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Tcecarenko [31]

3 years ago

9

In your gym class, your teacher can create teams of 4 for a relay race and have no students left over.The next day, your teacher

creates teams of 5 for dodge ball and has no students left over. What are some possible numbers of students in your class

1 answer:

Agata [3.3K]3 years ago

8 0

Answer: 20,40,60,80,100

Step-by-step explanation:

The possible numbers has be the multiples of 5 and 4 in other words the LCM.

The LCM of 5 and 4 are,

20,40,60, 80,100 ....

You might be interested in

If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that the d

katen-ka-za [31]

Answer:

We need a sample size of least 119

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Sample size needed

At least n, in which n is found when $M = 0.09$

We don't know the proportion, so we use $\pi = 0.5$ , which is when we would need the largest sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.09 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.09\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.09}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.09})^{2}$

$n = 118.6$

Rounding up

We need a sample size of least 119

6 0

3 years ago

Find the area of the triangle

elixir [45]

Answer: The area of the triangle is 252 :)

Step-by-step explanation:

M = 6

L = 6

K = 7

6 x 6 = 36 x 7 = 252

The area of the triangle is 252 :)

5 0

3 years ago

In 1982 Abby’s mother scored at the 93rd percentile in the math SAT exam. In 1982 the mean score was 503 and the variance of the

oksian1 [2.3K]

Answer:

The percentle for Abby's score was the 89.62nd percentile.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation(which is the square root of the variance) $\sigma$ , the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Abby's mom score:

93rd percentile in the math SAT exam. In 1982 the mean score was 503 and the variance of the scores was 9604.

93rd percentile. X when Z has a pvalue of 0.93. So X when Z = 1.476.

$\mu = 503, \sigma = \sqrt{9604} = 98$

So

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

$1.476 = \frac{X - 503}{98}$

$X - 503 = 1.476*98$

$X = 648$

Abby's score

She scored 648.

$\mu = 521 \sigma = \sqrt{10201} = 101$

So

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

$Z = \frac{648 - 521}{101}$

$Z = 1.26$

$Z = 1.26$ has a pvalue of 0.8962.

The percentle for Abby's score was the 89.62nd percentile.

3 0

3 years ago

TRIANGLE ABC IS DILATED BY A SCALE FACTOR OF 0.5 WITH THE ORIGIN AS THE CENTER OF DILATION, RESULTING IN THE IMAGE TRIANGLE A'B'

const2013 [10]

Answer: The length of the line B'C" is 1 unit.

Step-by-step explanation:

Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.

If A (2,2), B= (4,3) and C=(6,3).

Distance between (a,b) and (c,d): $D=\sqrt{(d-b)^2+(c-b)^2}$

Then, BC $=\sqrt{(3-3)^2+(6-4)^2}$

$\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}$

Length of image = scale factor x length in original figure

B'C' = 0.5 × BC

= 0.5 × 2

= 1 unit

Hence, the length of the line B'C" is 1 unit.

5 0

3 years ago

The tallest building on Earth is the Burj Khalifa in Dubai. It is 2,716 feet tall. Convert that height to meters.

satela [25.4K]

Answer:

828

Step-by-step explanation:

5 0

3 years ago