A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.

Part A. Write and solve a system of equations to model this situation.

Part B. Then explain the meaning of your solution.

The required, bike is the fastest among all the vehicles.

Unit conversion is defined as the conversion of units of the same identity through various methods such as, meters in kilometers and centimeters in kilometers.

1.
In 5 seconds skateboard traveled 90 feet.

SInce 1 feet = 30.48 centimeter
90 feet = 2743.2 centimeter

2.
In 5 seconds scooter traveled 1,020 inches
Since 1 inch = 2.54 centimeter,
1020 inches = 2590.8 centimeter

3.
In 5 seconds  bike traveled 4800 centimeters

4.
In 5 seconds go-kart traveled 0.03 kilometers

Since, 1  kilometers = 100000 centimeter

0.03  kilometers = 3000 centimeter

Now compare all the distances which one has the higher distance will be the fastest,
Bike > go-kart > skateboard > scooter.

Thus, Bike is the fastest vehicle.

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Answer:

1/ y= -3x + 12.96

2/ $9.99 for an entire album & $0.99 for a song

Step-by-step explanation:

We know that the

The amount charged for downloading individual songs = x dollars

And the amount charged for downloading an entire album = y dollars

Let's write a function for person A first

6x + 2y = 25.92

Solve, and we will get

y = -3x + 12.96

Now to person B

4x + 3y = 33.93

Putting the value of y from the first equation in the second

4x + 3(12.96 - 3x) = 33.93

- 5x = - 4.95

x = $0.99

Then we take

y = 12.96 - 3x

= 12.96 - 2.97

= $9.99

The distance that Peter rode more than Lauren is 398 m  .

In the question ,

it is given that ,

before stopping the distance that Peter rode is = 1km = 1000 m .

the distance that Lauren rode is = 602 m .

the difference in the distance can be calculated using the formula ,

So , the difference in the distance is = (distance rode by Peter) - (distance rode by Lauren) .

Substituting the values from above ,

we get ,

= 1000 - 602

on further simplification,

we get ,

= 398 m

Therefore , Peter rode 398m farther than Lauren .

The given question is incomplete , the complete question is

Peter rode her bike 1 km before stopping. Lauren rode 602 m before stopping. How many meter farther did Peter ride than Lauren ?

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The number of oil changes that Will and Owen would each have done is 6 oil changes respectively.

The number of hours it would take both Will and Owen is equal to 4 hours.

In order to write a system of equations to describe this situation, we would assign variables to the number of hours per oil change and number of oil changes respectively, and then translate the word problem into algebraic equation as follows:

Since Will has already finished 4 oil changes today, and can complete more at a rate of 2 oil changes per hour, we have;

y = 2x + 4     .....equation 1.

Since Owen just came on shift, and can finish 3 oil changes every hour, we have;

y = 3x     .....equation 2.

Next, we would determine the number of hours per oil changes they both would have each completed by equating equation 1 and equation 2 as follows;

3x = 2x + 4

3x - 2x = 4

x = 4 hours.

For the number of oil changes for Will, we have;

y = 2(4) + 4

y = 12 oil changes.

For the number of oil changes for Owen, we have;

y = 3(4)

y = 12 oil changes.

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Answer:

  300%

Step-by-step explanation:

You want to know what percentage 15 is of 5.

A ratio or fraction is converted to a percentage by multiplying by 100%.

 [tex]\dfrac{15}{5}\times100\% = \boxed{300\%}[/tex]

15 is 300% of 5.

Answer:

Step-by-step explanation:

To estimate the distance across the gorge, Jamal can use the following steps:

First, he can draw a diagram to represent the situation. He can label points Y, X, A, and B on the diagram and draw the lines YX and AB to represent the locations of the tree and the points he marked.

Next, he can use the Pythagorean Theorem to find the distance AC. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the side AC is the hypotenuse, and the sides YA and YC are the other two sides. Therefore, he can use the theorem to find AC as follows:

AC^2 = YA^2 + YC^2

He knows the values of YA (500ft) and YC (327ft), so he can substitute these values into the equation and solve for AC:

AC^2 = 500^2 + 327^2

AC^2 = 250000 + 107649

AC^2 = 357659

AC = √357659

AC ≈ 597.56 ft

Finally, he can use the distance AC to estimate the distance across the gorge. The distance across the gorge is equal to the distance from X to Y, which is equal to the sum of the distances from X to A and A to Y. Therefore, he can estimate the distance across the gorge as follows:

distance across gorge = XA + AY

distance across gorge = AC + YA + YC

distance across gorge = 597.56 ft + 500 ft + 327 ft

distance across gorge ≈ 1424.56 ft

This is Jamal's estimate of the distance across the gorge.

Answer:

N=3. you get this by using the proportion 6/N=1/1/2.

A number plus1/5 of the number can be expressed as n + 1/5n .

