An arrow shot into the air is 160t -16^2 feet above the ground t is seconds after it is released. During what period of time is the arrow above 384 feet?

Final answer:

To convert a whole number to a percentage, multiply the number by 100 and add the percent symbol. For instance, converting the whole number 3 to a percentage results in 300%.

Explanation:

How to Convert a Whole Number to a Percentage

To convert a whole number to a percentage, you simply multiply the number by 100 and add the percent (%) symbol to the result. This is because a percentage represents a part per hundred. For example, to convert the whole number 3 to a percentage, you multiply it by 100, which equals 300%. Here's the step-by-step process:

Start with the whole number (e.g., 3).

Multiply the whole number by 100 (3 x 100 = 300).

Add the percent symbol to express the result as a percentage (300%).

This method is a straightforward percentage calculation, turning a whole number into its equivalent percentage form.

Answer:

The model that is most appropriate for the set is:

                Quadratic.

Step-by-step explanation:

Clearly after looking at the graph of the function which is made from the given set of points ; we observe that the graph is similar to a graph of the quadratic function whose vertex is at (0,-2) and also the line x=0 is the axis of symmetry of the graph.

Since, the graph is symmetric to this line.

Hence, the model is:

Quadratic.

Final answer:

The question is related to the mathematics subject area and addresses the high school grade level. It involves understanding the normal distribution, mean, standard deviation, and the application of these concepts in quality control and filling volumes for beverage containers.

Explanation:

The subject of the question relates to the concept of normal distribution, which is a fundamental concept in statistics, a branch of mathematics. The student is provided with the information that beer bottles are filled so that they contain an average of 475 ml of beer, with the amount of beer being normally distributed and having a standard deviation of 8 ml. This scenario involves understanding concepts like mean, standard deviation, and the properties of a normal distribution.

To visualize similar quantities, consider that an eyedropper holds about 1 milliliter, a juice box holds about 25 centiliters (or 250 milliliters), and a soda bottle holds about 1 liter. The provided beer bottle contains roughly half the amount of a typical soda bottle. Knowledge of standard units such as liters and milliliters is essential in this context.

Furthermore, the question can be connected with practical scenarios such as the filling volumes for beverage containers, where manufacturers need to ensure that the bottles and cans contain the labeled amount of liquid. Quality control relies on statistics to test whether the actual amounts meet the desired standards, factoring in variations from measurement processes or filling mechanisms.

In 30 minutes, 250 gallons are filled in the swimming pool. In the same rate in 1 hours (which means 60 minutes), 500 gallons will be filled.

Let x be the number of hours it will take to fill the entire swimming pool which has the capacity of 25,000 gallons.

We need to set up a proportion like given below:

[tex] \frac{Number \; of \; Hours }{Amount \; of\; water \; in\; gallons} =\frac{x}{25,000} =\frac{1}{500} [/tex]

Solving the equation for x:

[tex] \frac{x}{25000} =\frac{1}{500} \\ Multiply \; 25000\; on\; both\; sides\; of\; the \; equation\\ \\ 25000 \times \frac{x}{25000} =\frac{1}{500} \times 25000\\ Simplify \; on \; both \; sides\\ \\ x \; = \; \frac{25000}{500} \; = 50 \; hours [/tex]

Conclusion:

The number of hours that will take to fill the pool is 50 hours !

Answer:

It is 8

Step-by-step explanation:

The six sections would be 1/12

The original number of spokes on the wheel was 36.

The question seeks to determine the original number of spokes on a bicycle wheel, given that the current number is 32 after reducing by 4. To find the original number of spokes, we need to use a simple algebraic equation that adds the removed spokes back to the current number.

Let x represent the original number of spokes. The manufacturer has reduced the number of spokes by 4, so we subtract 4 from the original number to get the current number of spokes. The equation that represents this scenario is:

x - 4 = 32

To find the original number of spokes, we need to solve for x:

x = 32 + 4

x = 36

Therefore, the original number of spokes on the wheel was 36.

Answer:

The equation for new function is [tex]y=\frac{1}{3}|x|[/tex]

Step-by-step explanation:

We have been given the absolute value parent function f(x) = |x| and this function is vertically compressed by a factor 3.

If we multiply the function with a constant (say a) then the parent function will get stretch/compressed vertically.

We have below conditions for vertical stretch and compression.

a > 1 => vertically stretch

0 < a < 1 => vertically compression

Hence, in order to vertical compression by a factor 3, we have to multiply the whole function by 1/3

Therefore, the equation for new function is [tex]y=\frac{1}{3}|x|[/tex]

Answer:

g(x) = 1/3 |x| !

Step-by-step explanation:

I hope this helps!

Final answer:

The total distance walked by someone from home to school and back depends on the distance covered in each direction, for example, if a person walks 2 kilometers to school and 2 kilometers back, the total distance walked is 4 kilometers.

Explanation:

The total distance walked by the guy from his house to school and back depends on the exact distance he covers in each direction. If he walks 2 kilometers to school and 2 kilometers back, then the total distance walked would be 4 kilometers.

Answer:

Step-by-step explanation:

Let's model the cost by the following exponential function: c (t) = (7.50) * (1.035) ^ t Where, c (t): cost of the movie after t years. 7.50: initial cost of the movie in $ 1,035: annual percentage increase due to inflation. t: time in years. for t = 0 We have: c (t) = (7.50) * (1.035) ^ 0 c (t) = (7.50) * (1) c (t) = 7.50 Answer: The graph that best models the function is: GRAPH 2 (from left to right).

