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3 years ago

Name two different ways to construct congruent angles

Mathematics

1 answer:

Norma-Jean [14]3 years ago

5 0

A first way is considering opposite angles:

Pick a point, $O$
Draw two rays $r,s$ starting from $O$
Let $\alpha$ be the angle between $r$ and $s$
Elongate both $r$ and $s$ with respect to $O$ to obtain the rays $r'$ and $s'$
The angle between $r'$ and $s'$ is also $\alpha$

Alternatively, you can start with a given angle, and then draw its bisector. By definition, the bisector cuts a given angle in two equal parts, so you divide an angle $\alpha$ in two parts, both measuring $\frac{\alpha}{2}$

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Help me please, <br><br>Calculate the external perimeter of the picture frame: <br>

Studentka2010 [4]

Perimeter of a parallelogram = 2(l+b)
= 2 (65+42)
= 2*107
= 214 cm

8 0

4 years ago

The cake density is 0.454 ounce per cubic inch and the fair price is $0.20 per ounce. What should be a fair price for each cake?

aleksklad [387]

Answer:

price = x * 0.2

price = x * 0.454 * 0.2

Step-by-step explanation:

In this case we must know either the mass of the cake or its volume.

Given the case that we know the mass of the cake, it would be:

price = x * 0.2

where x is the mass of the cake in ounces, that is to say if for example a cake has a mass of 10 ounces, it would be:

price = 10 * 0.2 = 2

which means that each cake costs $ 2

Given the case of the volume, we must first multiply the density by this volume in order to calculate the mass and finally the price.

price = x * 0.454 * 0.2

where x is the volume of the cake in cubic inches, if for example the volume is 10 cubic inches it would be:

price = 10 * 0.454 * 0.2 = 0.908

which means that each cake costs $ 0.9

5 0

3 years ago

60 is 1/100 of what?

Thepotemich [5.8K]

Answer:

60% or 0.6 as a decimal

4 0

3 years ago

Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the fiv

Dahasolnce [82]

Answer and Explanation:

Given : Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder.

To find :

a. Does the table show a probability distribution?

b. Find the mean and standard deviation of the random variable x.

Solution :

a) To determine that table shows a probability distribution we add up all six probabilities if the sum is 1 then it is a valid distribution.

$\sum P(X)=0.029+0.147+0.324+0.324+0.147+0.029$

$\sum P(X)=1$

Yes it is a probability distribution.

b) First we create the table as per requirements,

x P(x) xP(x) x² x²P(x)

0 0.029 0 0 0

1 0.147 0.147 1 0.147

2 0.324 0.648 4 1.296

3 0.324 0.972 9 2.916

4 0.147 0.588 16 2.352

5 0.029 0.145 25 0.725

∑P(x)=1 ∑xP(x)=2.5 ∑x²P(x)=7.436

The mean of the random variable is

$\mu=\sum xP(x)=2.5$

The standard deviation of the random sample is

$Variance=\sigma^2$

$\sigma^2=\sum x^2P(x)-\mu^2$

$\sigma^2=7.436-(2.5)^2$

$\sigma^2=7.436-6.25$

$\sigma^2=1.186$

$\sigma=\sqrt{1.186}$

$\sigma=1.08$

Therefore, The mean is 2.5 and the standard deviation is 1.08.

5 0

3 years ago

What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?

tatuchka [14]

The end behavior of a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

Degree - 3 (odd);

Leading coefficient - 2 (positive).

Then

when $x\rightarrow -\infty,$ then $f(x)\rightarrow -\infty;$
when $x\rightarrow \infty,$ then $f(x)\rightarrow \infty.$

See attached graph of the function for graphical illustration.

5 0

4 years ago

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