Y=2x-7 in point slope form

Mario's Pizza delivers pizzas within a 10-mile radius of the restaurant. Their delivery times are Normally distributed with a me

ivanzaharov [21]

Answer:

a) 0.30854

b) 0.21186

c) 0.23468

Step-by-step explanation:

Mario's Pizza delivers pizzas within a 10-mile radius of the restaurant. Their delivery times are Normally distributed with a mean delivery time of 30 minutes and a standard deviation of 10 minutes.

We solve using z score formula.

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Find the probability that a randomly selected customer will have to wait

a) less than 25 minutes

for x < 25 minutes

z = 25 - 30/10

z = -0.5

Probability value from Z-Table:

P(x<25) = 0.30854

b) more than 38 minutes

For x > 38 minutes

z = 38 - 30/10

z = 0.8

Probability value from Z-Table:

P(x<38) = 0.78814

P(x>38) = 1 - P(x<38) = 0.21186

c) between 26 and 32 minutes

For x = 26 minutes

z = 26 - 30/10

z = -0.4

Probability value from Z-Table:

P(x = 26) = 0.34458

For x = 32 minutes

z = 32 - 30/10

z = 0.2

Probability value from Z-Table:

P(x = 32) = 0.57926

The probability that a randomly selected customer will have to wait between 26 and 32 minutes is calculated as:

P(x = 32) - P(x = 26)

= 0.57926 - 0.34458

= 0.23468

4 0

3 years ago

Determine whether the triangles must be congruent. If so, name the postulate or theorem that justifies your answer. If not, expl

Alona [7]

Problem 16)

We use ASA (angle side angle) to show the two triangles are congruent. Why ASA instead of AAS? Because the single pair of sides are between the two angles.

--------------------------------------------

Problem 18)

Similar to problem 16, we'll have two pairs of congruent angles, and a pair of congruent sides. However, the sides are NOT between the two angles. So that means we use AAS in this case.

6 0

3 years ago

A line's slope is 1, and its y-intercept is -10. What is its equation in slope-intercept form?

alexira [117]

Answer: y = 1x -10

Step-by-step explanation:

8 0

3 years ago

1. An observer 80 ft above the surface of the water measures an angle of depression of 0.7o to a distant ship. How many miles is

dybincka [34]

Answer:

1. The distance of the ship from the base of the lighthouse is approximately 1.24 miles

2. a)The horizontal distance the plane must start descending is approximately 190.81 km

b) The angle the plane's path will make with the horizontal is approximately 18.835°

3. The depth of the submarine is approximately 107.51 m

Step-by-step explanation:

The

1. From the question, we have;

The height of the observer above the water = 80 ft.

The angle of depression of the ship from the observer, θ = 0.7°

Let the position of the observer be 'O', let the location of the ship be 'S', let the point directly above the ship at the level of the observer be 'H', we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{HS}{OH}$

$The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{HS}{tan(\theta) }$

HS = The height of the observer = 80 ft.

Therefore, we get;

$The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{80 \, ft.}{tan(0.7^{\circ}) } \approx 6,547.763 \ ft.$

The distance of the ship from the base of the lighthouse ≈ 6,547.763 ft. ≈ 1.24 miles

2. The elevation of the plane, h = 10 km

The angle of the planes path with the ground, θ = 3°

Similar to question (1) above, the horizontal distance the plane must start descending, d = t/(tan(θ))

∴ d = 10 km/(tan(3°)) ≈ 190.81 km

The horizontal distance the plane must start descending, d = 190.81 km

b) If the pilot start descending 300 km from the airport, the angle the plane's path will make with the horizontal, θ, will be given as follows;

From trigonometry, we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length}$

Where the opposite leg length = The elevation of the plane = 10 km

The adjacent leg length = The horizontal distance from the airport = 300 km

$\therefore tan(\theta) = \dfrac{10 \, km}{300 \, km} = \dfrac{1}{3}$

$\theta = arctan\left(\dfrac{1}{3} \right ) \approx 18.835^{\circ}$

The angle the plane's path will make with the horizontal, θ ≈ 18.835°

3. The angle at which the submarine makes the deep dive, θ = 21°

The distance the submarine travels along the inclined downward path, R = 300 m

By trigonometric ratios, we have;

The depth, of the submarine, 'd' is given as follows;

$si(\theta)= \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{d}{R}$

∴ d = R × sin(θ)

d = 300 m × sin(21°) ≈ 107.51 m

The depth of the submarine ≈ 107.51 m

7 0

3 years ago

On the coordinate grid, the graph of y= 3/x-1+3 is shown. it is a translation of y =3/x

crimeas [40]

Answer:

1 unit right and 3 units up

Step-by-step explanation:

The graph of the given function has equation

$f : y = \frac{3}{x - 1} + 3$

This is obtained after translating the graph of

$g : y = \frac{3}{x}$

We can rewrite f in terms g to obtain:

$f(x) = g(x - 1) + 3$

This is a shift to the right by 1 unit and and a shift up by 3 units.

Therefore

$y = \frac{3}{x - 1} + 3$

is a translation of

$y = \frac{3}{x}$

1 unit right and 3 units up

7 0

4 years ago