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lys-0071 [83]
1 year ago
11

Triangle not drawn to scale

Mathematics
1 answer:
const2013 [10]1 year ago
4 0

Answer:

b = 23.3

Step-by-step explanation:

First, we need to determine whether this is a right or non-right triangle.

We know that the sum of all the angles in a triangle must add up to 180, so we can add angles A and B and subtract the sum from 180:

180-(40+88)=180-128=52

The 52 indicates that it is a non-right triangle, so we must rely on either the law of sines or law of cosines to find the measure of b.

Given that we have angle A and its resulting side, a, along with angle B, we can use the law of sines:

\frac{sin A}{a}=\frac{sin B}{b}

\frac{sin 40}{15}=\frac{sin 88}{b}\\ \\ 15*sin 88=b * sin 40\\\\b=\frac{b*sin 40}{sin 88}\\ \\b=23.3216=23.3

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The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta
nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

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.

In this problem, we have that:

\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

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

By the Central Limit Theorem

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

Z = \frac{8.22 - 8.2}{0.018}

Z = 1.11

Z = 1.11 has a pvalue of 0.8665

X = 8.18

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

Z = \frac{8.18 - 8.2}{0.018}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0
3 years ago
What is 130% of 990? Round to the nearest hundredth.
pantera1 [17]

Answer:

1287

Step-by-step explanation:

Is means equals and of means multiply

W = 130% * 990

Change to decimal form

W = 1.30 * 990

W =1287

8 0
2 years ago
Read 2 more answers
Explain how you can tell if a rational expression is in simplest form. Include an example with your explanation.
yan [13]
The  numerator and denominators will  have no common factors.

For example 4/6 is not in its simplest form  because  both 4 and 6 can be divided by 2.  In simplest form this will be 2/3.
7 0
2 years ago
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4,800 that’s the answer for your equation

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aksik [14]

Answer:

63 m        

Step-by-step explanation:

We are given the following in the question:

Average speed of swimming = 45 m/min

Time = 1 minute 24 seconds

Converting time into minutes:

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Formula:

\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}

Putting values, we get.

45 = \dfrac{\text{Distance}}{1.4}\\\\\text{Distance} = 45\times 1.4 = 63\text{ m}

Thus, Alex swims for 63 m in 1 minute and 24 seconds.

6 0
3 years ago
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