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3 years ago

Round 17 5/8 to the nearest whole number.

Mathematics

2 answers:

Aleks04 [339]3 years ago

8 0

Multiply 17 times 8 add the 5 and divide by 8 again. You will come up with 17.625. Round it up to 18.

marusya05 [52]3 years ago

4 0

The nearest whole number to <span>17 5/8 would be 18.</span>

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What method most efficient to use to solve x^2+4x+3=0

Alik [6]

My recommendation would be to factor..
x² + 4x + 3 = 0 factor the left side into two binomials
(x + 3)(x + 1) = 0 set each of these binomials equal to zero and solve

x + 3 = 0 Implies x = -3
x + 1 = 0 implies x = -1

6 0

4 years ago

An 8.0 kg block is moving at 3.2 m/s. A net force of 10 N is constantly applied on the block in the direction of its movement, u

Softa [21]

Answer:

5.02 m/s

Step-by-step explanation:

We are given that

Mass of block,m=8 kg

Initial velocity,u=3.2 m/s

Net force ,F=10 N

Distance,s=6 m

We have to find the approximate final velocity of the block.

We know that $a=\frac{F}{m}$

Using the formula

$a=\frac{10}{8}=\frac{5}{4} m/s^2$

We know that

$v=\sqrt{u^2+2as}$

Using the formula

$v=\sqrt{(3.2)^2+2\times \frac{5}{4}\times 6}$

$v=5.02 m/s$

8 0

3 years ago

A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear the

LenKa [72]

Answer:

a) The probability that at least 5 ties are too tight is P=0.0432.

b) The probability that at most 12 ties are too tight is P=1.

Step-by-step explanation:

In this problem, we could represent the proabilities of this events with the Binomial distirbution, with parameter p=0.1 and sample size n=20.

a) We can express the probability that at least 5 ties are too tight as:

$P(x\geq5)=1-\sum\limits^4_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\geq5)=1-(0.1216+0.2702+0.2852+0.1901+0.0898)\\\\P(x\geq5)=1-0.9568=0.0432$

The probability that at least 5 ties are too tight is P=0.0432.

a) We can express the probability that at most 12 ties are too tight as:

$P(x\leq 12)=\sum\limits^{12}_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\leq 12)=0.1216+0.2702+0.2852+0.1901+0.0898+0.0319+0.0089+0.0020+0.0004+0.0001+0.0000+0.0000+0.0000\\\\P(x\leq 12)=1$

The probability that at most 12 ties are too tight is P=1.

5 0

3 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

Sandy paid $20.30 as the sales tax for a bike she bought. If the sales tax is

BigorU [14]

Answer:

21.72

Step-by-step explanation:

0.07 x 20.30

4 0

3 years ago