A boat travels about 8 kilometers per hour in
still water. If the boat is on a river that flows at a
constant speed of kilometers per hour, it can
travel at a 8 + r speed of kilometers per hour
downstream and 8 − r kilometers per hour
upstream. On the Chattahoochee river, the
boat can travel 4 kilometers upstream in the
same amount of time it takes to travel 12
kilometers downstream. What is the speed of the
river?

The solution set for the given inequality is {6, 7, 8, 9, 10,.....}.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -1/2(8x-32)< -4

Multiply by -2 on both the sides of an inequality, we get

(8x-32)>8

Add 32 on both the sides of an inequality, we get

8x>40

Divide 8 on both the sides of an inequality, we get

x>5

So, solution set is {6, 7, 8, 9, 10,.....}

Therefore, the solution set for the given inequality is {6, 7, 8, 9, 10,.....}.

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Answer: x = 11

Step-by-step explanation:

divide both sides by 12

12x/12 = 132/12

simplify it and you get your answer :)

x = 11

Answer:

6x - 5 = 6x - 5

Step-by-step explanation:

If we have the same quantity on both sides of the equation, then the equation becomes an identity — an equation that is true for any value of the present variables.

If we set 6x - 5 equal to 6x - 5, then there are infinite solutions.

For example,

when x is 3:

6(3) - 5 = 6(3) - 5

18 - 5 = 18 - 5

13 = 13 ✔

when x is 5:

6(5) - 5 = 6(5) - 5

30 - 5 = 30 - 5

25 = 25 ✔

Answer: 0.46.

Step-by-step explanation:

The probability that a randomly selected can of food will be corn is equal to the fraction of cans that are corn, out of the total number of cans.

Since 46 out of 100 people brought a can of corn, we can assume that there were 46 cans of corn donated. We do not know how many total cans were donated, but we can find out by using the fact that each person was required to bring one can of food. Therefore, the total number of cans donated is equal to the total number of people who attended the dance, which is 100.

So, the probability of selecting a can of corn is:

P(corn) = Number of cans of corn / Total number of cans

P(corn) = 46 / 100

Simplifying the fraction, we get:

P(corn) = 23 / 50

Therefore, the probability that a randomly selected can of food will be corn is 23/50 or approximately 0.46.

The equation of circle with center ( -6 , 3 ) is ( x + 6 )² + ( y - 3 )² = 9² , where the radius of circle r = 3 units

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be represented as r

Now , the first point is A ( -6 , 3 )

Let the second point be B ( -15 , 3 )

Let the third point be C ( 3 , 3 )

And , from the distance formula ,

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

The distance of AB = √ ( -15 + 6 )² + ( 3 - 3 )² = 9 units

The distance of AC = √ ( 3 + 6 )² + ( 3 - 3 )² = 9 units

The distance of BC = √ ( -15 - 3 )² + ( 3 - 3 )² = 18 units

So , the measure of AB = AC and the radius of the circle r = 3 units

Now , the center of the circle is A ( -6 , 3 )

where the standard form of a circle is

( x - h )² + ( y - k )² = r²,

On simplifying , we get

( x + 6 )² + ( y - 3 )² = 9²

Hence , the equation of circle is ( x + 6 )² + ( y - 3 )² = 9²

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The inverse function that represents the gallons g as a function of miles m is:

               g = m/35.

What is meant by the inverse of a function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " f ⁻¹ " or " F ⁻¹."

Given a function m = 35g

 where m = distance in miles travelled by the truck

            g = gallons of gas used to travel m distance

If the function is m = 35g

Then the inverse function is g = m/35.

The inverse of the given function tells us how many gallons of gas are needed for a given number of miles.

Therefore the inverse function that represents the gallons g as a function of miles m is:

               g = m/35.

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Measure of angle V is 103°.

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

Here is a six sided polygon, which is hexagon.

Sum of interior angles of a polygon = (n - 2) 180, where n is the number of sides of the polygon.

