The table shows the last holiday destination of 60 people.

This question asks how many distinct pairs of integers multiply to give 18.

(Put another way: how many rectangular dimensions can Jenn make using 18 blocks with height 1.)

The factor pairs of 18 are:

1 x 18
2 x 9
3 x 6

Therefore, Jenn can construct the park model in 3 different ways.

Response:

Step-by-step explanation:

We need to form an equation that illustrates the area that Felicia has covered, denoted as y, in relation to the number of tiles she utilized, represented by x.

Let x= Number of tiles

y=Area occupied by Felicia's tiles

The relationship between x and y is constant. Hence, it follows a direct proportion.

The equation for direct proportion is shown as

Where

k=The value of the ratio of x and y

x and y are variable factors

Here, we have k=9

Substituting the known values into the equation

leads us to

This represents the necessary equation depicting the area Felicia covered, y, in terms of the number of tiles utilized, x.

A typical regular hexagon consists of six equilateral triangles.

One of these is ΔAFM, where each angle measures 60°, so ∡AFM = 60°.

ΔABC is classified as an isosceles triangle, possessing an angle of ∡ABC = 120°, as each internal angle in a regular hexagon measures 120°.

Angles ∡BAC and ∡BCA each equal 30°, summing to 180° in total for the triangle.

Moreover, ∡ACF is congruent to ∡BCA = 30°. Therefore, we can deduce that angle ∡FAC equals 90°. The reasoning for this follows.

Best of luck!!!

The phone rang at exactly 11:59 PM. 

Answer:

Part 1

a) 0.0791

b) 0.000977

c) 0.7627

Part 2

a) 0.049

b) 0.067

c) 0.864 or 0.136 (depending on the exact question wording)

d) 0.806

Step-by-step explanation:

Part 1

Since each question presents 4 possibilities, and only one answer is correct per question.

The likelihood of answering a question correctly = (1/4) = 0.25

The chance of getting a question incorrect = 1 - 0.25 = 0.75

a) The probability of correctly answering the first question as the 5th implies answering the first four incorrectly, and then getting the last one correct.

0.75 × 0.75 × 0.75 × 0.75 × 0.25 = 0.0791

b) The probability that she answers all questions correctly

0.25 × 0.25 × 0.25 × 0.25 × 0.25 = 0.000977

c) Probability that she answers at least one question correctly = 1 - (probability that none are answered correctly) = 1 - (0.75⁵) = 1 - 0.2373 = 0.7627

Part 2

We will utilize the standard normal distribution for this

a) Area under (Z< -1.65) = P(z < -1.65) = 1 - P(z ≥ -1.65) = 1 - P(z ≤ 1.65) = 1 - 0.951 = 0.049

b) Area under (Z > 1.5) = P(z > 1.5) = 1 - P(z ≤ 1.5) = 1 - 0.933 = 0.067

c) P(z > -1.1) or P(z < -1.1)

P(z > - 1.1) = 1 - P(z ≤ -1.1) = 1 - 0.136 = 0.864

P(z < - 1.1) = 1 - P(z ≥ - 1.1) = 1 - P(z ≤ 1.1) = 1 - 0.864 = 0.136

d) |Z|>1.3 = P(-1.3 < z < 1.3) = P(z < 1.3) - P(z < -1.3)

P(z < 1.3) = 1 - P(z ≥ 1.3) = 1 - P(z ≤ -1.3) = 1 - 0.097 = 0.903

P(z < -1.3) = 1 - P(z ≥ -1.3) = 1 - P(z ≤ 1.3) = 1 - 0.903 = 0.097

P(z < 1.3) - P(z < -1.3) = 0.903 - 0.097 = 0.806