Elroy designs a platform for the new memorial at the local park. The platform is in the shape of a right trapezoidal prism. The base of the prism has an area of 4f * t ^ 2 and the prism stands 3. 2 feet high. As Elroy paints the platform, he calculates the surface area of the stand to be 7f * t ^ 2 (a) Elroy is asked to purchase roping that will be used to close off the area around the memorial. He purchases a length that is five times the perimeter of the platform in roping How much roping does he purchase? Show all work. (b) Elroy plans to add gold leaf to the sides of the platform but not to the two bases. What percent of the area of the platform will have gold leaf? Round your answer to the nearest whole number. Show all work

Answer:

given,

(x y)= (k -3)

so ,

5x- 2y= -24

or, 5k +6 =-24

or,5k =-24 - 6

or,5k= -30

therefore,

k=-6

Answer:

1. Volume = 1,323

2. Area = 866.64

Step-by-step explanation:

Volume of Prism = Area of base×height

First find the volume of the rectangular prism:

Volume of Rectangular Prism= w*h*l = (9)(14)(8) = 1,008

w = width = 14

h = height = 8

l = length = 9

Second find the volume of the triangular prism:

Volume of Triangular Prism= 1/2(b*h*l) = 1/2(5*14*9) = 1/2(630) = 315

b = base = 14

h = height = 5

l = length = 9

Now we just add the two volumes together

1,008 + 315 = 1323

Volume = 1,323

Now for the second figure, it is a capsule, to find the total surface area, we use the formula: A = 4πr² + 2πrh

a = 4 × 3.14 × 6² + 2 × 3.14 × 6 × 11

Multiply 4 and 3.14 to get 12.56

a = 12.56 × 6² + 2 × 3.14 × 6 × 11

Calculate 6 to the power of 2 and get 36

a = 12.56 × 36 + 2 × 3.14 × 6 × 11

Multiply 12.56 and 36 to get 452.16

a = 452.16 + 2 × 3.14 × 6 × 11

Multiply 2 and 3.14 to get 6.28

a = 452.16 + 6.28 × 6 × 11

Multiply 6.28 and 6 to get 37.68

a = 452.16 + 37.68 × 11

Multiply 37.68 and 11 to get 414.48

a = 452.16 + 414.48

Add 452.16 and 414.48 to get 866.64

Area = 866.64

As per inequality, it means that the value of x can be less than or equal to y.

Inequality in Mathematics

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >, <, ≤, or ≥ are used to denote an inequality, when the two expressions aren't always equal.

Type of Inequality

The given expression, x <= y denotes the type of inequality where the possible values of x are either less than y or equal to less. The value of x cannot be greater than y in any case.

Learn more about inequality here:

https://brainly.com/question/20383699

#SPJ4

After the third bounce, the basketball bounces up to approximately 42.19% of its original height, the tennis ball bounces up to approximately 29.63% of its original height, and the softball bounces up to approximately 2.7% of its original height.


To determine the fraction of each ball's original height that it bounces up to after the third bounce, we need to substitute x=3 into the expression given for each ball. a. basketball: 3/4 is the fraction of the drop height that the basketball reaches after one bounce. When x=3, the expression becomes (3/4)^3, which is approximately 0.4219. Therefore, the basketball bounces up to approximately 42.19% of its original height after the third bounce.
b. tennis ball: 2/3 is the fraction of the drop height that the tennis ball reaches after one bounce. When x=3, the expression becomes (2/3)^3, which is approximately 0.2963. Therefore, the tennis ball bounces up to approximately 29.63% of its original height after the third bounce.
c. softball: 3/10 is the fraction of the drop height that the softball reaches after one bounce. When x=3, the expression becomes (3/10)^3, which is approximately 0.027. Therefore, the softball bounces up to approximately 2.7% of its original height after the third bounce.
In conclusion, after the third bounce, the basketball bounces up to approximately 42.19% of its original height, the tennis ball bounces up to approximately 29.63% of its original height, and the softball bounces up to approximately 2.7% of its original height.

