Mrs. Evans is taking 9 students to an amusement park. Mr. Sanchez is taking 14 students to a water park. Each student will buy a ticket to the appropriate park and pay for a ride fee. Admission to the amusement park is 2 times that of the water park's admission as shown in the table. The total cost is the same for both groups of students.
Amusement Park
Water Park
Admission: $2x per student
Admission: $x per student
Ride Fee: $3.00
Which equation represents the problem?
Ride Fee: $4.50
O A) 9(x + 4.50) = 14(2x + 3.00)
O B) 9(x + 3.00) = 14(2x + 4.50)
O C) 9(2x + 4.50) = 14(x + 3. 00)
O D) 9(2x + 3. 00) = 14(x + 4.50)

The solution to the following functions are 1) 6x5-3x4, 3x4+1, 6x5-3x4, 3x4 / (2x-1),  2)(x-1)/x3, (x-1)/x2 - 1/x,  (x-1)/x3, x-1

The relationship between two sets of numbers is described mathematically by a function. It is a mathematical equation that assigns a unique output value to each input value inside a specific domain. Functions are frequently expressed by a letter, such as  F(x) = 3x+ 4 or g(x), where the letter indicates the function and the input value is represented by the variable x.

Functions can be either linear or nonlinear, and they can have a single or numerous outputs for each value of the input. They are frequently employed to simulate real-world situations and generate predictions based on available information. Functions can be graphed on a coordinate plane to visualise their behavior, and they can be combined or transformed using various mathematical operations.

How to solve?

1)a. (fg)(x) = (3x4)(2x-1) = 6x5-3x4

b. (f-g)(x) = (3x4) - (2x-1) = 3x4+1

c. (f *g )(x) = (3x4) * (2x-1) = 6x5-3x4

d. (f/g) (x) = (3x4) / (2x-1) = 3x4 / (2x-1)

2)a. (fg)(x) = (x-1/x2) * (1/x) = (x-1)/x3

b. (f-g)(x) = (x-1/x2) - (1/x) = (x-1)/x2 - 1/x

c. (f *g )(x) = (x-1/x2) * (1/x) = (x-1)/x3

d. (f/g) (x) = (x-1/x2) / (1/x) = (x-1)/x2 / (1/x) = (x-1)/x2 * x = x-1

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Answer:

---------------------------

Convert the statement into equation, considering the number as x, and solve:

Correct choice is B.

Answer:

z = 7

Step-by-step explanation:

We know that, sum of the exterior angles of a quadrilateral is added up to 360°.

Accordingly,

115 + 7z + 12z + 16z = 360

Combine like terms.

115 + 35z = 360

Subtract 115 from both sides.

35z = 360 - 115

35z = 245

Divide both sides by 35.

z = 7

The midpoint of AC is 0.5 where A is at -2 and C is at 3 on the number line.

A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.

Given that,

A and C are two points on number line.

A is at -2 and C is at 3

The midpoint of AC can be given by finding average of both the points,

Midpoint of AC = (-2 + 3) / 2

                          = 1 /2

                          = 0.5

The required midpoint of AC where A is at -2 and C is at 3 is 0.5.

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Answer:

21

Step-by-step explanation:

Answer:

582.1

Step-by-step explanation:

Answer: 8.8 (-8.8'F)

Step-by-step explanation:

What we know:

Temperature started as 7.2

Temperature ended as -1.6

We need to find the difference

How to solve:

By doing simple subtraction, we can solve this.

Process:

Write equation                                                   7.2 - (-1.6) = ?

Simplify                                                               7.2 + 1.6 = ?

Solve                                                                                 = 8.8

Solution:  {8.8 (-8.8'F)}

The temperature decreased by 8.8'F, but it increased/changed by -8.8'F.

Answer:

x= 19.5

Step-by-step explanation

sin58 = x/23

x = 23×sin58

x = 19.5

The number of fests of light that Mr Green needs 140 feet of lights

The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence.

From the formula for perimeter L x W which will give us.L being 5 and W being 3.5

The equation is 5 × 3.5 = 17.5.

With that being said I just need to multiply that answer by 8 which gives us 140. This means that he will need 140 feet of light in order to put light around each window.

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Answer: answer is b 12$.

Step-by-step explanation:

One of the factors is present in all of the items mentioned. The order of the value of the other factor will match the order of the value of the product.

