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3 years ago

2. Priscilla is drawing a map of her school that uses a scale in which 1.5 cm 1 point

Mathematics

1 answer:

lesantik [10]3 years ago

3 0

Answer:

The answer is 60cm. (b)

Step-by-step explanation:

For every 1.5cm on the map, it represents 3 ft on real-size scale.

In other words, for every 1cm on the map, it represents 3/1.5 = 2ft on real size scale.

If you want to find 120ft of real-size scale, you can use 120ft/2ft * 1cm which gives 60cm

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The amount of money Jamie earns is proportional to the number of hours she works. Jamie earns $62.50 working 5 hours. 1) Write a

AleksandrR [38]

To write your equation you need to find out what amount of money Jamie makes per hour. To do this take $62.50 and divide it by 5. The answer is $12.50 per hour.

Please see step 1 in the attached work to see the equation that is represented. Then substitute in 11 hours for h to find the total amount of money made. See part 2 in the attached work. The answer is $137.50 for working 11 hours.

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3 years ago

The system of equations is solved using the linear combination method.

Alborosie

The interpretation of 0 = -12 is (a) There are no solutions to the system because the equations represent parallel lines.

<h3>How to interpret the result?</h3>

The result is given as:

0 = -12

By comparison 0 and -12 do not have the same value

i.e. 0 ≠ - 12

This means that the system of equation has no solution

Hence, the interpretation of 0 = -12 is (a)

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1 year ago

Express 80 miles per hour in kilometers per hour

Anna [14]

80 miles per hour is 128.74752 kilometers per hour

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3 years ago

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Evaluate the dot product a⃗ ⋅b⃗ of a⃗ =3i^−8j^ and b⃗ =−2i^−6j^.

Mkey [24]

The "dot product" of two vectors has several different formulas.

Since you are given the x- and y-coordinates of both vectors a and b, we can apply the formula

a dot b = ax*bx + ay*by, where ax=x-component of vector a, by=y comp of vector b, and so on.

So, for the problem at hand, ax * bx + ay * by becomes

3(-2) + (-8)(-6) = -6 + 48 = 42 (answer). Note that the dot product (or "scalar product" is itself a scalar.

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3 years ago

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

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3 years ago