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3 years ago

Under the translation T(2, -3) the point (1, 6) will become (3, 9).

Mathematics

1 answer:

seraphim [82]3 years ago

3 0

Answer:

False (under assumption T(2,-3) means move it right 2 units and down 3 units).

Step-by-step explanation:

The statement is false.

T(2,-3) means move the point right 2 (so plus 2 on the x-coordinate) and down 3 units (so minus 3 on the y-coordinate).

So (1,6) will become (1+2,6-3)=(3,3) after the translation.

The point (1,12) will become (1+2,12-3)=(3,9).

If the statement were "Under the translation T(2,-3) the point (1,12) will become (3,9)", then it would be true.

Or!

If the statement were "Under the translation T(2,3) the point (1,6) will become (3,9)", then it would be true.

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An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 35, de

Amiraneli [1.4K]

Answer:

a) P=0.1721

b) P=0.3528

c) P=0.3981

Step-by-step explanation:

This sampling can be modeled by a binominal distribution where p is the probability of a project to belong to the first section and q the probability of belonging to the second section.

a) In this case we have a sample size of n=15.

The value of p is p=25/(25+35)=0.4167 and q=1-0.4167=0.5833.

The probability of having exactly 10 projects for the second section is equal to having exactly 5 projects of the first section.

This probability can be calculated as:

$P=\frac{n!}{(n-k)!k!}p^kq^{n-k}= \frac{15!}{(10)!5!}\cdot 0.4167^5\cdot0.5833^{10}=0.1721$

b) To have at least 10 projects from the 2nd section, means we have at most 5 projects for the first section. In this case, we have to calculate the probability for k=0 (every project belongs to the 2nd section), k=1, k=2, k=3, k=4 and k=5.

We apply the same formula but as a sum:

$P(k\leq5)=\sum_{k=0}^{5}\frac{n!}{(n-k)!k!}p^kq^{n-k}$

Then we have:

$P(k=0)=0.0003\\P(k=1)=0.0033\\P(k=2)=0.0165\\P(k=3)=0.0511\\P(k=4)=0.1095\\P(k=5)=0.1721\\\\P(k\leq5)=0.0003+0.0033+0.0165+0.0511+0.1095+0.1721=0.3528$

c) In this case, we have the sum of the probability that k is equal or less than 5, and the probability tha k is 10 or more (10 or more projects belonging to the 1st section).

The first (k less or equal to 5) is already calculated.

We have to calculate for k equal to 10 or more.

$P(k\geq10)=\sum_{k=10}^{15}\frac{n!}{(n-k)!k!}p^kq^{n-k}$

Then we have

$P(k=10)=0.0320\\P(k=11)=0.0104\\P(k=12)=0.0025\\P(k=13)=0.0004\\P(k=14)=0.0000\\P(k=15)=0.0000\\\\P(k\geq10)=0.032+0.0104+0.0025+0.0004+0+0=0.0453$

The sum of the probabilities is

$P(k\leq5)+P(k\geq10)=0.3528+0.0453=0.3981$

8 0

3 years ago

Suppose an investment of $1,800 doubles in value every 7 years. How much is the investment worth after 42 years?

almond37 [142]

X=2^n(1800)
x=2^6(1800)
x=$115,200

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3 years ago

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So in numeric form what is 700,000+40,000+9000+200 and +50

WARRIOR [948]

Answer: 749,250

Step-by-step explanation:

700,000 + 40,000= 740,000.

9,000+200+50= 9,250.

740,000 + 9,250 = 740,250.

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3 years ago

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A go kart top speed is 607,200 feet per hour. What is the speed in miles per hour

PolarNik [594]

One mile equals 5280 feet so

607,200/5280=115

So it’s 115 miles per hour

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3 years ago

A sample of 12 measurements has a mean of 8.5 and a sample of 20 measurements has a mean of 7.5. Find the mean of all 32 measure

nalin [4]

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