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evablogger [386]

2 years ago

14

The length of a rectangle is 2 centimeters less than five times the width of a rectangle. The area of the rectangle is 16 square

centimeters. Find the length and width of the rectangle.

1 answer:

Kisachek [45]2 years ago

6 0

Answer:

Length: 8 cm

Width: 2 cm

Step-by-step explanation:

Check the attachment.

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What is the difference between the solution of a linear

Snowcat [4.5K]

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

4 0

2 years ago

Work out the area of 5e parallelogram

Vedmedyk [2.9K]

Answer: The area is 268 cm squared (approximately)

Step-by-step explanation: The area of a parallelogram is given as ;

Area = b x h

Where b is the base and h is the vertical height. However the vertical height is not given, so we shall apply the trigonometric ratio to determine the vertical height. If we draw a straight line from the the top right vertex down to the base, we would have constructed a right angled triangle with hypotenuse 13cm, and reference angle 79 degrees. We can now calculate the vertical height as follows;

Sin 79 = opposite/hypotenuse

Sin 79 = h/13

By cross multiplication we now have

Sin 79 x 13 = h

0.9816 x 13 = h

12.76 = h

With the vertical height now known, we can calculate the area as follows

Area = b x h

Area = 21 x 12.76

Area = 267.96 cm squared

7 0

2 years ago

The minimum point on the graph of the equation y=f(x) is (−1,−3). What is the minimum point on the graph of the equation y=f(x−5

prohojiy [21]

Answer:

The minimum point is (4,-3)

Step-by-step explanation:

we know that

If the new equation is

y=f(x-5)

then

The Rule of the translation is

(x,y) -----> (x+5,y)

That means ----> The translation is 5 units at right

so

(−1,−3) ----> (-1+5,-3)

(−1,−3) ----> (4,-3)

5 0

3 years ago

Read 2 more answers

What is 1/144 as an expression using a negative exponent

MrRissso [65]

ANSWER

${12}^{ - 2}$

EXPLANATION

The given expression is

$\frac{1}{144}$

This is the same as:

$\frac{1}{12 \times 12}$

In index notation, we write this as

$\frac{1}{ {12}^{2} }$

To write this as a negative index, we use the property:

$\frac{1}{ {a}^{m} } = {a}^{- m}$

This implies that;

$\frac{1}{ {12}^{2} } = {12}^{ - 2}$

3 0

2 years ago

Suppose a certain type of fertilizer has an expected yield per acre of mu 1 with variance sigma 2, whereas the expected yield fo

mart [117]

Answer:

See the proof below.

Step-by-step explanation:

For this case we just need to apply properties of expected value. We know that the estimator is given by:

$S^2_p= \frac{(n_1 -1) S^2_1 +(n_2 -1) S^2_2}{n_1 +n_2 -2}$

And we want to proof that $E(S^2_p)= \sigma^2$

So we can begin with this:

$E(S^2_p)= E(\frac{(n_1 -1) S^2_1 +(n_2 -1) S^2_2}{n_1 +n_2 -2})$

And we can distribute the expected value into the temrs like this:

$E(S^2_p)= \frac{(n_1 -1) E(S^2_1) +(n_2 -1) E(S^2_2)}{n_1 +n_2 -2}$

And we know that the expected value for the estimator of the variance s is $\sigma$ , or in other way $E(s) = \sigma$ so if we apply this property here we have:

$E(S^2_p)= \frac{(n_1 -1 )\sigma^2_1 +(n_2 -1) \sigma^2_2}{n_1 +n_2 -2}$

And we know that $\sigma^2_1 = \sigma^2_2 = \sigma^2$ so using this we can take common factor like this:

$E(S^2_p)= \frac{(n_1 -1) +(n_2 -1)}{n_1 +n_2 -2} \sigma^2 =\sigma^2$

And then we see that the pooled variance is an unbiased estimator for the population variance when we have two population with the same variance.

8 0

2 years ago