Jorden drives to the store at 30 miles per hour. On her way home she averages only 20 miles per hour. If the total driving time

B. and D. represent functions

Answer:

50

Step-by-step clarification:

The equation that represents the total cost is in the format of a linear equation y = mx + c

Here, m signifies the slope of the line

c indicates the y-intercept, showing where the line intersects the y-axis

When the equation y = 150x + 50 is plotted, it will form a linear graph where the y-intercept corresponds to 50, as observed in the standard form of a linear equation.

Answer:

Given that the frog jumps every 10 seconds

   (using digits from a random number table)

• It requires 7 jumps with 2 in the reverse direction (either left or right) for the frog to get off the board in 60 seconds.
• Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
• Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.

Step-by-step explanation:

A frog positioned right at the center of a 5ft long board is 2.5 ft away from either edge.

Every 10 seconds, the frog jumps left or right.

If the frog's jumps are LLRLRL, it will remain on the board at the leftmost square.

If it jumps as LLRLL, it will jump off the board after fifty seconds.

Given that the frog jumps every 10 seconds

   (using digits from a random number table)

• It requires 7 jumps with 2 in reverse direction (either left or right) for the frog to get off the board in 60 seconds.
• Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
• Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.

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

Answer:

Upon solving for y, we find:

By substitution, we have:

Thus, we arrive at:

And for x, we determine:

This gives us a length of 76 and a width of 12.5.

Step-by-step explanation:

We are dealing with a rectangle. The formula for the perimeter is:

Here, x denotes the length and y the width. The following conditions can be established:

Substituting these values yields:

When we solve for y, we find:

By substitution, we obtain:

Thus, we conclude:

The length is found to be 76, while the width measures 12.5.