In gym class, the students are going to design and build obstacles for an upcoming field day. Before they can start building, each student has to submit a two-dimensional scale drawing of the obstacle they want to build. Barbara's drawing of her obstacle is shown below.




Note: Figure not drawn to scale.


In Barbara's drawing, the obstacle has a total area of______ square feet.

This obstacle will have a width of 4 feet. The volume of the obstacle is____cubic feet.

The graph of the circle equation is graph (d)

The equation is given as:

x^2 + y^2 - 4x + 9y -7 = 0

Rewrite as:

x^2 - 4x + y^2 + 9y = 7

Express (x^2 - 4x) and (y^2 + 9y) as perfect squares.

So, we have:

(x - 2)^2 + (y + 3)^2 = 7 + 4 +  20.25

Evaluate the sum

(x - 2)^2 + (y + 3)^2 = 31.25

A circle equation is represented as:

(x - h)^2 + (y - k)^2 = r^2

Where

Center = (h, k)

Radius = r

So, we have:

(h, k) = (2, -3)

r^2 = 31.25

r = 5.5

The circle that has a center of (2, -3) and a radius of 5.5 is graph d

Hence, the graph of the circle equation is graph (d)

Read more about circle equation at:

https://brainly.com/question/1559324

#SPJ1

Answer:

I think glide reflection

Step-by-step explanation:

a certain video on yt had explained the examples of similar look alike this picture

Answer:

0.1363636... = 3/22

Step-by-step explanation:

Let x = 0.1363636...

           100x = 13.6363636...

  (-)            x =   0.1363636...

------------------------------------------

              99x = 13.5

x = 13.5/99

x = 135/990

x = 27/198

x = 9/66

x = 3/22

0.1363636... = 3/22

0.1363636... is not equal to 1/33.

1/33 = 0.030303...

The approximate length of side AB is 14.0. The correct option is B. 14.0 units

From the question, we are to determine the measure of side AB

First, we will determine the measure of angle A

A + B + C = 180° (Sum of angles in a triangle)

A + 65° + 35° = 180°

A = 180° - 65° - 35°

A = 80°

Now, using the law of sines

c/sinC = a/sinA

c = AB

a = BC =  24

Thus,

c/sin35° = 24/sin80°

c = (24×sin35°)/sin80°

c = 13.978

c ≈ 14.0

∴ AB = 14.0

Hence, the approximate length of side AB is 14.0. The correct option is B. 14.0 units

Learn more on Law of sines here: https://brainly.com/question/24138896

#SPJ1

The angle m∠MLP in the rhombus is 56 degrees.

A rhombus has all its sides equal to each other.  The diagonals of a rhombus are angle bisectors.

Therefore,

m∠MLP = m∠MLO / 2

m∠MLO = 112°

m∠MLP = 112 / 2

Therefore,

m∠MLP = 56 degrees.

learn more on rhombus here: https://brainly.com/question/18651035

#SPJ1

Answer:

B. 56

Step-by-step explanation:

trust

Answer:

16 gallons of gas

Step-by-step explanation:

Two ways to answer this

1:

Find how many miles per gallon the car can go. Then, divide the amount the car needs to go with the miles per gallon. This gets you the gallons of gas needed to go the amount. In this case, 161 ÷ 7 = 23. 368 ÷ 23 = 16.

2:

Make a proportion. [tex]\frac{161}{7} = \frac{368}{x}[/tex]. Solve for x. 161 and 7 cancel out to get 23. [tex]\frac{23}{1} = \frac{368}{x}[/tex]. Now you can either divide 368 and 23 and multiply the quotient by 1 to get x, or you can cross multiply to get an equation you can solve. In the first case, 368 ÷ 23=16. 1*16=16. x=16. In the second case, 23x=368. Divide both sides by 23 and you get x = 16.