To know more about bounce visit :

https://brainly.com/question/29107543

#SPJ11

Answer:

1260

hope this helps

have a good day :)

Step-by-step explanation:

Step-by-step explanation:

2 x 2 x 3 x 3 x 5 x 13

= 2340

................

The Longest Increasing Subsequence (LIS) problem is a classic problem in dynamic programming. Given a sequence of numbers, the problem is to find the longest subsequence in which the numbers are in increasing order. For example, given the sequence {3, 1, 5, 2, 4}, the longest increasing subsequence is {1, 2, 4}, which has length 3.

The LIS problem can be solved using dynamic programming by defining an array to store the length of the longest increasing subsequence that ends at each position in the sequence. The array is initialized to 1, and then for each position i in the sequence, the length of the longest increasing subsequence that ends at i is calculated by finding the maximum length of any subsequence that ends at a position j < i and has a smaller value than the value at i. The final solution is the maximum length of any subsequence in the array.

Find out more  about dynamic programming

brainly.com/question/29809157

#SPJ4

The simplified form of the given expression, (2c7)(9c), is 18c⁸

From the question, we are to simplify the given expression
The given expression is

(2c7)(9c)

First, we will write the expression properly

The given expression written properly is

(2c⁷)(9c)

Now, we will simplify the expression

Simplifying the expression

(2c⁷)(9c)

Multiply

2c⁷ × 9c

Collect like terms

2×9 × c⁷ × c

18 × c⁷⁺¹

18 × c⁸

18c⁸

Hence, the expression is 18c⁸

Learn more on Simplifying an expression here: https://brainly.com/question/1280754

#SPJ1

The correct answers from the given lists are given as follows: Relation (a) a is (strictly) older than bA. irreflexiveB. asymmetricC. antisymmetricD. reflexiveE. transitive Relation (b) a and b have a common grandparentA.

irreflexiveB. antisymmetricC. symmetricD. reflexiveE. transitiveRelation (c) a has the same first name as bA. transitiveB. irreflexiveC. antisymmetricD. symmetricE. reflexiveRelation (d) a and b were born on the same dayA. transitiveB. reflexiveC. irreflexiveD. antisymmetricE. symmetric.

The given lists include different types of relations. Let's discuss the given relations one by one.(a) a is (strictly) older than b:This relation is irreflexive because a person can't be older than oneself. This relation is asymmetric because if a is older than b then it can't be possible that b is older than a.

This relation is antisymmetric because if a is older than b and b is older than a, then it means that a and b are the same person which is not possible. This relation is not reflexive because there is no one who is older than oneself. This relation is transitive because if a is older than b and b is older than c then a is also older than c.(b) a and b have a common grandparent:This relation is irreflexive because a person can't have a common grandparent with oneself. This relation is antisymmetric because if a has a common grandparent with b then it can't be possible that b has a common grandparent with a. This relation is symmetric because if a has a common grandparent with b then b also has a common grandparent with a. This relation is not reflexive because there is no one who has a common grandparent with oneself. This relation is transitive because if a has a common grandparent with b and b has a common grandparent with c then a also has a common grandparent with c.(c) a has the same first name as b:

This relation is transitive because if a has the same first name as b and b has the same first name as c then a has the same first name as c. This relation is irreflexive because a person can't have the same name as oneself. This relation is antisymmetric because if a has the same name as b then it can't be possible that b has the same name as a. This relation is symmetric because if a has the same name as b then b also has the same name as a. This relation is not reflexive because there is no one who has the same name as oneself.

(d) a and b were born on the same day: This relation is transitive because if a was born on the same day as b and b was born on the same day as c then a was born on the same day as c. This relation is reflexive because every person is born on the same day as oneself. This relation is irreflexive because no person is born on a different day than oneself. This relation is antisymmetric because if a was born on the same day as b then it can't be possible that b was born on the same day as a. This relation is symmetric because if a was born on the same day as b then b was also born on the same day as a.

