Refer to X. Find the length of tangent YZ

Tiana was designing a fish tank that could hold 5,364 ml of water. She's already filled the tank a quarter of the way. How many

gavmur [86]

Answer: 4.023 litres

Step-by-step explanation:

Find out what a quarter of the capacity of the tank is first:

= 5,364 * 1/4

= 1,341 ml

The number of ml left to fill up the tank is:

= 5,364 - 1,341

= 4,023 ml

1 litre = 1,000 ml

4,023 ml in litres = 4,023 / 1,000

= 4.023 litres

7 0

3 years ago

In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that

attashe74 [19]

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let X = number of soldiers killed by horse kicks in 1 year.

The random variable $X\sim Poisson(\lambda = 0.62)$ .

The probability function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,...$

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

= 1 - P (X = 0) - P (X = 1)

$=1-\frac{e^{-0.62}(0.62)^{0}}{0!}-\frac{e^{-0.62}(0.62)^{1}}{1!}\\=1-0.54335-0.33144\\=0.12521\\\approx0.1252$

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: $\lambda=7\times0.62=4.34$

Compute the probability of no deaths in a corps over 7 years as follows:

$P(X=0)=\frac{e^{-4.34}(4.34)^{0}}{0!}=0.01304\approx0.0130$

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

6 0

3 years ago

1. Algebra Find the values for x and y in ABCD.

Marta_Voda [28]

ANSWER

x=12, y=10

EXPLANATION

The diagonals of a parallelogram bisect each other.

This implies that;

AE=EC

$4x = 5y - 2$

$4x - 5y = - 2...(1)$

Also, DE=EB;

$2x = y + 14$

$y =2x - 14...(2)$

Put equation (2) in (1).

$4x - 5(2x - 14) = - 2$

Expand;

$4x - 10x + 70 = - 2$

$- 6x = - 72$

$x = 12$

Put x=2, into equation (2).

$y = 2(12) - 14$

$y = 10$

3 0

3 years ago

Find each f(c) using synthetic substitution. f(x) = –x7 + 4x6 – 4x5 – 6x4 – 3x3 – 6x2 – x – 2; c = –5

zmey [24]

Answer:

f(-5)=149603

Step-by-step explanation:

Synthetic Substitution

It's a method to find the value of a polynomial for a given value of x. The polynomial we want to evaluate is

$f(x) = -x^7 + 4x^6 - 4x^5 - 6x^4 - 3x^3 - 6x^2 - x - 2$

at x=-5

We can, of course, just replace x for -5 and compute the powers, products and sums and subtractions, but we can use the synthetic substitution to avoid the powers, just by multiplying and adding or subtracting. The method requires us to use only the coefficients of the ordered and complete polynomial as shown:

-1 4 -4 -6 -3 -6 -1 -2

Now we set up an arrangement where we can place some operations

-1 4 -4 -6 -3 -6 -1 -2

-5

The second row and a new third row will be filled by computing values as explained below.

The first value of the third row is the very same first coefficient (-1)

-1 4 -4 -6 -3 -6 -1 -2

-5

-1

The second value of the second row is the -5 times the first value of the third row: (-5)(-1)=5

Next value of the third row is the sum of the values above of it: 4+5=9

-1 4 -4 -6 -3 -6 -1 -2