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3 years ago

What two positive real numbers whose product is 50 have the smallest possible sum?

1 answer:

7 0

X * y = 50
y = 50 / x
S = x + y = x + 50 / x
S` = 1 - 50 / x²
1 - 50 / x² = 0
50 / x² = 1
x² = 50
x = √ 50 = 5 √2
y = 50 / 5√2 = 5 √2
Answer:
Those numbers are: x = 5√2 and y = 5√2.

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A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. Twenty percent of all purchasers select a

Elodia [21]

Answer:

Step-by-step explanation:

Given that:

There are 3 sizes of dishwasher soaps.

Twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the remaining 30% choose a 65-oz box. Let X1 and X2 denote the package sizes selected by two independently selected purchasers.

Therefore, $3 \times 3 = 9$ random samples of size 2 are taken from the population.

The information is well represented in the table below.

$x_1$ $x_2$ $p(x_1 \ x_2) = p(x_1)p(x_2)$ $\bar x = \dfrac{x_1+x_2}{2}$ $s^2= (x_1-\bar x)^2 +(x_2-\bar x)^2$

25 25 0.20×0.20=0.04 25 0

25 40 0.20×0.50=0.10 32.5 112.5

25 65 0.20×0.30= 0.06 45 800

40 25 0.50×0.20=0.10 32.5 112.5

40 40 0.50×0.50=0.25 40 0

40 65 0.50×0.30=0.15 52.5 312.5

65 25 0.30×0.20=0.06 45 800

65 40 0.30×0.50=0.15 52.5 312.5

65 65 0.30×0.30=0.09 65 0

The sample distribution of $\bar x$ is shown below as ;

$\bar x$ 25 32.5 40 45 52.5 65

$p(\bar x)$ 0.04 0.10+0.10 0.25 0.06+0.06 0.15+0.15 0.09

= 0.20 =0.12 =0.30

The value of $E(\bar x) = \sum \bar x \ P(\bar x)$

= 25(0.04) + 32.5(0.20) + 40(0.25) + 45(0.12) + 52.5(0.30) + 65(0.09)

= 44.5 oz

From the same table above ;

the sampling distribution of ${s^2}$ is be shown below;

${s^2}$ 0 112.5 312.5 800

0.04+0.25 0.10+0.10 0.15+0.15 0.06+0.06

+0.09

$p(s)^2$ = 0.38 =0.20 = 0.30 0.12

The value of $E(s)^2 =\sum s^2 .p(s)^2$

= (0×0.38)+(112.5×0.20)+(312.5×0.30)+(800×0.12)

=0+112+93.75+96

=301.75

5 0

3 years ago

Use substitution to solve the system of linear equations. In your final answer, include all of your work.

Fantom [35]

Replace 'y' with -3x+4

$x + \frac{1}{3} (-3x+4) = \frac{4}{3} \\ \\ x -x + \frac{4}{3} = \frac{4}{3} \\ \\ \frac{4}{3} = \frac{4}{3}$

The variable 'x' cancels out, leaving the True statement 4/3 = 4/3
This means that the 2 equations are identical regardless of what x and y are.

Answer: System is consistent and dependent, there are an infinite number of solutions.

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3 years ago

PLSSS HELP! triple r, then divide 10 by the result

Viefleur [7K]

3r/10? To find that we need an answer to set it equal to

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3 years ago

Scientists use the system of

AveGali [126]

Answer:

scientific notation is the system to write very large or very small number.

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3 years ago

Read 2 more answers

WILL GIVE BRAINLIEST<br> FIND VOLUME<br> 60 is the area of the base

scoundrel [369]

Hey so yeah this can be a challenging problem, Vol (V) is much easier to solve than surface area (SA), but I'll show you how it's done, my friend.
First of all, V (prism) = area of base (B) × h
We know that the height (h) of this prism is given, which we'll need later on: h = 5 ft, and area of base (B) is given as 60 ft2
So V = 60 ft2 × 5 ft = 300 ft3

So now for the hard part... how to calculate the SA of this prism

IF YOU DON'T NEED SA FOR THIS TYPE OF PROBLEM, DO NOT PROCEED!!!
[VERY DETAILED]

means solving the dimensions (sides) of that pesky polygon base (B) or lid.
The most important things about polygons are:
1) is it regular (same angle ° and side length)??
2) How many sides or angles??

This has to be regular, because they give you no other info so it has to be, in order to solve. And then it has 5 sides and angles = regular pentagon. ("penta" means 5).

Now there are 360° in any circle, so:
take the central angles of where the sides meet at the center forming triangles (see drawing above), each of those (5) central <'s = 360/5 = 72°
Now the apex of each of these triangles = 72°
but with our 5 triangles, we need to find the height of each triangle -- which is the midpoint of the side (base (b) of triangle), and h is perpendicular to this b. By bisecting that apex angle of 72, it forms 2 equal right triangles of
72/2 = 36°. So each right triangle has 36, 90, and?? 180-36-90 = 90-36 = 54°
let's call the base (b) = 1 side of pentagon
= side (s)
Therefore (see 2nd image drawn above) tangent (tan) of € = opposite/adjacent, or
tan (54) = h÷1/2b --> h = [tan (54)]×(1/2)b
1/2b = h/[tan (54)] = h/1.38

Also the area of each of the larger 5 triangles A(t) = 1/2b×h, and that area A(t) × 5 = area of whole pentagon base A(B)
So now after all that... our A(B) given at beginning = 60ft2. let's put it all together:
1/2b = h/[tan (54)] = h/1.38
A(t) = 1/2b×h, and A(B) = 5×A(t)
which means that A(B) = 5×(1/2b×h)
AND since the other calculation shows that 1/2b = h/1.38, plug that value into the A(B) formula...
.
.
.

now that we have height (h) of each triangle, we can go back to our tan equation for the triangle: tan (54) = 1.38 = h/(1/2b)
--> 1/2×b = h/1.38 --> base (b) = 2h/1.38
b = 2(4.06 ft)/1.38 = 8.12 ft/1.38 = 5.90 ft, for which b us also the width of each rectangular side panel (w)
length (l) of these sides was given as height of the whole prism = 5 ft

NOW FINALLY... THE FINAL SURFACE AREA OF THE PRISM (SA) = (2×A(B)) + (5×rectangular side)
SA = (2×60 ft2) + (5×(l×w)) = 120 ft2 + 5×5ft×5.9ft
SA = 120 ft2 + 147.62 ft2 = 267.62 ft2

4 0

3 years ago