Sum of the interior angles of the given polygon = (6 - 2) 180 = 720

So,

∠S + ∠T + ∠U + ∠V + ∠W + ∠X = 720°

90° + (9x - 19)° + 111° + (5x + 8)° + 128° + (7x + 3)° = 720°

9x + 5x + 7x + 90 - 19 + 111 + 8 + 128 + 3 = 720

21x + 321 = 720

21x = 399

x = 19

∠V = (5 × 19) + 8 = 103°

Hence the angle V is of measure 103°.

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Answer: please look at the image for the answer

Step-by-step explanation:

No, Mandisa's interpretation is incorrect because range does not describes the weight of the cats.

The range of a data set is the difference between the largest and smallest values in the set. In this case, the range of the data set is 5, which means the difference between the highest value and the lowest value is 5. This does not necessarily mean that half the cats at the shelter weigh no more than 5 pounds.

For example, if the smallest value is 2 and the largest value is 7, the range would be 7 - 2 = 5. This means that the range of the data set is 5, and yet the weight of a cat can be 7 pounds (more than 5 pounds). It does not mean that half the cats weigh no more than 5 pounds.

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The derivative of y = sin(x)cos(x) is 2sin(x)cos(x).Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)

The rule for derivatives of trigonometric functions states that the derivative of a trigonometric function is the product of the coefficient and the derivative of the other function in the product. This rule can be expressed mathematically using the following formula: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) For example, let's say that we want to calculate the derivative of the function y = sin(x)cos(x). Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x) Therefore, the derivative of y = sin(x)cos(x) is 2sin(x)cos(x).

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19 has an infinite number of multiples since we can multiply 19 by any positive integer to get a new multiple.

A multiple of number is product of that number and  other integer.

To find the multiples of 19, we need to multiply 19 by every positive integer. So, the multiples of 19 are:

19 × 1 = 19

19 × 2 = 38

19 × 3 = 57

19 × 4 = 76

19 × 5 = 95

19 × 6 = 114

19 × 7 = 133

19 × 8 = 152

19 × 9 = 171

19 × 10 = 190

and so on.

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The distance of P to Q is given as follows:

89.6 feet.

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

The parameters for this problem are given as follows:

a = 120, b = 100, C = 47º.

Hence the distance is obtained as follows:

c² = 120² + 100² - 2 x 120 x 100 x cosine of 47 degrees

c² = 8032

c = sqrt(8032)

c = 89.6 feet.

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Answer:

Step-by-step explanation:

[tex]\mathrm{3 (x - 10) = 63}[/tex]

Divide both sides by 3:-

[tex]\mathrm{x-10=\cfrac{63}{3} }[/tex]

Divide 63 by 3 = 21:-

[tex]\mathrm{x-10=21}[/tex]

Add 10 to both sides:-

[tex]\mathrm{x=21+10}[/tex]

Add 21 and 10 = 31:-

[tex]\mathrm{x=31}[/tex]

____________________

Hope this helps!

Step-by-step explanation:

Let n= The first number

Let x= The second number

(5n-7)+9x

This is if the number are different numbers.

If they are the same:

Let n= a number

(5n-7)+9n=

7n-7

Answer: Child ticket: $8, Adult ticket: $6

Step-by-step explanation:

Let's call the price of 1 adult ticket "a" and the price of 1 child ticket "c".

On the first day, the school sold 3 adult tickets for a total of 3a dollars, and 2 child tickets for a total of 2c dollars, for a total of 34 dollars. So, we have the equations:

3a + 2c = 34

On the second day, the school sold 3 adult tickets for a total of 3a dollars and 12 child tickets for a total of 12c dollars, for a total of 114 dollars. So, we have another equation:

3a + 12c = 114

We can now use these two equations to solve for the value of "a" and "c".

We can use substitution to solve for one variable, then substitute it back into either of the equations to solve for the other variable.

Let's solve for "a" by substituting the first equation into the second:

3a + 12c = 114

3a = 114 - 12c

a = (114 - 12c) / 3

Now that we have an equation for "a", we can substitute it back into the first equation to solve for "c":

3a + 2c = 34

3[(114 - 12c) / 3] + 2c = 34

114 - 12c + 2c = 34

-10c = -80

c = $8

So, the price of 1 adult ticket is

a = (114 - 12c) / 3

a = (114 - 12 * 8) / 3

a = (114 - 96) / 3

a = 18 / 3 = $6.

