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3 years ago

Helpp plzzzz

Mathematics

1 answer:

jasenka [17]3 years ago

6 0

Answer:

D. 3x^2 + 3/2 x - 9

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

... = ((1/2)x -3) + (3x² +x -6) . . . . . substitute for f(x) and g(x)

... = 3x² +x(1/2 + 1) + (-3 -6) . . . . . combine like terms

... = 3x² +(3/2)x -9 . . . . . matches selection D

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A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the pr

Gre4nikov [31]

Answer:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this: $P(-1.5 \leq Z \leq 1.5) = P(z$ Step-by-step explanation:

A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(50,12)$

Where $\mu=50$ and $\sigma=12$

Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We can find the probability required like this:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this:

$P(-1.5 \leq Z \leq 1.5) = P(z$

4 0

3 years ago

Two sides and an angle (SSA) of a triangle are given. Determine if the given measurements produce one triangle, two triangles, o

Mariana [72]

Answer:

1. c = 28.1, A = 19°, C = 144°

2. c = 2.0, A = 161°, C = 2°

Step-by-step explanation:

In general, if the given angle is not opposite the longest side, there will be two solutions. That is the case here.

Angle A can be found from the law of sines. It will be ...

A = arcsin(a/b·sin(b)) = arcsin(15.73/13.8·sin(17°)) ≈ arcsin(0.333261) ≈ 19.46°

or the supplement of that, 160.54°.

Angle C will be the angle required to make the sum of angles be 180°, either 143.53° or 2.47°.

Side c will be ...

c = b·sin(C)/sin(B) ≈ 47.2002×sin(C)

either 28.053 or 2.032.

There are two possible triangles:

(A, C, c) = (19°, 144°, 28.1) or (161°, 2°, 2.0)

8 0

4 years ago

20. <br> A.find the total area <br> B. Find the volume<br><br> Please explain :)

Debora [2.8K]

Check the first picture below, so the prism looks more or less like so.

now, check the second picture below, a triangular prism, is just 2 triangles and 3 rectangles.

so.. to get the total surface area of it, simply get the area of the rectangles and triangles, add them up, and that's the area of the prism.

the rectangles are just three each of 10x8
and to get the area of an equilateral triangle

$\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}\qquad 
\begin{cases}
s=\textit{length of a side}\\
----------\\
s=8
\end{cases}\implies A=\cfrac{8^2\sqrt{3}}{4}\\\\
-------------------------------\\\\
\textit{thus the areas added}
\\\\\\
(10\cdot 8)+(10\cdot 8)+(10\cdot 8)+\left(\frac{8^2\sqrt{3}}{4} \right)$

now, to get the volume of it, well, is just the area of a triangular face times the length, thus $\bf volume=V= \cfrac{8^2\sqrt{3}}{4}\cdot 10$