A vertical pole, 40 feet tall, casts a shadow onto the ground. If the angle of elevation from the tip of the shadow on the groun

The "successful" area is half the size of the overall triangle, thus using the concept of similar triangles, the likelihood that the area of triangle XYD does not exceed 12 is 1/4.

Answer:

a)

The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.

b)

This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.

c)

For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:

Step-by-step explanation:

Previous concepts

Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.

The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.

Part a

Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:

Where and

We seek the probability:

The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:

By applying this formula, we can find the probability:

Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.

Part b

This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.

Part c

In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:

The total number of bills and coins is 14.

Step-by-step explanation:

To minimize the count of bills and coins, start with the largest denominations that fit within the amount.

The change due is $39.49.

Start with:

-$20 bill (largest under $39.49)

Remaining: $19.49

-$10 bill (largest under $19.49)

Remaining: $9.49

-$5 bill (largest under $9.49)

Remaining: $4.49

Then:

4 × $1 bills (to cover $4.49)

Remaining: $0.49

-$0.25 coin (quarter)

Remaining: $0.24

2 × $0.10 coins (dimes)

Remaining: $0.04

4 × $0.01 coins (pennies)

The final composition includes:

1 twenty-dollar bill

1 ten-dollar bill

1 five-dollar bill

4 one-dollar bills

1 quarter

2 dimes

4 pennies

Totaling 14 pieces.

Answer:

0.40 feet

Step-by-step explanation:

For the first scenario, a 50-foot building casts a shadow of 1 foot. Let the angle of elevation of the sun from the shadow be denoted as θ.

Then:

Tan θ =

Tan θ =

Tan θ = 50

⇒ θ = 50

      = 88.8542

      =

The elevation angle is roughly .

For a 20-foot pole,

Tan θ =

Tan =

x =

 = 0.4015

 = 0.40 feet

The length of the pole's shadow is 0.40 feet.

Answer:

Please refer below.

Step-by-step explanation:

Given points:

• S(-3,6),T(0,7),U(1,4),and V(-5,2)

Translation rule:

• (x,y) → (x+7,y-9)

New coordinates after applying the rule:

• S'(4, -3), T'(7, -2), U'(8, -5), V'(2, -7)

For the graph, see attached.

The trapezoid highlighted in blue is STUV while the red trapezoid is S'T'U'V'