Multiply and simplify. 2x^4yx⋅6xy^2z^3

a) 12x^{6}y^{3}z^{3}
b) 12(xyz)^{12}
c) 12x^{4}y^{2}z^{3}
d) 8x^{6}y^{3}z^{3}

Final answer:

To decide the better purchase between two sizes of shampoo, the cost per ounce is calculated, showing that the 18oz option at $0.22 per ounce is more economical than the 24oz option at $0.25 per ounce.

Explanation:

To determine which shampoo option is the better buy, we calculate the cost per ounce for each option. Cost per ounce is calculated by dividing the total cost of the product by the total number of ounces.

For the 18oz shampoo at $3.99, cost per ounce = $3.99 / 18oz = $0.22 per ounce.

For the 24oz shampoo at $5.99, cost per ounce = $5.99 / 24oz = $0.25 per ounce.

The 18oz shampoo at $0.22 per ounce is the better buy compared to the 24oz shampoo at $0.25 per ounce because you are paying less per ounce.

Answer:

We have been given the two numbers:

[tex]3.05 \cdot 10^{-3}[/tex]

And [tex]8.92\cdot 10^{6}[/tex]

[tex]x^{-a}=\frac{1}{x^a}[/tex]

[tex]10^{-3}=\frac{1}{10^3}=\frac{1}{1000}[/tex]

So, [tex]3.05 \cdot 10^{-3}=\frac{3.05}{1000}[/tex]

[tex]\Rightarrow 0.00305[/tex]

And [tex]8.92\cdot 10^{6}=\frac{892}{100}\cdot {1000000}[/tex]

[tex]892\cdot 10000[/tex]

[tex]\Rightarrow 8920000[/tex]

[tex]3.05 \cdot 10^{-3}=0.00305[/tex]

[tex]8.92\cdot 10^{6}=8920000[/tex]

Answer:

Step-by-step explanation:

Mark make $22,260 including his base salary and the year-end bonus.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Mark base salary = $21,000

And, He got 6% ear-end bonus based on his salary.

Now,

Find the including his base salary and the year-end bonus as;

Since, Mark base salary = $21,000

And, He got 6% ear-end bonus based on his salary.

So, The bonus = 6% of $21,000

                       = 6/100 x 21,000

                       = 1,260

Thus, Total salary = $21,000 + $1,260

                           = $22,260

Thus, Mark make $22,260 including his base salary and the year-end bonus.

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Answer:

B) [tex]\displaystyle f(x) = -3[/tex]

Step-by-step explanation:

[tex]\displaystyle y ← f(x) \\ \\ y + 3 = 0; y = -3 \\ \\ f(x) = -3[/tex]

Answer : The value of 'x' is [tex]\frac{1}{2}[/tex]

Step-by-step explanation :

As we know that,

The perimeter of square = 4a

The perimeter of equilateral triangle = 3s

('a' is the side square and 's' is the side of equilateral triangle)

Given:

Side of square = a = 2x

Side of equilateral triangle = s = (2x+1/3)

As per question, the square and the triangle have the same perimeter. That means,

Perimeter of square = Perimeter of equilateral triangle

4a = 3s

Now put the value of 'a' and 's', we get the value of 'x'.

[tex]4\times (2x)=3\times (2x+\frac{1}{3})[/tex]

[tex]8x=6x+1[/tex]

[tex]8x-6x=1[/tex]

[tex]2x=1[/tex]

[tex]x=\frac{1}{2}[/tex]

Therefore, the value of 'x' is [tex]\frac{1}{2}[/tex]

When two forces act on an object with opposite directions and equal magnitudes, the net force can be zero, leading to equilibrium. This state of equilibrium ensures no acceleration in any direction. Internal forces within a system always occur in opposite pairs, resulting in a net internal force of zero.

Net Force Must Be Zero: When an object has two forces acting on it, the net force can equal zero if the forces are equal in magnitude but opposite in direction, canceling each other out. This results in a balanced force system, leading to equilibrium.

