Find the area of each polygon. Write the
equations and solve showing ALL the work.

a regular hexagon with an apothem of 3 ft

The total cost of the camera with sales tax included is $811.47.

The total cost refers to the summation of all the cost involved from the manufacturing to sales, it majorly involves the fix cost and variable cost.

To find the total cost we need to derive a formula

total cost = listed price + ( listed price x sales tax rate)

now by placing the values given in the question we can calculate the the total cost

listed price = $761. 98

sales tax rate = 6. 5%

then,

total cost = 761.98 + (761.98 x 0.065)

total cost = 761.98 + 49.49

total cost = $811.47

The total cost of the camera with sales tax included is $811.47.

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Type 1

this is a right triangle, the we can apply pythagoras

where a and b are sides and h the hypotenuse on this case L(leash)

replacing

simplify

now solve for L

The leash is 8.6ft

Type 2

we have a right triangle too

on this case the missing number is a side, not hypotenuse

remember pythagoras

and replace for this case

simplify

and solve for x

then le length of the side x is 4.44ft

The area of the region enclosed by y = e²ˣ, y = e⁴ˣ and x = 1 is approximately 0.77425 square units.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To sketch the bounded region enclosed by the curves, we first plot the two functions:

y = e²ˣ (in blue)

y = e⁴ˣ (in red)

And the line x = 1 (in green) which is a vertical line passing through x = 1.

We can see that the two functions e²ˣ and e⁴ˣ both increase rapidly as x increases. In fact, e⁴ˣ grows much faster than e²ˣ, so it quickly becomes the larger of the two functions. Additionally, both functions start at y = 1 when x = 0, and they both approach y = 0 as x approaches negative infinity.

To find the bounds of integration, we need to find the points where the two curves intersect. Setting e²ˣ = e⁴ˣ, we have:

e²ˣ = e⁴ˣ

2x = 4x

x = 0

So the two curves intersect at the point (0,1). Since e⁴ˣ grows much faster than e²ˣ, the curve y = e⁴ˣ will always be above the curve y = e²ˣ. Therefore, the region is bounded by the curves y = e²ˣ, y = e⁴ˣ, and the line x = 1.

To find the area of this region, we can integrate with respect to x or y. Since the region is vertically bounded, it makes sense to integrate with respect to x. The limits of integration are x = 0 and x = 1 (the vertical line).

The area A is given by:

A = ∫₀¹ (e⁴ˣ - e²ˣ) dx

= [ 1/4 * e⁴ˣ - 1/2 * e²ˣ ] from 0 to 1

= (1/4 * e⁴ - 1/2 * e²) - (1/2 * 1) + (1/4 * 1)

= 0.77425 (rounded to five decimal places).

Therefore, the area of the region enclosed by y = e²ˣ, y = e⁴ˣ and x = 1 is approximately 0.77425 square units.

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Answer:

Step-by-step explanation:

The two integers are 10 and 9

10 + 9 = 19

10 x 9 = 90

The two numbers are 9 and 10.

A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero

Let the two integers be x and y.

Given that, the sum of the integers is 19, therefore,

x + y = 19

x = 19 - y

Given that, the product of the integer is 90:

xy = 90

(19-y)y = 90

19y - y² = 90

y² -19y + 90 =0

y² -10y - 9y + 90 = 0

y(y - 10) -9(y - 10) = 0

(y -9)(y - 10) = 0

y = 9 and y = 10

Hence, the two numbers are 9 and 10.

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Answer:

Step-by-step explanation:

The statement that correctly compares the values of the 7s in 7.825 and 3.7 is:

The 7s in 7.825 are greater than the 7s in 3.7.

The 7s refer to the units place (the "ones" place) in decimal numbers. In 7.825, the 7s are 7 and in 3.7, the 7s are 7. When comparing the two numbers, we can see that the number 7.825 is greater than 3.7, which means the 7s in 7.825 are greater than the 7s in 3.7.

Answer:

The answer is 6.07 x 10^5

Step-by-step explanation:

Answer:

6.07 x 10^5

Step-by-step explanation:

khan

Answer:

25 girls

Step-by-step explanation:

We Know

The ratio of boys to girls is 4:5. For every 4 boys, there are 5 girls.

To get from 4 to 20, we multiply by 5.

We Take

5 x 5 = 25 girls

So, there are 25 girls in class.

Answer: 25 girls are in the class

Step-by-step explanation: You can set up the ratio 4:5 as a fraction, \(\frac{4}{5}\) to find your answer. You are given the fact that 20 boys are in the class so now you can solve 2 ways.

Option 1 - Set up the equation algebraically as \(\frac{20}{x}\), where x = number of girls and set that equal to \(\frac{4}{5}\). This way allows you to see that the fraction must have the same ratio as 4:5. You can see that 4 x 5 = 20, so the multiple factor is 5. The variable x must equal 5 x 5, so x = 25.

