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3 years ago

Jane buys a coat that is $18 off the orinigal price. This is a 30% discount. What is the original price of the coat?

1 answer:

6 0

Total cost - (total cost * 30%) = discounted price
$C - .3C = 18 \\ 
.7C =18 \\
C = \frac{18}{ \frac{7}{10}}\\
C=\frac{180}{7}\\
C= 25.7142857...$

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It is known that 10% of the 9-year old children in a town have three siblings. Fifteen 9-year old children are selected at rando

inn [45]

Using the binomial distribution, it is found that there is a 0.0555 = 5.55% probability that more than 3 of these selected children have three siblings.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

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, for the parameters, we consider that:

10% of the 9-year old children in a town have three siblings, hence p = 0.1.

Fifteen 9-year old children are selected at random, hence n = 15.

The probability that more than 3 of these selected children have three siblings is given by:

$P(X > 3) = 1 - P(X \leq 3)$

In which:

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

Then:

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

$P(X = 0) = C_{15,0}.(0.1)^{0}.(0.9)^{15} = 0.2059$

$P(X = 1) = C_{15,1}.(0.1)^{1}.(0.9)^{14} = 0.3432$

$P(X = 2) = C_{15,2}.(0.1)^{2}.(0.9)^{13} = 0.2669$

$P(X = 3) = C_{15,3}.(0.1)^{3}.(0.9)^{12} = 0.1285$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.2059 + 0.3432 + 0.2669 + 0.1285 = 0.9445$

P(X > 3) = 1 - 0.9445 = 0.0555

0.0555 = 5.55% probability that more than 3 of these selected children have three siblings.

More can be learned about the binomial distribution at brainly.com/question/24863377

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2 years ago

The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle possible, or two triangles p

kvv77 [185]

Answer: The way to work this problem is to sketch the SSA-described triangle.

Horizontally, mark a ray stemming from point C, going to the right.

From point C, at an angle of elevation of 20 degrees, draw a segment a = 6.3, ending at point B.

Now, from point B, draw a segment perpendicular to the horizontal ray and label it h, for altitude.

Calculate h = 6.3 sin 20o = 2.1547.

Now imagine that, dangling from point B, you have a segment of length c = 9.3; in fact, put a compass with steel point at B and radius 9.3, and draw a big arc. you'll see that it can intersect the horizontal ray only once; in its swing toward point C, due to c > a, there will be no second intersection of the ray (the arc 'overshoots' the ray).

Thus you see that only one solution exists, and the Law of Sines can be used to solve the triangle:

sin 20 / 9.3 = sin A / 6.3 and this leads to A = 13.4 degrees...and B = 180 - 20 - 13.4 = 146o.

I'll let you solve for b (side AC).

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3 years ago

After a power failure, the temperature in a freezer increased at an average rate of 2.5 °F per hour. The total increase was 7.5

makvit [3.9K]

YOU CAN WRITE AN EQUATION OF 7.5 Divide 2.5 = any letter

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3 years ago