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 12 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. _____

A lovely beach resort is Data Island. Since it first became a popular tourist destination more than 80 years ago, the earliest vacation homes have been constructed just a few steps from the beach. You are a real estate agent for a company that deals in vacation rentals and sales in the Data Islands. A report was recently presented to you by one of the interns on the data science team. The age of a house affects its price, according to the linear regression model they have ran. But this is absurd because newer homes ought to be more valuable.

1.  As the coefficient of Age is positive, so the older the house, the more price it is. Sig. (or p-value) = 0.000 which implies  that the co-efficient of Age is significant.

2.  This may be that the people who live there are reluctant to sell it, so they quote a higher price or the size of old houses are large or they may be located at prime location.

3.  We would ask new interns to consider other independent variables for the regression equation like size of house, location, etc.

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The mean and standard deviation of the sampling distribution is 70 and 2 respectively.

Given a random sample of 25 measurements means

n = 25.

Population with mean(µ)  70 means

µ = 70.

Population with standard deviation(σ) 10 means

σ = 10.

mean of sampling distribution is itself same as mean of population

so mean of sampling distribution is 70.

standard deviation of sampling distribution is

σ/[tex]\sqrt{n}[/tex].

put the value of σ= 10 and n =25.

10/[tex]\sqrt{25}[/tex] = 10/5 = 2

So mean of sampling distribution is 70 and standard deviation of sampling distribution is 2.

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To make the expression 3(x + 4) - 2(x + 4) + 0.5(x + 4)  equals 1.5, we make x in the linear equation equals -3

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

There are linear equations in one variable and linear equations in two variables.

In this problem given we have to simplify and equation the expression to 1.5 to make it an equation.

3(x + 4) - 2(x + 4) + 0.5(x + 4) = 1.5

3x + 12 -2x -8 + 0.5x + 2 = 1.5

3x - 2x + 0.5x + 12 - 8 + 2 = 1.5

1.5x + 6 = 1.5

Collect like terms

1.5x = 1.5 - 6

x = -3

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answer: 72 or 1572480 depends on how you do the math

Answer:

1) 312

2) 20

Step-by-step explanation:

4x78=312

78 divided by 4=19.5 rounded up =20

Probability of at least one people behind taller person = n-1/n.

From the question, we have

n people of different heights are lined up in a queue

Probability of at least one people behind taller person = 1 - 1/n =n-1/n

Probability:

The term probability refers to possibility. The occurrence of a random event is the focus of this mathematical field. There is a 0 to 1 value range. To determine the possibility of certain events, probability has been employed in mathematics. The likelihood of anything happening is often referred to as probability. You can better understand the outcomes of a random experiment by applying this fundamental theory of probability, which also holds true for the probability distribution. Utilize probability to gauge a situation's likelihood of happening. Numerous factors are difficult to forecast with absolute precision. Using it, we can only speculate on whether or how likely it is that an event will occur.

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The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.

She was given a starting wage of $48,000 from Company A, with annual raises of $2100.

The formula for Company A is

f(t) = 48000 + 2100t

She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.

The formula for Company B is

g(t) = 48000 × [tex](1 + 0.037)^t[/tex]

The value of f(t) and g(t),

t ------- f(t) ------- g(t)

0 ----- 48000 ----- 48000

1 ------ 52200 ----- 49776

2 ----- 54300 ----- 51617.71

3 ----- 56400 ----- 53527.56

The graphical representation of both the linear equations of company A and company B.

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Answer:

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The container put 320 ml amount of the acid in 60 seconds.

Given, a robotic machine fills containers with an acid solution at the rate of 140 + 3t milliliters ( ml ) per second, where t is in seconds and 0 ≤ t ≤ 60 .

we have to find the amount of acid solution put into the container in 60 sec

As, Amount of acid be A(t)

A(t) = 140 + 3t

A(60) = 140 + 3(60)

A(60) = 140 + 180

A(60) = 320

So, the container put 320 ml amount of the acid in 60 seconds.

Hence, the container put 320 ml amount of the acid in 60 seconds.

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Answer:

if 5x + 2 = 7x - 7 then the answer is x = 9/2.

Type I error is:

" Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29 "

Type II error is:

"Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29 "

What is proportion?

An equation in which two ratios are made equal is called a proportion. For instance, you could write the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.

In Statistics, a  type I error is the rejection of a true null hypothesis

and  a type II error is the non-rejection of a false null hypothesis

Given that p = 0.29 is accepted

Now type I error is

C. Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29

i.e. (false positive)

and type II error here is

B. Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29.

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Answer:

The volume increases 8-fold or by 700%.

Step-by-step explanation:

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If we pay 12.5 percent for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A % is a number that has neither dimensions nor a defined unit of measurement.

To calculate the percentage, we must divide the value by the entire amount and then multiply the result by 100.

