3 3/5 x 1 2/3 x 4 2/3

Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles

Answer:

83

Step-by-step explanation:

\( \frac{ - 332}{ - 4} = 83\)

The Vales of x in the equations are : 1) 3 (2) 1  (3) 5  (4) 14  (5) 10 respectively

A linear equation in one variable is that in which the highest power of its variable is 1

The given equations and their solutions are

2x +1 = 7

By collecting like terms we have

2x = 3

x = 3

2) The given equation is 4x +7 = 11

By collecting like terms we have

4x = 4

Making x the subject we have

x = 1

3) 2x -3 = 7

By collecting like terms we have

2x = 10

Making x the subject we have

x = 5

4) 1/2 x - 3 = 7

By collecting like terms we have

1/2x = 7

x= 14

5) The given equation is 3x - 11 = 19

By collecting like terms we have

3x= 30

Therefore x= 10

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Answer:

Let price of drink be x

price of tub y

You have 4x+2y=32.5 (1) and

x = y -3.5 (2)

Plug for x from (2) into (1):

4(y-3.5) + 2y = 32.5

4y -14 +2y = 32.5

6y = 14+32.5

y = (46.5)/6 = $7.75 the price of tub

x= y-3.5 = 7.75 - 3.5 = $4.75

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

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Answer:

36.8

Step-by-step explanation:

Use the Hundreths place to determine whether you round up or down for the tenths place. The hundreths place is 0 so 8 stays the same. 36.8

Answer:

18 minutes

Step-by-step explanation:

This is a simple calculation, all we really need to do is subtract...

Since we started at 3:14 and went to 3:32 pm it is really easy since it is in the same hour.

3:32pm - 3:14pm =

18 minutes

Hope this helps :)

Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

Answer:

-26

Step-by-step explanation:

Because -6+ -2= -8

-18- 8= -26

Answer:

C would be the correct number line

Step-by-step explanation:

5x ≥ - 17 - 3

5x ≥ -20

5x/5 ≥ -20/5

x ≥ 4

The system of inequalties in the graph is:

y > x^2 - 4

y < x^2 + 3

We can see two parabolas, one with an y-intercept at y = 3 and the region shaded is below that parabola.

And the other has an y-intercept at y = -4, and the region shaded is above that line.

Then the system will be something like:

y > x^2 - 4

y < x^2 + 3

That is the correct option.

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1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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Answer

C. Sam owes his dad $7.50

Step-by-step explanation:

because none are correct but tat is te closetes one

Answer:

(1,-4)

Step-by-step explanation:

There are 3 different ways to solve systems of equations, but for this equation, since both are in standard form, we will use elimination.

First, to solve by elimination, both equations must have at least 1 coefficient in common to cancel each other out.

In this case, we will make 2x and 4x equal each other. To do so, we will multiply all the terms in the first equation by 4 and all the terms in the second equation by 2.

This gives us the following equations:

8x - 36y = 152

8x + 10y = -32

Subtract 8x + 10y = −32 from 8x − 36y = 152 by subtracting like terms on each side of the equal sign:

8x −8x − 36y − 10y = 152+32

8x cancels out, leaving us with:

−36y − 10y = 152 + 32

Combine like terms:

-46y = 184.

Divide 184 by -46, which leaves us with y = -4.

Substitute −4 for y in 4x + 5y= −16:

4x + 5 (−4) = −16

Multiply 5 times −4, then add 20 to both sides of the equation.

This leaves us with 4x = 4, which when simplified equals x = 1.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

What is inequality?

An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.

c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).

d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.

Hence,

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

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Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

170 square inches

Step-by-step explanation:

triangle = 1/2 Base * height

1/2 *20 * 17  = 170 in^2

Answer:

Area of the Triangle is 170 in^2

Step-by-step explanation:

Area of Triangle: Area = 1/2 * Base * Height.

Base = 20 in.

Height = 17 in.