Option 2 - Multiply the amount of boys given to you by the reciprocal of the ratio. Instead of using \(\frac{4}{5}\), you have to use \(\frac{5}{4}\) because there are more girls than boys in the class. This allows you to finish the problem by multiplying 20 x \(\frac{5}{4}\) to get the result of \(\frac{100}{4}\), which you may know simplifies into 25.

Answer:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step-by-step explanation:

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step 1: Understand the problem.

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

Step 4: Look back (check and interpret).

The example using the polya's 4-steps in problem solving is created along with the answer.

Let's apply Polya's 4-step problem-solving process to the following word problem:

Problem: Lily has twice as many apples as John. Together, they have 27 apples. How many apples does each person have?

Step 1 - Understand the Problem:

To solve this problem, we need to find the number of apples that Lily and John each have. We know that Lily has twice as many apples as John, and together, they have 27 apples. We need to determine the number of apples for each person.

Step 2 - Devise a Plan:

Let's use algebra to represent the number of apples. Let's say the number of apples John has is "x." Since Lily has twice as many apples as John, the number of apples she has is "2x." We know that together, they have 27 apples, so we can set up an equation:

x + 2x = 27

Step 3 - Execute the Plan:

Now, we'll solve the equation to find the value of "x."

3x = 27

x = 27 / 3

x = 9

So, John has 9 apples. Now, we can find the number of apples Lily has:

Lily's apples = 2 * 9 = 18

Step 4 - Review the Solution:

John has 9 apples, and Lily has 18 apples. Together, they have 9 + 18 = 27 apples, which matches the information given in the problem. Therefore, the solution is correct.

Answer:

John has 9 apples, and Lily has 18 apples.

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Answer:

Length is 12 feet, and Width is 10 feet

Step-by-step explanation:

You can use an equation to come up with the answer but you are looking for width × (width + 2) = 120.

Answer:

steps below

Step-by-step explanation:

5th level of Pascal triangle: 1,5,10,10,5,1

(1+2x)⁵ = 1*1⁵*(2x)⁰+5*1⁴*2x+10*1³*(2x)²+10*1²*(2x)³+5*1¹(2x)⁴+1*1⁰*(2x)⁵

           = 1 + 10x + 40x² + 80x³ + 80x⁴ + 32x⁵   .. (1)

(1-2x)⁵ =  1  - 10x + 40x² - 80x³  + 80x⁴ - 32x⁵  .. (2)

(1)+(2): (1+2x)⁵ + (1-2x)⁵ = 160x⁴ + 80x² +2

a + bx + cx ?? suppose it's ax⁴ + bx² + cx, if you have other set up.. adjust by yourself

a = 160,    b = 80,    c = 2

Answer:

70 degrees

Step-by-step explanation:

120 + angle V = 180     V = 60

60 + 50 + ? = 180

? = 70

Answer:

- 6 1/2

Step-by-step explanation:

-4 - 2 1/2

Since the signs are the same, we add them together and take the signs

4+2 1/2 = 6 1/2

Take the sign

- 6 1/2

Answer:

(-4) - 2 1/2 = -6.5

Step-by-step explanation:

( −4 ) − 2 1/2 = -13/2

-13/2 = -6 1/2  

The percentage profit for the shop owner is 197.6%.

Percentage profit is the ratio of the profit on a good or item and the the cost price expressed as a percentage.

The cost price of the book in US dollars will be: 10 * 1/0.85 = 11.76 USD

Selling price in USD = 35 USD

Profit = 35 - 11.76

Profit = 23.24 USD

Percentage profit = 23.24/11.76 * 100%

Percentage profit = 197.6%

In conclusion, the percentage profit is the profit expressed as a percentage of the cost price.

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Answer:

Step-by-step explanation:

you can find videos on yt for that

Answer:

sorry, I'm not sure. you need a little more description though

Answer:

1y is the answer!

Step-by-step explanation:

-6y+7y=1y

Answer:

-6y + 7y = 1y

Step-by-step explanation:

\(32 - 6y + 7y - 2y^2\)

-6y + 7y = 1y

7y - 6y = 1y or y

the whole equation would be \(-2y^2+y+32\)

Answer:

62.5%

Step-by-step explanation:

64-40= 24 - this means the increase was more than half the original price.

40/64 = 0.625 * 100= 62.5%

can also be rounded up to 63%

Answer: B 12/5

Step-by-step explanation:

Since tanθ is opposite over adjacent which is 5/12. cotθ is the reciprocal of tanθ which is just 12/5.

Answer:

3 miles

Step-by-step explanation:

1/8*24=3

Answer:

Step-by-step explanation:

He ran 24 times around the track1

Circumfrence of track=1/8 Mile

Total distance he covered=1/8*24

Distance = 3 miles

Since the p-value (.040) is greater than the significance level (.01), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to support the claim that there are more than 70,000 defined words in the dictionary. The mean number of words per page is not significantly greater than 48.1 words.

