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2 years ago

9

Population 422 increasing by 10 people per year. Write an equation to determine the population (y) after any number of years (x)

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1 answer:

Ronch [10]2 years ago

5 0

Answer:

y = 10x + 422

Step-by-step explanation:

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Logariths, please help

Valentin [98]

Answer:

<em>{ - 2 , 8 } </em>

Step-by-step explanation:

$log_{4}$ ( x² - 6x ) = 2

4² = ( x² - 6x )

x² - 6x - 16 = 0

- 6 = - 8 + 2

- 16 = - 8 * 2

( x - 8 )( x + 2 ) = 0 ⇒ $x_{1}$ = - 2 , $x_{2}$ = 8

<em>{ - 2 , 8 }</em>

3 0

3 years ago

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 116.4-cm and a standard dev

Katarina [22]

Answer:

The probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is 0.65173.

Step-by-step explanation:

Step-by-step explanation:

We are given that a company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 259.2 cm and a standard deviation of 2.1 cm. For shipment, 17 steel rods are bundled together.

Let = the average length of rods in a randomly selected bundle of steel rods

The z-score probability distribution for the sample mean is given by;

Z = ~ N(0,1)

where, = population mean length of rods = 259.2 cm

= standard deviaton = 2.1 cm

n = sample of steel rods = 17

Now, the probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is given by = P( > 259 cm)

P( > 259 cm) = P( > ) = P(Z > -0.39) = P(Z < 0.39)

= 0.65173

The above probability is calculated by looking at the value of x = 0.39 in the z table which has an area of 0.65173.

3 0

3 years ago

Read 2 more answers

Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.

nignag [31]

Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

$\sin (x+y) = 3\sin (x-y)$

Using the identities

$\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\$

we get

$\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y$

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

$3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}$

7 0

4 years ago

Use the formula A = bh to find the height of a parallelogram with a base of 34 mm and an area of 612 mm2.

andreev551 [17]

Your height to the problem would 18mm you would just take 612/34=18

3 0

4 years ago

Which graph shows the solution to the system of linear inequalities y>1/3x+1, y>2x-3

ElenaW [278]

For this case we have the following system:

$y> \frac {1} {3} x + 1\\y> 2x-3$

To solve, we first change the inequality for an equality:

$y = \frac {1} {3} x + 1\\y = 2x-3$

Matching we have:

$\frac {1} {3} x + 1 = 2x-3\\\frac {1} {3} x-2x = -3-1\\- \frac {5} {3} x = -4\\\frac {5} {3} x = 4\\5x = 12\\x = \frac {12} {5}$

So:

$y = 2x-3\\y = 2 (\frac {12} {5}) - 3\\y = \frac {24} {5} -3\\y = \frac {9} {5}$

Thus, $(\frac {12} {5}, \frac {9} {5})$ is the point of intersection of the lines.

Answer:

The graphic is attached

6 0

3 years ago