do 3 over 4 and 9 over 12 form a proportion

The most accurate estimated sum of 181 and 204 is 380

The given numbers are 181 and 204

The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.

To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation

Round 181 to the nearest tens = 180

Round 204 to the nearest tens = 200

Then the sum of compatible numbers will be

180 + 200 = 380

Therefore, the most accurate estimation is 380

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This means car traveled 18 miles on ONE gallon of gas.

You should get 20 to 30 miles per gallon of petrol on average when driving your car. Some automobiles, nevertheless, can go up to 60 miles per gallon. Your car's efficiency varies depending on a number of factors, including miles. Car weight, unsafe driving practices, the environment, and shoddy maintenance are a few of the contributing causes.

Vehicle mileage was x miles.

x miles of gasoline equals x gallons of fuel.

Gasoline consumption is inversely proportional with the distance driven by an automobile.

distance traveled by car  = K× Gasoline used  

Using unitary method,

Distance traveled by car in 1 gallon of gas  = 18 × 1 miles.

Distance traveled by car in 1 gallon of gas  = 18 miles

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The missing sides of right triangles are, respectively:

Case 1: x = 18.910

Case 2: x = 23.584

Case 3: x = 15.890

Case 4: x = 16.659

Case 5: x = 24.111

And the angles of the right triangles are, respectively:

Case 6: 32°

Case 7: 31°

Case 8: 71°

Case 9: 71°

Case 10: 32°

The exact values of trigonometric functions:

Case 11: cos A = 12 / 13

Case 12: tan C = 3 / 4

Case 13: tan A = 3 / 4

And the trigonometric ratios of right triangles are:

Case 14: tan X = 1.3333

Case 15: sin A = 0.6000

Case 16: cos C = 0.3243

In this question we find 16 cases of right triangles that must be analyzed by trigonometric functions. Trigonometric functions is an important tool to determine missing sides and angles and relationships with sides. Most important trigonometric functions are described below:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Where:

Please notice that hypotenuse is the longest side of a right triangle.

The first five cases implies the determination of missing lengths in five right triangles:

Case 1

x = 20 · cos 19°

x = 18.910

Case 2

x = 20 / cos 32°

x = 23.584

Case 3

x = 10 / cos 51°

x = 15.890

Case 4

x = 15 / tan 42°

x = 16.659

Case 5

x = 19 / sin 52°

x = 24.111

The following five cases implies the determination of angles by means of direct and inverse trigonometric functions:

Case 6

tan θ = 16 / 26

tan θ = 8 / 13

θ = 31.608° (32°)

Case 7

tan θ = 6 / 10

θ = 30.964° (31°)

Case 8

tan θ = 76 / 26

θ = 71.114° (71°)

Case 9

tan θ = 67 / 23

θ = 71.053° (71°)

Case 10

tan θ = 26 / 42

θ = 31.759° (32°)

The next three cases implies the computation of the exact values of trigonometric functions:

Case 11

cos A = 24 / 26

cos A = 12 / 13

Case 12

tan C = 24 / 32

tan C = 3 / 4

Case 13

tan A = 27 / 36

tan A = 3 / 4

And the last three triangles implies the values of trigonometric ratios:

Case 14

tan X = 36 / 27

tan X = 4 / 3 (1.3333)

Case 15

sin A = 30 / 50

sin A = 3 / 5 (0.6000)

Case 16

cos C = 12 / 37 (0.3243)

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The lengths of the sides, measures of the angles and the values of the trigonometric ratios are as follows;

1) x ≈ 18.9

2) x ≈ 23.1

3) x ≈ 15.9

4) x ≈ 16.7

5) x ≈ 23.1

6) x ≈ 32°

7) x ≈ 31°

8) x ≈ 71°

9) x ≈ 71°

10) x ≈ 32°

11) cos(A) ≈ 0.9

Trigonometric ratios are expressions that specify the relationships between two sides of a right triangle and an interior angle of the triangle.

