Find the Least Common Multiple of these two monomials:

9a^2bc^3 and 30ab^2c^3

9a^2b^2c^3
3ab^3
90ab^3
90a^2b^2c^3

Final answer:

To determine how much pasta salad is needed for 49 people when 5 pounds serves 14 people, calculate the proportion based on ounces, resulting in 17.5 pounds needed for 49 people.

Explanation:

If 5 pounds of pasta salad serves 14 people, the amount needed for 49 people can be calculated by setting up a proportion because the number of people and the amount of pasta salad are directly proportional. First, we convert 5 pounds of pasta salad to ounces, since the standard conversion is 1 pound = 16 ounces, so 5 pounds equals 80 ounces.

Next, we set up the proportion as follows:

14 people → 80 ounces of pasta salad

49 people → x ounces of pasta salad

To solve for x, you cross-multiply and divide:

14x = 80 * 49

x = (80 * 49) / 14

x = 280 ounces

Thus, you will need 280 ounces of pasta salad, which is equivalent to 17.5 pounds (since 280 ounces divided by 16 ounces per pound equals 17.5 pounds). Therefore, for a picnic with 49 people, you should bring 17.5 pounds of pasta salad.

Answer:

  The equation has one solution

Step-by-step explanation:

Add 4y +1 and divide by 7.

  3y -1 = 13 -4y

  7y = 14

  y = 2

There is one solution.

Answer:

equal to 2

Step-by-step explanation:

The coordinates of the image after dilation with a scale factor of 1.5 are A(-12, -12), B(6, -3), and C(3, 3).

To find the coordinates of the image after a dilation, we need to multiply the coordinates of each point by the scale factor. The scale factor is 1.5, so multiplying the x-coordinate and y-coordinate of each point by 1.5 will give us the new coordinates.

For point A (-8, -8), the new x-coordinate is -8 * 1.5 = -12 and the new y-coordinate is -8 * 1.5 = -12. So the image of A is (-12, -12).

Using the same process, we can find the new coordinates for points B and C as well. The correct answer is option 2: A(-12, -12), B(6, -3), C(3, 3).

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n = necklace

b = bracelet

n +b =120

n = 120-b

3.50n + 2.50b = 330

11n + 5b = 880

3.5(120-b) +2.5b=330

420-3.5b + 2.5b = 330

420 -b = 330

-b = -90

B =90

N = 30

3.5*30= 105

2.5*90 = 225

225 +105 = 330

11*30 = 330

90*5 = 450

450 +330 = 780

90 bracelets and 30 necklaces

Answer:

[tex]V=630ft^3[/tex]

Step-by-step explanation:

This solid is composite by a triangular prism and a rectangular prism. So, let:

[tex]V_1=Volume\hspace{3}of\hspace{3}the\hspace{3}rectangular\hspace{3}prism\\V_2=Volume\hspace{3}of\hspace{3}the\hspace{3}triangular\hspace{3}prism[/tex]

Hence, the volume of the composite solid is:

[tex]V=V_1+V_2[/tex]

The volume of the rectangular prism is given by:

[tex]V_1=l*w*h[/tex]

Where:

[tex]l=length=8ft\\w=width=7.5ft\\h=height=7ft[/tex]

So:

[tex]V_1=8*7.5*7=420ft^3[/tex]

The volume of the triangular prism is given by:

[tex]V_2=\frac{1}{2} l*b*h[/tex]

Where:

[tex]l=Distance\hspace{3} between\hspace{3} the\hspace{3} triangular \hspace{3}faces=8ft\\b=length\hspace{3}of\hspace{3} one\hspace{3} side \hspace{3}of\hspace{3} the \hspace{3}triangle=7.5ft\\h=length \hspace{3} of \hspace{3} an \hspace{3}altitude \hspace{3} drawn \hspace{3} to \hspace{3} that \hspace{3}side=7ft[/tex]

So:

[tex]V_2=\frac{8*7.5*7}{2} =210ft^3[/tex]

Therefore:

[tex]V=420ft^3+210ft^3=630ft^3[/tex]

Lisa earned $385 in 10 days, which is highest among others.

Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.

Given that,

Money earned by Rita in one day = $20,

Therefore, money earned by Rita in 10 days = 10 x 20 = $200

Money earned by Lauren on first day = $2

Second day = $3,

Third day = $4, and so on....

Total money earned in 10 day by Lauren = 2 + 3 + 4 + .....11 = $65

Money earned by Richard in one day = $25,

Therefore, money earned by Richard in 10 days = 25 x 10 = $250

Lisa earned $1 for first day, $2 for 2nd day, $4 for 3rd day and $8 for 4th day and so on..

Total money earned by Lisa in 10 days = 1 + 2 + 4 + 8 + ........

= 10 x (10+1) x (20+1) / 6 = 385

Maximum amount is earned by Lisa, which is $385.

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The correct mathematical equation representing Michael's total cost at the state fair, considering his base fee and cost per ride, is y=4x+30.

The question centers around linear equations, a subject in mathematics. In this context, Michael's total cost of his trip to the state fair is calculated by his base fee, 30 dollars, plus the number of rides he goes on multiplied by the cost per ride, 4 dollars. The correct equation representing this situation would be y=4x+30, where y is the total cost, x is the number of rides he goes on, and 30 is the flat entry fee.

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Answer:

The cost of "s" shirts and "t" ties = $20s + $12t

Step-by-step explanation:

Given:

Shirt cost = $20 each

Ties cost = $12 each.

The number of shirts represented by "s" and the number of ties represented by "t"

Cost = $20*the number of shirts + $12*the number of ties

so, the cost of "s" shirts and "t" ties = 20s + 12t

Example:

If we want to find the cost 2 shirts and 3 ties, we need to plug s = 2 and t= 2 in the above expression.

The cost of 2 shirts and 3 ties = 20*2 + 12*3

= 40 + 36

= $76

The cost of 2 shirts and 3 ties is $76.

Solution:

0 is the correct option.

Explanation:

We have been given the number  π, which is an irrational number. The value of  π is 3.14

Now, let us multiply the number  π with the given numbers in option and see what type of number we get.

[tex]0\times \pi = 0\\\\1\pi \times \pi = \pi^2\\\\-\pi \times \pi = -\pi^2\\\\2\times \pi = 2\pi[/tex]

Among all the above result, only 0 is a ration number.

Hence, when we multiply 0 with  π then the result will be a rational number.

Answer:

A/0

Step-by-step explanation:

Answer:

[tex]3.22\times 10^{8}[/tex]

Step-by-step explanation:

In scientific notation we write a very large or very small number as the product of a number between 0 to 9 and the exponent of 10,

Here, the given number,

[tex]322,000,000[/tex]

[tex]=3.22\times 10^{8}[/tex]

Hence, the scientific notation of the given number is [tex]3.22\times 10^{8}[/tex]

A set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy. In your  case, the set builder notation  {x l x > } means that the set consists of all elements that are greater than.

Consider number line. Plot the point as unfilled circle that goes after > sigh and shade the ray that goes from this point to the right. Then another way to represent this solution is

( ,∞).

Answer: correct choice is C

Final answer:

The correct alternative representation of the set builder notation { x | x > A } in interval notation is ( A, ∞ ), which includes any number greater than A up to positive infinity, but does not include A itself.

Explanation:

The solution to an inequality given in set builder notation as { x | x > A } can be represented in interval notation in several ways, depending on the specifics of the inequality. If the set includes all numbers greater than A, but does not include the number A itself, the interval notation is ( A, ∞ ). This means that the solution set includes any number greater than A, extending to positive infinity, but it does not include A because of the use of the parenthesis.

Interval notation such as [ A, ∞ ) would mean that the set includes the number A and extends to positive infinity. However, this is not the correct representation if the initial set builder notation specifies that x is greater than A, not greater than or equal to A. Similarly, intervals ( -∞ , A ] and ( -∞ , A ) represent sets that include numbers less than or equal to A, and less than A, respectively, which again isn't the case here.

