74.50 per hour for billing for 4/12 hours what should be the total amount of the bill?

The given options are 1.7 cm, 71, 21, 1.7 cm, 2.2 cm, 4.3 cm, 53, 377, 2.1 cm, 42, 3.2 cm, 3.8 cm, 3.6 cm, 2.9 cm, 2.5 cm, 34, and 8 cm.

The summary of the answer is that the length of the side is 2.2 cm.

In trigonometry, it is common to use the concept of a right triangle to relate the lengths of its sides with the trigonometric functions. However, without additional context or information about the triangle or the specific problem, it is not possible to determine the length of the side accurately.

Among the given options, the length of the side closest to 2.2 cm is 2.2 cm itself. Therefore, based on the options provided, we can conclude that the length of the side is 2.2 cm. However, it is important to note that without further information or context, this is an assumption based solely on the given options and may not be the correct answer in a different context or problem.

Learn more about  trigonometry here :

https://brainly.com/question/12068045

#SPJ11

In 15 minutes, a water pump capable of pumping 13.2 gallons of water per minute will remove a total of 198 gallons of water from the pool.

If a water pump can pump 13.2 gallons of water in a pool every minute, we can calculate the amount of water it will remove in 15 minutes by multiplying the pumping rate by the duration. Therefore, 13.2 gallons/minute x 15 minutes = 198 gallons. During the 15-minute period, the water pump will continue to operate at a constant rate, removing water from the pool. Each minute, 13.2 gallons of water will be pumped out. When we multiply this rate by the duration of 15 minutes, we find that a total of 198 gallons of water will be removed from the pool. It's important to note that this calculation assumes a constant pumping rate without any interruptions or changes in efficiency.

learn more about efficiency here: brainly.com/question/10478611

#SPJ11

The number of pages read in 72 minutes is 144 pages.

When given a table of values, the relationship between the values ​​is often expressed as a rule or an equation. A formula that links the number of pages in a book to the number of minutes it takes to read it is often used in book reviews or book reports.  

Rule relating to the minutes, x, to the number of pages, y

Let us assume that reading x minutes corresponds to y pages. In other words, we want to identify an equation or formula that links the two variables.

The number of pages read in one minute is calculated by dividing the total number of pages by the total time it takes to read them.

y / x = k, where k is the constant of variation, or the number of pages that can be read in one minute. If the number of pages is directly proportional to the number of minutes, then the k value remains constant.

If we solve for y, we get the following:

y = kx

When the minutes equal 72, we will find the number of pages.

We know that k is a constant, so we may use any of the given (x, y) pairs.

The given minute value is x, and we want to find the corresponding page value, y.

Let us assume that 120 pages can be read in 60 minutes.

We may solve for k using this information:120 / 60 = k2 = k

Now that we know k, we may use the equation to determine the number of pages that can be read in 72 minutes:

y = kx

y = 2 * 72y = 144

to know more about minutes equation visit:

https://brainly.com/question/29477142

#SPJ11

The function h(x) is defined as shown below:

[tex]$$h(x) = \begin{cases} x+2, & \text{if }x <3 \\ -x+8, & \text{if }x\ge3 \end{cases}$$[/tex]

So, option A is the correct answer.

To find the range of h(x), we will analyze the value of h(x) at different values of x. We will start with values less than 3 and then move to values greater than or equal to 3.

Case 1: x < 3 For values of x less than 3, h(x) is given by:

h(x) = x + 2

For minimum value of x (approaching negative infinity), h(x) approaches negative infinity.

For maximum value of x (approaching 3 from left), h(x) approaches 5. So, the range of h(x) for x < 3 is:

-∞ < h(x) <5 Case 2: x ≥ 3

For values of x greater than or equal to 3, h(x) is given by:

h(x) = -x + 8

For minimum value of x (approaching 3 from right), h(x) approaches 5.

For maximum value of x (approaching infinity), h(x) approaches negative infinity.