The correct answers for each given relation are listed above.

To know more about  transitive Relation  :

brainly.com/question/30105699

#SPJ11

The functions covariance.p and covariance.s return different values because they use different formulas for calculating the covariance.

Covariance is a measure of how two variables are related to each other, and it is used to understand the linear relationship between two variables. The formula for calculating covariance depends on the type of data being analyzed. The covariance.p function calculates population covariance, while covariance.s calculates sample covariance.

The formula for population covariance uses N in the denominator, while the formula for sample covariance uses N-1 in the denominator. This is because the sample covariance formula is an unbiased estimator of the population covariance, and using N-1 instead of N corrects for the bias.

Therefore, the two functions return different values even when using the same data because they are calculating different types of covariance using different formulas.

For more questions like Function click the link below:

https://brainly.com/question/21145944

#SPJ11

The mathematical model representing the statement is: P = 8 × \(\frac{x}{y^2}\)

The proportionality defines the relationship between two or variables in terms of the changes observed one variable with respect to the changes in the related variables. The proportionality constant is the value of the variable when all the proportional variables are one.

According to the question, P varies directly as x and inversely as the square of y.

P ∝ \(\frac{x}{y^2}\)

Taking K as the constant of proportionality.

P = K \(\frac{x}{y^2}\)

P = 28/3 when x = 42, y = 6. Substituting value of the variables.

\(\frac{28}{3}=K\) × \(\frac{42}{6^2}\)

\(\frac{28}{3}=\) \(K\) × \(\frac{42}{36}\)

Multiplying the equation with 36/42

K = 28/3 × 36/42

K = 8

Substituting the proportionality of constant K in the equation.

The mathematical representing is: P = 8 × \(\frac{x}{y^2}\)

Learn more about Proportionality constant at:

https://brainly.com/question/29126727

#SPJ4

The given question is incomplete, complete question is:

Find a mathematical model representing the statement. (Determine the constant of proportionality.)

P varies directly as x and inversely as the square of y.

p = 28 /3 when x = 42 and y = 6.

the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

To solve this problem, we need to count the number of squares of each size that contain the black center square.

There is only one square of size\($5\times 5$\), which is the entire grid and obviously contains the black center square.

For squares of size\($4\times 4$\), there are \($4$\)possible squares that contain the black center square (one for each corner).

For squares of size\($3\times 3$,\) there are 9 possible squares that contain the black center square (one for each position that the center square could occupy, and then each of those squares could be oriented in three different ways).

For squares of size $2\times 2$, there are $16$ possible squares that contain the black center square (one for each pair of adjacent squares).

For squares of size \($1\times 1$\), there is only one possible square that contains the black center square (the center square itself).

Therefore, the total number of squares that contain the black center square is\($1 + 4 + 9 + 16 + 1 = \boxed{31}$.\)

learn more about squares

https://brainly.com/question/14198272

#SPJ11

There are 11 squares containing the black center square in the 5x5 grid.

To find the number of squares that contain the black center square, we'll consider the sizes of the squares and their positions in the 5x5 grid.
The black center square is a 1x1 square itself, so that's 1 square.
For 2 x 2 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
For 3x3 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle). So, that's 1 square.
4. For 4x4 squares containing the center square, there are 4 possible positions (the center square can be in any corner). So, that's 4 squares.
5. For 5x5 squares containing the center square, there is only 1 possible position (the center square is exactly in the middle).

So, that's 1 square.
Now, we'll add up the number of squares we found in each step:
1 + 4 + 1 + 4 + 1 = 11.

For similar question on squares.

https://brainly.com/question/23305357

#SPJ11

There is a 0.06% chance that a randomly selected individual from the population would have the same genotype as the evidence sample at the FGA locus.

