What is the lcm of 45 and 54?

Final answer:

The trace on the xy-plane of a sphere with center (-1, 3, -1) and radius 2 is a circle with center (-1, 3) and radius 2, represented by the equation (x + 1)² + (y - 3)² = 4.

Explanation:

The question asks to find the trace on the xy-plane of the sphere having a center at (-1, 3, -1) and a radius 2.

The trace on the xy-plane of a sphere is essentially the circle that is formed when the sphere intersects the xy-plane.

Since the center of the sphere is (-1, 3, -1), and the sphere intersects the xy-plane (z=0), we keep the x and y coordinates of the center the same for the circle, meaning the center of the circle will be (-1, 3). The radius of the circle remains the same as the sphere, which is 2.

The equation for a circle in the xy-plane with center (h, k) and radius r is given by (x - h)² + (y - k)² = r².

Therefore, plugging in the values for this specific circle gives us the equation (x + 1)² + (y - 3)² = 4.

This equation represents the trace of the sphere on the xy-plane.

The area of the two designs are given as 52 square inches and 61.375 square inches.

In these the second design 61.375 square inches is having the greater area.

If 500 envelops are made then area of paper = 61.375x500 =30687.5 square inches.

If envelops having 52 square inches are made out of 30687.5 square inches of paper ,number of envelops made =30687.5 ÷ 52=590.144

590 small envelops can be made having area as 52 square inches.

It is 590-500=90 more than the larger envelops made.

To find the size of turkey needed for 14 people, multiply their serving size by the number of people and convert it from pounds to grams

To calculate the size of turkey you will need, you first need to find the total weight of the turkey required for 14 people. Since you want to allow 3/4 lb of turkey for each person, the total weight of turkey required will be 14 * 3/4 lb.

Now, 1 lb is equal to 450g. So, to convert the weight from pounds to grams, you can multiply the weight in pounds by 450.

Therefore, to find the size of turkey you will need, multiply the total weight of turkey required in pounds (14 * 3/4) by 450. This will give you the answer in grams.

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Answer:

  the number decreased by 80%

Step-by-step explanation:

The percentage change can be computed using ...

  percent change = ((new value)/(old value) -1) × 100%

Putting the given numbers into this equation gives ...

  percent change = (6/30 -1) × 100% = -4/5 × 100%

  percent change = -80%

A negative sign on the percent change means the change was a decrease. The number of students who went to tutoring decreased by 80%.

Answer:

thanks

Step-by-step explanation:

The probability that three runners from the same school finishing first, second, and third can be calculated as the product (5/30) * (4/29) * (3/28). This uses the principles of probability in mathematics.

The problem involves the concept of probability in Mathematics. Let's break this question down using the principles of probability.

For the first runner to be from your school, the probability would be 5/30 as there are 5 runners from your school out of 30 total runners. After one runner from your school has won, there are now 4 runners left from your school and 29 total runners left. So, the probability of the second runner being from your school is 4/29. Similarly, the probability that the third runner is also from your school is 3/28 since there are now three left from your school and 28 in total.

The final probability is the product of all three of these probabilities, so:

P(all three top spots are from your school) = (5/30) * (4/29) * (3/28), which needs to be calculated to get the final result.

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The result is 0.00246, or about 0.25% chance.

To find the probability that three runners from your school place first, second, and third in a race with 30 runners, we need to consider the number of ways to select these three positions from your school's five runners and divide it by the total number of ways to select any three runners from all 30 participants.

Calculate the number of ways to choose 3 runners out of the 5 from your school:

[tex]C(5, 3) = \( \frac{5!}{3!(5-3)!} \) = 10[/tex]

Calculate the number of ways to arrange these 3 runners in the first, second, and third positions. This is equal to the number of permutations of 3 elements:

P(3) = 3! = 6

Calculate the total number of ways to choose 3 runners out of the 30 participants:

[tex]C(30, 3) = \( \frac{30!}{3!(30-3)!} \) = 4060[/tex]

Calculate the number of ways to arrange these 3 runners in the first, second, and third positions:

P(3) = 3! = 6

Finally, calculate the probability that 3 runners from your school place first, second, and third:

[tex]Probability = \( \frac{C(5, 3) \times P(3)}{C(30, 3) \times P(3)} \) = \( \frac{10 \times 6}{4060 \times 6} \) = \( \frac{10}{4060} \) = \( \frac{1}{406} \)[/tex]

Thus, the probability is approximately 0.00246 (or 1/406).

Final answer:

To solve the expression 2(√(80/5) - 5), we simplify the square root first, then subtract 5, and finally multiply by 2, which results in the solution -2.

Explanation:

To solve the expression 2(√(80/5) - 5), let's first simplify the square root and the division inside it.

We have √(80/5) = √16 = 4, since 80 divided by 5 is 16, and the square root of 16 is 4.

Next, we subtract 5 from 4: 4 - 5 = -1.

Finally, we multiply the result by 2: 2 * (-1) = -2.

Therefore, the solution to the expression 2(√(80/5) - 5) is -2.

The answer to the given question is: [tex]\[ 2\left(\frac{\sqrt{80}}{5} - 5\right) = \frac{2\sqrt{80}}{5} - 10 \][/tex]

To solve the expression step by step:

 1. First, simplify the square root within the parentheses. The number 80 can be factored into [tex]\( 16 \times 5 \)[/tex], and since [tex]\( \sqrt{16} = 4 \),[/tex] we can rewrite[tex]\( \sqrt{80} \) as \( 4\sqrt{5} \).[/tex]

[tex]\[ 2\left(\frac{4\sqrt{5}}{5} - 5\right) \][/tex]

2. Next, distribute the 2 across the terms inside the parentheses:

[tex]\[ 2 \times \frac{4\sqrt{5}}{5} - 2 \times 5 \][/tex]

 3. Simplify each term:

[tex]\[ \frac{8\sqrt{5}}{5} - 10 \][/tex]

 4. At this point, we have the simplified form of the expression. However, if we want to combine the terms into a single fraction, we need a common denominator. The second term, -10, can be written as [tex]\( \frac{-10 \times 5}{5}[/tex]) to get the common denominator of 5:

[tex]\[ \frac{8\sqrt{5}}{5} - \frac{50}{5} \][/tex]

 5. Now, subtract the two fractions:

[tex]\[ \frac{8\sqrt{5} - 50}{5} \][/tex]

 6. This is the final simplified form of the expression. It cannot be simplified further algebraically because [tex]\( 8\sqrt{5} \)[/tex] and 50 do not have common factors other than 1.

Therefore, the final answer is: [tex]\[ \boxed{\frac{8\sqrt{5} - 50}{5}} \][/tex]

[tex]\[ 2\left(\frac{\sqrt{80}}{5} - 5\right) \][/tex]

And the final simplified answer is: [tex]\[ 2\left(\frac{\sqrt{80}}{5} - 5\right) = \frac{2\sqrt{80}}{5} - 10 \][/tex]

The formula for a parabola with roots at x=-8 and x=-4, and which passes through the point (0,-7), is y = -7/32(x + 4)(x + 8).

The formula we're looking for is in the form of a quadratic function, generally expressed as

y = ax² + bx + c. Our roots are -8 and -4, which we represent in the factors of the equation as (x + 4) and (x + 8). As coefficients multiply to a, we seek a that makes our function pass through the specific point (0, -7). Thus, we substitute the point into the function giving -7 = a(0+4)(0+8) leading us to a = -7/32. So, the equation of the parabola asked is

y = -7/32(x + 4)(x + 8).

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