So, the range of h(x) for x ≥ 3 is: 5 ≤h(x) <∞

Therefore, the range of h(x) is: -∞ < h(x) < ∞

This is equivalent to option A. So, option A is the correct answer.

Note: When the range of a function is the set of all real numbers, we can also represent it as "(-∞, ∞)" or "ℝ".

To know more about maximum visit

https://brainly.com/question/16696252

#SPJ11

The question provides that the blades of a ceiling fan rotate around a fixed axis and begin to rotate with a constant angular acceleration such that they are rotating at 10 revolutions per second after a certain period of time.

After 60 turns, the fan will be rotating at 15 revolutions per second.

Solution:The given data is:Initial angular speed, ω₁ = 0 (since they start from rest)

Final angular speed, ω₂ = 15 revolutions/sec

Angular acceleration, α = constant

Number of revolutions for the first part, n₁ = 60

Number of revolutions for the second part, n₂ = (total revolutions) - (n₁) = (60 + 10) - 60 = 10 revolutions

Using the formula for the angular velocity, ω = ω₀ + αt

and the formula for the number of revolutions, n = ωt / 2π

We can find out the time required to reach a final speed of 15 rev/s as follows:15 = 0 + αt ⇒ t = 15 / α

The total time required to reach a speed of 15 rev/s would be the sum of the time required to reach a speed of 10 rev/s and the time required to reach 15 rev/s.t = t₁ + t₂ ⇒ t₂ = t - t₁

We can find the value of t₁ from the formula for the number of revolutions during the first part of the motion as follows:n₁ = ω₁t₁ / 2π0 = αt₁² / 2 + ω₁t₁ / 2π ⇒ t₁ = 0

Using the formula for the number of revolutions, we can find the value of t₂ as follows:n₂ = (ω₁t₂ + 1/2 αt₂²) / 2π ⇒ t₂ = 20/α

The value of α can be found by equating the two formulas for t₂ obtained above:

20/α = 15 / α + t₁⇒ α = 100 / 3 rad/s²

We can now substitute this value in the formulas for t and t₂ to find the times required to reach speeds of 10 and 15 rev/s respectively.t₁ = 0 s, t₂ = 60 / 3 = 20 s

Answer: The time required for the blades of the ceiling fan to rotate with a constant angular acceleration before rotating at 10 revolutions per second is 0 seconds and the time required to reach a speed of 15 revolutions per second is 20 seconds.

To know more about acceleration, visit

https://brainly.com/question/2303856

#SPJ11

Given,Number of moles of Aluminum fluoride = 12.52 mol AlF3The chemical equation of the reaction between aluminum oxide and fluorine is given by;

2Al2O3 + 6F2 → 4AlF3 + 3O2From the balanced equation above; 2 moles of Al2O3 will produce 4 moles of AlF3Hence, 1 mole of Al2O3 will produce 4/2 = 2 moles of AlF3Number of moles of Aluminum oxide needed to react with fluorine to produce 12.52 moles of aluminum fluoride = 12.52/2 = 6.26 moles Therefore, more than 250 moles of aluminum oxide are needed to react with fluorine to produce 12.52 moles of aluminum fluoride.

To know more about moles visit:

https://brainly.com/question/15209553

#SPJ11

The division expression is 7 divided into 3 which can be represented in unit form as follows; 7 ÷ 3 = 2 R1, this means that 7 divided by 3 equals 2, with a remainder of 1.

The remainder is the value left after an integer has been divided by a divisor, such as the number left over after a long division of 7 ÷ 3. Therefore, the value of circle plus circle is given by the formula: $$\text{Circle plus Circle} = πr_1^2 + πr_2^2$$ where r1 and r2 are the radii of the two circles respectively. If the values of the radii are provided, then we can substitute them in the above formula to find the value of circle plus circle.

