what is the answer to the following questions 32 − 14

The surface area of the cube is  3 6/16 cm²

To determine the value of the surface area of the cube, we need too know the formula

The formula for calculating the surface area of a cube is represented as;

Surface area = 6a²

Such that the variable 'a' is the length of the side of the cube

From the information given, we have that;

a = 3/4

Substitute the value, we get;

Surface area = 6 (3/4)²

find the squares

Surface area = 6(9/16)

Multiply the values

Surface area = 3 6/16 cm²

Learn about cubes at: https://brainly.com/question/1972490

#SPJ1

There are two buildings that you want to have in the amusement park.

a) The expression that represents the area of the gift shop, in terms of x, is

Area = length x width

Area = (20x + 24) (36x - 20)

Area = 720[tex]x^{2}[/tex] + 208x - 480

Therefore, the area of the gift shop is 720[tex]x^{2}[/tex]  + 208x - 480 square feet.

b) The expression that represents the perimeter of the gift shop, in terms of x, is

Perimeter = 2(length + width)

Perimeter = 2(20x + 24 + 36x - 20)

Perimeter = 2(56x + 4)

Perimeter = 112x + 8

Therefore, the perimeter of the gift shop is 112x + 8 feet.

c) If the perimeter is going to be 176 feet, we can set the expression for the perimeter equal to 176 and solve for x

112x + 8 = 176

Subtracting 8 from both sides

112x = 168

Dividing both sides by 112

x = 1.5

Now that we know x, we can substitute it into the expressions for the length and width of the gift shop

Length = 20x + 24 = 20(1.5) + 24 = 54 feet

Width = 36x - 20 = 36(1.5) - 20 = 34 feet

Therefore, the dimensions of the gift shop are 54 feet by 34 feet.

To know more about buildings here

https://brainly.com/question/10499103

#SPJ1

For given triangle,  Length of XY and YZ is equal to 7√2.

What is a triangle's definition?

A triangle has three straight sides and three angles. It is one of the basic shapes in geometry and has many properties and applications in mathematics and everyday life. The sum of the interior angles of a triangle is always 180 degrees, and there are different types of triangles depending on their side lengths and angle measures and it includes 6 types of triangles.

Now,

If one of the angles of a right triangle is 90 degrees and another angle is 45 degrees, then the third angle must also be 45 degrees. This means that the triangle is a 45-45-90 triangle, which has a special property that the two legs are congruent and the hypotenuse is the square root of 2 times the square length of each leg.

In this case, the hypotenuse is given as 14, so we can set up the following equation:

14 = √2x²

where x is the length of each leg of the triangle. To solve for x, we can square both sides of the equation:

14² = 2x²

196 = 2x²

x² = 98

x = 7√2

So, each leg of the triangle has a length of 7√2, and the hypotenuse has a length of 14.

Hence,

             Length of XY and YZ is equal to 7√2.

To know more about triangles visit the link

brainly.com/question/2773823

#SPJ1

Answer:

Step-by-step explanation:

Split it into 3 shapes.

2 triangles and 1 square.

The squares answer is 53.25 And for the triangles you would get 26 and there are 2 triangles so 52.

52+53.25=105.25.

To construct a 98% confidence interval,  the critical value is 2.624.

We have,

98% Confidence Interval

Sample size, n= 15

At 98%,

Degree = n-1

             = 15-1= 14

So, For a 98% confidence level with 14 degrees of freedom, the critical value is 2.624.

