In a wooded area, you randomly select 10 trees and find that 3 are tagged. You conclude that there is a 30% probability of randomly selecting a tagged tree.

A. Empirical
B. Theoretical

Therefore, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

A car is traveling at a speed of [tex]75[/tex] km/h.

As we know,

[tex]1km=1000m[/tex]

[tex]1h=60s[/tex]

So,

[tex]75[/tex] km/h=[tex]\frac{75(1000)}{3600}[/tex] m/s

[tex]=\frac{75000}{3600}\\\\[/tex]

Hence, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

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[tex] p\%=\dfrac{p}{100}\to 75\%=\dfrac{75}{100}=0.75\\\\n-the\ number\\\\the\ equation:\\\\n+0.75n=80\\\\1.75n=80\ \ \ \ |:1.75\\\\n=\dfrac{80\cdot100}{1.75\cdot100}\\\\n=\dfrac{8000}{175}\\\\n=\dfrac{8000:25}{175:25}\\\\n=\dfrac{320}{7}\\\\n=45\dfrac{5}{7} [/tex]

To determine how much hardener is required for 16 containers of resin, multiply 55 mL by 16 to get 880 mL, and then convert this to liters by dividing by 1,000, resulting in 0.88 liters of hardener needed.

To determine how much hardener should be added to 16 containers of resin, we must multiply the amount needed for one container by the number of containers. The formula given states that 55 mL of hardener is required for each container of resin. To find the total amount for 16 containers, we perform the following multiplication:

Therefore, 0.88 liters of hardener should be added to 16 containers of resin.

Final answer:

To determine the amount of hardener needed for 16 containers of resin, multiply 55 mL by 16 to get 880 mL and then convert that to liters, resulting in 0.88 liters of hardener.

Explanation:

To find out how much hardener should be added to 16 containers of resin, where each container requires 55 mL of hardener, you need to do a simple multiplication operation. Multiply the amount of hardener needed for one container by the number of containers:

Therefore, you should add 0.88 liters of hardener to the 16 containers of resin.

Answer:

Sure, I'd be happy to show you how to simplify this expression. Here are the steps:

1. In this expression, we have three numbers that are being multiplied together, 2, x^2, and y, and the entire product is raised to the power of 3.

2. Let's take each part of the product individually and raise them to the power of 3.

  For the first part, 2 raised to the power of 3: this gives us 8, since 2 * 2 * 2 equals 8.

3. The next part is [tex]x^2[/tex] raised to the power of 3. When raising a power to another power, we multiply the powers together. Therefore, (x^2)^3 becomes x^(2*3), which can be simplified to x^6.

4. Finally, y raised to the power of 3 remains as y^3.

5. So, when we put together all three parts, we obtain the simplified expression, and (2x^2y)^3 simplifies to 8x^6y^3.

So, the simplified expression for (2x^2y) ^3 is 8x^6y^3.

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Answer:

The value of x is 12 in

Step-by-step explanation:

Given the right angled triangle having sides 5 in , 13 in and x in

We have to find the value of x.

By applying Pythagoras theorem, we get

[tex]Hypotenuse^{2} = Base^{2} + Perpendicular^{2}[/tex]

⇒ [tex]13^{2}=x^{2}+5^{2}[/tex]

⇒  [tex]169=25+x^{2}[/tex]

⇒  [tex]x^{2} = 144[/tex] ⇒ x=12 in

Hence, length of base is x in i.e 12 in

The linear function that represents this graph is given by:

y = 300 - 0.6667x.

A linear function is modeled by:

y = mx + b

In which:

From the graph, when x = 0, y = 300, hence the y-intercept is of b = 300. The amount decays to 0 when the x-intercept is of x = 450, hence the slope is given by:

m = -300/450 = -0.6667.

Which means that the equation is:

y = 300 - 0.6667x.

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Answer:

is greater for data set 2 ; is greater for data set 2

Step-by-step explanation:

The range is found by subtracting the highest and lowest value.  The range of the first plot would be

34-21 = 13.

The range of the second plot would be

36-12 = 24.

The mean is found by adding together all of the data points and dividing by the number of data points.  For the first plot, the sum of the data is 274 and there are 10 data points; this makes the mean 274/10 = 27.4.

For the second plot, the sum of the data is 280.5 and there are 10 data points; this makes the mean 280.5/10 = 28.05.

The range is greater for data set 2.

Then mean is greater for data set 2.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Consider the data plot for 13 to 15 years olds.

Mean = Average of the values

          = (21 + 24 + 26 + 27 + 27 + 28 + 28 + 28 + 31 + 34) / 10

          = 27.4

Range = Maximum value - Minimum value

           = 34 - 21

          = 13

Consider the data plot for 16 to 18 years olds.

Mean = Average of the values

          = (12 + 21 + 28 + 28 + 28 + 28 + 30.5 + 34 + 35 + 36) / 10

          = 28.05

Range = Maximum value - Minimum value

           = 36 - 12

          = 24

Hence the range and mean are greater for data set 2.

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