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4 years ago

A boat traveled 27 miles in 2 hours.At this rate,how many miles will the boat in 1/2 hour?

Mathematics

1 answer:

serious [3.7K]4 years ago

7 0

$\frac{27 \: miles \div 2}{2 \: hours \div 2} = \frac{13.5 \: miles}{1 \: hour}$

$\frac{13.5 \: miles \div 2}{1 \: hour \div 2} = \frac{6.75 \: miles}{0.5 \: hour}$

The boat will travel 6.75 or

$6 \frac{3}{4}$

miles in 1/2 hour.

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Directions: Read, analyze, and choose the letter of the correct answer. Write your

svetoff [14.1K]

1) The normal room temperature is said to be about 20°C

2) 5 day is equivalent to 120 hr

3) 756 m³/s is equivalent 56000 L/s

4) It would take the snail 5 hours to crawl 75 m

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

1) The normal room temperature is said to be about 20°C

2) 1 day = 24 hr

5 day = 5 day * 24 hr per day = 120 hr

3) 1 m³ = 1000 L

756 m³/s = 56 m³/s * 1000 L/m³ = 56000 L/s

4) 1 m = 100 cm

75 m = 7500 cm

Time = 7500 / (25 cm/min) = 300 min = 5 hours

Find out more on equation at: brainly.com/question/2972832

#SPJ1

6 0

2 years ago

1. The SAT test scores have an average value of 1200 with a standard deviation of 105. A random sample of 35 scores is selected

AveGali [126]

Answer:

a) The shape is bell shaped, because of the single peak at the center, that is the mean.

The mean of the sampling distribution of the sample mean is 1200.

The standard deviation of the sampling distribution of the sample mean for samples of size 35 is 17.75.

b) There is a 2.07% probability that the sample mean will be larger than 1235.

c) 85.68% probability that the sample mean will fall within 25 points of the population mean.

d) There is a 7.22% probability that the sample mean will be less than 1175.

Step-by-step explanation:

Problems of normally distributed samples can be 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

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

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 This p-value is the probability that the value of the measure is greater than X.

In this case, we have that:

The SAT test scores have an average value of 1200 with a standard deviation of 105. A random sample of 35 scores is selected for study. So $\mu = 1200, \sigma = 105, n = 35$ .

A) What is the shape, mean(expected value) and standard deviation of the sampling distribution of the sample mean for samples of size 35?

The shape is bell shaped, because of the single peak at the center, that is the mean.

The mean of the sampling distribution of the sample mean is the same as the sample mean. So, the mean of the sampling distribution of the sample mean is 1200.

The standard deviation of the sampling distribution of the sample mean for samples of size 35 is the sample standard deviation divided by the square root of the size of the sampling distribution.

$s = \frac{105}{sqrt{35}} = 17.75$

The standard deviation of the sampling distribution of the sample mean for samples of size 35 is 17.75.

B) What is the probability that the sample mean will be larger than 1235?

This is 1 subtracted by the pvalue of Z when $X = 1235$ .

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

$Z = \frac{1235 - 1200}{17.15}$

$Z = 2.04$

$Z = 2.04$ has a pvalue of 0.9793

So there is a 1-0.9793 = 0.0207 = 2.07% probability that the sample mean will be larger than 1235.

C) What is the probability that the sample mean will fall within 25 points of the population mean?

This is the subtraction of the pvalue of the Z score when X = 1225 by the pvalue of the Z score when X = 1175.

So:

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

$Z = \frac{1225 - 1200}{17.15}$

$Z = 1.46$

$Z = 1.46$ has a pvalue of 0.9279

X = 1175 is going to have $Z = -1.46$ , that has a pvalue of 0.0722.

This means that there is a 0.9297 - 0.0729 = 0.8568 = 85.68% probability that the sample mean will fall within 25 points of the population mean.

D) What is the probability that the sample mean will be less than 1175?

X = 1175 has $Z = -1.46$ , that has a pvalue of 0.0722.

This means that there is a 7.22% probability that the sample mean will be less than 1175.

3 0

3 years ago

The human resources manager at a company records the length, in hours, of one shift at work, X. He creates the probability distr

Oliga [24]

The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.

<h3>How to evaluate the probability of a random variable getting at least some fixed value?</h3>

Suppose the random variable in consideration be X, and it is discrete.

Then, the probability of X attaining at least 'a' is written as:

$P(X \geq a)$

It is evaluated as:

$P(X \geq a) = \sum_{\forall \: x_i \geq a} P(X = x_i)$

The probability distribution of X is:

x f(x) = P(X = x)

6 0.02
7 0.11

8 0.61

9 0.15

10 0.09

Worker working at least 8 hours means X attaining at least 8 as its values.

Thus, probability of a worker chosen at random working 8 hours is

P(X ≥ 8) = P(X = 8) + P(X = 9) +P(X = 10) = 0.85 ≈ 0.84 approx.

By the way, this probability distribution seems incorrect because sum of probabilities doesn't equal to 1.

The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.

Learn more about probability distributions here:

brainly.com/question/14882721

7 0

3 years ago

Geoff works, earning $17.50 per hour plus a $200 one-time hiring bonus. In Geoff's first week, week, his pay including the bonus

Elza [17]

Geoff works, earning $17.50 per hour plus a $200 one-time hiring bonus. In Geoff's first week, week, his pay including the bonus was $637.50

Write and solve an equation to find how many hours h Geoff worked his first week.
plsssss. mark as brilliant

5 0

3 years ago

MATH GRADE 8 15. a) and b)

Elden [556K]

Answer: 1300 cm³

a) Find the volume of the entire rectangle and subtract the volume of the missing section. Volume = L · w · h

Solid = Rectangle - Missing section

= L · w · h - L · w · h

= 16 · 10 · 10 - 10 · 6 · 5

= 1600 - 300

= 1300

b) Find the volume of each section of the rectangle (base, left wing right wing) and add them. Volume = L · w · h

Solid = Base + Left wing + Right wing

= L · w · h + L · w · h + L · w · h

= 16 · 10 · 5 + 5 · 10 · 5 + 5 · 10 · 5

= 800 + 250 + 250

= 1300

The answer from (a) is the same as (b) $\checkmark$

6 0

4 years ago