The area of a circle is given by the formula A = πr² where A is the area of the circle and r is the radius. Therefore, the formula for the value of circle plus circle is given by Circle plus Circle = πr1² + πr2² where r1 and r2 are the radii of the two circles respectively. As we already know that a circle is a geometric figure having no end. It has many properties. One of its properties is that its area can be measured. When we talk about the area of a circle, we are referring to the region enclosed by it. The area of a circle is given by the formula: A = πr², where A is the area of the circle and r is its radius. The symbol π represents the constant pi, which is approximately equal to 3.14. Therefore, the area of a circle is proportional to the square of its radius. If we have two circles with radii r1 and r2, then the area of the first circle is given by A1 = πr1², and the area of the second circle is given by A2 = πr2².

To know more about represented visit:

https://brainly.com/question/31291728

#SPJ11

The tree is approximately 10.3 meters tall. The distance between Karla's shadow and the tree's shadow is 6.2 meters.

Let's use similar triangles to solve this problem. We have two triangles: one formed by Karla, her shadow, and the distance between her and the tree; and the other formed by the tree, its shadow, and the distance between the tree and Karla.

Let's call the height of the tree "h." According to the given information, Karla's height is 1.6 meters, and the distance between Karla and the tree is 13.5 meters.

Using the concept of similar triangles, we can set up the following proportion:

h/1.6 = (h + 6.2)/(13.5)

Cross-multiplying and solving for "h," we get:

13.5h = 1.6(h + 6.2)

13.5h = 1.6h + 9.92

11.9h = 9.92

h ≈ 9.92/11.9

h ≈ 0.8336

Rounding to the nearest 0.1 meter, the height of the tree is approximately 10.3 meters.

Learn more about meters here: brainly.com/question/372485

#SPJ11

The line joining the midpoint of a median to a vertex of a triangle trisects the side opposite the vertex considered.

Let's consider a triangle ABC with median AD and midpoint M of AD. We want to prove that line BM trisects the side AC at point N.

To prove this, we can use the following steps:

Draw line BM and extend it to meet side AC at point N.

Since M is the midpoint of AD, we have AM = MD.

By the midpoint theorem, we also know that BM is half of AD, so BM = MD.

Therefore, we have AM = MD = BM.

We also know that triangles ABM and NBC are similar by angle-angle similarity, since they share angle B and have angles ABD and CBN that are alternate interior angles.

This means that the corresponding sides are proportional, so we have: AB/BM = BN/NC AB/MD = BN/NC (substituting BM=MD)

Multiplying both sides by 2, we get: AB/AD = 2BN/NC

Since AD is a median, we know that AB/AD = 1/2.

Substituting this into equation from step 7, we get: 1/2 = 2BN/NC

Solving for BN, we get: BN = NC/2.

This shows that line BM trisects side AC at point N.

Therefore, we have proved that the line joining the midpoint of a median to a vertex of a triangle trisects the side opposite the vertex considered.

Learn more about median here

https://brainly.com/question/26177250

#SPJ11

Based on the above, the length of the arch should be approximately 7.85 meters.

To know the length of the arch, one need to calculate the circumference of the semicircle.

The circumference of a full circle is: C = 2πr

Note that the semicircle is (180°), so one need to divide the circumference by 2 to get the length of the arch:

Length of the arch = C/2 = (2πr)/2 = πr

Given the radius (r) of 2.5m, one need to substitute the value into the formula:

Length of the arch = π × 2.5

= 3.14 × 2.5

=7.85 meters

Therefore, the architect should build the arch with a length of about 7.85 meters.

Learn more about arch  from

https://brainly.com/question/28108430

#SPJ4

See text below

An architect designs the main arch of the nave of a church in the shape of a semicircle (180°), with a radius of 2.5m. How long should that arch be built?

To calculate a 15% tip for a restaurant bill of $42.40, we multiply the bill amount by 0.15 to find the tip amount. The result will provide the tip amount, which can be added to the bill to get the total amount to pay. Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To calculate a 15% tip, we take 15% of the bill amount. The tip amount is found by multiplying the bill amount by the decimal equivalent of 15%, which is 0.15.

