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Ronch [10]
3 years ago
6

The vertices of a trapezoid are located at (1, 2), (3, 1), (3, 5), (1, 4). The trapezoid is translated 4 units to the right. Wha

t are the coordinates of the image of the trapezoid?
Mathematics
1 answer:
padilas [110]3 years ago
6 0

Answer:

Suppose that we have a given point (x, y)

If we translate this point N units to the right, then the new coordinates of the point are:

(x + N, y)

Ok, now if we know that the vertices of the trapezoid are:

(1, 2), (3, 1), (3, 5), (1, 4)

And we move the whole figure 4 units to the right, then all the vertices are moved 4 units to the right.

Then the new vertices of the figure will be:

(1 + 4, 2) = (5, 2)

(3 + 4, 1) = (7, 1)

(3 + 4, 5) = (7, 5)

(1 + 4, 4) = (5, 4)

Then the coordinates of the image of the trapezoid (of the new vertices) are:

(5, 2),  (7, 1), (7, 5),  (5, 4)

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Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day
o-na [289]

Answer:

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890 miles

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given mean of the Population = 100 miles per day</em>

<em>Given standard deviation of the Population = 23 miles per day</em>

<em>Let 'X' be the normal distribution</em>

<em>Let x₁ = 86</em>

<em />Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61<em />

<em>Let x₂= 86</em>

<em />Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086<em />

<u><em>Step(ii):</em></u><em>-</em>

<em> The probability that a truck drives between 86 and 125 miles in a day.</em>

<em>P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)</em>

<em>                       = P(Z≤ 1.08) - P(Z≤ -0.61)</em>

<em>                       = 0.5 +A(1.08) - ( 0.5 - A(-0.61))    </em>

<em>                       = A(1.08) + A(0.61)             ( A(-Z)=  A(Z)</em>

<em>                       = 0.3599 + 0.2291</em>

<em>                      = 0.5890</em>

<u><em>Conclusion:-</em></u>

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890  miles per day

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