Darren made a display board in the shape of a trapezoid.


Part A


The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length


of the shorter base.


4 yd


2 yd


2 yd


b


What are the lengths of the height and the longer base? Enter your answers in the boxes.


h =


yd


b=


yd


Part B


Use the measurements from Part A to find the area of Darren's display board.


o 8 yd?


12 yd?


O 16 yd


24 yd2

The radius of gyration of the plate about the x-axis is [tex]6 \sqrt{6} / 5[/tex] units.

To find the radius of gyration of a plate covering the region bounded by [tex]y = x^2[/tex], x = 6, and the x-axis with respect to the x-axis, we need to use the formula:

[tex]k_x = \sqrt{(I_x / A)}[/tex]

where [tex]k_x[/tex] is the radius of gyration, [tex]I_x[/tex] is the moment of inertia of the plate about the x-axis, and A is the area of the plate.

We can calculate the area A of the plate as follows:

[tex]A = \int\limits^6_0 { x^2}\, dx\\= [x^3/3]\ from\ 0\ to\ 6\\= 72[/tex]

To find the moment of inertia [tex]I_x[/tex], we can use the formula:

[tex]I_x = \int\ {y^2} \, dA[/tex]

where y is the perpendicular distance of an element of area [tex]dA[/tex] from the x-axis. We can express y in terms of x as y = x². Therefore, we have:

[tex]dA = y dx = x^2 dx\\I_x = \int\limits^6_0 { x^2 (x^2)} dx\\= \int\limits^6_0 {x^4}\, dx\\= [x^5/5]\ from\ 0\ to\ 6\\= 6^5/5[/tex]

Substituting these values into the formula for [tex]k_x[/tex], we get:

[tex]k_x = \sqrt{(I_x / A)}\\= \sqrt{((6^5/5) / 72)}\\= \sqrt{(6^3 / 5)}\\= 6 \sqrt{6} / 5[/tex]

Therefore, the radius of gyration of the plate about the x-axis is [tex]6 \sqrt{6}/ 5[/tex] units.

Learn more about radius of gyration of a plate.

brainly.com/question/31402406

#SPJ11

To solve exercise 3 on the first page of the handout, we need to first isolate y in the given equation 2.23 - 3y = 8, which gives us y = -1.59.

To find y", we need to differentiate both sides of the equation with respect to x twice. The first derivative gives us:
-3(dy/dx) = 0
Simplifying, we get dy/dx = 0.
Differentiating again, we get:
-3d^2y/dx^2) = 0
Simplifying, we get d^2y/dx^2 = 0.

Therefore, the equation we obtain after differentiating both sides of the given equation with respect to x is d^2y/dx^2 = 0, which is the second derivative of y with respect to x.
To solve the equation given on the first page of the handout, 2.23 - 3y = 8, first isolate y:
1. Subtract 2.23 from both sides: -3y = 5.77
2. Divide both sides by -3: y = -5.77/3
Your answer: y = -5.77/3

The original equation doesn't have any x terms, so differentiation with respect to x is not applicable in this case.

To know more about Isolate click here .

brainly.com/question/7741418

#SPJ11

The height of the triangle is given as follows:

[tex]h = 2\sqrt{3}[/tex] cm.

The area of the triangle is given as follows:

[tex]A = 4\sqrt{3}[/tex] cm².

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering an equilateral triangle, in which all the side lengths are of 4, we have a right triangle in which:

Hence the height is obtained as follows:

h² + 2² = 4²

h² = 12

[tex]h = \sqrt{3 \times 4}[/tex]

[tex]h = 2\sqrt{3}[/tex] cm

The area of a triangle is given as half the multiplication of the base and of the height, hence:

[tex]A = 0.5 \times 4 \times 2 \sqrt{3}[/tex]

[tex]A = 4\sqrt{3}[/tex] cm².

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

The density of deer for 400 square miles is around 1:4 based on stated number of deers.