Given the restaurant bill of $42.40, we can find the tip amount by performing the calculation: $42.40 * 0.15 = $6.36.

Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To check if the answer is reasonable, we can consider the percentage amount and the total bill. A 15% tip is generally considered an average or moderate tip amount. Given the bill of $42.40, a tip of $6.36 seems reasonable in relation to the bill total.

However, tipping customs may vary in different regions or based on personal preferences. It is always advisable to consider the overall service quality and local tipping practices when determining an appropriate tip amount.

Learn more about decimal equivalent here:

https://brainly.com/question/28517838

#SPJ11

The simplified ratio is: 3 : 1. This means that for every 3 liters of white paint, 1 liter of red paint is used in the mixture.

To find the ratio of white paint to red paint, we need to compare the amounts of white paint and red paint used. The given information states that mixing pink paint requires 3 liters of white paint and 1 liter of red paint.

The ratio of white paint to red paint can be expressed as:

White : Red

To simplify this ratio to its lowest terms, we need to find the greatest common divisor (GCD) of the two numbers (3 and 1) and divide both numbers by it.

The GCD of 3 and 1 is 1, as there are no common factors other than 1. Therefore, we divide both numbers by 1:

3 ÷ 1 = 3

1 ÷ 1 = 1

The ratio 3 : 1 represents the proportional relationship between white paint and red paint in terms of liters. It indicates that for every 3 liters of white paint, only 1 liter of red paint is needed to achieve the desired mixture.

This ratio is already in its simplest form since the GCD of 3 and 1 is 1, and there are no further common factors to divide both numbers by.

In conclusion, the ratio of white paint to red paint in the mixture is 3 : 1.

Learn more about ratio at: brainly.com/question/13419413

#SPJ11

The correct representation of the equation "z minus 6 = 1.4" in words is "The difference of a number and z is the same as one and four-tenths."

The equation "z minus 6 = 1.4" can be represented in words as "The difference of a number and z is the same as one and four-tenths." This representation accurately conveys the meaning of the equation.

Let's break down the equation to understand its components. "z minus 6" represents the difference between the number z and 6. The equal sign indicates that this difference is equal to "1.4", which means one and four-tenths.

Now let's analyze the answer choices:

"The difference of a number and z is the same as one and four-tenths." This choice correctly represents the equation, expressing that the difference between a number and z is equal to 1.4.

"A number subtracted from one and four-tenths is equal to six." This choice represents a different equation, where a number is subtracted from 1.4, resulting in six. It does not match the original equation.

"Six less than a number is the same as one and four-tenths." This choice represents a different equation, where six is subtracted from a number, resulting in 1.4. It does not match the original equation.

"Six decreased by a number is equal to one and four-tenths." This choice represents a different equation, where six is decreased by a number, resulting in 1.4. It does not match the original equation.

Learn more about equation at: brainly.com/question/29657983

#SPJ11

The solution to the equation start fraction lower t over 6 end fraction = 12 is lower t = 72. And, to check the solution we have substituted the value we got for lower t in the original equation and verified if it satisfies the equation or not.

The given equation is,start fraction lower t over 6 end fraction = 12To solve for the equation we have to first, cross-multiply both sides of the equation with 6. This will help us to get rid of the fraction.start fraction lower t over 6 end fraction = 12. Multiplying both sides by 6:lower t = 72The solution for the given equation is, lower t = 72.Now, we have to check whether the solution we found is correct or not. We can do this by substituting the value we got for lower t in the original equation.start fraction lower t over 6 end fraction = 12Putting the value of lower t, we get:start fraction 72 over 6 end fraction = 12. Simplifying this, we get:12 = 12.The value of lower t we found satisfied the original equation, therefore the solution is correct.

To know more about fraction, visit:

https://brainly.com/question/10354322

#SPJ11

a) The radian measure is 5π radians.

b) The radian measure is (3πr)/2 radians.

