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3 years ago

A circle with its dimensions in inches (in), is shown what is the area in square inches of half the circle

1 answer:

8 0

If you could tell us the dimensions of the circle we would gladly help you with your question. However it is almost impossible to find the area of half of the circle without knowing the dimensions.

Hope this helps!

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Find the values of x and y

vitfil [10]

Hi there!

$\large\boxed{y = 12, x = 3}$

The two trapezoids are similar, so we can determine a common scale factor:

OL/UR = NM/TS

9/3 = 6/2

3 = 3

Trapezoid ONML is 3x larger than UTSR, so:

RS = 4, LM = y

3RS = LM

3 · 4 = y = 12.

Find x using the same method:

3UT = ON

3(2x+1) = 4x + 9

6x + 3 = 4x + 9

2x = 6

x = 3.

4 0

3 years ago

in the diagram,the pyramid has a rectangular base.ifthe pyramid has a volume of 176 cmcube and the height of 11cm ,find the valu

SOVA2 [1]

The formula of pyramid:
$v = \frac{1}{3} ah$
Where v is the volume, a is the base area and h is the height.

We can then put the given information into the formula:

176 = (1/3)(3x × x)(11)

(176 × 3) / 11 = 3x^2

3x^2 = 48

x^2 = 48/3

x = _/16

x = 4

3 0

3 years ago

A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) usi

lbvjy [14]

Using the distributions, it is found that there is a:

a) 0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

b) 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

c) 0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item a:

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

20 tosses, hence $n = 20$ .
Fair coin, hence $p = 0.5$ .

The probability is P(X = 10), thus:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{20,10}.(0.5)^{10}.(0.5)^{10} = 0.1762$

0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item b:

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

The probability of an exact value is 0, hence 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item c:

For the approximation, the mean and the standard deviation are:

$\mu = np = 20(0.5) = 10$

$\sigma = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.5)} = \sqrt{5}$

Using continuity correction, this probability is $P(10 - 0.5 \leq X \leq 10 + 0.5) = P(9.5 \leq X \leq 10.5)$ , which is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 9.5.