What is the solution of the equation 8 5/6 = r + 5 1/3?

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The speed of the boat in still water is 12 miles per hour, and the speed of the current is 9 miles per hour.

To solve this problem, we can use the concept of relative speed and the formula: Distance = Speed x Time.

Let's denote the speed of the boat in still water as 's' (in miles per hour) and the speed of the current as 'c' (in miles per hour).

When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the speed downstream is s + c.

Similarly, when the boat is traveling upstream (against the current), its effective speed is decreased by the speed of the current. Therefore, the speed upstream is s - c.

Given:

Distance downstream = 210 miles

Time downstream = 10 hours

Using the formula: Distance = Speed x Time, we can write the equation for the downstream journey as:

210 = (s + c) x 10

Simplifying the equation, we have:

21 = s + c

Similarly, for the upstream journey:

Distance upstream = 210 miles

Time upstream = 70 hours

The equation for the upstream journey becomes:

210 = (s - c) x 70

Simplifying:

3 = s - c

Now we have a system of equations:

21 = s + c

3 = s - c

We can solve this system of equations to find the values of 's' and 'c'. Adding the two equations together, we get:

24 = 2s

s = 12

Substituting the value of 's' back into either equation, we find:

3 = 12 - c

c = 9

Therefore, the speed of the boat in still water is 12 miles per hour, and the speed of the current is 9 miles per hour.

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a boat traveled 210 miles downstream and back. the trip downstream took 10 hrs. the trip back took 70 hours. Use the concept of relative speed to solve this problem.

True: On the graph above, f(1) = 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line and passes through the points (-1, -2) and (1, 4) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (4 - (-2))/(1 - (-1))(x - (-1))

y + 2 = 6/2(x + 1)

y = 3(x + 1) - 2

y = 3x + 3 - 2

y = 3x + 1

When x = 1, the value of y is given by;

y = 3x + 1

y = f(1) = 3(1) + 1

y = f(1) = 4.

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Answer:

-84

Step-by-step explanation:

Let the number be x. Then we have,

\(\frac{x}{-7}\) (the quotient of a number and -7)

\(\frac{x}{-7}-2\) (decreased by 2)

\(\frac{x}{-7}-2=10\) (is 10)

Now we can solve for x,:

\(\frac{x}{-7}-2=10\)

\(\frac{x}{-7}=12\)

\(x=-84\)

So, the original number is -84

Answer:

-84

Step-by-step explanation:

\(\frac{n}{-7}\) -2 = 10

add 2 to each side to get:

\(\frac{n}{-7}\) = 12

multiply each side by -7 to get:

n = -84

The midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0. To approximate the area under the curve using a midpoint approximation, we divide the interval [0, 4) into four subintervals of equal width.

The width of each subinterval is (4 - 0) / 4 = 1.

Now, we need to evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval.

The midpoints of the subintervals are: 0.5, 1.5, 2.5, and 3.5.

Evaluating the function at these midpoints, we get:

f(0.5) = 2 * 0.5 * (0.5 - 4) * (0.5 - 8) = 6

f(1.5) = 2 * 1.5 * (1.5 - 4) * (1.5 - 8) = -54

f(2.5) = 2 * 2.5 * (2.5 - 4) * (2.5 - 8) = 54

f(3.5) = 2 * 3.5 * (3.5 - 4) * (3.5 - 8) = -6

Now, we calculate the sum of these values and multiply it by the width of the subinterval:

Area ≈ (6 + (-54) + 54 + (-6)) * 1 = 0.

Therefore, the midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0.

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After solving we got to know that,

a) \(f(x,y)=2x-4y\)  f is onto.

b) \(f(x,y) = -1|x|\)  f is not onto.

c) \(f(x,y)=x^2\)  f is onto.

d) \(f(x, y) =x^y\)  f is not onto.

To determine which of the given functions are onto, we need to examine whether each function can generate every possible output value in Z.

(a) \(f(x,y) = 2x - 4y\)

To show that f is onto, we need to show that every element in Z is a possible output value of f. We can rearrange the equation to solve for y: \(y = (2x - z)/4\), where z is the desired output value in Z. This equation shows that any value of z in Z can be obtained by choosing appropriate values of x and y. Therefore, f is onto.

