Find the surface area of the composite figure.



A three-dimensional L-shaped figure is made of two rectangular prisms joined at a right angle. A horizontal rectangular prism has a length of eight inches, a width of two inches, and a height of two inches. A vertical rectangular prism connected at the right end of the other prism has a length of two inches, a width of two inches, and a height of eight inches.

The distance from the bottom of the building to the point where the ladder is touching the building for triangle 2, obtained using trigonometric ratio of tangent is 12 feet. The correct option is therefore;

12 feet

The trigonometric ratios are the value relationship between an interior angle of a right triangle and two of the sides of the triangle.

The right triangles are similar, therefore, the tangent of the angle the ladder makes with the ground are the same, which indicates;

tan(θ) = (Length of the side facing the angle θ) ÷ (Length of the side adjacent to the angle θ)

The side facing the angle is the distance from the bottom to the point where the ladder touches the building.

The adjacent to the angle is the horizontal distance from the bottom to the ladder to the building.

Therefore; tan(θ) = 18/12 = x/8

Where x = The distance from the bottom of the building to the point the ladder touches the building for triangle 2

18/12 = x/8

x = 18/12 × 8 = 12

The distance, x = 12 feet

Learn more on the tangent of an angle here: https://brainly.com/question/13952108

#SPJ1

Answer:

12?

Step-by-step explanation:

I'm not too sure! I am in the middle of taking the test right now.

Answer: 4:20 and 13:65

Step-by-step explanation: First one is 4 x 5 and second one you would do 65/5

The earthquake registered 3.6 on the Richter scale.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

R = log(A/0.0001)

The amplitude of the earthquake was of 0.3954, hence the magnitude of the earthquake is obtained as follows:

R = log(0.3954/0.0001)

R = 3.6.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Answer:

90Y + 36

Step-by-step explanation:

just multiply the length by the width.

9 X (8y + 4 + 2y)

= 9 X (10y + 4)

= 90Y + 36

The correct probability from the two-way table is given as follows:

B. P(120 lb | 2,000 - 2,500 cal) is different of P(120 lb).

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Then the probabilities are given as follows:

Hence statement B is true.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The complete solution to the system is 25/17, 61/17, 2/17 respectively.

Using the Gauss-Jordan elimination method to find the solution of the system of linear equations represented by the given augmented matrix:

Starting matrix:

[1 -2/3 -1/3 | 1]

[1 -2 6 | -17]

[-3 -7 3 | -43]

Add Row 1 to Row 2 and Row 3:

[1 -2/3 -1/3 | 1]

[0 -4/3 17/3 | -18]

[0 -1 0 | -40]

Multiply Row 2 by -3/4:

[1 -2/3 -1/3 | 1]

[0 1 -17/4 | 27/2]

[0 -1 0 | -40]

Add Row 1 to Row 2 and Row 3:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 -17/4 | -13/2]

Multiply row 3 by -4/17:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 1 | 2/17]

Add Row 3 to Row 1 and Row 2:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

Therefore, the solution of the system of linear equations is:

x = 25/17

y = 61/17

z = 2/17

So the solution is [25/17, 61/17, 2/17].

Thus the completed augmented matrix is:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

Find out more on matrix here: https://brainly.com/question/2456804

#SPJ1

The restaurant sold at least 22 fruit salads for exactly 25% of the week.

The restaurant sold at least 30 ice creams for exactly 75% of the week.

The restaurant sold at least 28 ice creams and fruit salads for exactly 50% of the week.

In Mathematics and Statistics, a box plot is a chart that is used to visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the data (information) provided about the sales of the number of ice creams and the number of fruit salads sold, the five-number summary for the given number of fruit salads sold include the following:

For the number of ice creams sold, we have:

Read more on boxplot here: brainly.com/question/29648407

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

1≠0.346485

Step-by-step explanation:

The correct statement is the center of the circle does not lie on the x-axis or the y-axis.

Given the equation of a circle, x² + y² – 2x – 8 = 0. Transform this equation in standard form of equation of circle

The standard form of the equation is (x – 1)² + y² = 8, and the radius of this circle is not the same as the radius of the circle whose equation is x² + y² = 9. Also, the center of the circle does not lie on the x-axis or the y-axis.

Therefore, the correct statement is the center of the circle does not lie on the x-axis or the y-axis.

Learn more about Circle here:

brainly.com/question/11833983

#SPJ1

The pattern involves squaring the sum of the given numbers.

Here's the process for each equation:

3+2=5, then [tex]5^2=25[/tex]

5+4=9, then [tex]9^2=81[/tex]

2+2=4, then [tex]4^2 = 16[/tex]

On careful analysis of the given pattern and answers, I am able to observe that this is a pattern-based numerical puzzle where the standard rules of arithmetic do not apply.

In this case, the pattern involves squaring the sum of the given numbers.

Here's the process for each equation:

3+2=5, then [tex]5^2=25[/tex]

5+4=9, then [tex]9^2=81[/tex]

2+2=4, then [tex]4^2 = 16[/tex]

So, the answer is obtained by first adding the numbers and then squaring the result.

