An open cylindrical tank is 150 feet in diameter and 180 feet high. The lateral surface area of the tank (no top and no bottom) is to be painted with paint that covers 225 square feet per gallon. When filled each cubic foot of the tank holds approximately 7.5 gallons of gasoline valued at $2.75 per gallon.
a) Find the number of gallons of paint required for a single coat of paint.
b) Find the total value of the gasoline in the filled tank.

The width of the rectangular prism shaped toolbox is 10 inches.

A prism is a three-dimensional geometric shape that has two parallel and congruent bases that are connected by a set of parallelograms or rectangles. A prism is named according to the shape of its base, such as triangular prism, rectangular prism, or hexagonal prism.

A prism is characterized by its length, width, and height, and it has a volume equal to the product of its base area and its height. The lateral faces of a prism are parallelograms or rectangles, and the edges of a prism where the lateral faces meet the bases are perpendicular to the bases.

Now,

To find the width of the toolbox, we can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

We are given that the volume of the toolbox is 4,500 cubic inches, the length is 30 inches, and the height is 15 inches.

Then

4,500 = 30 x width x 15

Simplifying the right side, we get:

4,500 = 450 * width

Dividing both sides by 450, we get:

width = 10 inches

Therefore, the width of the toolbox is 10 inches.

To know more about prism visit the link

https://brainly.com/question/29722724

#SPJ1

Using the equation of circle and the equation of the tangent, the coordinates of point A are (-5,-1), the coordinates of point X are (-3,-7).

Find the equation of the circle.

The center of the circle is at (-1,-3). The radius of the circle is unknown. The equation of the circle is:

\((x+1)^2+(y+3)^2=r^2\)

The slope of AB can be calculated as;

The equation of line AB is y = x + 4. The slope of line AB is 1.

The equation of line XY, which is parallel to line AB.

The slope of line XY is also 1, since they are parallel. The equation of line XY is:

\(y=x+c\)

Plug in the point (-1,-3) to solve for the y-intercept of line XY.

\(-3=-1+c\\c=-4\)

The equation of line XY is y=x-4.

The coordinates of point A are the point of intersection of line AB and line XY.

To find the coordinates of point A, we need to solve the system of equations:

\(y=x+4\\y=x-4\)

The solution to this equation is x = 0. We can plug this value into either equation to solve for y. This gives us y=-4. Therefore, the coordinates of point A are (0,-4).

The coordinates of point X are the point of intersection of line XY and the circle.

To find the coordinates of point X, we need to solve the system of equations:

\(y=x-4\\(x+1)^2+(y+3)^2=r^2\)

We can solve this system of equations by substituting the equation y=x-4 into the equation

\((x+1)^2+(x-4+3)^2=r^2\)

Expanding the terms in the equation gives us:

\(x^2+2x+1+(x^2-x+9)=r^2\)

Combining like terms gives us:

\(2x^2+x+10=r^2\)

We are given that the center of the circle is at (-1,-3). Therefore, the radius of the circle is the distance between the point (-1,-3) and the point (0,-4). This distance is 1. Therefore, the equation of the circle is:

\((x+1)^2+(y+3)^2=1\)

We can substitute this equation into the equation 2x² + x +10= r² to solve for r. This gives us:

\(2x^2+x+10=1\)

Combining like terms gives us:

\(2x^2+x-9=0\)

Factoring the equation gives us:

\((x-1)(2x+9)=0\)

The solutions to this equation are x = 1 and x = -9/2. We can discard the solution x = -9/2, since it is outside the range of the real numbers. Therefore, the radius of the circle is 1.

The coordinates of point A are (-5,-1).

The coordinates of point X are (-3,-7).

Learn more on equation of circle here;

https://brainly.com/question/24810873

#SPJ1

Answer:

Where is the paper?

