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3 years ago

True or false: the diagonals of a rectangle bisect opposite angles

Mathematics

1 answer:

solong [7]3 years ago

8 0

Answer:

False

Step-by-step explanation:

diagonals don't have to be congruent or bisect each other. The diagonals of a rectangle bisect its angles.

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Kaleb makes an investment at 5.2 percent simple interest. At the end of 1 year, the total value of the investment is $2419.60. H

Dafna11 [192]

The future amount of the current deposit given that the interest is simple and yearly is computed through the equation,
F = P x (1 + in)
where P is the principal amount, F is the future amount, i is the interest (in decimal form) and n is the number of years.

In this certain problem, we substitute the known values to the equation and solve for P,
2419.60 = P x (1 + (0.052)(1))
P = 2300
Thus, the initial investment was worth $2,300.

3 0

3 years ago

What's (7x/2-5x+3)+(2x/2+4x-6)

Anika [276]

I'm assuming that when you wrote "(7x/2-5x+3)+(2x/2+4x-6)," you actually meant "(7x^2-5x+3)+(2x^2+4x-6). Correct me if I'm wrong here.

+(7x^2-5x+3)
+(2x/2+4x-6)
-------------------
=9x^2 - x - 3 (answer)

5 0

3 years ago

A government report gives a 99% confidence interval for the proportion of welfare recipients who have been receiving welfare ben

juin [17]

Answer:

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

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

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

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".

Solution to the problem

The population proportion have the following distribution

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

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

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

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

5 0

3 years ago

The ratio of boys to girls in a group is 3:1. If there are 28 more boys than girls, work out how many people there are in total.

puteri [66]

Answer:

84:56, I think?

3 x 28 for the boys then minus 28 for the girls

3 0

3 years ago

Write the equation y=-1/2x+3 in standard form.

cricket20 [7]

Begin by multiplying both sides by 2 to get rid of the fraction. The standard form for a line is Ax + By = C, no fractions allowed. By multiplying we get 2y=-1x+3. Now move the -1x over by adding and we have the standard form we are looking for: x + 2y = 3.

7 0

3 years ago

True or false: the diagonals of a rectangle bisect opposite angles​

True or false: the diagonals of a rectangle bisect opposite angles