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the time between high and low tide i 7. 8 hour. At high tide the depth of water i 19. 2 feet, while at low tide the depth i 5. 1 feet. So roughly 2 hours and 15 minutes, the depth will be 12 feet

What is depth?

a measurement made through an object or body of material, typically horizontally inward from an outer surface, upward from an upper surface, or upward from the top of something considered to be one of multiple layers. deepness, the property of being deep.

(0,6)

(8,20)

(16,6)

y = C*sin( k*pi*x) + 6 since (0,6) is given

C(sin(k*pi*8) + 6 = 20

C(sin(k*pi*8) = 14 <--- label this equation ALPHA

Also,

C(sin(k*pi*16) + 6 = 6

C(sin(k*pi*16) = 0

since C cannot be zero,  k*pi*16 must be 180 = pi

                                          k*16 = 1

 k = 1/.16

C(sin( (1/16)*pi*8) = 14

C ( sin (pi/2) ) = 14

C = 14

D(t) = 14 sin( (pi/16) t ) + 6 where D is the depth and t is time

12 = 14 sin((pi/16)t) + 6

6/14 = sin((pi/16)t)

arcsin(3/7)*16/pi = t

t = 2.25572...

So roughly 2 hours and 15 minutes, the depth will be 12 feet

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Answer:

b=-2

Step-by-step explanation:

I dont have the steps srry :(

Answer:

b = -2

Step-by-step explanation:

7b + 3-4b= 3 - 3 (b +4)

[tex]\frac{7}{30}[/tex] of water is left in the pitcher

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

According to the given information

Total water in container = [tex]\frac{5}{6}[/tex]

Total water used to water the plants = [tex]\frac{3}{5}[/tex]

Water left in pitcher = [tex]\frac{5}{6} - \frac{3}{5}[/tex]

Taking LCM we will get

= [tex]\frac{25-18}{30}[/tex]

= [tex]\frac{7}{30}[/tex]

[tex]\frac{7}{30}[/tex] of water is left in the pitcher

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In the provided figure, the value of y is 5.5 units.

Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The values of all trigonometric functions depending on the ratio of sides of a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

Here,

cos 30°=b/15

b=15*cos 30°

b=13 units

since this is square so all sides are equal.

sin 30°=p/15

p=15*sin 30°

p=7.5 units

required difference=13-7.5

=5.5 units

The value of y in the given figure is 5.5 units.

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The formula to find the common difference of an arithmetic sequence is: d = a(n) - a(n - 1), where a(n) is a term in the sequence, and a(n - 1) is its previous term in the sequence

What is arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. For instance, the number sequence 5, 7, 9, 11, 13, and 15 has a common difference of 2 in arithmetic.

Sequences can in fact begin at any number that we choose. A sequence with the general word an is commonly notated as ann=1 a n n = 1.

or d = (an + 1 - an) (an – an-1). AP reduces if the common difference is negative. For instance, the AP drops in these numbers: -4, -6, -8.

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Answer: 2/8

Step-by-step explanation: 2/16 can be simplified to 1/8, 1/8 + 5/8 = 6/8, since a whole bone is 8/8, or 1. 8/8 - 6/8 = 2/8

so, once more, the answer is 2/8.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6\%\ of\ 33.00}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\ of\ 33.00}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\times33.00}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\times 33}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\times \dfrac{33}{1}}[/tex]

[tex]\mathsf{= \dfrac{6\div2}{100\div2}\times \dfrac{33}{1}}[/tex]

[tex]\mathsf{= \dfrac{3}{50}\times\dfrac{33}{1}}[/tex]

[tex]\mathsf{= \dfrac{3\times 33}{50 \times1}}[/tex]

[tex]\mathsf{= \dfrac{99}{50}} \mathsf{\rightarrow 1 \dfrac{49}{50}}[/tex]

[tex]\huge\text{Answer: }[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{99}{50} \ or\ 1\dfrac{49}{50}}}\huge\checkmark[/tex]

[tex]\uparrow\large\text{Either those should work because they are equivalent to (equal to)}\\\large\text{each other}\uparrow[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex]\boxed{\textbf{a}-\dfrac{3}{2}\textbf{b}}[/tex]

[tex]\boxed{10 \textbf{a}-15\textbf{b}}[/tex]

[tex]\boxed{-4 \textbf{a}+6\textbf{b}}[/tex]

[tex]\boxed{2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}}[/tex]

Step-by-step explanation:

Given vector:

[tex]\overrightarrow{\rm FG}=2 \textbf{a}-3\textbf{b}[/tex]

Two vectors are parallel if one can be written as a scalar multiple of the other.

