A gold, a silver, and a bronze medal are awarded in an Olympic event. In how many possible ways can the medals be awarded for a

<span>0.002 1/10 of what
=> (1/10)a = 0.002
=> Multiply both sides by 10 to solve for the unknown number, since we need the value whose one-tenth is 0.002.
=> 10 x (1/10)a = 10 x 0.002
=>  a = 0.02

Therefore, 0.002 is one-tenth of 0.02.
To verify, divide 0.02 by 10.
=> 0.02 / 10
=> 0.002
Hence, the solution is confirmed.

</span>

Let x represent the number of pages in the U.S. Tax Code and y denote the pages in the King James Bible.

According to the provided information,
x= y+18,528 ⇒ y=x-18,528
x+y = 21,472 ⇒ x+(x-18,528) = 21,472 ⇒ x+x-18,528 = 21,472 ⇒ 2x= 18,528+21,472 ⇒ 2x = 40,000 ⇒ x=40,000/2 = 20,000 pages

Therefore, the U.S. tax code consists of 20,000 pages.

Answer:

Step-by-step solution:

Leon’s older brother’s height is feet

feet

Because Leon is 1/3 foot shorter than his brother,

Leon’s height =

Convert to like fractions by multiplying numerator and denominator: multiply 3 for the first fraction and 4 for the second.

So, Leon’s height =

feet

Therefore, Leon’s height is feet.

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

Let x represent the number of caps

cost per cap = $6

cost for x caps = 6x

shipping charge = $25

overall budget = $1000

We can set up the following inequality:

Because the total amount cannot exceed 1000, we have

25 + 6x ≤ 1000

6x ≤ 975

x ≤ 162.5

rounding,

x ≤ 163

This means she can purchase a maximum of 163 caps.