1) The opposite side = 20 × sin(19°) ≈ 6.5

The adjacent side = 20 × cos(19°) ≈ 18.91

2) cos(30°) = 20/x

cos(30°) = (√3)/2, therefore;

(√3)/2 = 20/x

x = 20/((√3)/2) = 40·√3/3 ≈ 23.1

x ≈ 23.1

3) cos(51°) = 10/x

Therefore;

x = 10/(cos(51°)) ≈ 15.9

4) tan(42°) = 15/x

Therefore;

x = 15/(tan(42°)) ≈ 16.7

x ≈ 16.7

5) sin(52°) = 19/x

Therefore;

x = 19/(tan(52°))

x = 20/(cos(30°)) ≈ 23.1

x ≈ 23.1

6) tan(x) = 16/26

tan(x) = 16/26 = 8/13

x = arctan(8/13) ≈ 32°

7) tan(x) = 6/10

tan(x) = 6/10 = 3/5

x = arctan(3/5) ≈ 31°

8) tan(x) = 76/26

tan(x) = 76/26 = 38/13

x = arctan(38/13) ≈ 71°

9) tan(x) = 67/23

x = arctan(67/23) ≈ 71°

x ≈ 71°

10) tan(x) = 26/42

tan(x) = 26/42 = 13/21

tan(x) = 13/21

x = arctan(13/21) ≈ 32°

11) The trigonometric ratios for cosine indicates that we get;

cos(A) = 24/26 ≈ 0.9

12) Trigonometric ratio for tangent indicates that we get;

tan(C) = 24/32 = 0.75

13) tan(A) = 27/36

27/36 = 3/4

Therefore; tan(A) = 3/4 = 0.75

14) tan(x) = 36/27 = 4/3

tan(x) = 4/3 = 1 1/3

15) sin(A) = 30/50 = 3/5

sin(A) = 3/5 = 0.6

16) cos(C) = 12/37 ≈ 0.32

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Answer:

x=120

Step-by-step explanation:

sum of angles is 540

given two right angles which is 90

90+90=180

540-180=360

360/3=120

The number of elements in the sample space for this experiment are 969 by combination formula.

In an experiment where a person eating at a cafeteria choose 3 out of the 19 vegetables on offer, the number of elements in the sample space is 969.

A sample space of an experiment is the set of all possible outcomes of a random experiment. So the number of elements in a sample space is the total number of possible outcomes of  the experiment.

Here the experiment is choosing 3 vegetables from a set of 19 vegetables offered. The total number of ways to choose 3 out of 19 distinct vegetables = [tex]^{19}C_{3}[/tex]

= [tex]\frac{19!}{3!\times16!}[/tex]

= 969

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A measurement that shows the circumference of each of the buttons in centimeters is: D. 37.7 cm.

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circle = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of a circle = πr²

36π = π × r²

Radius, r = √36

Radius, r = 6 centimeters.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

Circumference of a circle = 2πr

Circumference of a circle = 2 × 3.14 × 6

Circumference of a circle = 37.7 cm.

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Complete Question:

Rolando is making buttons that are shaped like circles. Each button has an area of 36π square centimeters. Which measurement shows the circumference of each of the buttons in centimeters?

Answer

A 113.1 cm

B 18.8 cm

C56.5 cm

D 37.7 cm

The duration of the call for the same cost is, 3 minutes.

A system of equations, y = 4 + x

                                       y = 1 + 2x

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Let's let t be the duration of the call in minutes.

Then, the cost of the call under David's plan would be:

4 + t

And the cost of the call under Alec's plan would be:

1 + 2t

Since the costs are the same, we can set these two expressions equal to each other and solve for t:

4 + t = 1 + 2t

Simplifying and solving for t, we get:

t = 3

Therefore, a call of 3 minutes duration would cost exactly the same under both plans.

