Please put the following numbers in order largest to smallest: 19/50; 0.37; 40%

Let x = 6.2
Define y as half of x: y = 0.5x
Calculate y: y = 0.5 × 6.2 = 3.1
Calculate z by subtracting x and y from 14.5: z = 14.5 - 6.2 - 3.1 = 5.2
Each variable corresponds to a triangle side

The likelihood of all sprinklers functioning properly in a fire stands at 0.0282. This was determined via the Binomial probability distribution since the activation of sprinklers occurs independently. There are two potential outcomes: they either function correctly or they do not. The binomial distribution is used to calculate the probabilities over multiple trials. The resulting equation b(x; n, P) = P(X=x) considers the number of successes, probability of success in a singular attempt, and the number of trials involved. The computations conclude with the probability being reflected as 0.0282.

This scenario is similar to a compound interest problem where the following formula is utilized:

Here:

C is the principal amount

j stands for the interest rate

n represents the number of periods

M is the total amount

By applying this formula to our issue, we establish:

C equals the initial population

j indicates the annual growth rate

n corresponds to the years elapsed

M signifies the final population

Let's proceed with the calculations...

C = 14000

j = 3% = 3/100 = 0.03

n = 6

M =?

Substituting the known values and calculating gives us:

M = C.

M = 14000.

M = 14000.

M = 14000. 1.19

M = 16,716.7

Thus, the result is 16,717

:-)

Answer:

a. i) Please refer to the attached graph representing the equation $10·x + $12·y = $300

ii) The intercepts indicate the maximum number of short-sleeve (at the x-intercept) and long-sleeve shirts (at the y-intercept) that can be ordered.

Step-by-step explanation:

The details provided are as follows:

Cost of each short-sleeve shirt = $10

Cost of each long-sleeve shirt = $12

Total budget available = $300

The equation for total spending is given by $10·x + $12·y = $300

Where;

x = Number of short-sleeved shirts

y = Number of long-sleeved shirts

Rearranging the equation into slope-intercept form, we have:

$10·x + $12·y = $300

$12·y = $300 - $10·x

y = $300/$12 - $10·x/$12

y = 25 - 5/6·x

Attached is the graph produced using Microsoft Excel

The coordinates that can be used for graph plotting are as follows:

x, y

(0, 25)

(5, 20.83)

(10, 16.67)

(15, 12.5)

(20, 8.33)

(25, 4.17)

(30, 0)

The x-intercept denotes the quantity of short-sleeve shirts purchasable with a $300 budget, while the y-intercept signifies the quantity of long-sleeve shirts achievable under the same budget.

Option C is correct. Step-by-step explanation: We need to identify which options are equivalent to 7/3. By evaluating each option: Option A: 9/49 is incorrect as it cannot be further simplified to yield multiples adequate to match. Option B: 18/42 reduces to 3/7, which does not equal 7/3, hence, incorrect. Option C: 42/18 divides down to 7/3, marking it as the correct choice. Option D: 49/9 also cannot be simplified to produce valid multiples.