Meaning that the correct option is given by the last option.

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The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

You mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quarts of purple paint.

Let 'x' be the amount of blue paint and 'y' be the amount of red paint. Then the equations are given as,

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

x / y = 3/2                        ...1

x + y = 5                          ...2

From equations 1 and 2, then we have

(3/2) y + y = 5

(5/2) y = 5

y = 2 quart

Then the value of 'x' is given as

x + 2 = 5

x = 3 quart

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

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Answer:

A)  6x - 27

Step-by-step explanation:

Given expression:

[tex]-9(x + 3) + 15x[/tex]

Apply the distributive property:

[tex]\implies -9 \cdot x -9 \cdot 3+15x[/tex]

[tex]\implies -9x -27+15x[/tex]

Collect like terms:

[tex]\implies -9x+15x -27[/tex]

Combine like terms:

[tex]\implies 6x -27[/tex]

Answer:

[tex] \sf \: a) \: 6x - 27[/tex]

Step-by-step explanation:

Now we have to,

→ simplify the given expression.

The expression is,

→ -9(x + 3) + 15x

Let's simplify the expression,

→ -9(x + 3) + 15x

→ -9x - 27 + 15x

→ (-9x + 15x) - 27

→ (6x) - 27

→ 6x - 27

Hence, the answer is 6x - 27.

Therefore ,a s a result, the answer to the given equation problem is that a carpet costs $2072.

When all of the highest powers of the variables are equal to one, an equation is said to be linear. The parts are linked together. Another name for this kind of problem is a one-degree equation. The following paragraphs will teach you how to solve a linear equation in one or two variables using the usual form, formula, graph, and directions.

Here,

Given :

50a + 12h is the floor area of a square foot.

where h is the amount of hours.

Thus.

When t=6 and a=40

So ,

the price of carpeting

=> Price = 50a plus 12h

=> Cost = 50*40 + 12*6

=> Cost = 2000 + 72

=> Cost = 2072

As a result, the answer to the given equation's problem is that a carpet costs $2072.

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The option A that is 2 days after being planted, the two plants will of the same height( Where the two lines intersect in a graph).

How to know if the lines intersect in the graph of a function?

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

And after solving both equations if the values of x and y satisfies both equations then they intersect at that values of x and y.

Now,

On Monday, Eric planted a 3-centimeter-high tomato plant and a 5-centimeter-high tomato plant in his garden.

The graph models the growth of each plant since the day they were planted.

The intersection of the two lines represents the days after being planted were the two plants the same height.

The answer is that 2 days after being planted, the two plants are the same height.

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The answer is that 2 days after being planted, the two plants are the same height.

How to know if a point lies in the graph of a function?

The answer is that 2 days after being planted, the two plants are the same height.

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On solving the provided question, we can say that = 9227446, depreciation  If round at hundredth, then, Number of tree = 9227400.

Identify the asset's cost. Get the asset's total depreciable value by deducting the projected salvage value from the asset's purchase price. Determine the asset's useful life. The annual depreciation amount is obtained by dividing the sum of steps (2) and (3) by the figure determined in steps (3).

Depreciation is the practice of deducting the cost of a company asset over a number of years as opposed to just one. There are four primary ways to depreciate assets: linear, twofold declining, sum of the years' digits, and manufacturing units.

As it is given, 1% of left tree is decaying every year.

Number of tree left after 8 years.

A = P{1-R/100}^ = 10M{1-1%/100}^  

= 10M *(0.99)^

= 9227446

If round at hundredth, then,

Number of tree = 9227400.

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The required equation is y=x/3+3

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here the line passes through the points (3,4) and (0,3)

Thus the slope intercept form of the line passing through these points is

y=x/3+3 where m=4-3/3-0 is the slope of the line

Hence, The required equation is y=x/3+3

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The expression 3(x-2) is equivalent to 3x - 6.

When you distribute the 3 to the term inside the parentheses, you multiply 3 by x and by -2, resulting in 3x - 6.

This is because the distributive property states that for any real numbers a, b, and c, the expression a(b+c) is equivalent to ab + ac. In this case, we have a = 3, b = x, and c = -2, so we can apply the distributive property and get 3x - 6.

You can also think of it as 3 multiplied by (x-2)

3x - 32 = 3x - 6

Answer:

7 and 40

Step-by-step explanation:

for you to get the next number you have to add 7 to that number...then add 1 to the number you have gotten then continue like that

eg: to get 8 you had to add 7 to 1 now to get the next number add 1 to 8 to get 9 then add 7 to 9 to get 16 then continue like that

47 percent of the sandwiches had turkey.

