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3 years ago

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A certain quadrilateral has two pairs of parallel sides. The opposite sides are equal in length. There are also 4 right angles.

What is the total length of the shorter pair of sides, if the longer pair measures 16cm each, and the figure has a perimeter of 56cm?

1 answer:

DENIUS [597]3 years ago

6 0

Answer:

12 + 12 = 24

Step-by-step explanation:

P = 2L + 2W

P = 2*16 + 2W

P = 56

56 = 32 + 2W Subtract 32 from both sides

56 - 32 = 2W

24 = 2W Divide by 2

24/2 = 2W/2

12 = W

The answer you want is 2 * 12 = 24

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Obtain the general solution to the equation. (x^2+10) + xy = 4x=0 The general solution is y(x) = ignoring lost solutions, if any

alukav5142 [94]

Answer:

$y(x)=4+\frac{C}{\sqrt{x^2+10}}$

Step-by-step explanation:

We are given that a differential equation

$(x^2+10)y'+xy-4x=0$

We have to find the general solution of given differential equation

$y'+\frac{x}{x^2+10}y-\frac{4x}{x^2+10}=0$

$y'+\frac{x}{x^2+10}y=4\frac{x}{x^2+10}$

Compare with

$y'+P(x) y=Q(x)$

We get

$P(x)=\frac{x}{x^2+10}$

$Q(x)=\frac{4x}{x^2+10}$

I.F= $e^{\int\frac{x}{x^2+10} dx}=e^{\frac{1}{2}ln(x^2+10)}$

$e^{ln\sqrt(x^2+10)}=\sqrt{x^2+10}$

$y\cdot \sqrt{x^2+10}=\int \frac{4x}{x^2+10}\times \sqrt{x^2+10} dx+C$

$y\cdot \sqrt{x^2+10}=\int \frac{4x}{\sqrt{x^2+10}}+C$

$y\cdot \sqrt{x^2+10}=4\sqrt{x^2+10}+C$

$y(x)=4+\frac{C}{\sqrt{x^2+10}}$

6 0

3 years ago

A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and

mr Goodwill [35]

Answer:

Bias for the estimator = -0.56

Mean Square Error for the estimator = 6.6311

Step-by-step explanation:

Given - A normally distributed random variable with mean 4.5 and standard deviation 7.6 is sampled to get two independent values, X1 and X2. The mean is estimated using the formula (3X1 + 4X2)/8.

To find - Determine the bias and the mean squared error for this estimator of the mean.

Proof -

Let us denote

X be a random variable such that X ~ N(mean = 4.5, SD = 7.6)

Now,

An estimate of mean, μ is suggested as

$\mu = \frac{3X_{1} + 4X_{2} }{8}$

Now

Bias for the estimator = E(μ bar) - μ

= $E( \frac{3X_{1} + 4X_{2} }{8}) - 4.5$

= $\frac{3E(X_{1}) + 4E(X_{2})}{8} - 4.5$

= $\frac{3(4.5) + 4(4.5)}{8} - 4.5$

= $\frac{13.5 + 18}{8} - 4.5$

= $\frac{31.5}{8} - 4.5$

= 3.9375 - 4.5

= - 0.5625 ≈ -0.56

∴ we get

Bias for the estimator = -0.56

Now,

Mean Square Error for the estimator = E[(μ bar - μ)²]

= Var(μ bar) + [Bias(μ bar, μ)]²

= $Var( \frac{3X_{1} + 4X_{2} }{8}) + 0.3136$

= $\frac{1}{64} Var( {3X_{1} + 4X_{2} }) + 0.3136$

= $\frac{1}{64} ( [{3Var(X_{1}) + 4Var(X_{2})] }) + 0.3136$

= $\frac{1}{64} [{3(57.76) + 4(57.76)}] } + 0.3136$

= $\frac{1}{64} [7(57.76)}] } + 0.3136$

= $\frac{1}{64} [404.32] } + 0.3136$

= $6.3175 + 0.3136$

= 6.6311

∴ we get

Mean Square Error for the estimator = 6.6311

6 0

3 years ago

A certain triangle has two 45° angles. What type of triangle is<br> it?

wariber [46]

Answer:

an acute triangle

Step-by-step explanation:

an acute triangle has angles that are less than 90 degrees

right triangles have a right angle

obtuse triangles have angles greater than 90 degrees

5 0

3 years ago

The table shows ordered pairs of the function y = 16 0. 5x. A 2-column table with 6 rows. The first column is labeled x with ent

zvonat [6]

Option 3 is the correct answer. The missing values of (x, y) is (8, 20).

<h3>How do you find out the values?</h3>

Given that the function is,

$y = 16 + 0.5x$

The function is a linear equation that can be solved graphically. The values of both variables x and y can be found on different points along with the straight-line graph.

Also, for every value of x, there is a corresponding value of y.

For the given options, we put the values of x to find the corresponding value of y.

For option 1, put x = 0 in the given function,

$y = 16 + 0.5\times 0\\y = 16$

But for x=0, y= 18, hence option 1 is not correct.

For option 2, put x = 5 in the given function,

$y = 16 + 0.5\times 5\\y = 18.5$

But for x=5, y= 19.5, hence option 2 is not correct.

For option 3, put x = 8 in the given function,

$y = 16 + 0.5\times 8\\y = 20$

But for x=8, y= 20, hence option 3 is the correct answer.

Hence we can conclude that option 3 is the correct answer. The missing values of (x, y) is (8, 20).

To know more about the function, follow the link given below.

brainly.com/question/5245372.

7 0

2 years ago

What is greater 3 qt or 6 pt

Nastasia [14]

6 Pints is EQUAL to 3 Quarts

3 0

3 years ago

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