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3 years ago

50 points! I will mark brainliest! This is due ASAP! So please hurry... random answer will be reported ;)

Mathematics

2 answers:

bagirrra123 [75]3 years ago

7 0

Answer:

choice 4) right scalene (one right angle and the side opposite that angle is the longest side)

choice 1) obtuse isosceles (one angle greater than 90 degrees and 2 equal length legs)

Step-by-step explanation:

Cloud [144]3 years ago

4 0

Answer:

D. right scalene

B. obtuse scalene

Step-by-step explanation:

The reason for this is because, it has a right angle so therefore, it already can be only B or D. However isosceles talk about having two sides of equal length. This triangle does not therefore, it cannot be B. That means it can only be D. right scalene

You immediately know that it is a obtuse because of the way it looks and the fact that there is a 130 degrees angle in the triangle. Therefore, you only have A and B and since isosceles triangles have two equal acute angles that won't work. Therefore, your only answer would be obtuse scalene.

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In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

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

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

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

5 0

3 years ago

If f(x) = 5x-3, which expression represents its inverse function?

valentinak56 [21]

Answer:

Pretty sure it's C

Step-by-step explanation:

For inverse functions, I do the opposite operation

the only logical inverse function I see working in this expression would be C

divide the 5 from 5x and add the 3

Also, subtract the f(x) on both sides to get the "- y"

so, you get : 5/x + 3 = - y (f(x) is just "y")

4 0

3 years ago

Harry worked 7 hours last week. This is 1__3as many hours as Aidan worked. How many hours did Aidan work?

vitfil [10]

Answer:

Step-by-step explanation:

1/3= 0.33

7/0.33

7 0

3 years ago

Factorise the following using the Difference of Two Squares or Perfect Squares rule: a) (2x-2)^2 - (x+4)^2 b) (3x+4) (3x-4)

emmainna [20.7K]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$(2x-2)^2 - (x+4)^2 \\\\=(2x-2-(x+4))(2x-2+x+4)\\\\=(2x-2-x-4)(3x+2)\\\\=\boxed{(x-6)(3x+2)}$

$(3x+4) (3x-4)\\\\=(3x)^2-4^2\\\\=\boxed{9x^2-16}$

Thank you.

7 0

3 years ago

Simultaneous equations 2x+3y=13 4x-y=-2

Rufina [12.5K]

Answer:

(0.5, 4 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 13 → (1)

4x - y = - 2 → (2)

Multiplying (2) by 3 and adding to (1) will eliminate the term in y

12x - 3y = - 6 → (3)

Add (1) and (3) term by term to eliminate y

14x = 7 ( divide both sides by 14 )

x = 0.5

Substitute x = 0.5 into either of the 2 equations and evaluate for y

Substituting into (1)

2(0.5) + 3y = 13

1 + 3y = 13 ( subtract 1 from both sides )

3y = 12 ( divide both sides by 3 )

y = 4

Solution is (0.5, 4 )

3 0

4 years ago