Therefore, to construct a 98% confidence interval, the critical value is 2.624.

learn more about confidence interval here:

brainly.com/question/17034620

#SPJ1

A. Here's a sketch of a horizontal pipe at a maximum slope (1/2 inch per foot) and a minimum slope (1/4 inch per foot):   / / / / / / / / / / / / / / / / / / /

 / / / / / / / / / / / / / / / / / / /

/ / / / / / / / / / / / / / / / / / /

/ / / / / / / / / / / / / / / / / / /

The pipe on the left has a slope of 1/4 inch per foot, while the pipe on the right has a slope of 1/2 inch per foot.B. To determine the minimum and maximum angles, we need to use trigonometry. If we let the angle that the pipe makes with the horizontal be θ, then we have:Minimum angle: tan(θ) = 1/48 (since 1/4 inch per foot is equivalent to 1 inch of drop over 48 inches of horizontal distance) θ ≈ 1.2 degreesMaximum angle: tan(θ) = 1/24 (since 1/2 inch per foot is equivalent to 1 inch of drop over 24 inches of horizontal distance) θ ≈ 2.4 degreesSo the minimum angle is approximately 1.2 degrees and the maximum angle is approximately 2.4 degrees.C. To determine if the slope of Enrico's pipe is acceptable, we need to calculate the slope of the pipe in inches per foot. Enrico's pipe runs a horizontal distance of 172 inches and drops 6 inches. The slope is:Slope = Drop / Horizontal distance = 6 / 172Slope = 0.0349 inches per inchTo convert this to slope in inches per foot, we multiply by 12:Slope = 0.4188 inches per footSince this slope is between the acceptable range of 1/4 inch per foot and 1/2 inch per foot, Enrico's pipe slope is acceptable.


Correct me if I am wrong

A. Sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below. B. the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively. C. Yes, pipe slope is acceptable according to the given criteria.

B. Determine the minimum and maximum angles:

To find the angle, use the tangent function. The tangent of an angle is equal to the ratio of the height to the horizontal distance travelled.

Minimum angle:

Tangent of the angle= 1/4 inch per foot

Tangent of the angle = 0.25 inches per foot

Minimum angle (in degrees) = arctan(0.25)

Minimum angle ≈ 14.0 degrees

Maximum angle:

Tangent of the angle = 1/2 inch per foot

Tangent of the angle = 0.5 inches per foot

Maximum angle (in degrees) = arctan(0.5)

Maximum angle ≈ 26.6 degrees

C. Enrico's drain pipe:

Horizontal distance travelled  = 172 inches

Drop from the horizontal = 6 inches

Slope of the pipe = Drop / Run

Slope of the pipe = 6 / 172

Slope of the pipe ≈ 0.0349 inches per inch

To convert the slope to inches per foot:

Slope = 0.0349 × 12

Slope ≈ 0.4188 inches per foot

Hence, sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below, the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively, and yes, pipe slope is acceptable according to the given criteria.

Learn more about Maximum here:

https://brainly.com/question/30693656

#SPJ4

The area of the rectangle is 48 in².

The area of the triangle is 24 in².

The area of the triangle is half the area of the rectangle.

To calculate the area of a rectangle, we multiply the length of the rectangle by its width. And to calculate the area of a triangle we multiply the base of the triangle to the height of the triangle and divide by 2.

To calculate the area of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Also, the area of the triangle is given by the formula below

Where:

Substitute into equation 2

Hence, the area of the triangle is half the area of the rectangle.

Learn more about area here: https://brainly.com/question/28470545

#SPJ1

Answer:

17.7

Step-by-step explanation:

using the pythagorean theorem, plug in and solve.

hi

with Pythagoras we have :

13²+12² = 313

so answer is [tex]\sqrt{313}[/tex] ≈ 17.7  rounded.

After rounding 475.189 to the nearest hundredth we get 475.19 .

Rounding of a number is a process of approximating the original number to some decimal points resulting the original number to shorten up for more explicit representation.

Rules of rounding a number to its nearest hundredth is,

The original number would be rounded up to two decimal places as it represents to its hundredth decimal place.

If the digit after the second decimal place of the original number is greater than (equals to) 5 then we round up the number, by increasing the previous place value digit by 1.

And if the digit after the second decimal place of the original number is lesser than 5 then we round down the number, by decreasing the previous place value digit by 1.