This puzzle demonstrates that the logic behind the equations is different from traditional arithmetic, showcasing the importance of understanding the pattern to get the correct answer.

Read more about sum here:

https://brainly.com/question/24205483

#SPJ1

The correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction and 4/7 is incorrect answer

The pupil made an error in their addition of 3/5 and 1/2, resulting in an incorrect answer of 4/7.

To solve the task correctly, we need to find a common denominator for 3/5 and 1/2.

The least common multiple of 5 and 2 is 10, so we can rewrite the fractions with a denominator of 10 as follows:

3/5 = 6/10

1/2 = 5/10

Now we can add the fractions:

6/10 + 5/10 = 11/10

Hence, the correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ1

Number of tickets one can purchase from 56 dollars is 7.

Given that, 4 football tickets costs $32.

So, the cost of one football ticket = Total cost/Number of tickets

= 32/4

= $8

Number of tickets purchased for $56 = 56/8

= 7

Using variation

4:32::x:56

32x=56×4

x=7

Therefore, there are 7 tickets one can purchase from 56 dollars.

Learn more about the direct variation here:

https://brainly.com/question/13977805

#SPJ1

The slope of the line passing through the given points is -2.5.

To find the slope of a line passing through two points, we need to use the formula:

Slope = (Change in y) / (Change in x

We can choose any two points from the given table to find the slope of the line. Let's choose the points (4, 19) and (6, 14).

Change in y = 14 - 19 = -5

Change in x = 6 - 4 = 2

Slope = (-5) / 2 = -2.5

Therefore, the slope of the line passing through the given points is -2.5.

The slope of a line represents the steepness of the line. If the slope is positive, the line is increasing as we move from left to right. If the slope is negative, the line is decreasing as we move from left to right. A slope of 0 represents a horizontal line, while an undefined slope represents a vertical line.

In this case, the slope of -2.5 indicates that the line is decreasing at a moderate rate as we move from left to right. The higher the absolute value of the slope, the steeper the line.

It is important to note that the slope is constant for any two points on a straight line. Therefore, we can choose any other two points from the table to find the slope, and we will get the same result.

For more such questions on passing through

https://brainly.com/question/29797273

#SPJ11

(a) The sum of the interior angles of a regular octagon is 1,080⁰.

(b) The measure of one interior angle is 135⁰.

(c) The sum of the exterior angles of the octagon is 360⁰.

The sum of the interior angles of a regular octagon is calculated as follows;

The formula for sum of interior angles is given as;

sum of interior angles = (n - 2) x 180

where;

The number of sides of a regular octagon = 8

sum of interior angles = (n - 2) x 180

sum of interior angles = (8 - 2) x 180

sum of interior angles = 1,080⁰

The measure of one interior angle = 1,080 / 8 = 135⁰

The sum of exterior angles of a polygon = 360⁰, so the sum of the exterior angles of the octagon is 360⁰.

Learn more about exterior angles here: https://brainly.com/question/2546141

#SPJ1

The value of x is 5.

Using Angle Sum Property

The sum of the angles in a triangle is always 180 degrees. So, we can set up an equation:

9x-1 + 62 + 74 = 180

Simplifying the equation:

9x + 135 = 180

9x = 45

x = 5

Therefore, x is 5.

Learn more about Angle Sum Property here:

https://brainly.com/question/21364160

#SPJ1

When t = 0, the value of n is approximately 3.93 million. The estimated number of people who moved to another state in 2005 is approximately 1.68 million. The predicted number of people who moved to another state in 2014 is approximately 6.81 million.

we need to substitute the given values of t (years since 1990) into the equation n = 0.03t² - 0.6t + 3.93. Let's calculate the values accordingly:

a. When t = 0 (which corresponds to the year 1990), we substitute this value into the equation:

n = 0.03(0)² - 0.6(0) + 3.93

n = 0 + 0 + 3.93

n ≈ 3.93

So, when t = 0, the value of n is approximately 3.93 million. In this context, it means that in the year 1990, around 3.93 million people moved to another state.

b. To estimate the number of people who moved to another state in 2005 (t = 2005 - 1990 = 15), we substitute this value into the equation:

n = 0.03(15)² - 0.6(15) + 3.93

n = 0.03(225) - 9 + 3.93

n = 6.75 - 9 + 3.93

n ≈ 1.68

Therefore, the estimated number of people who moved to another state in 2005 is approximately 1.68 million.

c. To predict the number of people who moved to another state in 2014 (t = 2014 - 1990 = 24), we substitute this value into the equation:

n = 0.03(24)² - 0.6(24) + 3.93

n = 0.03(576) - 14.4 + 3.93

n = 17.28 - 14.4 + 3.93

n ≈ 6.81

Hence, the predicted number of people who moved to another state in 2014 is approximately 6.81 million.

For more such questions on number , Visit:

https://brainly.com/question/26460978

#SPJ11

Answer:

Yes, (s + t)^2 is equivalent to s^2 + 2st + t^2. This can be shown through the process of expanding the expression (s + t)^2 using the FOIL method (multiplying first, outer, inner, and last terms).

