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vfiekz [6]
2 years ago
9

A square rotated about its center by 360º maps onto itself at(1,2,3,4) different angles of rotation. You can reflect a square on

to itself across (2,4,8,16)different lines of reflection. NextReset
Mathematics
1 answer:
Sladkaya [172]2 years ago
7 0

A square rotated about its center by 360º maps onto itself at 90°, 180°, 270° and 360° - 4 different angles of rotation.

You can reflect a square onto itself across two diagonals and two segments that connects the middlepoints of opposite sides - 4 different lines of reflection.

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Automobile mechanics conduct diagnostic tests on 150 new cars of a particular make and model to determine the extent to which th
Aleks04 [339]

Answer:

99% Confidence interval: (0.185,0.375)                                                  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 150

Number of cars that have faulty catalytic converters, x = 42

\hat{p} = \dfrac{x}{n} = \dfrac{42}{150} = 0.28

99% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58

Putting the values, we get:

0.28\pm 2.58(\sqrt{\frac{0.28(1-0.28)}{150}}) = 0.28\pm 0.095\\\\=(0.185,0.375)

The​ 99% confidence interval for the true proportion of new cars with faulty catalytic converters is​ (0.185,0.375)

8 0
2 years ago
Use a daily production cost C for x units. A manufacturer of gas grills has daily production costs of C = 400 – 5x + 0.125x2, wh
Lady bird [3.3K]
The function given is a quadratic function, so the graph will be a parabola. It'll look similar to the photo attached. The minimum cost will be at the vertex of the parabola because that is its lowest point! To find the x-value of the vertex (which is what the question is looking for), use the vertex formula: x = -b/2a. The variable b is the coefficient of the x term in the function, and the variable a is the coefficient of the x² term. In this case, a = 0.125 and b = -5.
x = -(-5)/2(0.125)
x = 5/0.25
x = 20
So, 20 gas grills should be produced each day to maintain minimum costs. Hope that helps! :)

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Step-by-step explanation:

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