Here in 475.189 the digit after second decimal is 9 which is greater than 5, hence we round up the number by increasing the previous value (that is, second decimal digit)  by 1 we get 475.19 (to the nearest hundredth).

To know more about rounding of here

https://brainly.com/question/29878750

#SPJ4

The axis of symmetry for y = (x - 1)² - 4 is x = 1.

Given the equation in the question;

y = (x - 1)² - 4

The axis of symmetry for a parabola in standard form is expressed as:

y = a(x - h)² + k is the vertical line passing through the vertex (h, k).

Comparing y = (x - 1)² - 4 to the standard form

We can see that h = 1 and k = -4.

Therefore, the vertex is (1, -4).

Since the axis of symmetry is the vertical line passing through the vertex, the equation of the axis of symmetry is

x = 1.

Therefore, the axis of symmetry is x = 1.

Learn more about axis of symmetry here: https://brainly.com/question/29107199

#SPJ1

Answer:

x² - 4 = 0

Step-by-step explanation:

choices: x² - 4 = 0, x² = -4, 3x² + 12 = 0, 4x² = 16, 2(x-2)² = 0

to find x= -2, 2

x² - 4 = 0

(x + 2) (x - 2) = 0

x = -2, 2

The probability that a lightbulb will last between 1,950 and 2,050 hours is 0.84, or 84%.

To solve this problem, we need to find the probability that the lifespan of a lightbulb will fall between 1,950 and 2,050 hours.

First, we need to standardize the distribution using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For x = 1,950 hours:

z = (1,950 - 1,975) / 25 = -1

For x = 2,050 hours:

z = (2,050 - 1,975) / 25 = 3

Now, we need to find the area under the standard normal distribution curve between z = -1 and z = 3. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 3 is 0.9987. Therefore, the area between z = -1 and z = 3 is:

0.9987 - 0.1587 = 0.84

for such more question on  probability

https://brainly.com/question/13604758

#SPJ11

The expected value of X is 7, and the standard deviation of X is 2.42 respectively.

The average of X's potential values is the expected value of X. We must first determine the sum of all potential x values multiplied by each value's associated probability before we can determine the expected value.

Calculate the expected value of X

Expected value = (2×(1/36)) + (3×(2/36)) + (4×(3/36)) + (5×(4/36)) + (6×(5/36)) + (7×(6/36)) + (8×(5/36)) + (9×(4/36)) + (10×(3/36)) + (11×(2/36)) + (12×(1/36))

Expected value = 7

Calculate the variance of X

Variance = (2-7)2×(1/36) + (3-7)2×(2/36) + (4-7)2×(3/36) + (5-7)2×(4/36) + (6-7)2×(5/36) + (7-7)2×(6/36) + (8-7)2×(5/36) + (9-7)2×(4/36) + (10-7)2×(3/36) + (11-7)2×(2/36) + (12-7)2×(1/36)

Variance = 5.83

Calculate the standard deviation of X

Standard deviation = √(variance)

Standard deviation = 2.42

To know more about standard deviation visit:

https://brainly.com/question/475676

#SPJ4

Complete Question:

Consider the roll of two dice. Let X be a random variable representing the sum of the number of dots appearing on each of the dice. The probabilities of each possible value of X are as follows:

x             P(x)

2            1/36

3            2/36

4            3/36

5            4/36

6            5/36

7            6/36

8            5/36

9            4/36

10           3/36

11            2/36

12            1/36

Determine the expected value and standard deviation of X.

The value of k is given as follows:

k = 2.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For this problem, we have that the parameters are given as follows:

Hence the equation to obtain k is given as follows:

[tex]\sin{45^\circ} = \frac{\sqrt{2}}{k}[/tex]

[tex]\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{k}[/tex]

k = 2.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The surface area of the rectangular pyramid is 75 m².

Surface area is the sum of all the surfaces on each side of a three-dimensional shape.