Step-by-step explanation:

Answer:

Step-by-step explanation:

T+4 = -7

T = -7 -4

T = -11

Step-by-step explanation:

please mark me as brainlest

Answer:

70%

Step-by-step explanation:

30/100 as a decimal is 0.3

To get to a percent, you have to move the decimal two spaces to the right. (Even if there is nothing after the number, add a zero)

move it two spaces = 30.

Put a percent behind it = 30%

Also, CENT means 100. Basically percent means per 100, so it's 30 out of 100 which is 30%

--SO 100% - 30% = 70% so 70% of the stickers werent used.

-Sienna Sushi <3

Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

learn more about period of oscillation from

https://brainly.com/question/22499336

#SPJ1

Answer:

y = -4, x = 9

Step-by-step explanation:

If a line is horizontally passing through a point, then the equation of that line must be the y-value of that coordinate point. Likewise, if a line is passing vertically through a point, then the equation of that line must be the x-value of that coordinate point.

Apply the theory to this problem.

The equation for the horizontal line is y = -4

The equation for the vertical line is x = 9

the car is approximately 22.4 meters away from the tower.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

we can write:

tan(55 degrees) = 32 / d

To solve for "d", we can rearrange the equation:

d = 32 / tan(55 degrees)

Using a calculator, we can evaluate the tangent of 55 degrees:

tan(55 degrees) = 1.428

d = 22.4 meters

Therefore, the car is approximately 22.4 meters away from the tower.

Learn more about  Trigonometric Functions, by the following link.

brainly.com/question/24349828

#SPJ1

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

Learn more about LCM here :

https://brainly.com/question/6756370

#SPJ1

The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.

To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:

1. Bank Statement Balance:

Cash on deposit at July 31: Br.4,964.47

2. Adjusted Bank Balance:

Bank Statement Balance: Br.4,964.47

3. Deposit not on the statement: + Br.410.90

(Adjusted Bank Balance: Br.5,375.37)

Erroneously charged check: + Br.79

(Adjusted Bank Balance: Br.5,454.37)

Outstanding checks:

Check 801: - Br.100.00

Check 888: - Br.10.25

Check 890: - Br.294.50

Check 891: - Br.205.00

(Adjusted Bank Balance: Br.4,844.62)

4. Incorrectly charged check: + Br.90

(Adjusted Bank Balance: Br.4,934.62)

5. Collection of interest-bearing note: + Br.500

(Adjusted Bank Balance: Br.5,434.62)

6. Interest earned: + Br.24.75

(Adjusted Bank Balance: Br.5,459.37)

7. Incorrectly recorded check: - Br.90

(Adjusted Bank Balance: Br.5,369.37)

8. Collection fee: - Br.5.00

(Adjusted Bank Balance: Br.5,364.37)

9. NSF check: - Br.50.25

(Adjusted Bank Balance: Br.5,314.12)

10. Service charge: - Br.12.70

(Adjusted Bank Balance: Br.5,301.42)

Adjusted Ledger Balance:

Bank Balance in ABC's Ledger: Br.4,173.83

Reconciled Bank Balance: Br.5,301.42

Reconciled Ledger Balance: Br.4,173.83

Journal Entry:

To record the bank reconciliation, we make the following journal entry:

Debit: Cash (Ledger Balance adjustment) - Br.5,301.42

Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47

Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)

This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.

The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.

For more such questions on bank

https://brainly.com/question/25711082

#SPJ8

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

For more such answers on coordinates

https://brainly.com/question/30227780

#SPJ8

Answer:

31

Step-by-step explanation:

3 times the same question ?

but yes, the formula for Jamal's salary is

S = 250 + 50v

now we know for that week that S = 1800

so, now we solve for v :

1800 = 250 + 50v

1550 = 50v

155 = 5v

v = 31

so, Jamal sold 31 vacuums in that week.

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

Since 3 feet is a yard, one foot is 1/3.

So that is the answer.

Answer:

1/3

1 mile to yards as a fraction would probably be 1/3. I'm not so sure...