To test the claim that the mean number of words per page is greater than 48.1 words, we will use a one-sample t-test. We will follow these steps:

Step 1: Identify the null and alternative hypotheses
H0: µ ≤ 48.1 (null hypothesis: the mean number of words per page is less than or equal to 48.1)
H1: µ > 48.1 (alternative hypothesis: the mean number of words per page is greater than 48.1)

Step 2: Calculate the test statistic (t-score)
t = (x - µ) / (s / √n)
t = (53.5 - 48.1) / (16.5 / √20)
t ≈ 1.84

Step 3: Calculate the P-value
Using a t-distribution table or calculator, find the P-value associated with the t-score 1.84 and degrees of freedom (n-1) = 19. Since this is a one-tailed test, we don't need to divide the P-value by 2. The P-value is approximately 0.041.
Test Statistic: To calculate the test statistic, we will use the formula:

t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the given values, we get: t = (53.5 - 48.1) / (16.5 / √20) = 1.86.
P-value: Using a t-distribution table with 19 degrees of freedom (n-1), we find the p-value to be .040 (one-tailed).

Step 4: Compare the P-value with the significance level (α)
Since the P-value (0.041) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Step 5: State the final conclusion
We do not have sufficient evidence to support the claim that the mean number of words per page is greater than 48.1 words at a 0.01 significance level. Consequently, we cannot support the claim that there are more than 70,000 defined words in the dictionary.

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To solve this problem, we need to find the number of ways the 10 different movies can be stored on 40 computers. Since each computer can have at most one movie, we can think of this as arranging the 10 movies in a specific order on the 40 computers.

The number of different ways the 10 movies can be stored on the 40 computers is 10!. The calculation is given as follows:

To find the number of ways to arrange the movies, we can use permutations. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items being arranged.
In this case, we have 10 movies and 40 computers, so n = 10 and r = 40.
Plugging these values into the formula, we get:
10P40 = 10! / (10 - 40)! = 10! / (-30)!

Now, we need to simplify this expression. To do that, we can use the fact that 0! = 1.
So, -30! = (-30) * (-31) * (-32) * ... * (-1) * 0! = (-30) * (-31) * (-32) * ... * (-1) * 1 = (-30) * (-31) * (-32) * ... * (-1)

Now we can calculate 10P40:
10P40 = 10! / (-30)! = 10! / [(-30) * (-31) * (-32) * ... * (-1)]

Since we have 10! in the numerator and a long negative product in the denominator, we can simplify the expression further:
10P40 = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(-30) * (-31) * (-32) * ... * (-1)]

Now we can evaluate the numerator and denominator separately:
Numerator: 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 10!
Denominator: (-30) * (-31) * (-32) * ... * (-1)

Since the movies are different and it matters which movie is stored on which computer, we have 10! ways to arrange the movies. So, the number of different ways the 10 movies can be stored on the 40 computers is 10!

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Answer: y = 2x - 7

Step-by-step explanation:

Just remember, when in doubt use the formula y = mx + b

Good luck!

Given:

The graph of a function.

To find:

The range of the function.

Solution:

Domain is the set of input values for which the function is defined.

Range is the set of output values or y-values.

From the given graph it is clear that the function is defined between -2 and 1.

The graph of the function is a horizontal line and it gives the value 1 for each input between -2 and 1.

It means the range of the graphed function is 1.

Therefore, the correct option is C.

Answer:1

Step-by-step explanation:

Since the ages of students at a university are normally distributed with a mean of 21, the percentage of the student body that is at least 21 years old is: 50%.

A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean have a higher frequency than the data that are far from the mean.

For all normal distributions, the mean is always located at the center with 50 percent (50%) or 0.5 of the distribution to either side, which is right or left of the distribution.

In this context, the percentage of student body that is at least 21 years old is represented by the percentage to the left of the normal distribution, which is 50 percent (50%):

P(x ≤ 21) = 50%

P(x ≤ 21) = 50/100

P(x ≤ 21) = 0.5.

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Answer:

y=1x+7

Step-by-step explanation:

umm

y=1x+7

A tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Cost of the food = $25.30

Tax on the food cost = 8%

Tax amount

= 8% of 25.30

= 0.08  × 25.30

= 2.204

Total cost of food before tip = 25.30 + 2.204 = $27.504

Tip given = 32.24 - 27.504 = 5.036

Tip percentage

= 5.036 / 27.504 × 100%

= 18.31%

≈ 18%

Hence a tip of 18% was given to the restaurant after the meal and tax to the nearest percentage.

Percentage increases and decreases are calculated by computing the difference between two numbers or by comparing that difference to the starting value.

One can calculate how significantly the initial value has changed mathematically by dividing the result by the starting value and using the absolute value of the difference between the two values.

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9514 1404 393

Answer:

  15/28

Step-by-step explanation:

We can rearrange the problem a bit and make it a little simpler.

  1 2/7 - 3/4 = (1 -3/4) + 2/7 = 1/4 + 2/7

  = (7+4·2)/(4·7) = 15/28

_____

The sum of fractions can always be found by ...

  \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\\\\\dfrac{1}{4}+\dfrac{2}{7}=\dfrac{1\cdot7+4\cdot2}{4\cdot7}=\dfrac{7+8}{28}=\dfrac{15}{28}\)