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3 years ago

Please help!! It’s engenuity.

Mathematics

1 answer:

MakcuM [25]3 years ago

4 0

9514 1404 393

Answer:

Step-by-step explanation:

The applicable rules of exponents are ...

(a^b)/(a^c) = a^(b-c)

(a^b)^c = a^(bc)

a^-1 = 1/a

$\left(\dfrac{(2a^{-3}b^4)^2}{(3a^5b)^{-2}}\right)^{-1}=\dfrac{(3a^5b)^{-2}}{(2a^{-3}b^4)^2}=\dfrac{3^{-2}a^{-10}b^{-2}}{2^2a^{-6}b^8}=\dfrac{1}{3^22^2}a^{-10-(-6)}b^{-2-8}\\\\=\boxed{\dfrac{1}{36a^4b^{10}}}$

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A ferry will safely accommodate 82 tons of passenger cars. Assume that the meanweight of a passenger car is 2 tons with standard

Shalnov [3]

Answer:

The probability that the maximum safe-weight will be exceeded is <u>0.0455 or 4.55%</u>.

Step-by-step explanation:

Given:

Maximum safe-weight of 37 cars = 82 tons

∴ Maximum safe-weight of 1 car (x) = 82 ÷ 37 = 2.22 tons (Unitary method)

Mean weight of 1 car (μ) = 2 tons

Standard deviation of 37 cars = 0.8 tons

So, standard deviation of 1 car is given as:

$\sigma=\frac{0.8}{\sqrt{37}}=0.13$

Probability that maximum safe-weight is exceeded, P(x > 2.22) = ?

The sample is normally distributed (Assume)

Now, let us determine the z-score of the mean weight.

The z-score is given as:

$z=\frac{x-\mu}{\sigma}\\\\z=\frac{2.22-2}{0.13}\\\\z=\frac{0.22}{0.13}=1.69$

Now, finding P(x > 2.22) is same as finding P(z > 1.69).

From the z-score table of normal distribution curve, the value of area under the curve for z < 1.69 is 0.9545.

But we need the area under the curve for z > 1.69.

So, we subtract from the total area. Total area is 1 or 100%.

So, $P(z > 1.69) = 1 - P(z < 1.69)$

$P(z>1.69)=1-0.9545=0.0455\ or\ 4.55\%$

Therefore, the probability that the maximum safe-weight will be exceeded is 0.0455 or 4.55%.

8 0

4 years ago

A biker travels 5 feet in 0.5 seconds. At this exact speed, how far will the biker travel in a minute?

tino4ka555 [31]

600 ft. This is because you travel 10 feet per second and there are 60 seconds in a minute. 10 x 60 =600

7 0

3 years ago

in 2005, the total waste generated in a certain country was 3.474x10^9 pounds. also in 2005, the countrys population was 1.23x10

Serggg [28]

Answer:

2824

Step-by-step explanation:

Take the number of pounds and divide by the number of people:

3.474×10⁹ / 1.23×10⁶

Divide the coefficients and subtract the exponents:

(3.474 / 1.23) × 10⁹⁻⁶

2.824×10³

So the country produced about 2,824 pounds of garbage per person in 2005.

7 0

3 years ago

Determine the equation of the line passing through the points <br> (4,-1) and (-2,-4)

jenyasd209 [6]

Answer:

y = 1/2x - 3

Step-by-step explanation:

the slope:

$m=\frac{-4-(-1)}{-2-4} =\frac{-4+1}{-6} =\frac{-3}{-6} =\frac{3}{6} =\frac{1}{2}$

the equation:

with the point (4, -1)

$y-(-1)=\frac{1}{2} (x-4)$

$y+1=\frac{1}{2}x-2$

$y=\frac{1}{2} x-2-1$

$y=\frac{1}{2} x-3$

I hope this help you

8 0

3 years ago

Find all rational zeros of P(x)=6x^4-x^3-55x^2+9x+9

o-na [289]

Answer: x = -3, -1/3, 1/2, 3

Step-by-step explanation:

6 0

3 years ago