A number is defined as it is an arithmetic value which is used to represent the given quantity or in making calculations. Hence, a number is a mathematical concept which is used to count, measure, and label it . Thus, we can say that numbers form the basis of mathematics.

n = number

A number in which we plus 1/5 of the number then it can be expressed as;

1 + 1/5 n

6/5 + n

n + 1/5 n

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Answer: -3.5

Step-by-step explanation:

The speed of the cyclist in miles per hour is 16 miles per hour

The speed of an object is the rate of change of the object's distance over time

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

A cyclist rides 8 miles in 30 minutes.

The parameters in the above statement can be further expressed as

Distance = 8 miles

Time = 30 minutes

This means that the distance is 8 miles and the time taken to cover the distance is 30 minutes

Convert the minutes to hour

So, we have

Time = 0.5 hour

The speed of the cyclist in miles per hour is then calculated as

speed = 8 miles/0.5 hour

Evaluate the quotient

speed = 16 miles/hour

Hence, the cyclist' speed is 16 miles/hour

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The value of the x for the given condition will be 4.14.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that, ∠1 =10x-22, ∠2=3x+7

Since they are vertically opposite angles they are equal.

∠1 = ∠2

10x-22 = 3x+7

10x-3x=7+22

7x=29

x=29/7

x=4.14°

Thus, the value of the x for the given condition will be 4.14.

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The value of x is 15, for the given pair of parallel lines.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Lines y and z are parallel,

And angles are (10x-22)° and 3x+7)°

The supplementary angle of (10x-22)° is 180° - (10x-22)°.

Since, lines y and z are parallel, therefore,

angle 180° - (10x-22)° and (3x+7)° will be equal.

180° - (10x-22)°  = (3x+7)°

180° = 3x+7 + 10x - 22

180 = 13x - 15

195 = 13x

x = 15

The required value of x is 15.

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Answer: 5 trust me

Step-by-step explanation: trust me

The required type of p-value would she want to obtain is small p-value.

Hypothesis testing is a type of measurable surmising that utilizes information from an example to make inferences about a populace boundary or a populace probability distribution. Initial, a speculative supposition that is made about the boundary or dispersion.

P-value  shows that the outcomes are genuinely huge.

P-value  in Measurements assists with performing speculation test and it assists with deciding the meaning of the outcomes.

A little P-value  commonly (P<0.05) demonstrates solid proof against the invalid speculation in this way, we reject the invalid speculation, on opposite when P-esteem is enormous we can't dismiss the invalid speculation.

Thus, required answer is small p-value.

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The equation of line is given below:

a) m = 2 , b = -3

b) m = -3/2 , b = -2

c) m = not defined , b = none

d) m = 0 , b = -8

e) m = [tex]\frac{2}{3}[/tex] , b = -4

What do you mean by equation of line?

A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. A number of points that together form a line of axes, represented as a set of variables x,y, form an algebraic equation called the line equation.

Slope intercept form of the line is y = mx - b where m is the slope of the line and b is the x-intercept

a) y = 2x + 3

On comparing the equation with y = mx - b, we get m = 2 , b = -3

b) 2y = -3x -4

⇒ y = ( -3x -4 )/2

⇒ y = [tex]\frac{-3x}{2}[/tex] - 2

On comparing the equation with y = mx - b, we get m = -3/2 , b = -2

c) x = -10

⇒ x + 10 =  0

On comparing the equation with y = mx - b, we get m = not defined , b = none

d) y= 8

On comparing the equation with y = mx - b, we get m = 0 , b = -8

e) 3y = 2x + 12

⇒ y = (2x + 12)/3

⇒ y = [tex]\frac{2x}{3}[/tex] + 4

On comparing the equation with y = mx - b, we get m = [tex]\frac{2}{3}[/tex] , b = -4

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The required solution of the nonlinear equation is (4, 13) and (2, 1).

Given that,
To solve the nonlinear system of equations for real solutions. y =x²-3, 6x-y=11.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
y =x²-3  - - - - - [1]

6x-y=11
From equation 1,
6x -x² + 3 = 11
x² - 6x + 8 = 0
x = 4, and 2

Substitute this x's in equation 1
That gives for the above x's,
y = 13 and 1

Thus, The required solution of the nonlinear equation is (4, 13) and (2, 1).

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The given inequality in the graph is represented by the inequality y < x - 2. The correct option is C.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given that the graph is attached to the question and shows one of the inequalities from the options.

When the inequalities are plotted on the desmos graph it is observed that the inequality which represents the graph is y < x − 2.

Therefore, the given inequality in the graph is represented by the inequality y < x - 2. The correct option is C.

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To correct Sarah's answer, the standard form of the given value would be = 4.01 × 10^⁹ km.

Standard form is defined as the simplified method of representation of large numericals using decimal number, between 1.0 and 10.0, which is then multiplied by a power of 10.

The distance between the earth and Mars = 4.01 x 100,000,000 kilometers.

There are 9 digits in 100,000,000,

Therefore to write the standard form of the given distance of 4.01 x 100,000,000 kilometers would be;

4.01 × 10^⁹ km.

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The coordinates of points C are (4,1).

The coordinates of the points D are (3, 2) respectively.

y = mx + c. Conversely,is the formula of coordinate that help to find  satisfy to the equation y = mx + c is always lie on the line with the gradient m and y-intercept of c.