The formula for the velocity, v is √2E/m

Kinetic energy is half the mass multiplied by the square of the speed of the object

It is written thus;

Kinetic energy = 1/ 2 × m × v²

To solve for 'v' mean that we should make 'v' the subject of formula

E = 1/ 2 mv²

E = [tex]\frac{mv^2}{2}[/tex]

cross multiply

[tex]2E = mv^2[/tex]

To make 'v' the subject, we have

[tex]v = \sqrt{\frac{2E}{m} }[/tex]

Thus, the formula for the velocity, v is √2E/m

Learn more about Kinetic energy here:

https://brainly.com/question/25959744

#SPJ1

Since the standard deviation for the population is known, the z-distribution is used as the sampling distribution basis for this hypothesis test.

In this problem, the standard deviation for the population is known, hence the z-distribution is used.

More can be learned about which distribution to use, the t-distribution or the z-distribution, at https://brainly.com/question/15869521

#SPJ1

Probability is 17.5% that 3 of them entered a profession closely related to their college

According to the statement

we have given that survey of 300 college graduates, 46% reported that they entered a profession closely and

We know that  For each college graduate, there are only two possible outcomes. Either they have entered a profession closely related to their college major, or they have not. The probability of a college graduate having entered a profession closely related to their college major is independent of other college graduates, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

This is P(X = 3) when n = 8. and the value of p is 0.46 put the value in the binomial formula then the outcome of answer will 17.5%

So, Probability is 17.5% that 3 of them entered a profession closely related to their college

Learn more about Binomial here https://brainly.com/question/13602562

#SPJ4

The value is 52. 674

We have;

4(3) / 4(8) +.9(7.8 x 7.45)

From BODMAS, we have that we must must open up the bracket

= [tex]\frac{12}{32} + 0. 9 (58. 11)[/tex]

Divide the fraction to get decimals

= [tex]0. 375 + 52. 299[/tex]

Add the decimals

= [tex]52. 674[/tex]

Thus, the value is 52. 674

Learn more about BODMAS here:

https://brainly.in/question/48777244

#SPJ1

New mean is 2.53% larger than the original mean.

What is mean?

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

We can find the percentage larger is the mean of the new list in comparison with the original as shown below:

Given, set of number 55, 70, 81, 83, 88, 91

Median= (81+83)/2

= 164/2

= 82

Mean = (55+70+81+83+88+91)/6

= 468/6

= 78

New value which is added = 82*1.12

= 91.84

New Mean = (55+70+81+83+88+91+91.84)/7

= 559.84/7

= 79.97

Increase in mean = 79.97-78

=1.97

increase percentage (1.97/78) *100

= 2.53%

Hence, new mean is 2.53% larger than the original mean.

Learn more about Mean here:

https://brainly.com/question/17060018

#SPJ4

Answer:

[tex]2 \tan (6x)+2 \sec (6x)+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

[tex]\displaystyle \int \dfrac{12}{1-\sin (6x)}\:\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int a\:\text{f}(x)\:\text{d}x=a \int \text{f}(x) \:\text{d}x$\end{minipage}}[/tex]

If the terms are multiplied by constants, take them outside the integral:

[tex]\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)}\:\:\text{d}x[/tex]

Multiply by the conjugate of 1 - sin(6x) :

[tex]\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)} \cdot \dfrac{1+\sin(6x)}{1+\sin(6x)}\:\:\text{d}x[/tex]

[tex]\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{1-\sin^2(6x)} \:\:\text{d}x[/tex]

[tex]\textsf{Use the identity} \quad \sin^2 x+ \cos^2 x=1:[/tex]

[tex]\implies \sin^2 (6x) + \cos^2 (6x)=1[/tex]

[tex]\implies \cos^2 (6x)=1- \sin^2 (6x)[/tex]

[tex]\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{\cos^2(6x)} \:\:\text{d}x[/tex]

Expand:

[tex]\implies 12\displaystyle \int \dfrac{1}{\cos^2(6x)}+\dfrac{\sin(6x)}{\cos^2(6x)} \:\:\text{d}x[/tex]

[tex]\textsf{Use the identities }\:\: \sec \theta=\dfrac{1}{\cos \theta} \textsf{ and } \tan\theta=\dfrac{\sin \theta}{\cos \theta}:[/tex]

