Alexandra keeps a record of her fixed and total expenses each month. Last month, she spent a little more than usual on variable

Response:

B. 255 m

Detailed breakdown:

utilize similar triangles

L / 60 = 85 / 20

L = (85 * 60) / 20

L = 255 m

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:

1.5 miles per hour

Step-by-step explanation:

Multiply 132 feet by 60 seconds to get 7920. Subtract 5280, the number of feet in a mile, leaving you with 1 mile and an additional 2640 feet, which amounts to half a mile.

Answer:

The formula to determine the distance Jane's trainer bikes is .

Detailed explanation:

A diagram has been included for clarity.

Known values:

Distance biked to the south = 16 miles

Distance ran west = 12 miles

We need to determine the distance covered by Jane's trainer.

Solution:

Let the biking distance be represented by 'x'.

We will assume it forms a right-angled triangle.

According to the Pythagorean theorem, it states that;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides."

When set in equation form, this gives us;

Thus, the equation representing the distance biked by Jane's trainer is .

Upon solving, we find;

Consequently, Jane's trainer covers a distance of 20 miles.

Answer:

D.

Step-by-step explanation:

This function is piece-wise, meaning you will have two equations along with distinct domains. The equation x squared plus 3 illustrates a parabolic curve, while x plus 4 is depicted as a linear function. There is a specific reason why the point on the parabola is open at x equals 4; this signifies that the value does not satisfy the equation. Therefore, x cannot equal 4 for the parabola, so its domain is x less than 4. The closed point on the linear function indicates that when x is 4, it is part of the solution for that equation and graph. Consequently, the domain for the linear function is x greater than or equal to 4. Hope this clarifies things!