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2 years ago

If 2m = 4x and 2w = 8x, what is m in terms of w?

Mathematics

2 answers:

Mariana [72]2 years ago

6 0

2^m=2^n take the natural log of both sides

m*ln2=n*ln2 divide both sides by ln2

m=n

CaHeK987 [17]2 years ago

6 0

You can simply divide the eqution or you substitute the value of x in any equation.

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preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found tha

VladimirAG [237]

Answer:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

n=369

Step-by-step explanation:

1) Notation and definitions

$X=40$ number of the selected labourers opt for a new incentive scheme.

$n=100$ random sample taken

$\hat p=\frac{40}{100}=0.4$ estimated proportion of the selected labourers opt for a new incentive scheme.

$p$ true population proportion of the selected labourers opt for a new incentive scheme.

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

2) Solution tot he problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

And rounded up we have that n=369

8 0

2 years ago

Vince weighs 160 pounds and his friend nadir weighs 140 nadir calculated that his weight on another planet would be about 56lb a

chubhunter [2.5K]

Vince would weigh 64 pounds

3 0

2 years ago

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Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be

makkiz [27]

Answer:

Mary is filling 36 cups per minute, which is faster than Jorge.

Step-by-step explanation:

Lets get Jorge's time :

As the rate is constant, we can find the slope to know the number of cups he is filling per minute.

Slope is found using: $\frac{y2-y1}{x2-x1}$

= $\frac{53-25}{5-3}$

= $\frac{28}{2}=14$

From the table lets get Mary's time:

$\frac{99-81}{1-0.5}$

= $\frac{18}{0.5}=36$

Another data: $\frac{63-45}{2-1.5}$

= $\frac{18}{0.5}=36$

Therefore, we can see that Mary is filling 36 cups in a minute and Jorge is filling 14 cups.

Hence, the correct answer is : Mary is filling 36 cups per minute, which is faster than Jorge.

7 0

2 years ago

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Match each set of prices with the correct percent of increase or decrease.

cricket20 [7]

Take the
(original price - new price)/original price
then multiply by 100
If it is a positive number, it is a decrease.
If it is a negative number, it is an increase.

original price: $63.00
new price: $56.07
11% decrease

original price: $12.25
new price: $13.23
8% increase

original price: $98.00
new price: $108.78
11% increase

original price: $37.50
new price: $34.50
8% decrease

7 0

1 year ago

In Jana's closet she has 5 pairs of black shoes and 11 pairs of leather shoes. Two of her pairs of shoes are both black and leat

Delvig [45]

Answer:

Step-by-step explanation:

I'm not sure about the 2nd one, though I think it is D, BUT DON"T TAKE MY WORD ON IT! On the first one the answer is C, add 5 + 11, then because 2 pairs are black and leather, subtract 2 from both sides.

8 0

2 years ago

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