As a forensic scientist, one of your important tasks is to determine the likelihood that a particular piece of evidence matches a specific individual.

To determine the random match probability for the evidence sample at the FGA locus, you will need to compare it to the reference sample. The reference sample is typically obtained from a suspect or a known individual who is not a suspect in the crime. The reference sample for the FGA locus has a genotype of 16,17.

The random match probability is the probability that a randomly selected individual from the population would have the same genotype at a specific locus as the evidence sample. To calculate this probability, you will need to use the allele frequency of the FGA locus in the population. This frequency is typically obtained from a large database of individuals.

Let's assume that the allele frequency for the FGA locus is 0.03 for the 16 allele and 0.02 for the 17 allele. To calculate the random match probability, you will need to multiply these two frequencies together since the evidence sample has both alleles present. This gives us a probability of 0.0006 or 0.06%.

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

Complete Question:

You are a forensic scientist and you are able to obtain the following 3 CODIS STR genotypes from an evidence sample found at a crime scene:

Locus       Evidence Genotype

D55818    6,10

FGA         16,17

VWA        11,12

Based on the reference sample, what is the random match probability for the evidence sample at the FGA locus?

Answer:

\(16\:\mathrm{ft^2}\)

Step-by-step explanation:

Trish's initial garden had an area of \(8\cdot8=64\:\mathrm{ft^2}\). After expanding her garden to be 10 feet by 8 feet, the garden has an area of \(8\cdot 10=80 \:\mathrm{ft^2}\). Therefore, the garden was expanded by \(80-64=\boxed{16\:\mathrm{ft^2}}\)

Answer: 4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Write 10% as 10/100

Of means multiply (as a math term) --

Consequently, the final step becomes 10/100 x 40:

- Multiply 10 and 40: 400

- Divide the 400 by 100 = 4

Have a nice day ~!

Answer:

Rounded to the nearest tenth, 7.4 feet long.

Step-by-step explanation:

Tyrone has a rectangular storage unit. We are given the width and the diagonal length.

So we can use Pythagorean Theorem.

3^2 + b^2 = 8^2

9 + b^2 = 64

subtract 9 from both sides

b^2 = 55

b = sqrt55

b is around 7.4161984871, so b rounded to the nearest tenth is 7.4 feet long.

Answer:

11. at the 5 minute point the object would have travelled 50 Meters.

12. The average speed of the object is 10 meters per minute.

13. It will take the object 12 minutes to reach 120 Meters.

Explanation:

The object would be the blue line, the numbers on the bottom row are each connected to the numbers on the left side as if it were a graph so for each minute it would be 10 meters. If it were to connect 2 to ten then the answer would be five meters per minute and if the one were connected to the 40 it would be 40 per minute and so on... if more explaining is needed comment down below and i´d be happy to assist you!

The fraction of the occupied apartments is 9/10.

In mathematics, a fraction is a symbol for a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

Given that,

Total apartments in the building = 200.

Also,

The number of apartments leased by realtor = 180

The fraction of the apartments which is occupied by realtor

= number of apartments leased /Total apartments

= 180 / 200

= 18 / 20

= 9 / 10

The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.

To know more about Fraction on:

https://brainly.com/question/10708469

#SPJ1

Answer:

SAS, because vertical angles are congruent.

The statement "rxy = 0" represents the null hypothesis in correlation analysis, indicating no linear relationship between variables x and y.

In correlation analysis, the correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, usually denoted as x and y. When the statement "rxy = 0" is made, it refers to the null hypothesis in correlation testing. The null hypothesis states that there is no significant correlation between the variables.

If the correlation coefficient (r) between x and y is found to be exactly 0, it suggests that there is no linear relationship between the variables. This means that changes in x are not associated with any predictable changes in y.

