Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it 8 inches.
how far did chubby run?
i need the answer in terms of pi

To choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet with 10 different kinds of ice cream and 6 kinds of toppings, you can use the concept of combinations. The total number of ways to choose is 1800.

To determine the number of ways to choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet, we can use the concept of combinations. We have 10 different kinds of ice cream to choose from, and we want to choose 3 of them. The number of combinations can be calculated using the formula:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of objects (10 ice cream flavors) and r is the number of objects to be chosen (3 ice cream flavors), and ! denotes factorial.

In this case, the number of combinations of ice cream flavors is:

C(10, 3) = 10! / (3!(10-3)!) = 120

Similarly, we have 6 different kinds of toppings to choose from, and we want to choose 2 of them. The number of combinations of toppings is:

C(6, 2) = 6! / (2!(6-2)!) = 15

Therefore, the total number of ways to choose 3 kinds of ice cream and 2 kinds of toppings is the product of the number of combinations of ice cream flavors and toppings:

Total number of ways = 120 * 15 = 1800

The scenario described in the question involves using a rope to whirl a bucket in a vertical circle. This relates to the physics concepts of centripetal force, tension in the rope, and gravity. The tension in the rope provides the centripetal force needed for the curved path of the bucket, and the scenario implies a constant speed and a counterbalance between tension and gravity at the highest point of the circle.

The question involves a principle of physics known as centripetal force, which is the force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body, towards the fixed point of the instantaneous center of curvature of the path.

In this case, the 60 cm rope tied to the bucket and whirled in a vertical circle becomes a system where the bucket, the force of gravity, and the tension in the rope all play a part. When the bucket is whirled, it experiences a centripetal force that keeps it moving in a circle. This force comes from the tension in the rope, which always pulls the bucket towards the center of the circle (the hand holding the rope). Hence, there are two key forces in this scenario - the force of gravity, pulling the bucket downward, and the tension in the rope providing the centripetal force.

Since the question does not state otherwise, we can reasonably assume that the movement is steady, implying the speed of the bucket is constant. In such a case, the swinging bucket will rise to a certain point, where the tension in the rope and the gravity cancel each other, causing the bucket to start falling back to the other side, therefore, forming the vertical circular path.

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Answer:

[tex]x=6.11  feet[/tex]

Step-by-step explanation:

Given that in a fulcrum weights are perfectly balanced.

One side 40 lb weight is there and another side 50 lb weight is given

Let x be the length of 40 lb weight from fulcrum.  Then 50 lbs is at a distance of 11-x.

Then we have since weights are perfectly balanced

[tex]40x = 50(11-x)\\90x=550\\x=6.111[/tex]

Thus we get [tex]x=6.11[/tex]feet

Answer:

x ≥ 0

Step-by-step explanation:

The function is graphed starting at 0 and going up the positive x-axis.

These are numbers that are greater than 0; thus the domain is greater than or equal to 0, or

x ≥ 0

The domain of the function is (d) x >= 0

From the graph, we have the following highlight:

Since 0 is inclusive, we make use of the greater than or equal to inequality

Hence, the domain of the function is (d) x >= 0

Read more about domain at:

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Answer:

NONE OF THE ABOVE!!

Step-by-step explanation:

A regular polygon is equilateral and equiangular, and also, can be inscribed into a circle. The polygon shown doesn't meet any of these conditions.

Answer:

0

if you were confused to the one on top

Answer:

Scale factor = [tex] \frac{1}{2} [/tex]

Explanation:

The purple shape is a dilation of the black shape.

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

Now findd the scale factor.

If given two shapes and need to find the scale factor, We must know which one was the original and which one is the image or the new shape. Then we need to know the length of corresponding sides and set them up in a ratio like so:

Scale Factor = [tex] \frac{purple}{black} [/tex]

Scale factor = [tex] \frac{10}{20} = \frac{1}{2} [/tex]

Using the Angle Bisector Theorem solve for x.

The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

As, we see the figure, AD bisects angle A

So, Applying Angle Bisector theorem, we get,

[tex] \frac{AC}{CD} =\frac{AB}{BD} [/tex]

[tex] \frac{AC=15}{CD=3} =\frac{AB=(4x+1)}{BD=5} [/tex]

[tex] \frac{15}{3} =\frac{4x+1}{5} [/tex]

15 divide by 3 gives 5

So, we have

5=[tex] \frac{4x+1}{5} [/tex]

To get rid of fractions let us multiply by 5 on both sides

5*5=[tex] \frac{5*(4x+1)}{5} [/tex]

25=[tex] \frac{1*(4x+1)}{1} [/tex]

25=4x+1

To solve for x, let us subtract 1 from both sides

25-1=4x+1-1

24=4x+0

Or, 4x=24

To solve for x, let us divide by 4 on both sides

[tex] \frac{4}{4}x=\frac{24}{4} [/tex]

x=6

Answer: x=6

Given:

one U.S dollar equals 3.70 rands. To find how many rands does 450 U.S dollars equal to, we need to multiply 450 with 3.70

Solution:

[tex] 1 \; U.S \; dollars \; = \; 3.70 \; rands\\ \\ 450\; U.S\; dollars= 450 \times 3.7 \; rands=1665 \; rands [/tex]

Conclusion:

1665 rands equals $450.