[tex]\implies 12\displaystyle \int \sec^2(6x)+\dfrac{\tan(6x)}{\cos(6x)} \:\:\text{d}x[/tex]

[tex]\implies 12\displaystyle \int \sec^2(6x)+\tan(6x)\sec(6x) \:\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Integrating $ \sec kx \tan kx$}\\\\$\displaystyle \int \sec kx \tan kx\:\text{d}x= \dfrac{1}{k}\sec kx\:\:(+\text{C})$\end{minipage}}[/tex]

[tex]\implies 12 \left[\dfrac{1}{6} \tan (6x)+\dfrac{1}{6} \sec (6x) \right]+\text{C}[/tex]

Simplify:

[tex]\implies \dfrac{12}{6} \tan (6x)+\dfrac{12}{6} \sec (6x)+\text{C}[/tex]

[tex]\implies 2 \tan (6x)+2 \sec (6x)+\text{C}[/tex]

Learn more about indefinite integration here:

https://brainly.com/question/27805589

https://brainly.com/question/28155016

Substitute [tex]y=6x[/tex] and [tex]dy=6\,dx[/tex] to transform the integral to

[tex]\displaystyle \int \frac{12}{1-\sin(6x)} \, dx = 2 \int \frac{dy}{1 - \sin(y)}[/tex]

Now substitute [tex]t=\tan\left(\frac y2\right)[/tex] and [tex]dt=\frac12 \sec^2\left(\frac y2\right) \, dy[/tex] to transform this to

[tex]\displaystyle 2 \int \frac{dy}{1 - \sin(y)} = 2 \int \frac1{1-\frac{2t}{1+t^2}}\cdot\frac{2\,dt}{1+t^2} = 4 \int \frac{dt}{(t-1)^2}[/tex]

Finally, substitute [tex]s = t-1[/tex] and [tex]ds=dt[/tex] to get

[tex]\displaystyle 4 \int \frac{dt}{(t-1)^2} = 4 \int \frac{ds}{s^2} = -\dfrac4s + C[/tex]

Now recover the antiderivative in terms of [tex]x[/tex].

[tex]\displaystyle \int \frac{12}{1-\sin(6x)} \, dx = -\frac4s + C \\\\ ~~~~~~~~ = -\frac4{t-1} + C \\\\ ~~~~~~~~ = -\frac4{\tan\left(\frac y2\right) - 1} + C \\\\ ~~~~~~~~ = \boxed{-\frac4{\tan(3x) - 1} + C}[/tex]

Answer: 1

Step-by-step explanation: Any number raised to zero is always 1.

The best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):

A class can be defined as a user-defined blueprint (prototype) or template that is typically used by software programmers to create objects and define the data types, categories, and methods that should be associated with these objects.

In object-oriented programming (OOP) language, a class that is written or created to implement an interface in a software would most likely implement all of that interface's method declarations without any coding error.

In this scenario, the best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):

Read more on class here: brainly.com/question/20264183

#SPJ1

Complete Question:

A car dealership needs a program to store information about the cars for sale. For each car, they want to keep track of the following information: number of doors (2 or 4), whether the car has air conditioning, and its average number of miles per gallon. Which of the following is the best design?

(A) Use four unrelated classes: Car, Doors, AirConditioning, and MilesPerGallon.

(B) Use a class Car with three subclasses: Doors, AirConditioning, and MilesPerGallon.

(C) Use a class Car, with fields: numDoors, hasAir, and milesPerGallon.

(D) Use a class Car, with subclasses of Doors, AirConditioning, and MilesPerGallon.

(E) Use classes: Doors, AirConditioning, and MilesPerGallon, each with a subclass Car.

Answer:

15

Step-by-step explanation:

First side is 20

Second side is 20 * (3/2), as it is 1 and 1 half times longer than the first

Second side is 30(as calculated above)

65-20-30 = 15

The height of the rectangular cereal box is 40 cm.

Volume of a rectangular prism = lwh

where

Therefore,

10000 = 25 × 10 × h

10000 = 250h

h = 10000 / 250

h = 40 cm

learn more on rectangular prism here: https://brainly.com/question/16600853

#SPJ1

Answer:

the answer might be 13.5

Using the mean concept, the average collection for a student in this school was of $16.13.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

The number of students is given as follows:

82 + 74 + 96 + 99 = 351.

