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7 days ago

The scatter plot below can be used to find the approximate rate at which water flows through a garden hose. The line of best fit

for the scatter plot can be described by the equation y = 4/5x. If the rate, in gallons per minute, continues, approximately how many gallons of water will flow from the hose in 45 minutes?
36
39
56
24

Mathematics

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Tags are placed to the left leg and right leg of a bear in a forest. Let A1 be the event that the left leg tag is lost and the e

babunello [11817]

Answer:

0.75 = 75% chance that only one tag is lost, provided at least one tag is lost

Step-by-step explanation:

Independent events:

If A and B are independent events, then:

$P(A \cap B) = P(A)*P(B)$

Conditional probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

Here

P(B|A) refers to the probability of event B occurring, given that event A has occurred.

$P(A \cap B)$ is the probability of both A and B occurring together.

P(A) is the probability of event A occurring.

In this scenario:

Event A: At least one tag is missing

Event B: Only one tag is missing.

Each tag has a 40% likelihood of being lost, which is equal to 0.4.

Probability of at least one tag missing:

The events can be considered as either no tags are missing or at least one is. Their probabilities sum to 1. Thus

$p + P(A) = 1$

p is the probability that none are lost. Each tag has a 60% = 0.6 chance of not being lost, and since they are independent,

p = 0.6*0.6 = 0.36

Then

$P(A) = 1 - p = 1 - 0.36 = 0.64$

Intersection:

The intersection of at least one lost (A) and exactly one lost (B) is precisely one lost.

Then

Probability of at least one lost:

The first being lost (0.4 chance) and the second not lost (0.6 chance)

The first not being lost (0.6 chance) and the second lost (0.4 chance)

$P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48$

Calculate the probability that exactly one tag is lost, given that at least one tag is lost (round to two decimal places).

$P(B|A) = \frac{0.48}{0.64} = 0.75$

0.75 = 75% likelihood that precisely one tag is lost, assuming at least one tag is lost

8 0

2 months ago

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the h

babunello [11817]

Answer:

The height of the triangular pyramid base is represented by s√3/2 units.

Step-by-step explanation:

This question focuses on calculating the height of the equilateral triangle at the base of the oblique pyramid.

According to the question, the equilateral triangle side has a length of a units.

Let’s review some properties of equilateral triangles:

a. All sides are identical in length, in this case, side s represents all sides.

b. All angles measure the same, at 60 degrees each.

c. Drawing a perpendicular line from the top vertex to the base divides the triangle into two right triangles, which have angles of 60 and 30 degrees, respectively.

To find the height of this triangular base, we can utilize either of the two right-angled triangles.

Recall the angles of 30, 60 and the side length s.

For height h calculation, trigonometric functions will assist us.

The relevant trigonometric relationship involves the sine of the angle (where side length s is the hypotenuse and height h is the opposite side relative to the 60-degree angle).

Thus, we can express this as:

Sine of an angle = opposite side length/hypotenuse length

sin 60 = h/s

Consequently, h = s sin 60.

In surd form, this yields:

sin 60 = √3/2.

Therefore, we find:

h = s * √3/2 = s√3/2 units.

3 0

2 months ago

day and night kennel charges $20 per day plus a food fee of $15 to board a pet. home away from home kennel charges $30 per day p

PIT_PIT [12445]

Let n denote the number of days and C the total cost; Charges by Day and Night kennel, C=15+20n Charges by Home Away from Home; C=5 + 30n The resulting system of equations would be; C=15+20n C=5+30n

8 0

1 month ago

Read 2 more answers

A special shape is 2.02 m long and 1.22 m wide. A double row of tiles makes a border . Each tile is 2cm by 2cm. How many tiles a

Svet_ta [12734]

Response:

6.48

Detailed explanation:

The calculation required to determine the number of tiles for the border is presented below:-

$= 2 \times (length + breadth)$