To determine the radian measure corresponding to a certain number of orbits in a circular orbit, we need to know the circumference of the orbit.

The circumference of a circle is given by the formula C = 2πr, where C represents the circumference and r represents the radius.

Let's assume the radius of the circular orbit is denoted by "r."

(a) To find the radian measure for 2.5 orbits:

The total angle covered in 2.5 orbits is equivalent to 2.5 times the full circumference of the orbit.

Angle = 2.5 * (2πr) = 5πr

Therefore, the radian measure corresponding to 2.5 orbits is 5π radians.

(b) To find the radian measure for 3/2 orbit:

The total angle covered in 3/2 of an orbit is equivalent to (3/2) times the full circumference of the orbit.

Angle = (3/2) * (2πr) = 3πr/2

Therefore, the radian measure corresponding to 3/2 of an orbit is (3πr)/2 radians.

To learn more about radian here:

https://brainly.com/question/28990400

#SPJ4

By converting -1 2/3 to an improper fraction, we get -5/3. To add these fractions, we need to find a common denominator, which is 6. Adding the fractions gives us 5/6. Therefore, -1 2/3 - (-5/6) is equal to 5/6.

To perform the addition and subtraction of rational numbers, we start by converting -1 2/3 to an improper fraction. We multiply the whole number (-1) by the denominator of the fraction (3), which gives us -3. Adding the result to the numerator (2) gives us -3 + 2 = -1. So, -1 2/3 can be represented as -5/3.

Next, we rewrite the expression as -5/3 - (-5/6). When we subtract a negative number, it is equivalent to adding the positive value. So, -(-5/6) becomes +5/6.

To add fractions, we need a common denominator. In this case, the common denominator is 6. We multiply the numerator and denominator of -5/3 by 2 to get -10/6. Therefore, the expression becomes -10/6 + 5/6.Now that the fractions have the same denominator, we can add the numerators. -10/6 + 5/6 equals -5/6.

Hence, the final result of -1 2/3 - (-5/6) is 5/6.

To learn more about  common denominator click here : brainly.com/question/29048802

#SPJ11

The missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

Based on the given information, we can determine the missing values as follows:

Original price (OP): Let's assume the original price is represented by "x".

Rate of discount (RD): We know that the amount of discount (AD) is Php60.00, and we can calculate the rate of discount as follows:

AD = OP * RD

60 = x * RD

Sale Price (SP): The sale price is calculated by subtracting the amount of discount from the original price:

SP = OP - AD

240 = x - 60

To find the missing values, we need to solve the system of equations formed by the two equations above:

Equation 1: 60 = x * RD

Equation 2: 240 = x - 60

From Equation 2, we can rearrange it to solve for x:

x = 240 + 60

x = 300

Substituting x = 300 into Equation 1, we can solve for the rate of discount:

60 = 300 * RD

RD = 60 / 300

RD = 0.2

Therefore, the missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

for such more question on missing values

https://brainly.com/question/12858312

#SPJ8

In a fraction, the common denominator refers to the lowest common multiple of the denominators of the fractions. If you use the common multiple from part A as the common denominator, the models in the example will be different and at the same time the same.

A common multiple is the product of two or more factors that are common. In other words, it is a number that is a multiple of two or more integers.

Let's take an example of finding the common multiple of 6 and 8:

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ...

The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

Therefore, the common multiples of 6 and 8 are: 24, 48, 72, 96, 120, 144, ...

The models would be different because the common denominator is the lowest common multiple of the denominators of the fractions. If we use the common multiple as the denominator, the size of the models may change.

Let's take an example:

Suppose we have two fractions, 1/2 and 2/3. The denominators are 2 and 3. The common multiple is 6.

If we use 6 as the common denominator, the fractions become:

1/2 = 3/6 (we multiplied the numerator and denominator by 3)

2/3 = 4/6 (we multiplied the numerator and denominator by 2)

The models would be different because the sizes are based on the denominators of the fractions. If we change the denominator, the size of the model may also change.