To calculate the surface area of the rectangular pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equaation 1

Learn more about Surface area here: https://brainly.com/question/1297098

#SPJ1

The weights in a weighted moving average are selected by: Trial and error, Fitting to a regression line, Guessing, Experience.

The methods for selecting weights in weighted moving averages are trial and error, fitting to a regression line, and experience.

When selecting weights for weighted moving averages, the following methods can be used:
Trial and error:

Testing different weight combinations to find the best fit for the data.
Fitting to a regression line:

Analyzing the relationship between the data points and assigning weights accordingly.
Experience:

Using prior knowledge and understanding of the data or similar situations to determine appropriate weights.

For similar question on average.

https://brainly.com/question/29219210

#SPJ11

 Trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

With weighted moving averages, the weights can be selected using various methods. Here are the applicable methods from your given options:

1. Trial and error fitting: Weights can be selected by testing different combinations of weights and observing their impact on the accuracy of the model.

2. Fitting to a regression line: Weights can be determined by fitting a regression line to the data and using the coefficients of the regression line as the weights.

3. Experience: Domain knowledge or past experience with similar data can help in selecting appropriate weights.

In summary, trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

to learn more about regression line click here:

https://brainly.com/question/17731558

#SPJ11

The volume of the solid created by revolving a curve f(x) around the y-axis is  2π [tex]\int\limits^a_b {xf(x)} \, dx[/tex]

What is the cylindrical shell?

A region enclosed by two identically sized cylinders with the same central axis is known as a cylindrical shell. We often denote the height of the cylinders by H, the inner cylinder's radius by r, and the thickness of the shell by t, resulting in a larger cylinder's radius equal to r + t.

Here,

We consider a strip of height y = f(x), and width dx; it is x units away from the axis of rotation.

Now, we rotate this strip about the y-axis; we obtain a cylindrical shell with  

radius = x

height = f(x)

thickness = dx

The volume of cylindrical shell = (circumference)×(height)×thickness

= (2πx)×(f(x))×dx

The volume of revolution = 2π [tex]\int\limits^a_b {xf(x)} \, dx[/tex]

Hence, the volume of the solid created by revolving a curve f(x) around the y-axis is  2π [tex]\int\limits^a_b {xf(x)} \, dx[/tex]

To learn more about the cylindrical shell from the given link

https://brainly.com/question/30689905

#SPJ4

Answer:

Let's start by using a proportion to find the total number of questions on the test. We know that Charles answered 23 questions correctly and received a grade of 92%, which means he missed 8% of the questions.

Let x be the total number of questions on the test. Then 8% of the questions that Charles missed can be expressed as 0.08x.

The number of questions that Charles answered correctly plus the number of questions he missed must add up to the total number of questions on the test:

23 + 0.08x = x

Simplifying and solving for x, we get:

0.92x = 23

x = 23 / 0.92

x ≈ 25

Therefore, the total number of questions on the test was approximately 25.

Answer:

105

cause you do

P arenthaces

E xponents

M ultiplication D ivision

A dd

S ubtract

The calcuated value of the proportionality constant (y to x) is 15

To find the proportionality constant between the distance and time, we can use the formula:

proportionality constant = y/x

where y is the distance and x is the time.

From the graph, we know that when x = 1, y = 15. Therefore, the proportionality constant can be calculated as follows:

proportionality constant = y/x = 15/1 = 15

So, the proportionality constant between the distance and time is 15.

Read more about proportional relationship at

https://brainly.com/question/14654228

#SPJ1

Answer:

Step-by-step explanation:

x = [tex]\sqrt{12^{2}+9^{2} }[/tex]

x = 15

The integer conversion specifier that would display the hexadecimal digit "a" is "x".
d) x

To display the hexadecimal digit "a" using an integer conversion specifier.
The "x" specifier is used for displaying an integer value in hexadecimal format with lowercase letters (i.e., a, b, c, etc.), while "X" would display the value in uppercase letters (i.e., A, B, C, etc.).