The sum is:

82 x 26.75 + 74 x 12.25 + 96 x 15.50 + 99 x 10.85 = $5662.15

Hence the mean is:

M = $5662.15/351 = $16.13.

More can be learned about the mean of a data-set at https://brainly.com/question/24628525

#SPJ1

Answer:

1

Step-by-step explanation:

When dividing fractions i use the method KFC(keep flip change) :

Keep the first fraction :

[tex]\frac{14a^{2} }{10b^{2} }[/tex]

Flip the second fraction :

[tex]\frac{15b^{2} }{21a^{2} }[/tex]

Change the function :

÷ → ×

Now write your new equation :

[tex]\frac{14a^{2} }{10b^{2} }[/tex] ×  [tex]\frac{15b^{2} }{21a^{2} }[/tex]

Now multiply the numerators together and the denominators together :

14a² × 15b²  = 210a²b²

10b² × 21a² = 210a²b²

Now make this into a fraction again :

210a²b² / 210a²b²

Anything divided by itself is always 1 so :

210a²b² / 210a²b² = 1

Hope this helped and have a good day

The explanation regarding the vector is illustrated below.

It should be noted that vector A with components a, b, c, can be written as (a, b, c) or in terms of unit vectors as ai + bj + ck.

In this case, the letters I, j, and k are the standard symbols for the unit vectors in the x, y, and z directions.

Therefore, if A = (3,4,5( you can write A = 3i + 4j + 5k.

If B = (1, 1, 1), you can write B = I + j + k.

Then A - B is the vector whose component are the difference in each components.

Learn more about vector on:

brainly.com/question/25705666

#SPJ1

Answer:

The answer would be 36cm².

Step-by-step explanation:

⇒ Two prisms are similar.

⇒ Scale factor = 3:8

⇒ The ratio of the surface area is 9:64.

⇒ So S₁ : S₂ = 9:64

⇒ S₁ : 256 = 9:64

⇒ S₁ = 36cm²

This would mean that the answer is 36 centimeters ² (squared).

If the function is

[tex]y = 4 e^x \cos(3x)[/tex]

then we have derivatives

[tex]Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)[/tex]

[tex]D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)[/tex]

Now consider the linear ODE

[tex]aD^2y + bDy + cy = 0[/tex]

Substituting [tex]y[/tex] and its derivatives reduces the equation to

[tex](-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0[/tex]

Now,

[tex]-24a - 12b = 0 \implies b = -2a[/tex]

[tex]-32a + 4b + 4c = 0 \implies c = 10a[/tex]

Then the minimal ODE with the given solution is

[tex]aD^2y -2a Dy + 10ay = 0[/tex]

or

[tex]\boxed{D^2y  -2 Dy + 10y = 0}[/tex]

Answer: [tex]y+5=-2(x+4)[/tex]

Step-by-step explanation:

See attached image.

Answer:

482.84u², 42.5cm², 51.5ft²

Step-by-step explanation:

1) A = 2(1 + √2)a²

A = 2(1 + √2)(80 / 8)²

A = 482.84units²

2) Square = 5²

Square = 25

T1 = 3 x 5 / 2

T1 = 7.5

T2 = 4 x 5 / 2

T2 = 10

Total = 10 + 7.5 + 25

Total = 42.5cm²

3) Rect = 4(8 + 3)

Rect = 44

T1 = 2 x 3 / 2

T1 = 3

T2 = 3 x 3 / 2

T2 = 4.5

Total = 3 + 4.5 + 44

Total = 51.5ft²

Answer:

(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units

Answer: 24

Step-by-step explanation:

1. Number Them

Elf and Dwarf = 1

Hobbit = 2

Wizard = 3

Man = 4

* Elf and Dwarf are put together so that they are always sitting together

2. Multiply

1 x 2 x 3 x 4 = 24

Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

Answer:

3x+2=2190

3x=2190-2

3x=2188

x=2188÷3

x=729