What is the value of the expression<br> [(1+5) X2-5] X2 <br> ( X is for multiplication)

Nata [24]

$~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)$

$\text{The derivative is now in a form of}~ x^A (B + C \log_D (x))$

3 0

2 years ago

If necessary, round to the nearest tenth and label your answer <br>10ft <br>4ft <br><br><br>

MrRa [10]

Answer:

Step-by-step explanation:

$H^2+4^2=10^2\\\\H^2+16=100\\\\H^2=100-16=84\\\\H=\sqrt{84}\approx9.2\ ft$

8 0

3 years ago

Two times one number added to three times a second number is 21. Five times the first number added to three times the second is

lisabon 2012 [21]

Answer:

d. 3 and 5

Step-by-step explanation:

the first number will be x and the second number will be y

2x + 3y = 21

2(3) + 3(5) = 21

6 + 15 = 21

5x + 3y = 30

5(3) + 3(5) = 30

15 + 15 = 30

7 0

3 years ago

Read 2 more answers

Write an expression using the Distributive Property that can be used to find the quotient of 36 divided by 3

e-lub [12.9K]

So the answer is 36÷3= because that is an expression and the answer is 12 in case you need to know the answer

3 0

3 years ago

Read 2 more answers

Consider the following. 12, 7, 18, 23, 24, 27 Compute the population standard deviation of the numbers. (Round your answer to tw

avanturin [10]

Answer:

(a) $\sigma = 7.04$

(b) $\sigma = 14.1$

(c) The population standard deviation is multiplied by k

Step-by-step explanation:

Given

$Dataset: 12, 7, 18, 23, 24, 27$

Solving (a): The population standard deviation

Start by calculating the mean

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

$\mu = \frac{12+7+18+23+24+27}{6}$

$\mu = \frac{111}{6}$

$\mu = 18.5$

The population standard deviation is:

$\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}$

This gives:

$\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}$

$\sigma = \sqrt{\frac{297.5}{6}}$

$\sigma = \sqrt{49.5833}$

$\sigma = 7.04$

Solving (b): Double the dataset and calculate the new population standard deviation

The new dataset is:

$Dataset: 24, 14, 36, 46, 48, 54$

Start by calculating the mean

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

$\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}$

$\mu = \frac{222}{6}$

$\mu = 37$

The population standard deviation is:

$\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}$

This gives:

$\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}$

$\sigma = \sqrt{\frac{1190}{6}}$

$\sigma = \sqrt{198.33}$

$\sigma = 14.1$

Solving (c): What happens when the dataset is multiplied by k

In (a), we have:

$\sigma = 7.04$

In (b), when the dataset is doubled,

$\sigma = 14.1$

This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:

i.e.

$New \sigma = k * \sigma$

4 0

3 years ago

What is the value of the expression [(1+5) X2-5] X2 ( X is for multiplication)