The density of deer will be given by the formula -

Population density of deer = number of deer/ area

Population density is the amount or number of individuals of a population on land per unit area.

Keep the value in formula to find the population density

Population density = 100/400

Cancelling zero as common in both numerator and denominator

Population density = 1:4

Thus, there is 1 deer for every 4 square mile.

Learn more about density -

https://brainly.com/question/13902749

#SPJ4

Answer:

13 units

Step-by-step explanation:

To find the distance between the two points, use the distance formula.

[tex]\sqrt{(x-x)^{2}+(y-y)^{2} }[/tex]

Plug in the point values.

[tex]\sqrt{(-8--3)^{2}+(-6-6)^{2} }[/tex]

Simplify the parenthesis.

[tex]\sqrt{(5)^2+(-12)^2}[/tex]

Get rid of the parenthesis.

[tex]\sqrt{25+144}[/tex]

Simplify.

[tex]\sqrt{169}[/tex]

Solve.

13 units

The percentage of plastic beads on clearance is 98.99%.

To calculate the percentage of plastic beads on clearance, you need to divide the number of plastic beads by the total number of beads and then multiply by 100 to get the percentage.

In this case, the total number of beads on clearance is the sum of plastic beads and metal beads:

In this question, you are given the number of plastic beads and metal beads on clearance, and you are asked to find the percentage of plastic beads.

To do this, you need to calculate the total number of beads on clearance by adding the number of plastic beads and the number of metal beads.

Once you have the total number of beads, you can find the percentage of plastic beads by dividing the number of plastic beads by the total number of beads.

And then multiplying by 100 to convert the answer into a percentage. This formula can be expressed as:

Percentage of plastic beads = (Number of plastic beads / Total number of beads) x 100%

Plugging in the given values, we get:

Total number of beads = 882 + 18 = 900

Percentage of plastic beads = (882 / 900) x 100% = 98.99%

So, the answer is that 98.99% of the beads on clearance are plastic.

Learn more about percentage of plastic beads

brainly.com/question/30169957

#SPJ11

Answer:

Not enough info

Step-by-step explanation:

Volume of cone formula is: V = 1/3 π r²h

You did not give the radius so it is not possible to find the solution

If radius is given, isolate h by dividing the V by 1/3 π r²

Then simplify the left side of the equation and that is what h is

The dealer should have sold the article for 103,500 naira to make a profit of 15%.

Let C be the cost price of the composition.  According to the problem, the dealer  vended the composition at a loss of 10, so he  entered 90 of the cost price.  thus, 90 of C is equal to 81,000 naira.

C =  81,000

C =  81,000/0.9

 C =  90,000  

So, the cost price of the composition is 90,000 naira.

  Now, let's find out the selling price  needed to make a profit of 15   Let S be the  needed selling price to make a profit of 15.  We know that profit chance is equal to( profit/ cost price) × 100.

Thus,(15/100) × 90,000 =

S- 90,000 , 500

=  S- 90,000  

S =  90,000 13,500

S =  103,500

Learn more about profit at

https://brainly.com/question/30949131

#SPJ4

The count of duration that is needed for Dr. Aghedo's money to be deposited is 22.3 years, under the condition that if interest is compounded continuously at a rate of 3. 1

The derived formula for doubling time with continuous compounding is applied to evaluate the length of time it takes to double the money in an account or investment that has continuous compounding. The formula is
Doubling time = ln 2 / r

Here,
r =annual interest rate as a decimal.

For the required case, the interest rate is 3.1% that can be written as  0.031 in the form of decimal. Then the doubling time will be
Doubling time = ln 2 / 0.031
≈ 22.3 years

Then, it should take approximately 22.3 years for Dr. Aghedo's money to double if interest is compounded continuously at a rate of 3.1%.
To learn more about annual interest
https://brainly.com/question/30500391
#SPJ4

Answer:

Step-by-step explanation:

I can provide you with general information about radical functions and their graphs, but I cannot design a bridge for you.

