Find The Length S Of The Arc That Subtends A Central Angle Of Measure 5 Rad In A Circle Of Radius 4 Cm. (2024)

Gentiana has $12 left to spend on the pizza pie as of the equation model.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,

Let the amount spend on pizza pie be x,
According to the question,
40 = 10 + 25% of 40 + 20% of 40 + x

40 = 10 + 40 × 0.25 + 40 × 0.20 + x
40 = 10 + 10 + 8 + x
x = 40 - 28
x = 12

Thus, Gentiana has $12 left to spend on the pizza pie as of the situation model.

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In the regrouping to use a different expression for the number in place of * is 11 thousands.

Here we have to write the regroup to express the number as 71,830 = 6 ten thousands + 11 thousands + 8 hundreds + 3 tens

What in elementary math is regrouping?

When doing mathematical operations like addition or subtraction, regrouping is the process of creating groups of ten. When dealing with double digits, this happens most frequently. Technically, though, it happens whenever you get a response that is more than 10.

Where using regrouping, you may frequently solve addition or subtraction problems, and this is when the Place Value Table comes in extremely handy.

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The lines of equations y = 3x - 8 and y = 3x - 12 have same slope but they are parallel to each other and have no solution.

What is system of equations?

A System of Linear Equations is when we have two or more linear equations are working together.

The first equation is y = 3x - 8.

The second equation is y = 3x -12.

Substituting the value of y from equation 1 in equation 2 -

y = 3x -12

3x - 8 = 3x - 12

3x - 3x = -12 + 8

0 = 4

There is no x-intercept.

Substituting the value of x in equation 1 -

y = 3x - 8

y = 3(0) - 8

y = 0 - 8

y = -8

So, the lines do not intersect each other.

Therefore, the equations have same slope but do not have any solution.

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For every quart, there are 4 cups. In two quarts, there are eight cups. In four quarts, there are sixteen cups. A 5 quart container holds 20 cups.

In cups, how many quarts are there?For every quart, there are 4 cups. In two quarts, there are eight cups. In four quarts, there are sixteen cups. A 5 quart container holds 20 cups.2 pints, 4 cups, 32 ounces, and 1 US liquid quart are all equivalent to 1/4 gallon. It's vital to keep in mind when converting any dry ingredient that a dry quart is equivalent to 4.6546 cups.The U.S. liquid quart is equivalent to two liquid pints, which is one-fourth of a U.S. gallon (57.75 cubic inches, or 946.35 cubic centimeters); the dry quart is equal to two dry pints, which is one-third of a bushel (67.2 cubic inches, or 1,101.22 cubic cm).

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Step-by-step explanation:

the volume of the cube at the beginning is

edge³ = 16³ = 4096 cm³

after 1 minute it is 4101 cm³

that means the edge is then

cubic root(4101) = 16.00650777... cm

the surface area of a cube is

6×edge²

at the beginning it was

6×16² = 1536 cm²

after 1 minute (and the increased volume) it is

6×16.00650777...² = 1,537.249746... cm²

at that moment the surface area is increasing at

1.249745825... cm²/ minute

The percentage of vehicles that have four wheels are trucks is 30%.

What is Percentage?

Percentage is defined as the parts of a number per fraction of 100. So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Number of trucks that are four wheels = 127 - 76 = 51

Number of trucks that have more than four wheels = 76

Total number of trucks = 127

Number of non trucks that are four wheels = 120

Number of non trucks that have more than four wheels = 18

Total number of non trucks = 138

Total number of four wheels = 51 + 120 = 171

Number of trucks that are four wheels = 51

Percentage of vehicles that have four wheels are trucks = (51 / 171) × 100 = 29.82 ≈ 30%

Hence 30% of the for wheeler vehicles are trucks.

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The complete question is as follows :

A street traffic coordinator records data about the number of vehicles with 4 wheels and the number of vehicles with more than 4 wheels that drive over a bridge. Her data is shown.

Of the 127 trucks that drive over the bridge, 76 have more than 4 wheels. Of the 138 non-trucks that drive over the bridge, 120 have 4 wheels

What percentage of vehicles that have four wheels are trucks? Round your answer to the nearest whole percent.

