Which table shows a function that is decreasing only over the interval (–1, ∞)? A 2-column table with 6 rows. The first column i

Answer:

(a) 6 units

(b) 4 units

(c) 7 units

(d) 9.22 units

(e) 7.21 units

(f) 8.06 units

Step-by-step explanation:

The distance between two points, (x₁, y₁, z₁) and (x₂, y₂, z₂), can be calculated using;

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

According to the problem;

(a) The distance from (4, -7, 6) to the xy-plane

The xy-plane corresponds to where z equals 0, so

xy-plane = (4, -7, 0).

Thus, the distance d is calculated from (4, -7, 6) to (4, -7, 0)

d = √[(4 - 4)² + (-7 - (-7))² + (0 - 6)²]

d = √[(0)² + (0)² + (-6)²]

d = √(-6)²

d = √36

d = 6

Thus, the distance to the xy-plane is 6 units

(b) The distance from (4, -7, 6) to the yz-plane

The yz-plane is located where x is 0, hence

yz-plane = (0, -7, 6).

So, the distance d is from (4, -7, 6) to (0, -7, 6)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 6)²]

d = √[(4)² + (0)² + (0)²]

d = √(4)²

d = √16

d = 4

Thus, the distance to the yz-plane is 4 units

(c) The distance from (4, -7, 6) to the xz-plane

The xz-plane exists where y is 0, meaning

xz-plane = (4, 0, 6).

The distance d from (4, -7, 6) to (4, 0, 6)

d = √[(4 - 4)² + (-7 - 0)² + (6 - 6)²]

d = √[(0)² + (-7)² + (0)²]

d = √[(-7)²]

d = √49

d = 7

Thus, the distance to the xz-plane is 7 units

(d) The distance from (4, -7, 6) to the x-axis

The x-axis is defined by y and z being 0, which implies

x-axis = (4, 0, 0).

Thus, the distance d is from (4, -7, 6) to (4, 0, 0)

d = √[(4 - 4)² + (-7 - 0)² + (6 - 0)²]

d = √[(0)² + (-7)² + (6)²]

d = √[(-7)² + (6)²]

d = √[(49 + 36)]

d = √(85)

d = 9.22

Hence, the distance to the x-axis is 9.22 units

(e) The distance from (4, -7, 6) to the y-axis

The y-axis is defined where x and z are both 0, thus

y-axis = (0, -7, 0).

Thus, the distance d is from (4, -7, 6) to (0, -7, 0)

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 0)²]

d = √[(4)² + (0)² + (6)²]

d = √[(4)² + (6)²]

d = √[(16 + 36)]

d = √(52)

d = 7.22

Thus, the distance to the y-axis is 7.21 units

(f) The distance from (4, -7, 6) to the z-axis

The z-axis is defined by x and y being 0, which gives

z-axis = (0, 0, 6).

Thus, the distance d is calculated from (4, -7, 6) to (0, 0, 6)

d = √[(4 - 0)² + (-7 - 0)² + (6 - 6)²]

d = √[(4)² + (-7)² + (0)²]

d = √[(4)² + (-7)²]

d = √[(16 + 49)]

d = √(65)

d = 8.06

Thus, the distance to the z-axis is 8.06 units

Response: B

Detailed explanation: This represents a quadratic function due to its parabolic shape, and it intersects the y-axis at 1.

Answer:

The anticipated number of tests required to identify 680 acceptable circuits is 907.

Step-by-step explanation:

For any circuit, there are two potential results: it either passes the test or it fails. The likelihood of passing is independent between circuits. Therefore, we apply the binomial probability distribution to address this scenario.

Binomial probability distribution

This distribution calculates the chance of obtaining exactly x successes across n trials, where x has only two possible outcomes.

To find the expected number of trials to achieve r successes with a probability p, the formula is given by:

Circuits from a specific factory pass a certain quality evaluation with a probability of 0.75.

Thus, to determine the expected number of tests needed for 680 acceptable circuits, let’s denote this as E where r = 680.

The expected number of tests necessary to find 680 acceptable circuits is 907.

Answer:

Red paint will cover 262 square feet

Step-by-step explanation:

The lateral surface area represents the surface area of the sides of the ramp without including the top and bottom surfaces

This ramp has three surfaces

The two sides are triangular with dimensions of length 20 and height 8.5

The back consists of a rectangular shape with length 12 and height 8.5

Step 1: Calculating the Area of Triangle

The area of the triangular side =

The area of the triangle =

The area of the triangle =    

Thus, the area of the triangle = 85 square feet

Area of both triangles =  =  170

Step 2: Finding the Area of Rectangle

Area of rectangle =

therefore,

Area of the rectangular back = = 102  square feet

Step 3: Calculating the total lateral surface area

Overall Lateral Surface Area

= Area of triangles + Area of Rectangle

= 272 square feet

Answer:

Choice C. $6,012

Step-by-step explanation:

We know that

The formula to find the depreciated value is given by

where

V stands for the depreciated value

P represents the original value

r corresponds to the depreciation rate in decimal

t refers to the Number of Time Periods

In this scenario, we have

t = 7 years

P = $8,000

r = 0.04

Plug these into the formula mentioned earlier

Hope this assists you:)