In order to design a bridge that will safely cross the ravine, you would need to take into account a wide range of factors, including the length and width of the ravine, the types of materials that can be used to construct the bridge, the weight and size of the vehicles that will be crossing the bridge, and the weather and environmental conditions in the area. This would likely require the expertise of a civil engineer or other trained professional.

Regarding radical functions, they are functions that involve a radical symbol (such as a square root) in their equation. The graph of a radical function is typically a curve that starts at the point (0,0) and moves upwards and to the right. The shape of the curve will depend on the specific radical function and the values of its parameters.

To solve a radical function, you would typically isolate the radical term on one side of the equation and then square both sides of the equation to eliminate the radical. However, it is important to be careful when squaring both sides, as this can introduce extraneous solutions that do not satisfy the original equation.

There are 5 combinations with one flavor, 10 combinations with two flavors, and 10 combinations with three flavors, resulting in 25 possible combinations in total.

a. Only one flavor is there.

b. Buko can be paired with 4 other flavors and Ube can be paired with 3 remaining flavors.

c. 10 combinations of three flavors.

a. There is only one flavor: Since the box contains only one flavor, there are 5 possible combinations (Buko, Ube, Pineapple, Yema, and Mango).

b. There are two flavors:
- Buko can be paired with 4 other flavors (Ube, Pineapple, Yema, Mango).
- Ube can be paired with 3 remaining flavors (Pineapple, Yema, Mango).
- Pineapple can be paired with 2 remaining flavors (Yema, Mango).
- Yema can be paired with 1 remaining flavor (Mango).
In total, there are 10 combinations of two flavors.

c. There are three flavors:
- There are 5 flavors in total, and we want to choose 3. We can use the formula for combinations: C(n, k) = n! / (k!(n-k)!), where n is the total number of flavors and k is the number of flavors to choose.
- C(5, 3) = 5! / (3!(5-3)!) = 10 combinations of three flavors.

So, there are 5 combinations with one flavor, 10 combinations with two flavors, and 10 combinations with three flavors, resulting in 25 possible combinations in total.

To know more about combinations, refer to the link below:

https://brainly.com/question/20211959#

#SPJ11

Answer:

C.

Step-by-step explanation:

3 = 1.5 * 2

9 = 1.5 * 6

15 = 1.5 * 10

33 = 1.5 * 22

The average number of books bought per year by customers in the survey is approximately 4.85 books.

To find the average number of books bought per year, we need to calculate the mean of the data set. We can do this by using the formula:

Average = (Sum of all data points) / (Number of data points)

However, we do not have the actual number of data points. Instead, we have percentages. Therefore, we need to convert the percentages into actual numbers.

Out of 100 customers surveyed:

30% bought 3 books, which is equal to 30/100 x 100 = 30 customers

25% bought 5 books, which is equal to 25/100 x 100 = 25 customers

45% bought 6 books, which is equal to 45/100 x 100 = 45 customers

Now, we can calculate the average number of books bought per year using the formula mentioned earlier:

Average = (30 x 3) + (25 x 5) + (45 x 6) / (30 + 25 + 45)

Simplifying the above equation, we get:

Average = (90 + 125 + 270) / 100

Therefore, the average number of books bought per year is:

Average = 485/100

Average = 4.85 books per year (rounded to two decimal places)

To know more about average here

https://brainly.com/question/16956746

#SPJ4

Answer:

there both symmetrical

Answer:

Congruent

Step-by-step explanation:

When visualizing how two angles are related, try squashing the two parallel lines into each other. When you do that with these angles, they go from appearing like =\= to appearing like -\-, with x and y being catty-corner from each other.

Because the parallel lines are straight, x and y are both half of a pair that adds up to 180. However, x and y aren't sharing a straight line, so they cannot add up to 180 with each other. That leaves only one possibility, that x and y have the same angle measure.