First, we can rewrite (s + t)^2 as (s + t)(s + t).

Now, we do the multiplication and combine like terms:

s*s + s*t + t*s + t*t

s^2 + st + st + t^2

s^2 + 2st + t^2

The volume of small solid is 24 cm³ and volume of big solid is 216 cm³.

Given that

Height of small solid = 4 cm = h₁

Width of small solid = 2 cm = w₁

Length of small solid = 3 cm = L₁

Width of big solid = 6 cm = w₂

Let,

Height of small solid = h₂

Length of small solid = L₂

Since we know that volume of solid  = length x width x height

Therefore,  volume of small solid = 4x2x3 = 24 cm³

Since both the solids are similar,

So,

⇒ w₁/w₂ = h₁/h₂

⇒     2/6 = 4/h₂

⇒     h₂ = 12 cm

Also,

w₁/w₂ = L₁/L₂

⇒2/6 = 3/L₂

⇒    L₂= 9 cm

Hence , the volume of big box = 6x12x9

                                                   = 216 cm³

To learn more about cuboid visit:

https://brainly.com/question/29568631

#SPJ1

The solution to the system of equations is given as follows:

Considering the augmented matrix, the system of equations is defined as follows:

Adding the first and third equations, we have that:

-4x - 6y = -36.

From the second equation, we have that:

2x + 3y = 18.

The addition equation is a multiple of this equation, hence the system has an infinite number of solutions.

From the second equation, we have that:

2x + 3y = 18.

x + 1.5y = 9

x = 9 - 1.5y.

The definition for z is given as follows:

z = x + y - 7.

Hence the variable y is:

y = z - x + 7.

The variable x is of:

x = 9 - 1.5(z - x + 7)

x = 9 - 1.5z + 1.5x - 10.5

0.5x = 1.5 + 1.5z

x = 3z + 3.

The variable y is:

y = z - 3z - 3 + 7

y = -2z + 4.

Hence the solution is:

More can be learned about a system of equations at https://brainly.com/question/13729904

#SPJ1

Realized income is NOT part of your budget.

Income that has really been received or generated within a certain period is referred to as realized income. It stands for the money that has been made or acquired through a variety of sources, including work, investments, or commercial ventures.

Realized income is a crucial part of a budget since it shows the actual cash that a person or organization has available for budgeting and financial planning.

The income is what may be used for a variety of costs, savings, investments, or other financial objectives.

In order to appropriately reflect the financial resources available for controlling spending and making financial decisions, realized income is often included as part of a budget.

Learn more about the budget here:

https://brainly.com/question/31952035

#SPJ1

Answer:

1,000 - 50x > 600

-50x > -400

$0.00 < x < $8.00

The unknown angle measure is 70 degrees.

We are given that;

The values 40° 70° 110° 180°

Now,

One possible equation to find the unknown angle measure is:

180 - 40 - 70 = ?

This equation is based on the fact that the sum of the angles in a triangle is 180 degrees. To solve for ?, we can subtract 40 and 70 from both sides of the equation:

180 - 40 - 70 = ? - 40 - 70 180 - 110 = ? 70 = ?

The solution is ? = 70 degrees.

Therefore, by equation the answer will be 70 degrees.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

The measure of the angle BCA is 50 degrees.

The angles at the circumference subtended by the same arc are equal.

The angles at the circumference on the same segment theorem states that angles in the same segment of the circle are equal.

Therefore, let's use the theorem to find the angle ∠BCA in the circle.

Hence,

∠BCA = ∠BOA

Finally,

∠BCA =  50 degrees.

learn more on tangent here: https://brainly.com/question/29052640

#SPJ1

The graph of its image after the composition is shown in graph.

We have to given that;

XY with endpoints are,

⇒ X (-3, 1) and Y (4,-5)

Now, After Translation (x, y)→(x, y + 2) we get;

X = (- 3, 1)

X' = (- 3, 1 + 2) = (- 3, 3)

Y = (4, - 5)

Y' = (4, - 3)

And, After Rotation: 90° about the origin.

That is, (x, y) = (y, - x)

The points of image are,

X'' = (3, 3)

Y'' = (- 3, - 4)

Thus, The graph of its image after the composition is shown in graph.

Learn more about the transformation visit:

https://brainly.com/question/30097107

#SPJ1

The probability of just thunder is 0.196.

We have,

The probability of rain P(A) = 1/2

The probability of thunder and raining P(A ∩ B) = 1/3

The probability of rain and thunder P(A U B) = 11/30

Now,

Using the addition rule of probability.

P(A U B) = P(A) + P(B) - P(A∩B)

Substituting.

11/30 = 1/2 + P(B) - 1/3

11/30 - 1/2 + 1/3 = P(B)

P(B) = 0.196

The probability of just thunder is 0.196.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Answer:

Step-by-step explanation:

X is the horizontal line and Y is the vertical line. :)