Therefore, the correct answer is 2nd option

Final answer:

The angle of rotation of a regular octagon is 45°, and the measure of an interior angle of a regular octagon is 135°.

Explanation:

The angle of rotation for a regular octagon can be found by dividing the full circle of 360 degrees by the number of sides, which is 8 for an octagon. Therefore, the angle of rotation is 360° / 8 = 45°.

The measure of an interior angle of a regular octagon is determined by the formula (n-2) × 180° / n, where 'n' is the number of sides. Substituting 8 for 'n', the measure of an interior angle is (8-2) × 180° / 8 = 6 × 180° / 8 = 135°.

The next two terms of the sequence 0.3, -0.09, and 0.0027 are -0.00027 and 0.000027, achieved by continuously multiplying each term by -1/10.

To find the next terms of the sequence 0.3, -0.09, and 0.0027, you need to understand the pattern in the sequence. Here, each term is multiplied by -1/10 (or -0.1) to get the next term. So, to find the next term, we multiply the last given term (0.0027) by -1/10, which gives -0.00027. Therefore, the fourth term of the sequence is -0.00027. For the fifth term, we do the same process and multiply -0.00027 by -1/10, to get 0.000027. So, the next two terms in the sequence are -0.00027 and 0.000027.

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Answer: The answer is 2√37 units.

Step-by-step explanation:  Given that the line segment YZ has endpoints Y(0, 5) and Z(12, 3). We are to find the length of the line segment YZ.

The length of YZ will be the distance between the endpoints Y and Z.

The distance between Y and Z will be given by

[tex]YZ=\sqrt{(0-12)^{2}+(5-3)^2}=\sqrt{144+4}=\sqrt{148}=2\sqrt{37}=12.16\sim 12.1.[/tex]

Thus, the length of YZ is 12.1 units.

Millimeters are preferred for measuring a penny because they offer greater precision and accuracy, enabling us to measure the dimensions of small objects like a penny with closer to exact measurements.

It is preferable to measure a penny in millimeters because millimeters provide a more precise and accurate measurement due to their smaller size compared to centimeters. The standard width of a penny is 1.9 cm, which is equivalent to 19 mm. Since scientists have established the convention of using the degree of precision dependent on the measuring device, millimeters are more appropriate for small objects like a penny to get an accurate measurement. A millimeter allows us to report the size of the penny to the nearest millimeter, facilitating a precise estimation.

When choosing a unit of measurement, one must consider the object's size and the necessary precision. For very small objects like a paper clip or a penny, millimeters would give the most accurate measurement, compared to centimeters, which are 10 times bigger and could provide a less accurate measurement. Therefore, for tasks requiring precise measurements of small dimensions, millimeters are preferred.

Answer:

50 miles per hour

Step-by-step explanation:

200 ÷ 4 = 50

200 = miles in 4 hours

50 = miles in 1 hour

Final answer:

The speed of the car is calculated by dividing the distance traveled (200 miles) by the time taken (4 hours), resulting in a speed of 50 miles per hour.

Explanation:

To determine the speed of the car, we use the formula for speed, which is distance traveled divided by the time taken. In this case, the car travels 200 miles in 4 hours. Plugging in numbers, we calculate the speed as follows:

Therefore, the speed of the car is 50 miles per hour (mph).

Answer:

[tex](-3,-6)[/tex]

and

[tex](-3,2)[/tex].

Step-by-step explanation:

The given point is [tex](-3,0)[/tex].

If we want to use a point to create a line with an undefined slope through [tex](-3,0)[/tex], then that point must have the same x-coordinates as the given point.

Since the given point, [tex](-3,0)[/tex] has an x-coordinate of [tex]-3[/tex], we check all the points that have an x-coordinate of -3.

The correct answers are;

[tex](-3,-6)[/tex]

and

[tex](-3,2)[/tex].

These point will make the slope undefined, because it will result in division by zero.