The models would be the same because they represent the same fractions.

Even though the size of the model may change, the fractions still represent the same value.

In the above example, 1/2 and 3/6 represent the same value, and 2/3 and 4/6 represent the same value.

Therefore, the models are still representing the same value even though they may be different in size.

To know more about multiple visit:

https://brainly.com/question/14059007

#SPJ11

Average seawater salinity = 3.5%100g of salt has been left after seawater has evaporatedThe mass of salt dissolved in 100g of seawater will be 3.5g (since salinity is 3.5%)Let x be the mass of seawater that needs to be evaporated to leave 100g of salt.

According to the law of conservation of mass,Mass of salt in the solution before = Mass of salt in the solution afterTherefore, 100g of salt that has been left after evaporation was originally dissolved in x grams of seawater.

Therefore, the mass of salt in that seawater would have been 3.5% of x.Using the above information, we can write an equation as follows:0.035x = 100g Therefore, about 2857.14 g or 2.85714 kg of seawater needs to have evaporated to leave 100 g of salt.

To know more about Average seawater visit :

https://brainly.com/question/32267736

#SPJ11

Answer:

I believe it's A

Step-by-step explanation:

Answer:

  27

Step-by-step explanation:

You want to know the ACT composite test score for the 87.49th percentile, given the ACT scores have a mean of 21.0 and a standard deviation of 5.2.

The Z-table in the first attachment shows you the Z-value of the 87.49th percentile is 1.10+0.05 = 1.15.

The corresponding score is ...

  X = μ +σZ

  X = 21.0 +5.2·1.15 ≈ 27

A learner must earn a score of 27 to be at the 87.49th percentile on the ACT composite test.

<95141404393>

The line of best fit is a straight line that best fits the scattered data points on a scatterplot. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

In this particular case, the equation of the line of best fit is y = -6x + 97, where x represents the number of absences and y represents the final grade.

This means that for every additional absence a student has, their final grade is expected to decrease by 6 points. The y-intercept of 97 means that if a student had zero absences, their predicted final grade would be 97.

It is important to note that the line of best fit is a prediction, and not a definitive statement about the relationship between the variables. While it can provide some insight into the relationship between the number of absences and final grade, there may be other factors that are not taken into account by the model.

Additionally, the equation of the line of best fit is only valid within the range of the data used to create the model. Extrapolating beyond this range may not produce accurate predictions.

Overall, the line of best fit is a useful tool for analyzing relationships between variables, but it should be used with caution and in conjunction with other analyses to get a complete understanding of the relationship between variables.

To know more about straight line visit:

https://brainly.com/question/31693341

#SPJ11

The expressions that represent a 20% discount off the price of an item that originally costs d dollars are A. 0.8d and C. d-0.2d.

A 20% discount off the original price means that the discounted price is equal to 80% (100% - 20%) of the original price. Therefore, we can calculate the discounted price by multiplying the original price (d) by 0.8 (representing 80%).

Expression A (0.8d) represents the discounted price as 80% of the original price (d), so it is correct. Expression C, d-0.2d" represents a 20% discount off the price of an item that originally costs d dollars.

How to find the expressions at https://brainly.com/question/22173102

#SPJ4

Full question is:

Select all the expressions below which represent a 20% discount off the price of an item that originally costs d dollars.

A. 0.8d

B. d-0.2

C. d-0.2d

D. 1-0.2d​​

An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. the dimensions of the compartment are 4m × 6m × 3m.

Find the dimensions of the compartment. Solution:The volume of a rectangular prism is given by;[tex]`V= l × w × h`[/tex] Given that the compartment's volume is 72 cubic meters, let's substitute[tex]`V = 72`[/tex]

cubic meters;[tex]`l × w × h = 72`[/tex]

We also know that;[tex]w = l + 2h = l - 1[/tex]

Substituting w and h in terms of l, we get;[tex]`l(l+2)(l-1) = 72`[/tex]Expanding,

we get;[tex]`l(l²-1) + 2(l²-1) = 72`[/tex]

Simplifying, we get;[tex]`l³ + l² - 2l - 74 = 0`[/tex]

We will use trial and error method to find one of the roots,`l= 4`.

