In the number 15.42, how is the value of the digit "2" different from the value of the digit "2" in the number 12.54?

Which event has a probability of 1/2? Select all that apply.

Ymorist [56]

C, E, and F have 50 50 chance

4 0

2 years ago

A cable television compan is laying cable in an area with underground utilities. Two subdivisions are located on opposite sides

Schach [20]

Answer:

Step-by-step explanation:

Given:

Point Q = Q is on the north bank 1200 m east of P $40/m to lay cable underground and $80/m way to lay the cable.

Lets denote T be a point on north bank, therefore, point T is t m east and 100m north of P.

Note that 0 < t < 1200

Distance from P to T using Pythagoras theorem:

PT^2 = PQ^2 + QT^2

PT = √(t²+100²) = √(t²+10,000)

Distance from T to Q:

TQ = 1200 - t

From above, Cable from P to T is underwater, and costs $80/m to lay.

Cable from T to Q is underground, and costs $40/m to lay.

Total cost of the cable:

C(t) = 80√(t²+10,000) + 40(1200 - t)

Cost is at its minimum: when dC/dt = C'(t) = 0 and d^2C/dt^2 = C''(t) > 0

dC/dt = C'(t)

= 80 * 1/2 (t² + 10,000)^(-1/2) × 2t + 40 × (-1)

dC/dt = C'(t)

= 80t/√(t² + 10,000) - 40 = 0

80t/√(t² + 10,000) = 40

80t = 40√(t² + 10,000)

2t = √(t² + 10,000)

square both sides:

4t² = t² + 10,000

3t² = 10,000

t² = 10,000/3

t = 100/√3

≈ 57.735

d^2C/dt^2 =

C''(t) = [80√(t² + 10,000) - 80t × t/√(t²+10,000)] /√(t²+10,000)

C''(t) = [(80(t²+10,000) - 80t²) / √(t²+10,000)] /√(t²+10,000)

C''(t) = 800,000 / (t² + 10,000)^(3/2)

C''(t) > 0 for all t

Therefore C(t) is minimized at t = 100/√3

C(100/√3) = 80√(10,000/3 + 10,000) + 40 × (1200 - 100/√3)

= 80 √(40,000/3) + 48,000 - 4000/√3

= 16000/√3 + 48,000 - 4000/√3

= 48,000 + 12,000/√3

= 48,000 + 4,000√3

= 4000 (12 + √3)

≈ 54,928.20

Minimum cost is $54,928.20

This occurs when cable is laid underwater from point P to point T(57.735 m east and 100m north of P) and then underground from point T to point Q (1200 - 57.735)

= 1142.265 m

5 0

3 years ago

The ratio of the width to the length of a painting is 3 to 7. If the painting is 42 in. long how wide is it

belka [17]

If length is 42 inches, then width is 18 inches.

Step-by-step explanation:

We are given ratio of width to the length of a painting i.e 3 to 7. If the painting is 42 inches long, then how wide it is?

Solving:

$\frac{width}{length}=\frac{width}{length}\\ \frac{3}{7}=\frac{w}{42}\\ Cross\,\,multiply:\\3*42=w*7\\126=w*7\\w=\frac{126}{7}\\w=18$

So, If length is 42 inches, then width is 18 inches.

Keywords: Ratio

Learn more about Ratio at:

#learnwithBrainly

8 0

2 years ago

--/: Lesson Quiz<br> Why is subtracting an expression similar to distributing a -1?

o-na [289]

Answer:

You increase each term inside the parentheses by -1 in order to subtract each term, since the subtraction is the additive inverse

3 0

2 years ago

A person's hourly pay rate, r, is found by dividing the total amount

marishachu [46]

Translating the words into formula, we have

$r = \dfrac{p}{w}$

In fact, we have that the pay rate is the total payment divided by the number of hours worked.

We can solve this formula for w in two steps: starting from the formula above, multiply both sides by w:

$rw = p$

And then divide both sides by r:

$w = \dfrac{p}{r}$

4 0

3 years ago