Researchers use statistical tests, such as hypothesis testing, to evaluate whether the observed correlation coefficient is significantly different from 0. If the calculated correlation coefficient is significantly different from 0, the null hypothesis is rejected, indicating evidence of a linear relationship between x and y. However, if the calculated correlation coefficient is close to 0, it supports the null hypothesis, suggesting no linear relationship between the variables.


Learn more about Correlation click here :brainly.com/question/28091015

#SPJ11

×

For the value θ = 5π/6, the values of cos θ, sin θ, and tan θ are approximately -0.87, 0.50, and -0.58 respectively.

To find the values, we can use the unit circle and the definitions of the trigonometric functions.

In the unit circle, θ = 5π/6 corresponds to a point on the unit circle in the third quadrant. The x-coordinate of this point gives us the value of cos θ, while the y-coordinate gives us the value of sin θ.

The x-coordinate at θ = 5π/6 is -√3/2, rounded to -0.87. Therefore, cos θ ≈ -0.87.

The y-coordinate at θ = 5π/6 is 1/2, rounded to 0.50. Therefore, sin θ ≈ 0.50.

To find the value of tan θ, we can use the identity tan θ = sin θ / cos θ. Substituting the values we obtained, we get tan θ ≈ (0.50) / (-0.87) ≈ -0.58.

Read more about trigonometric here:

https://brainly.com/question/29156330

#SPJ11

The time it will it take him to grade 150 papers is 32 minutes, 4 seconds

It is important to note that proportion is a method of comparison in which two expressions or equations are made equal to each other.

From the information given, we have that;

Mr. B grades a total of 12.5 papers in 2.7 minutes.

Then, for 150 papers, we would have;

If 12. 5 papers = 2.7 minutes

Then 150 papers = x

Cross multiply the values

12.5x = 2.7(150)

multiply the values

12.5x = 405

Divide the values by the coefficient of x, we get;

x = 405/12.5

x = 32 minutes, 4 seconds

Learn about proportion at: https://brainly.com/question/1781657

#SPJ1

The area of the bases of the second triangular pyramid will be 3 times the first one.

What is a triangular pyramid?

A tetrahedron is a four-sided, three-dimensional object that is also known as a triangular pyramid. Its triangular base is formed by three triangles, the sides of which meet at the apex above the base.

We are given that a triangular pyramid with a volume of 90 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = \(\frac{1}{3}\) * A * H

⇒ 90 = \(\frac{1}{3}\) * A * 15

⇒ 90 = A * 5

⇒ A = 18 square inches.

Similarly, another pyramid with a volume of 270 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = \(\frac{1}{3}\) * A * H

⇒ 270 = \(\frac{1}{3}\) * A * 15

⇒ 270 = A * 5

⇒ A = 54 square inches.

Hence, the area of the bases of the second triangular pyramid will be 3 times the first one.

Learn more about triangular pyramid from the given link

https://brainly.com/question/21864491

#SPJ1

The length of the side k = 6.92 cm

Given a triangle ABC with sides measuring a, b, and c, and the equation a2 + b2 = c2, Make another triangle with sides of lengths a and b and a right angle. The Pythagorean theorem dictates that the hypotenuse of this triangle is the same length as the hypotenuse of the first triangle, c = a2 + b2.

Given, a triangle = ΔIJk

The measurement of the sides I and J are given

I = 1.3 cm

j = 6.8 cm

and angle k is given as 45°

According to the Pythagoras theorem

\(i^2 + j^2 = k^2\)

\(1.3^2 + 6.8^2\)

= 1.69 + 46.24

= 47.93

On taking square root we get

k = 6.92 cm

To know more about the Pythagoras Theorem you may visith the link which is mentioned below:

https://brainly.com/question/21926466

#SPJ4

a) The % of students who passed math is 49%.

b)  % of the total number of students who live off campus is 44%

c)  % of the total number of students who live off campus passed math 33%

d) The students who live off campus tend to pass more than those who live on campus.

The 200 college students who took math last term were interviewed.