By substitution, we get;[tex]w = 4 + 2 = 6m h = 4 - 1 = 3m[/tex]

Thus, the compartment dimensions are 4m × 6m × 3m. The width is 6 meters, the length is 4 meters, and the height is 3 meters.

To know more about rectangular visit:

https://brainly.com/question/21416050

#SPJ11

Given, Brad's dinner bill, including a 16% tip, is $10.44. We need to find the amount of the bill before the tip.Let the amount of the bill before the tip be x.So, the bill amount including the tip of 16% will be x + (16/100)x or (116/100)x.

This is because, if x is the bill amount, the tip is 16% of x, which is (16/100)x, then the total bill amount will be x + (16/100)x or (116/100)x.

We know that the bill amount including the tip is $10.44. So,(116/100)x = 10.44=> x = (10.44 × 100)/116= $9 (approx) Therefore, the amount of the bill before the tip is $9. Answer: $9.

To know more about tip visit:

brainly.com/question/17142182

#SPJ11

To find out how many children and how many adults attended the event, we can set up a system of equations based on the given information.

Let's use the variables c and a to represent the number of children and adults, respectively. The total number of people who attended the event is 100, and the total amount collected at the door is $626. Each child ticket costs $5, and each adult ticket costs $8. By setting up and solving a system of equations, we can determine the values of c and a.

Let c represent the number of children and a represent the number of adults who attended the event. We can set up the following system of equations based on the given information:

Equation 1: c + a = 100 (total number of people who attended the event)

Equation 2: 5c + 8a = 626 (total amount collected at the door)

We can solve this system of equations using various methods such as substitution, elimination, or matrix methods. Here, we'll solve it using the substitution method.

From Equation 1, we have c = 100 - a. Substitute this value into Equation 2:

5(100 - a) + 8a = 626

500 - 5a + 8a = 626

3a = 126

a = 42

Substitute the value of a into Equation 1:

c + 42 = 100

c = 58

Therefore, 58 children and 42 adults attended the event.

To learn more about variables click here:

brainly.com/question/15078630

#SPJ11

The simplified expression for the area of the shape is 8x square units.

In the given figure of rectangle,

Given that,

Length of rectangle = 2x

And width of rectangle = 4

Since we know that,

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

We also know that,

Area of rectangle = length x width

                             = (2x)(4)

                             = 8x

Hence expression of area = 8x square units.

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ4

The complete question is attached below:

To find approximately how many seconds the rock took to reach the ground, we need to determine when the height, h(t), becomes zero.

Setting h(t) = 0 in the equation -4.9t^2 + 49 = 0, we can solve for t.

-4.9t^2 + 49 = 0

4.9t^2 = 49

t^2 = 49 / 4.9

t^2 = 10

t ≈ √10

Therefore, the rock took approximately √10 seconds to reach the ground.

learn more about:- seconds here

https://brainly.com/question/24237610

#SPJ11

Devika poured out 4.2 ounces of water, which is approximately 35% of the water in the full bottle.

To find out how much water was in the full bottle, we can set up a proportion.

Let x represent the amount of water in the full bottle (in ounces). We know that 4.2 ounces is 35% of x.

We can set up the proportion:

4.2 / x = 35 / 100

To solve for x, we can cross-multiply:

4.2 * 100 = 35 * x

420 = 35x

Dividing both sides of the equation by 35:

420 / 35 = x

12 = x

Therefore, there were approximately 12 ounces of water in the full bottle.

So, Devika estimated that she poured out about 35% of the water in the full bottle, which corresponds to approximately 4.2 ounces.

Learn more about water here

https://brainly.com/question/29291605

#SPJ11