Find the whole amount of what you're looking for to get a percentage of.

To calculate the percentage, divide the number.

Add 100 to the value.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, 35% is equal to the fraction 0.35 or the decimal 0.35.

The value of the number out of 100 is the proportion of the number. For instance, there are 26 females and 24 boys in a class. As a result, 52 out of 100 students in the class are females, or 52% of the class.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Percentages.

According to our question

47+53= 100%,

So 1= 1%

= 47x1= 47, So it equals 47%.

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Answer:67/24

Step-by-step explanation:

i did it

Answer:

y = 0.20x + 12.5

Lets set the cost of the cost as the y-axis and the amount of fish as the x-axis. 12.50, a constant and the y-intercept, is the price when you don't have any fish.

0.2 is the slope and in this case, the amount of 1 fish.

0.2x + 12.5 is the total amount as every fish added adds 20 cents. 12.5 is the fishtank which you need to get before getting any fish.

Line connecting each of the triangle's points, passing through points (6,7) along the route (2), (5), (4), and (6) are the points (4,1).

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners.

given

A shape is upside down and enlarged on the side opposite the center of expansion when you raise a shape with a negative scale factor.

points include

(2,5)

(4,5)

(4,1)

Create a line connecting each of the triangle's points, passing through points (6,7) along the route (2), (5), (4), and (6) are the points (4,1).

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The journal entries required on February 28, 2021, for Selkirk Company to accrue interest and to record the discounting are as follows:

Debit Interest Receivable $225

Credit Interest Revenue $225

Debit Cash $15,048

Debit Interest Expense $177

Credit Note Receivable $15,000

Credit Interest Receivable $225

When a note receivable is discounted, the following steps are followed:

February 28, 2021

Interest Receivable $225 Interest Revenue $225

Cash $15,048 Interest Expense $177 Note Receivable $15,000 Interest Receivable $225

Note receivable = $15,000

Interest = 9%

Maturity period = 6 months (Jan 1, 2021, to July 1, 2021) or 180 days

Discount date = February 28, 2021

Maturity value = $15,675 ($15,000 + $15,000 x 9% x 6/12)

Discount = $627 ($15,675 x 12% x 120/360)

Proceeds = $15,048 ($15,675 - $627)

Accrued interest = $225 ($15,000 x 9% x 60/360)

Note's carrying value on February 28, 2021, = $15,225 ($15,000 + $225)

Interest expense = $177 ($15,048 - $15,225)

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The points to be graphed are (0, -3) and (1.8, 0). The graph of the equation is shown in the attached image

In order to graph the equation of the line 3y-5x=-9:

First, find the value of x when y = 0:

3y-5x=-9, when y = 0:

3(0) - 5x=-9

- 5x = -9

x = 9/5

x = 1.8

Also, find the value of y when x = 0:

3y-5x=-9, when x = 0:

3y - 5(0) = -9

3y = -9

y = -9/3

y = -3

Therefore,  the values to be plotted on our graph are (0, -3) and (1.8, 0). The image of the graph is attached

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Answer:

8

Step-by-step explanation:

Let the AP numbers be: ( a - 3d ), ( a - d ), a, ( a + d ), ( a + 3d )

We are given that sum of all these numbers is 40.

⇒ a - 3d + a - d + a + a + d + a + 3d = 40

⇒ 5a + 4d - 4d = 40

⇒ 5a = 40

⇒ a = 40 / 5 = 8

We know that the middle term of the five numbers given is 'a'.

As a result, the given AP's middle term is 8.

Good luck <3

By simply dividing the reduced value by 12, the value of 120 decreases by 12%, yielding a percentage drop of 102.

In mathematics, a ratio or number expressed as a fraction of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." However, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100. A percent symbol (%) should be placed next to a number to indicate that it is a percentage. For instance, you score a 75% on a test if you properly answer 75 out of 100 questions (75/100). When calculating percentages, multiply the result by 100 after dividing the amount by the total. By multiplying (value/total) by 100%, the percentage is determined.

given

The value of the percentage decrease

= · 120 - (15% × 120)

=  120 - 15% × 120

=  85 ÷ 100 × 120

= 85 × 120 ÷ 100 = 102

You may calculate the percentage drop by simply dividing the lowered value by the original value and multiplying the result by 100.

