Brandon is shopping at Old Navy during a sale. All shorts are $16 each and all T-shirts are $10 each. He has $100 to spend and w

Response:

Step-by-step breakdown:

Kevin has already gathered five and a half gallons of water for his trip

He understands that he requires a minimum of 20 gallons of water for the journey.

The water is packaged in 32-fluid ounce (quarter-gallon) containers.

1 fluid ounce equals 0.0078125 gallons

32-fluid ounce

Let x represent the number of 32-fluid ounce (quarter-gallon) containers needed to collect at least 20 gallons of water for the trip.

One container holds 0.25 gallons of water

Therefore, x containers hold 0.25x gallons of water

Thus, Kevin's total gallons of water =

Since it is given that he needs at least 20 gallons of water for the trip.

Hence,

Thus, the algebraic inequality representing this scenario is

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

Answer:

a. the class with the highest number of observations.

Step-by-step explanation:

The mode refers to the value within a dataset that appears most frequently. This indicates that it occurs with greater frequency than other values.

In a histogram, the modal class denotes the category that has the most observations, demonstrating that the variables in that category have a higher occurrence than those in others. Consequently, the answer sought is option a.

Answer:

The formula representing the penny's height as a function of time is:

After 7 seconds, the height of the penny will reach 667 feet.

Step-by-step explanation:

The penny experiences free fall.

With an initial velocity of zero and an initial height of h(0)=1,451.

Gravity acts as the acceleration, measured as g=32 ft/s^2.

The model can be initiated by analyzing speed:

Then, the height is expressed as:

The height of the penny at approximately 7 seconds can be calculated as:

After 7 seconds, the penny will stand at a height of 667 feet.

Each LED bulb, along with installation labor, is priced at
.. $6.95 +$3 = $9.95

For 100 bulbs over a span of 10 years, that equals (100*10) = 1000 bulb·years. At $9.95 per bulb, 5 bulb·years are obtained, and thus the projected total cost for 1000 bulb·years is
.. (1000 b·y)*($9.95/(5 b·y)) = $1990

In summary, for a decade, the installation and changes of 200 bulbs in 100 lamps amount to $1990. Therefore, the yearly cost is...
.. $1990/(10 yr) = $199/yr