Write the perimeter of the floor plan shown as an algebraic expression in x.

I believe there are 1,600 students enrolled in metaphysics.

Answer:

The illustration provided shows the graph

Step-by-step explanation:

Let

x ------> number of times Emma cuts the grass

y ------> hours Emma spends babysitting

it is known that

------> represents the inequality of the scenario

The solution is the shaded region above the solid line where both x and y are positive

The equation for the solid line is represented as

The slope of the line is negative

The y-intercept is at the point (the y-value when x is zero)

The x-intercept is at (the x-value when y equals zero)

therefore

The illustration provided shows the graph

Answer:

Gus must fill the cylindrical bucket three times to get it filled for the tank

Step-by-step explanation:

Extracting essential details from the query:-

*** A fish tank has a volume of 4710 inches^3

*** The tank owner utilizes a cylindrical bucket for filling the tank

*** The bucket has a radius of 5 inches and a height of 20 inches

*** We need to compute how many times Gus has to fill the bucket to fully fill the fish tank.

Since the container used for filling the tank is cylindrical, we will apply the formula for finding a cylinder's volume to derive the bucket's volume used for filling the tank.

Volume of a cylinder = π × r^2 × h. The radius of the cylindrical bucket is stated as 5 inches while the height is mentioned as 20 inches.

The bucket's volume is therefore calculated as 3.14 × 5^2 × 20 = 1570 inches^3

Next, it is given that the fish tank’s capacity is 4710 inches^3. To find out how many times the bucket can fill the tank, we must divide the tank's volume by the bucket's volume:

4710/1570 = 3 full buckets.

Thus, Gus has to fill the bucket three times for filling the fish tank completely without spillage.

Answer:

Here’s the response provided

Step-by-step explanation:

Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³

As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in

The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

The total volume of the flask = Volume of the cylinder  + Volume of the sphere = 2.36 + 47.71 = 50.07 in³

<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.

The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

Thus, the new volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume

In order to determine this probability, we calculate using this difference: To obtain these probabilities, it’s possible to utilize normal standard distribution tables, a calculator, or software like Excel. The accompanying figure displays the results achieved. Here’s a detailed breakdown of the steps: Relevant concepts include the normal distribution, which describes a probability distribution that is symmetric regarding the mean, demonstrating that occurrences close to the mean are more likely than those farther away. The Z-score represents a statistical measure illustrating how far a value is from the average of a set, expressed in standard deviations. For our analysis, let X denote the random variable representing weights in a population, with its distribution characterized by: We’re specifically interested in this probability. The most effective approach to address this issue is through the standard normal distribution and the Z-score calculation, expressed as: Applying this formula to our probability provides the following: This allows us to calculate this probability with the provided difference: We use standard distribution tables, a calculator, or Excel for determining these probabilities. The graph illustrates the resulting outcome.