Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 16 cm.

(1) How many equilateral triangles are there? _____

(2) What is the measure of each of the three angles in the equilateral triangle? _____

(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____

(4) What is the vocabulary word for the segment a? _____

(5) What is the length of the short side of one of the 30-60-90 triangles? _____

(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____

(8) What is the height of one of the the equilateral triangles? _____

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____

Answer:

36 cm

Step-by-step explanation:

504/14=36

The inequality that can be used to represent the information that a number is no less than 48 will be n > 48.

Inequality simply means a mathematical expression that is used in which the sides aren't equal to each other.

It should be noted that the expression that a number is no less than 48 means the number is greater than 48. Therefore, the inequality is n > 48.

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Answer: The correct answer is n≥48

Step-by-step explanation: Give me the brainiest

Step-by-step explanation:

sqrt(5x)×(sqrt(8x²) - 2×sqrt(x)) =

sqrt(5x × 8x²) - 2×sqrt(5x × x) =

sqrt(40x) × x - 2x × sqrt(5) =

2x×sqrt(10x) - 2x×sqrt(5)

therefore, the last option is correct.

Answer:

Three tenths/ 3/10

Step-by-step explanation:

1/5 divided by 2/3 is 0.3 which is equal to 3/10

Answer:

Simplifying

6r + r + -5r = 0

Combine like terms: 6r + r = 7r

7r + -5r = 0

Combine like terms: 7r + -5r = 2r

2r = 0

Solving

2r = 0

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Divide each side by '2'.

r = 0

Simplifying

r = 0

7r-5r < this is the answer

6r+r=7r

3 Years

Compound interest is a multiplier that affects the new value each time.

If the compound interest is 10% per annum, the multiplier each year is 1.1.

Year 1: $1000 * 1.1 = $1100

Year 2: $1100* 1.1 = $1210

Year 3: $1210* 1.1 = $1331

This means that it will take 3 years for $1000 to amount to $1331 at 10% per annum.

Alternatively, you can use a logarithm. The calculation can be written as:

1000 * [tex]1.1^n[/tex] = 1331, where n is the number of years.

Rearranged, this gives [tex]1.1^n[/tex] = 1331/1000 or [tex]1.1^n[/tex] = 1.331.

A logarithm can work out the value of n, and is written in the form log1.1(1.331), which gives a value of 3.

Answer: C

Step-by-step explanation: the guy up top is correct:)

Answer:

Exact Form:

C=23/24

Decimal Form:

C=0.9583

Step-by-step explanation:

Answer:

A: the area of the walls that are being painted

C: the cost per gallon of different paints

F: the number of square feet that can be painted per gallon of paint

Step-by-step explanation:

Based on the investment ratio and the amount invested, the amount that Zach invested is $102,857.14.

First thing to do is to add up the numbers in the ratio:

= 1 + 2 + 0.5

= 3.5

The amount that Zach invested is:

= Zach's ration/ Sum of ratio x Amount invested

= 1 / 3.5 x 360,000

= $102,857.14

In conclusion, Zach invested $102,857.14.

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Answer:

  6 shirts

Step-by-step explanation:

The cost of a shirt and 2 ties is ...

  $18.50 +2(7.50) = $33.50

For $205, Frank can buy $205/$33.50 = 6.12 sets of shirt and ties.

Frank can buy 6 shirts (and 12 ties) for an amount less than $205.

_____

Additional comment

Frank's cost will be $201 for that purchase.

Answer:

1

Step-by-step explanation:

[tex] \frac{6}{12} + \frac{1}{2} \\ = \frac{1}{2} + \frac{1}{2} \\ = \frac{2}{2} \\ = \frac{1}{1} \\ = 1[/tex]

The number of years it would take the amount to triple is 25 years.

The formula that would be used to determine the number of years it would take the balance to triple is:

FV = PV  x [tex]e^{r}[/tex]N

Where:

3 = [tex]e^{0.044}[/tex]N

Take the log of both sides

log(3) / log(e) /  (0.044) = 25 years

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Answer:

Step-by-step explanation:

20=total marbles

  7/20 × 6/20=  21/400   or 5.25%

   red     white

hi i know i'm late but might as well add my answer!

here's your answer: B D E or

B.choosing 1 red marble

D.choosing 1 white marble, replacing it, and choosing another white marble

E.choosing 1 white marble    

hope i helped

Answer:

b d and e

Step-by-step explanation:

ya

Answer

B, the second choice

Step-by-step explanation:

the domain is defined as all possible x values of a function and the range is defined as all possible y values, so the domain would be all real numbers since x can be any value, and the range cannot be more than 3, since y=3 is the vertex of the parabola.

