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3 years ago

Find the value of x. #9,10,11,&12

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

7 0

Answer:

Step-by-step explanation:

9). It's given in the triangle → Two angles are equal in measure

Therefore, by the definition of an isosceles triangle, opposite sides of the equal angles are equal in measure.

x = 12

10). Two sides of the given triangles are equal in length.

By the definition of an isosceles triangle, opposite angles of the equal sides of the triangle will be equal in measure.

Therefore, y = 55°

By the triangle sum theorem,

x° + y° + 55° = 180°

x° + 55° + 55° = 180°

x = 180 - 110

x = 70°

11). By the definition of an isosceles triangle, opposite sides of the equal angles will be equal in measure.

x + 3 = 12

x = 9

12). By the definition of an isosceles triangle, opposite angles of the equal sides of the triangle will be equal in measure.

m∠2 = 53°

x + 65 = 53

x = 53 - 65

x = -12

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Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with

worty [1.4K]

Answer:

$z$

Step-by-step explanation:

Assuming this complete question:

"Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean $\mu =26$ kilograms and standard deviation $\sigma=4.2$ kilograms. Let x be the weight of a fawn in kilograms. Convert the following z interval to a x interval.

$X$ "

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 weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(26,4.2)$

Where $\mu=26$ and $\sigma=4.2$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

We know that the Z scale and the normal distribution are equivalent since the Z scales is a linear transformation of the normal distribution.

We can convert the corresponding z score for x=42.6 like this:

$z=\frac{42.6-26}{4.2}=3.95$

So then the corresponding z scale would be:

$z$

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3 years ago

A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at th

OlgaM077 [116]

Answer:

Interval [16.34 , 21.43]

Step-by-step explanation:

First step. <u>Calculate the mean</u>

$\bar X=\frac{(23+18+23+12+13+23)}{6}=18.666$

Second step. <u>Calculate the standard deviation</u>

$\sigma =\sqrt{\frac{(23-18.666)^2+(18-18.666)^2+(23-18.666)^2+(12-18.666)^2+(13-18.666)^2+(23-18.666)^2}{6}}$

$\sigma=\sqrt\frac{18.783+0.443+18.783+44.435+5.666+18.783}{6}$

$\sigma=\sqrt{17.815}=4.22$

As the number of data is less than 30, we must use the t-table to find the interval of confidence.

We have 6 observations, our level of confidence DF is then 6-1=5 and we want our area A to be 80% (0.08).

We must then choose t = 1.476 (see attachment)

Now, we use the formula that gives us the end points of the required interval

$\bar X \pm t\frac{\sigma}{\sqrt n}$

where n is the number of observations.

The extremes of the interval are then, rounded to the nearest hundreth, 16.34 and 21.43

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