A stockbroker bought 55 shares of stock for $44.31 each.

The curve

kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

4 0

2 years ago

Match the statement to the property it shows.

xxMikexx [17]

Answer:

If MN = XY, and XY = AB, then MN = AB. Transitive Property

If AB = CD, then CD = AB. Symmetric Property

Segment CD is congruent to segment CD. Reflexive Property

Step-by-step explanation:

Transitive property states that for all reall numbers a, b, and c, if a = b, b = c, then a = c.

Symmetric Property states that for all real numbers a and b, if a = b, then b = a.

Reflexive Property states that for every real number a, a=a

6 0

3 years ago

Read 2 more answers

There are 180 calories per 26 grams of a certain cereal. Find how many calories are in 65 grams of this cereal.

den301095 [7]

Answer:

450=65g

Step-by-step explanation:

8 0

2 years ago

Toll Brothers is a luxury home builder that would like to test the hypothesis that the average size of new homes exceeds 2,400 s

boyakko [2]

Answer:

Since the pvalue of the test is 0.09 > 0.01, we do not reject the null hypothesis that the average size of new homes is of 2400 square feet.

Step-by-step explanation:

Toll Brothers is a luxury home builder that would like to test the hypothesis that the average size of new homes exceeds 2,400 square feet. Test to see if the average size of new homes exceeds 2,400 square feet.

At the null hypothesis, we test if the average is of 2400 square feet, that is:

$H_o: \mu = 2400$

At the alternate hypothesis, we test if the average is greater than 2400 square feet, that is:

$H_a: \mu > 2400$

The test statistic is:

Since we have the standard deviation for the sample, we use the t-distribution.

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

2400 is tested at the null hypothesis:

This means that $\mu = 2400$

A random sample of 36 newly constructed homes had an average of 2,510 square feet with a sample standard deviation of 480 square feet.

This means that $n = 36, X = 2510, s = 480$

Test statistic:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{2510 - 2400}{\frac{480}{\sqrt{36}}}$

$t = 1.375$

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a sample mean of at least 2510, which is the pvalue of t = 1.375 with 36 - 1 = 35 degrees of freedom, using a one-tailed test.

With the help of a calculator, this pvalue is of 0.09

Since the pvalue of the test is 0.09 > 0.01, we do not reject the null hypothesis that the average size of new homes is of 2400 square feet.

6 0

2 years ago

Tarush is a landscape architect. For his first public project he is asked to create a small scale drawing of a garden to be plac

SashulF [63]

Given:

The garden is a right triangle with base 10m and height 15m.

To draw:

The garden such that 1 unit on the grid below represents 2 m.

Solution:

We have,

1 unit = 2 m

So,

1 m = 0.5 units

Using this conversion, we get

10 m = 5 units

15 m = 7.5 units

Therefore, the base garden on the grid is 5 units and height is 7.5 units as shown below.

6 0

3 years ago