In this case, Reduced Value equals Original Value - New Value.

By simply dividing the reduced value by 12, the value of 120 decreases by 12%, yielding a percentage drop of 102.

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The volume of the solid is 4π([tex]\frac{19}{6}[/tex]) and the integral of the f(x) , the line 2y=x, and x=2 is 3([tex]e^{4}[/tex] -1).

What is integral ?

An integral is a mathematical concept that is used to calculate the area under a curve or the total amount of change in a variable over a certain interval.

1)The first step is to find the intersection of the lines 2y=x and x=2. They will intersect at (2,1).

The second step is to find the intersection of the lines 2y=x and x=0. They will intersect at (0,0).

The third step is to find the integral over the region.

∫∫ (6e^(x^2))dxdy = ∫[0,2] (6e^(x^2))dx ∫[0,x/2] dy = ∫[0,2] (6e^(x^2))dx (x/2) = [3e^(x^2)] at [0,2] = 3e^(4) - 3e^(0) = 3(e^4 -1).

2)To find the volume of this solid, we can use the method of cylindrical shells.

we can find the function of the surface (1/3)x+(1/2)y+(1/4)z=1

by using cylindrical coordinates:

x = rcosθ , y = rsinθ , z = z

and substitute them in the equation (1/3)x+(1/2)y+(1/4)z=1

(1/3)rcosθ+(1/2)rsinθ+(1/4)z=1

(1/3)r(cosθ+2sinθ)+(1/4)z=1

z = 4(1-(1/3)r(cosθ+2sinθ))

V = ∫∫∫ 4(1-(1/3)r(cosθ+2sinθ)) rdrdθdz = 4π ∫[0,3] (1-(1/3)r(cosθ+2sinθ)) r^2 dr = 4π ∫[0,3] (1-r+(2/3)r^2) dr = 4π(3 - (3/2) + (2/3)) = 4π(19/6).

Hence , The volume of the solid is 4π([tex]\frac{19}{6}[/tex]) and the integral of the f(x) , the line 2y=x, and x=2 is 3([tex]e^{4}[/tex] -1).

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The expression 5 - g has two terms in it, "5" and "g" where 5 is a constant and g is a variable.

To find the number of terms in an algebraic expression, you find out the number of signs that separate the terms and these signs only include the plus and minus signs. In this case 5 - g has two terms, 5 and g.

A term can be a number, a variable, a product of two or more variables, or a number and a variable product. An algebraic expression can be made up of a single term or a group of terms. For example, the two terms in the expression 4x + y are 4x and y. It should be noted that the terms combine to form the expression.

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Answer:

-2x + 9

Step-by-step explanation:

-2(x - 7) + (-5)

-2x + 14 -5

-2x + 9

The value of a and b for the given quadrilateral to be a parallelogram is a = 16 and b = 4.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

We know that the opposite sides of a parallelogram are equal in length so we can equate the two sides as follows:

For a:

2a + 6 = 3a -10

Isolate the value of a by moving all the values having a to one side:

2a + 6 = 3a -10

3a - 2a = 6 + 10

a = 16

For b:

6b - 3 = 5b + 1

Isolate the value of b by moving all the values having b to one side:

6b - 3 = 5b + 1

6b - 5b = 1 + 3

b = 4

Hence, the value of a and b for the given quadrilateral to be a parallelogram is a = 16 and b = 4.

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Answer:

.........,..........,.

Step-by-step explanation:

.................. .....

Answer: Pretend the function g(x)=4x+1 is x and replace x in f(x) with it

Step-by-step explanation:

Upon solving the decimals, The expression which is equivalent to 0.125 are -12.5 ÷ 10²⇒ 0.125 and 1,250 ÷ 10⁴ ⇒ 0.125.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

Decimal fractions and recurring (repeating or non-terminating, like) decimals are the three different sorts of decimals (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).

1.25 ÷ 10       ⇒ 0.125

Upon solving the decimals,

12.5 ÷ 10²       ⇒ 0.125

0.125 ÷ 100    ⇒ 0.00125

1,250 ÷ 10⁴     ⇒ 0.125

12.5 ÷ 1           ⇒ 12.5

125 ÷ 1,000    ⇒ 0.0125

The expression which is equivalent to 0.125 are -

12.5 ÷ 10²       ⇒ 0.125

1,250 ÷ 10⁴     ⇒ 0.125

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Answer:

[tex]\frac{35}{12}[/tex]

Step-by-step Explanation:

The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.