Choose the correct simplification of the expression a^7b^8/a^4b^4
A: a^11b^12
B: a^3b^4
C: 1/a^3b^4
D: 1/a^3b^2

Final answer:

When a number cube is rolled 63 times, it is predicted to land on a factor of 6, specifically 1, 2, 3, or 6, a total of 42 times. This prediction is based on the probability of 2/3 for each roll to result in a factor of 6.

Explanation:

A student asked: A number cube is rolled 63 times. Predict how many times the cube will land on a number that is a factor of 6.

To answer this, we first identify the factors of 6 on a six-sided number cube, which are 1, 2, 3, and 6. Because each side of a perfectly weighted cube has an equal chance of landing face up, the probability of landing on a factor of 6 each time the cube is rolled is determined by the number of sides with factors of 6 out of the total number of sides. In this case, 4 out of the 6 sides are factors of 6 (1, 2, 3, and 6).

The probability of landing on a factor of 6 for each roll is 4/6, which simplifies to 2/3. To predict how many times the number cube will land on a factor of 6 in 63 rolls, we multiply the total number of rolls by the probability of landing on a factor of 6:

Predicted occurrences = Total rolls × Probability = 63 × (2/3) = 42

Therefore, we predict that the number cube will land on a factor of 6 a total of 42 times out of 63 rolls.

Answer: If AC = 15 and BC = 12, AB = 9

If AC = 14 and BC = 11, 9 > AB > 8

Radius = AB = 8.66...

IDO NOT KNOW SORRY IF IT DIDNT HELP

Answer: The answer is 8.7  :)

The answer is      2             . I took the test, its right, Sqdancefan is right   :)

[tex]\silver\ per\ gold\\\\\dfrac{75\ silver}{15\ gold}=\dfrac{75}{15}\ silver\ per\ gold=5\ silver\ per\ gold\\\\Answer:\ C.\ 5[/tex]

Answer:

C bc i know

Step-by-step explanation:

Follow below steps:

The problem involves finding the radius of a quarter circle given its perimeter. The perimeter of a full circle is known as its circumference, represented by the formula C = 2πr for a circle of radius r. However, for a quarter circle, only 1/4 of this circumference plus twice the radius (the straight sides of the quarter circle) constitutes the perimeter. Therefore, the perimeter (P) can be expressed as P = (πr)/2 + 2r.

Given that the perimeter is 32.13, we use the formula to set up the equation 32.13 = (πr)/2 + 2r. To solve for r, combine the like terms to get (2 + π/2)r = 32.13 and then isolate r by dividing both sides of the equation by (2 + π/2). Using the approximate value of π = 3.14159, you continue with the arithmetic to find the exact value of the radius.

Remember that precision is important in mathematics. When providing an answer, consider the number of significant figures supplied in the given data and maintain the same level of precision in the final answer.

The radius of the quarter circle is 20.48 units.

To find the radius of a quarter circle given its perimeter, we can start by understanding the formula for the perimeter of a circle.

The perimeter of a full circle is given by [tex]\( P = 2\pi r \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle. Since we are dealing with a quarter circle, the perimeter would be one-fourth of the perimeter of a full circle.

The radius of the quarter circle as [tex]\( R \)[/tex]. Then, the perimeter of the quarter circle is [tex]\( \frac{1}{4} \times 2\pi R = \frac{\pi R}{2} \)[/tex].

The perimeter of the quarter circle is 32.13 units, we can set up the equation:

[tex]\[ \frac{\pi R}{2} = 32.13 \][/tex]

To solve for [tex]\( R \)[/tex], isolate it by multiplying both sides of the equation by [tex]\( \frac{2}{\pi} \)[/tex]:

[tex]\[ R = 2 \times \frac{32.13}{\pi} \][/tex]

[tex]\[ R \approx 20.48 \][/tex]

the general rule for estimating is to look at the digit to the right of the digit you want to estimate. Estimating or rounding to the nearest whole number means looking at the digit to the right of the decimal. if you see a digit greater than 5,round up, an if it's less than 5, round down. we would go to the right of 18.3 which would be (6.37), so we're going to to round that to the nearest whole number which would be 7 because it's more than 5. this shows how you estimate 18.3 an (6.37) hope this helps have a good day♡

The solution to the equation is 6 if equation is 6(2x - 11) + 15 = 21 the answer is 6.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a mathematical equation:

6(2x - 11) + 15 = 21

DIstributive property:

12x - 66 + 15 = 21

Subtraction property:

12x -51 = 21

Add 51 on both side:

12x -51 + 51 = 21 + 51

12x = 72   (adding like terms)

x = 6 (divide by 12 on both side)

Thus, the solution to the equation is 6 if equation is 6(2x - 11) + 15 = 21 the answer is 6.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ2

Ben builds ladders of different heights and put the number of rungs depending upon height of any particular ladder. He uses an equation for this construction that is given by :-

r = h ÷ 0.8

where h is the height of the ladder and r is the number of rungs in that ladder.

As we increase the height of the ladder, we need more rungs. If we decrease height, we would need lesser rungs.

Thereby, the number of rungs depend on the height of the ladder. It means value of r depends on value of h.

So r is dependent variable, and h is the independent variable.

Hence, option A is correct i.e. the height of the ladder.

Final answer:

Abigail will need to use 0.8 cup of flour to make 60% more pancakes than the original recipe.

Explanation:

To determine how much flour Abigail needs to use, we can set up a proportion based on the increase in the number of pancakes. If her mother's recipe calls for 1/2 cup of flour for a certain number of pancakes, and Abigail wants to make 60% more pancakes, then she will need 60% more flour. To calculate the amount of flour, we can multiply the original amount by 1.6 (which is 100% + 60%).

Flour needed = 1/2 cup * 1.6 = 0.8 cup

Therefore, Abigail will need to use 0.8 cup of flour to make 60% more pancakes than the original recipe.

The distance from the edge of Frank's garden to the center of the garden is about 2.815 feet.

To find the approximate distance from the edge of Frank's garden to the center, we first need to determine the radius of the circular garden. We are given the area (A) of the garden, which is 100 square feet. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

We can rearrange the formula to solve for the radius:

r² = A / π

Now, plug in the given area:

r² = 100 ft² / π

Calculate the square of π (approximately 3.1416):

r² = 100 / 3.1416

r² = 31.8309

Now, find the square root of r² to get the radius:

r ≈ √31.8309

r = 5.63 ft

Now that we have the radius, we can find the distance from the edge to the center. In a circle, the distance from the edge to the center is half the radius. So, we can calculate this as follows:

Distance from edge to center ≈ (1/2) * radius

Distance from edge to center ≈ (1/2) * 5.63 ft

Distance from edge to center ≈ 2.815 ft