Answer:

The answer is C.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

y=2x+1

Step-by-step explanation:

y-5/x-2=2

2x-4=y-5

y=2x+1

Answer:

10^2

Step-by-step explanation:

10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2

Answer:

100

Step-by-step explanation:

Hope it helps

Using the t-distribution, it is found that since the test statistic is less than the critical value for the left tailed test, there is not enough evidence to show that the patients with schizophrenia have less TBV on average than a  patient that is considered normal.

At the null hypothesis, we test if patients with schizophrenia do not have less TBV on average than a  patient that is considered normal, that is, the subtraction is not negative, hence:

[tex]H_0: \mu_S - \mu_N \geq 0[/tex]

At the alternative hypothesis, we test if they have less, that is, if the subtraction is negative, hence:

[tex]H_1: \mu_S - \mu_N < 0[/tex]

Regarding each sample, the mean and standard deviation are found using a calculator.

[tex]\mu_N = 1463339.2, s_N = 125458.28 , n_N = 32[/tex]

[tex]\mu_S = 1445132.3, s_S = 171355.8, n_S = 30[/tex]

We have the standard deviation for each sample, hence, the t-distribution will be used.

The standard errors are given by:

[tex]Se_N = \frac{125458.28}{\sqrt{32}} = 22178.1[/tex]

[tex]Se_S = \frac{171355.8}{\sqrt{30}} = 31285.1[/tex]

The distribution of the difference has mean and standard error given by:

[tex]\overline{x} = \mu_S - \mu_N = 1445132.3 - 1463339.2 = -18206.9 [/tex]

[tex]Se = \sqrt{Se_N^2 + Se_S^2} = \sqrt{22178.1^2 + 31285.1^2} = 38348.7[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{Se}[/tex]

In which [tex]\mu[/tex] is the value tested at the hypothesis.

Hence:

[tex]t = \frac{\overline{x} - \mu}{Se}[/tex]

[tex]t = \frac{-18206.9 - 0}{38348.7}[/tex]

[tex]t = -0.47[/tex]

The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.1 and 32 + 30 - 2 = 60 df is [tex]t^{\ast} = 2[/tex]

Since the test statistic is less than the critical value for the left tailed test, there is not enough evidence to show that the patients with schizophrenia have less TBV on average than a  patient that is considered normal.

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[tex]8:16\implies \cfrac{8}{16}\implies \cfrac{1}{2}\implies 1:2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{16}{31}\qquad \bigotimes~\hfill \cfrac{1}{3}\qquad \bigotimes~\hfill \cfrac{1}{2}\qquad \textit{\large \checkmark}~\hfill \cfrac{12}{24}\implies \cfrac{1}{2}\qquad \textit{\large \checkmark}[/tex]

Answer:

1/2. and 12/24

they are both halves just as the ratio is half of the given number

Answer:

40%

Step-by-step explanation:

2/5 = 40/100 = 40%

Answer:

22

Step-by-step explanation:

Answer:

you would need three wholes because each whole would represent a loaf of pumpkin bread

Answer:

1/5    1   2  

Step-by-step explanation:

Answer:

The scale is 1:18 for the entire room, 1 inch in the diagram for 18 inches IRL

Step-by-step explanation:

12 inches = 1 foot

Convert the feet to inches, then divide both sides of the ratio by the # of inches in the diagram

So for length:

10:(15*12)

10:180

1:18

And for width:

8:12(12)

8:144

1:18

Answer:

18 inches

Step-by-step explanation:

The question asks for scale of inches in the drawing and the actual room, so first convert 15 ft and 12 ft into inches.

1 foot= 12in x 1ft= 12 inches

15 feet= 12in x 15ft = 180 inches

12 feet= 12in x 12ft = 144 inches

The room is 180 inches long and 144 inches wide.

To find the scale, set up a proportion to the drawing to the room.

[tex]\frac{10}{8} =\frac{180}{144}[/tex]

You can see that the scale is 18 inches because to get from 180 to 10, you multiply by 18, and the same thing as 8, you would multiply 8 by 18 to get to 144.

Answer:

3 cube root of 15

Step-by-step explanation:

theres your simple radical form

8(152/3) is 405 1/3 in simplest radical form.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

405 1/3 is equivalent to (405*3 + 1)/3 = 1216/3.

To express 1216/3 in simplest radical form, we can first simplify it by dividing both the numerator and denominator by their greatest common factor, which is 8.

1216/3 = (8*152)/3 = 8(152/3)

Now, we can see that 152/3 cannot be simplified any further, so the simplest radical form of 405 1/3 is: 8(152/3)

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