The given values for uo and u3 are uo = 1 and u3 = 21. We can use the recurrence relation Un+2 = 2 * Un+1+1* Un to find the remaining terms:

U1 = U3 - 2U2 - 1*U0
U1 = 21 - 2U2 - 1*1
U1 = 20 - 2U2

U2 = U1 - 2U0 + 1*U0
U2 = 20 - 2U0 + 1*1
U2 = 19 - 2U0

Therefore, the first four terms are: 1, 19, -17, -53

So, the answer is: 1, 19, -17, -53.

Learn more about recurrence relation: https://brainly.com/question/4082048

#SPJ11

To find the elasticity of demand for the function q = D(x) = 460 - x, we can use the formula:

Elasticity = (% change in quantity demanded) / (% change in price)

a) Since the demand function given does not include a price variable, we can assume that price is constant. Therefore, the elasticity of demand for this function is constant and equal to -1.

b) To find the elasticity at x = 103, we need to calculate the percentage change in quantity demanded when x increases from 103 to 104.

At x = 103, quantity demanded is q = D(103) = 460 - 103 = 357.

At x = 104, quantity demanded is q = D(104) = 460 - 104 = 356.

The percentage change in quantity demanded is:

(% change in quantity demanded) = [(new quantity - old quantity) / old quantity] x 100

= [(356 - 357) / 357] x 100 = -0.28%

Since the elasticity of demand is -1, we can say that demand is inelastic at x = 103.

c) To find the elasticity at x = 205, we need to calculate the percentage change in quantity demanded when x increases from 205 to 206.

At x = 205, quantity demanded is q = D(205) = 460 - 205 = 255.

At x = 206, quantity demanded is q = D(206) = 460 - 206 = 254.

The percentage change in quantity demanded is:

(% change in quantity demanded) = [(new quantity - old quantity) / old quantity] x 100

= [(254 - 255) / 255] x 100 = -0.39%

Since the elasticity of demand is -1, we can say that demand is inelastic at x = 205.
Hi! I'd be happy to help you with your question on elasticity of demand.

a) To find the elasticity, we first need the formula for price elasticity of demand (PED), which is:

PED = (% change in quantity demanded) / (% change in price)

Here, we have the demand function D(x) = 460 - x, where x is the price.

b) To find the elasticity at x = 103, we first need to calculate the quantity demanded, which is:

q = D(103) = 460 - 103 = 357

Now, we'll find the derivative of the demand function with respect to price:

dq/dx = -1

Next, we'll use the formula for PED:

PED = (dq/dx * x) / q = (-1 * 103) / 357 = -103/357 ≈ -0.289

Since the absolute value of PED is less than 1, demand is inelastic at x = 103.

c) To find the elasticity at x = 205, we'll follow the same steps:

q = D(205) = 460 - 205 = 255

PED = (dq/dx * x) / q = (-1 * 205) / 255 ≈ -0.804

Again, the absolute value of PED is less than 1, so demand is inelastic at x = 205.

Learn more about mathematics here: brainly.com/question/15209879

#SPJ11

The height of the building is approximately 102.3 feet, rounded to the nearest tenth.

Step 1: Draw a right triangle with Sheila's eye-height as the base, the building's height as the vertical side, and the distance between Sheila and the building as the horizontal side.

Step 2: We are given the angle of elevation (71 degrees) and the horizontal distance (33 feet). To find the vertical distance, we can use the tangent function in trigonometry. The formula is:
tan(angle) = (opposite side) / (adjacent side)

Step 3: Plug in the given values into the formula:
tan(71) = (vertical distance) / 33

Step 4: Solve for the vertical distance:
vertical distance = 33 * tan(71) ≈ 96.9 feet

Step 5: Add Sheila's eye-height to the vertical distance to find the total height of the building:
total height = eye-height + vertical distance
total height = 5.4 + 96.9 ≈ 102.3 feet

The height of the building is approximately 102.3 feet, rounded to the nearest tenth.

learn more about "Height":- https://brainly.com/question/12446886

#SPJ11

The fraction value of 0.64 is 16/25 using the greatest common factor method to represent. There are no repeating digits in value.