The current age of Sam is 30 years and Harry is 10 years.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

Let Sam's age be y years and Harry's age be x years.

Sam is currently three times harry's age.

The equation formed: y = 3x

Sam's age is also 10 more than twice harry's age.

The equation formed: y = 2x + 10

Substitute the value of y from first equation in second equation:

3x = 2x + 10

x = 10

Put the value of x in first equation:

y = 3x = 3*10 = 30

Thus, the current age of Sam is 30 years and Harry is 10 years.

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At 7.4 ( round to nearsest tenth) meters mark will Ario be present when Miguel starts the race. So, option (c) is right choice here.

We have, Miguel and his brother Ario are both deciding to a race.

Total length of pool = 25 meters

But they are standing 3 meters from one side of a 25-meter pool when both are decide to race.

So, the length of racing area = 25 - 3 = 22 meters.

Also, Miguel said that he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1 : 4. Let us assume, the Ario’s completed meters be "x meters" . Then, Ario’s remaining meters = 22 - x

so, x : 22- x = 1 : 4

=> x/(22 - x) = 1/4

=> 4x = 22 - x

=> 5x = 22

=> x = 22/5 = 4.4

Ario position when Miguel starts the race with respect to pool's length = 4.4 meter + 3 meters

= 7.4 meter

Hence, required length is 7.4 meters.

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Complete question:

We have to rearrange the question as

Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4. At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.

a) 4 meters

b) 6 meters

c) 7.4 meters

d) 7 meters

Answer: Hi

We can use the information given to set up the inequality:

Weight of refrigerators + weight of pianos <= 6900 (since the truck can carry no more than 6900 lb)

We can use the weight of each item to write the inequality in terms of x (number of refrigerators) and y (number of pianos):

300x + 525y <= 6900

To graph the inequality, we can use the x and y values as coordinates and plot them on a coordinate plane. The line representing the inequality would be a boundary line, with all the points that satisfy the inequality on one side of the line, and all the points that do not satisfy the inequality on the other side of the line.

To check if 12 refrigerators and 9 pianos will overload the truck, we can substitute these values into the inequality:

300(12) + 525(9) = 3900 + 4725 = 8625

Since 8625 is greater than 6900, which is the maximum weight the truck can carry, 12 refrigerators and 9 pianos would overload the truck.

Step-by-step explanation:

To sum up, the inequality 300x + 525y <= 6900 represents the weight that the truck can carry. The points that satisfy the inequality (such as (4, 6) or (10, 3)) would represent a combination of refrigerators and pianos that the truck can carry, while the points that do not satisfy the inequality (such as (12, 9)) would represent a combination that overloads the truck.

The value of the slope indicates that the average cost of a haircut is increased by 2 US dollars each year.

What is the average cost?

We are aware that it is determined by the cost-to-production ratio. The sum of the fixed cost and the variable cost is referred to as the total cost, which is also known as the unit cost. As a result, Average Cost is calculated as Total Cost/Number of Units or (Fixed Cost + Variable Cost)/Number of Units.

Here, we have

In this case, we use the linear function y = 2x + 25, where x is the time after 1985, measured in years, and y is the average cost of a haircut. The slope of the model is m = 2 USD yr.

It means that the average cost of a haircut increased by 2 every year after 1985.

In 1985, y=0, and the cost is 25

In 1986, y=1, and the cost is 25+2 = 27

In 1987, y=2, and the cost is 25+4 = 29

and so on.

Hence, the value of the slope indicates that the average cost of a haircut is increased by 2 US dollars each year.

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To distribute 33 treat to her 6 dogs Ariana has 1947792 ways

Since the order of distribution doesn't matter we will apply concepts of combination.

combination = nCr =n!/(r!(n-r!)

where n is the total number of objects

r is the number of chosen objects from the total.

Here, 33C6 =36!/6!.30!

= 36x35x34x33x32x31/6x5x4x3x2

1947792

Therefore, Ariana can distribute 33 treats between her 6 dogs in 1947792 ways.