So, if the interest rate is 12.5%, our total loan payment would be:

112.5/100 × 6,000 = $6,750.

The monthly payment would be if there was no buildup and other agreement in payment:

6750/12*10

6750/120

$56.25

Therefore, if we pay 12.5% for 10 years, our monthly payment for a $6000 loan will be about (C) $55.58.

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Complete question:

How much would you pay monthly on a $6,000 loan if you pay 12.5 percent for 10 years?

a. $87.90

b. $70.32

c. $55.58

d. $125.00?

The type of variable required is Qualitative with two possible outcomes.

An estimate level of uncertainty is expressed by a range of values known as a confidence interval.

Keeping in mind, the z-score and other data's decimal places should be preserved when generating the confidence interval upper and lower bounds. The responses will be accurate and round-off errors will be prevented.

Also, the confidence interval boundaries are expressed in percentages. The maximum value of 0.8740, for instance, is 87.4% in decimal notation.

Make sure to specify the confidence level, the percentage of the population that the confidence interval actually captures, and the bounds expressed in percentages when expressing the meaning of the confidence interval.

Hence, the type of variable required to construct a confidence interval for a population​ proportion is Qualitative with 2 possible outcomes.

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Adjacent angles of a parallelogram are supplementary.

[tex]x+2x=180 \\ \\ 3x=180 \\ \\ x=\boxed{60}[/tex]

The highest score is 32 points.

Given,

Mean score of 8 players =14.5

After removing highest score then,

Mean score of 7 players =12

let

the sum of all score be 'x'

highest score be 'y'

At first,

[tex]Mean=\frac{sum\ of\ all\ scores}{total\ number\ of\ scores}\\\\14.5=\frac{x}{8}\\\\x=116[/tex]

after removing the highest score, mean  will be

[tex]Mean=\frac{sum\ of\ all\ scores-highest\ score}{number\ of\ scores}\\\\12=\frac{x-y}{7}\\\\x-y=84[/tex]

substituting 'x'

[tex]116-y=84\\\\116-84=y\\\\y=32[/tex]

Thus, the highest score is 32 points.

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The combined sample mean for sample one, whose size equals 8 scores and mean equals 2, and for sample second, whose size equals 4 scores and mean equals 8, is 4..

A combined sample mean is calculated by taking the mean of each group and combining (adding) the results of each average.

We have given that,

For First sample :

Sample size ,n₁ = 8 scores

sample mean, m₁ or X₁-bar = 2

Sample 2 :

Sample size, n₂ = 4

sample mean , m₂ or X₂-bar = 8

Combined sample mean is given by,

M or X-bar =( n₁× x₁-bar + n₂ × x₂-bar)/(n₁+n₂)

plug all the known values in above formula

=> M = (8×2 + 4×8 )/12

=> M = 48/12 = 4

Hence, combined sample mean is 4 .

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Dominic should lower or maintain his sodium intake to below 2,300 mg/day.

The Chronic Disease Risk Reduction (CDRR) consumption of 2,300 mg/day was recently developed due to connections between high sodium intake and the risk of hypertension. It is anticipated that sodium intake below this level will lower the risk of chronic diseases.

Adults may be at risk for chronic diseases if their sodium intake exceeds their CDRR intake. The population's cardiovascular health may be improved by efforts to reduce sodium consumption. Among healthy individuals, lowering daily sodium intake to CDRR is anticipated to lower the risk of developing chronic diseases, primarily by lowering blood pressure.

Hence, sodium intake to below 2,300 mg/day can reduce his risk of chronic disease.

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The length of hypotenuse is 10. It can be obtained by using Pythagorean Theorem.

What is Pythagorean theorem?

It is a theorem which gives the relationship between the length of base, perpendicular height, and hypotonus. This relationship is valid only for a right angled triangle.

The length of hypotenuse is given by the following formula:

[tex]h=\sqrt{b^2+p^2}[/tex]

Here, h is the length of hypotenuse, b is the length of base, and p is the length of perpendicular.

Substitute 6 for b and 8 for p in the above equation.

[tex]h=\sqrt{6^2+8^2}\\=\sqrt{36+64}[/tex]

Now, take the square root of 100.

[tex]h=\sqrt{100}\\=10[/tex]

Hence, the length of hypotenuse is 10.

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Answer:

Function: V(t) = 40,000(0.81^(4t))

Quarterly rate of change: -19.00%

Step-by-step explanation:

um, I'm going to use elimination method to solve this simultaneous equation

x+2y=-6.......... equation 1

6x+2y=4........ equation 2

subtract equation 2 from equation 1

-5x = -10

x = -10/-5

x=2

substitute x=2 in equation 1

therefore equation 1 becomes

2+2y=-6

2y=-6-2

2y=-8

y=-8/2

y=-4

The probability of rolling a die 10 times and obtaining odd digit 8 or less of the rolls is 529/512 = 1.033

Let us call, getting an odd no. on a roll of die, Success.