To graph the system of equations, we can plot the two expressions for the cost of the call on the y-axis and the duration of the call on the x-axis. The two equations are:

y = 4 + x

y = 1 + 2x

Plotting these two lines on the same graph, we get:

The solution is the point where the two lines intersect, which is (3, 7). This confirms that a call of 3 minutes duration would cost exactly the same under both plans, and the cost would be $7.

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Answer:

Step-by-step explanation:

Let's say Trace's age is "x".

Then, Hunter's age would be (x+3)

And Jacob's will be 2*(x+3)

The Total of three ages would be

x+(x+3)+2*(x+3)=49

4x+9=49

4x=40    

x=10

So Trace is 10 years old

     Hunter is 13 years old

     Jacob is 26 years old.

Answer: no. it is not in standard form

We cannot find the x-intercept of this  equation by substituting 0 for y and solving for the x.

Step-by-step explanation:

Answer:

The ordered pair for point B after it has been reflected over both the x and y-axis is (4, 6).

This is due to the rule for reflecting over the x-axis, which is to negate the value of the y-coordinate of each point, but leave the x-value the same. This means that after reflecting point B over the x-axis, it's new coordinates would be (-4, 6).

The rule for reflecting over the y-axis is to negate the value of the x-coordinate of each point, but leave the y-value the same. This means that after reflecting point B' over the y-axis, it's new coordinates would be (4, 6).

Answer: Jamie burned 420 calories on Tuesday

Step-by-step explanation:

Cross method is best for this question

Let x = calories burnt on tuesday
480 is 100%
x is 7/8 (or 87.5%)

∴
(480*87.5%) ÷ 100%
= 420 ÷ 100%
= 420

Therefore, Jamie burned 420 calories on Tuesday

Answer:

Step-by-step explanation:

10

The work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.

We can use Hooke's law to find the force required to stretch the spring 4 inches from its natural length:

[tex]F = kx[/tex]

where F is the force in pounds, x is the displacement in inches, and k is the spring constant in pounds per inch (which we want to find).

Since 18 foot-pounds of work is required to stretch the spring 4 inches, we know that the work done is equal to the potential energy stored in the spring:

[tex]W = (1/2) k x^2[/tex]

Solving for k, we get:

[tex]k = (2W) / x^2[/tex]

Plugging in the values for W and x, we get:

[tex]k = (2 * 18) / (4^2) = 2.25[/tex]

So the spring constant is 2.25 pounds per inch.

Now we can use Hooke's law again to find the force required to stretch the spring an additional 3 inches:

[tex]F = kx[/tex]

= [tex]2.25 * 3[/tex]

= 6.75 pounds

Finally, we can find the work required to stretch the spring an additional 3 inches:

[tex]W = (1/2) k x^2[/tex]

= [tex](1/2) * 2.25 * 3^2[/tex]

= 10.125 foot-pounds

Therefore, the work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.

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The slope-intercept form of the equation of the line is y = x + 6.

A linear equation with a degree of one is referred to as an equation of the line. Two variables, x, and y, are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The equation of the line's general form is:

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The formula for calculating the line's slope is

Slope = ( 6 - 4) / ( 2 - 0)

Slope = 1

The y-intercept will be calculated as:-

y = mx + c

y = x +c

6 = c

The equation of the line can be written as:-

y = x + 6

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The number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

The probability of cookies sold in shape of dog is:

P = 35/85

The number of cookies sold that would be in the shape of the dog in the next 51 cookies is:

N = 51 (P)

N = 51 (35/85)

N = 21

Hence, the number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.

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It signifies the number of dogs that Bella feeds. The number of observations in dataset is an important characteristic that helps to determine the size of data and potential variability of data.

The table of the number of cups of dog food that each dog should be fed each day is a dataset that contains multiple observations. Each row in the table represents one observation for one dog, with information about the number of cups of dog food that the dog should be fed each day.

The number of observations in this data set is equal to the number of dogs that Bella will be feeding at the shelter. Each observation in the dataset represents a single unit of information, in this case, the number of cups of dog food that a particular dog should be fed.