Combination in mathematics is a way of choosing or distributing selected items from a list of the total set with distinct values. It is used when there is no repetition and order doesn't matter. It can also be depicted as permutation/r!

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If the average price of regular unleaded gasoline excluding taxes was $3.06 per gallon then the percentage of gasoline stations had prices within 3 standard deviations of the mean is 99.74% .

The Average Price of the gasoline (μ) is = $3.06 per gallon ;

the standard deviation price per gallon (σ) is = 0.06 ;

we have to find the percent of gasoline that had prices within 3 standard deviations of the mean ;

the the 3 standard deviation is calculated by :

⇒ [tex](\mu \pm 3\sigma )[/tex]

On substituting the values ,

we get ;

⇒ [tex](\mu - 3\sigma , \mu +3\sigma)[/tex]

⇒ [tex](3.06 - 3\times 0.06 , 3.06 + 3\times 0.06)[/tex]

= (2.88 , 3.24) ;

Step two ;

Now , We have to calculate P(2.88 < X < 3.24)

= [tex]P(\frac{2.88-3.06}{0.06} < Z < \frac{3.24-3.06}{0.06} )[/tex]

= [tex]P(-3 < z < 3) ;\\[/tex]

which means , [tex]P(z < 3) - P(Z < -3)[/tex] ;

= 0.9987 - 0.0013 ;

= 0.9974 ≈ 99.74% .

Therefore , the required percent of gasoline is 99.74% .

The given question is incomplete , the complete question is

In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3. 06 per gallon according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon .

What percentage of gasoline stations had prices within 3 standard deviations of the mean ?

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Answer:

The average points received by those students who did not pass the test successfully would be 4 points.

Step-by-step explanation:

Step 1: We know that all students wrote the test and received an average of 6 points.

Step 2: We also know that 60% of those students passed the test successfully and received an average of 8 points.

Step 3: This means that the remaining 40% of students did not pass the test successfully.

Step 4: Since the average points for all students was 6 points and the average points for those who passed the test was 8 points, the average points for those who did not pass the test would be 4 points.

There are several ways to classify triangles, but two common methods are by their side lengths and by their angles.

Classification by side length:
Scalene triangle: a triangle with no congruent sides
Isosceles triangle: a triangle with two congruent sides
Equilateral triangle: a triangle with three congruent sides
Classification by angle measure:
Acute triangle: a triangle with all angles measuring less than 90 degrees
Right triangle: a triangle with one angle measuring exactly 90 degrees
Obtuse triangle: a triangle with one angle measuring more than 90 degrees
It is worth noting that a triangle can be both classified by its side lengths and angles, for example, a right isosceles triangle is a triangle with one right angle and two congruent sides or it can be a right triangle with all congruent angles.

Answer:

25

Step-by-step explanation:

5x - 5 + 2x + 10 = 180

7x + 5 = 180

7x = 175

x =25

Answer: the answer to this question is X = 25

The degree for 5x - 5 = 5(25) - 5 = 120 degrees (we are putting 25 in for x to get the sum of the degree)

The degree for 2x+10 = 2(25)+10 = 60 degrees (we are putting 25 in for x to get the sum of the degree)

Let's walk through the steps:

Step 1: Simplify both sides of the equation.

5x−5+2x+10=180

5x+−5+2x+10=180

(5x+2x)+(−5+10)=180 (Combine Like Terms)

7x+5=180

Step 2: Subtract 5 from both sides.

7x+5−5=180−5

7x=175

Step 3: Divide both sides by 7.

7x/7 = 175/7

x = 25

The point of intersection of concurrent lines is called the point of concurrency.

Concurrent lines are lines that intersect at a single common point. This point of intersection is also known as the point of concurrency.

It can also be said that concurrent lines are lines that pass through a common point and this point is known as the point of intersection or point of concurrency.

In geometric figures, there are some special point of concurrency. For example, in a triangle, there are three special point of concurrency: the incenter, the circumcenter, and the orthocenter. The incenter is the center of the inscribed circle, the circumcenter is the center of the circumcircle and orthocenter is the point where the three altitudes of the triangle intersect.

