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4 years ago

Simplify: ...............

Mathematics

1 answer:

Helga [31]4 years ago

5 0

The answer can be shown in both exact and decimal forms.

Exact form:
$\sqrt{61 - 24}\sqrt{5}$

Decimal form:
2.70820393...

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Solve for y.<br> 3(y-2) = y +4-2(-5y-2)<br> Simplify your answer as much as possible.

choli [55]

Answer:

y = -7/4

Step-by-step explanation:

5 0

3 years ago

A fire station is to be located along a road of length A, A < q. If fires occur at points uniformly chosen on (0, A), where s

Shtirlitz [24]

Answer:

Step-by-step explanation:

Given that X is uniform in the interval (0,A)

X is continuous since it represents the distance

A fire station is to be located along a road of length A, A < q. If fires occur at points uniformly chosen on (0, A), we should find where the station be located so as to minimize the expected distance from the fire

Distance can be taken as absolute values here as either side is the same.

E(|x-a|] is to be minimum

E(|x-a|)=E(x-a) for 0<x<a

=E(a-x), for a<x<A

Using integral we find this value

$E(|x-a|)=\int\limits^a_0 {x-a} \, dx +=\int\limits^A_a -{x-a} \, dx\\f(a)=\frac{a^2}{2} -\frac{(A-a)^2}{2}$

$f(a)=\frac{a^2}{2} +\frac{(A-a)^2}{2} \\f'(a) = a-(A-a)\\f"(a) =2$

Using calculus we find that f" is positive so when f' =0 we get solution

f'(a) =0 gives

$a=\frac{A}{2}$

Hence fire station to be located at the mid point of 0 and A

8 0

4 years ago

From a bowl containing five red, three white, and seven blue chips, select four at random and without replacement. Compute the c

snow_lady [41]

Answer:

The probability is $\frac{5}{9}$

Step-by-step explanation:

Let A be the event of one red, zero white, and three blue chips,

And, B is the event of at least three blue chips,

Since, A ∩ B = A (because If A happens that it is obvious that B will happen )

Thus, the conditional probability of A if B is given,

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

Now, red chips = 5,

White chips = 3,

Blue chips = 7,

Total chips = 5 + 3 + 7 = 15

Since, the probability of one red, zero white, and three blue chips, when four chips are chosen,

$P(A)=\frac{^5C_1\times ^3C_0\times ^7C_3}{^{15}C_4}$

$=\frac{5\times 35}{1365}$

$=\frac{175}{1365}$

$=\frac{5}{39}$

While, the probability that of at least three blue chips,

$P(B)=\frac{^8C_1\times ^7C_3+^8C_0\times ^7C_4}{^{15}C_4}$

$=\frac{8\times 35+35}{1365}$

$=\frac{315}{1365}$

$=\frac{3}{13}$

Hence, the required conditional probability would be,

$P(\frac{A}{B})=\frac{5/39}{3/13}$

$=\frac{65}{117}$

$=\frac{5}{9}$

4 0

3 years ago

Write the equation of the line in slope-intercept form.

finlep [7]

Answer
y=mx+b
y=2x-7

Explanation
m = the “common difference” between two points
In this graph, it’s 2 because every time the line moves across the x axis by 1, it increases in 2 in the y axis

b = the point that intercepts the y axis; the y-intercept
In this graph, the point intercepts the y axis at -7 (the y-intercept is -7)

7 0

3 years ago

Use area model to explain the product 4.6 and 3. Write the product in standard form, word form and expanded form.

enyata [817]

Answer: Product = 13.8

Step-by-step explanation:

<u>As we have to use area model :</u>

So, we

Let length of rectangle be 4.6

Let breadth of rectangle be 3

As we know that

Area of rectangle is given by

$Length \times breadth\\\\=4.6\times 3\\\\=13.8\text{ squared units }$

Now, we must write in standard form, word form and expanded form:

So,

Standard form = 13.8

Word form = thirteen and 8 tenths

Expanded form is given by

$13.8=1\times 10+3\times 1+8\times \frac{1}{10}$

3 0

3 years ago

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