A farmer plants a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the

Mathematics

1 answer:

miss Akunina [59]2 years ago

4 0

Answer:

The statement which is not true about the sample is;

The sample of 10 plants was a census of the corn plants

Step-by-step explanation:

The statement out of the given statements which is not true about the sample is "The sample of 10 plants was a census of the corn plants"

The 10 unique number corn which the farmer randomly selects of which he then count the number of ears in the corn and multiply by 100 so as to quickly arrive at an estimate of the total number of ears of corn for the crop, without individually counting the ears on each plant from the 100 plants

A census is a counting and individual enumeration procedure to collect and record characteristic information and details of the all the members that make up a given population

Therefore, the farmer is finding an estimate of the number of ears of in the plants rather than taking a census of the ears of corn on each plants in the population of 100 plants

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Substitution to evaluate the indefinite integral

gregori [183]

Answer:

$\displaystyle \int {e^{5x}} \, dx = \boxed{ \frac{e^{5x}}{5} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {e^{5x}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u:
$\displaystyle u = 5x$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = 5 \ dx$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\\end{aligned}$
[Integral] Apply Integration Method [U-Substitution]:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\\end{aligned}$
[Integral] Apply Exponential Integration:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\\end{aligned}$
[u] Back-substitute:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\& = \boxed{ \frac{e^{5x}}{5} + C } \\\end{aligned}$