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All lines having equation of the type y=k are parallel to the x-axis .

What is Equation of Straight line ?

Equation of Straight line as follows : y = mx+b

where m is the slope of the line

c is the y intercept

Hence, this is the most common equation of a straight line used in the geometry .

The slope of the x-axis is 0 and the origin lies on the x-axis

Hence, The equation of the x-axis

could be,

y - 0 = 0 (x-0)

y = 0

As parallel lines have equal slope, all lines having the equation of the type y=k will have slope 0.

Hence, All lines having equation of the type y=k are parallel to the x-axis

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The point (x, y) is the reflection of the line y is x across the point (x, y) (y, x). The point (x, y) is the reflection of the line y is-x across the point (x, y) (-y, -x).

How do you determine the x- and y-axis reflection points?

The point (x, y) is the reflection of the line y=x across the point (x, y) (y, x). The point (x, y) is the reflection of the line y=-x across the point (x, y) (-y, -x).

The x-coordinates stay the same when a point is reflected across the X-axis. However, the Y-coordinates are changed into the corresponding signs. As a result, the point's (x, y) reflection across the X-axis is (x, -y).

The point (x, y) is the reflection of the line y=x across the point (x, y) (y, x). The point (x, y) is the reflection of the line y=-x across the point (x, y) (-y, -x).

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An equation that models the volume, V, of the cement in the container in terms of h is V = π[tex]r^2[/tex]h. The time at which the volume is 80π cubic feet is 6 minutes.

In the given question, we have to write an equation that models the volume, V, of the cement in the container in terms of h, then use the equation to determine the time at which the volume is 80π cubic feet.

The given radius r = 4 feet

Rate of filling the cylinder = 10 inches/minutes

Firstly we convert inches into feet.

As we know that;

1 inches = 1/12 feet. So

Rate of filling the cylinder = 10/12 feet/minutes

Rate of filling the cylinder = 5/6 feet/minutes

Height (h) in time 't' minutes = h = 5/6 t

Volume after t minutes

V = π[tex]r^2[/tex]h

Now putting the values

V = [tex]\pi\times(4)^2\times\frac{5}{6}t[/tex]

V = [tex]\pi\times16\times\frac{5}{6}t[/tex]

V = [tex]\frac{40\pi}{3}t[/tex]

As given that volume is 80π cubic feet.

Now, V = 80π

80π = [tex]\frac{40\pi}{3}t[/tex]

Multiply by 3 on both side, we get

240π = 40πt

Divide by 40π on both side, we get

t = 240π/40π

t = 6 minutes

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The multiplicative opposite of a number, say, N, is act for by 1/N or N-1. It is also called reciprocal, obtain from the Latin word ‘reciprocals ‘. The meaning of inverse is something which is converse.

The reciprocal of a number obtained is like that when it is multiplied by the original number, the value equals identity 1.

In other words, it is a method of dividing a number by its own to produce identity 1, such as N/N = 1.

When any number is multiplied by its particular multiplicative inverse, the resultant value is equal to 1.

multiplicative inverse of a is 1/a

(4/-7) =4/7

i.e., multiplicative inverse of 4/7 is -7/4.

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Answer: Scroll down

Step-by-step explanation:

Image one:

1. Using SAS similarity, we can find 48/60 = 20/ML

1200 = 48 ML

ML = 1200/48 = 25 = Circle one

2. 24/x+5 = 54/36

x = 11

3. 20/36 is not equal to 24/42, so the triangles are not similar, = D

Image two:

1. 21/17.5 = 18/15 = 1.2

PQR is similar to D

2. D because then the ratios of the sides are all 3:1, and thats SSS similarity.

Image three:

1. Given

2. Property of cross multiplication

3. Given

4. SAS

Finished :>

1. Using Radicals the number √17 has a value of 4.123.

2. √510 =260100.

3. √4x = 2√x.

Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).