Shawna's new score is 2 and the equation to represent Shawna’s new score would be, New score = Current score + Result of black cube + Result of red cube

What exactly are algebraic expressions?

Algebraic expressions are expressions made up of variables and constants. Additional algebraic operations include addition, subtraction, and division.

If the result of a red numbered cube represents a negative number, then we can represent the result of the red cube as -5. Similarly, if the result of a black numbered cube represents a positive number, we can represent the result of the black cube as +3.

Shawna's current score is 4, and her new score is obtained by adding the results of the two cubes to her current score. We can represent this situation with the following equation:

New score = Current score + Result of black cube + Result of red cube

Substituting the values we have for the result of the black cube, the result of the red cube, and Shawna's current score, we get:

New score = 4 + 3 + (-5)

Simplifying, we get:

New score = 2

Therefore, Shawna's new score is 2 and the equation to represent Shawna’s new score would be, New score = Current score + Result of black cube + Result of red cube.

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The length of JM is given as follows:

JM = 16.875.

Similar polygons are polygons that share these two features presented as follows:

The polygons for this problem are similar, hence the proportional relationship for the segment lengths is given as follows:

16/15 = JM/18

Then the length of JM is obtained applying cross multiplication as follows:

16JM = 15 x 18

JM = 15 x 18/16

JM = 16.875.

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68.4 is approximately 95% of 72.

Here, we have,

To find out what percent of 72 is 68.4, we can follow these steps:

Step 1: Divide 68.4 by 72.

68.4 / 72 = 0.95

Step 2: Convert the decimal to a percentage by multiplying by 100.

0.95 * 100 = 95

Therefore, 68.4 is approximately 95% of 72.

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Solving the equations for each given variables, we have:

a. t = 15

b. a = 12.5

c. p = 5/2

d.

y = 4

Finding the value of a variable in an equation involves solving the equation for that variable. This process typically involves several steps, including isolating the variable on one side of the equation, using inverse operations to simplify the expression, and substituting known values into the equation to find the value of the variable.

Therefore:

a. 2/5t = 6

Multiply both sides by 5/2:

t = 6 * 5/2

t = 15

b. -4.5 = a - 8

Add 8 to both sides:

-4.5 + 8 = a

12.5 = a

a =12.5

c. 1/2 + p = 3

p = 3 - 1/2

p = 5/2

d. -12 = -3y

-12/-3 = y

4 = y

y = 4

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(9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

Two or more expressions with an Equal sign is called as Equation.

For the first 8 hours: The flat rate is $9.50 per hour, so 15% of that rate is 0.15 x 9.50 = $1.43.

The cost for the first 8 hours is (9.50 + 1.43) x 8 = $96.64.

For the next 8 hours: The flat rate is still $9.50 per hour, so 10% of that rate is 0.10 x 9.50 = $0.95.

The cost for the next 8 hours is (9.50 + 0.95) x 8 = $76.40.

Total cost estimate = $96.64 + $76.40 = $173.04

We can also write the equations for the costs as follows:

For the first 8 hours: Cost = (9.50 + 0.15 x 9.50) x Hours = 1.15 x 9.50 x Hours

For the next 8 hours: Cost = (9.50 + 0.10 x 9.50) x Hours = 1.10 x 9.50 x Hours

Using these equations, we can calculate the cost for any number of hours up to 16.

Hence, (9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

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Answer:

(9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

Step-by-step explanation:

59 is a prime number.

This means that it cannot be divided evenly by any other number except for 1 and itself. A composite number, on the other hand, can be divided evenly by at least one other number besides 1 and itself.

To determine if a number is prime or composite, you can use a simple test. Start by dividing the number by 2. If the result is a whole number, then the number is composite.

If the result is not a whole number, try dividing by 3, 4, 5, and so on until you find a whole number result or until you reach the square root of the original number. If you reach the square root without finding a whole number result, then the number is prime.

