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2 years ago

Please help me i’ll really appreciate it (it’s problem 3 btw)

Mathematics

2 answers:

Flura [38]2 years ago

4 0

Answer:

1. 1500

2. 95.71%

Step-by-step explanation:

1. If a number is a ± b, then the relative error is b/a

35000 - 33500 = 1500

Amount of error = 1500

2. Percentage of two given data = smaller divided by larger then x 100

33500 / 35000 = 0.95714285714

0.95714285714 x 100 = 95.71%

Ksenya-84 [330]2 years ago

3 0

Answer

1: 1500
2:95.71%

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The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologi

Alex Ar [27]

This question is incomplete, the complete question;

The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologists based on their academic degree and years of experience. 36 psychologists responded who had a just received their masters degree in 2003. The average was $48,800 with a standard deviation of $16,800.

The 95% Confidence Interval is ($, $ )

Answer:

at 95%, confidence interval is ( $43312, $54288 )

Step-by-step explanation:

Given the data in the question;

sample size n = 36

mean x' = 48,800

standard deviation σ = 16,800

at 95% confidence level;

∝ = 1 - 95% = 1 - 0.95 = 0.05

∝/2 = 0.05 / 2 = 0.025

z critical value, $Z_{\alpha/2$ = 1.96

now, confidence interval for population mean is given by the formula

x' ± $Z_{\alpha/2$ ( σ/√n )

so we substitute

⇒ 48800 ± 1.96( 16800/√36 )

⇒ 48800 ± 1.96( 2800 )

⇒ 48800 ± 5488

⇒ 48800 - 5488, 48800 + 5488

⇒ ( 43312, 54288 )

Therefore, at 95%, confidence interval is ( $43312, $54288 )

6 0

2 years ago

Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3).

marissa [1.9K]

Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:

$A=\frac{3\sqrt{3}}{2} a^2$

Where $A$ is the area of the regular hexagon

$a$ is the side length of the regular hexagon

Also, it's Perimeter is given by:

$P=6a$

Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.

A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.

Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.

Let us now find the distance between the points D and E using the distance formula which is as:

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Where $d$ is the distance.

$(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance $d$ )

Applying the above formula we get:

$d=\sqrt{(8-4)^2+(0-0)^2} =\sqrt{4^2}=4$

$\therefore d=4$

We know that this distance is the side length of the given regular hexagon.

$\therefore d=a=4$

Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:

$a_{small}=4-\frac{40}{100}\times 4=2.4$

Thus, the area of the smaller hexagon will be:

$A_{small}=\frac{3\sqrt{3}}{2} a_{small}^2=\frac{3\sqrt{3}}{2} (2.4)^2\approx14.96$ unit squared

and the new smaller perimeter will be:

$P_{small}=6a_{small}=6\times 2.4=14.4$ unit

Which are the required answers.

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3 years ago

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bazaltina [42]

<span>Information is given(reasons are in the parenthesis)

Angle A and angle B are supplementary. Angle B and Angle C are supplementary (given)

DC is parallel to AB (consecutive interior angles are supplementary )
BC is parallel to AD (consecutive interior angles are supplementary)

ABCD is a parallelogram (definition of parallelogram, has to pairs of parallel sides)</span>

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3 years ago

1. Ron makes $1,659 a month. What is the maximum monthly rent he can afford?

Mashutka [201]

Here are my notes for monthly rents:

<span>Landlords typically require that your annual income is at least 40 times the monthly rent. For example, if you and your roommate are looking at a $3,000 per month apartment, the landlord would require a combined income of $3,000 × 40, which equals $120,000. To determine how much rent you (and your potential roommates) can afford, simply divide your combined annual incomes by 40.
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I hope my guide has come to your help. God bless and have a nice day ahead!

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3 years ago

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Write the following as a decimal, use repeating decimals when necessary 6/11

STatiana [176]

Answer:

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Step-by-step explanation:

I used my calculator for it I am terribly sorry if it's wrong

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2 years ago