Simplify. 5/12x1/12=

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

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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.

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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]

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In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.
The volume of a cone is given by the formula V = (1/3)πr²h here r is the radius of the base and h is the height of the cone.

Now we have differentiate this formula concerning t to get
dV/dt = (1/3)πr²dh/dt + (2/3)πrh²dr/dt.

It is given to us  that water is coming out a giant cone shaped funnel at a rate of 15 cubic inches per second, then we  can say that
dV/dt = -15 cubic inches per second

Therefore the funnel has a maximum radius of 40 inches and a height of 75 inches. We need to evaluate  dh/dt
If h = 15 inches.

In order to find dh/dt,
we need to evaluate  dr/dt and place it in  equation for dV/dt.

Therefore, to find dr/dh = r/h.
Given
when h = 75 inches,
r = 40 inches.
Therefore, dr/dh
= 40/75.

Staging this into the equation for dV/dt,

-15 = (1/3)π(40²)(dh/dt) + (2/3)π(40)(15)²(40/75)

Here simplification takes place


dh/dt = -0.4π/3
≈ -0.42 cubic inches per second
In the event  of alteration in the rate at which the water level of the funnel is changing when the water is 15 inches high is 0.42 cubic inches per second.


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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.

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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.

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.

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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.

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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

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The scatter plot reveals a positive connection since the y-values grow as the x-values grow.

An example of a graph that employs Cartesian coordinates to show values for two categories for a collection of data is a scatter plot, sometimes referred to as a scatter diagram. Each pixel in the data's representations is a point with a horizontal position (indicating the value of one variable) and a vertical displacement (representing the value of the other variable). In order to observe correlations among variables and spot patterns in the data, scatter plots is utilised. They are frequently employed in data processing, statistics, and academic studies.

given

The scatter plot reveals a positive connection since the y-values grow as the x-values grow.

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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.

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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).

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Answer:

105

cause you do

P arenthaces

E xponents

M ultiplication D ivision

A dd

S ubtract

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.

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by solving the following equation we can conclude that the value of 4¤(5¤6) is 72.

Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.

given,

To find the value of 4¤(5¤6), we need to evaluate the expression from the inside out, following the order of operations.

We must first determine the worth of 5¤6. Using the given operation, we have:

5¤6 = 5*6 - 6 = 24

Now we can substitute this value into 4¤(5¤6) and evaluate:

4¤(5¤6) = 4¤24 = 4*24 - 24 = 96 - 24 = 72

Therefore, the value of 4¤(5¤6) is 72.

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Answer:

42.39

Step-by-step explanation:

The formula for the volume of a cylinder:

V= πr^2h

Substitute values into the formula that was given:

π = 3.14

r = 3/2

h = 6

3.14(1.5^2)6=

3.14(13.5)=

42.39

I hoped this solved your problem <3

(I took the FLVS test too and got it right)

To find the area of a specific parallelogram, we need to know the length of its base and the height.

To find the area of a parallelogram, we multiply the base of the parallelogram by its height, where the height is the perpendicular distance between the base and its opposite side. So, the formula for the area of a parallelogram is:

Area = base x height

where the base and height are both expressed in the same units.

We know that the area of the parallelogram can be given as bh or absinα

Thus we have for each of the parallelograms shown;

1) 6 * 4 = 24 ft^2

2) 9 * 5 = 45 yd^2

3) 8 * 10 sin 45 = 56.6 cm^2

4) 5 * 11 sin 60 = 47.6 m^2

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Answer: To find the proportion of students who performed worse than Aaron, we need to find the area to the left of his score of 989 on the normal distribution curve.

First, we need to standardize Aaron's score using the formula:

z = (x - mu) / sigma

where x is the score, mu is the mean, and sigma is the standard deviation.

Plugging in the values, we get:

z = (989 - 1100) / 200 = -0.55

Next, we look up the area to the left of z = -0.55 on the standard normal distribution table, or use a calculator to find:

P(Z < -0.55) = 0.2912

Therefore, the proportion of students who performed worse than Aaron is approximately 0.2912, or 29.12% (rounded to 2 decimal places).

Step-by-step explanation:

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.

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.

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The standard deviation of the height distribution is approximately 6 inches (since 6 is half of 12), which corresponds to option (C).

The distribution of the heights of students in a large class is roughly Normal, with an average height of 68 inches, and approximately 95% of the heights are between 62 and 74 inches.

The height distribution is approximately Normal, we can use the empirical rule, which states that approximately 95% of the data falls within 2 standard deviations of the mean, to estimate the standard deviation.

The range of heights within which approximately 95% of the students fall is from 62 to 74 inches.

This range is 12 inches wide, and it corresponds to 2 standard deviations from the mean.

Thus, we have:

2 standard deviations = range of 95% of the data = 74 - 62 = 12 inches

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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

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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 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.

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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.

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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)

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