3. A manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the lifetime y (thousands of holes drilled) of four bits at each of five speeds x. The data were: x: 60 | 60 | 60 60 | 80 80 80 80 100 100 y: 4.6 3.8 4.9 4.5 4.7 5.8 5.5 5.4 5.0 4.5 x: 100 100 120 120 120 120 140 140 | 140 140 y: 3.2 4.8 4.1 4.5 4.0 3.8 3.6 | 3.0 3.5 3.4 Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear? a. Is there any evident outlier? If so, does it have high influence? b. Test the paired data for lack of fit at 5% level of significance. c. d. Fit the best regression model on Y based on X. Provide justifications.

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A: Total female = 133+43 = 178 Total "did not graduate" = 55+43 = 98 Grand total= (126+55+133+43)  =…

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A: By Mean value theorem, if a function f is differentiable on a, b, then there exist c∈a, b such that…

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A: Explanation of the answer is as follows

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Q: What does 42 =

A: 4^2 means  4×4

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A: Eigenvalue: A number  is said to be an eigenvalue of a matrix A if there exists a non-zerovector x…

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A: The given series is ∑n=1∞x-3nn25n. Let an=x-3nn25n, then an+1=x-3n+1n+125n+1. Apply ratio test,…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.