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2 years ago

Please help the following questions

Mathematics

1 answer:

insens350 [35]2 years ago

6 0

Answer:

Option D

Step-by-step explanation:

Assume that these polygons were similar. You could tell that if they were, ABCD ~ EFGH, and is already noted by the answer choices. We can conclude that AB ~ EF, CD ~ GH and so on. To prove that these shapes are similar, we must form a like proportionality among these side;

$EF / AB = GH / CD\\5 / 8 = 4 / 2.5,\\0.625 \neq 1.6\\\\Conclusion - Option D$

As the proportions we formed were to equal to one another, the solution must be option D!

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It takes21 minutes for 5 people to paint 7walls. How many minutes does it take 3people to paint 5 walls?

scoray [572]

so 5 people work each one for 21 minutes, that means 21+21+21+21+21 minutes altogether, namely 105 minutes, it took that long for 7 walls, hmmmm how long for just one wall then? well, 105 ÷ 7, namely 15 minutes then, for just 1 wall.

now, if it takes 15 minutes of work to do one wall, what about 5 walls? well, that'd be 15*5 or 75 minutes.

so if we have 3 folks working, how much would each one work? well, 75 ÷ 3, namely 25 minutes, so each of them will work 25 minutes, namely 25+25+25 minutes, so in 25 minutes, they'll be done with 5 walls.

8 0

3 years ago

Tumor counts: A cancer laboratory is estimating the rate of tumorigenesis in two strains of mice, A and B. They have tumor count

Igoryamba

Answer:

The observed tumor counts for the two populations of mice are:

Type A mice = 10 * 12 = 120 counts

Type B mice = 13 * 12 = 156 counts

Step-by-step explanation:

Since type B mice are related to type A mice and given that type A mice have tumor counts that are approximately Poisson-distributed with a mean of 12, we can then assume that the mean of type A mice tumor count rate is equal to the mean of type B mice tumor count rate.

This is because the Poisson distribution can be used to approximate the the mean and variance of unknown data (type B mice count rate) using known data (type A mice tumor count rate). And the Poisson distribution gives the probability of an occurrence within a specified time interval.

3 0

3 years ago

The amount of time it takes Isabella to wait for the bus is continuous and uniformly distributed between 3 minutes and 15 minute

madam [21]

Answer:

33.33% probability that it takes Isabella more than 11 minutes to wait for the bus

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

For this problem, we have that:

Uniformly distributed between 3 minutes and 15 minutes:

So $a = 3, b = 15$

What is the probability that it takes Isabella more than 11 minutes to wait for the bus?

Either she has to wait 11 or less minutes for the bus, or she has to wait more than 11 minutes. The sum of these probabilities is 1. So

$P(X \leq 11) + P(X > 11) = 1$

We want P(X > 11). So

$P(X > 11) = 1 - P(X \leq 11) = 1 - \frac{11 - 3}{15 - 3} = 0.3333$

33.33% probability that it takes Isabella more than 11 minutes to wait for the bus

4 0

3 years ago

In a simple random sample of 300 boards from this shipment, 12 fall outside these specifications. Calculate the lower confidence

Lyrx [107]

Answer:

The 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

Step-by-step explanation:

In a random sample of 300 boards the number of boards that fall outside the specification is 12.

Compute the sample proportion of boards that fall outside the specification in this sample as follows:

$\hat p =\frac{12}{300}=0.04$

The (1 - α)% confidence interval for population proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The critical value of z for 95% confidence level is,

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.04\pm1.96\sqrt{\frac{0.04(1-0.04)}{300}}\\=0.04\pm0.022\\=(0.018, 0.062)\\\approx(1.8\%, 6.2\%)$

Thus, the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

6 0

2 years ago

Combine like terms to write an equivalent expression for 4y to the power of 2 + 6x - 2y to the power of 2 + 12x

Triss [41]

I think it is 2 y ^ 2 + 1 8 x

8 0

2 years ago