If the point C is divides AB in the ratio 2:3, then the coordinates of C are;

Xc=2(1)+3(6)/2+3

Xc=2+18/5

Xc=20/5 = 4

Yc=2(4)+3(-1)/2+3

Yc=8-3/5

Yc=5/5 = 1

The coordinates of points C are (4,1).

If the point D divides the  AC in the ratio 3:2, then the coordinates of D are-

Xc= 3(1)+2(6)/3+2

Xc=3+12/5

Xc=15/5 = 3

Yc=3(4)+2(-1)/3+2

Yc=12-2/5

Yc=10/5=2

The coordinates of the point D are (3, 2).

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Answer:

Step-by-step explanation:

Rounding to 1 sig fig:

12 becomes 10

478 becomes 500 (that hurts)

Multiply

10 x 500 = 5000

[Actual value of 12 x 478 is 5736. The reason the estimated value is lower is due to the fact that going from 12 to 10 was a reduction of 17%, while going from 478 to 500 was an increase of only 5%]

The rate of change of the area is 3868.48 cm2/min

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

A = A(r) (r)

r = r(t) (t)

A = A(r(t))

The chain rule can be used to resolve this kind of issue.

Rate of area change:

(dA/dr)(dr/dt) = dA/dt

A=r2 dA/dr = 2r

dr/dt [given] = 7 cm/min

(2r)(7 cm/min) = (dA/dt)

If r = 88 cm,

dA/dt = 2π (88 cm) (7 cm/min) ≅ 3868.48 cm2/min

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The exact distance Adam traveled was v miles is 334.488 miles.

What is distance ?

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance travelled between them are not the same. Distance traveled is the total length of the path traveled between two positions. Travel distance is not a vector.

Exact = 334.488 miles

Rounded, 72 × 5 = 360

There were 3 decimal places in the factors, so after multiplying all the digits, put a decimal point 3 places from the right.

Your estimate from the rounded numbers is supposed to help confirm a reasonable answer.

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Step-by-step explanation:

The answer is

[tex] \frac{1}{ab} [/tex]

because

[tex] \frac{1}{a(a + b)} + \frac{1}{b(a + b)} = \frac{1}{ab} [/tex]

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Options B, C and D are the situations it is appropriate to use a sample.

Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method.  The sample is chosen by a random method as every subject in the sample is assigned a number.

Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searching people and collecting data from them.

Therefore, options B, C and D are the situations it is appropriate to use a sample.

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Answer:

B,C,D

Step-by-step explanation:

The function has been shifted down by 8 units.

Here given the function,

y = x

Required that,

Find the transformation that results in: y = x - 8

When a function f(x) is shifted by b units, the new function g(x) is defined as g(x) = f(x) - b.

In this instance:

y = x

b = 8

As a result, the new function is:

y = x - b

8 should be substituted for b.

y = x - 8

Hence, the function is shifted 8 units downward,

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Therefore , the price per ticket is $12,the equation used is y=12x, the theatre made $3936 by selling 328 ticket and the relationship is proportional.

An algebraic equation is a linear equation. Each term in a linear equation is either a constant or the result of a constant plus one variable. In the case of a linear equation with two variables, the graph is a straight line.

Here,

A) From the given  we can find the price per ticket

which is => y/x

=> 60/5

=>12

Therefore the price per ticket is $12

B)The equation can be used to represent the graph is

y= 12x

C) The theater were to sell 328 tickets they would make

=> 328*12=3936

Therefore the money would they make is $3936

D)The relationship proportional as we can see from the graph

Therefore , the price per ticket is $12,the equation used is y=12x, the theatre made $3936 by selling 328 ticket and the relationship is proportional.

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The output will be if Input (x) = a number is y = 3x - 8, so option D is correct.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

Input (x) = a number,

Output (y) = 8 less than 3 times x.

Assume a number x which is an input,

3 times of x  = 3x,

8 less than 3 times of x = 3x - 8

Therefore, the output will be if Input (x) = a number is y = 3x - 8.

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Answer:

Hope this help :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

-x+6y= 5  ----1

2x - 12y = -10 ----2

6y = x + 5

y = (x + 5)/6

2x -12(x + 5)/6 = -10

2x - 2x + 5 = -10

0 = -15

so, x and y have no value

The value of the sixth term of the sequence will be negative 64.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

If the first term (a₁) is 2 and the relation is aₙ = -2aₙ₋₁.

The second term is given as,

a₂ = -2a₂₋₁

a₂ = -2a₁

a₂ = -2 x 2

a₂ = - 4

The third term is given as,

a₃ = -2a₃₋₁

a₃ = -2a₂

a₃ = -2 x ( - 4)

a₃ = 8

The fourth term is given as,

a₄ = -2a₄₋₁

a₄ = -2a₃

a₄ = -2 x 8

a₄ = - 16

The fifth term is given as,

a₅ = -2a₅₋₁

a₅ = -2a₄

a₅ = -2 x (- 16)

a₅ = 32

The sixth term is given as,

a₆ = -2a₆₋₁

a₆ = -2a₅

a₆ = -2 x 32

a₆ = - 64

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Answer: -64

Step-by-step explanation: