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3 years ago

Is black......blue or red???

Mathematics

2 answers:

Len [333]3 years ago

6 0

Black is black.
Blue is blue.
Red is red.

Anna007 [38]3 years ago

3 0

Answer:

uhm what's the special occasion?

and black cannot be blue or red...they are separate colors

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. A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and six 75-W bulbs. Suppose that three bulbs ar

yaroslaw [1]

Answer:

a) 59.34%

b) 44.82%

c) 26.37%

d) 4.19%

Step-by-step explanation:

(a)

There are in total 4+5+6 = 15 bulbs. If we want to select 3 randomly there are K ways of doing this, where K is the combination of 15 elements taken 3 at a time

$K=\binom{15}{3}=\frac{15!}{3!(15-3)!}=\frac{15!}{3!12!}=\frac{15.14.13}{6}=455$

As there are 9 non 75-W bulbs, by the fundamental rule of counting, there are 6*5*9 = 270 ways of selecting 3 bulbs with exactly two 75-W bulbs.

So, the probability of selecting exactly 2 bulbs of 75 W is

$\frac{270}{455}=0.5934=59.34\%$

(b)

The probability of selecting three 40-W bulbs is

$\frac{4*3*2}{455}=0.0527=5.27\%$

The probability of selecting three 60-W bulbs is

$\frac{5*4*3}{455}=0.1318=13.18\%$

The probability of selecting three 75-W bulbs is

$\frac{6*5*4}{455}=0.2637=26.37\%$

Since the events are disjoint, the probability of taking 3 bulbs of the same kind is the sum 0.0527+0.1318+0.2637 = 0.4482 = 44.82%

(c)

There are 6*5*4 ways of selecting one bulb of each type, so the probability of selecting 3 bulbs of each type is

$\frac{6*5*4}{455}=0.2637=26.37\%$

(d)

The probability that it is necessary to examine at least six bulbs until a 75-W bulb is found, supposing there is no replacement, is the same as the probability of taking 5 bulbs one after another without replacement and none of them is 75-W.

As there are 15 bulbs and 9 of them are not 75-W, the probability a non 75-W bulb is $\frac{9}{15}=0.6$

Since there are no replacement, the probability of taking a second non 75-W bulb is now $\frac{8}{14}=0.5714$

Following this procedure 5 times, we find the probabilities

$\frac{9}{15},\frac{8}{14},\frac{7}{13},\frac{6}{12},\frac{5}{11}$

which are

0.6, 0.5714, 0.5384, 0.5, 0.4545

As the events are independent, the probability of choosing 5 non 75-W bulbs is the product

0.6*0.5714*0.5384*0.5*0.4545 = 0.0419 = 4.19%

3 0

3 years ago

a student found the slope of a line that passes through the points (1,14) and (3,4) to be 5. what mistake did she make?

SSSSS [86.1K]

M = (y2-y1)/(x2-x1)
= (4-14)/3-1
= -10/2
= -5

4 0

3 years ago

8(x) = x^3 - 3 What is the value of x when g(x) = 24? Enter the answer in the box.

IRINA_888 [86]

Answer:

x=3

Step-by-step explanation:

x³ - 3 =24

x³ = 27

x = 3

6 0

2 years ago

For problems a - d, write the function in the form LaTeX: y=ab^x. y = a b x . a) LaTeX: y=3\sqrt{4^{2x}} y = 3 4 2 x b) LaTeX: y

elixir [45]

Step-by-step explanation:

To write the equation in LaTeX in form y = ab^x or $ab^x$ for y = abx .........(1)

(a) LaTeX: y=3\sqrt{4^{2x}} y = 3 4 2 x can be written in mathematical form as

$y=3\sqrt{4^{2x}}$ ; y = 342x

on comparing with equation (1) we get a =3 and b =4

⇒y = 34^x or $34^x$

(b) LaTeX: y=\frac{\sqrt[3]{5^{3x}}}{2} y = 5 3 x 3 2 can be written in mathematical form as

$y=\frac{\sqrt[3]{5^{3x}}}{2}$ ; y = 342x

on comparing with equation (1) we get a =0.5 and b =5

⇒y = $\frac{1}{2}5^x$

(c)LaTeX: y=8^{x+2} y = 8 x + 2 can be written in mathematical form as

$y=8^{x+2}$

on comparing with equation (1) we get a =64 and b =8

y = $64 . 8^x$

(d)LaTeX: y=\frac{3^{2x+1}}{\sqrt{3^{2x}}} can be written in mathematical form as

$y=\frac{3^{2x+1}}{\sqrt{3^{2x}}}$ = $3^{x+1}$ = $3 . 3^x$

on comparing with equation (1) we get a =3 and b =3

y = $3 . 3^x$

7 0

3 years ago

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

RUDIKE [14]

9514 1404 393

Answer:

$1571

Step-by-step explanation:

If we assume that y is profit in dollars, the maximum value of y is revealed by a graph to be ...

ymax = $1571

The maximum profit the company can make is $1571 at a selling price of $45 each.

_____

The function can be written in vertex form as ...

y = -(x^2 -90x) -454

y = -(x^2 -90x +45^2) -454 +45^2

y = -(x -45)^2 +1571

Because the leading coefficient is negative, we know this vertex represents a maximum. (x, y) = (45, 1571) at the vertex. Maximum profit is $1571.

8 0

2 years ago