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3 years ago

Victor drew trapezoid PQRS on a coordinate plane p(7,4) q(10,4) r(13,-1) s(8,-1) what is length in units of side ps

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

Answer:

PS= $\sqrt{26}units$

Step-by-step explanation:

Given : PQRS is a trapezoid on a coordinate plane P(7,4) Q(10,4) R(13,-1) S(8,-1).

To find:: Length of the side PS

Solution : Using the distance formula, we can find the length of the side PS, therefore

PS= $\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2}$

PS= $\sqrt{(-1-4)^{2}+(8-7)^2 }$

PS= $\sqrt{(-5)^2+(1)^2}$

PS= $\sqrt{25+1}$

PS= $\sqrt{26}units$

which is the required length of the side PS.

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A candy is in the shape of a sphere. The candy has a radius of 1.5 centimeters. Which of the following is closest to the volume

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Read 2 more answers

A manufacturer produces bearings, but because of variability in the production process, not all of the bearings have the same di

Lena [83]

Answer:

Proportion of all bearings falls in the acceptable range = 0.9973 or 99.73% .

Step-by-step explanation:

We are given that the diameters have a normal distribution with a mean of 1.3 centimeters (cm) and a standard deviation of 0.01 cm i.e.;

Mean, $\mu$ = 1.3 cm and Standard deviation, $\sigma$ = 0.01 cm

Also, since distribution is normal;

Z = $\frac{X -\mu}{\sigma}$ ~ N(0,1)

Let X = range of diameters

So, P(1.27 < X < 1.33) = P(X < 1.33) - P(X <=1.27)

P(X < 1.33) = P( $\frac{X -\mu}{\sigma}$ < $\frac{1.33 -1.3}{0.01}$ ) = P(Z < 3) = 0.99865

P(X <= 1.27) = P( $\frac{X -\mu}{\sigma}$ < $\frac{1.27 -1.3}{0.01}$ ) = P(Z < -3) = 1 - P(Z < 3) = 1 - 0.99865

= 0.00135

P(1.27 < X < 1.33) = 0.99865 - 0.00135 = 0.9973 .

Therefore, proportion of all bearings that falls in this acceptable range is 99.73% .

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