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2 years ago

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The track team is trying to reduce their time for a relay race. First they reduce their time by 2.1 minutes. Then they are able

to reduce that time by 1/10. If their final time is 3.96 minutes, what was their beginning time?
What was the track teams initial relay time in minutes?

1 answer:

klemol [59]2 years ago

3 0

Answer: 15.7 minutes

Step-by-step explanation:

Let x be the time in the beginning (in minutes).

Given: The track team is trying to reduce their time for a relay race.

First they reduce their time by 2.1 minutes.

Then they are able to reduce that time by 10

If their final time is 3.96 minutes, then

x-t1-t2= 3.6
x= 3.6+ t1+ t2
x= 3.6+ 2.1+ 10
x= 15.7

Hence, their beginning time was 15.7 minutes.

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Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims th

Naddika [18.5K]

Answer:

0.9256

Step-by-step explanation:

Given that a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit

Let X be the number of customers who buy from her store, on a certain day of the week, buy coffee during their visit

X is Binomial (35, 0.55)

since each customer is independent of the other and there are two outcomes.

By approximation to normal we find that both np and nq are >5.

So X can be approximated to normal with mean = np = 19.25

and std dev = $\sqrt{npq} \\=2.943$

Required probability = prob that fewer than 24 customers in the sample buy coffee during their visit on that certain day of the week

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2 years ago

Find b, given that a = 20, angle A = 30°, and angle B = 45° in triangle ABC

Kamila [148]

<span>The side b is opposite to the angle B, applying the law of the sines, we have:

</span> $\frac{a}{sinA} = \frac{b}{sinB}$
$\frac{20}{sin30^0} = \frac{b}{sin45^0}$
$\frac{20}{ \frac{1}{2} } = \frac{b}{ \frac{ \sqrt{2} }{2} }$
$20* \frac{ \sqrt{2} }{2} = b* \frac{1}{2}$
$\frac{20 \sqrt{2} }{2} = \frac{b}{2}$
$2*b =2*20 \sqrt{2}$
$2b = 40 \sqrt{2}$
$b = \frac{40 \sqrt{2} }{2}$
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2 years ago

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A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mea

uysha [10]

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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

In a set with mean $\mu$ and standard deviation $\sigma$ , 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of size n, the mean is $\mu*n$ and the standard deviation is $s = \sqrt{n}*\sigma$

In this question:

$n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250$

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

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

By the Central Limit Theorem

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

$1.28 = \frac{X - 6328125}{11250}$

$X - 6328125 = 1.28*11250$

$X = 6342525$

The 90th percentile for the distribution of the total contributions is $6,342,525.

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2 years ago

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mihalych1998 [28]

6i/ (1+i)

multiply by the complex conjugate (1-i)/(1-i)

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(6+6i)/2

3+3i

Answer: 3+3i

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