(b) \(f(x,y) = -1|x|\)

The function f maps every pair (x, y) to a negative or zero value. Since there are positive integers in Z, f cannot generate every possible output value in Z. Therefore, f is not onto.

(c) \(f(x,y) = x^2\)

The function f maps every pair (x, y) to a non-negative integer. Every non-negative integer is a possible output value of f, so f is onto.

(d) \(f(x, y) = x^y\)

For any given y, there are positive and negative output values of f. Therefore, f cannot generate every possible output value in Z. Therefore, f is not onto.

In summary, the functions \(f(x, y) = 2x - 4y\) and \(f(x, y) =\) \(x^2\) are onto, while \(f(x, y) = -1|x|\) and \(f(x, y) = x^y\)are not onto.

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Answer:

861.56 km2

Step-by-step explanation:

the formula for the area of a trapazoid is

a= (a+b/2) + h

Answer:

60 degrees

Step-by-step explanation:

It measures 60 degrees

Tip: the wider the angle, the bigger the degree.

Hope this helps!

Answer: Let's call the first term of the arithmetic progression "a" and the common difference "d". Then we can use the following formulas to find the second, fifth, and seventh terms:

- The second term is a + d.

- The fifth term is a + 4d.

- The seventh term is a + 6d.

We are given that the sum of the second and seventh terms is 25:

(a + d) + (a + 6d) = 25

Simplifying this equation, we get:

2a + 7d = 25 ...(1)

We are also given that the fifth term is 15:

a + 4d = 15 ...(2)

Now we can solve for the common difference "d" by using equations (1) and (2) to form a system of two equations in two variables. One way to do this is to solve equation (2) for "a" in terms of "d", and then substitute that expression for "a" into equation (1):

a = 15 - 4d ...(3)

Substituting equation (3) into equation (1), we get:

2(15 - 4d) + 7d = 25

Simplifying this equation, we get:

30 - 8d + 7d = 25

Solving for "d", we get:

d = -5

Therefore, the common difference is -5.

Step-by-step explanation:

The distance that Vikram's car can travel on a full tank of fuel, based on the car dashboard is 680 miles

The car's dashboard shows proportions of 8 lines which means that this can be used to find the rate of fuel consumption by the car.

After 255 miles travelled, Vikram's car shows the arrow at the 5th proportion. This means that the amount of fuel in terms of proportion used is:

= 8 - 5

= 3

In decimals, this is:

= Proportions used / Total proportions

= 3 / 8

= 0.375

The distance the car can go on a full tank is:

= Distance car has gone / Proportion of fuel taken

= 255 / 0.375

= 680 miles

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Answer: 520

Step-by-step explanation:

195/3= 65

65*8=520

According to the question we have  the correct answer is option 2, with a volume of 1664 cubic units.

The volume of the solid lying under the circular paraboloid z = x^2 + y^2 and above the rectangle R = (-4, 4] x [-6, 6] can be found using a double integral. First, set up the integral with respect to x and y over the given rectangular region:

Volume = ∬(x^2 + y^2) dA

To evaluate this integral, we will use the limits of integration for x from -4 to 4, and for y from -6 to 6:

Volume = ∫(from -4 to 4) ∫(from -6 to 6) (x^2 + y^2) dy dx

Now, integrate with respect to y:

Volume = ∫(from -4 to 4) [(y^3)/3 + y*(x^2)](from -6 to 6) dx

Evaluate the integral at the limits of integration for y:

Volume = ∫(from -4 to 4) [72 + 12x^2] dx

Next, integrate with respect to x:

Volume = [(4x^3)/3 + 4x*(72)](from -4 to 4)

Evaluate the integral at the limits of integration for x:

Volume = 1664

Therefore, the correct answer is option 2, with a volume of 1664 cubic units.

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The number of the lions that live in the region investigated by the considered scientist is 80.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we're specified that:

Let we take:

x = number of lions the scientist located and tagged on thursday.

Then, we get:

x - 10 = number of lions the scientist located (and assumingly found that they're tagged) on friday,

4 = number of lions he found tagged on friday.

