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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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The system of equations are graphed in the image below, showing that they have infinitely many solutions, which include (3, 0) and (0, 3).

The values of a pair of x and y that will make two different equations in a system true is the solution to the system of equations.

By graphing, we can determine the solution by finding the x and y coordinates of the point that both lines of the equations intersect at.

The lines of x + y = 3 and 5x + 5y = 15 are graphed in the image below, which is the same blue line. This shows that the equations have infinitely many solutions such as (3, 0) and (0, 3).

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The required amount of the space available is 0.045 cubic meter.

We need to determine Space inside the steps.

The Volume is defined as the mass of object per unit density.

The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2

                                 =  0.06 - 0.015

                                 =    0.045 cubic meter

Hence, the required amount of the space available will be 0.045 cubic meter.

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Answer:

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

Step-by-step explanation:

DID ANYONE HEAR ABOUT THE NEW PLANET IN THE SOLAR SYSTEM!!!!!!!!!!

ITS CALLED PLANET X or the 9TH PLANET!!! GO CHECK IT OUT!!!!!!!!!

Answer:

the slope of tangent equals (y2 - y1) / (x2 - x1)

let the first point (x1 , y1 ) equals ( -1 , -2 )

and the second point (x2 , y2 ) equals (3 ,10)

so the slope equal (10+2)/(3+1) = 3

the equation is y-y1 =m(x-x1)

the answer is y+2=3(x+1)

Answer:

I believe it's 4 I hope this helps

Answer:

it would only be 8, unless you need to go down to the decimal point then it would be 8.25

Step-by-step explanation:

it would be 8 because if you need to find how many bananas you have, to do this you would divide 15 by 2 and get 7.5 then you multiply those by 5 to get the number of bananas which would be 37.5, and then if 8 mangos = 30 bananas you only have 8 mangos.

(sorry if this is very jumbled and hard to understand, also getting brainliest would help, thank you)

Answer:

308

Step-by-step explanation:

22 x 15.4 = 338.8

338.8 / 1.1 = 308

There is a probability of 94/315 that the problem will be solved.

We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.

The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.

The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.

The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.

The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.

To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:

2/7 + 4/7 + 4/9 = 94/315

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Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.

We need to combine 3 members out of 15. The number of ways we can do so is given by:

C(15,3) =

Answer:

5000 kilogram/cubic meter

Step-by-step explanation:

The density of an object with a mass of 20g and a volume of 4ml is 5 g/ml

Density is the measurement of quantity or mass per unit of volume in a particular substance.

Given an object with mass = 20 g and volume = 4 ml

Density = mass/volume

Therefore, density of the object = 20/4 = 5 g/ml

Hence, the density of an object with a mass of 20g and a volume of 4ml is 5 g/ml

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Answer:

(6+3)+5=(3x?)+5

9+5=(3×3)+5

14=9+5

14=14

so,the missing factor is 3.

Answer:

use graph d for the answer

Answer:

D

Step-by-step explanation:

The filled in dot means equal to

Then you need to look for the one that has 4 and the ray shows that the sqrt of x is greater than 4

So it is D

Answer:

176

Step-by-step explanation:

15² - 7² = (15+7)*(15-7) = 22*8 = 176

check: 225 - 49 = 176

In order to convert a fraction to a decimal number, we just need to divide the numerator by the denominator.

For example, for the fraction 1/4, we need to divide 1 by 4, so the result would be 0.25.

In the fraction 3/10, dividing 3 by 10, we have the result 0.3.

In the fraction 12/8, dividing 12 by 8, we have the result 1.5.

Some fractions don't correspond to a finite decimal number.

For example, the fraction 1/3 is equivalent to 0.333..., which has an infinite number of decimal places.

Please find full question attached

Answer:

A. Town A has more variability than town B

B. See attachment for explanation of differences

Explanation:

Find attachment

Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

The time that would be taken for the money to double is 9 years.

Given that a compound interest has to do with the type of interest that is charged both on the principal and on the interest. We know that the principal is the money that was invested.

Let the principal be P and let the time taken be t. Let us now apply the formula;

A = P(1 + r)^n

Where A = 2P and r = 0.08

2P = P(1 + 0.08)^n

2P/P = (1.08)^n

2 = (1.08)^n

ln2 = nln1.08

n = ln2/ln1.08

n = 0.693/0.077

n = 9

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Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

Answer:

a. -3

Step-by-step explanation:

-2 turns into 6 by multiplying it by -3.

the same from 6 to -18, from -18 to 54, ...

so, an/an+1 = -3

Answer:

Question 1:

78 - 5 - 7

Question 2:

\( - \frac{1}{6} \)

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

Line m and m is a straight line

The prime number that cannot be in the set is A . 2.

Prime number:

In math, prime number is a natural number greater than 1 that is not a product of two smaller natural numbers

Given,

Here we need to find the prime number that is not in the set, if if the sum of a set of ten different positive prime numbers is an even number.

Here we know that, all prime numbers except the first prime number are odd except 2.

And here we assume that the two prime numbers are different,

So, if one of the prime number is 2 which is even, the other prime number would be odd and hence sum of the prime numbers would be odd as sum of an even and an odd number is always odd.

Where as if none of the prime numbers are odd, then both the prime numbers would be odd and hence sum of the prime numbers would be even as sum of two odd numbers is always even.

There the correct option is A. 2.

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Sumita get £2.77 amount in change for buys a set of earphones.

Since, We know that;

Subtraction in mathematics means that is taking something away from a group or number of objects.

And, When you subtract, what is left in the group becomes less.

We have to given that;

Sumita buys a set of earphones for £7.23.

And, She pays with the amount £10.

Since,  When you subtract, what is left in the group becomes less.

Here, To find the amount to get amount of change.

Hence, We can formulate;

To find the change amount we can subtract cost of earphone from pay amount which she pay.

Thus, WE get;

The Change Amount getting by her is,

⇒ Amount =  £10 - £7.23

⇒ Amount = £2.77

Therefore, We get;

⇒ Amount = £2.77

That is,

£2.77 amount in change for buys a set of earphones.

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Answer:

3/8

Step-by-step explanation:

With unlike denominators find the Least Common Denominator (LCD)

LCD = 8

Multiplying numerators and denominators to get the LCD in all fraction denominators

=3/4 times 2/2−3/8

Then rewriting the equation with the equivalent fractions

=6/8−3/8

With like denominators we can operate on just the numerators

=6−3/8

=3/8

Example: (2x - 4) x=7 so (2x (x=7) - 4) =18