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Lapatulllka [165]
1 year ago
15

B. To make salad dressing for the fruit salad, Mrs. Santos uses 2/4 cup oil, 1 cup orange juice, and 3/4 cup honey. How many cup

s of salad dressing does this make? Explain how you found your answer.
Mathematics
2 answers:
zalisa [80]1 year ago
8 0

Add all

\\ \rm\rightarrowtail \dfrac{2}{4}+\dfrac{3}{4}+\dfrac{4}{4}

\\ \rm\rightarrowtail \dfrac{2+3+4}{4}

\\ \rm\rightarrowtail \dfrac{9}{4}

\\ \rm\rightarrowtail 2\dfrac{1}{4}cups

Ket [755]1 year ago
5 0

Answer:

\sf 2 \frac14 \ cups

Step-by-step explanation:

Add the amounts together:

\sf \implies \dfrac24+1+\dfrac34

Convert the whole number 1 into a fraction with denominator 4:

\sf \implies \dfrac24+\dfrac44+\dfrac34

As all the denominators are the same, we can simply add the numerators:

\sf \implies \dfrac{2+4+3}4

\sf \implies \dfrac94

Finally, convert the improper fraction into a mixed number:

\sf \implies 2 \frac14 \ cups

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a 1 thousandth or 0.001

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Which step should be performed first when simplifying 25 − (14 − 8) + 3 × 2?
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Answer:

(14-8)

Step-by-step explanation:

Heres why:

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2 years ago
Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.
zhannawk [14.2K]

Answer:

3.4594

Step-by-step explanation:

To change the base of a logarithm

• log_{b} x = \frac{log_{c}x }{log_{c}b }

where c represents the new base

Changing the base from 2 to 10

log_{2} 11 = \frac{log_{10}11 }{log_{10}2 } ≈ 3.4594

4 0
3 years ago
The amount of coffee that a filling machine puts into an 8 dash ounce 8-ounce jar is normally distributed with a mean of 8.2 oun
Inessa [10]

Answer:

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 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 theore.

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 question, 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 dash ounce 8-ounce jars by the mean of a random sample of 100​ jars, will be at most 0.02​ ounce

That is, probability of the sample mean between 8.2-0.02 = 8.18 and 8.2 + 0.02 = 8.22, which is the pvalue of Z when X = 8.22 subtracted by the pvalue of Z when X = 8.18.

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

73.3% probability that the sampling error made in estimating the mean amount of coffee for all 8 dash ounce 8-ounce jars by the mean of a random sample of 100​ jars, will be at most 0.02​ ounce

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