For example, with the number 59:

59 / 2 = 29.5 (not a whole number)
59 / 3 = 19.67 (not a whole number)
59 / 4 = 14.75 (not a whole number)
59 / 5 = 11.8 (not a whole number)
59 / 6 = 9.83 (not a whole number)
59 / 7 = 8.43 (not a whole number)
59 / 8 = 7.38 (not a whole number)

Since we have reached the square root of 59 without finding a whole number result, we can conclude that 59 is a prime number.

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Supplementary angles are important in mathematics because they have a sum of 180 degrees.

This property is used in various geometric constructions and proofs, as well as in solving real-world problems involving angles. For example, in trigonometry, the concept of supplementary angles is used to determine the values of trigonometric functions for angles greater than 90 degrees.

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The solution is: the cost of renting one chair is $2.25

the cost of renting one table is $8.25.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Let x represent the cost of renting one chair.

Let y represent the cost of renting one table.

The total cost to rent 3 chairs and 5 tables is $48. This means that

3x + 5y = 48 - - - - - - - - - -1

The total cost to rent 6 chairs and 2 tables is $30. This means that

6x + 2y = 30 - - - - - - - - - -2

Multiplying equation 1 by 6 and equation equation 2 by 3, it becomes

18x + 30y = 288

18x + 6y = 90

Subtracting, it becomes

24y = 198

y = 198/24 = 8.25

Substituting y = 8.25 into equation 1, it becomes

3x + 5 × 8.25 = 48

3x + 41.25 = 48

3x = 48 - 41.25

= 6.75

x = 6.75/3

= 2.25

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Answer:

Step-by-step explanation:

Let us consider the Ginger to be x years old.

Therefore, her grandmother will be 10x years old(10 times Ginger's age)

So,

10x+x=66

(adding both Ginger and her grandmother's age)

11x=66

(adding x and 10x)

x=66/11

x=6

Ginger's age is 6.

Her grandmother is 10 times her age.

Therefore she is 60 years old.

Seraphina's speed has increased by a factor of around 23% compared to the first hour.

What Is a Change in Percentage?

The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.

How can you determine the percentage to the closest tenth?

Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.

Percent Change Formula = [tex]\frac{ (Final value -Initial value)}{ (Initial value)}[/tex]× 100

Percent Change               = [tex]\frac{(74-60)}{60}[/tex]× 100

…                                     = [tex]\frac{14}{60}[/tex] × 100

...                                     ≈ 0.23333 × 100

Percent Change             ≈ 23.33%

The pace of Seraphina increased by around 23% in the second hour compared to the first.

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The diameter of the pizza to the nearest inch is 11 inches.

Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:

C = πd

And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:

5.5 = (1/8)C

So we can substitute the formula for the circumference into this equation:

5.5 = (1/8)(πd)

Solving for d, we can multiply both sides by 8/π:

d = (5.5)(8/π)

Calculating the approximate value of π as 3.14, we get:

d ≈ (5.5)(8/3.14) = 11 inches

So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.

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380 liters of natural oil is needed

The ratio of natural oil to synthetic oil is 4:5

Total number of petrolyn oil is 855

4x + 5x= 855

9x= 855

x= 855/9

x= 95

The number of natural oil is 4x

= 4(95)
= 380

Hence the number of liters of natural oil that is needed is 380

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The number of rectangular table is equal to 5 rectangular tables.

The number of circular table is equal to 5 circular tables.

In order to write a linear system of equations to describe this situation, we would a assign variable to the number of circular table and the number of rectangular table respectively, and then translate the word problem into a linear equation as follows:

Since there are 9 tables and 80 chairs set up with 8 chairs each for the circular table and 10 chairs each for the rectangular table, a linear equation to model this situation is given by:

8x + 10y = 80    .......equation 1.

x + y = 9            .......equation 2.

In this scenario, we would use an online graphing calculator to plot the linear system of equations in order to determine the solution (point of intersection) as shown in the image attached below, which is at the ordered pair (5, 4).

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Answer:

the answer is D (4,∞)

Step-by-step explanation:

3n-12>4n-16

C.L.T.

3n-4n>-16+12

-n>-4

n>4