Answer:

The volume of the box is 0.09375 inches cube.

Step-by-step explanation:

Given : This box is 3/4 inches long, 1/2 inches wide, and 1/4 inches deep.

To find : What is the volume of the box ?          

Solution :

The dimension of the box is,

Length = [tex]l=\frac{3}{4}[/tex] inches

Breadth = [tex]b=\frac{1}{2}[/tex] inches

Height = [tex]h=\frac{1}{4}[/tex] inches

The formula of volume of the box is

[tex]V=l\times b\times h[/tex]

[tex]V=\frac{3}{4}\times \frac{1}{2}\times\frac{1}{4}[/tex]

[tex]V=\frac{3}{4\times 2\times 4}[/tex]

[tex]V=\frac{3}{32}[/tex]

[tex]V=0.09375in^3[/tex]

Therefore, The volume of the box is 0.09375 inches cube.

The volume of the box is 3/32 cubic inches.

Given

This box is 3/4 inches long, 1/2 inches wide, and 1/4 inches deep.

The volume of the box is given by-product of length, width, and height.

The volume of the box is determined by the following formula;

[tex]\rm Volume \ of \ box =Height\times Width \times length[/tex]

Substitute all the values in the formula;

[tex]\rm Volume \ of \ box =Height\times Width \times length\\\\\rm Volume \ of \ box =\dfrac{3}{4}\times \dfrac{1}{2} \times \dfrac{1}{4}\\\\\rm Volume \ of \ box =\dfrac{3}{32} \ cubic \ inches[/tex]

Hence, the volume of the box is 3/32 cubic inches.

To know more about the Volume of the box click the link given below.

https://brainly.com/question/13749063

Solution: (1) The expression [tex](5\sqrt{3} )^x[/tex]  [tex]\text{ is written as }[/tex] [tex]5^x3^{\frac{x}{2}[/tex].

[tex](5\sqrt{3} )^x=5^x(\sqrt{3} )^x\\(5\sqrt{3} )^x=5^x(3^\frac{1}{2} )^x\\(5\sqrt{3} )^x=5^x3^\frac{x}{2}[/tex]

The value of u is [tex]\frac{x}{2}[/tex].

(2) The expression [tex](\frac{1}{2})^x-3[/tex] is written as [tex]2^{-x}-3[/tex].

[tex](\frac{1}{2})^x-3=(2^{-1})^x-3\\(\frac{1}{2})^x-3=2^{-x}-3[/tex]

The value of u is -x.

(3) The expression [tex]\frac{9}{3\sqrt{3} }[/tex] is written as [tex]\sqrt{3} (2^0)[/tex].

[tex]\frac{9}{3\sqrt{3} }=\frac{9}{3\sqrt{3} }(\frac{\sqrt{3}}{\sqrt{3}} )\\\frac{9}{3\sqrt{3} }=\frac{9(\sqrt{3}) }{3(3) }\\\frac{9}{3\sqrt{3} }=\sqrt{3} \\\frac{9}{3\sqrt{3} }=\sqrt{3}(2^0)[/tex]

THe value of u is 0.

(4)The expression [tex]\frac{16}{3(\sqrt{2^{x}} )}[/tex] is written as [tex]\frac{1}{3}(2^{4-\frac{x}{2}})[/tex].

[tex]\frac{16}{3(\sqrt{2^{x}} )}=\frac{2^4}{3(2^x)^{1/2}}\\\frac{16}{3(\sqrt{2^{x}} )}=\frac{1}{3}(2^{4-\frac{x}{2}})[/tex]

The value of u is [tex]4-\frac{x}{2}[/tex].

Final Answer:

1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]

2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]

3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]

4. [tex]\( \frac{16}{3\sqrt{2^x}} \) in the form \( 2^u \): \( 2^{(2x-4)/3} \)[/tex]

Explanation:

1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]

To express [tex]\( (5\sqrt{3})^x \)[/tex] in the form [tex]\( 3^u \)[/tex], we use the logarithmic property [tex]\( a^{\frac{1}{n}} = n\sqrt[n]{a} \)[/tex]. Applying this, we get [tex]\( 5\sqrt{3} = 3^{\frac{\log_3(5\sqrt{3})}{\log_3(3)}} \)[/tex], and raising it to the power ( x ) yields the desired form.

2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]

To rewrite [tex]\( (1/2)^{x-3} \)[/tex] in the form [tex]\( 2^u \)[/tex], we use the property [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex]. Applying this, we transform the expression to [tex]\( 2^{-(x-3)} \)[/tex], achieving the desired form.

3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]

By canceling out the common factor of 3 in the numerator and denominator, we simplify [tex]\( \frac{9}{3\sqrt{3}} \)[/tex]to [tex]\( 2^{2/3} \), as \( \sqrt{3} = 3^{1/2} \)[/tex].

4. [tex]\( \frac{16}{3\sqrt{2^x}} \)[/tex] in the form [tex]\( 2^u \): \( 2^{(2x-4)/3} \)[/tex]

Applying the property[tex]\( a^{-b} = \frac{1}{a^b} \)[/tex] to the denominator, we simplify [tex]\( \frac{16}{3\sqrt{2^x}}[/tex] to [tex]\( 2^{(2x-4)/3} \)[/tex], achieving the desired form.