Each of the following sentences contains an error in the use of tenses. Revise each sentence to correct the error.

EXAMPLE: Frida not only wrote the story but also has illustrated it. Frida not only wrote the story but also illustrated it. or Frida not only has written the story but also has illustrated it.

By then I will receive my first paycheck.

Each sentence in the following paragraph contains an error in pronoun usage. Identify each error, and then give the pronoun form that is correct according to the rules of formal standard usage.

EXAMPLE: Satoshi Yabuuchi is the artist whom created the sculptures shown below.

• whom-who*

Critics generally agree that few sculptors today are as inventive as him.

Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of to be less than 0.001. sin(0.3)

Explain the error in this simplification of radical expressions.

$$\sqrt{-2}\sqrt{-8}=\sqrt{-2(-8)}=\sqrt{16}=4$$

(a) Use Simpson's Rule to approximate each integral. (b) Estimate the error in using the approximation. Express the answer rounded to three decimal places. (c) Determine the number of subintervals needed to guarantee that an approximation has an error less than or equal to 0.0001. $\int_{-1}^{0} \frac{d x}{\sqrt{1-x^{3}}}; \quad n=4$

The Radius of the spherical ball is found by measuring the volume of sphere (by finding how much water displaces ) it is determined that the volume is 40 cubic centimeters with a tolerance no more than $1 \%$
a) Use differentials to approximate the relative error in measuring the Radius b) Find the corresponding percentage error in measuring the radius ? c) Interpret the results in the context of the problem

Think about Compared to $H_0: \mu=55$ versus $H_1: \mu \neq 55$. a. What kind of error would you commit if you didn't rule out the null hypothesis even though it was incorrect? b. If you reject the null hypothesis even though it is correct, what kind of error would you be making?

The area of a right triangle with a hypotenuse of H is calculated using the formula A=

$$\frac { 1 } { 4 } H ^ { 2 } \sin 2 \theta$$

, where

$$\theta$$

is one of the acute angles. Use differentials to approximate the error in calculating A if H=4 cm (exactly) and

$$\theta$$

is measured to be

$$30 ^ { \circ }$$

, with a possible error of

$$\pm 15 ^ { \prime }$$

.

Each of the following sentences contains an error in pronoun usage. Identify the error, and then give the pronoun form that is correct according to the rules of formal, standard usage.

EXAMPLE: Do you know whom won the women's 100-meter dash at the 2008 summer Olympic Games?

• whom-who*

Kyle was here looking for Josh and yourself.

Error Analysis A composite figure is made up of a semicircle and a rectangle. The width of the rectangle is 3 centimeters, and the diameter of the semicircle is 5 centimeters. Derek calculated the perimeter of the figure like this:

$$\begin{aligned} P & =3+3+5+\pi d \\ & =(11+5 \pi) \mathrm{cm} \end{aligned}$$

Find and correct Derek's error.

Underline the error in each of the following sentences. Then, above the error, write the word correctly. If a sentence is already correct, write C after it.

Example 1. Due to a dry spell, the water level has $\overset{\textit{\color{#c34632}{receded}}}{{\underline{\text{receeded}}}}$.

Do you think the others will acceed to our plan?

(a) Use the Trapezoidal Rule to approximate each integral. (b) Estimate the error in using the approximation. Express the answer rounded to three decimal places. (c) Determine the number of subintervals needed to guarantee that an approximation has an error less than or equal to 0.0001. $\int_{0}^{1} \frac{d x}{\sqrt{1+x^{3}}}; \quad n=3$

Each sentence in the following paragraph contains an error in pronoun usage. Identify each error, and then give the pronoun form that is correct according to the rules of formal standard usage.

EXAMPLE: Satoshi Yabuuchi is the artist whom created the sculptures shown below.

• whom-who*

Whom do you think could resist these engaging faces?

Most of the following sentences contain errors in pronoun-antecedent agreement. If a sentence contains an error in agreement, rewrite the sentence to correct the error. If a sentence is already correct, write $C$. EXAMPLE:The band is practicing the selections that they will perform in the statewide competition.

The band is practicing the selections that it will perform in the statewide competition.

The jury will receive their instructions from the judge.