The, clearly, the probability p of Success is 3/6 = 1/2.

Hence, q = 1 −p = 1/2

If, X = x denotes the no. of success in n trials, then, X is a

Binomial Random Variable, with parameters

n = 10, and, p = 1/2.

Binomial Random Variable:

This is a specific type of discrete random variable. A binomial random variable counts how often a particular event occurs in a fixed number of tries or trials. For a variable to be a binomial random variable, ALL of the following conditions must be met:

Then, the Probability of x success out of n trials, i.e.,

P (X = x), is,

P (X = x) = p(x) =ⁿCₓ pˣ , qⁿ⁻ˣ, x = 0,1,2, ........, n

In our case,

P (X = x) = ¹⁰Cₓ (1/2)ˣ (1/2)¹⁰⁻ˣ ,x = 0,1,2,..., 10, i.e.,

P (X = x) = p(x) = ¹⁰Cₓ (1/2)¹⁰ = ¹⁰Cₓ /1024, x = 0, 1, ..., 10.

Hence,

The Required Probability = P( X< 8),

⇒ P (X = 0)+ P( X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) +P(X = 6) +  P(X= 7) +  P(X =8)

⇒ 1/1024 ( 1 + 10 + 45 + 120 +210 + 252 + 210 + 120 +90)

⇒ 1/1024 ×1058

⇒ 529 / 512

⇒ 1.033

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Answer:

y+5-1/3x=7 find y and then x to find the corresponding values

y = 5 - 1/3x + 7

y = 5 - 1/3(x) + 7

y = 5 - (1/3)x + 7

y = (5 - 1/3x) + 7

y = (5 + 7) - (1/3)x

y = 12 - (1/3)x

For y = 12,

12 - (1/3)x = 12

(1/3)x = 0

x = 0

Therefore, when y = 12, x = 0.

Answer:

  28 ft²

Step-by-step explanation:

You want the area of a triangle with a base of 7' and a height of 8'.

The formula for the area of a triangle is ...

  A = 1/2bh

where b is the base of the triangle, and h is the height perpendicular to the base.

Here, it is convenient to use the side marked 7' as the base of the triangle. The distance marked 8' is the perpendicular distance from the base to the top of the triangle. So, the area is ...

  A = 1/2(7 ft)(8 ft) = 28 ft²

The area of the triangle is 28 square feet.

__

Additional comment

As you can see, the vertex opposite the base does not need to lie above the base segment. All that matters is the perpendicular distance from that vertex to the base line.

Answer:

C. 150

Step-by-step explanation:

Divide 1,350 by 9, which gives you 150 (with no remainders)

Answer:

150

Step-by-step explanation:

1350 divided by 9

There are two different ways in which he can choose 9 sandwitches. It can be solve by the concept of permutation and combination.

What is permutation and combination?

A permutation is an arrangement of several items taken one at a time or all at once in a specific order.

Combinations are based entirely on grouping. Combinations can be used to determine how many different groups that can be created from the available items.

Since all vegitarian sandwiches looks like same and all sandwitches with meat looks like same hence, their order will not affect the number of choice.

If 8 sandwitches are vegitarian then 1 sandwitch must be with meat. So that total sandwithches becomes 9.

If all 9 sindwitches are vegetarian then there is no option to choose another sandwitch. Because he can choose only 9 sandwitches.

Hence, there are two different ways in which he can choose 9 sandwitches.

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The equivalent expression of -5 + 4(-3x+6) -4x is -29 - 16x

From the question, we have the following parameters that can be used in our computation:

-5 + 4(-3x+6) -4x

Open the bracket in the above expression

This gives

-5 + 4(-3x+6) -4x = -5 - 12x - 24 -4x

Collect the like terms in the above expression

This gives

-5 + 4(-3x+6) -4x = -5 - 24 - 12x  -4x

Evaluate the like terms in the above expression

This gives

-5 + 4(-3x+6) -4x = -29 - 16x

Hence, the equivalent expression is -29 - 16x

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2p+3q=16 and p+q=35 are system of equations used to find the number p of two-point shots and the number q of three-point shots you make

Two or more expressions with an Equal sign is called as Equation.

We need to find the number p of two-point shots and the number q of three-point shots you make.

a total of 16 two-point and three-point shots in a basketball game.

2p+3q=16

Total score is of 35 points.

p+q=35

These two equations 2p+3q=16 and p+q=35 can be used to find the  number p of two-point shots and the number q of three-point shots you make.

Hence, 2p+3q=16 and p+q=35 are system of equations used to find the number p of two-point shots and the number q of three-point shots you make

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The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given phrase,

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1

y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2

Substitute, point (−6, −3)

-3 ≥ (2/3)(-6) + 1

-3 ≥ -3  

Substitute in second inequality,

-3 < (-1/4)(-6) + 2

-3 < 7/2

Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".

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