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The expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1.

The exponential expression that is equivalent to 100,000 • 1/100,000 is:

[tex](10^5) * (10^-5)[/tex]

To simplify this expression using addition or multiplication on the powers, we can use the property of exponents that states:

[tex]a^m *a^n = a^{(m+n)[/tex]

This means that when we multiply two numbers with the same base, we can add their exponents to simplify the expression. However, this property does not work for division, as we need to subtract the exponents instead.

Using this property, we can simplify the expression as follows:

[tex](10^5) * (10^-5) = 10^{(5-5)} = 10^0 = 1[/tex]

Therefore, the expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1. We can see that in this case, addition and multiplication do not help us simplify the expression, but we can use the exponent property to do so.

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Based on the distance covered by Zebra and Giraffe in mentioned time, the Zebra can be said to run faster.

Firstly, the question requires a candidate to be familiar with the concept of speed. We know that speed is associated with distance and time as -

Speed = distance/time

So, taking the case for Giraffe

Speed = 280/20

Performing division

Speed = 14 m/s

Taking the case of Zebra

Speed = 204/12

Performing division

Speed = 17 m/s

We see that in unit time or one second, the distance covered by the two animals is different. The one covering larger distance comparatively will be said to run faster. So, zebra runs faster.

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The table of question is attached in the picture.

Jayden needs to purchase 3900 square feet of sod to cover his front and back yards.

The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then multiplying or dividing to find the value of the whole. In this case, the unit we will use is square feet.

To calculate the area of the front yard, we need to multiply its length by its width. So, we have:

Area of front yard = Length x Width = 50 ft x 70 ft = 3500 sq ft

To find the area of the back yard, we use the same formula:

Area of back yard = Length x Width = 10 ft x 40 ft = 400 sq ft

Now, we need to add the two areas to find the total area that requires sod. So, we have:

Total area = Area of front yard + Area of back yard

=> 3500 sq ft + 400 sq ft = 3900 sq ft

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The linear equation of the line which passes through the points (-2, -3) and (2, -1) is:

   y + 3 = 0.5 (x + 2)

What is meant by a linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is a straight line equation.

It is of the form: y = mx + c

where m = slope of the line

c = x-intercept of line.

The linear equation of a line is:

y - y₁ = m ( x - x₁)

Given two points on the line

(x₁ , y₁) = (-2, -3)

(x₂ , y₂) = (2, -1)

m = slope of line =  (y₂ - y₁) / (x₂ - x₁) = (-1 - (-3)) / (2 - (-2)) = 2/4 = 1/2

Now substituting this value in the general equation, we can write the equation as:

y - (-3) = 1/2 ( x -(-2))

y + 3 = 0.5 (x + 2)

Therefore the linear equation of the line which passes through the points (-2, -3) and (2, -1) is:

   y + 3 = 0.5 (x + 2)

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If a cuboid weighs 100N and has sides 5cm by 10cm, then the area of cuboid is 0.005m².

Weight of the cuboid = 100N

Sides of the cuboid = 5cm by 10cm

A solid structure or a three-dimensional shape in geometry is called a cuboid. It is similar to a cube in that a cuboid can become a cube by changing the angles between faces or the lengths of the edges. A convex polyhedron with the same polyhedral graph as a cube is referred to as a cuboid in mathematics.

Calculating the area of the Cuboid -

= 5cm × 10cm

= 50cm²

Converting -

Area of Cuboid

= 50/10000 m²

= 0.005 m²

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Object is kind of a vector with the same size as the coefficients in the linear regression model.

In the least squares optimization target, the sum of squared errors (SSE) is typically minimized with respect to the coefficients of the linear regression model. The gradient of the SSE with respect to the coefficients is a vector that provides the direction of steepest ascent, or the direction in which the SSE increases the most rapidly. Setting this gradient vector to zero and solving for the coefficients yields the least squares solution to the linear regression problem.

