0.567 as a fraction
Only the 5 and 7 repeats

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.

The slope of the line is 12.

The equation of a line in slope-intercept form is y=mx+b, where m is the slope, is the y-intercept, and x and y are a point on the line.

In order to determine the slope from the given equation do the following:

2x−4y=10 (Subtract 2x from both sides.)

−4y=−2x+10 (Divide both sides by -4.)

y=−2x−4+10−4 (Simplify.)

y=12x−52

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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Answer:

C. 14 cm

Step-by-step explanation:

According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the measure of the third side.

Given,

The longest side of an isosceles obtuse triangle measures 20 centimeters.

Let x be the measure of the other two congruent sides,

By the above property,

20 < x + x

20 < 2x

10 < x

Thus, the measure of congruent sides must be greater than 10 cm,

Now, In an isosceles obtuse triangle, the square of the longest side is greater than the sum of squares of the other two congruent sides.

[tex](20)^2>x^2+x^2[/tex]

[tex]400>2x^2[/tex]

[tex]200>x^2[/tex]

[tex]10\sqrt{2}>x[/tex]

Since, √2 = 1.41421356≈ 1.41

[tex]\implies x < 10\times 1.41\implies x < 14.1[/tex]

Hence, the greatest possible whole-number value of the congruent side lengths is 14.

Option C is correct.

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.

Susan's total income remains $16,000 regardless of the number of hours she works, up to the point where her earnings from work alone would exceed her government benefits. This design of the assistance program potentially reduces her incentive to work more hours. Opportunity costs must also be factored in, which can further influence her decisions.

Creating Susan's Income Table

Susan has the option to work up to 1,800 hours a year at $8 per hour. If Susan does not earn any income, she is entitled to $16,000 in government benefits. However, for every dollar she earns, her government support reduces by the same amount. To understand Susan's situation better, we can create a table showing various scenarios.

Let's assume Susan decides to work 500 hours in a year:

If Susan works more, her earnings increase but her benefits decrease, keeping her total income stagnant at $16,000, until she surpasses the threshold of $16,000 in earnings. This suggests the assistance program may limit her incentive to work more hours as the additional work does not increase her total income. Moreover, Susan must consider opportunity costs, such as childcare expenses, that might further reduce her incentive to work additional hours.

The Impact of Government Assistance on Work Incentives

Opportunity costs play a crucial role in Susan's decision-making. If the costs of working (like paying for childcare) exceed the benefits of working additional hours, she might opt to work less or not at all. Therefore, assistance programs can impact individual's work choices by affecting the marginal benefit of working additional hours.

Answer:

Choice B) Sometimes

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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0.42 as a fraction in simplest form is 21 / 50 .

To express 0.42 as a fraction in simplest form, we need to convert the decimal to a fraction .

The decimal 0.42 can be written as 42/100 .

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2 .

42 ÷ 2 = 21

100 ÷ 2 = 50

42 / 100 = 21 / 50

The simplified fraction is 21 / 50 .

Therefore, 0.42 as a fraction in simplest form is 21 / 50 .

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To express 0.42 as a fraction in simplest form, divide 42 by 100 and simplify the fraction by finding the greatest common factor.

To express 0.42 as a fraction in simplest form, you can write it as 42/100 and then simplify it by dividing both the numerator and the denominator by the greatest common factor, which is 2. Dividing both 42 and 100 by 2 gives you 21/50, which is the simplest form of 0.42 as a fraction.

The correct answer is:

The Rules of Practice under Circular 230.

Explanation:

An unenrolled return preparer is someone that is not an attorney, CPA, enrolled agent, enrolled retirement plan agent, or enrolled actuary, who prepares and signs a person's tax return as the paid preparer. They may also be someone who prepares a return but is not required to sign the return.

According to the IRS, unenrolled return preparers must comply with the rules of practice and conduct in order to exercise limited practice before the IRS.

There are two specific sets of rules that apply in Circular 230:

Duties and restrictions relating to practice (Subpart B of Cir. 230), and conduct considered to exhibit incompetence or disrepute (Subpart C, Section 10.51 of Cir. 230).

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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Answer:

The possible numbers for the blank are 5601, 8452, 93647 etc.

Step-by-step explanation:

Consider the provided information.

Blank divided by 7 is greater than 800

Let say the number should be in blank is x.

Now we need to find the value of x so that it divided by 7 gives a value greater than 800.

This can be written as:

[tex]\frac{x}{7}>800[/tex]

Solve the above inequality for x.

[tex]x>800\times 7[/tex]

[tex]x>5600[/tex]

The value of x should be greater than 5600.

We can select any number which is greater than 5600.

The possible choice for the blank are 5601, 8452, 93647 etc.

Note there are infinite number greater than 5600 so you can choose any of them.

The number of weeks will the boys weigh the same amount is 15 weeks and the weight is 180 lb.

Given,

Justin and Tyson are beginning an exercise program to train for football season.

Justin weighs 150 lb and hopes to gain 2 lb per week.

Tyson weighs 195 lb and hopes to lose 1 lb per week.

We need to find in how many weeks will the boys weigh the same amount If the plan works and the weight be.

If 3 miles = 2 hours

For 4 miles the number of hours is:

3 miles = 2 hours

4/3 x 3 miles = 4/3 x 2 hours

4 miles = 8/3 hours

We have,

Justin:

Justin weighs 150 lb and hopes to gain 2 lb per week.

Let the number of weeks be W.

We can write the weight of Justin after W weeks as:

150  + 2W _____(1)

Tyson :

Tyson weighs 195 lb and hopes to lose 1 lb per week.

Let the number of weeks be W.

We can write the weight of Tyson after W weeks as:

195 - 1W _____(2)

Now,

The number of weeks both weighs the same:

From (1) and (2)

150 +2W = 195 - 1W

2W + 1W = 195 - 150

3W = 45

W = 45/3

W = 15

We can see that,

From (1) and (2)

150  + 2W = 150 + 2 x 15 = 150 + 30 = 180

195 - 1W = 195 - 1 x 15 = 195 - 15 = 180

Thus the number of weeks will the boys weigh the same amount is 15 weeks and the weight is 180 lb.

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