Convert: 120 quartsgallons

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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A = 139°

B = 139°

You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.

The angle around a point always add up to 360°, so add the 41° angles.

41 + 41 = 82°

Then minus this by 360°.

360 - 82 = 278°

And to work out one angle, which gives you the angle for both, divide 278 by two.

278 ÷ 2 = 139°

Both A and B have an angle of 139°

Example:

To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:

3x - 5 = -2x + 7

5x = 12

x = 12/5

Then, plug x = 12/5 into either equation and solve for y:

y = 3(12/5) - 5

y = 36/5 - 25/5

y = 11/5

Therefore, the point of intersection is (12/5, 11/5).

If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:

slope = tan(41 degrees) ≈ 0.87

y = mx + b

y = 0.87x + 0

Then, you can use the same method as before to find the point of intersection with another line.

_______________________________________________________

The answer is 139 degrees, using the method I gave.

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Answer:

the answer is 4

Step-by-step explanation:

i added and subtracted and got 4

Answer:

-8,-7

Step-by-step explanation:

I think

Answer:

try pressing the help button, it looks like it mightve glitched

Step-by-step explanation:

Answer:

1. C

2. D

Step-by-step explanation:

1.

Pattern A is adding by 2's (1 -> 3, 4 -> 6, 7 -> 9 and so on).

Pattern B is multiplying by 2's (2 -> 4, 3 -> 6, 4 -> 8 and so on).

2.

If 0.25 gallons of paint = 24 ft^2, then 1 gallon will equal?

Set up an equation:

Variable x = area of ft^2 for 1 gallon of paint

0.25/24 = 1/x

Cross multiply

0.25 × x = 24 × 1

0.25x = 24

To make calculations easier, you can convert the decimal into a fraction: 0.25 = 1/4

1/4x = 24

Multiply both sides by 4

1x = 96

x = 96 ft^2

Check your work:

0.25/24 = 1/96

0.25 × 96 = 24 × 1

24 = 24

Correct

The inequality that represents c, the number of candles she needs to sell to pay for a visit to Knotts costing $100 when each candle is sold for $5, is expressed as: c ≥ 20.

The inequality c * 5 ≥ 100 is derived from the fact that each candle is sold for $5, so the total amount of money she earns from selling c candles is given by 5c. This amount must be greater than or equal to the cost of the visit, which is $100.

By multiplying both sides of the inequality by 1/5, we get c ≥ 20, which means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

Therefore, the answer is: c ≥ 20.

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We need to show that if we choose right triangle with the interior angle θ, the ratios of the sides will be the same as shown in below figure.

The mathematical subject of trigonometry is the study of the connections between the angles and sides of triangles. It entails investigating trigonometric functions like sine, cosine, and tangent, which examine the relationship between a triangle's sides' lengths and its angles.

Let's consider a right triangle with acute angles α and β, as shown below:

To relate the sides of this triangle, we can use the Pythagorean theorem:

a² + b² = c²

Now, let's define the six trigonometric functions in terms of the sides of the triangle:

Sin(θ) = a/c

Cos(θ) = b/c

tan(θ) = a/b

csc(θ) = c/a

sec(θ) = c/b

cot(θ) = b/a

We want to show that these functions are well-defined, i.e., they do not depend on the particular triangle we choose. To do this, we need to show that if we choose another right triangle with the same interior angle θ, the ratios of the sides will be the same.

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The sequence of transformations that proves that the shapes are similar is given as follows:

B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5

First, we have that the orientation of the figure, hence it was reflected.

The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.

The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:

3/2 = 1.5.

Hence option B is the correct option for this problem.

The missing parts of the problem are given by the image presented at the end of the answer.

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The statements that are true are B and D.

Given are some statements we need to check which is true.

Let's analyze each statement:

A. 4 is a perfect cube.

False. 4 is not a perfect cube because there is no integer that can be cubed to give 4.

B. 16 is a perfect square.

True. 16 is a perfect square because it can be expressed as 4^2, where 4 is an integer.

C. 2,197 is both a perfect square and a perfect cube.

False. 2,197 is not a perfect square because there is no integer that can be squared to give 2,197.

However, it is a perfect cube because 13³ equals 2,197.

D. 8 is a perfect cube.

True. 8 is a perfect cube because it can be expressed as 2³, where 2 is an integer.

E. 18 is neither a perfect square nor a perfect cube.

True. 18 is neither a perfect square nor a perfect cube because there is no integer that can be squared or cubed to give 18.

Therefore, the statements that are true are B and D.