Answer:

The answer is 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the object starts with a value [tex]V_0[/tex], and a annual percent of decay d, after a year the value will be

[tex]V_1 = V_0 * d[/tex]

after 2 years, taking now  [tex]V_1[/tex] as the starting value

[tex]V_2 = V_1 * d = V_0 * d * d [/tex]

[tex]V_2 = V_0 * d^2 [/tex]

and so on, after n years the value will be:

[tex]V_n = V_0 * d^n[/tex]

Now, in 1997 the value was $9500, in 2012 the value was $5000. Between 1997 and 2012 there are 15 years, so, our equation will be:

[tex] \$5000 = \$ 9500 * d^{15}[/tex]

Working it a little

[tex] \frac{\$5000}{\$ 9500} = d^{15}[/tex]

[tex] (\frac{\$5000}{\$ 9500})^{1/15} = d[/tex]

[tex] (0.5263})^{1/15} = d[/tex]

[tex] 0.9581 = d[/tex]

This mean that, after a year, the value will be at 95.81 %, this is, a decay rate of 4.19%.

Answer:

y²-2y+3

Step-by-step explanation:

We write the dividend, y³-y²+y+3, under the box and the divisor, y+1, to the left of the box.

We first divide y³ by y; this is y².  We write this above the box, over -y².  We multiply the divisor by y²:  

y²(y+1) = y³+y²

This goes under the divisor.  We then subtract:

(y³-y²)-(y³+y²) = -2y².  We then bring down the next term, y; this gives us -2y²+y.

We then divide -2y² by y; this is -2y.  This goes above the box beside the y² in the quotient.  We then multiply the divisor by -2y:

-2y(y+1) = -2y²-2y

We now subtract:

(-2y²+y)-(-2y²-2y) = 3y.  We bring down the last term, 3; this gives us 3y+3.  We divide 3y by y; this is 3.  This goes beside the -2y in the quotient.  We then multiply this by the divisor:

3(y+1) = 3y+3.  We then subtract:  (3y+3)-(3y+3) = 0

This makes the quotient y²-2y+3.

We calculate P to be approximately $7,759.58, which is the amount Ryan invested initially.

To determine the initial investment that Ryan made, which grew to $12,835.94 after 10 years with an annual interest rate of 4.31% compounded monthly, we will use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

We know that:

A = $12,835.94

r = 4.31/100 = 0.0431

n = 12

t = 10

We need to solve for P:

P = A /[tex](1 + r/n)^{nt}[/tex]

Substituting the known values, we get:

P =[tex]$12,835.94 / (1 + 0.0431/12)^{12*10}[/tex]

P = $12,835.94 / [tex](1 + 0.0035925)^{120}[/tex]

P = $12,835.94 / ([tex]1.0035925)^{120}[/tex]

Calculating the value inside the parenthesis first:

[tex](1.0035925)^{120}[/tex] = 1.654297553

Now, we divide the final amount by this compound factor:

P = $12,835.94 / 1.654297553

P ≈ $7,759.58

Therefore, Ryan's initial investment was approximately $7,759.58.

Answer:

the estimate is an over estimate because 2.19 time 6 equals 13.14 and you  sya 15 dollors so so it is an over estimate

Step-by-step explanation

i hope this helps i hate math

Answer:

√74

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + 5^2 = c^2

49 + 25 = c^2

74 = c^2

√74 = √c^2

The number of distinct ways the letters in TALLAHASSEE can be arranged is calculated using permutations with repetitions. It involves taking the factorial of the total number of letters and dividing by the factorial of the number of times each letter repeats.

To determine the number of distinct ways the letters in TALLAHASSEE can be arranged, we must consider it as a permutation problem with repeating elements. We need to calculate the factorial of the total number of letters and then divide by the factorial of the number of times each individual letter repeats.

The word TALLAHASSEE contains 11 letters in total:

The permutation formula considering repetitions is:

Number of arrangements = Total letters factorial / (Product of each letter's factorial)

Therefore:

Number of arrangements = 11! / (2! * 2! * 2! * 2!)

This would give us the total number of distinct arrangements of the letters in TALLAHASSEE.

Answer: 3.A

Step-by-step explanation: At the exallent rating

Answer:

c is correct

Step-by-step explanation:

The lengths of the two pieces of wire, when one is formed into a square and the other into a circle with equal areas, are approximately 186.3 inches and 133.7 inches respectively.

To solve this problem, we first need to understand that the total perimeter of both the square and the circle made from the wire lengths equal to the original wire length, which is 320 inches. Suppose the length of the wire used for the square is 'a' and the length for the circle is 'b'. So, 'a + b = 320' inches.

Given that, the areas of both the square and the circle are equal. The area of a square is side^2 and the side of our square will be 'a/4' (since a square has four equal sides) and the area of a circle is πr^2, with the circumference being 2πr or 'b' in this case, so the radius is 'b / (2π)'.

Setting these two areas equal gives us the equation '(a/4)^2 = π * (b/ (2π))^2'. Solving this system of equations, we find that 'a' is approximately 186.3 inches and 'b' is approximately 133.7 inches.

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Answer:      x<−2

(just had a test)

hope this helps