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2 years ago

Triangle QRS is to be dilated using the rule D Subscript P, three-fourths.

Mathematics

1 answer:

horrorfan [7]2 years ago

4 0

The distance from the center of dilation, P, to.the image vertice S' is; 6 units.

<h3>What is the distance from the center of dilation, P, to the image S'?</h3>

It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.

Ultimately, since the dilation factor is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6 units.

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Step-by-step explanation:

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x= 2 + 4

x = 6

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A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 stude

bulgar [2K]

Answer:

a) 20.61%

b) 21.82%

c) 42.36%

d) 4 withdrawals

Step-by-step explanation:

This situation can be modeled with a binomial distribution, where p = probability of “success” (completing the course) equals 80% = 0.8 and the probability of “failure” (withdrawing) equals 0.2.

So, the probability of exactly k withdrawals in 20 cases is given by

$\large P(20;k)=\binom{20}{k}(0.2)^k(0.8)^{20-k}$

We are looking for

P(0;20)+P(0;1)+P(0;2) =

$\large \binom{20}{0}(0.2)^0(0.8)^{20}+\binom{20}{1}(0.2)^1(0.8)^{19}+\binom{20}{2}(0.2)^2(0.8)^{18}=$

0.0115292150460685 + 0.0576460752303424 + 0.136909428672063 = 0.206084718948474≅ 0.2061 or 20.61%

Here we want P(20;4)

$\large P(20;4)=\binom{20}{4}(0.2)^4(0.8)^{16}=0.218199402\approx 0.2182=21.82\%$

Here we need

$\large \sum_{k=4}^{20}P(20;k)=1-\sum_{k=1}^{3}P(20;k)$

But we already have P(0;20)+P(0;1)+P(0;2) =0.2061 and

$\large \sum_{k=1}^{3}P(20;k)=0.2061+P(20;3)=0.2061+0.205364 \approx 0.4236=42.36\%$

For a binomial distribution the <em>expectance </em>of “succeses” in n trials is np where p is the probability of “succes”, and the expectance of “failures” is nq, so the expectance for withdrawals in 20 students is 20*0.2 = <em>4 withdrawals.</em>

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3 years ago

Find the measure of each angle listed below. Enter only numbers without space.

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9514 1404 393

Answer:

∠PTQ = 45°
∠QTR = 15°
∠PTS = 120°

Step-by-step explanation:

Parallelogram PTSR is divided into two equilateral triangles by diagonal RT. All of the acute angles in that quadrilateral are 60°, and the obtuse angles are 120° (2×60° and also the supplement of 60°).

Triangle PTQ is an isosceles right triangle, so its acute angles are 45°.

∠PTQ = 45°

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4/3 × 3.14 = 4.186 → 4.19

4.19 × 2.2³ = 44.6

Hence, 44.6 is the answer.

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