Many of the amenities at a local ski hill are operated using gas generators. To transport gasoline to the top of the mountain, a special trailer has been designed. The trailer bed is in the shape of a square with a side length of 1.5 m. They wish to attach a cylindrical shaped gas tank to the trailer which is as large as possible, but cannot be taller than the trailer bed is. Determine the dimensions, volume and surface area of the gas tank.

Using it's formula, considering a loan of $10,000, the regular monthly payments required to pay off the loan will be of $221.3.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

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

P = 10,000, r = 0.0299, n = 4 x 12 = 48.

Then:

r/12 = 0.0299/12 = 0.00249167.

Hence, the monthly payment will be given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 10000\frac{0.00249167(1+0.00249167)^{48}}{(1+0.00249167)^{48} - 1}[/tex]

A = 221.3.

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Based on the graph that Aaron made, we can infer that the inequality he solved is | x + 2 | < 3.

The value of x in the graphed inequality is:

-5 < x < 1

If 2 was added to both sides, the least value would be - 3 and the highest value would be 3.

The inequality then becomes:

-3 < x < 3

This in line with the first option which is that when 2 is added to any value of x, it will be less than 3.

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The equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

The equation of the new line will be:-

y - y₁ = m ( x - x₁ )

Since the line is parallel to the line y = -2x - 5 so slope will be same m = -2 now the coordinates are ( -1, 3).

y - ( 3) = -2 [( x - (-1) ]

y - 3 = -2x - 2

y = -2x + 3 -2

Y = -2x + 1

Therefore the equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.

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Answer: 7

Step-by-step explanation:

By the angle bisector theorem,

[tex]\frac{21}{14}=\frac{3x-12}{6}\\21(6)=14(3x-12)\\126=14(3x-12)\\9=3x-12\\21=3x\\x=\boxed{7}[/tex]

Answer:

A. [tex]y\leq \frac{1}{2}x+2[/tex]

Step-by-step explanation:

First, let's find the slope of the line, so we can eliminate some answers.

From point (0,2) we can go up 1 and over to the right 2 to the point of (2,3). Slope is rise over run so 1 over 2.

This eliminates C and D.

The last part is to recognize that y being less than the equation will result in the shaded region being below the line. If y was greater than the equation then the shaded region would be above the line.

Therefore, the correct answer would be A. [tex]y\leq \frac{1}{2}x+2[/tex].

Hope this helps! If you have questions about my work please let me know down in the comments!

Answer:

[tex]y\leq \frac{1}{2}x+2[/tex]

Step-by-step explanation:

The first part of finding our answer is finding the slope of the line. The image attached shows this.

[tex]\frac{rise}{run} = \boxed{\frac{1}{2}}[/tex]

This means the slope is [tex]\frac{1}{2}[/tex], removing the bottom 2 answer choices.

Now we have to choose between the [tex]\leq[/tex] and [tex]\geq[/tex] sign. Since the shaded area is below the line, it will be the [tex]\leq[/tex]. (If it was the [tex]\geq[/tex] sign, the shaded area would be above the line.) This marks the first answer as the correct answer.

Answer:

6 + 7/10x + 2/y

Step-by-step explanation:

Hope this helps :)

Answer: aₙ = -11 + 7(n - 1)

Step-by-step explanation: The equation of an arithmetic sequence is

aₙ = a₁ + d(n - 1).

a₁ is the first term.

d is the common difference.

The point R is the point which is not coplanar with points C, D and E.

We need to find the point which is not coplanar with points C, D and E.

The points that lie on the same plane are called coplanar points.

In the given figure there are five planes which are as follows:

BCUD, BRAE, BRAC, BTDE, ACUDE

Now, points C,D and E lie in plane ACUDE.

In the plane ACUDE points A, C, U, D, E and S lies.

From the options point, R is not lining in the same plane as C, D and E lies.

Therefore, the point R is the point which is not coplanar with points C, D and E.

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Answer:

B

Step-by-step explanation:

look at the graph. y is negative from x>2, so interval is 2<x<infinity.

in other case y=0 for x=2, y<0 for infinity<x<2

Answer:

The intervel that describes where the graph is negative is C :)

I hope this helps you!

Step-by-step explanation:

Answer:

The formation of the equation is odd, but I assume it's supposed to be:
4k - 10k = -8k

-6k = -8k
-6k + 8k = -8k + 8k
2k = 0
[tex]\frac{2k}{2}[/tex] = [tex]\frac{0}{2}[/tex]
k = 0

Answer:

Answer = 25 miles

Step-by-step explanation:

We can make an equation based off of this information in the form of 4.25x+4=110.25. When we solve for x we find that it equals 25.