Therefore, in this context, " " is likely a vector of coefficients that are being optimized to minimize the SSE.

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Answer:

(6 x 1.5 + 4.9) x 4 = 55.6

Step-by-step explanation:

A helium tank shaped like a cylinder has 2,401π in³ of space inside the tank. If the diameter of the helium tank is 14 inches,  its height is 1 inch.

Volume is a measure of the amount of space occupied by a three-dimensional object or a region of space. It is usually measured in units such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or liters (L).

For a solid object, such as a cube, cylinder, or sphere, volume is calculated by measuring the length, width, and height of the object and using a formula that is specific to that shape. For irregularly shaped objects, such as rocks or trees, volume can be determined by using techniques such as water displacement.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we are given the diameter of the cylinder, which is 14 inches. The radius of the cylinder is half of the diameter, so r = 7 inches.

We are also given the volume of the cylinder, which is 2,401π cubic inches.

Using the formula for the volume of a cylinder, we can set up the following equation:

2,401π = π(7)²h

Simplifying this equation, we get:

2,401 = 49h

Dividing both sides by 49, we get:

h = 49/49 = 1

Therefore, the height of the helium tank is 1 inch.

However, this answer seems unlikely since the height of the tank should be greater than its radius. Therefore, there may be an error in the given volume or diameter of the tank.

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the answer is A its height is 49

The statement is equivalent to numerical value 81.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is the statement as -

"base 3 and exponent 4"

We can write mathematically as -

{x} = 3⁴

{x} = 3 x 3 x 3 x 3

{x} = 81

Therefore, the statement is equivalent to numerical value 81.

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The value of x, given the triangle, the length of the side and the angle, would be

The angle given is 23 degrees and the sides given are 15 and x. These two sides are the hypotenuse and the opposite sides which means that the operation to be used is Sin.

The value of x would therefore be :

Sin ( angle ) = Opposite / Hypotenuse

Sin ( 23 ) = x / 15

x = 15 x Sin ( 23 )

The value of x is:

x = 15 x Sin ( 23 )

x = 5. 86

x = 5. 9 units

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The percentage of the data values are greater than 24 is 75%.

A box and whisker plot is a special type of graph that is used to show groups of number data and how they are spread. It shows the median, which is the middle value of the numbers in your data, the lowest number, the highest number and the quartiles, which divides the data into four equal groups.

So as per the given question box-whisker plot represents some data set. There is a number 24 just corresponding to it there is a vertical line which shows that 24 is the first quartile of the data and here 24 is the 75th percentile.

It means that there is 75% values are greater than 24.

Therefore, the percentage of the data values are greater than 24 is 75%.

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The value of the expression as a constant is 49.5

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

3(5x - 1) + b(2x - 7)

For the expression to be a constant, the following must be true

b(2x) = -3(5x)

Divide by x

b(2) = -3(5)

Divide by 2 and remove bracket

b = -7.5

Substitute the known values in the above equation, so, we have the following representation

3(5x - 1) -7.5(2x - 7)

So, we have

15x - 3 - 15x + 52.5

Evaluate the like terms

49.5

Hence, the constant is 49.5

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Answer:

Step-by-step explanation:

V≈62.83ft³

I hope it helped you out.

The expression that equals 2D−3C in standard form is -2s² - 11s - 7

Algebraic expressions are defined as expressions that are composed of coefficients, variables, terms,  factors and constants.

From the information given, we have that;

D=1−s^2 −s and C=3+3s,

To determine the expression for 2D - 3C

substitute the values of the expressions, we get;

2(1-s² - s) - 3(3 + 3s)

expand the bracket

2 - 2s² - 2s - 9 -9s

collect the like terms or factors, we get;

-2s² - 2x - 9s - 9 + 2

Add or subtract the values

-2s² - 11s - 7

Hence, the expression is -2s² - 11s - 7

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