The given decimal value = 0.64

There are no repeating numbers in the given decimal number 0.64.

To convert the given number into a fraction, we need to multiply the value with 10 on both sides to move the decimal point two places to the right.

0.64 × 100/100 = 64/100

Now simply this value by dividing both the numerator and denominator with the greatest common factor of both values. The greatest common factor is 4.

64/100 = 16/25

Therefore, we can represent the fraction value of 0.64 as 16/25.

To learn more about Fraction

https://brainly.com/question/29766013

#SPJ4

Answer:

The system of equations to describe the situation is:

* $10x + 54 = 11y$

* $y = 11x$

To solve using substitution, we can substitute the second equation into the first equation. This gives us:

* $10x + 54 = 11(11x)$

* $10x + 54 = 121x$

* $-11x = -54$

* $x = 5$

We can then substitute this value of $x$ into the second equation to solve for $y$. This gives us:

* $y = 11(5)$

* $y = 55$

Therefore, the student council will need to sell 55 T-shirts to cover their costs. The costs will be $54 + $10(55) = $604.

Here is the solution in a table format:

| Variable | Value |

|---|---|

| $x$ | 5 |

| $y$ | 55 |

| Cost | $604 |

I hope this helps!

Step-by-step explanation:

The value of x in the similar figures is 2.33

When two figures have the same shape but their sizes are different, then such figures are called similar figures

The two polygons are similar

We have to find the value of x

Let us form a proportional equation

4590/21=510/x

4590x=21×510

4590x=10710

Divide both sides by 4540

x=10710/4590

x=2.33

Hence, the value of x in the similar figures is 2.33

To learn more on Polygon click:

https://brainly.com/question/24464711

#SPJ1

The two true statements are:

A "When the time starts, there are 13.5 gallons of water in the pool."

C "The water is draining at a rate of 1.25 gallons per minute."

Here we have the linaer equation y = –1.25x + 13.5 that represents the gallons of water y left in an inflatable pool after x minutes.

And we want to see which of the given statements are true.

We can see that the slope is -1.25, this means that the volume of water is reducing (due to the negative sign) then the statement C is true.

We also can see that the y-intercept is 13.5, that would be the initial volume of water in the pool, then the statement A "When the time starts, there are 13.5 gallons of water in the pool." is also true.

Learn more about linear equations at.

https://brainly.com/question/1884491

#SPJ1

The total number of possible lock combination using the 40 possible numbers for making lock of 3 numbers is equal to 64,000.

Possible number used for lock combination are 40.

Range is 0 - 39.

Total number chosen for lock combination is equal to 3.

Since there are 40 possible numbers to choose from for each of the three positions on the combination lock.

The total number of possible combinations is equal to ,

40 x 40 x 40

= 40^3

= 64,000

Therefore, there are 64,000 possible lock combinations when choosing 3 numbers out of 40 possible numbers, assuming repeated numbers are allowed.

learn more about combination here

brainly.com/question/9304221

#SPJ4

Answer:

rita and john are susseful the job

js school

We can expect  4 giant swallowtails to visit Ellie's garden.

In total, there were 96 butterfly visits (32 monarchs + 56 gulf fritillaries + 8 giant swallowtails).

Now, we can calculate the probability of a giant swallowtail visit:
Probability

= (number of giant swallowtails) / (total butterfly visits)

= 8/96

= 1/12

Given that 48 butterflies visit her garden, we can expect the number of giant swallowtails to be:
Expected giant swallowtails

= (total butterflies) × (probability of giant swallowtails)

= 48 × (1/12)

= 4

So, we can expect approximately 4 giant swallowtails to visit Ellie's garden out of the 48 butterflies.