Options "H" and "h" are not standard integer conversion specifiers for displaying hexadecimal values.

Hence d) x is correct.

For similar question on conversion.

https://brainly.com/question/28244843

#SPJ11

The required amount of stock is of $950 for  both brokers charge the same commission from the linear equation in one variable.

Let the total amount of stock be x (in dollars).

Fierro Brothers charges their customers a $19 flat fee per trade. Whereas, the Sondo Investment House charges 2% as the commission of trade.

Thus the given condition is Fierro Brothers charges equal commission fee on the required amount of stock as Sondo Investment house.

This relation can be shown in terms of linear equation as,

19 = 2% of x

⇒ 19 = (2/100)x

This linear equation is in the form of linear equation in one variable.

⇒ x= 19*(100/2)

⇒ x = 950

Therefore, on single trade of stock of $950 Fierro Brothers charges $19 fee (flat) as their commission which is equal to the commission earned by Sondo Investment House at the rate of 2% on trade.

To know more about linear equation in one variable here

https://brainly.com/question/31120842

#SPJ4

No, tripling the length of time for the investment does not double the interest earned with compound interest.

When interest is compounded, the interest earned depends not only on the length of time, but also on the interest rate and the number of compounding periods.

For example, if an investment of $100 earns 5% annual interest compounded annually for 1 year, the interest earned would be:

Interest = $100 x 0.05 = $5

If the same investment is compounded for 2 years instead of 1, the interest earned would be:

Interest = $100 x (1 + 0.05)^2 - $100 = $10.25

As we can see, doubling the length of time for the investment does not double the interest earned with compound interest.

The interest earned depends on the interest rate and the number of compounding periods as well.

Read more about compound interest at

https://brainly.com/question/24924853

#SPJ1

The sum of the expression is simplified to give x² + 11x - 6/(x-3)(x+3)

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

These mathematical expressions are also made up of arithmetic operations such as;

From the information given, we have the expression as;

x-2/x-3  + 10x/x² - 9

Find the lowest common factor, we have;

(x-2)(x+3) + 10x/(x-3)(x+3)

expand the bracket

x² + 3x - 2x - 6 +10x/(x-3)(x+3)

Now, add the like terms, we get;

x² + 11x - 6/(x-3)(x+3)

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

The mean of the game is 9

To find the mean of a game with two possible outcomes, we need to multiply the value of each outcome by its probability and then add the results.

Let X be the random variable representing the outcome of the game. The first outcome has a value of 5 and a probability of 0.2, while the second outcome has a value of 10 and a probability of 0.8.

Thus, the expected value or mean of the game can be calculated as:

E(X) = (0.2 x 5) + (0.8 x 10)

= 1 + 8

= 9

Therefore, the mean of the game is 9

Learn more about mean

https://brainly.com/question/31101410

#SPJ4

The answer of the given question based on the circle is ,  the answer is option (d) 8/3π.

In geometry, an arc is  portion of circumference of a circle. It is  curved line that connects two points on  circle. The length of arc is proportional to the angle that it subtends at the center of the circle.

Since EFB is a straight line and EB is a diameter of the circle, angle EFB subtends the entire circle at F. Therefore, the angle subtended by arc EFD is the difference between the angles subtended by arcs EF and EB.

Arc EF subtends a full circle at F, so its angle is 2π radians. Arc EB subtends a straight angle at F, so its angle is π radians.

Therefore, the angle subtended by arc EFD is:

2π - π = π

The length of arc is given by formula L = rθ, where r is  radius of  circle and θ is  angle (in radians) subtended by  arc at  center of  circle.

In this case, r = 4 and θ = π, so the length of the arc corresponding to angle EFD is:

L = rθ = 4π

Therefore, the answer is (d) 8/3π.

To know more about Radius visit:

https://brainly.com/question/12922563

#SPJ1