That means, x -10 is same number as 4

or, we get:

\(x - 10 = 4\\\text{Adding 10 on both the sides}\\\\x = 14\)

That means, on thursday, the scientist located and tagged 14 lions.

Now, suppose that the region had 'y' number of lions,

Then, as per the data in the question,

one-fifth of y =  number of lions located by scientist on thursday

or, we get:
\(\dfrac{y}{5} = x\\\\\dfrac{y}{5} = 14\\\\\text{Multiplying 5 on both the sides}\\\\y = 80\)

Thus, the number of lions that live in the region considered is 80

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The total number of lines is 70.

We have given that,

A scientist wants to estimate the number of lions living in a region.

On Thursday, he locates and tags some lions.

On Friday he returns and locates 10 less lions than he had on Thursday.

He notices that 4 of the lions are tagged

The scientist works out an estimate for the total number of lions living in the region.

we have to determine the no of lines in the length.

on Thursday no.of lines=x

on friday=(x-10)=4

x-10=4

add like terms

Like terms are terms whose variables and their exponents such as the 2 in x^2 are the same.

x=10+4

x=14

No.of total lions =5th of (no. of tagged on Thursday.)

=5(14)

=70

Therefore the total number of lines is 70.

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The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of the tree. Hence the distance to the top of tree = 3h + 2.

Using Pythagoras theorem:

(3h + 2)² = h² + 70²

9h² + 12h + 4 =  h² + 70²

8h² + 12h - 66 = 0

h = 2.22 feet

The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree

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The distance from the bird to the top of the tree is 61.95 feet.

We have,

Angle of elevation to the top of the tree: 38 degrees.

Angle of elevation to the bird: 60 degrees.

Distance from the base of the tree to your position: 84 feet.

Let the distance from the bird to the top of the tree as 'x'.

Using Trigonometry

tan(38) = height of the tree / 84

height of the tree = tan(38) x 84

and, tan(60) = height of the tree / x

x = height of the tree / tan(60)

Substituting the value of the height of the tree we obtained earlier:

x = (tan(38) x 84) / tan(60)

x ≈ 61.95 feet

Therefore, the distance from the bird to the top of the tree is 61.95 feet.

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The positive difference between the greatest possible perimeter and the least possible perimeter of a parallelogram with three vertices at specific points can be calculated.

The greatest possible perimeter of the parallelogram occurs when the fourth vertex is at the farthest distance from the given three vertices. In this case, the fourth vertex would be the reflection of point A across the line formed by points B and C. By finding the distance between the three given vertices and the reflection of point A, we can determine the maximum perimeter.

The least possible perimeter of the parallelogram occurs when the fourth vertex is at the closest distance to the given three vertices. In this case, the fourth vertex would be the reflection of point A across the line formed by points B and C. By finding the distance between the three given vertices and the reflection of point A, we can determine the minimum perimeter.

The positive difference between the greatest possible perimeter and the least possible perimeter can be obtained by subtracting the minimum perimeter from the maximum perimeter. This value represents the range of possible perimeters for the parallelogram based on the given three vertices.

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Answer:

See below.

Step-by-step explanation:

20.

\( \sqrt{43} - \pi = 6.5574 - 3.1416 = 3.4158 \)

Plot the number between 3.4 and 3.5, but much closer to 3.4 than to 3.5 since it is approximately 3.42.

21.

(7.3 * 10^6) / (3.2 * 10^4) = 7.3/3.2 * 10^6/10^4 = 2.3 * 10^2

1. x = π/6 + 2πn/3, for any integer n

2. Is not possible to solve (I think)

3. x = π/4 + πn, for any integer n

Answer:

sin 870 degree = sin 870° =   sin( 720°+ 150°  ) sin 150° = sin 30° = 1/2

Step-by-step explanation:

Since the researcher is merely observing and comparing existing groups without any manipulation or intervention, this study is classified as an observational study.

In an observational study, the researcher observes and collects data on existing groups or individuals without intervening or manipulating any variables. In this case, the researcher selected two groups of grocery shoppers (one group shopping at a health food supermarket and the other at a neighborhood grocery store) and observed their food costs over a month. The researcher did not control or manipulate any factors or assign participants to specific groups.

