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3 years ago

A pile of sand has a weight of 90kg the sand is put into a small bag and a medium bag and a large bag in the ratio 2:3:7

Mathematics

1 answer:

Finger [1]3 years ago

3 0

90kg of sand had been puted in 3 bags but in 2+3+7=12 parts.
90kg/12=7.5kg
Small bag has 2 parts which is 7.5kg*2=15kg
Medium bag has 3 parts which is 7.5kg*3=22.5kg
Large bag has 7 parts which is 7.5kg*7=52.5kg
2:3:7=15kg:22.5kg:52.5kg
15kg+22.5kg+52.5kg=90kg

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At how many different times will the digit 7 appear on a digital clock in 24 hours?(show your work and explain your strategy bel

exis [7]

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3 years ago

The triangles below are similar. What is the length of ? A. 17 cm C. 19 cm B. 18 cm D. 20 cm

denis-greek [22]

Answer:

B. 18 cm.

Step-by-step explanation:

Because they are similar, we can say that segment AC corresponds to segment DF, and segment AB corresponds to segment ED. So, we can set up a proportion.

$\frac{16}{24} =\frac{12}{x}$

$\frac{2}{3} =\frac{12}{x}$

2 * x = 12 * 3

2x = 36

x = 18

So, the length of ED is B. 18 cm.

Hope this helps!

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3 years ago

A random sample of 20 students yielded a mean of ¯x = 72 and a variance of s2 = 16 for scores on a college placement test in mat

Helen [10]

Answer:

The 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

Step-by-step explanation:

1) Data given and notation

$s^2 =16$ represent the sample variance

s=4 represent the sample standard deviation

$\bar x$ represent the sample mean

n=20 the sample size

Confidence=98% or 0.98

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical values.