Therefore, the following vectors are parallel to FG:

[tex]\textbf{a}-\dfrac{3}{2}\textbf{b}=\dfrac{1}{2}(2 \textbf{a}-3\textbf{b})[/tex]

[tex]10 \textbf{a}-15\textbf{b}=5(2 \textbf{a}-3\textbf{b})[/tex]

[tex]-4 \textbf{a}+6\textbf{b}=-2(2 \textbf{a}-3\textbf{b})[/tex]

[tex]2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}=6\textbf{a}-9\textbf{b}=3(2 \textbf{a}-3\textbf{b})[/tex]

Answer:

the answer is 306.25 feet and b is 8 sec

Step-by-step explanation:

Explanation

The height of the ball as a function of the time is given by the following formula:

A. Maximum height of the ball

To find the value of the maximum height, we maximum the function h(t) computing its first derivative and equalling the result to zero:

Solving the last equation for t, we get time t when the height is maximum:

So the maximum height is given by the value of h(t) when t = 2.5:

The maximum height is 196ft.

B. Time until the ball hits the ground

The ball will hit the ground when h(t) = 0. So we must find the value of t such that:

Solving this equation is equivalent to finding the roots of a second-order polynomial:

Where:

• a = -16,

,

• b = 80,

,

• c = 96.

The roots of this polynomial are given by the following formula:

s

Answer

A. The maximum height of the ball is 196 ft.

Answer:

Step-by-step explanation:

can you send a much clear image its to blurry I can not read it.

On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.

Here,

[tex]\frac{U}{5} = \frac{17}{11} \\\\[/tex]

[tex]U = \frac{17}{11} X 5\\[/tex]

[tex]U = \frac{85}{11}\\ U = 7.72[/tex]

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A function is a relationship between inputs where each input is related to exactly one output.

The value of f(x) at x = 5 is -23.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -4 |x| - 3

The value of f(x) at x = 5.

f(5) = -4 |5| - 3

f(5) = -4 x 5 - 3

f(5) = -20 - 3

f(5) = -23

Thus,

The value of f(x) at x = 5 is -23.

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The cylindrical wheels covers about 9428.7 squared centimeter

This is the total area covering the entire body of the cylinder.

The formula of surface area of a cylinder is given as;

A = 2πrh + 2πr²

A = 2(22/7) × 30 × 20 + 2(22/7)×30²

A = 9428.57 cm²

The area of the wheel is 9428.7cm²

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Answer:

Step-by-step explanation:

Answer:

c=65

Step-by-step explanation:

a=115

180-115=b

b=65

b=c

c=65

The closest percentage volume that has drained out is 46%

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

V(t) = 4522(0.94)^t

The initial volume is calculated when t = 0

So, we have

V(0) = 4522(0.94)^0

Evaluate

V(0) = 4522

The new volume is calculated when t = 10

So, we have

V(10) = 4522(0.94)^10

Evaluate

V(10) = 2435.62

The percentage is then calculated as

Percentage = (V(10) - V(0))/(V(0))

So, we have

Percentage = (2435.62 - 4522)/4522

Evaluate

Percentage = -46%

Hence, the percentage is 46%

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The box and whisker plot that represents the data given is option D (see attachment below).

The box and whisker plot that represents a data set will display the five-number summary of the data, which include minimum and maximum values, upper quartiles and lower quartiles, and the median of the data.

Given the data set, 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30, the five-number summary that would be displayed on the box and whisker plot include:

Minimum: 6 (at the beginning of the whisker to the left)

First Quartile: 13 (at the beginning of the edge of the box)

Median: 21 (at the middle line on the box)

Third Quartile: 27 (at the end of the edge of the box)

Maximum: 30 (at the end of the whisker to the right)

Therefor, the box and whisker plot would be the option D (see image below).

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Answer: its around 25,000 during the end of august

Step-by-step explanation:

Answer:

(4,12) Quadrant l

(-5,2) Quadrant ll

(-9,-4) Quadrant lV

(3,-3) Quadrant lll

Step-by-step explanation:

hope this helps!