Area = 1/2 * 20 in * 17 in

Area = 10 in * 17 in

Area = 170 in^2

Answer:

(a) Independent variable:  b (number of bags sold)

    Dependent variable:  p(b)  (profit)

(b) 25

(c) 84700

(d) 70

(e) b < 25

Step-by-step explanation:

(a) Independent variable:  b (number of bags sold)

    Dependent variable:  p(b)  (profit)

(b) To break even, set p(b) to zero and solve for b:

⇒ 350b - 8750 = 0

⇒ 350b = 8750

⇒ b = 8750 ÷ 350

⇒ b = 25

(c) Substitute b = 267 into equation and solve for p(b):

⇒ 350(267) - 8750 = 84700

(d) Set p(b) to 15750 and solve for b:

⇒ 350b - 8750 = 15750

⇒ 350b = 15750 + 8750

⇒ 350b = 24500

⇒ b = 24500 ÷ 350

⇒ b = 70

(e) If she breaks even when she sells 25 bags, if she sells less than 25 bags she will have a negative profit. So b < 25

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.

It follows from the task content that the equation which correctly represents the Given situation is to be determined.

Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;

Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.

Consequently, answer choice C; w = 5 × 15 is correct.

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Answer:

The opposite side and opposite of angles of parallelogram are equal. An these opposite sides an opposite angles make up for a congruent triangles, with the two diagonal being the sides of these two congruent triangle. Hence the diagonals of the parallelogram are equal.

Hope it will help you.

f(x) = x^3 - 6x^2 + 12x the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. The critical value that will give you a relative maximum is x = 4. The critical value that will give you a relative minimum is x = -2.

The derivative of the given function is f'(x) = 3x^2 - 12x + 12. Setting this equal to 0 gives us x = 0 and x = 4. By the first derivative test, we can determine that the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. Therefore, the critical value that will give us a relative maximum is x = 4 and the critical value that will give us a relative minimum is x = -2. This can be verified by finding the second derivative of the function, which is f''(x) = 6x -12. Setting this equal to 0 gives us x = 2, which is between the two critical values. Since the second derivative is negative for x < 2, the critical value at x = -2 will give us a relative minimum and since it is positive for x > 2, the critical value at x = 4 will give us a relative maximum.

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Answer:

60 attempts

Step-by-step explanation:

Divide 51 by .85, and you get 60!

The representation that is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time is a Line Plot

A line plot, or dot plot/strip plot, is a simple visual method of displaying data that shows the spread of values on a horizontal scale. A frequent application of it is to graphically display the occurrence or spread of a solitary factor.

A line plot generally displays individual data points as a small dot or short line segment along a specific axis, usually the horizontal axis. The location of the dot or line segment indicates the numerical value of the data point. Usually, the up and down axis showcases the frequency or the number of times a particular value occurs.

With this type of Table, the top is always X and the bottom is always Y.

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Trapezoid WXYZ is located at W(0,5) X(3,8) Y(7,8) and Z(10,5). After a translation 8 units left, the new coordinates of the vertices are w(0,-3), X(3,0), Y(7,0) and Z(10,-3).

What is trapezoid?

In mathematics, a quadrilateral with at least one set of parallel edges is referred to as a trapezoid in American and Canadian English, or a trapezium in British and other types of English. In Euclidean mathematics, a trapezoid is a convex parallelogram by definition. The bases of the trapezoid are the horizontal edges.

Given,

W(0,5) X(3,8) Y(7,8) and Z(10,5)

If A(x,y), after being translated left c units, then A(x,y) is written as A(x,y-c)

Then the new coordinates of the vertices are written as-

W(0,5) after being translated left 8 units written as w(0,-3)

X(3,8) after being translated left 8 units written as X(3,0)

Y(7,8) after being translated left 8 units written as Y(7,0)

Z(10,5) after being translated left 8 units written as Z(10,-3)

Hence the new coordinates of the vertices are w(0,-3), X(3,0), Y(7,0) and Z(10,-3)

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Answer:

Step-by-step explanation:

Wuh