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Answer:

  D.  31

Step-by-step explanation:

The edge dimension of a cube is the cube root of the volume. For the two boxes that are 1331 m³, the height is ...

  ∛(1331 m³) = 11 m

For the box that is 729 m³, the height is ...

  ∛(729 m³) = 9 m

Then the total height of the stack of boxes is ...

  11 m + 11 m + 9 m = 31 m

Answer:

31

Step-by-step explanation:

I took the test on Edmentum, have a good day hope it helps :)

Answer:

Step-by-step explanation:

Our expression given: 3(x-6) + 2y

A. Substitute x = -7 and y = 10 into the equation.

\(3( - 7 - 6) + 2(10)\)

Use the Distributive Property:

\( - 21 - 18 + 20\)

Solve:

\( - 19\)

B. Substitute x = 5 and y = -2 into the equation.

\(3(5 - 6) + 2( - 2)\)

Use the Distributive Property:

\(15 - 18 + -4\)

Solve:

\(-7\)

C. Substitute x = 0 and y = 6 into the equation.

\(3(0 - 6) + 2(6)\)

Use the Distributive Property:

\( - 18 + 12\)

Solve:

\(-6\)

D. Substitute x = 3 and y = 3 into the equation.

\(3(3 - 6) + 2(3)\)

Use the Distributive Property:

\(9 - 18 + 6\)

Solve:

\(-3\)

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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The length of leg is equal to 100 based on the length of hypotenuse and angle.

The length of leg will be calculated using Pythagoras theorem as the stated triangle is right angled triangle. Based on the theorem, se have side A is hypotenuse. So, sin theta = perpendicular/hypotenuse, where theta will be 90 degree and perpendicular is leg. Let us represent the leg as x.

sin 90 = x/ A

Keep the value of sin 90, which is 1

1 = x/100

Rearrange the equation in terms of x along with performing multiplication

x = 100

Hence, the length of leg is 100.

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Answer:

Choice B, 10 inch pizza to himself

Step-by-step explanation:

1. Half of 16 inch pizza= 8 inch

2. 10 inch pizza to himself= well, 10 inch

10>8

Answer:

Pizza B

Step-by-step explanation:

Half of a 16 inch pizza would be 8-inch. Since a 10-inch pizza is more than an 8-inch pizza, you would have to go with Pizza B.

Hope this helps!

-kiniwih426

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Answer:

8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

-10 + x(-2)

x = -9

Step 2: Evaluate

A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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Answer:

m = 2

Step-by-step explanation:

To find the slope, simply use this equation:

m = y2 - y1 / x2 - x1

Now we need to insert some points:

m = 10 - 0 / 11 - 6

m = 10/5

m = 2

Therefore, the slope of the line is 2.

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Answer:

1. ⅔

2. 4/3

3. 3.14

4. Sphere

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Step-by-step explanation:

\( \frac{3}{4} = \frac{w}{28}\)

\( \frac{3}{4} = \frac{w}{4 \times 7} \)

\(3 = \frac{w}{7} \)

\(w = 21\)

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

To write a quadratic function to represent the height h of the acrobat t seconds after the jump, we can use the following formula:

\(h(t) = -16t^2 + vt + h0\)

Where h0 is the initial height of the acrobat, which is 25 feet, and v is the initial vertical velocity, which is 4 ft/s. Plugging in these values, we get:

\(h(t) = -16t^2 + 4t + 25\)

To find how long it will take for her to land safely on the net, we need to find the time at which h(t) = 5. In other words, we need to solve the equation:

\(-16t^2 + 4t + 25 = 5\)

Simplifying this equation, we get:

\(-16t^2 + 4t + 20 = 0\)

Dividing both sides by -4, we get:

\(4t^2 - t - 5 = 0\)

Now we can use the quadratic formula to solve for t:

\(t = (-b ± \sqrt(b^2 - 4ac)) / 2a\)

Where a = 4, b = -1, and c = -5. Plugging in these values, we get:

\(t = (1 ± \sqrt(1 + 4(4)(5))) / 8\)

Simplifying this equation, we get:

\(t = (1 ± 9) / 8\)

So, the two solutions are:

\(t = 1 and t = -5/4\)

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

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Answer:

No

Step-by-step explanation:

The largest number would have 6 counters in the 10s and the remainder the in the 1s column making the number 63 which is greater than 51.111

Solution

Evaluate each function below for the given equation

17.

f(2) is when the value of x = 2

18.

g(5) is when the value of x = 5

19.

f(-1) is when the value of x = -1