To learn about probability: https://brainly.com/question/13604758

#SPJ11

It would cost $735 to buy a cover for the pool at $0.30 per square foot

From the complete question (see attachment), we have the following parameters that can be used in our computation:

Unit rate = $0.30 per square foot

Dimensions = 10 inches by 20 inches

Scale = 2 inches : 7 feet

Using the above as a guide, we have the following:

Total cost = Unit rate * Area of pool

Where

Area of the pool = 10 inches * 20 inches

Using the scale, we have

Area of the pool = (10 * 7/2)* (20 * 7/2) square feet

Area of the pool = 2450 square feet

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

Total cost = $0.30 per square feet * 2450 square feet

This gives

Total cost = $735

Hence, it would cost $735 to buy a cover for the pool

Read more about unit rates at

https://brainly.com/question/4895463

#SPJ1

Complete question

The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below (see attachment)

How much would it cost to buy a cover for the pool that cost $0.30 per square foot

The measure of the angle WXY is 152 degrees

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

Using the above as a guide, we have the following:

m∠MYW = 104 - 90

m∠MYW = 14

The inscribed angle opposite to the same arc is half of the external angle

So, we have

mw = 2 * m∠MYW

mw = 2 * 14

mw = 28 degrees

Also, we have

my = 180 degrees

So, we have

Angle WXY = 180 - 28

Evaluate the difference

Angle WXY = 152

Hence, the measure of the angle is 152 degrees

Read more about angles at

https://brainly.com/question/98924

#SPJ1

(a) Linus's score for Test 1 is 80. (b) The percentage increase in his test score from Test 2 to Test 3 is 4.3%.

(a) Let's denote Linus's score in Test 1 as "x." Since he received 12 more marks in Test 2, his score for Test 2 is "x + 12." The 15% improvement means that (x + 12) is 115% of x:

x + 12 = 1.15x

Now, we can solve for x:

12 = 0.15x

x = 12 / 0.15

x = 80

So, Linus's score in Test 1 was 80.

(b) Linus made a 4-mark improvement in Test 3, so his score was (x + 12) + 4, which is (80 + 12) + 4 = 96. To find the percentage increase from Test 2 to Test 3, we can use the formula:

Percentage increase = ((New score - Old score) / Old score) * 100

Percentage increase = ((96 - 92) / 92) * 100

Percentage increase = (4 / 92) * 100

Percentage increase ≈ 4.35

The percentage increase in his test score from Test 2 to Test 3 is approximately 4.3% (correct to 1 decimal place).

Learn more about Percentage:

https://brainly.com/question/24877689

#SPJ11

A. 52 = 8n + 4, B. 4(2n + 1) = 52 and C. 4 = 52 – 8n are the equivalent equations.

Simplifying the equations, we have

A. 52 = 8n + 4

8n = 48

n = 6

To see this, first simplify equation B:

4(2n + 1) = 52

8n + 4 = 52

8n = 48

n = 6

C. 4 = 52 – 8n

8n = 48

n = 6

Then simplify equation D:

4n = 48

n = 12

As you can see, equations A, B and C are equivalent and both simplify to n = 6.

Therefore, the correct answers are A, B and C.

Read more about equivalent expressions at

https://brainly.com/question/15775046

#SPJ1

She is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.

You asked if Christy is correct when she said that her rate increased each hour, from 8 to 12 to 16 miles per hour. Let's analyze the data given in the table and see if she's right.

The table shows the distance Christy jogged and the corresponding time:
- 10 miles in 2 hours
- 15 miles in 3 hours
- 20 miles in 4 hours

To find her jogging rate for each time period, we need to divide the distance by the time.

1. For the first 2 hours:
Jogging rate = distance / time = 10 miles / 2 hours = 5 miles per hour

2. For the first 3 hours:
Jogging rate = distance / time = 15 miles / 3 hours = 5 miles per hour

3. For the first 4 hours:
Jogging rate = distance / time = 20 miles / 4 hours = 5 miles per hour

Christy's jogging rate remained constant at 5 miles per hour throughout her run. Therefore, she is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.

To know more about rate, visit:

https://brainly.com/question/23634231#

#SPJ11