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3 years ago

The weight needed to balance a lever varies inversely with the distance

Mathematics

1 answer:

Andrews [41]3 years ago

5 0

Let w represents the weight and d represents the distance.

It is given that

The weight needed to balance a lever varies inversely with the distance from the fulcrum to the weight. A 120-lb weight is placed on a lever, 5 ft from the fulcrum.

$w = \frac{k}{d}$

Substituting the values of w and d, we will get

$120= \frac{k}{5}
\\
k =600lb \ ft$

Using the value of k which is 600, with the above equation and the given value of d which is 8, we will get

$w = \frac{600}{8} = 75lb$

Therefore the correct option is B .

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A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

VMariaS [17]

Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

Step-by-step explanation:

Previous concepts

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 means 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$

Now we have everything in order to replace into formula (1):

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

5 0

3 years ago

Write each percent as a fraction and as a decimal to the nearest hundredth.

Nataly [62]

Each as a fraction 42/100 35/100 18/100 100/100

8 0

3 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

statuscvo [17]

Let's start by visualising this concept.

Number of grains on square:
1 2 4 8 16 ...

We can see that it starts to form a geometric sequence, with the common ratio being 2.

For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
$T_n = ar^{n - 1}$
$T_{15} = 2^{14} = 16384$

Thus, there are 16, 384 grains on the fifteenth square.

The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
$S_n = \frac{a(r^{n} - 1)}{r - 1}$
$S_{15} = \frac{2^{15} - 1}{2 - 1}$
$S_{15} = 2^{15} - 1 = 32767$

Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.

6 0

3 years ago

Read 2 more answers

Which simplified fraction is equal to 0.53? 1) 24/45 2) 8/15 3) 48/90 4) 5/9

Shalnov [3]

To express a decimal number (with a finite decimal expression) in a fraction, you work like this: the numerator is the number without decimale separator (you simply pretend it's not there), while the denominator will be $10^n$ , where n is the number of digits after the decimal separator.