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Using the Pythagorean Rule we know that player A is 19.2 ft away from us.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

The Pythagorean Rule can be used to determine the distance between you and Player A since the distances between you, Player A, and Player B are in the shape of a right-angled triangle.

c² = a² + b²

Where;

c = hypotenuse = Distance between you and player A

a = Length of the triangle

b = Height of triangle

Then, calculate as follows:

c² = 12² + 15²

c² = 144 + 225

c = √369

c = 19.2 ft

Therefore, using the Pythagorean Rule we know that player A is 19.2 ft away from us.

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Correct question:

During a basketball game, you want to pass the ball to either Player A or Player B. You estimate that Player B is about 15 feet from you, as shown. How far away from you is Player A?

Answer:

1 5/12

Step-by-step explanation:

subtract 3 3/4 - 2 1/3 and you get 1 5/12

Answer:

17/12

Step-by-step explanation:

I turned the two fractions into improper fractions and made them have the same denominators. Then I subtracted.

There are 83210 subscribers after 5 days

The given parameters are:

The number of subscribers each day is calculated as:

f(n) = a * (1-r)^n

This gives

f(n) = 93000 * (1 - 2.2%)^n

Evaluate the difference

f(n) = 93000 * 0.978^n

At 5 days, we have:

f(5) = 93000 * 0.978^5

Evaluate

f(5) = 83210

Hence, there are 83210 subscribers after 5 days

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9514 1404 393

Answer:

Step-by-step explanation:

The given equation is in slope-intercept form:

  y = mx +b . . . . . . line with slope m and y-intercept b

For the purpose of this question, you need to recognize that the line with equation ...

  y = -7x +8

has a slope (x-coefficient) of -7.

The parallel line will have the same slope (x-coefficient).

The perpendicular line will have a slope that is the opposite reciprocal of this:

  m = -1/(-7) = 1/7

Each line will have a y-intercept (b) that makes the line go through the given point. The y-intercept can be found by solving the slope-intercept equation for b:

  b = y - mx . . . . . . where (x, y) is the point you want the line to go through

__

parallel line:

  b = -2 -(-7)(-6) = -2 -42 = -44

The equation of the parallel line is y = -7x -44.

__

perpendicular line:

  b = -2 -(1/7)(-6) = -14/7 +6/7 = -8/7

The equation of the perpendicular line is y = 1/7x -8/7.

None of the above. To form a standard triangle, all 3 sides must be of equal length.

Answer:

22

Step-by-step explanation:

21.994

5+ round up

The item that is not an item in the income statement is b. Furniture & Fixture as it is considered a fixed asset and is reported on the balance sheet instead.

The income statement, also known as the profit and loss statement, provides a summary of a company's revenues, expenses, gains, and losses over a specific period. It helps to assess the financial performance of a business. The income statement typically includes various items such as revenues, cost of goods sold, operating expenses, interest income or expense, and other gains or losses.

a. Discount allowed is a revenue item that represents the discounts given to customers as an incentive for early payment or other reasons. It is usually reported as a deduction from sales revenue.

c. Furniture & Fixture is not typically included in the income statement. Instead, it is considered a non-operating or non-recurring item and is generally classified as a fixed asset on the balance sheet. Fixed assets represent long-term investments made by a company for its operations.

d. Discount received is also not an item in the income statement. It represents the discounts received by a company from its suppliers for early payment or other reasons. Similar to discount allowed, it is usually reported as a deduction from the respective expense account.

In summary, b. Furniture & Fixture is the item that is not included in the income statement. It is considered a fixed asset and is reported on the balance sheet instead.

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X=3

Step-by-step explanation:

\(6 \frac{1}{9}x + 3 \frac{1}{3}x = 28\frac{1}{3} \)

\(6 \frac{1}{9}x + 3 \frac{3}{9}x = 28\frac{1}{3} \\ \\ 9 \frac{4}{9}x = 28\frac{1}{3} \)

x=3

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Answer:

12

Step-by-step explanation:

The problem written out is -3 x -4 and that is positive 12.