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2 years ago

Find three consecutive even integers whose sum 72

Mathematics

2 answers:

kotykmax [81]2 years ago

6 0

Answer:

22, 24 and 26.

Step-by-step explanation:

hope that helps, homie.

vova2212 [387]2 years ago

3 0

22, 24, 26

Step-by-step explanation:

2n - 2 + 2n + 2n + 2 = 72

6n = 72

n = 72/6

n = 12

∴ so three consecutive even integers whose sum is 72 :

2n - 2

= 2(12) - 2

= 24 - 2

= 22

= 2(12)

= 24

2n + 2

= 2(12) + 2

= 24 + 2

= 26

verification

22 + 24 + 26

= 46 + 26

= 72 ✓✓

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Simplify the expression. Write the answer in scientific notation (7x10-6) (3x10-2

shtirl [24]

Answer:

21 X 10^-8 is the correct answer

Step-by-step explanation:

(7X3) X 10^(-6-2)

21 X 10^ -8

4 0

2 years ago

Calculate the sample standard deviation of data from Question 1 76,45,64,80,92

mash [69]

Answer:

$S.D = 15.98$

Step-by-step explanation:

Given: 76,45,64,80,92

Required: Determine the standard deviation

We start by calculating the mean

$Mean = \frac {\sum x}{n}$

Where x-> 76,45,64,80,92 and n = 5

$Mean = \frac {76+45+64+80+92}{5}$

$Mean = \frac{357}{5}$

$Mean = 71.4$

Subtract Mean (71.4) from each of the given data

$76 - 71.4 = 4.6\\45 - 71.4 = -26.5\\64 - 71.4 = -7.4\\80 - 71.4 = 8.6\\92 - 71.4 = 20.6$

Determine the absolute value of the above result

$|4.6| = 4.6\\|-26.5| = 26.5\\|-7.4| = 7.4\\|8.6| = 8.6\\|20.6| = 20.6$

Square Individual Result

$4.6^2 = 21.16 \\26.5^2 = 702.25\\7.4^2 = 54.76\\8.6^2 = 73.96\\20.6^2 = 424.36$

Calculate the mean of the above result to give the variance

$Mean = \frac {\sum x}{n}$

$Mean = \frac{21.16 + 702.25 + 54.76 + 73.96 + 424.36}{5}\\Mean = \frac{1276.49}{5}\\Mean = 255.298$

Hence, Variance = 255.298

Standard Deviation is calculated by $\sqrt{Var}$

$SD = \sqrt{255.298}$

$S.D = 15.9780474402$

$S.D = 15.98 (Approximated)$

6 0

3 years ago

Hello again! This is another Calculus question to be explained.

podryga [215]

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions

Function Notation

Exponential Property [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Property [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

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:

We are given the following and are trying to find the second derivative at x = 2:

$\displaystyle f(2) = 2$

$\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}$

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

$\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}$

When we differentiate this, we must follow the Chain Rule: $\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]$

Use the Basic Power Rule:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')$

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]$

Simplifying it, we have:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]$

We can rewrite the 2nd derivative using exponential rules:

$\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}$

To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:

$\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}$

When we evaluate this using order of operations, we should obtain our answer:

$\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219$

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

Unit: Differentiation

5 0

2 years ago

Use a factor tree to find the prime factorization of each number

andre [41]

Let's say you had the number 70.

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5 2

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7 0

2 years ago

Help with this please. Thanks

nata0808 [166]

9514 1404 393

Answer:

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Step-by-step explanation:

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Sin = Opposite/Hypotenuse

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x ≈ 3.0

3 0

2 years ago