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yuradex [85]
3 years ago
8

Giovanna,Frances, and their dad each carried a ten pound bag of soil into the back yard. After putting soil in the first flower

bed, Giovanna's bag was 5/8 full, Frances bag was 2/5 full, and their dad's was 3/4 full. How many pounds of soil did they put in the first flower bed all together (how to work it out)
Mathematics
2 answers:
Hoochie [10]3 years ago
7 0

12.25 pounds of soil

<h3>Further explanation</h3>

<u>Given:</u>

Giovanna, Frances, and their dad each carried a 10-pound bag of soil into the back yard. After putting soil in the first flower bed:

  • Giovanna's bag was \frac{5}{8} full,
  • Frances bag was \frac{2}{5} full, and
  • their dad's was \frac{3}{4} full.

<u>Question:</u>

How many pounds of soil did they put in the first flower bed altogether?

<u>The Process:</u>

Let us create each diagram for each of their 10-pound bags of soil.

  • Giovanna's: \boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}}\boxed{\frac{10}{8}} = 10 \ pounds. \boxed{1 \ unit = \frac{10}{8} = 1.25 \ pounds}
  • France's: \boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}}\boxed{\frac{10}{5}} = 10 \ pounds. \boxed{1 \ unit = \frac{10}{5} = 2 \ pounds}
  • Dad's: \boxed{\frac{10}{4}}\boxed{\frac{10}{4}}\boxed{\frac{10}{4}}\boxed{\frac{10}{4}} = 10 \ pounds. \boxed{1 \ unit = \frac{10}{4} = 2.5 \ pounds}

Let us calculate how many pounds of soil did they put in the first flower bed altogether. After putting soil,

  • Giovanna's bag was \frac{5}{8} full or 5 of 8 units. Hence, Giovanna put 3 of 8 units, or \boxed{\boxed{ \ 3 \times 1.25 \ pounds = 3.75 \ pounds \ }}.
  • Frances's bag was \frac{2}{5} full or 2 of 5 units. Hence, Frances put 3 of 5 units, or \boxed{\boxed{ \ 3 \times 2 \ pounds = 6 \ pounds \ }}.
  • Dad's bag was \frac{3}{4} full or 3 of 4 units. Hence, Dad put 1 of 4 units, or \boxed{\boxed{ \ 1 \times 2.5 \ pounds = 2.5 \ pounds \ }}.

We add up to be \boxed{ \ 3.75 + 6 + 2.5 = 12.25 \ }.

Thus, they put 12.25 pounds of soil in the first flower bed altogether.

- - - - - - - - - -

Quick Steps:

\boxed{ \ \Bigg(\bigg(1 - \frac{5}{8}\bigg) + \bigg(1 - \frac{2}{5}\bigg) + \bigg(1 - \frac{3}{4} \bigg) \Bigg) \times 10 \ pounds \ }

Least common multiple (LCM) of 8, 5, and 4 are 40.

\boxed{ \ \Bigg(\bigg(\frac{40}{40} - \frac{25}{40}\bigg) + \bigg(\frac{40}{40} - \frac{16}{40}\bigg) + \bigg(\frac{40}{40} - \frac{30}{40} \bigg) \Bigg) \times 10 \ pounds \ }

\boxed{ \ \bigg(\frac{15}{40} + \frac{24}{40} + \frac{10}{40} \bigg) \times 10 \ pounds \ }

\boxed{ \ \frac{49}{40} \times 10 \ pounds \ }

\boxed{ \ \frac{49}{4} \ pounds \ }

\boxed{ \ \frac{48}{4} + \frac{1}{4} \ pounds \ }

\boxed{ \ 12\frac{1}{4} \ pounds \ }

\boxed{\boxed{ \ 12.25 \ pounds \ }}

<h3>Learn more</h3>
  1. How many times does he switch strokes during the race? brainly.com/question/11494844  
  2. How many cookies will each student get brainly.com/question/328039
  3. Create and solve a story problem about two friends and their weekly allowance brainly.com/question/2968321

Keywords: Giovanna, Frances, their dad, each carried, a 10-pound bag of soil, into the back yard, after putting soil, in the first flower bed, 5/8 full, 2/5, 3/4, how many, they put, altogether

Greeley [361]3 years ago
3 0
First find the common denominator
5/8=25/40
2/5=16/40
3/4=30/40
Next you can cross multiply
25/40=x/10 pounds
16/40=x/10 pounds
30/40=x/10 pounds
First
25(10)/40= 6.25 pounds
16(10)/40= 4pounds
30(10)/40= 7.5 pounds
These are the amounts that were left in the bag

10-6.25=3.75
10-4=6
10-7.5=2.5

3.75+6+2.5= 12.25

All together they put 12.25 pounds of soil in the flower bed

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   -     -      -

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5 0
3 years ago
A particular fruit's weights are normally distributed, with a mean of 212 grams and a standard deviation of 20 grams.
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Answer:

220 grams.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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:

\mu = 212, \sigma = 20, n = 22, s = \frac{20}{\sqrt{22}} = 4.264

If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?

We have to find the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.

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

By the Central Limit Theorem

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

1.88 = \frac{X - 212}{4.264}

X - 212 = 1.88*4.264

X = 220

The answer is 220 grams.

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