The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

Learn more about percentage here:

https://brainly.com/question/24339661

#SPJ1

Answer:

Step-by-step explanation:

The answer is B

Answer:

I believe the answer will be Line A.

Step-by-step explanation:

The measure of the angle of the straight line is equal to 180 degrees. the measure of the ∠HLI and ∠ILM is equal to the which is 30 degrees. Thus option 4 is the correct option.

An endlessly long row of evenly spaced dots that spans in both directions makes up a line. Its length is the only dimension it has. A geometry called an angle is created when two line segments, lines, or rays intersect.

Given information-

The measure of the angle KLH is 120 degrees.

The image is attached below for the given problem.

The angle of the straight line

The measure of the angle of the straight line is equal to 180 degrees.

The line KLM is a straight line thus the angle of the line KLM is equal to 180 degrees.

The value of the angle ILH is 30 degrees given in the figure.

The value of the angle KLH is given in the question which is equal to 120 degrees. Thus,

∠KLM = ∠ILM + ∠KLH + ∠ILH

Take the angle KLH and the angle ILH on the other side,

∠ILM = ∠KLM - ∠KLH - ∠ILH

∠ILM = 180 - 120 - 30

∠ILM = 30

Thus the measure of the is 30 degrees.

As the measure of the is equal to the which is 30 degrees. Thus option 4 is the correct option.

Learn more about the angle of the straight line here;

brainly.com/question/24024505

#SPJ1

Answer:

d. mAngleHLI = mAngleILM

Step-by-step explanation:

trust

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

For more such questions on Pythagorean theorem:

https://brainly.com/question/28981380

#SPJ8

Answer:

2

Step-by-step explanation:

9m + 25m + 22 = 90

34m = 90 - 22

34m = 68

m = 68 / 34

m = 2

Answer:

m = 2

Step-by-step explanation:

GLI forms a 90 degree angle

Set your formula up as

90 = 9m + 25m + 22

90 - 22 = 34m

68 = 34m

68/34 = m

2 = m

Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

9514 1404 393

Answer:

  x = g(y) = (4 -5y)/(7 -5y)

Step-by-step explanation:

The inverse function y = f(x) is found by solving x = f(y) for y.

  \(x=f(y)\\\\x=\dfrac{4-7y}{5-5y}\\\\5x-5xy=4-7y\qquad\text{multiply by $(5-5y)$}\\\\7y-5xy=4-5x\qquad\text{add $(7y-5x)$}\\\\y=\dfrac{4-5x}{7-5x}\)

You apparently want this written as a function of y:

  x = g(y) = (4 -5y)/(7 -5y)

Answer:

x = 1.4

y = 1.4

Step-by-step explanation:

Mark brainliest

The solution of the system is (4, 2).

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

We have the system of inequalities:

x + y ≥ 6

x ≥ 4

To find the solution:

Solve as a system of equations.

x + y = 6

And x = 4.

Then y = 2.

Therefore, (4, 2) is the solution of the system.

To learn more about the systems of inequalities;

https://brainly.com/question/19526736

#SPJ1

Answer:The solution of the system is (4, 2).

What are systems of inequalities?

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

We have the system of inequalities:

x + y ≥ 6

x ≥ 4

To find the solution:

Solve as a system of equations.

x + y = 6

And x = 4.

Then y = 2.

Therefore, (4, 2) is the solution of the system.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is the answer because you have to use the formula of volume

which is L x W x H then you get your answer

Answer:

22, Twenty Two

Step-by-step explanation:

A good way to look at multiplying 11 is that the number, if it’s under 10, will then be two of that number. For instance, 4 x 11 = 44, 6 x 11 = 66, and so on and so forth.

Hope This Helped!

The meaning of the ratio is given as follows:

The ratio is interpreted applying the proportions in the context of the problem.

A company mixes fertilizer and soil in a 4 to 9 ratio by weight, hence the denominator of the fraction corresponding to the part of each substance is of:

4 + 9 = 13.

Then the fractions are given as follows:

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1