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2 years ago

2. The seniors at our high school decided to play a prank on the principal by completely filling his office with

Mathematics

2 answers:

Kobotan [32]2 years ago

7 0

Answer:

C. 12,600

Step-by-step explanation:

You can try a rough approximation by finding the volume of the room, finding the volume of one basketball, an dividing the first volume by the second one. This method will give a large estimate since there will be empty space between the balls.

volume of room:

V = L * W * H = 15 * 20 * 10 ft^3 = 3,000 ft^3

volume of one ball:

circumference = 29 in.

From the circumference we find the radius.

circumference = 2(pi)r

2(pi)r = 29 in.

r = (29 in.)/(2pi) = 4.61549 in.

Now we convert inches to feet.

4.61549 in. = 4.61549/12 ft = 0.384624 ft

Now we use the radius of a ball in ft to find the volume of a ball in cubic feet.

V = (4/3)(pi)r^3 = (4/3)(3.14159)(0.384624 ft)^3 = 0.23834 ft^3

Now we divide the volume of the room by the volume of a ball.

number of balls = (3,000 ft^3)/(0.23834 ft^3) = 12,587

The closest answer is C. 12,600

melisa1 [442]2 years ago

3 0

Answer:

idk

Step-by-step explanation:

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On a coordinate plane, 2 trapezoids are shown. The first trapezoid has points A (negative 1, negative 2), B (1, negative 2), C (

Liula [17]

Answer:

The true statements are:

The rule for the translation can be written as T-3, 1(x, y). ⇒ 1st

The rule for the translation can be written as (x, y) → (x - 3, y + 1) ⇒ 4th

Step-by-step explanation:

Let us revise the rule of the translation:

If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)
If the point (x , y) translated vertically up by k units then its image is (x , y + k)
If the point (x , y) translated vertically down by k units then its image is (x , y - k)

The vertices of trapezoid ABCD are:

A (-1 , -2) , B (1 , -2) , C (2 , -5) , D (-2 , -5)

The vertices Of trapezoid A'B'C'D' are:

A' (-4 , -1) , B' (-2 , -1) , C' (-1 , -4) , D' (-5 , -4)

Trapezoid ABCD is translated to form Trapezoid A'B'C'D'

By using the rules of translation above:

∵ A = (-1 , -2) and A' = (-4 , -1)

- The rule of translation is (x , y) → (x + h , y + k)

∵ x = -1 and x + h = -4

∴ -1 + h = -4

- Add 1 to both sides

∴ h = -3

∵ y = -2 and y + k = -1

∴ -2 + k = -1

- Add 2 to both sides

∴ k = 1

The rule of translation is (x , y) → (x - 3 , y + 1)

The trapezoid ABCD has been translated 3 units to the left and 1 unit up

You can check your answer by doing the same steps with the other 3 vertices you will have the same values of h and k

The true statements are:

The rule for the translation can be written as T-3, 1(x, y).

The rule for the translation can be written as (x, y) → (x - 3, y + 1)

9 0

2 years ago

Read 2 more answers

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and

Black_prince [1.1K]

Answer:

0.33411

The probability that a particular criminal trial lasted atleast 24 days is 0.33411

Step-by-step explanation:

The random variable X is normally distributed with a mean of 21 and standard deviation of 7

;

X ~ N(μ = 21 ; σ = 7)

X ~ N(21, 7)

Probability that a trial lasted atleast 24 days :

P(X ≥ 24) :

The standardized score :

Z = (x - μ) / σ ; (24 - 21) / 7 ; 3 / 7 = 0.4286

Hence,

P(Z ≥ 0.4286) = 0.33411

The probability that a particular criminal trial lasted atleast 24 days is 0.33411

6 0

2 years ago

The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the

navik [9.2K]

Answer:

a) 0.019

b) 0.563

c) x = 1.966 hours

Step-by-step explanation:

E(X) = 1

Exponential random variable's probability function is given as

P(X=x) = λ e^(-λ.x)

The cumulative distribution function is given as

P(X ≤ x) = 1 - e^(-λ.x)

a) The time between the arrivals of small aircraft at a county airport that is exponentially distributed.

But the number of planes that land every hour will be obtained using the Poisson distribution formula.

It is the best for discrete systems.

Poisson distribution formula is given as

P(X = x) = (e^-λ)(λˣ)/x!

λ = 1 aircraft per hour.

The probability that more than three aircraft arrive within an hour = P(X > 3)

P(X > 3) = 1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

P(X > 3) = 1 - 0.98101 = 0.01899 = 0.019 to 3 d.p

b) If 30 separate one-hour intervals are chosen, what Is the probability that no interval contains more than three arrivals

Probability of one 1-hour interval not containing more than 3 arrivals = 1 - P(X > 3)

= 1 - 0.01899 = 0.98101

Probability that thirty 1-hour intervals will not contain more than 3 arrivals = (0.98101)³⁰ = 0.5626 = 0.563 to 3 d.p

c) Determine the length of an interval of time (In hours) such that the probability that no arrivals occur during the interval is 0.14

We can now use the cumulative distribution function for exponential random variable for this

P(X ≤ x) = 1 - e^(-λ.x)

P(X > x) = 1 - P(X ≤ x)

P(X > x) = e^(-λ.x)

λ = 1, x = ?,

0.14 = e⁻ˣ

e⁻ˣ = 0.14

In e⁻ˣ = In 0.14 = -1.966

-x = -1.966

x = 1.966 hours

Hope this Helps!!!

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2 years ago

Mary Hernandez had a policy with a $250 deductible which paid 80% of her covered charges less deductible. She had medical expens

Nataly_w [17]

A. the insurance company's payment = $14,392
$18240 - $250 = 17990 x 80% = $14,392

b. <span>the 20% copayment
17990 * 20% = $3598
</span>
<span>c. Mary's total cost
$250 + $3598 = $3848
</span>

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2 years ago

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If we let the domain be all animals, and S(x) = "x is a spider", I(x) = " x is an insect", D(x) = "x is a dragonfly", L(x) = "x

Sonbull [250]

Answer:

The conditional statement "∀x, If x is an insect, then x has six legs" is derived from the statement "All insects have six legs" using "a. existential" generalization

Step-by-step explanation:

In predicate logic, existential generalization is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier in formal proofs.

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2 years ago