The total number of students who live on campus =32 +80 = 112

The total number of students who live off campus =66 +22 = 88

a) The number of students who passed math = 32 + 66 =98

Therefore the % of the students who passed math = \(\frac{98}{200} * 100 = 49\)%

b) % of the total number of students who live off campus = \(\frac{88}{200} * 100 = 44%\)%

c) % of the total number of students who live off campus passed math = \(\frac{66}{200} * 100 = 33%\)%

d) For evidence that students who live off campus tend to pass more than those who live on campus, we need to calculate the % of the total number of students who live on campus who passed in math =

\(\frac{32}{200} * 100 = 16%\)%

Therefore the students who live off campus tend to pass more than those who live on campus.

Learn more about percentages here:

https://brainly.com/question/30348137

#SPJ1

Answer:

x = -3

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

You can just do +x on both sides so: 0=3+x and then -3 on both sides: -3=x.

Using the trignometry functions we now know that the distance from point A to point B is 1,156.1 ft.

Distance is the sum of an object's movements, regardless of orientation.

Distance can be defined as the amount of space an object has covered, regardless of its beginning or ending point.

A scalar number, distance.

The entire path that an object has taken can be used to determine distance.

The entire distance travelled by a car, for instance, would be 13 km if it traveled 5 km east, 8 km north, and back again.

So, the distance from point A to B would be:

Considering the flat planet -

tan5 = 131 / d₁

d₁ = 131/tan5 = 1,497.3368... ft

d₂ = 131/tan21 = 341.2666674...ft

Distance:

1497.3368 - 341.26666 = 1,156.1 ft

Therefore, using the trignometry functions we now know that the distance from point A to point B is 1,156.1 ft.

Know more about distance here:

https://brainly.com/question/26550516

#SPJ1

Correct question:

A boat is heading towards a lighthouse, whose beacon light is 131 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 5°, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 21°. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessary.

The function y as a function of a in the given equation y'''+4y'=0 cannot be determined with the provided information. The equation is a third-order linear homogeneous differential equation, but the initial conditions y(0), y'(0), and y''(0) are given in terms of x instead of a. Without additional information or constraints relating a and x, it is not possible to find a specific solution for y as a function of a.

The given differential equation is y'''+4y'=0, where y represents a function of x. The initial conditions provided are y(0) = -5, y'(0) = -18, and y''(0) = 12. However, the function y(x) = 2 - 3sin(5x) - 9cos(5x) does not satisfy these initial conditions.

To find a general solution for the given differential equation, we can solve the characteristic equation. Let's assume y(x) = e^(rx), where r is a constant. Substituting this into the differential equation, we get the characteristic equation r^3 + 4r = 0. By factoring out an r, we have r(r^2 + 4) = 0. This equation has three roots: r = 0 and r = ±2i.

The general solution to the differential equation is then y(x) = c1e^(0x) + c2e^(2ix) + c3e^(-2ix), where c1, c2, and c3 are constants to be determined based on the initial conditions. However, without additional information or constraints relating a and x, we cannot determine the values of these constants or find a specific solution for y as a function of a.

Learn more about equation click here: brainly.com/question/29657988

#SPJ11

The equation that represents the relationship between the number of hours needed to complete a trip, h, and the driving speed, s, is h = 5/s. This means that the number of hours needed to complete the trip is inversely proportional to the driving speed.

When the driving speed is 60 miles per hour, the number of hours needed to complete the trip is 5 (h = 5/60). If the driving speed is increased to 90 miles per hour, the number of hours needed to complete the trip is 5/90 (h = 5/90).

In general, as the driving speed increases, the number of hours needed to complete the trip decreases.

To summarize, the equation that represents the inverse relationship between the number of hours needed to complete a trip and the driving speed is h = 5/s. This equation can be used to determine the number of hours needed to complete a trip at any given speed.

For more such questions on Speed & Time.

https://brainly.com/question/29248622#

#SPJ11