Hope that helps! :)

Answer:

C. interquartile range

Step-by-step explanation:

using this to show im right

"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."

Hope This Helped

Answer:

Step-by-step explanation:

Formula:

Lateral surface area = perimeter of the base × height

………………………………………………………………

perimeter of the base = 2×(1.5+3) = 9

height = 4.

then

Lateral surface area = 9 × 4 = 36

Area of two bigger rectangles

Area of two smaller rectangles

LSA

#1

Volume

#2

Radius=10/2=5cm

Volume

#3

Volume

#4

#5

radius=8/2=4

Volume

Answer:

1)  314 cm³

2)  523.33 cm³

3)  87.92 in³

4)  11 cm

5)  502.4 cm³

Step-by-step explanation:

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]

[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]

Given:

[tex]\implies 81=a^2[/tex]

[tex]\implies a=\sqrt{81}[/tex]

[tex]\implies a=9\: \sf cm[/tex]

Substitute the given values into the formula and solve for h:

[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]

The correct option that defines repeating decimals correctly is Option B;

a decimal that has a recurring sequence of numbers that follow a pattern.

A repeating decimal is also called a recurring decimal and it is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.

From the above definition, it means that the correct option that defines repeating decimals correctly is Option B.

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Answer:

your answer will be 85 1/3ins

Step-by-step explanation:

16x 5 1/3 = 85.3333333333

then I took the 85 and the 1/3

and just put em together

Answer:

280°

Step-by-step explanation:

using the relationship

π radians = 180° , then substituting gives

[tex]\frac{14\pi }{9}[/tex] = [tex]\frac{14(180)}{9}[/tex] = 14 × 20 = 280°

Answer:

a) 8

Step-by-step explanation:

The prime factors for 24 are 2, 2, 2, 3 -> The greatest is 3

The prime factors for 35 are 5, 7 -> The smallest is 5

So the sum is 3+5=8

Answer: some perfect cubes are

8 (2^3)

27 (3^3)

64 (4^3)

there are many perfect cubes

maybe there is more to this question?

Step-by-step explanation:

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500e^{0.07\cdot 6}\implies A=1500e^{0.42}\implies A\approx 2282.94[/tex]

Answer:

By proportional method

[tex] \frac{4}{6} = \frac{5}{x} [/tex]

4x= 30

x= 7.5

Answer:

12.6

Step-by-step explanation:

4.2×3=12.6

I hope this answer can help you

Answer:

1.4 kg

Step-by-step explanation:

Given :

⇒ Watermelon (Peter) = 3 × Papaya (Paul)

⇒ Watermelon (Peter) = 4.2 kg

=============================================================

Solving :

⇒ 4.2 = 3 × Papaya (Paul)

⇒ Papaya (Paul) = 1.4 kg

Therefore the mass of the papaya is 1.4 kg.

Answer:

76.5in²

Step-by-step explanation:

First we will find the area of the square. This is done by multiplying the side length (9in) by itself.

[tex]9 * 9 = \boxed{81}[/tex]

The area of the square is 81in².

Next we will find the area of the triangular hole. We can use the formula [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle (3) and h is the height of the triangle (3).

[tex]\frac{1}{2}bh\\\frac{1}{2}(3)(3)\\\frac{9}{2}\\\boxed{4.5}[/tex]

The area of the triangle is 4.5in².

Now we can find the area of the figure by subtracting the area of the square and the area of the triangular hole.

[tex]81 - 4.5 = \boxed{76.5}[/tex]

The area of the figure is 76.5in².

That is the answer

- Kan Academy Advance

To factorize something:

 ⇒ need to simplify the equation to its most basic form

Let's solve:

  [tex]2x^2+6x=2(x^2+3x)=2x(x+3)[/tex]

Thus the factorized form is ⇒ [tex]2x(x+3)[/tex]

Answer: 2x(x+3)

Hope that helps!

Answer:

Solution:

→ 2x(x + 3)

Step-by-step explanation:

Method:

→ Common factor

→ Rewrite in factored form

Answer:

we need a pic of the graph to be able. to work this out.

THANK YOU

Answer:

It's 5.

Step-by-step explanation:

8-3= 5

The volume of the given cone.

[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]

[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]

Let's solve!

Substitute the values according to the formula.

[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]

[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]

Therefore, the volume of the given cone is 75.36 cubic yards.