On a map, 1 inch represents 1,000 miles. If the area of a country is actually 16 million

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Mandarinka [93]

$\frac{5}{a + 3} = \frac{3}{a - 2}$

$5(a - 2) = 3(a + 3)$

$5a - 10 = 3a + 9$

$5a - 3a = 9 + 10$

$2a = 19$

$a = \frac{19}{2} = 9 \frac{1}{2}$

$Answer = D.) a = 9 \frac{1}{2}$

$\textbf{Spymore}$

4 0

4 years ago

The thickness X of aluminum sheets is distributed according to the probability density function f(x) = 450 (x2 - x) if 6 < x

grandymaker [24]

Solution :

Given :

$f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.$

1. Cumulative distribution function

$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$

$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx$

$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$

$=\frac{1}{450} \int_6^x (x^2-x) \ dx$

$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$

$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right]$

$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$

2. Mean $E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$

$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$

$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$

$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$

$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right)$

$=\frac{1}{450} [4608 - 252]$

= 17.2857

5 0

3 years ago

Boris wants to buy pineapples and watermelons, He wants to buy a total of at least 16 fruits (condition A) with $60 at most (con

snow_tiger [21]

Answer: The answer is 10 watermelons.

Step-by-step explanation: Given that Boris is going to buy pineapples and watermelons, a total of at least 16 fruits with $60 at most. The graph in the question represents the constraints on the number of pineapples P and watermelons W Boris buys.

From the graph, we have for condition A:

Two points are (16,0) and (0,16). So, the first constraint in equation form will be

$P-0=\dfrac{16-0}{0-16}(W-16)\\\\\Rightarrow W+P=16.$

And the constraint will be

$P+W\geq 16.$

Also, from the graph, we have for condition B:

Two points are (20,0) and (0,15). So, the second constraint in equation form will be

$P-0=\dfrac{15-0}{0-20}(W-20)\\\\\Rightarrow 3P+4W=60.$

And the constraint will be

$3P+4W\leq 60.$

If Boris buy 6 pineapples, then from conditions A and B, we have

$W\geq 10~~\textup{and}~~W\leq 10.5.$

These will give us that W = 10.

Thus, Boris can buy 10 Watermelons to meet both his constraints.

8 0

4 years ago

Read 2 more answers

two numbers have these properties, both numbers are greater than 8. Their highest common factor is 8. their lowest common muliti

mafiozo [28]

Answer:

16 and 40

Step-by-step explanation:

Hello,

We need to find the factors of 80

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.

Which can be 2, 2, 2, 2, and 5 (these numbers would go into all the factor completely without any reminder.)

This leaves us with two numbers 2 and 5

If the highest common factor (H.C.F) of both numbers is 8

And the lowest common multiple (L.C.M) = 80

Multiply the numbers by the highest common factor (H.C.F)

2 × 8 = 16

5 × 8 = 40

The numbers are 16 and 40

8 0

3 years ago

If = 12 cm and m=5 cm what is the length of n?<br> A 11 cm<br> B.10 cm<br> C. 13 cm<br> D. 14 cm

Temka [501]

Answer:

C

Step-by-step explanation:

12^2+5^2=c^2

144+25=c^2

169=c^2

Square root 169 and you get 13

7 0

2 years ago