When multiplying or dividing, it is standard practise for the final result to contain the same number of significant figures as the number with the fewest significant figures. The division of two numbers can be calculated using the following formula: Dividend Divisor = Quotient + Remainder. The number that is being divided in this case is known as the dividend.

The number that divides the number (dividend) into equal parts is known as the divisor.

1. [tex]\sqrt{17}\\[/tex] = 4.123 (The values of the number √17 is 4.123.)

2. √510

= 510^2

=(500+10)^2

=500^2+10^2+2×500×10

=250000+100+10000

=260100.

3. √4x = 2√x.

because 4 = 2*2

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There are four main ways to solve a system of equations: graphing, elimination, substitution, and matrices.

What is equation?

The value of [tex]\alpha ^0 = (5\alpha ^0) =1[/tex], as anything raised to the power of 0 is equal to 1. Hence, the answer to the equation [tex]5\alpha ^0 + (5\alpha ^0)[/tex] is 6.

What are exponents and its laws?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The value of [tex]\alpha ^0 = (5\alpha ^0) =1[/tex], as anything raised to the power of 0 is equal to 1.

Substituting the value of [tex]\alpha ^0 =(5\alpha ^0) = 1[/tex] in the given equation we have:

5(1) + 1 = 6

Hence, the answer to the equation [tex]5\alpha ^0 + (5\alpha ^0)[/tex] is 6.

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Answer: m∠ABC and m∠ABD are the measures of angles in a triangle. The sum of the measures of the angles in a triangle is always 180°.

So if we know two of the angles, we can use this information to find the measure of the third angle.

Given that m∠ABC= (8x-48)°, m∠ABD=44°

we can find the measure of the third angle, m∠BCD by:

m∠ABC + m∠ABD + m∠BCD = 180

(8x-48) + 44 + m∠BCD = 180

m∠BCD = 180 - (8x-48) - 44

m∠BCD = 180 - 8x + 4

m∠BCD = (180 - 8x + 4)°

However, Since we don't know the value of x, the measure of angle BCD is not determined.

Step-by-step explanation:

Of the four variables, employee number, pay rate, hire date, and sex, the "Sex" variable is the best fit to use as a dummy variable.

The variable "Sex" is the best fit to use as a dummy variable. A dummy variable is used to represent a categorical variable with a numerical value, such as 0 or 1. In this case, "Sex" is a categorical variable with two categories (male and female) and can be transformed into a dummy variable with values 0 or 1 to represent the categories. The other variables, Employee Number, Pay Rate, and Hire Date, are not categorical variables and would not be appropriate to use as dummy variables.

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The ratios 40/18 and 27/11 are not equal because 20/9 and 3/1 are different fractions. They stand for various proportional connections between two quantities, in other words.

Why are there ratios not equivalent?

We need to see if the ratios of 40/18 and 27/11 fall to the same fraction when the numerator and denominator are both divided by their largest common factor (GCF).

Given that the GCF of 40 and 18 is 2, we can obtain 20/9 by reducing both the numerator and denominator of 40/18 by 2. Since the GCF of 27 and 11 is also 11, we obtain 3/1 when we divide the numerator and denominator of 27/11 by 11.

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Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.

what is variables ?

A variable is, to put it simply, a quantity that may be altered and is not fixed. The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types. a quantity that could take any of a range of values. a variable's sign; something that is variable; a component of a scientific experiment that is potentially subject to change.

given

Like terms are those terms that share the same factors.

Consequently, phrases that have identical variables raised to the same exponent are considered similar terms.

What are 25, -3x, and 3x called then , Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.

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There is a population of 334,476 in the city next year.

How to predict population in a city

In this case we find the case of a city, whose population reports an exponential growth. Exponential growth model is now described:

p' = p · (1 + r / 100)ⁿ

Where:

p - Initial population, no unit.p' - Final population, no unit.r - Growth rate, in percentage.n - Number of periods, in years.

If we know that p = 326,000, r = 2.6 and n = 1, then the final population of the city is:

p' = 326,000 · (1 + 2.6 / 100)¹

p' = 334,476

The population of the city next year is 334,476.

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