Examples of Equilibrium: One example is a car moving at a constant speed on a highway due to balanced forces. In static equilibrium, both the net force and net torque on an object must be zero, showing no acceleration in any direction.

Internal Forces: Internal forces within a system always appear in equal and opposite pairs, resulting in a net internal force of zero within the system.

75% of secure hike emergency radios are likely to play 30 minutes or longer after 30 cranks, while only 50% of streamline crank radios are likely to play 30 minutes or longer after 30 cranks.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that Azul performed an experiment to determine which crank powered radio works best he crank 15 randomly selected radios of each branch 30 times at the same speed.

He measured how long the radio played in minutes before running out pal the results of the experiment are displayed in the box plot.

The sample results show that the crank powered radio of Branch A had a slightly higher average play time than the crank powered radio of Branch B, with a median play time of around 9 minutes and a range of 4-16 minutes.

75% of secure hike emergency radios are likely to play 30 minutes or longer after 30 cranks, while only 50% of streamline crank radios are likely to play 30 minutes or longer after 30 cranks.

Hence, 75% of secure hike emergency radios are likely to play 30 minutes or longer after 30 cranks, while only 50% of streamline crank radios are likely to play 30 minutes or longer after 30 cranks.

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Azul performed an experiment to determine which crank powered radio works best. He cranked 15 randomly selected radios of each brand 30 times at the same speed and measured how long the radios played in minutes before running out of power. The result of the experiment is displayed in the box plot below.

Secure hike emergency radio 4.0 21,22,24,25,25,25,25,26,27,29,30,30,30,30,33

Streamline radio 25,25,27,28,29,30,30,30,34,36,36,38,39,42

A. 50% of streamline crank radios are likely to play 30 minutes or longer after 30 cranks, while only 25% of secure hike emergency radios ARE LIKELY to play 30 minutes or longer after 30 cranks.

B. 75% of secure hike emergency radios ARE LIKELY to play 30 minutes or longer after 30 cranks, while only 50% of streamline crank radios ARE LIKELY to play 30 minutes or longer after 30 cranks.

C. 100%of x- streamline crank radios ARE LIKELY to play 30 minutes or longer after 30 cranks, while only 25% of secure hike radios ARE LIKELY to play 30 minutes or longer after 30 cranks.

Given is a square pyramid with a base length of 5 centimeters and a height of 6 centimeters.

The volume formula of square pyramid is given by :-

[tex] volume = \frac{1}{3} (base\; area)(height) [/tex]

Base area would be a square of side length equal to 5 centimeters.

Area of square = (side)² = 5 × 5 = 25 squared centimeters.

Now, volume of square pyramid = [tex] \frac{1}{3} (25)(6) [/tex] = 50 cubic centimeters.

So, final answer is 50 cubic centimeters.

Answer: c for apex

Step-by-step explanation:

Answer:c is correct

Step-by-step explanation:

Answer:

All students in each grade.

Step-by-step explanation: This is the answer that givs the most variablity. Your welx if its correct :)

Juanita keeps 25% of the profit from her ice cream shop.

The shop makes $750 per month.

We have to find how much money Juanita will keep.

By the given condition,

Juanita will keep 25% of $750 profit

Now 25% of $750 is 25 /100 * 750

= 18750/100

= $187.50

Therefore Juanita will keep $187.50 of her total profit of $750 per month.

Hope this helps..!!

Thank you :)

1. The value of x is 3.96

2. The value of x is 3.75

Similar triangles are triangles with equal corresponding side ratios and equal corresponding angles.

For two triangles to be Similar, the ratio of their corresponding sides must be equal.

Using similar triangles theorem;

1. x /6 = 3.3/5

5x = 19.8

x = 3.96

2. x/1.5 = 10/4

4x = 1.5 × 10

4x = 15

x = 15/4

x = 3.75