LCM of 15, 30, and 45

The smallest positive integer k such that 1350k is a perfect cube is found by prime factorizing 1350 and ensuring that all prime exponents in its factorization are multiples of 3. The missing exponents for 2 and 5 are 2 and 1 respectively, so multiplying by k=20 achieves this.

To find the smallest positive integer k such that 1350k is a perfect cube, we start by factoring 1350 into its prime factors. We have 1350 = 2 × 3^3 × 5^2. In order for a number to be a perfect cube, all the exponents in its prime factorization must be multiples of 3 since a cube of any number is that number multiplied by itself three times. In the prime factorization of 1350, the exponent of 2 is 1 (which is 2 short of a multiple of 3) and the exponent of 5 is 2 (which is 1 short of a multiple of 3).

To make the number a perfect cube, we need to multiply it by a k such that the prime factorization of the result has all exponents as multiples of 3. Therefore, we need one more 2 to make the exponent of 2 equal to 3, and we need one more 5^1 to make the exponent of 5 equal to 3. This gives us a k of 2^2 × 5^1 = 4 × 5 = 20. So, k=20 is the smallest positive integer that, when multiplied by 1350, results in a perfect cube.

Answer:

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Step-by-step explanation:

The measure of angle S is [tex]38^\circ[/tex] and the measure of angle T is [tex]111^\circ[/tex] and this can be determined by using the property of sum of interior angles.

Given :

Apply the property of the sum of the interior angles of the triangle in order to determine the angles R, S, and T.

[tex]\rm \rm \angle R +\rm \angle S+\rm \angle T = 180^\circ[/tex]

31 + (x + 4) + (3x + 9) = 180

Simplify the above equation in order to determine the value of 'x'.

4x + 13 = 149

4x = 136

[tex]\rm x = 34^\circ[/tex]

Now, the measure of angle S is:

[tex]\rm \angle S = x + 4 = 34 + 4 = 38^\circ[/tex]

[tex]\rm \angle T = 3x + 9 = 3(34) + 9= 111^\circ[/tex]

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To calculate how many meters Micheal walks per second, we divide the distance he walks (30 meters) by the time (20 seconds), resulting in a walking speed of 1.5 meters per second.

The question asks us to calculate how many meters Micheal walks per second, given that he walks 30 meters in 20 seconds. To find this, we use the formula for speed, which is the distance traveled divided by the time taken. Here, the distance is 30 meters and the time is 20 seconds.

Thus, the speed (meters per second) is calculated as follows:

Therefore, Micheal walks at a speed of 1.5 meters per second.

In the scoring question, 6 represents the missed extra points. For the second question, Jacob initially subtracted 3 from both sides of the equation, then he multiplied both sides by 1/2 to solve for x.

1.) Given the equation for the total score of the football team, 7t - 6, where t represents the number of touchdowns. Each touchdown is worth 7 points (6 points for the touchdown and a possible extra 1 point). If the total score is 7t - 6, then the 6 in the equation represents the number of extra points missed. So the correct answer is C.

2.) As for Jacob's method on solving the equation 2x + 3 = 5, he should first isolate the term with x by using the addition property of equality, subtracting 3 from both sides.

This changes the equation to 2x = 2. Afterwards, he can use the multiplication property of equality by multiplying both sides by 1/2 to solve for x.

Therefore, it sounds like Jacob added -3 to both sides and multiplied both sides by 1/2, which makes the correct answer A.

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The value of 79 times 24 is 1896.

Here,

We have to find 79 times 24 multiply 80 by 24 and take off a group of 24.

What is Product?

The multiply of two or more number is called product.

Now,

To find 79 times 24 as;

Multiply 80 by 24 and take off a group of 24.

We can solve this as;

80 x 24 - 24 = 1920 - 24 = 1896

Hence, The value of 79 times 24 is 1896.

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The number is 182,000.

We needs to find a number that, when 5000 is added to it, equals 187,000. To solve this, we will perform a subtraction operation.

Step 1: Recognize that '5000 more than the number' means we will add 5000 to the number.

Step 2: The result is given as 187,000. So, we set up the equation as follows:

Number + 5000 = 187,000

Step 3: To find the original number, we subtract 5000 from 187,000.

Number = 187,000 - 5000

Step 4: Perform the subtraction to find the number.

Number = 182,000

Therefore, the number is 182,000.

the family has exceeded their available minutes by 75 minutes. There are no minutes left; instead, they have gone over their limit.

The problem states that a family of three shares a cell phone plan with 675 minutes per month and asks how many minutes are left if each person uses exactly 250 minutes.

Here's the step-by-step calculation:

1. Calculate the total minutes used by all three people:

  Each person uses 250 minutes, so for three people, the total usage would be [tex]\( 250 \times 3 \).[/tex]

2. Subtract the total usage from the total minutes available in the plan:

  The plan has 675 minutes, so we subtract the total usage from this amount to find out how many minutes are left.

Let's do the math:

1. Total minutes used by three people:

[tex]\[ 250 \text{ minutes/person} \times 3 \text{ people} = 750 \text{ minutes} \][/tex]

2. Minutes left in the plan:

[tex]\[ 675 \text{ minutes} - 750 \text{ minutes} \][/tex]

If the calculation results in a negative number, it means that the family has used more minutes than the plan provides. Let's calculate.

The total minutes used by three people, each using 250 minutes, is:

[tex]\[ 250 \text{ minutes/person} \times 3 \text{ people} = 750 \text{ minutes} \][/tex]

When we subtract the total minutes used from the total plan minutes:

[tex]\[ 675 \text{ minutes} - 750 \text{ minutes} = -75 \text{ minutes} \][/tex]

This means that the family has exceeded their available minutes by 75 minutes. There are no minutes left; instead, they have gone over their limit.

The gratuity for the service provided is $180.

Initial Repair Cost = $1,200

Sales Tax = 6%

Gratuity = 15%

Therefore, based on the above information, the gratuity will be:

= Gratuity percentage × Cost

= 15% × $1200

= 0.15 × $1200

= $180

Therefore, the gratuity is $180

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To find the number of servings, divide the total amount of mashed potatoes (47 1/2 cups) by the amount in each serving (1 1/4 cups), resulting in 38 servings.

To calculate the number of servings the cook made, we need to divide the total amount of mashed potatoes by the amount in each serving:

First, we have 47 1/2 cups of mashed potatoes in total.

We know that one serving is 1 1/4 cups of mashed potatoes.

To find out how many servings there are, divide the total cups (47.5) by the cups per serving (1.25):
47.5 ÷ 1.25 = 38 servings.

So the cook made 38 servings of mashed potatoes.

The measure of its complement and its supplement will be 90° - x° and 180° - x°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

An angle measures x°.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees. Then the angle will be

⇒ 90° - x°

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees. Then the angle will be

⇒ 180° - x°

Then the measure of its complement and its supplement will be 90° - x° and 180° - x°.

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